%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW322+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 09:06:15 AM UTC 2026
% Result : Theorem 151.54s 151.85s
% Output : Proof 151.83s
% 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_empty,axiom,
! [V_Ga_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))),
file('theBenchmark.p',fact_empty) ).
fof(fact_hoare__derivs_Oequations_I1_J,axiom,
! [V_a_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))),
file('theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).
fof(fact_triple_Oinject,axiom,
! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_c] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_H_2),V_com_H_2),V_fun2_H_2)
<=> ( V_fun2_2 = V_fun2_H_2
& V_com_2 = V_com_H_2
& V_fun1_2 = V_fun1_H_2 ) ),
file('theBenchmark.p',fact_triple_Oinject) ).
fof(fact_cut,axiom,
! [V_Ga_2,V_ts_2,V_G_H_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_G_H_2,V_ts_2)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_G_H_2)
=> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2) ) ),
file('theBenchmark.p',fact_cut) ).
fof(fact_hoare__derivs_Oinsert,axiom,
! [V_ts_2,V_t_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2)
=> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),V_t_2),V_ts_2)) ) ),
file('theBenchmark.p',fact_hoare__derivs_Oinsert) ).
fof(fact_derivs__insertD,axiom,
! [V_ts_2,V_t_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),V_t_2),V_ts_2))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2)
& c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_derivs__insertD) ).
fof(fact_finite__imageI,axiom,
! [V_h_2,T_d,V_F_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_h_2),V_F_2))) ),
file('theBenchmark.p',fact_finite__imageI) ).
fof(fact_finite_OinsertI,axiom,
! [V_a_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2))) ),
file('theBenchmark.p',fact_finite_OinsertI) ).
fof(fact_finite_OemptyI,axiom,
! [T_c] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_finite_OemptyI) ).
fof(fact_image__eqI,axiom,
! [T_c,V_A_2,T_d,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_d),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_image__eqI) ).
fof(fact_insertE,axiom,
! [V_A_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_A_2)))
=> ( V_a_2 != V_b_2
=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_insertE) ).
fof(fact_insertCI,axiom,
! [V_b_2,V_B_2,V_a_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_B_2))
=> V_a_2 = V_b_2 )
=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) ),
file('theBenchmark.p',fact_insertCI) ).
fof(fact_emptyE,axiom,
! [V_a_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_emptyE) ).
fof(fact_image__constant,axiom,
! [V_c_2,T_d,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_COMBK(T_d,T_c),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_d),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_image__constant) ).
fof(fact_image__constant__conv,axiom,
! [V_c_2,T_d,T_c,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_COMBK(T_d,T_c),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_d),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,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_d,hAPP(c_COMBK(T_d,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_image__constant__conv) ).
fof(fact_insert__image,axiom,
! [V_f_2,T_d,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_d),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) ),
file('theBenchmark.p',fact_insert__image) ).
fof(fact_singleton__iff,axiom,
! [V_a_2,V_b_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),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_b_2 = V_a_2 ),
file('theBenchmark.p',fact_singleton__iff) ).
fof(fact_singletonE,axiom,
! [V_a_2,V_b_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),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_b_2 = V_a_2 ),
file('theBenchmark.p',fact_singletonE) ).
fof(fact_equalityCE,axiom,
! [V_c_2,T_c,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) )
=> ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_equalityCE) ).
fof(fact_eq__mem__trans,axiom,
! [V_A_2,T_c,V_b_2,V_a_2] :
( V_a_2 = V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_eq__mem__trans) ).
fof(fact_eqelem__imp__iff,axiom,
! [V_A_2,T_c,V_y_2,V_x_2] :
( V_x_2 = V_y_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)) ) ),
file('theBenchmark.p',fact_eqelem__imp__iff) ).
fof(fact_eqset__imp__iff,axiom,
! [V_x_2,T_c,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_eqset__imp__iff) ).
fof(fact_mem__def,axiom,
! [V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
<=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_mem__def) ).
fof(fact_finite__code,axiom,
! [V_A_2,T_c] :
( class_Finite__Set_Ofinite(T_c)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
file('theBenchmark.p',fact_finite__code) ).
fof(fact_finite,axiom,
! [V_A_2,T_c] :
( class_Finite__Set_Ofinite(T_c)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
file('theBenchmark.p',fact_finite) ).
fof(fact_insert__code,axiom,
! [V_x_2,V_A_2,V_y_2,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_c),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_insert__commute,axiom,
! [V_A_2,V_y_2,V_x_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),
file('theBenchmark.p',fact_insert__commute) ).
fof(fact_insert__absorb2,axiom,
! [V_A_2,V_x_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2),
file('theBenchmark.p',fact_insert__absorb2) ).
fof(fact_image__image,axiom,
! [V_A_2,V_g_2,T_e,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_e,T_c,hAPP(hAPP(c_COMBB(T_d,T_c,T_e),V_f_2),V_g_2)),V_A_2),
file('theBenchmark.p',fact_image__image) ).
fof(fact_equals0D,axiom,
! [V_a_2,T_c,V_A_2] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
file('theBenchmark.p',fact_equals0D) ).
fof(fact_empty__iff,axiom,
! [V_c_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_empty__iff) ).
fof(fact_ex__in__conv,axiom,
! [V_A_2,T_c] :
( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
<=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ex__in__conv) ).
fof(fact_all__not__in__conv,axiom,
! [V_A_2,T_c] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_all__not__in__conv) ).
fof(fact_insert__absorb,axiom,
! [V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),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_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2))
=> ( hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_c),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_c] : hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2))),
file('theBenchmark.p',fact_insertI1) ).
fof(fact_rev__image__eqI,axiom,
! [T_d,V_f_2,V_b_2,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( V_b_2 = hAPP(V_f_2,V_x_2)
=> hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_imageI,axiom,
! [V_f_2,T_d,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) ),
file('theBenchmark.p',fact_imageI) ).
fof(fact_image__iff,axiom,
! [V_A_2,V_f_2,T_d,V_z_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)))
<=> ? [B_x] :
( V_z_2 = hAPP(V_f_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_image__iff) ).
fof(fact_finite_Oequations_I1_J,axiom,
! [T_c] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_finite_Oequations_I1_J) ).
fof(fact_singleton__inject,axiom,
! [V_b_2,V_a_2,T_c] :
( 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_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
=> V_a_2 = V_b_2 ),
file('theBenchmark.p',fact_singleton__inject) ).
fof(fact_doubleton__eq__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
<=> ( ( V_b_2 = V_c_2
& V_a_2 = V_d_2 )
| ( V_b_2 = V_d_2
& V_a_2 = V_c_2 ) ) ),
file('theBenchmark.p',fact_doubleton__eq__iff) ).
fof(fact_insert__not__empty,axiom,
! [V_A_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_insert__not__empty) ).
fof(fact_empty__not__insert,axiom,
! [V_A_2,V_a_2,T_c] : c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2),
file('theBenchmark.p',fact_empty__not__insert) ).
fof(fact_finite__insert,axiom,
! [V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
file('theBenchmark.p',fact_finite__insert) ).
fof(fact_image__is__empty,axiom,
! [V_A_2,V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(T_d,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_d,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_image__is__empty) ).
fof(fact_image__empty,axiom,
! [V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_image__empty) ).
fof(fact_empty__is__image,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,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_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_B_2)),
file('theBenchmark.p',fact_image__insert) ).
fof(fact_the__elem__eq,axiom,
! [V_x_2,T_c] : c_Set_Othe__elem(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2,
file('theBenchmark.p',fact_the__elem__eq) ).
fof(fact_bot__fun__def,axiom,
! [V_x_2,T_d,T_c] :
( class_Orderings_Obot(T_c)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_d,T_c)),V_x_2) = c_Orderings_Obot__class_Obot(T_c) ),
file('theBenchmark.p',fact_bot__fun__def) ).
fof(fact_bot__empty__eq,axiom,
! [V_x_2,T_c] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_bot__empty__eq) ).
fof(fact_triple_Osimps_I2_J,axiom,
! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_c,T_d] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_d,T_c,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_d),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2),
file('theBenchmark.p',fact_triple_Osimps_I2_J) ).
fof(fact_triple_Orecs,axiom,
! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_c,T_d] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_d,T_c,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_d),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2),
file('theBenchmark.p',fact_triple_Orecs) ).
fof(fact_folding__one_Oinsert,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one(T_c,V_f_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))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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_bot__apply,axiom,
! [V_x_2,T_d,T_c] :
( class_Orderings_Obot(T_c)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_d,T_c)),V_x_2) = c_Orderings_Obot__class_Obot(T_c) ),
file('theBenchmark.p',fact_bot__apply) ).
fof(fact_escape,axiom,
! [V_Qa_2,V_c_2,V_Ga_2,T_c,V_Pa_2] :
( ! [B_Z,B_s] :
( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_c_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_c),hAPP(V_Qa_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) )
=> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_escape) ).
fof(fact_folding__one__idem_Oinsert__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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_hoare__derivs_Oequations_I7_J,axiom,
! [V_a2_2,V_a1_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))),
file('theBenchmark.p',fact_hoare__derivs_Oequations_I7_J) ).
fof(fact_hoare__derivs_OSkip,axiom,
! [V_Pa_2,V_Ga_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))),
file('theBenchmark.p',fact_hoare__derivs_OSkip) ).
fof(fact_conseq1,axiom,
! [V_Pa_2,V_Qa_2,V_c_2,V_P_Ha_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_P_Ha_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
=> ( ! [B_Z,B_s] :
( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
=> hBOOL(hAPP(hAPP(V_P_Ha_2,B_Z),B_s)) )
=> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_conseq1) ).
fof(fact_folding__one__idem_Oidem,axiom,
! [V_x_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one__idem(T_c,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_eq__mem,axiom,
! [V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_fequal,V_y_2)))
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_eq__mem) ).
fof(fact_folding__one_Osingleton,axiom,
! [V_x_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2)
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_folding__one_Osingleton) ).
fof(fact_folding__one__idem_Oin__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one__idem(T_c,V_f_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,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_pred__equals__eq,axiom,
! [V_S_2,V_R_2,T_c] :
( hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2) = hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2)
<=> V_R_2 = V_S_2 ),
file('theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_folding__one_Oclosed,axiom,
! [V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oclosed) ).
fof(fact_conseq2,axiom,
! [V_Qa_2,V_Q_Ha_2,V_c_2,V_Pa_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Q_Ha_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
=> ( ! [B_Z,B_s] :
( hBOOL(hAPP(hAPP(V_Q_Ha_2,B_Z),B_s))
=> hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s)) )
=> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_conseq2) ).
fof(fact_Comp,axiom,
! [V_R_2,V_d_2,V_Qa_2,V_c_2,V_Pa_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Qa_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_Comp) ).
fof(fact_the__elem__def,axiom,
! [V_X_2,T_c] : c_Set_Othe__elem(T_c,V_X_2) = c_HOL_OThe(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),hAPP(c_fequal,V_X_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_the__elem__def) ).
fof(fact_LoopF,axiom,
! [V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_c),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_Pa_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))),
file('theBenchmark.p',fact_LoopF) ).
fof(fact_folding__one__idem_Ohom__commute,axiom,
! [V_N_2,V_h_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one__idem(T_c,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_c),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
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_d,T_c] :
( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_d),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__one_Oremove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one(T_c,V_f_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(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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,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_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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_F_2,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oremove) ).
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_d,T_c] :
( c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_d),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_finite__induct,axiom,
! [V_Pa_2,V_F_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
=> ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
=> ( ! [B_x,B_F] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_F))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),B_F))
=> ( hBOOL(hAPP(V_Pa_2,B_F))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_c),B_x),B_F))) ) ) )
=> hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ),
file('theBenchmark.p',fact_finite__induct) ).
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_d,T_c] :
( c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_d),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_image__ident,axiom,
! [V_Y_2,T_c] : hAPP(c_Set_Oimage(T_c,T_c,c_COMBI(T_c)),V_Y_2) = V_Y_2,
file('theBenchmark.p',fact_image__ident) ).
fof(fact_DiffE,axiom,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_DiffE) ).
fof(fact_DiffI,axiom,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_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_DiffI) ).
fof(fact_finite__Diff,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_finite__Diff) ).
fof(fact_Diff__idemp,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_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_Diff__idemp) ).
fof(fact_folding__image__simple__idem_Oidem,axiom,
! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,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_DiffD2,axiom,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ),
file('theBenchmark.p',fact_DiffD2) ).
fof(fact_DiffD1,axiom,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_DiffD1) ).
fof(fact_Diff__iff,axiom,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Diff__iff) ).
fof(fact_Diff__cancel,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,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_Diff__cancel) ).
fof(fact_Diff__empty,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_A_2,
file('theBenchmark.p',fact_Diff__empty) ).
fof(fact_empty__Diff,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),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)),
file('theBenchmark.p',fact_empty__Diff) ).
fof(fact_finite__Diff2,axiom,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__Diff2) ).
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_d,T_c] :
( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_d),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_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).
fof(fact_insert__Diff1,axiom,
! [V_A_2,V_B_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_B_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_insert__Diff1) ).
fof(fact_insert__Diff__if,axiom,
! [V_A_2,V_B_2,V_x_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_B_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_insert__Diff__if) ).
fof(fact_insert__Diff__single,axiom,
! [V_A_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_c),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_c] : 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_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c] : 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_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_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_Diff__insert) ).
fof(fact_finite__Diff__insert,axiom,
! [V_B_2,V_a_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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_a_2),V_B_2))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_finite__Diff__insert) ).
fof(fact_folding__image__simple_Oempty,axiom,
! [V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2)
=> hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = V_z_2 ),
file('theBenchmark.p',fact_folding__image__simple_Oempty) ).
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_d,T_c] :
( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_d),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_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oremove) ).
fof(fact_insert__Diff,axiom,
! [V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_c),V_a_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = V_A_2 ),
file('theBenchmark.p',fact_insert__Diff) ).
fof(fact_Diff__insert__absorb,axiom,
! [V_A_2,V_x_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),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)))) = V_A_2 ),
file('theBenchmark.p',fact_Diff__insert__absorb) ).
fof(fact_folding__one_Oinsert__remove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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_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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oinsert__remove) ).
fof(fact_fun__diff__def,axiom,
! [V_x_2,V_B_2,V_A_2,T_d,T_c] :
( class_Groups_Ominus(T_c)
=> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,T_c)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ),
file('theBenchmark.p',fact_fun__diff__def) ).
fof(fact_com_Osimps_I12_J,axiom,
! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H),
file('theBenchmark.p',fact_com_Osimps_I12_J) ).
fof(fact_com_Osimps_I13_J,axiom,
! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP,
file('theBenchmark.p',fact_com_Osimps_I13_J) ).
fof(fact_com_Osimps_I16_J,axiom,
! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
file('theBenchmark.p',fact_com_Osimps_I16_J) ).
fof(fact_com_Osimps_I17_J,axiom,
! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP,
file('theBenchmark.p',fact_com_Osimps_I17_J) ).
fof(fact_com_Osimps_I46_J,axiom,
! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
file('theBenchmark.p',fact_com_Osimps_I46_J) ).
fof(fact_com_Osimps_I47_J,axiom,
! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
file('theBenchmark.p',fact_com_Osimps_I47_J) ).
fof(fact_minus__apply,axiom,
! [V_x_2,V_B_2,V_A_2,T_d,T_c] :
( class_Groups_Ominus(T_c)
=> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,T_c)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ),
file('theBenchmark.p',fact_minus__apply) ).
fof(fact_fun__upd__image,axiom,
! [V_y_2,V_f_2,T_d,V_A_2,V_x_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(c_Set_Oimage(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(c_Set_Oimage(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_d),V_y_2),hAPP(c_Set_Oimage(T_c,T_d,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_fun__upd__image) ).
fof(fact_finite__empty__induct,axiom,
! [V_Pa_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(V_Pa_2,V_A_2))
=> ( ! [B_a,B_A] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_A))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),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_c,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_c),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) )
=> hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) ) ),
file('theBenchmark.p',fact_finite__empty__induct) ).
fof(fact_fun__left__comm__idem__remove,axiom,
! [T_c] : c_Finite__Set_Ofun__left__comm__idem(T_c,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_c),hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)))),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_fun__left__comm__idem__remove) ).
fof(fact_the__sym__eq__trivial,axiom,
! [V_x_2,T_c] : c_HOL_OThe(T_c,hAPP(c_fequal,V_x_2)) = V_x_2,
file('theBenchmark.p',fact_the__sym__eq__trivial) ).
fof(fact_fun__upd__triv,axiom,
! [V_x_2,V_f_2,T_d,T_c] : c_Fun_Ofun__upd(T_c,T_d,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__iff,axiom,
! [V_y_2,V_x_2,V_f_2,T_d,T_c] :
( c_Fun_Ofun__upd(T_c,T_d,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_fun__upd__upd,axiom,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_d,T_c] : c_Fun_Ofun__upd(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_z_2),
file('theBenchmark.p',fact_fun__upd__upd) ).
fof(fact_fun__upd__same,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_d] : hAPP(c_Fun_Ofun__upd(T_d,T_c,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__apply,axiom,
! [V_y_2,V_f_2,T_d,T_c,V_x_2,V_z_2] :
( ( V_z_2 != V_x_2
=> hAPP(c_Fun_Ofun__upd(T_c,T_d,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_c,T_d,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__twist,axiom,
! [V_d_2,V_b_2,V_m_2,T_d,T_c,V_c_2,V_a_2] :
( V_a_2 != V_c_2
=> c_Fun_Ofun__upd(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_m_2,V_c_2,V_d_2),V_a_2,V_b_2) ),
file('theBenchmark.p',fact_fun__upd__twist) ).
fof(fact_fun__upd__other,axiom,
! [V_y_2,V_f_2,T_d,T_c,V_x_2,V_z_2] :
( V_z_2 != V_x_2
=> hAPP(c_Fun_Ofun__upd(T_c,T_d,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__idem,axiom,
! [T_c,T_d,V_y_2,V_x_2,V_f_2] :
( hAPP(V_f_2,V_x_2) = V_y_2
=> c_Fun_Ofun__upd(T_d,T_c,V_f_2,V_x_2,V_y_2) = V_f_2 ),
file('theBenchmark.p',fact_fun__upd__idem) ).
fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
! [V_z_2,V_x_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,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_fun__upd__def,axiom,
! [V_b_2,V_f_2,T_d,T_c,V_a_2,V_x_2] :
( ( V_x_2 != V_a_2
=> hAPP(c_Fun_Ofun__upd(T_c,T_d,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_c,T_d,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 ) ),
file('theBenchmark.p',fact_fun__upd__def) ).
fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
! [V_g_2,T_e,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2)
=> c_Finite__Set_Ofun__left__comm__idem(T_e,T_d,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_d),T_e),V_f_2),V_g_2)) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) ).
fof(fact_fun__left__comm__idem__insert,axiom,
! [T_c] : c_Finite__Set_Ofun__left__comm__idem(T_c,tc_fun(T_c,tc_HOL_Obool),c_Set_Oinsert(T_c)),
file('theBenchmark.p',fact_fun__left__comm__idem__insert) ).
fof(fact_com_Osimps_I5_J,axiom,
! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
<=> ( V_com_2 = V_com_H_2
& V_fun_2 = V_fun_H_2 ) ),
file('theBenchmark.p',fact_com_Osimps_I5_J) ).
fof(fact_com_Osimps_I3_J,axiom,
! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
<=> ( V_com2_2 = V_com2_H_2
& V_com1_2 = V_com1_H_2 ) ),
file('theBenchmark.p',fact_com_Osimps_I3_J) ).
fof(fact_the__eq__trivial,axiom,
! [V_a_2,T_c] : c_HOL_OThe(T_c,hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2,
file('theBenchmark.p',fact_the__eq__trivial) ).
fof(fact_fold__graph_H_Ointros_I2_J,axiom,
! [V_y_2,V_z_2,V_f_2,T_d,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( c_Nitpick_Ofold__graph_H(T_c,T_d,V_f_2,V_z_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)))),V_y_2)
=> c_Nitpick_Ofold__graph_H(T_c,T_d,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_Diff1__fold__graph,axiom,
! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_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))))),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,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_inj__on__insert,axiom,
! [V_A_2,V_a_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_d,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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))))
& c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_inj__on__insert) ).
fof(fact_folding__one_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one(T_c,V_f_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(c_Finite__Set_Ofold(T_c,T_c,V_f_2),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__one_Oeq__fold_H) ).
fof(fact_minus__fold__remove,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,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_c),hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)))),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))))),V_B_2),V_A_2) ),
file('theBenchmark.p',fact_minus__fold__remove) ).
fof(fact_the__inv__into__def,axiom,
! [V_x_2,V_f_2,V_A_2,T_d,T_c] : hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_c,hAPP(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(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),V_x_2))),
file('theBenchmark.p',fact_the__inv__into__def) ).
fof(fact_subset__insert__iff,axiom,
! [V_B_2,V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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))))),V_B_2)) ) ) ),
file('theBenchmark.p',fact_subset__insert__iff) ).
fof(fact_diff__single__insert,axiom,
! [V_B_2,V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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))))),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2))) ) ),
file('theBenchmark.p',fact_diff__single__insert) ).
fof(fact_setsum__diff1,axiom,
! [V_f_2,V_a_2,V_A_2,T_c,T_d] :
( class_Groups_Oab__group__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum__diff1) ).
fof(fact_setsum__diff1__ring,axiom,
! [V_f_2,V_a_2,V_A_2,T_c,T_d] :
( class_Rings_Oring(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ),
file('theBenchmark.p',fact_setsum__diff1__ring) ).
fof(fact_override__on__def,axiom,
! [V_g_2,V_f_2,T_d,V_A_2,V_a_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ),
file('theBenchmark.p',fact_override__on__def) ).
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_equalityI,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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)),V_B_2),V_A_2))
=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_equalityI) ).
fof(fact_subsetD,axiom,
! [V_c_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_subsetD) ).
fof(fact_empty__subsetI,axiom,
! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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_empty__subsetI) ).
fof(fact_inj__on__empty,axiom,
! [V_f_2,T_d,T_c] : c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),
file('theBenchmark.p',fact_inj__on__empty) ).
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_le__funE,axiom,
! [V_x_2,V_g_2,V_f_2,T_c,T_d] :
( class_Orderings_Oord(T_d)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ),
file('theBenchmark.p',fact_le__funE) ).
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_predicate1D,axiom,
! [V_x_2,V_Qa_2,V_Pa_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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_order__antisym__conv,axiom,
! [V_x_2,V_y_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_le__funD,axiom,
! [V_x_2,V_g_2,V_f_2,T_c,T_d] :
( class_Orderings_Oord(T_d)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ),
file('theBenchmark.p',fact_le__funD) ).
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_rev__predicate1D,axiom,
! [V_Qa_2,T_c,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_c,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_order__eq__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( V_x_2 = V_y_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),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_le__fun__def,axiom,
! [V_g_2,V_f_2,T_c,T_d] :
( class_Orderings_Oord(T_d)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2))
<=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ),
file('theBenchmark.p',fact_le__fun__def) ).
fof(fact_setsum__commute,axiom,
! [V_A_2,V_B_2,V_f_2,T_e,T_d,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),tc_fun(tc_fun(T_e,tc_HOL_Obool),T_c),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_c),T_e),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c)),hAPP(c_COMBC(T_d,T_e,T_c),V_f_2))),V_A_2)),V_B_2) ),
file('theBenchmark.p',fact_setsum__commute) ).
fof(fact_equalityE,axiom,
! [T_c,V_B_2,V_A_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),V_B_2))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
file('theBenchmark.p',fact_subset__trans) ).
fof(fact_equalityD2,axiom,
! [T_c,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) ),
file('theBenchmark.p',fact_equalityD2) ).
fof(fact_equalityD1,axiom,
! [T_c,V_B_2,V_A_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),V_B_2)) ),
file('theBenchmark.p',fact_equalityD1) ).
fof(fact_set__eq__subset,axiom,
! [T_c,V_B_2,V_A_2] :
( V_A_2 = V_B_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(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__eq__subset) ).
fof(fact_subset__refl,axiom,
! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_A_2)),
file('theBenchmark.p',fact_subset__refl) ).
fof(fact_subset__inj__on,axiom,
! [V_A_2,V_B_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_subset__inj__on) ).
fof(fact_inj__on__def,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_c),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__on__id2,axiom,
! [V_A_2,T_c] : c_Fun_Oinj__on(T_c,T_c,c_COMBI(T_c),V_A_2),
file('theBenchmark.p',fact_inj__on__id2) ).
fof(fact_the__inv__into__f__eq,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( hAPP(V_f_2,V_x_2) = V_y_2
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(c_Fun_Othe__inv__into(T_c,T_d,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__into__f__f,axiom,
! [V_x_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(c_Fun_Othe__inv__into(T_c,T_d,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__onto,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> hAPP(c_Set_Oimage(T_d,T_c,c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_c,T_d,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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> c_Fun_Oinj__on(T_d,T_c,c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) ),
file('theBenchmark.p',fact_inj__on__the__inv__into) ).
fof(fact_the__inv__into__into,axiom,
! [V_B_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ),
file('theBenchmark.p',fact_the__inv__into__into) ).
fof(fact_setsum__diff__nat,axiom,
! [V_f_2,V_A_2,V_B_2,T_c] :
( 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),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),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_Nat_Onat),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,tc_Nat_Onat),V_f_2),V_B_2)) ) ),
file('theBenchmark.p',fact_setsum__diff__nat) ).
fof(fact_setsum__subtractf,axiom,
! [V_A_2,V_g_2,V_f_2,T_d,T_c] :
( class_Groups_Oab__group__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Ominus__class_Ominus(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_g_2),V_A_2)) ),
file('theBenchmark.p',fact_setsum__subtractf) ).
fof(fact_fold__def,axiom,
! [V_A_2,V_z_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_Finite__Set_Ofold(T_d,T_c,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_c,c_Finite__Set_Ofold__graph(T_d,T_c,V_f_2,V_z_2,V_A_2)),
file('theBenchmark.p',fact_fold__def) ).
fof(fact_endo__inj__surj,axiom,
! [V_f_2,V_A_2,T_c] :
( 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)),hAPP(c_Set_Oimage(T_c,T_c,V_f_2),V_A_2)),V_A_2))
=> ( c_Fun_Oinj__on(T_c,T_c,V_f_2,V_A_2)
=> hAPP(c_Set_Oimage(T_c,T_c,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_c] :
( 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_A_2),hAPP(c_Set_Oimage(T_c,T_c,V_f_2),V_A_2)))
=> c_Fun_Oinj__on(T_c,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_finite__surj__inj) ).
fof(fact_inj__on__image__set__diff,axiom,
! [V_B_2,V_A_2,V_C_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_C_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
=> hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_inj__on__image__set__diff) ).
fof(fact_inj__onD,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,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_c),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_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_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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( V_x_2 != V_y_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_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ),
file('theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_inj__on__diff,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> c_Fun_Oinj__on(T_c,T_d,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_inj__on__diff) ).
fof(fact_setsum__diff,axiom,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( class_Groups_Oab__group__add(T_d)
=> ( 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(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_setsum__diff) ).
fof(fact_fold__graph_H_Ointros_I1_J,axiom,
! [V_z_2,V_f_2,T_d,T_c] : c_Nitpick_Ofold__graph_H(T_c,T_d,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__graph_H_Ointros_I1_J) ).
fof(fact_fold__graph_H_Oequations_I1_J,axiom,
! [V_a2_2,V_a1_2,T_d,T_c] : c_Nitpick_Ofold__graph_H(T_c,T_d,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),V_a2_2),
file('theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
fof(fact_fold__empty,axiom,
! [V_z_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_Finite__Set_Ofold(T_d,T_c,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = V_z_2,
file('theBenchmark.p',fact_fold__empty) ).
fof(fact_f__the__inv__into__f,axiom,
! [V_y_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
=> hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ),
file('theBenchmark.p',fact_f__the__inv__into__f) ).
fof(fact_set__mp,axiom,
! [V_x_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__mp) ).
fof(fact_set__rev__mp,axiom,
! [V_B_2,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__rev__mp) ).
fof(fact_in__mono,axiom,
! [V_x_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_in__mono) ).
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_subset__empty,axiom,
! [V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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)) ),
file('theBenchmark.p',fact_subset__empty) ).
fof(fact_finite__subset,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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)) ) ),
file('theBenchmark.p',fact_finite__subset) ).
fof(fact_rev__finite__subset,axiom,
! [V_A_2,V_B_2,T_c] :
( 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_A_2),V_B_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ),
file('theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_insert__mono,axiom,
! [V_a_2,V_D_2,V_C_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_D_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_D_2))) ),
file('theBenchmark.p',fact_insert__mono) ).
fof(fact_subset__insertI2,axiom,
! [V_b_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) ),
file('theBenchmark.p',fact_subset__insertI2) ).
fof(fact_subset__insertI,axiom,
! [V_a_2,V_B_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2))),
file('theBenchmark.p',fact_subset__insertI) ).
fof(fact_image__mono,axiom,
! [V_f_2,T_d,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,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_d,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)))
<=> ? [B_AA] :
( V_B_2 = hAPP(c_Set_Oimage(T_d,T_c,V_f_2),B_AA)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),B_AA),V_A_2)) ) ),
file('theBenchmark.p',fact_subset__image__iff) ).
fof(fact_double__diff,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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)),V_B_2),V_C_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_D_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,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_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
file('theBenchmark.p',fact_Diff__subset) ).
fof(fact_thin,axiom,
! [V_Ga_2,V_ts_2,V_G_H_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_G_H_2,V_ts_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2) ) ),
file('theBenchmark.p',fact_thin) ).
fof(fact_weaken,axiom,
! [V_ts_2,V_ts_H_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_H_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)),V_ts_2),V_ts_H_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2) ) ),
file('theBenchmark.p',fact_weaken) ).
fof(fact_asm,axiom,
! [V_Ga_2,V_ts_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)),V_ts_2),V_Ga_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2) ),
file('theBenchmark.p',fact_asm) ).
fof(fact_empty__fold__graphE,axiom,
! [V_x_2,V_z_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,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_d,T_c] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,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__graph_OemptyI) ).
fof(fact_fold__graph_Oequations_I1_J,axiom,
! [V_z_2,V_f_2,T_d,T_c] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,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__graph_Oequations_I1_J) ).
fof(fact_fold__graph__imp__finite,axiom,
! [V_x_2,V_A_2,V_z_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_x_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
file('theBenchmark.p',fact_fold__graph__imp__finite) ).
fof(fact_pred__subset__eq,axiom,
! [V_S_2,V_R_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_R_2),V_S_2)) ),
file('theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_finite__imageD,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)))
=> ( c_Fun_Oinj__on(T_d,T_c,V_f_2,V_A_2)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__imageD) ).
fof(fact_subset__insert,axiom,
! [V_B_2,V_A_2,V_x_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_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_subset__insert) ).
fof(fact_insert__subset,axiom,
! [V_B_2,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_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),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_insert__subset) ).
fof(fact_subset__singletonD,axiom,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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)))))
=> ( 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)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_subset__singletonD) ).
fof(fact_finite__surj,axiom,
! [V_f_2,V_B_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) ) ),
file('theBenchmark.p',fact_finite__surj) ).
fof(fact_image__diff__subset,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_image__diff__subset) ).
fof(fact_fold__graph_OinsertI,axiom,
! [V_y_2,V_z_2,V_f_2,T_d,V_A_2,V_x_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_y_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_c),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_setsum__diff1__nat,axiom,
! [V_f_2,V_A_2,V_a_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_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_d,T_c] :
( c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,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_inj__on__fun__updI,axiom,
! [V_x_2,V_y_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
=> c_Fun_Oinj__on(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2),V_A_2) ) ),
file('theBenchmark.p',fact_inj__on__fun__updI) ).
fof(fact_override__on__apply__in,axiom,
! [V_g_2,V_f_2,T_d,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ),
file('theBenchmark.p',fact_override__on__apply__in) ).
fof(fact_override__on__apply__notin,axiom,
! [V_g_2,V_f_2,T_d,V_A_2,V_a_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ),
file('theBenchmark.p',fact_override__on__apply__notin) ).
fof(fact_override__on__emptyset,axiom,
! [V_g_2,V_f_2,T_d,T_c] : c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_f_2,
file('theBenchmark.p',fact_override__on__emptyset) ).
fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,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_fun__left__comm__idem_Ofold__insert__idem,axiom,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2)) ) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).
fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one__idem(T_c,V_f_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_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,V_f_2),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).
fof(fact_folding__one__idem_Osubset__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( 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__one__idem_Osubset__idem) ).
fof(fact_inj__on__iff__surj,axiom,
! [V_A_H_2,T_d,T_c,V_A_2] :
( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,B_f),V_A_2)),V_A_H_2))
& c_Fun_Oinj__on(T_c,T_d,B_f,V_A_2) )
<=> ? [B_g] : hAPP(c_Set_Oimage(T_d,T_c,B_g),V_A_H_2) = V_A_2 ) ),
file('theBenchmark.p',fact_inj__on__iff__surj) ).
fof(fact_fun__left__comm_Ofold__rec,axiom,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,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(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_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_fun__left__comm_Ofold__rec) ).
fof(fact_fold1Set_Ointros,axiom,
! [V_x_2,V_A_2,V_a_2,V_f_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,V_f_2,V_a_2,V_A_2),V_x_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_x_2)) ) ),
file('theBenchmark.p',fact_fold1Set_Ointros) ).
fof(fact_flat__lub__def,axiom,
! [V_b_2,V_A_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))
=> c_Partial__Function_Oflat__lub(T_c,V_b_2,V_A_2) = c_HOL_OThe(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),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_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))
=> c_Partial__Function_Oflat__lub(T_c,V_b_2,V_A_2) = V_b_2 ) ),
file('theBenchmark.p',fact_flat__lub__def) ).
fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_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_fun__left__comm_Ofold__insert__remove) ).
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_d,T_c] :
( c_Nitpick_Ofold__graph_H(T_c,T_d,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_c,T_d,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),B_y)
& hBOOL(hAPP(hAPP(c_member(T_c),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_c,tc_HOL_Obool)) ) ) ),
file('theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_c_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_d_2)) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_fun__left__comm_Ofold__insert2,axiom,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,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(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,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_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,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(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2)) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).
fof(fact_finite__subset__induct,axiom,
! [V_Pa_2,V_A_2,V_F_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_A_2))
=> ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
=> ( ! [B_a,B_F] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_F))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),B_a),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),B_a),B_F))
=> ( hBOOL(hAPP(V_Pa_2,B_F))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_c),B_a),B_F))) ) ) ) )
=> hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ),
file('theBenchmark.p',fact_finite__subset__induct) ).
fof(fact_setsum_Oremove,axiom,
! [V_g_2,V_x_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( 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(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_setsum_Oremove) ).
fof(fact_fun__left__comm_Ofun__left__comm,axiom,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,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_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_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__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__right__cancel,axiom,
! [V_c_2,V_a_2,V_b_2,T_c] :
( class_Groups_Ocancel__semigroup__add(T_c)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_a_2)
<=> V_b_2 = V_c_2 ) ),
file('theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__left__cancel,axiom,
! [V_c_2,V_b_2,V_a_2,T_c] :
( class_Groups_Ocancel__semigroup__add(T_c)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_c_2)
<=> V_b_2 = V_c_2 ) ),
file('theBenchmark.p',fact_add__left__cancel) ).
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__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_c_2,T_c] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),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_c_2,V_a_2,T_c] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__le__cancel__right) ).
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_fun__left__comm_Ofun__left__comm__apply,axiom,
! [V_g_2,T_e,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2)
=> c_Finite__Set_Ofun__left__comm(T_e,T_d,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_d),T_e),V_f_2),V_g_2)) ),
file('theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).
fof(fact_setsum__addf,axiom,
! [V_A_2,V_g_2,V_f_2,T_d,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Oplus__class_Oplus(T_c)),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_d,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_g_2),V_A_2)) ),
file('theBenchmark.p',fact_setsum__addf) ).
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_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_x_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,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_empty__fold1SetE,axiom,
! [V_x_2,V_f_2,T_c] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,V_A_2),V_x_2))
=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_fold1Set__nonempty) ).
fof(fact_setsum_Odistrib,axiom,
! [V_h_2,V_g_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Groups_Oplus__class_Oplus(T_d)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_A_2)) ) ),
file('theBenchmark.p',fact_setsum_Odistrib) ).
fof(fact_diff__eq__diff__eq,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Groups_Oab__group__add(T_c)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_c_2),V_d_2)
=> ( V_a_2 = V_b_2
<=> V_c_2 = V_d_2 ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,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_fun__left__comm_Ofold__equality,axiom,
! [V_y_2,V_A_2,V_z_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_y_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2) = V_y_2 ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).
fof(fact_fold1Set__sing,axiom,
! [V_b_2,V_a_2,V_f_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(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)))),V_b_2))
<=> V_a_2 = V_b_2 ),
file('theBenchmark.p',fact_fold1Set__sing) ).
fof(fact_setsum_Oinsert,axiom,
! [V_g_2,V_x_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( 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(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)) ) ) ),
file('theBenchmark.p',fact_setsum_Oinsert) ).
fof(fact_setsum__insert,axiom,
! [V_f_2,V_a_2,V_F_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_F_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_F_2)) ) ) ),
file('theBenchmark.p',fact_setsum__insert) ).
fof(fact_setsum_Oinsert__remove,axiom,
! [V_x_2,V_g_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_setsum_Oinsert__remove) ).
fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
! [V_z_2,V_A_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2))) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).
fof(fact_setsum__diff1_H,axiom,
! [V_f_2,V_a_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ),
file('theBenchmark.p',fact_setsum__diff1_H) ).
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_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> ? [B_y_H] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,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_fold1Set_Oequations,axiom,
! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a1_2),V_a2_2)),V_a3_2))
<=> ? [B_a,B_A] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,V_f_2,B_a,B_A),V_a3_2))
& hAPP(hAPP(c_Set_Oinsert(T_c),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_c),B_a),B_A) ) ),
file('theBenchmark.p',fact_fold1Set_Oequations) ).
fof(fact_insert__fold1SetE,axiom,
! [V_x_2,V_X_2,V_a_2,V_f_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_X_2)),V_x_2))
=> ~ ! [B_a,B_A] :
( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_c),B_a),B_A)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,V_f_2,B_a,B_A),V_x_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),B_a),B_A)) ) ) ),
file('theBenchmark.p',fact_insert__fold1SetE) ).
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_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_v_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),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_c,T_d,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).
fof(fact_fold__graph__permute__diff,axiom,
! [V_a_2,V_x_2,V_A_2,V_b_2,T_c] :
( class_Groups_Oab__semigroup__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),V_b_2,V_A_2),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_b_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_x_2)) ) ) ) ),
file('theBenchmark.p',fact_fold__graph__permute__diff) ).
fof(fact_setsum__reindex__cong,axiom,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_d,T_c,T_e] :
( class_Groups_Ocomm__monoid__add(T_e)
=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( V_B_2 = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)
=> ( ! [B_a] :
( hBOOL(hAPP(hAPP(c_member(T_c),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_d,T_e),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),V_g_2),V_A_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__reindex__cong) ).
fof(fact_psubset__insert__iff,axiom,
! [V_B_2,V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),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))))),V_B_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_psubset__insert__iff) ).
fof(fact_comm__monoid__big_Oinfinite,axiom,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_d,T_c] :
( c_Big__Operators_Ocomm__monoid__big(T_c,T_d,V_f_2,V_z_2,V_F_2)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),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_Max__mono,axiom,
! [V_N_2,V_M_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_M_2),V_N_2))
=> ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_c,V_N_2))) ) ) ) ),
file('theBenchmark.p',fact_Max__mono) ).
fof(fact_Min__antimono,axiom,
! [V_N_2,V_M_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_M_2),V_N_2))
=> ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_c,V_M_2))) ) ) ) ),
file('theBenchmark.p',fact_Min__antimono) ).
fof(fact_finite__nonempty__imp__fold1Set,axiom,
! [V_f_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,V_A_2),B_x1)) ) ),
file('theBenchmark.p',fact_finite__nonempty__imp__fold1Set) ).
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_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_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_c] :
( class_Orderings_Olinorder(T_c)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( V_x_2 != V_y_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
file('theBenchmark.p',fact_psubset__trans) ).
fof(fact_less__fun__def,axiom,
! [V_g_2,V_f_2,T_c,T_d] :
( class_Orderings_Oord(T_d)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,T_d)),V_f_2),V_g_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_g_2),V_f_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2)) ) ) ),
file('theBenchmark.p',fact_less__fun__def) ).
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_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_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__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_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__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_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_linorder__antisym__conv2,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv2) ).
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_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_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_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_linorder__antisym__conv1,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv1) ).
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_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_order__le__less,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__le__less) ).
fof(fact_less__le__not__le,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Opreorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_less__le__not__le) ).
fof(fact_order__less__le,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
<=> ( V_x_2 != V_y_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__less__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_linorder__not__le,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__not__less,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_linorder__not__less) ).
fof(fact_psubsetD,axiom,
! [V_c_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_psubsetD) ).
fof(fact_add__less__cancel__right,axiom,
! [V_b_2,V_c_2,V_a_2,T_c] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__cancel__left,axiom,
! [V_b_2,V_a_2,V_c_2,T_c] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__less__cancel__left) ).
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__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__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__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__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_not__psubset__empty,axiom,
! [V_A_2,T_c] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_not__psubset__empty) ).
fof(fact_diff__eq__diff__less,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_c_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2)) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_subset__psubset__trans,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,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)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,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)),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_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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_c,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_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,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_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_psubset__eq) ).
fof(fact_fun__left__comm,axiom,
! [T_c] :
( class_Groups_Oab__semigroup__mult(T_c)
=> c_Finite__Set_Ofun__left__comm(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c)) ),
file('theBenchmark.p',fact_fun__left__comm) ).
fof(fact_fun__left__comm__idem,axiom,
! [T_c] :
( class_Lattices_Oab__semigroup__idem__mult(T_c)
=> c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c)) ),
file('theBenchmark.p',fact_fun__left__comm__idem) ).
fof(fact_setsum__right__distrib,axiom,
! [V_A_2,V_f_2,T_d,V_r_2,T_c] :
( class_Rings_Osemiring__0(T_c)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),hAPP(c_Groups_Otimes__class_Otimes(T_c),V_r_2)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_setsum__right__distrib) ).
fof(fact_setsum__left__distrib,axiom,
! [V_r_2,V_A_2,V_f_2,T_d,T_c] :
( class_Rings_Osemiring__0(T_c)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Otimes__class_Otimes(T_c)),V_f_2)),V_r_2)),V_A_2) ),
file('theBenchmark.p',fact_setsum__left__distrib) ).
fof(fact_setsum__product,axiom,
! [V_B_2,V_g_2,T_e,V_A_2,V_f_2,T_d,T_c] :
( class_Rings_Osemiring__0(T_c)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),tc_fun(tc_fun(T_e,tc_HOL_Obool),T_c),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,T_c)),T_d),c_COMBB(T_c,T_c,T_e)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ),
file('theBenchmark.p',fact_setsum__product) ).
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_inj__on__strict__subset,axiom,
! [V_A_2,V_B_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2))) ) ),
file('theBenchmark.p',fact_inj__on__strict__subset) ).
fof(fact_Min_Osingleton,axiom,
! [V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_Min_Osingleton) ).
fof(fact_Max_Osingleton,axiom,
! [V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_Max_Osingleton) ).
fof(fact_fold__graph__insert__swap,axiom,
! [V_z_2,V_y_2,V_A_2,V_b_2,T_c] :
( class_Groups_Oab__semigroup__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),V_b_2,V_A_2),V_y_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_z_2),V_y_2))) ) ) ),
file('theBenchmark.p',fact_fold__graph__insert__swap) ).
fof(fact_Min__le,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),V_x_2)) ) ) ),
file('theBenchmark.p',fact_Min__le) ).
fof(fact_Max__ge,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2))) ) ) ),
file('theBenchmark.p',fact_Max__ge) ).
fof(fact_Min__in,axiom,
! [V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),V_A_2)) ) ) ),
file('theBenchmark.p',fact_Min__in) ).
fof(fact_Max__in,axiom,
! [V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),V_A_2)) ) ) ),
file('theBenchmark.p',fact_Max__in) ).
fof(fact_less__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] :
( class_Rings_Oordered__ring(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ),
file('theBenchmark.p',fact_less__add__iff2) ).
fof(fact_less__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] :
( class_Rings_Oordered__ring(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
file('theBenchmark.p',fact_less__add__iff1) ).
fof(fact_le__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] :
( class_Rings_Oordered__ring(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ),
file('theBenchmark.p',fact_le__add__iff2) ).
fof(fact_le__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] :
( class_Rings_Oordered__ring(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
file('theBenchmark.p',fact_le__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] :
( class_Rings_Oring(T_c)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2)
<=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ),
file('theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_eq__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] :
( class_Rings_Oring(T_c)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ),
file('theBenchmark.p',fact_eq__add__iff1) ).
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_crossproduct__noteq,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_c)
=> ( ( V_c_2 != V_d_2
& V_a_2 != V_b_2 )
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_crossproduct__noteq) ).
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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_crossproduct__eq,axiom,
! [V_z_2,V_x_2,V_y_2,V_w_2,T_c] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_c)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),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_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__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_setsum__strict__mono,axiom,
! [V_g_2,V_f_2,V_A_2,T_c,T_d] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add(T_d)
& class_Groups_Ocomm__monoid__add(T_d) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_d),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_A_2))) ) ) ) ),
file('theBenchmark.p',fact_setsum__strict__mono) ).
fof(fact_Min_Oremove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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(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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Min_Oremove) ).
fof(fact_Max_Oremove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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(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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Max_Oremove) ).
fof(fact_fold1__eq__fold,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Groups_Oab__semigroup__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c)),V_a_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_fold1__eq__fold) ).
fof(fact_fold1__insert,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Groups_Oab__semigroup__mult(T_c)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( 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(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_fold1__insert) ).
fof(fact_setprod_Oremove,axiom,
! [V_g_2,V_x_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( 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(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_setprod_Oremove) ).
fof(fact_Min__eqI,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),B_y)) )
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Min__eqI) ).
fof(fact_Max__eqI,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_y),V_x_2)) )
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Max__eqI) ).
fof(fact_minus__Max__eq__Min,axiom,
! [V_S_2,T_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),V_S_2)) ) ) ),
file('theBenchmark.p',fact_minus__Max__eq__Min) ).
fof(fact_minus__Min__eq__Max,axiom,
! [V_S_2,T_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),V_S_2)) ) ) ),
file('theBenchmark.p',fact_minus__Min__eq__Max) ).
fof(fact_ComplI,axiom,
! [V_A_2,V_c_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ),
file('theBenchmark.p',fact_ComplI) ).
fof(fact_inj__uminus,axiom,
! [V_A_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> c_Fun_Oinj__on(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c),V_A_2) ),
file('theBenchmark.p',fact_inj__uminus) ).
fof(fact_neg__equal__iff__equal,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Groups_Ogroup__add(T_c)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_minus__equation__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Groups_Ogroup__add(T_c)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) = V_b_2
<=> hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2) = V_a_2 ) ),
file('theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_equation__minus__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Groups_Ogroup__add(T_c)
=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)
<=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) ) ),
file('theBenchmark.p',fact_equation__minus__iff) ).
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_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_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_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_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_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__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_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_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_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_compl__eq__compl__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Lattices_Oboolean__algebra(T_c)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_compl__eq__compl__iff) ).
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__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__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_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_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_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_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__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_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__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_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__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__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_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_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_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_uminus__apply,axiom,
! [V_x_2,V_A_2,T_d,T_c] :
( class_Groups_Ouminus(T_c)
=> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,T_c)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_uminus__apply) ).
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_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_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_fun__Compl__def,axiom,
! [V_x_2,V_A_2,T_d,T_c] :
( class_Groups_Ouminus(T_c)
=> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,T_c)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_fun__Compl__def) ).
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_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_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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2)),V_z_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_z_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_z_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_le__max__iff__disj) ).
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_c] :
( class_Lattices_Oboolean__algebra(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_le__minus__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) ) ),
file('theBenchmark.p',fact_le__minus__iff) ).
fof(fact_minus__le__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),V_a_2)) ) ),
file('theBenchmark.p',fact_minus__le__iff) ).
fof(fact_neg__le__iff__le,axiom,
! [V_a_2,V_b_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_neg__le__iff__le) ).
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_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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_y_2),V_z_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2)),V_z_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_min__le__iff__disj) ).
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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2)),V_z_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_less__max__iff__disj) ).
fof(fact_neg__less__iff__less,axiom,
! [V_a_2,V_b_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),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_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),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_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) ) ),
file('theBenchmark.p',fact_less__minus__iff) ).
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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2)),V_z_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_y_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_min__less__iff__conj) ).
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_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_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_c] :
( class_Rings_Oidom(T_c)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_b_2)
<=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)
| V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_square__eq__iff) ).
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_ComplE,axiom,
! [V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_ComplE) ).
fof(fact_ComplD,axiom,
! [V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_ComplD) ).
fof(fact_Compl__iff,axiom,
! [V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))
<=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_Compl__iff) ).
fof(fact_Max_OF__eq,axiom,
! [V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omax(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_Max_OF__eq) ).
fof(fact_Min_OF__eq,axiom,
! [V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_Min_OF__eq) ).
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_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_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_Compl__anti__mono,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ),
file('theBenchmark.p',fact_Compl__anti__mono) ).
fof(fact_Compl__subset__Compl__iff,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) ),
file('theBenchmark.p',fact_Compl__subset__Compl__iff) ).
fof(fact_setprod__timesf,axiom,
! [V_A_2,V_g_2,V_f_2,T_d,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Otimes__class_Otimes(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_g_2),V_A_2)) ),
file('theBenchmark.p',fact_setprod__timesf) ).
fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
! [T_c] :
( class_Orderings_Olinorder(T_c)
=> c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)) ),
file('theBenchmark.p',fact_min__max_Ofun__left__comm__idem__sup) ).
fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
! [T_c] :
( class_Orderings_Olinorder(T_c)
=> c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)) ),
file('theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).
fof(fact_min__max_Ofold1__belowI,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)),V_a_2)) ) ) ),
file('theBenchmark.p',fact_min__max_Ofold1__belowI) ).
fof(fact_fold1__below__iff,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)),V_x_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ) ) ),
file('theBenchmark.p',fact_fold1__below__iff) ).
fof(fact_min__max_Obelow__fold1__iff,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_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_c),V_x_2),B_x)) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).
fof(fact_setsum__negf,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( class_Groups_Oab__group__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Ouminus__class_Ouminus(T_c)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)) ),
file('theBenchmark.p',fact_setsum__negf) ).
fof(fact_fold1__strict__below__iff,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)),V_x_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),B_x),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),B_x)) ) ) ) ) ),
file('theBenchmark.p',fact_strict__below__fold1__iff) ).
fof(fact_fold1__antimono,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2))) ) ) ) ),
file('theBenchmark.p',fact_fold1__antimono) ).
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_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_subset__Compl__self__eq,axiom,
! [V_A_2,T_c] :
( 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)),V_A_2)))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_subset__Compl__self__eq) ).
fof(fact_setprod_Odistrib,axiom,
! [V_h_2,V_g_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Groups_Otimes__class_Otimes(T_d)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_A_2)) ) ),
file('theBenchmark.p',fact_setprod_Odistrib) ).
fof(fact_fold1__singleton__def,axiom,
! [V_a_2,V_f_2,T_c,V_g_2] :
( V_g_2 = c_Finite__Set_Ofold1(T_c,V_f_2)
=> hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c] : hAPP(c_Finite__Set_Ofold1(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)))) = V_a_2,
file('theBenchmark.p',fact_fold1__singleton) ).
fof(fact_folding__one_Oeq__fold,axiom,
! [V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,V_f_2),V_A_2) ) ),
file('theBenchmark.p',fact_folding__one_Oeq__fold) ).
fof(fact_min__max_Ofold__sup__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) ) ) ),
file('theBenchmark.p',fact_Max_Oin__idem) ).
fof(fact_min__max_Ofold__inf__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_b_2),V_A_2)) ) ),
file('theBenchmark.p',fact_min__max_Ofold__inf__insert) ).
fof(fact_Min_Oin__idem,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) ) ) ),
file('theBenchmark.p',fact_Min_Oin__idem) ).
fof(fact_fold1__def,axiom,
! [V_A_2,V_f_2,T_c] : hAPP(c_Finite__Set_Ofold1(T_c,V_f_2),V_A_2) = c_HOL_OThe(T_c,c_Finite__Set_Ofold1Set(T_c,V_f_2,V_A_2)),
file('theBenchmark.p',fact_fold1__def) ).
fof(fact_setprod_Oinsert,axiom,
! [V_g_2,V_x_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( 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(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)) ) ) ),
file('theBenchmark.p',fact_setprod__insert) ).
fof(fact_min__max_Osup__le__fold__sup,axiom,
! [V_b_2,V_a_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_b_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).
fof(fact_min__max_Ofold__inf__le__inf,axiom,
! [V_b_2,V_a_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_a_2),V_b_2))) ) ) ),
file('theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).
fof(fact_Max__insert,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)) ) ) ),
file('theBenchmark.p',fact_Max__insert) ).
fof(fact_Min__insert,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)) ) ) ),
file('theBenchmark.p',fact_Min__insert) ).
fof(fact_Max_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) ) ) ) ),
file('theBenchmark.p',fact_Max_Osubset__idem) ).
fof(fact_Min_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) ) ) ) ),
file('theBenchmark.p',fact_Min_Osubset__idem) ).
fof(fact_Max_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).
fof(fact_Min_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).
fof(fact_setprod_Oinsert__remove,axiom,
! [V_x_2,V_g_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_setprod_Oinsert__remove) ).
fof(fact_fold1__insert__idem,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Oab__semigroup__idem__mult(T_c)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)) ) ) ),
file('theBenchmark.p',fact_fold1__insert__idem) ).
fof(fact_fold1__eq__fold__idem,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Lattices_Oab__semigroup__idem__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_fold1__eq__fold__idem) ).
fof(fact_Max_Oinsert,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Max_Oinsert) ).
fof(fact_Min_Oinsert,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Min_Oinsert) ).
fof(fact_Max_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Max_Oinsert__remove) ).
fof(fact_Min_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Min_Oinsert__remove) ).
fof(fact_Max_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_Max_Oeq__fold_H) ).
fof(fact_Min_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_Min_Oeq__fold_H) ).
fof(fact_semilattice__big_OF__eq,axiom,
! [V_A_2,V_F_2,V_f_2,T_c] :
( c_Big__Operators_Osemilattice__big(T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,V_f_2),V_A_2) ) ),
file('theBenchmark.p',fact_semilattice__big_OF__eq) ).
fof(fact_dual__min,axiom,
! [T_c] :
( class_Orderings_Olinorder(T_c)
=> c_Orderings_Oord_Omin(T_c,hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_c))) = c_Orderings_Oord__class_Omax(T_c) ),
file('theBenchmark.p',fact_dual__min) ).
fof(fact_dual__max,axiom,
! [T_c] :
( class_Orderings_Olinorder(T_c)
=> c_Orderings_Oord_Omax(T_c,hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_c))) = c_Orderings_Oord__class_Omin(T_c) ),
file('theBenchmark.p',fact_dual__max) ).
fof(fact_max__ord__max,axiom,
! [T_c] :
( class_Orderings_Oord(T_c)
=> c_Orderings_Oord__class_Omax(T_c) = c_Orderings_Oord_Omax(T_c,c_Orderings_Oord__class_Oless__eq(T_c)) ),
file('theBenchmark.p',fact_max__ord__max) ).
fof(fact_min__ord__min,axiom,
! [T_c] :
( class_Orderings_Oord(T_c)
=> c_Orderings_Oord__class_Omin(T_c) = c_Orderings_Oord_Omin(T_c,c_Orderings_Oord__class_Oless__eq(T_c)) ),
file('theBenchmark.p',fact_min__ord__min) ).
fof(fact_Max_Oclosed,axiom,
! [V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Max_Oclosed) ).
fof(fact_Min_Oclosed,axiom,
! [V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Min_Oclosed) ).
fof(fact_fold1__in,axiom,
! [V_A_2,T_c] :
( class_Groups_Oab__semigroup__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_fold1__in) ).
fof(fact_min__max_OSup__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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(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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oremove) ).
fof(fact_min__max_OInf__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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(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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oremove) ).
fof(fact_Compl__eq__Compl__iff,axiom,
! [V_B_2,V_A_2,T_c] :
( 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_c,tc_HOL_Obool)),V_B_2)
<=> V_A_2 = V_B_2 ),
file('theBenchmark.p',fact_Compl__eq__Compl__iff) ).
fof(fact_double__complement,axiom,
! [V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = V_A_2,
file('theBenchmark.p',fact_double__complement) ).
fof(fact_min__max_OInf__le__Sup,axiom,
! [V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2))) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__le__Sup) ).
fof(fact_min__max_OInf__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).
fof(fact_min__max_OSup__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).
fof(fact_min__max_OInf__fin_Osingleton,axiom,
! [V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).
fof(fact_min__max_OSup__fin_Osingleton,axiom,
! [V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).
fof(fact_min__max_OInf__fin_OF__eq,axiom,
! [V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).
fof(fact_min__max_OSup__fin_OF__eq,axiom,
! [V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omax(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).
fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).
fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).
fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).
fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) = V_a_2 ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).
fof(fact_min__max_Osup__Inf__absorb,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) = V_a_2 ) ) ),
file('theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).
fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold__idem_H) ).
fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold__idem_H) ).
fof(fact_min__max_OInf__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).
fof(fact_min__max_OSup__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).
fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__remove) ).
fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__remove) ).
fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold_H) ).
fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).
fof(fact_min__max_OInf__fin_Oclosed,axiom,
! [V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).
fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Ohom__commute) ).
fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ohom__commute) ).
fof(fact_Max_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_c,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_Max_Ohom__commute) ).
fof(fact_Min_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_c,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_Min_Ohom__commute) ).
fof(fact_hom__fold1__commute,axiom,
! [V_N_2,V_h_2,T_c] :
( class_Lattices_Oab__semigroup__idem__mult(T_c)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_hom__fold1__commute) ).
fof(fact_min__max_Ofold__sup__le__sup,axiom,
! [V_c_2,V_b_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),V_b_2)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_b_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).
fof(fact_min__max_Oinf__le__fold__inf,axiom,
! [V_c_2,V_b_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),B_x)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_c_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).
fof(fact_card__Diff2__less,axiom,
! [V_y_2,V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),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))))),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) ) ) ),
file('theBenchmark.p',fact_card__Diff2__less) ).
fof(fact_card__Diff1__less,axiom,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),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)))))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) ) ),
file('theBenchmark.p',fact_card__Diff1__less) ).
fof(fact_inj__image__Compl__subset,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))) ),
file('theBenchmark.p',fact_inj__image__Compl__subset) ).
fof(fact_fold__image__insert,axiom,
! [V_z_2,V_g_2,V_a_2,V_A_2,T_c,T_d] :
( class_Groups_Oab__semigroup__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_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(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_g_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),V_A_2)) ) ) ),
file('theBenchmark.p',fact_fold__image__insert) ).
fof(fact_setsum__mono,axiom,
! [V_g_2,V_f_2,V_K_2,T_c,T_d] :
( ( class_Groups_Oordered__ab__semigroup__add(T_d)
& class_Groups_Ocomm__monoid__add(T_d) )
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_K_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,B_i)),hAPP(V_g_2,B_i))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_K_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_K_2))) ) ),
file('theBenchmark.p',fact_setsum__mono) ).
fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).
fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).
fof(fact_Max__Un,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_c,V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_Max__Un) ).
fof(fact_Min__Un,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_c,V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_Min__Un) ).
fof(fact_top1I,axiom,
! [V_x_2,T_c] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_x_2)),
file('theBenchmark.p',fact_top1I) ).
fof(fact_sup1E,axiom,
! [V_x_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_sup1CI,axiom,
! [T_c,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_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
file('theBenchmark.p',fact_sup1CI) ).
fof(fact_UNIV__I,axiom,
! [V_x_2,T_c] : hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_UNIV__I) ).
fof(fact_UnE,axiom,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_UnE) ).
fof(fact_UnCI,axiom,
! [V_A_2,V_B_2,V_c_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) )
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UnCI) ).
fof(fact_finite__option__UNIV,axiom,
! [T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(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__option__UNIV) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_c,T_d),tc_HOL_Obool))))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,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__Plus__UNIV__iff) ).
fof(fact_finite__Prod__UNIV,axiom,
! [T_d,T_c] :
( 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_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__Prod__UNIV) ).
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_Un__UNIV__left,axiom,
! [V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Un__UNIV__left) ).
fof(fact_Un__UNIV__right,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Un__UNIV__right) ).
fof(fact_Un__absorb,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
file('theBenchmark.p',fact_Un__absorb) ).
fof(fact_Un__commute,axiom,
! [V_B_2,V_A_2,T_c] : 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_c,tc_HOL_Obool)),V_B_2),V_A_2),
file('theBenchmark.p',fact_Un__commute) ).
fof(fact_Un__left__absorb,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_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_c,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Un__left__absorb) ).
fof(fact_Un__left__commute,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Un__left__commute) ).
fof(fact_Un__assoc,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Un__assoc) ).
fof(fact_bex__Un,axiom,
! [V_Pa_2,V_B_2,V_A_2,T_c] :
( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) )
<=> ( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_B_2)) )
| ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_bex__Un) ).
fof(fact_ball__Un,axiom,
! [V_Pa_2,V_B_2,V_A_2,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_B_2))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ) ),
file('theBenchmark.p',fact_ball__Un) ).
fof(fact_top__apply,axiom,
! [V_x_2,T_d,T_c] :
( class_Orderings_Otop(T_c)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_d,T_c)),V_x_2) = c_Orderings_Otop__class_Otop(T_c) ),
file('theBenchmark.p',fact_top__apply) ).
fof(fact_sup1I1,axiom,
! [V_B_2,T_c,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_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
file('theBenchmark.p',fact_sup1I1) ).
fof(fact_sup1I2,axiom,
! [V_A_2,T_c,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_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
file('theBenchmark.p',fact_sup1I2) ).
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_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_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__fun__def,axiom,
! [V_x_2,V_g_2,V_f_2,T_d,T_c] :
( class_Lattices_Olattice(T_c)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,T_c)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
file('theBenchmark.p',fact_sup__fun__def) ).
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_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__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_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_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__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_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_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__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_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_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__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_sup__apply,axiom,
! [V_x_2,V_g_2,V_f_2,T_d,T_c] :
( class_Lattices_Olattice(T_c)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,T_c)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
file('theBenchmark.p',fact_sup__apply) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,T_d),tc_HOL_Obool))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_finite__fun__UNIVD2) ).
fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
=> ( hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_Compl__partition,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__partition) ).
fof(fact_Compl__partition2,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__partition2) ).
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_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_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_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_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__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_le__iff__sup,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Lattices_Osemilattice__sup(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_y_2) = V_y_2 ) ),
file('theBenchmark.p',fact_le__iff__sup) ).
fof(fact_le__sup__iff,axiom,
! [V_z_2,V_y_2,V_x_2,T_c] :
( class_Lattices_Osemilattice__sup(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_y_2)),V_z_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_le__sup__iff) ).
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__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_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_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_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__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_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_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_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_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_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__eq__bot__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Lattices_Obounded__lattice__bot(T_c)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_c)
<=> ( V_y_2 = c_Orderings_Obot__class_Obot(T_c)
& V_x_2 = c_Orderings_Obot__class_Obot(T_c) ) ) ),
file('theBenchmark.p',fact_sup__eq__bot__iff) ).
fof(fact_Un__iff,axiom,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Un__iff) ).
fof(fact_UnI1,axiom,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UnI2) ).
fof(fact_sup__max,axiom,
! [T_c] :
( ( class_Orderings_Olinorder(T_c)
& class_Lattices_Osemilattice__sup(T_c) )
=> c_Lattices_Osemilattice__sup__class_Osup(T_c) = c_Orderings_Oord__class_Omax(T_c) ),
file('theBenchmark.p',fact_sup__max) ).
fof(fact_Un__empty__left,axiom,
! [V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = V_B_2,
file('theBenchmark.p',fact_Un__empty__left) ).
fof(fact_Un__empty__right,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_A_2,
file('theBenchmark.p',fact_Un__empty__right) ).
fof(fact_Un__empty,axiom,
! [V_B_2,V_A_2,T_c] :
( hAPP(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_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_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_Un__empty) ).
fof(fact_finite__Un,axiom,
! [V_Ga_2,V_F_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_Ga_2)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Ga_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ),
file('theBenchmark.p',fact_finite__Un) ).
fof(fact_finite__UnI,axiom,
! [V_Ga_2,V_F_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Ga_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ),
file('theBenchmark.p',fact_finite__UnI) ).
fof(fact_Un__insert__right,axiom,
! [V_B_2,V_a_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),
file('theBenchmark.p',fact_Un__insert__right) ).
fof(fact_Un__insert__left,axiom,
! [V_C_2,V_B_2,V_a_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Un__insert__left) ).
fof(fact_Un__upper1,axiom,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),
file('theBenchmark.p',fact_Un__upper1) ).
fof(fact_Un__upper2,axiom,
! [V_A_2,V_B_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),
file('theBenchmark.p',fact_Un__upper2) ).
fof(fact_subset__Un__eq,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),V_B_2) = V_B_2 ),
file('theBenchmark.p',fact_subset__Un__eq) ).
fof(fact_Un__absorb1,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),V_B_2) = V_B_2 ),
file('theBenchmark.p',fact_Un__absorb1) ).
fof(fact_Un__absorb2,axiom,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
file('theBenchmark.p',fact_Un__absorb2) ).
fof(fact_Un__least,axiom,
! [V_B_2,V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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_C_2)) ) ),
file('theBenchmark.p',fact_Un__least) ).
fof(fact_Un__mono,axiom,
! [V_D_2,V_B_2,V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
file('theBenchmark.p',fact_Un__mono) ).
fof(fact_image__Un,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_B_2)),
file('theBenchmark.p',fact_image__Un) ).
fof(fact_Un__Diff__cancel,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Un__Diff__cancel) ).
fof(fact_Un__Diff__cancel2,axiom,
! [V_A_2,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2),
file('theBenchmark.p',fact_Un__Diff__cancel2) ).
fof(fact_Un__Diff,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,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_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Un__Diff) ).
fof(fact_UNIV__not__empty,axiom,
! [T_c] : c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_UNIV__not__empty) ).
fof(fact_finite__UNIV,axiom,
! [T_c] :
( class_Finite__Set_Ofinite(T_c)
=> 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__UNIV) ).
fof(fact_subset__UNIV,axiom,
! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_subset__UNIV) ).
fof(fact_inj__eq,axiom,
! [V_y_2,V_x_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,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_fold__image__empty,axiom,
! [V_z_2,V_g_2,V_f_2,T_d,T_c] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = V_z_2,
file('theBenchmark.p',fact_fold__image__empty) ).
fof(fact_fun__left__comm__idem__sup,axiom,
! [T_c] :
( class_Lattices_Osemilattice__sup(T_c)
=> c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)) ),
file('theBenchmark.p',fact_fun__left__comm__idem__sup) ).
fof(fact_sup__Un__eq,axiom,
! [V_x_2,V_S_2,V_R_2,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_R_2),V_S_2))) ),
file('theBenchmark.p',fact_sup__Un__eq) ).
fof(fact_range__composition,axiom,
! [V_g_2,V_f_2,T_e,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,hAPP(hAPP(c_COMBB(T_e,T_c,T_d),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_e,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_e,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))),
file('theBenchmark.p',fact_range__composition) ).
fof(fact_inj__fun,axiom,
! [T_e,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> c_Fun_Oinj__on(T_c,tc_fun(T_e,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,T_d),T_c),c_COMBK(T_d,T_e)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__fun) ).
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_fold__image__def,axiom,
! [V_g_2,V_f_2,T_d,T_c] : hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_d,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)),
file('theBenchmark.p',fact_fold__image__def) ).
fof(fact_card__insert__le,axiom,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)))) ),
file('theBenchmark.p',fact_card__insert__le) ).
fof(fact_card__mono,axiom,
! [V_A_2,V_B_2,T_c] :
( 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_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ),
file('theBenchmark.p',fact_card__mono) ).
fof(fact_card__seteq,axiom,
! [V_A_2,V_B_2,T_c] :
( 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_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
=> V_A_2 = V_B_2 ) ) ),
file('theBenchmark.p',fact_card__seteq) ).
fof(fact_card__image__le,axiom,
! [V_f_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) ),
file('theBenchmark.p',fact_card__image__le) ).
fof(fact_pigeonhole,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_d),V_A_2)))
=> ~ c_Fun_Oinj__on(T_d,T_c,V_f_2,V_A_2) ),
file('theBenchmark.p',fact_pigeonhole) ).
fof(fact_card__image,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ),
file('theBenchmark.p',fact_card__image) ).
fof(fact_insert__is__Un,axiom,
! [V_A_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_A_2),
file('theBenchmark.p',fact_insert__is__Un) ).
fof(fact_Diff__subset__conv,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))) ),
file('theBenchmark.p',fact_Diff__subset__conv) ).
fof(fact_Diff__partition,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ),
file('theBenchmark.p',fact_Diff__partition) ).
fof(fact_psubset__card__mono,axiom,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ),
file('theBenchmark.p',fact_psubset__card__mono) ).
fof(fact_inj__on__Un__image__eq__iff,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,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(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)
<=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).
fof(fact_rangeI,axiom,
! [T_d,V_x_2,V_f_2,T_c] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))),
file('theBenchmark.p',fact_rangeI) ).
fof(fact_range__eqI,axiom,
! [T_d,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_b_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))) ),
file('theBenchmark.p',fact_range__eqI) ).
fof(fact_image__eq__fold__image,axiom,
! [V_f_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_d,tc_HOL_Obool),T_c,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_d,tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_d)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))),V_A_2) ),
file('theBenchmark.p',fact_image__eq__fold__image) ).
fof(fact_Diff__UNIV,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Diff__UNIV) ).
fof(fact_Compl__Diff__eq,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2),
file('theBenchmark.p',fact_Compl__Diff__eq) ).
fof(fact_inj__image__eq__iff,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> ( hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)
<=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_inj__image__eq__iff) ).
fof(fact_Compl__empty__eq,axiom,
! [T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_Compl__UNIV__eq,axiom,
! [T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_finite__compl,axiom,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))
<=> 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__compl) ).
fof(fact_Compl__eq__Diff__UNIV,axiom,
! [V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_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_A_2),
file('theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).
fof(fact_inj__singleton,axiom,
! [T_c] : c_Fun_Oinj__on(T_c,tc_fun(T_c,tc_HOL_Obool),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))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),
file('theBenchmark.p',fact_inj__singleton) ).
fof(fact_finite__range__imageI,axiom,
! [V_f_2,T_e,V_g_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_e),hAPP(c_Set_Oimage(T_d,T_e,hAPP(hAPP(c_COMBB(T_c,T_e,T_d),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))) ),
file('theBenchmark.p',fact_finite__range__imageI) ).
fof(fact_the__inv__f__f,axiom,
! [V_x_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Fun_Othe__inv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,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_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_d,T_c] :
( c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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_Oeq__fold__g,axiom,
! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2),V_z_2),V_A_2) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [V_f_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
<=> hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ) ),
file('theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(fact_eq__card__imp__inj__on,axiom,
! [V_f_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2)
=> c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_diff__card__le__card__Diff,axiom,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) ),
file('theBenchmark.p',fact_diff__card__le__card__Diff) ).
fof(fact_fold__sup__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_c] :
( class_Lattices_Osemilattice__sup(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_b_2),V_A_2)) ) ),
file('theBenchmark.p',fact_fold__sup__insert) ).
fof(fact_card__psubset,axiom,
! [V_A_2,V_B_2,T_c] :
( 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_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_card__psubset) ).
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_range__ex1__eq,axiom,
! [V_b_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [V_f_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
=> ( c_Fun_Oinj__on(T_c,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_c,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_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_finite__UNIV__surj__inj,axiom,
! [V_f_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
=> ( hAPP(c_Set_Oimage(T_c,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_c,tc_HOL_Obool))
=> c_Fun_Oinj__on(T_c,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_finite__UNIV__surj__inj) ).
fof(fact_inj__image__subset__iff,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_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_inj__image__subset__iff) ).
fof(fact_image__set__diff,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)) ),
file('theBenchmark.p',fact_image__set__diff) ).
fof(fact_surj__Compl__image__subset,axiom,
! [V_A_2,V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,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_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)))) ),
file('theBenchmark.p',fact_surj__Compl__image__subset) ).
fof(fact_folding__one__idem_Ounion__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_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__one__idem_Ounion__idem) ).
fof(fact_comm__monoid__big_OF__eq,axiom,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_d,T_c] :
( c_Big__Operators_Ocomm__monoid__big(T_c,T_d,V_f_2,V_z_2,V_F_2)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_comm__monoid__big_OF__eq) ).
fof(fact_card__Diff1__le,axiom,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),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)))))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) ),
file('theBenchmark.p',fact_card__Diff1__le) ).
fof(fact_sup__le__fold__sup,axiom,
! [V_b_2,V_a_2,V_A_2,T_c] :
( class_Lattices_Osemilattice__sup(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_b_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_sup__le__fold__sup) ).
fof(fact_card__inj__on__le,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2))) ) ) ),
file('theBenchmark.p',fact_card__inj__on__le) ).
fof(fact_card__bij__eq,axiom,
! [V_g_2,V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2))
=> ( c_Fun_Oinj__on(T_d,T_c,V_g_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_d,T_c,V_g_2),V_B_2)),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
=> hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(c_Finite__Set_Ocard(T_d),V_B_2) ) ) ) ) ) ),
file('theBenchmark.p',fact_card__bij__eq) ).
fof(fact_card__Diff__subset,axiom,
! [V_A_2,V_B_2,T_c] :
( 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),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_c),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_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ),
file('theBenchmark.p',fact_card__Diff__subset) ).
fof(fact_union__fold__insert,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_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_Finite__Set_Ofold(T_c,tc_fun(T_c,tc_HOL_Obool),c_Set_Oinsert(T_c)),V_B_2),V_A_2) ),
file('theBenchmark.p',fact_union__fold__insert) ).
fof(fact_fold1__Un2,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Lattices_Oab__semigroup__idem__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_fold1__Un2) ).
fof(fact_inj__on__iff__card__le,axiom,
! [V_B_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
=> ( ? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,B_f),V_A_2)),V_B_2))
& c_Fun_Oinj__on(T_c,T_d,B_f,V_A_2) )
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2))) ) ) ),
file('theBenchmark.p',fact_inj__on__iff__card__le) ).
fof(fact_card__Diff__singleton__if,axiom,
! [V_x_2,V_A_2,T_c] :
( 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(c_Finite__Set_Ocard(T_c),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))))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_c),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))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_card__Diff__singleton__if) ).
fof(fact_card__Diff__singleton,axiom,
! [V_x_2,V_A_2,T_c] :
( 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(c_Finite__Set_Ocard(T_c),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))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('theBenchmark.p',fact_card__Diff__singleton) ).
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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__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_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_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_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__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__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__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_one__reorient,axiom,
! [V_x_2,T_c] :
( class_Groups_Oone(T_c)
=> ( c_Groups_Oone__class_Oone(T_c) = V_x_2
<=> V_x_2 = c_Groups_Oone__class_Oone(T_c) ) ),
file('theBenchmark.p',fact_one__reorient) ).
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_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__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,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_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_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_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_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__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_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_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_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_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_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_setprod__eq__1__iff,axiom,
! [V_f_2,V_F_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,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_c),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_setprod__1,axiom,
! [V_A_2,T_d,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(c_COMBK(T_c,T_d),c_Groups_Oone__class_Oone(T_c))),V_A_2) = c_Groups_Oone__class_Oone(T_c) ),
file('theBenchmark.p',fact_setprod__1) ).
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_c] :
( class_Rings_Oring__1__no__zero__divisors(T_c)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_c)
<=> ( V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Groups_Oone__class_Oone(T_c))
| V_x_2 = c_Groups_Oone__class_Oone(T_c) ) ) ),
file('theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_setprod_Oempty,axiom,
! [V_g_2,T_d,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_c) ),
file('theBenchmark.p',fact_setprod_Oempty) ).
fof(fact_setprod__empty,axiom,
! [V_f_2,T_d,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_c) ),
file('theBenchmark.p',fact_setprod__empty) ).
fof(fact_setprod__infinite,axiom,
! [V_f_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_d) ) ),
file('theBenchmark.p',fact_setprod__infinite) ).
fof(fact_setprod_Oinfinite,axiom,
! [V_g_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_d) ) ),
file('theBenchmark.p',fact_setprod_Oinfinite) ).
fof(fact_card__eq__setsum,axiom,
! [V_A_2,T_c] : hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_c),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2),
file('theBenchmark.p',fact_card__eq__setsum) ).
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_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_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__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__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_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__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__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_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_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_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_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_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_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_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__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_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_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_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__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_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_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_setprod__delta,axiom,
! [V_b_2,V_a_2,V_S_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_d))),V_S_2) = c_Groups_Oone__class_Oone(T_d) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_d))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
file('theBenchmark.p',fact_setprod__delta) ).
fof(fact_setprod__delta_H,axiom,
! [V_b_2,V_a_2,V_S_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_d))),V_S_2) = c_Groups_Oone__class_Oone(T_d) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_d))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
file('theBenchmark.p',fact_setprod__delta_H) ).
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__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_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_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_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__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__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_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__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_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__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_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_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__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_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__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_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_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__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_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_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_fold__image__distrib,axiom,
! [V_h_2,V_g_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Groups_Otimes__class_Otimes(T_d)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),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)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_h_2),c_Groups_Oone__class_Oone(T_d)),V_A_2)) ) ),
file('theBenchmark.p',fact_fold__image__distrib) ).
fof(fact_card_Oinsert,axiom,
! [V_x_2,V_A_2,T_c] :
( 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(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),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_c),V_A_2)) ) ),
file('theBenchmark.p',fact_card_Oinsert) ).
fof(fact_setprod_OF__eq,axiom,
! [V_g_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_d) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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),c_Groups_Oone__class_Oone(T_d)),V_A_2) ) ) ),
file('theBenchmark.p',fact_setprod_OF__eq) ).
fof(fact_setprod_Oeq__fold,axiom,
! [V_g_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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),c_Groups_Oone__class_Oone(T_d)),V_A_2) ) ),
file('theBenchmark.p',fact_setprod_Oeq__fold) ).
fof(fact_card_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),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_c),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_card_Oinsert__remove) ).
fof(fact_card_Oremove,axiom,
! [V_x_2,V_A_2,T_c] :
( 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(c_Finite__Set_Ocard(T_c),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_c),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_card_Oremove) ).
fof(fact_card__Diff__insert,axiom,
! [V_B_2,V_a_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_B_2))
=> hAPP(c_Finite__Set_Ocard(T_c),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_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,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_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__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_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_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__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__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__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_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_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_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_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_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_ord_OatMost__iff,axiom,
! [V_k_2,V_less__eq_2,V_i_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OatMost(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OatLeast(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OlessThan(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OgreaterThan(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_c,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_OatLeastLessThan__iff,axiom,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_c,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_ord_OgreaterThanAtMost__iff,axiom,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_c,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_setprod__gen__delta,axiom,
! [V_c_2,V_b_2,V_a_2,V_S_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_d),V_c_2),hAPP(c_Finite__Set_Ocard(T_c),V_S_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_d),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ),
file('theBenchmark.p',fact_setprod__gen__delta) ).
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_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_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_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_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_Sup__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( 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(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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oremove) ).
fof(fact_iso__tuple__UNIV__I,axiom,
! [V_x_2,T_c] : hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_iso__tuple__UNIV__I) ).
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_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_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_Sup__fin_Osingleton,axiom,
! [V_x_2,T_c] :
( class_Lattices_Olattice(T_c)
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_Sup__fin_Osingleton) ).
fof(fact_setprod__constant,axiom,
! [V_y_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(c_COMBK(T_d,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_d),V_y_2),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)) ) ),
file('theBenchmark.p',fact_setprod__constant) ).
fof(fact_Sup__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( 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(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oin__idem) ).
fof(fact_Sup__fin_OF__eq,axiom,
! [V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_Sup__fin_OF__eq) ).
fof(fact_Sup__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).
fof(fact_Sup__fin_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Osubset__idem) ).
fof(fact_Sup__fin_Ounion__idem,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,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(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Ounion__idem) ).
fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).
fof(fact_Sup__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oinsert) ).
fof(fact_Sup__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).
fof(fact_Sup__fin_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).
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_c] :
( class_Rings_Olinordered__semidom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Oone__class_Oone(T_c)),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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__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_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__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__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__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_c] :
( class_Rings_Olinordered__semidom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Oone__class_Oone(T_c)),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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__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__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__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__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__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_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__inject__exp,axiom,
! [V_n_2,V_m_2,V_a_2,T_c] :
( class_Rings_Olinordered__semidom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Oone__class_Oone(T_c)),V_a_2))
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_n_2)
<=> V_m_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_power__inject__exp) ).
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_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__power__power,axiom,
! [T_c] :
( class_Power_Opower(T_c)
=> c_Power_Opower__class_Opower(T_c) = c_Power_Opower_Opower(T_c,c_Groups_Oone__class_Oone(T_c),c_Groups_Otimes__class_Otimes(T_c)) ),
file('theBenchmark.p',fact_power__power__power) ).
fof(fact_Sup__fin_Oclosed,axiom,
! [V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oclosed) ).
fof(fact_inj__vimage__singleton,axiom,
! [V_a_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,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_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_c),c_HOL_OThe(T_c,hAPP(hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ),
file('theBenchmark.p',fact_inj__vimage__singleton) ).
fof(fact_Sup__fin_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_c,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Ohom__commute) ).
fof(fact_SUPR__fold__sup,axiom,
! [V_f_2,V_A_2,T_c,T_d] :
( class_Complete__Lattice_Ocomplete__lattice(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_d)),V_f_2)),c_Orderings_Obot__class_Obot(T_d)),V_A_2) ) ),
file('theBenchmark.p',fact_SUPR__fold__sup) ).
fof(fact_setprod__mono__one__right,axiom,
! [V_f_2,V_S_2,V_T_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_T_2),V_S_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_d) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_T_2),V_S_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_d) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_T_2) ) ) ) ),
file('theBenchmark.p',fact_setprod__mono__one__left) ).
fof(fact_fold__Un__disjoint,axiom,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( 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(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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),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)),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),c_Groups_Oone__class_Oone(T_d)),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_fold__Un__disjoint) ).
fof(fact_inf1I,axiom,
! [T_c,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_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ),
file('theBenchmark.p',fact_inf1I) ).
fof(fact_inf1E,axiom,
! [V_x_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_SUP1__I,axiom,
! [T_d,V_b_2,V_B_2,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),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_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
file('theBenchmark.p',fact_SUP1__I) ).
fof(fact_SUP2__I,axiom,
! [T_e,T_d,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_SUP2__I) ).
fof(fact_IntI,axiom,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_IntE) ).
fof(fact_finite__Int,axiom,
! [V_Ga_2,V_F_2,T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Ga_2))
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_Ga_2))) ),
file('theBenchmark.p',fact_finite__Int) ).
fof(fact_vimageI,axiom,
! [T_d,V_B_2,T_c,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_c),V_b_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_B_2))) ) ),
file('theBenchmark.p',fact_vimageI) ).
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_Int__absorb,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
file('theBenchmark.p',fact_Int__absorb) ).
fof(fact_Int__commute,axiom,
! [V_B_2,V_A_2,T_c] : 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_c,tc_HOL_Obool)),V_B_2),V_A_2),
file('theBenchmark.p',fact_Int__commute) ).
fof(fact_Int__left__absorb,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_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_c,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Int__left__absorb) ).
fof(fact_Int__left__commute,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Int__left__commute) ).
fof(fact_vimage__Int,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_Ovimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)),
file('theBenchmark.p',fact_vimage__Int) ).
fof(fact_Int__assoc,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Int__assoc) ).
fof(fact_vimage__code,axiom,
! [V_x_2,V_A_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_c,T_d,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_inf1D1,axiom,
! [V_x_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_inf1D2,axiom,
! [V_x_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_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_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__fun__def,axiom,
! [V_x_2,V_g_2,V_f_2,T_d,T_c] :
( class_Lattices_Olattice(T_c)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,T_c)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
file('theBenchmark.p',fact_inf__fun__def) ).
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__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__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_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__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__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_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__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__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_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__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__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__apply,axiom,
! [V_x_2,V_g_2,V_f_2,T_d,T_c] :
( class_Lattices_Olattice(T_c)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,T_c)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
file('theBenchmark.p',fact_inf__apply) ).
fof(fact_vimage__ident,axiom,
! [V_Y_2,T_c] : hAPP(c_Set_Ovimage(T_c,T_c,c_COMBI(T_c)),V_Y_2) = V_Y_2,
file('theBenchmark.p',fact_vimage__ident) ).
fof(fact_image__vimage__eq,axiom,
! [V_A_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))),
file('theBenchmark.p',fact_image__vimage__eq) ).
fof(fact_finite__UN,axiom,
! [V_B_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,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(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_x))) ) ) ),
file('theBenchmark.p',fact_finite__UN) ).
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_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_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__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_le__iff__inf,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Lattices_Osemilattice__inf(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),V_y_2) = V_x_2 ) ),
file('theBenchmark.p',fact_le__iff__inf) ).
fof(fact_le__inf__iff,axiom,
! [V_z_2,V_y_2,V_x_2,T_c] :
( class_Lattices_Osemilattice__inf(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_y_2),V_z_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_le__inf__iff) ).
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__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_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_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_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__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_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_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_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_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_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__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__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_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__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__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__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__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_c] :
( class_Lattices_Obounded__lattice__top(T_c)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_c)
<=> ( V_y_2 = c_Orderings_Otop__class_Otop(T_c)
& V_x_2 = c_Orderings_Otop__class_Otop(T_c) ) ) ),
file('theBenchmark.p',fact_inf__eq__top__iff) ).
fof(fact_vimage__eq,axiom,
! [V_B_2,V_f_2,T_d,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)))
<=> hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),V_B_2)) ),
file('theBenchmark.p',fact_vimage__eq) ).
fof(fact_vimageD,axiom,
! [V_A_2,V_f_2,T_d,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2)))
=> hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),V_A_2)) ),
file('theBenchmark.p',fact_vimageD) ).
fof(fact_vimageI2,axiom,
! [T_d,V_A_2,V_a_2,V_f_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2))) ),
file('theBenchmark.p',fact_vimageI2) ).
fof(fact_Int__iff,axiom,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Int__iff) ).
fof(fact_IntD1,axiom,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_IntD1) ).
fof(fact_IntD2,axiom,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ),
file('theBenchmark.p',fact_IntD2) ).
fof(fact_inf__min,axiom,
! [T_c] :
( ( class_Orderings_Olinorder(T_c)
& class_Lattices_Osemilattice__inf(T_c) )
=> c_Lattices_Osemilattice__inf__class_Oinf(T_c) = c_Orderings_Oord__class_Omin(T_c) ),
file('theBenchmark.p',fact_inf__min) ).
fof(fact_vimage__empty,axiom,
! [V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_vimage__empty) ).
fof(fact_Int__empty__left,axiom,
! [V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Int__empty__left) ).
fof(fact_Int__empty__right,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Int__empty__right) ).
fof(fact_disjoint__iff__not__equal,axiom,
! [V_B_2,V_A_2,T_c] :
( 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))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_B_2))
=> B_x != B_xa ) ) ),
file('theBenchmark.p',fact_disjoint__iff__not__equal) ).
fof(fact_vimage__mono,axiom,
! [V_f_2,T_d,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_B_2))) ),
file('theBenchmark.p',fact_vimage__mono) ).
fof(fact_vimage__UNIV,axiom,
! [V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_vimage__UNIV) ).
fof(fact_insert__inter__insert,axiom,
! [V_B_2,V_A_2,V_a_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),
file('theBenchmark.p',fact_insert__inter__insert) ).
fof(fact_vimage__Un,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)),
file('theBenchmark.p',fact_vimage__Un) ).
fof(fact_Int__lower1,axiom,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
file('theBenchmark.p',fact_Int__lower1) ).
fof(fact_Int__lower2,axiom,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)),
file('theBenchmark.p',fact_Int__lower2) ).
fof(fact_Int__absorb2,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),V_B_2) = V_A_2 ),
file('theBenchmark.p',fact_Int__absorb2) ).
fof(fact_Int__absorb1,axiom,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
file('theBenchmark.p',fact_Int__absorb1) ).
fof(fact_Int__greatest,axiom,
! [V_B_2,V_A_2,V_C_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_Int__greatest) ).
fof(fact_Int__mono,axiom,
! [V_D_2,V_B_2,V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
file('theBenchmark.p',fact_Int__mono) ).
fof(fact_Int__UNIV__left,axiom,
! [V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = V_B_2,
file('theBenchmark.p',fact_Int__UNIV__left) ).
fof(fact_Int__UNIV__right,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = V_A_2,
file('theBenchmark.p',fact_Int__UNIV__right) ).
fof(fact_Int__Un__distrib,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Int__Un__distrib) ).
fof(fact_Un__Int__distrib,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Un__Int__distrib) ).
fof(fact_Int__Un__distrib2,axiom,
! [V_A_2,V_C_2,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),
file('theBenchmark.p',fact_Int__Un__distrib2) ).
fof(fact_Un__Int__distrib2,axiom,
! [V_A_2,V_C_2,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),
file('theBenchmark.p',fact_Un__Int__distrib2) ).
fof(fact_Un__Int__crazy,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),
file('theBenchmark.p',fact_Un__Int__crazy) ).
fof(fact_vimage__Diff,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,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_Ovimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)),
file('theBenchmark.p',fact_vimage__Diff) ).
fof(fact_Diff__Int__distrib,axiom,
! [V_B_2,V_A_2,V_C_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_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_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)),
file('theBenchmark.p',fact_Diff__Int__distrib) ).
fof(fact_Int__Diff,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Int__Diff) ).
fof(fact_Diff__Int__distrib2,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Diff__Int__distrib2) ).
fof(fact_Diff__Int2,axiom,
! [V_B_2,V_C_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2),
file('theBenchmark.p',fact_Diff__Int2) ).
fof(fact_inj__on__Int,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2)
=> c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_inj__on__Int) ).
fof(fact_vimage__Compl,axiom,
! [V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2)),
file('theBenchmark.p',fact_vimage__Compl) ).
fof(fact_fun__left__comm__idem__inf,axiom,
! [T_c] :
( class_Lattices_Osemilattice__inf(T_c)
=> c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)) ),
file('theBenchmark.p',fact_fun__left__comm__idem__inf) ).
fof(fact_inf__Int__eq,axiom,
! [V_x_2,V_S_2,V_R_2,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_R_2),V_S_2))) ),
file('theBenchmark.p',fact_inf__Int__eq) ).
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_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_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_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_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__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,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_Int__insert__right,axiom,
! [V_B_2,V_A_2,V_a_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_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) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_Int__insert__right) ).
fof(fact_Int__insert__left,axiom,
! [V_B_2,V_C_2,V_a_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) ) ),
file('theBenchmark.p',fact_Int__insert__left) ).
fof(fact_Int__insert__right__if0,axiom,
! [V_B_2,V_A_2,V_a_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_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) ),
file('theBenchmark.p',fact_Int__insert__right__if0) ).
fof(fact_Int__insert__left__if0,axiom,
! [V_B_2,V_C_2,V_a_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2) ),
file('theBenchmark.p',fact_Int__insert__left__if0) ).
fof(fact_Int__insert__right__if1,axiom,
! [V_B_2,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_Int__insert__right__if1) ).
fof(fact_Int__insert__left__if1,axiom,
! [V_B_2,V_C_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) ),
file('theBenchmark.p',fact_Int__insert__left__if1) ).
fof(fact_image__vimage__subset,axiom,
! [V_A_2,V_f_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,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_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2)) = V_A_2 ),
file('theBenchmark.p',fact_surj__image__vimage__eq) ).
fof(fact_image__Int__subset,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_d,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_B_2)))),
file('theBenchmark.p',fact_image__Int__subset) ).
fof(fact_Diff__triv,axiom,
! [V_B_2,V_A_2,T_c] :
( 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(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,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_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Diff__disjoint) ).
fof(fact_Un__Int__assoc__eq,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) ),
file('theBenchmark.p',fact_Un__Int__assoc__eq) ).
fof(fact_Un__Diff__Int,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),V_B_2)) = V_A_2,
file('theBenchmark.p',fact_Un__Diff__Int) ).
fof(fact_Diff__Un,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,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_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Diff__Int) ).
fof(fact_SUP__UN__eq,axiom,
! [V_x_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d))),V_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2))) ),
file('theBenchmark.p',fact_SUP__UN__eq) ).
fof(fact_Compl__disjoint,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__disjoint) ).
fof(fact_Compl__disjoint2,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,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_Compl__disjoint2) ).
fof(fact_Compl__Int,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),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__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2)),
file('theBenchmark.p',fact_Compl__Int) ).
fof(fact_Compl__Un,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),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__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2)),
file('theBenchmark.p',fact_Compl__Un) ).
fof(fact_Diff__Compl,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Diff__Compl) ).
fof(fact_Diff__eq,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)),
file('theBenchmark.p',fact_Diff__eq) ).
fof(fact_vimage__singleton__eq,axiom,
! [V_b_2,V_f_2,T_d,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))))
<=> hAPP(V_f_2,V_a_2) = V_b_2 ),
file('theBenchmark.p',fact_vimage__singleton__eq) ).
fof(fact_fold__inf__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_c] :
( class_Lattices_Osemilattice__inf(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_b_2),V_A_2)) ) ),
file('theBenchmark.p',fact_fold__inf__insert) ).
fof(fact_inf__Sup__absorb,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) = V_a_2 ) ) ),
file('theBenchmark.p',fact_inf__Sup__absorb) ).
fof(fact_vimage__insert,axiom,
! [V_B_2,V_a_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)),
file('theBenchmark.p',fact_vimage__insert) ).
fof(fact_finite__vimageD,axiom,
! [V_F_2,V_h_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_d,V_h_2),V_F_2)))
=> ( hAPP(c_Set_Oimage(T_c,T_d,V_h_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))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_F_2)) ) ),
file('theBenchmark.p',fact_finite__vimageD) ).
fof(fact_vimage__subsetD,axiom,
! [V_A_2,V_B_2,V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_d,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_d,T_c,V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_vimage__subsetD) ).
fof(fact_finite__vimageI,axiom,
! [V_h_2,T_d,V_F_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
=> ( c_Fun_Oinj__on(T_d,T_c,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Ovimage(T_d,T_c,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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = V_A_2 ),
file('theBenchmark.p',fact_inj__vimage__image__eq) ).
fof(fact_inj__on__image__Int,axiom,
! [V_B_2,V_A_2,V_C_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_C_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
=> hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)) ),
file('theBenchmark.p',fact_image__Int) ).
fof(fact_disjoint__eq__subset__Compl,axiom,
! [V_B_2,V_A_2,T_c] :
( 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(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)),V_B_2))) ),
file('theBenchmark.p',fact_disjoint__eq__subset__Compl) ).
fof(fact_vimage__const,axiom,
! [T_d,V_A_2,V_c_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_d,T_c,hAPP(c_COMBK(T_c,T_d),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_d,T_c,hAPP(c_COMBK(T_c,T_d),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_vimage__const) ).
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_d,T_c] :
( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
=> hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_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_fold__inf__le__inf,axiom,
! [V_b_2,V_a_2,V_A_2,T_c] :
( class_Lattices_Osemilattice__inf(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),V_b_2))) ) ) ),
file('theBenchmark.p',fact_fold__inf__le__inf) ).
fof(fact_fold1__belowI,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Lattices_Osemilattice__inf(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),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_c] :
( class_Lattices_Osemilattice__inf(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_A_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_c),V_x_2),B_x)) ) ) ) ) ),
file('theBenchmark.p',fact_below__fold1__iff) ).
fof(fact_setsum__Un__Int,axiom,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( 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_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_setsum__Un__Int) ).
fof(fact_vimage__subsetI,axiom,
! [V_A_2,V_B_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_d,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_Ovimage(T_c,T_d,V_f_2),V_B_2)),V_A_2)) ) ),
file('theBenchmark.p',fact_vimage__subsetI) ).
fof(fact_setprod_Ounion__inter,axiom,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( 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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_setprod_Ounion__inter) ).
fof(fact_setprod__Un__Int,axiom,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( 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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_setprod__Un__Int) ).
fof(fact_card_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_c] :
( 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_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ),
file('theBenchmark.p',fact_card_Ounion__inter) ).
fof(fact_card__Un__Int,axiom,
! [V_B_2,V_A_2,T_c] :
( 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_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_card__Un__Int) ).
fof(fact_card__Diff__subset__Int,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hAPP(c_Finite__Set_Ocard(T_c),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_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_card__Diff__subset__Int) ).
fof(fact_vimage__if,axiom,
! [V_B_2,T_d,V_d_2,V_A_2,V_c_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_d_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_d,T_c,hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBC(T_d,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_d),c_If(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_d_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_d,T_c,hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBC(T_d,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_d),c_If(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,tc_HOL_Obool)),V_B_2) ) ) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_d_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_d,T_c,hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBC(T_d,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_d),c_If(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_d_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_d,T_c,hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBC(T_d,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_d),c_If(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ) ) ),
file('theBenchmark.p',fact_vimage__if) ).
fof(fact_folding__one_Ounion__inter,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one(T_c,V_f_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(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__one_Ounion__inter) ).
fof(fact_folding__one_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c] :
( c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( 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__one_Ounion__disjoint) ).
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_d,T_c] :
( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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_setsum__Un__disjoint,axiom,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( 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(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_c,T_d] :
( class_Groups_Oab__group__add(T_d)
=> ( 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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_Groups_Ominus__class_Ominus(T_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
file('theBenchmark.p',fact_setsum__Un) ).
fof(fact_setprod__Un__disjoint,axiom,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( 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(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( 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(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_setprod_Ounion__disjoint) ).
fof(fact_sup__SUPR__fold__sup,axiom,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( class_Complete__Lattice_Ocomplete__lattice(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_d),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_d)),V_f_2)),V_B_2),V_A_2) ) ),
file('theBenchmark.p',fact_sup__SUPR__fold__sup) ).
fof(fact_card__Un__disjoint,axiom,
! [V_B_2,V_A_2,T_c] :
( 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(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ),
file('theBenchmark.p',fact_card__Un__disjoint) ).
fof(fact_inj__on__Un,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,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__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
& c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2)
& c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_inj__on__Un) ).
fof(fact_fold__image__Un__Int,axiom,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( 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_Groups_Otimes__class_Otimes(T_d),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)),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),c_Groups_Oone__class_Oone(T_d)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
file('theBenchmark.p',fact_fold__image__Un__Int) ).
fof(fact_fold1__Un,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Groups_Oab__semigroup__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( 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(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_fold1__Un) ).
fof(fact_Sup__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( 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(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_c,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__sup__class_Osup(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,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_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( 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))
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,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(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Ounion__disjoint) ).
fof(fact_Min_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_c,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_Min_Ounion__inter) ).
fof(fact_Min_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( 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))
=> c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_c,V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Min_Ounion__disjoint) ).
fof(fact_Max_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_c,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_Max_Ounion__inter) ).
fof(fact_Max_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( 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))
=> c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_c,V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Max_Ounion__disjoint) ).
fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( 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))
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).
fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( 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(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( 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))
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__disjoint) ).
fof(fact_setsum__Un__nat,axiom,
! [V_f_2,V_B_2,V_A_2,T_c] :
( 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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),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_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_c,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_setsum__Un__nat) ).
fof(fact_vimage__eq__UN,axiom,
! [V_B_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Ovimage(T_c,T_d,V_f_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),c_Set_Oinsert(T_d)),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))),
file('theBenchmark.p',fact_vimage__eq__UN) ).
fof(fact_image__eq__UN,axiom,
! [V_A_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,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_d),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_image__eq__UN) ).
fof(fact_UN__I,axiom,
! [V_B_2,V_b_2,T_d,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(V_B_2,V_a_2)))
=> hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_UN__I) ).
fof(fact_le__SUPI,axiom,
! [V_M_2,V_A_2,V_i_2,T_c,T_d] :
( class_Complete__Lattice_Ocomplete__lattice(T_d)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),V_M_2))) ) ),
file('theBenchmark.p',fact_le__SUPI) ).
fof(fact_SUP__subset,axiom,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( class_Complete__Lattice_Ocomplete__lattice(T_d)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_B_2),V_f_2))) ) ),
file('theBenchmark.p',fact_SUP__subset) ).
fof(fact_SUP__const,axiom,
! [V_M_2,T_c,V_A_2,T_d] :
( class_Complete__Lattice_Ocomplete__lattice(T_d)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),hAPP(c_COMBK(T_d,T_c),V_M_2)) = V_M_2 ) ),
file('theBenchmark.p',fact_SUP__const) ).
fof(fact_UN__insert,axiom,
! [V_B_2,V_A_2,V_a_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_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)),
file('theBenchmark.p',fact_UN__insert) ).
fof(fact_UN__simps_I3_J,axiom,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UN__simps_I3_J) ).
fof(fact_UN__UN__flatten,axiom,
! [V_C_2,V_B_2,V_A_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_e),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,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_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_e),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)),
file('theBenchmark.p',fact_UN__simps_I9_J) ).
fof(fact_ball__UN,axiom,
! [V_Pa_2,V_B_2,V_A_2,T_d,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),hAPP(V_B_2,B_x)))
=> hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ),
file('theBenchmark.p',fact_ball__UN) ).
fof(fact_UN__extend__simps_I9_J,axiom,
! [V_C_2,V_B_2,T_e,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
file('theBenchmark.p',fact_UN__extend__simps_I9_J) ).
fof(fact_SUP1__iff,axiom,
! [V_b_2,V_B_2,V_A_2,T_d,T_c] :
( hBOOL(hAPP(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_b_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_SUP1__iff) ).
fof(fact_SUP2__iff,axiom,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_SUP2__iff) ).
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_UN__iff,axiom,
! [V_B_2,V_A_2,T_d,V_b_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_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)))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_UN__iff) ).
fof(fact_UNION__empty__conv_I2_J,axiom,
! [V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UNION__empty__conv_I2_J) ).
fof(fact_UN__constant,axiom,
! [V_c_2,T_d,T_c,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_c_2)) = V_c_2 )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UN__constant) ).
fof(fact_UN__empty2,axiom,
! [V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_UN__empty2) ).
fof(fact_UNION__empty__conv_I1_J,axiom,
! [V_B_2,V_A_2,T_d,T_c] :
( c_Orderings_Obot__class_Obot(tc_fun(T_c,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)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UNION__empty__conv_I1_J) ).
fof(fact_UN__subset__iff,axiom,
! [V_B_2,V_A_2,V_I_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_I_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ),
file('theBenchmark.p',fact_UN__subset__iff) ).
fof(fact_UN__simps_I10_J,axiom,
! [V_B_2,V_A_2,V_f_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_e,T_d,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_c,tc_HOL_Obool),T_e),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_e,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Set_Oimage(T_d,T_c,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_e,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,tc_HOL_Obool),T_d),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_e,V_f_2),V_A_2)),V_B_2),
file('theBenchmark.p',fact_UN__extend__simps_I10_J) ).
fof(fact_UN__Un__distrib,axiom,
! [V_B_2,V_A_2,V_I_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_d,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_d),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_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,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_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_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_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_M_2)),
file('theBenchmark.p',fact_UN__Un) ).
fof(fact_UN__simps_I5_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d),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_OSUPR(T_d,tc_fun(T_c,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_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),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_OSUPR(T_d,tc_fun(T_c,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_d,V_A_2,T_c] : 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_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_d,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_d,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_e,V_A_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e)),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_d),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2))),V_B_2))),
file('theBenchmark.p',fact_Int__UN__distrib2) ).
fof(fact_SUP__commute,axiom,
! [V_f_2,V_B_2,T_e,V_A_2,T_d,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),T_c,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,T_c),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,T_c),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),T_c,T_e),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2)),hAPP(c_COMBC(T_d,T_e,T_c),V_f_2))) ),
file('theBenchmark.p',fact_SUP__commute) ).
fof(fact_SUPR__apply,axiom,
! [V_x_2,V_f_2,V_A_2,T_e,T_d,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,T_c)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),hAPP(hAPP(c_COMBC(T_d,T_e,T_c),V_f_2),V_x_2)) ),
file('theBenchmark.p',fact_SUPR__apply) ).
fof(fact_UN__simps_I6_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),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_OSUPR(T_d,tc_fun(T_c,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_I6_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_d,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_UN__extend__simps_I6_J) ).
fof(fact_vimage__UN,axiom,
! [V_B_2,V_A_2,T_e,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Set_Ovimage(T_c,T_d,V_f_2)),V_B_2)),
file('theBenchmark.p',fact_vimage__UN) ).
fof(fact_UN__insert__distrib,axiom,
! [V_B_2,V_a_2,T_d,V_A_2,V_u_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_u_2),V_A_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_UN__insert__distrib) ).
fof(fact_UN__upper,axiom,
! [V_B_2,T_d,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UN__upper) ).
fof(fact_UN__absorb,axiom,
! [V_A_2,T_d,V_I_2,V_k_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_k_2),V_I_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2) ),
file('theBenchmark.p',fact_UN__absorb) ).
fof(fact_UN__extend__simps_I1_J,axiom,
! [V_B_2,V_a_2,T_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_UN__extend__simps_I1_J) ).
fof(fact_UN__singleton,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_c,tc_HOL_Obool)),V_A_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)))) = V_A_2,
file('theBenchmark.p',fact_UN__singleton) ).
fof(fact_UN__simps_I1_J,axiom,
! [V_B_2,V_a_2,T_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UN__simps_I1_J) ).
fof(fact_SUP__le__iff,axiom,
! [V_u_2,V_M_2,V_A_2,T_d,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),V_M_2)),V_u_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,B_x)),V_u_2)) ) ) ),
file('theBenchmark.p',fact_SUP__le__iff) ).
fof(fact_less__SUP__iff,axiom,
! [V_f_2,V_A_2,T_d,V_a_2,T_c] :
( ( class_Orderings_Olinorder(T_c)
& class_Complete__Lattice_Ocomplete__lattice(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),V_f_2)))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_less__SUP__iff) ).
fof(fact_UN__extend__simps_I2_J,axiom,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,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_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,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_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,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_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UN__simps_I2_J) ).
fof(fact_fold__image__Un__one,axiom,
! [V_f_2,V_T_2,V_S_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_d) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_f_2),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_f_2),c_Groups_Oone__class_Oone(T_d)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_f_2),c_Groups_Oone__class_Oone(T_d)),V_T_2)) ) ) ) ),
file('theBenchmark.p',fact_fold__image__Un__one) ).
fof(fact_setprod__Un__one,axiom,
! [V_f_2,V_T_2,V_S_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_d) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_T_2)) ) ) ) ),
file('theBenchmark.p',fact_setprod__Un__one) ).
fof(fact_setprod_Ounion__inter__neutral,axiom,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( 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) = c_Groups_Oone__class_Oone(T_d) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_setprod_Ounion__inter__neutral) ).
fof(fact_Inf__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( 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(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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oremove) ).
fof(fact_INFI__fold__inf,axiom,
! [V_f_2,V_A_2,T_c,T_d] :
( class_Complete__Lattice_Ocomplete__lattice(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_d)),V_f_2)),c_Orderings_Otop__class_Otop(T_d)),V_A_2) ) ),
file('theBenchmark.p',fact_INFI__fold__inf) ).
fof(fact_card__Suc__Diff1,axiom,
! [V_x_2,V_A_2,T_c] :
( 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(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_c),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)))))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ) ),
file('theBenchmark.p',fact_card__Suc__Diff1) ).
fof(fact_Inf__fold__inf,axiom,
! [V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_Inf__fold__inf) ).
fof(fact_InterE,axiom,
! [V_X_2,V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_C_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_C_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),V_X_2)) ) ),
file('theBenchmark.p',fact_InterD) ).
fof(fact_finite__Inter,axiom,
! [V_M_2,T_c] :
( ? [B_x] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_x))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_x),V_M_2)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_M_2))) ),
file('theBenchmark.p',fact_finite__Inter) ).
fof(fact_INF1__D,axiom,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),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_INF1__E,axiom,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,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_c),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_INF1__E) ).
fof(fact_INT__D,axiom,
! [V_a_2,V_B_2,V_A_2,T_d,V_b_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_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)))
=> ( hBOOL(hAPP(hAPP(c_member(T_d),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_INT__D) ).
fof(fact_INT__E,axiom,
! [V_a_2,V_B_2,V_A_2,T_d,V_b_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_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)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_INT__E) ).
fof(fact_INF2__D,axiom,
! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_INF2__D) ).
fof(fact_INF2__E,axiom,
! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
=> ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_INF2__E) ).
fof(fact_finite__INT,axiom,
! [V_A_2,T_d,V_I_2,T_c] :
( ? [B_x] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_A_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2))) ),
file('theBenchmark.p',fact_finite__INT) ).
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_Int__Inter__image,axiom,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_d,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_d),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)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_C_2))),
file('theBenchmark.p',fact_Int__Inter__image) ).
fof(fact_INFI__apply,axiom,
! [V_x_2,V_f_2,V_A_2,T_e,T_d,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_e,T_c)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),hAPP(hAPP(c_COMBC(T_d,T_e,T_c),V_f_2),V_x_2)) ),
file('theBenchmark.p',fact_INFI__apply) ).
fof(fact_Un__Inter,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),
file('theBenchmark.p',fact_Un__Inter) ).
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__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_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_INF__commute,axiom,
! [V_f_2,V_B_2,T_e,V_A_2,T_d,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),T_c,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,T_c),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,T_c),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),T_c,T_e),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2)),hAPP(c_COMBC(T_d,T_e,T_c),V_f_2))) ),
file('theBenchmark.p',fact_INF__commute) ).
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_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_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_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_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__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_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_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_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_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_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_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_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__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_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_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_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_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__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_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_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_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_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__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_Inter__UNIV,axiom,
! [T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Inter__UNIV) ).
fof(fact_Inf__fin__Inf,axiom,
! [V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2) ) ) ),
file('theBenchmark.p',fact_Inf__fin__Inf) ).
fof(fact_Inter__anti__mono,axiom,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2))) ),
file('theBenchmark.p',fact_Inter__anti__mono) ).
fof(fact_Inter__lower,axiom,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2)) ),
file('theBenchmark.p',fact_Inter__lower) ).
fof(fact_Inter__empty,axiom,
! [T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Inter__empty) ).
fof(fact_Int__eq__Inter,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))))),
file('theBenchmark.p',fact_Int__eq__Inter) ).
fof(fact_Inter__insert,axiom,
! [V_B_2,V_a_2,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(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),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2)),
file('theBenchmark.p',fact_Inter__insert) ).
fof(fact_Inter__Un__distrib,axiom,
! [V_B_2,V_A_2,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2)),
file('theBenchmark.p',fact_Inter__Un__distrib) ).
fof(fact_INT__iff,axiom,
! [V_B_2,V_A_2,T_d,V_b_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_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)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,B_x))) ) ),
file('theBenchmark.p',fact_INT__iff) ).
fof(fact_INT__simps_I5_J,axiom,
! [V_B_2,V_a_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d),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_d,tc_fun(T_c,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_d,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)),
file('theBenchmark.p',fact_INT__extend__simps_I5_J) ).
fof(fact_INT__subset__iff,axiom,
! [V_A_2,V_I_2,T_d,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_I_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ),
file('theBenchmark.p',fact_INT__subset__iff) ).
fof(fact_INTER__UNIV__conv_I2_J,axiom,
! [V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).
fof(fact_INTER__UNIV__conv_I1_J,axiom,
! [V_B_2,V_A_2,T_d,T_c] :
( c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).
fof(fact_INT__extend__simps_I10_J,axiom,
! [V_f_2,V_B_2,T_e,V_A_2,T_c,T_d] : 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(T_e,tc_fun(T_c,tc_HOL_Obool),T_d),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_e,V_f_2),V_A_2)),V_B_2),
file('theBenchmark.p',fact_INT__extend__simps_I10_J) ).
fof(fact_INT__simps_I10_J,axiom,
! [V_B_2,V_A_2,V_f_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_e,T_d,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_c,tc_HOL_Obool),T_e),V_B_2),V_f_2)),
file('theBenchmark.p',fact_INT__simps_I10_J) ).
fof(fact_Un__INT__distrib2,axiom,
! [V_B_2,V_J_2,T_e,V_A_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e)),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_d),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2))),V_B_2))),
file('theBenchmark.p',fact_Un__INT__distrib2) ).
fof(fact_INT__extend__simps_I6_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_d,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_INT__extend__simps_I6_J) ).
fof(fact_Un__INT__distrib,axiom,
! [V_A_2,V_I_2,T_d,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2)),V_A_2)),
file('theBenchmark.p',fact_Un__INT__distrib) ).
fof(fact_INT__extend__simps_I7_J,axiom,
! [V_B_2,V_C_2,T_d,V_A_2,T_c] : 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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_INT__extend__simps_I7_J) ).
fof(fact_INT__simps_I6_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
file('theBenchmark.p',fact_INT__simps_I6_J) ).
fof(fact_INT__simps_I7_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d),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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)),
file('theBenchmark.p',fact_INT__simps_I7_J) ).
fof(fact_INT__Int__distrib,axiom,
! [V_B_2,V_A_2,V_I_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_d,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_d),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_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_B_2)),
file('theBenchmark.p',fact_INT__Int__distrib) ).
fof(fact_INT__extend__simps_I9_J,axiom,
! [V_C_2,V_B_2,T_e,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
file('theBenchmark.p',fact_INT__extend__simps_I9_J) ).
fof(fact_INT__simps_I9_J,axiom,
! [V_C_2,V_B_2,V_A_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_e),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)),
file('theBenchmark.p',fact_INT__simps_I9_J) ).
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_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_vimage__INT,axiom,
! [V_B_2,V_A_2,T_e,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Set_Ovimage(T_c,T_d,V_f_2)),V_B_2)),
file('theBenchmark.p',fact_vimage__INT) ).
fof(fact_le__Inf__iff,axiom,
! [V_A_2,V_b_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_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_c),V_b_2),B_x)) ) ) ),
file('theBenchmark.p',fact_le__Inf__iff) ).
fof(fact_Inf__less__iff,axiom,
! [V_a_2,V_S_2,T_c] :
( ( class_Orderings_Olinorder(T_c)
& class_Complete__Lattice_Ocomplete__lattice(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Complete__Lattice_OInf__class_OInf(T_c,V_S_2)),V_a_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),B_x),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) ) ) ),
file('theBenchmark.p',fact_Inf__less__iff) ).
fof(fact_power_Opower_Opower__Suc,axiom,
! [V_n_2,V_a_2,V_times_2,V_one_2,T_c] : hAPP(hAPP(c_Power_Opower_Opower(T_c,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_c,V_one_2,V_times_2),V_a_2),V_n_2)),
file('theBenchmark.p',fact_power_Opower_Opower__Suc) ).
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_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_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_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_le__INF__iff,axiom,
! [V_M_2,V_A_2,T_d,V_u_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),V_M_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_u_2),hAPP(V_M_2,B_x))) ) ) ),
file('theBenchmark.p',fact_le__INF__iff) ).
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_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__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__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__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_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_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_INF__less__iff,axiom,
! [V_a_2,V_f_2,V_A_2,T_d,T_c] :
( ( class_Orderings_Olinorder(T_c)
& class_Complete__Lattice_Ocomplete__lattice(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),V_f_2)),V_a_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_INF__less__iff) ).
fof(fact_INT__insert__distrib,axiom,
! [V_B_2,V_a_2,T_d,V_A_2,V_u_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_u_2),V_A_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_INT__insert__distrib) ).
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_INT__lower,axiom,
! [V_B_2,T_d,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ),
file('theBenchmark.p',fact_INT__lower) ).
fof(fact_INF__INT__eq,axiom,
! [V_x_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d))),V_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2))) ),
file('theBenchmark.p',fact_INF__INT__eq) ).
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_INT__absorb,axiom,
! [V_A_2,T_d,V_I_2,V_k_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_k_2),V_I_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2) ),
file('theBenchmark.p',fact_INT__absorb) ).
fof(fact_INF__const,axiom,
! [V_M_2,T_c,V_A_2,T_d] :
( class_Complete__Lattice_Ocomplete__lattice(T_d)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),hAPP(c_COMBK(T_d,T_c),V_M_2)) = V_M_2 ) ),
file('theBenchmark.p',fact_INF__const) ).
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_INT__constant,axiom,
! [V_c_2,T_d,T_c,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_c_2)) = V_c_2 )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INT__constant) ).
fof(fact_INT__empty,axiom,
! [V_B_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_INT__empty) ).
fof(fact_INT__extend__simps_I1_J,axiom,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,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_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,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__extend__simps_I2_J,axiom,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
file('theBenchmark.p',fact_INT__extend__simps_I2_J) ).
fof(fact_INT__insert,axiom,
! [V_B_2,V_A_2,V_a_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_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)),
file('theBenchmark.p',fact_INT__insert) ).
fof(fact_INT__Un,axiom,
! [V_M_2,V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_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_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_M_2)),
file('theBenchmark.p',fact_INT__Un) ).
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_UN__simps_I7_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d),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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)),
file('theBenchmark.p',fact_UN__simps_I7_J) ).
fof(fact_UN__extend__simps_I7_J,axiom,
! [V_B_2,V_C_2,T_d,V_A_2,T_c] : 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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_UN__extend__simps_I7_J) ).
fof(fact_Inter__Un__subset,axiom,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_Inter__Un__subset) ).
fof(fact_Compl__UN,axiom,
! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,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)) = 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_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool))),V_B_2)),
file('theBenchmark.p',fact_Compl__UN) ).
fof(fact_Compl__INT,axiom,
! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),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_OSUPR(T_d,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_d),c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool))),V_B_2)),
file('theBenchmark.p',fact_Compl__INT) ).
fof(fact_Inf__fin_Osingleton,axiom,
! [V_x_2,T_c] :
( class_Lattices_Olattice(T_c)
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_Inf__fin_Osingleton) ).
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_Inf__lower,axiom,
! [V_A_2,V_x_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2)),V_x_2)) ) ),
file('theBenchmark.p',fact_Inf__lower) ).
fof(fact_INF__subset,axiom,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( class_Complete__Lattice_Ocomplete__lattice(T_d)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),V_f_2))) ) ),
file('theBenchmark.p',fact_INF__subset) ).
fof(fact_Inf__singleton,axiom,
! [V_a_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_a_2 ),
file('theBenchmark.p',fact_Inf__singleton) ).
fof(fact_Inf__empty,axiom,
! [T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OInf__class_OInf(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_c) ),
file('theBenchmark.p',fact_Inf__empty) ).
fof(fact_Inf__UNIV,axiom,
! [T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OInf__class_OInf(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_c) ),
file('theBenchmark.p',fact_Inf__UNIV) ).
fof(fact_Inf__insert,axiom,
! [V_A_2,V_a_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2)) ),
file('theBenchmark.p',fact_Inf__insert) ).
fof(fact_INT__simps_I1_J,axiom,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,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_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INT__simps_I2_J) ).
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_INT__extend__simps_I3_J,axiom,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,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_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))),V_B_2) ) ),
file('theBenchmark.p',fact_INT__extend__simps_I3_J) ).
fof(fact_INT__simps_I3_J,axiom,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INT__simps_I3_J) ).
fof(fact_INT__extend__simps_I4_J,axiom,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
file('theBenchmark.p',fact_INT__extend__simps_I4_J) ).
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_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_INF__leI,axiom,
! [V_M_2,V_A_2,V_i_2,T_c,T_d] :
( class_Complete__Lattice_Ocomplete__lattice(T_d)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ),
file('theBenchmark.p',fact_INF__leI) ).
fof(fact_sup__Inf__absorb,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,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_c] :
( class_Lattices_Olattice(T_c)
=> ( 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(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oin__idem) ).
fof(fact_Inf__fin_OF__eq,axiom,
! [V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_Inf__fin_OF__eq) ).
fof(fact_INT__simps_I4_J,axiom,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INT__simps_I4_J) ).
fof(fact_card__insert__if,axiom,
! [V_x_2,V_A_2,T_c] :
( 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(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_c),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ) ) ),
file('theBenchmark.p',fact_card__insert__if) ).
fof(fact_card__insert__disjoint,axiom,
! [V_x_2,V_A_2,T_c] :
( 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(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_c),V_A_2)) ) ),
file('theBenchmark.p',fact_card__insert__disjoint) ).
fof(fact_Inf__binary,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),V_b_2) ),
file('theBenchmark.p',fact_Inf__binary) ).
fof(fact_inf__Inf__fold__inf,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_B_2),V_A_2) ) ),
file('theBenchmark.p',fact_inf__Inf__fold__inf) ).
fof(fact_Inf__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).
fof(fact_Inf__fin_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Osubset__idem) ).
fof(fact_Inf__fin_Ounion__idem,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,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__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ounion__idem) ).
fof(fact_Inf__le__Sup,axiom,
! [V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2))) ) ) ),
file('theBenchmark.p',fact_Inf__le__Sup) ).
fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).
fof(fact_inf__INFI__fold__inf,axiom,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( class_Complete__Lattice_Ocomplete__lattice(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_d),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_d)),V_f_2)),V_B_2),V_A_2) ) ),
file('theBenchmark.p',fact_inf__INFI__fold__inf) ).
fof(fact_card__insert,axiom,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_c),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_card__insert) ).
fof(fact_Inf__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oinsert) ).
fof(fact_Inf__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,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)))))) )
& ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).
fof(fact_Inf__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( 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(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_c,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(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,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_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( 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))
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,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__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).
fof(fact_Inf__fin_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).
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_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_Inf__fin_Oclosed,axiom,
! [V_A_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oclosed) ).
fof(fact_finite__fun__UNIVD1,axiom,
! [T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,T_d),tc_HOL_Obool))))
=> ( hAPP(c_Finite__Set_Ocard(T_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
=> 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__UNIVD1) ).
fof(fact_Inf__fin_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_c] :
( class_Lattices_Olattice(T_c)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_c,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ohom__commute) ).
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_Inter__def,axiom,
! [V_S_2,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_c,tc_HOL_Obool))),
file('theBenchmark.p',fact_Inter__def) ).
fof(fact_INTER__eq__Inter__image,axiom,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,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_d,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_A_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),
file('theBenchmark.p',fact_Inter__image__eq) ).
fof(fact_INF2__iff,axiom,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_INF2__iff) ).
fof(fact_INF1__iff,axiom,
! [V_b_2,V_B_2,V_A_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ),
file('theBenchmark.p',fact_INF1__iff) ).
fof(fact_zero__reorient,axiom,
! [V_x_2,T_c] :
( class_Groups_Ozero(T_c)
=> ( c_Groups_Ozero__class_Ozero(T_c) = V_x_2
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_zero__reorient) ).
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_power__eq__0__iff,axiom,
! [V_n_2,V_a_2,T_c] :
( ( class_Rings_Ozero__neq__one(T_c)
& class_Rings_Ono__zero__divisors(T_c)
& class_Rings_Omult__zero(T_c)
& class_Power_Opower(T_c) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_c)
<=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
file('theBenchmark.p',fact_power__eq__0__iff) ).
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_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_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( c_Groups_Ozero__class_Ozero(T_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ),
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_c] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_c)
=> ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_add__0__iff) ).
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_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_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_mult__eq__0__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Rings_Oring__no__zero__divisors(T_c)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_c)
<=> ( V_b_2 = c_Groups_Ozero__class_Ozero(T_c)
| V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
file('theBenchmark.p',fact_mult__eq__0__iff) ).
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_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_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_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_eq__iff__diff__eq__0,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Groups_Oab__group__add(T_c)
=> ( V_a_2 = V_b_2
<=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_right__minus__eq,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Groups_Ogroup__add(T_c)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_c)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_right__minus__eq) ).
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_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_neg__equal__zero,axiom,
! [V_a_2,T_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) = V_a_2
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [V_a_2,T_c] :
( class_Groups_Ogroup__add(T_c)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_equal__neg__zero,axiom,
! [V_a_2,T_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [V_a_2,T_c] :
( class_Groups_Ogroup__add(T_c)
=> ( c_Groups_Ozero__class_Ozero(T_c) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)
<=> c_Groups_Ozero__class_Ozero(T_c) = V_a_2 ) ),
file('theBenchmark.p',fact_neg__0__equal__iff__equal) ).
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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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__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__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__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_sum__squares__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Rings_Olinordered__ring__strict(T_c)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_c)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_c)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
file('theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
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__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_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_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_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_setsum__0,axiom,
! [V_A_2,T_d,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(c_COMBK(T_c,T_d),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ),
file('theBenchmark.p',fact_setsum__0) ).
fof(fact_power_Opower_Opower__0,axiom,
! [V_a_2,V_times_2,V_one_2,T_c] : hAPP(hAPP(c_Power_Opower_Opower(T_c,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__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_sum__squares__le__zero__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Rings_Olinordered__ring__strict(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_c)))
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_c)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
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_sum__squares__gt__zero__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Rings_Olinordered__ring__strict(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_y_2),V_y_2))))
<=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_c)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_c) ) ) ),
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_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_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__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__nonneg__eq__0__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Groups_Oordered__comm__monoid__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_y_2))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_c)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_c)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ),
file('theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
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_double__add__le__zero__iff__single__add__le__zero,axiom,
! [V_a_2,T_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ),
file('theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [V_a_2,T_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ),
file('theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
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_zero__le__mult__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Rings_Olinordered__ring__strict(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_mult__le__0__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Rings_Olinordered__ring__strict(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_mult__le__0__iff) ).
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__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__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__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__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__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__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_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__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_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__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__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_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_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_zero__less__double__add__iff__zero__less__single__add,axiom,
! [V_a_2,T_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ),
file('theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [V_a_2,T_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ),
file('theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
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_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_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_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_mult__less__cancel__right__disj,axiom,
! [V_b_2,V_c_2,V_a_2,T_c] :
( class_Rings_Olinordered__ring__strict(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_c_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [V_b_2,V_a_2,V_c_2,T_c] :
( class_Rings_Olinordered__ring__strict(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_c_2,T_c] :
( class_Rings_Olinordered__ring__strict(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__pos) ).
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__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__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_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_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_mult__less__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_c_2,T_c] :
( class_Rings_Olinordered__ring__strict(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__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__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__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__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_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__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_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_le__iff__diff__le__0,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))) ) ),
file('theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_less__iff__diff__less__0,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))) ) ),
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_neg__0__le__iff__le,axiom,
! [V_a_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ),
file('theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_le__minus__self__iff,axiom,
! [V_a_2,T_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ),
file('theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_neg__le__0__iff__le,axiom,
! [V_a_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_minus__le__self__iff,axiom,
! [V_a_2,T_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ),
file('theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_less__minus__self__iff,axiom,
! [V_a_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ),
file('theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_neg__0__less__iff__less,axiom,
! [V_a_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ),
file('theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_neg__less__0__iff__less,axiom,
! [V_a_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_neg__less__nonneg,axiom,
! [V_a_2,T_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__less__nonneg) ).
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_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_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_eq__neg__iff__add__eq__0,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Groups_Ogroup__add(T_c)
=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
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_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__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_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_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_setsum__empty,axiom,
! [V_f_2,T_d,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_c) ),
file('theBenchmark.p',fact_setsum__empty) ).
fof(fact_setsum_Oempty,axiom,
! [V_g_2,T_d,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_c) ),
file('theBenchmark.p',fact_setsum_Oempty) ).
fof(fact_setsum_Oinfinite,axiom,
! [V_g_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d) ) ),
file('theBenchmark.p',fact_setsum_Oinfinite) ).
fof(fact_setsum__infinite,axiom,
! [V_f_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d) ) ),
file('theBenchmark.p',fact_setsum__infinite) ).
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_setprod__zero__iff,axiom,
! [V_f_2,V_A_2,T_c,T_d] :
( ( class_Rings_Ono__zero__divisors(T_d)
& class_Rings_Ocomm__semiring__1(T_d) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d)
<=> ? [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_d)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_setprod__zero__iff) ).
fof(fact_setprod__zero,axiom,
! [V_f_2,V_A_2,T_c,T_d] :
( class_Rings_Ocomm__semiring__1(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ? [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_d)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d) ) ) ),
file('theBenchmark.p',fact_setprod__zero) ).
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_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_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_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_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_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__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_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_card_Oempty,axiom,
! [T_c] : hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_card__infinite) ).
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_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_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_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__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_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_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_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_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_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_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_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_c),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_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_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_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__le__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_c_2,T_c] :
( class_Rings_Olinordered__ring__strict(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_c_2,T_c] :
( class_Rings_Olinordered__ring__strict(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__neg) ).
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__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__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__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__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__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__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__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__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__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__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_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_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_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_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_card__eq__0__iff,axiom,
! [V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_card__eq__0__iff) ).
fof(fact_card__ge__0__finite,axiom,
! [V_A_2,T_c] :
( 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_c),V_A_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
file('theBenchmark.p',fact_card__ge__0__finite) ).
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_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_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_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_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_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_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__Suc0__iff,axiom,
! [V_f_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_c),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_c),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_setsum__eq__Suc0__iff) ).
fof(fact_setsum__eq__1__iff,axiom,
! [V_f_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_c),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_c),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_setsum__eq__1__iff) ).
fof(fact_setsum__delta,axiom,
! [V_b_2,V_a_2,V_S_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_d))),V_S_2) = c_Groups_Ozero__class_Ozero(T_d) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_d))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__delta) ).
fof(fact_setsum__delta_H,axiom,
! [V_b_2,V_a_2,V_S_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_d))),V_S_2) = c_Groups_Ozero__class_Ozero(T_d) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_d))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__delta_H) ).
fof(fact_setprod__pos__nat__iff,axiom,
! [V_f_2,V_S_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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_c,tc_Nat_Onat),V_f_2),V_S_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),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_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_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__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_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_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_card__gt__0__iff,axiom,
! [V_A_2,T_c] :
( 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_c),V_A_2)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
& V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_card__gt__0__iff) ).
fof(fact_finite__UNIV__card__ge__0,axiom,
! [T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,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_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
file('theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
fof(fact_setsum_Oeq__fold,axiom,
! [V_g_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Oplus__class_Oplus(T_d)),V_g_2),c_Groups_Ozero__class_Ozero(T_d)),V_A_2) ) ),
file('theBenchmark.p',fact_setsum_Oeq__fold) ).
fof(fact_setsum_OF__eq,axiom,
! [V_g_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Oplus__class_Oplus(T_d)),V_g_2),c_Groups_Ozero__class_Ozero(T_d)),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_setsum__restrict__set,axiom,
! [V_B_2,V_f_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_d))),V_A_2) ) ),
file('theBenchmark.p',fact_setsum__restrict__set) ).
fof(fact_card__def,axiom,
! [V_A_2,T_c] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_c,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_c),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_card_Oeq__fold__g,axiom,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_c,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_c),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_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_triple_Osize_I1_J,axiom,
! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_c,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_triple_Osize_I1_J) ).
fof(fact_even__less__0__iff,axiom,
! [V_a_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ),
file('theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_triple_Osize_I2_J,axiom,
! [V_fun2_2,V_com_2,V_fun1_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_triple_Osize_I2_J) ).
fof(fact_card_Ounion__inter__neutral,axiom,
! [V_B_2,V_A_2,T_c] :
( 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)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ),
file('theBenchmark.p',fact_card_Ounion__inter__neutral) ).
fof(fact_setsum__mono2,axiom,
! [V_f_2,V_A_2,V_B_2,T_c,T_d] :
( class_Groups_Oordered__comm__monoid__add(T_d)
=> ( 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_A_2),V_B_2))
=> ( ! [B_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_b))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_B_2))) ) ) ) ),
file('theBenchmark.p',fact_setsum__mono2) ).
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_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_lessThan__eq__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_lessThan__eq__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_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_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_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_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_setsum__lessThan__Suc,axiom,
! [V_n_2,V_f_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_lessThan__iff,axiom,
! [V_k_2,V_i_2,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_i_2),V_k_2)) ) ),
file('theBenchmark.p',fact_lessThan__iff) ).
fof(fact_lessThan__subset__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_lessThan__subset__iff) ).
fof(fact_lessThan__strict__subset__iff,axiom,
! [V_n_2,V_m_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_n_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_lessThan__strict__subset__iff) ).
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_single__Diff__lessThan,axiom,
! [V_k_2,T_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_single__Diff__lessThan) ).
fof(fact_double__eq__0__iff,axiom,
! [V_a_2,T_c] :
( class_Groups_Olinordered__ab__group__add(T_c)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_arith__series__general,axiom,
! [V_n_2,V_d_2,V_a_2,T_c] :
( class_Rings_Ocomm__semiring__1(T_c)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),c_Groups_Oone__class_Oone(T_c))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_c)),c_Nat_Osemiring__1__class_Oof__nat(T_c))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),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_setsum__Un__zero,axiom,
! [V_f_2,V_T_2,V_S_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_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_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_T_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum__Un__zero) ).
fof(fact_setsum_Ounion__inter__neutral,axiom,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( 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) = c_Groups_Ozero__class_Ozero(T_d) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).
fof(fact_card__Suc__eq,axiom,
! [V_k_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),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_c,tc_HOL_Obool)) )
& hAPP(c_Finite__Set_Ocard(T_c),B_B) = V_k_2
& ~ hBOOL(hAPP(hAPP(c_member(T_c),B_b),B_B))
& V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_c),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_c,T_d] :
( ( class_Groups_Oordered__ab__semigroup__add(T_d)
& class_Groups_Ocomm__monoid__add(T_d) )
=> ( 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_A_2),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_B_2))) ) ) ) ),
file('theBenchmark.p',fact_setsum__mono3) ).
fof(fact_Ints__odd__less__0,axiom,
! [V_a_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ) ),
file('theBenchmark.p',fact_Ints__odd__less__0) ).
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_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_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_Ints__of__nat,axiom,
! [V_n_2,T_c] :
( class_Rings_Oring__1(T_c)
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),c_Int_Oring__1__class_OInts(T_c))) ),
file('theBenchmark.p',fact_Ints__of__nat) ).
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__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_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_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_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_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_of__nat__eq__iff,axiom,
! [V_n_2,V_m_2,T_c] :
( class_Nat_Osemiring__char__0(T_c)
=> ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)
<=> V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_of__nat__eq__iff) ).
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__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__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_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_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_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__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__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_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_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_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_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_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_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_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_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_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_int__setsum,axiom,
! [V_A_2,V_f_2,T_c] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_c),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__setprod,axiom,
! [V_A_2,V_f_2,T_c] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_c),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
file('theBenchmark.p',fact_int__setprod) ).
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_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_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_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_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_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__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_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_c] :
( class_Rings_Olinordered__semidom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),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_of__nat__le__iff,axiom,
! [V_n_2,V_m_2,T_c] :
( class_Rings_Olinordered__semidom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),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_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_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_of__nat__setsum,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( class_Rings_Osemiring__1(T_c)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,T_d),c_Nat_Osemiring__1__class_Oof__nat(T_c)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_of__nat__setsum) ).
fof(fact_inj__of__nat,axiom,
! [T_c] :
( class_Nat_Osemiring__char__0(T_c)
=> c_Fun_Oinj__on(tc_Nat_Onat,T_c,c_Nat_Osemiring__1__class_Oof__nat(T_c),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__of__nat) ).
fof(fact_Ints__0,axiom,
! [T_c] :
( class_Rings_Oring__1(T_c)
=> hBOOL(hAPP(hAPP(c_member(T_c),c_Groups_Ozero__class_Ozero(T_c)),c_Int_Oring__1__class_OInts(T_c))) ),
file('theBenchmark.p',fact_Ints__0) ).
fof(fact_Ints__add,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Rings_Oring__1(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Int_Oring__1__class_OInts(T_c)))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_c))) ) ) ),
file('theBenchmark.p',fact_Ints__add) ).
fof(fact_Ints__mult,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Rings_Oring__1(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Int_Oring__1__class_OInts(T_c)))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_c))) ) ) ),
file('theBenchmark.p',fact_Ints__mult) ).
fof(fact_Ints__diff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Rings_Oring__1(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Int_Oring__1__class_OInts(T_c)))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_c))) ) ) ),
file('theBenchmark.p',fact_Ints__diff) ).
fof(fact_Ints__1,axiom,
! [T_c] :
( class_Rings_Oring__1(T_c)
=> hBOOL(hAPP(hAPP(c_member(T_c),c_Groups_Oone__class_Oone(T_c)),c_Int_Oring__1__class_OInts(T_c))) ),
file('theBenchmark.p',fact_Ints__1) ).
fof(fact_Ints__minus,axiom,
! [V_a_2,T_c] :
( class_Rings_Oring__1(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),c_Int_Oring__1__class_OInts(T_c))) ) ),
file('theBenchmark.p',fact_Ints__minus) ).
fof(fact_Ints__power,axiom,
! [V_n_2,V_a_2,T_c] :
( class_Rings_Oring__1(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_c))) ) ),
file('theBenchmark.p',fact_Ints__power) ).
fof(fact_of__nat__setprod,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( ( class_Rings_Osemiring__1(T_c)
& class_Groups_Ocomm__monoid__mult(T_c) )
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,T_d),c_Nat_Osemiring__1__class_Oof__nat(T_c)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_of__nat__setprod) ).
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_setsum__constant,axiom,
! [V_A_2,V_y_2,T_d,T_c] :
( class_Rings_Osemiring__1(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(c_COMBK(T_c,T_d),V_y_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_d),V_A_2))),V_y_2) ),
file('theBenchmark.p',fact_setsum__constant) ).
fof(fact_of__nat__0__less__iff,axiom,
! [V_n_2,T_c] :
( class_Rings_Olinordered__semidom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),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_Ints__double__eq__0__iff,axiom,
! [V_a_2,T_c] :
( class_Int_Oring__char__0(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
file('theBenchmark.p',fact_Ints__double__eq__0__iff) ).
fof(fact_Ints__odd__nonzero,axiom,
! [V_a_2,T_c] :
( class_Int_Oring__char__0(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_Ints__odd__nonzero) ).
fof(fact_semiring__1__class_Oof__nat__code,axiom,
! [V_n_2,T_c] :
( class_Rings_Osemiring__1(T_c)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_c,hAPP(hAPP(c_COMBC(T_c,T_c,T_c),c_Groups_Oplus__class_Oplus(T_c)),c_Groups_Oone__class_Oone(T_c)),V_n_2,c_Groups_Ozero__class_Ozero(T_c)) ),
file('theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).
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_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_setsum__bounded,axiom,
! [V_K_2,V_f_2,V_A_2,T_c,T_d] :
( ( class_Rings_Osemiring__1(T_d)
& class_Groups_Oordered__ab__semigroup__add(T_d) )
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,B_i)),V_K_2)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_d),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_K_2))) ) ),
file('theBenchmark.p',fact_setsum__bounded) ).
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_image__minus__const__atLeastLessThan__nat,axiom,
! [V_x_2,V_y_2,V_c_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_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_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
& ( 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_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_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_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) ) ),
file('theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).
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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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__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_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_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_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_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_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_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__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__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_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_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_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_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_atLeastLessThan__inj_I2_J,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2))
=> V_b_2 = V_d_2 ) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).
fof(fact_atLeastLessThan__inj_I1_J,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2))
=> V_a_2 = V_c_2 ) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).
fof(fact_atLeastLessThan__eq__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2))
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)
<=> ( V_b_2 = V_d_2
& V_a_2 = V_c_2 ) ) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__eq__iff) ).
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_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_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_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_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_atLeastLessThan__empty,axiom,
! [V_a_2,V_b_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_a_2))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_atLeastLessThan__empty) ).
fof(fact_atLeastLessThan__empty__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_atLeastLessThan__empty__iff) ).
fof(fact_atLeastLessThan__empty__iff2,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).
fof(fact_atLeastLessThan__subset__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_a_2)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
! [V_n_2,V_m_2,V_f_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_ivl__disj__un_I17_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I17_J) ).
fof(fact_setsum__shift__bounds__nat__ivl,axiom,
! [V_n_2,V_k_2,V_m_2,V_f_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_ivl__diff,axiom,
! [V_m_2,V_n_2,V_i_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_i_2),V_n_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,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_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I11_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_setsum__add__nat__ivl,axiom,
! [V_f_2,V_p_2,V_n_2,V_m_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( 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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_c),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_setsum__diff__nat__ivl,axiom,
! [V_f_2,V_p_2,V_n_2,V_m_2,T_c] :
( class_Groups_Oab__group__add(T_c)
=> ( 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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_c),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_of__nat__aux_Osimps_I1_J,axiom,
! [V_i_2,V_inc_2,T_c] :
( class_Rings_Osemiring__1(T_c)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(T_c,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_c] :
( class_Rings_Osemiring__1(T_c)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(T_c,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_c,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_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_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_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_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_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_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_UN__UN__finite__eq,axiom,
! [V_A_2,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,tc_HOL_Obool)),tc_fun(T_c,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_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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_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_Int__atLeastLessThan,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastLessThan) ).
fof(fact_ivl__disj__un_I8_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),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_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I2_J) ).
fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
! [V_k_2,V_f_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_setsum__head__upt__Suc,axiom,
! [V_f_2,V_n_2,V_m_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( 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_c),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_c),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_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_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_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_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_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_setsum__op__ivl__Suc,axiom,
! [V_f_2,V_m_2,V_n_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( ( ~ 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_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_c) ) ) ),
file('theBenchmark.p',fact_setsum__op__ivl__Suc) ).
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_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_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__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_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_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_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_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_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_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_UN__finite2__subset,axiom,
! [V_B_2,V_k_2,V_A_2,T_c] :
( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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_UN__finite2__eq,axiom,
! [V_B_2,V_k_2,V_A_2,T_c] :
( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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_c,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_c,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_UN__finite__subset,axiom,
! [V_C_2,V_A_2,T_c] :
( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_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_ivl__disj__un_I3_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I3_J) ).
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_image__INT,axiom,
! [V_j_2,V_B_2,V_A_2,T_e,V_C_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_C_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_e),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)),V_C_2)) )
=> ( hBOOL(hAPP(hAPP(c_member(T_e),V_j_2),V_A_2))
=> hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_e),c_Set_Oimage(T_c,T_d,V_f_2)),V_B_2)) ) ) ),
file('theBenchmark.p',fact_image__INT) ).
fof(fact_com_Osize_I4_J,axiom,
! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_com_Osize_I4_J) ).
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__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_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__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__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__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_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_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_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_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_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_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_greaterThanLessThan__empty,axiom,
! [V_k_2,V_l_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_k_2))
=> c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_greaterThanLessThan__empty) ).
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_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_image__uminus__greaterThanLessThan,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).
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_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__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_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_com_Osize_I1_J,axiom,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_com_Osize_I1_J) ).
fof(fact_ivl__disj__int_I9_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I9_J) ).
fof(fact_Int__greaterThanLessThan,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__greaterThanLessThan) ).
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_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_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_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_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_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_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_ivl__disj__un_I15_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I15_J) ).
fof(fact_com_Osize_I6_J,axiom,
! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_com_Osize_I6_J) ).
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_ivl__disj__un_I4_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I4_J) ).
fof(fact_Powp__mono,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_c,V_A_2)),c_Predicate_OPowp(T_c,V_B_2))) ),
file('theBenchmark.p',fact_Powp__mono) ).
fof(fact_card__Plus__conv__if,axiom,
! [V_B_2,T_d,V_A_2,T_c] :
( ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
=> hAPP(c_Finite__Set_Ocard(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
=> hAPP(c_Finite__Set_Ocard(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2)) ) ),
file('theBenchmark.p',fact_card__Plus__conv__if) ).
fof(fact_com_Osize_I12_J,axiom,
! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_com_Osize_I12_J) ).
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__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_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_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__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_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_greaterThanAtMost__empty,axiom,
! [V_k_2,V_l_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_k_2))
=> c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_greaterThanAtMost__empty) ).
fof(fact_greaterThanAtMost__empty__iff,axiom,
! [V_l_2,V_k_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),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_c] :
( class_Orderings_Oorder(T_c)
=> ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_k_2,V_l_2)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_k_2),V_l_2)) ) ),
file('theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).
fof(fact_ivl__disj__un_I20_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,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_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I14_J) ).
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_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_com_Osize_I9_J,axiom,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_com_Osize_I9_J) ).
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_Int__greaterThanAtMost,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__greaterThanAtMost) ).
fof(fact_image__uminus__atLeastLessThan,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__atLeastLessThan) ).
fof(fact_image__uminus__greaterThanAtMost,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).
fof(fact_ivl__disj__int_I10_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I10_J) ).
fof(fact_finite__Plus__iff,axiom,
! [V_B_2,V_A_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__Plus__iff) ).
fof(fact_finite__Plus,axiom,
! [V_B_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,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_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) ),
file('theBenchmark.p',fact_finite__PlusD_I2_J) ).
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_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_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_card__Plus,axiom,
! [V_B_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
=> hAPP(c_Finite__Set_Ocard(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2)) ) ),
file('theBenchmark.p',fact_card__Plus) ).
fof(fact_ivl__disj__un_I16_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I16_J) ).
fof(fact_com_Osize_I14_J,axiom,
! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_com_Osize_I14_J) ).
fof(fact_UNIV__Plus__UNIV,axiom,
! [T_d,T_c] : c_Sum__Type_OPlus(T_c,T_d,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_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_c,T_d),tc_HOL_Obool)),
file('theBenchmark.p',fact_UNIV__Plus__UNIV) ).
fof(fact_Plus__eq__empty__conv,axiom,
! [V_B_2,V_A_2,T_d,T_c] :
( c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_c,T_d),tc_HOL_Obool))
<=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
& V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_Plus__eq__empty__conv) ).
fof(fact_setprod__diff1,axiom,
! [V_a_2,V_f_2,V_A_2,T_c,T_d] :
( class_Fields_Ofield(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_d)
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ) ),
file('theBenchmark.p',fact_setprod__diff1) ).
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_setsum__nonneg__0,axiom,
! [V_i_2,V_f_2,V_s_2,T_c,T_d] :
( class_Groups_Oordered__ab__group__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_s_2))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_i))) )
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_d)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),V_s_2))
=> hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) ) ),
file('theBenchmark.p',fact_setsum__nonneg__0) ).
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_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_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_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_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_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_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_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_setsum__divide__distrib,axiom,
! [V_r_2,V_A_2,V_f_2,T_d,T_c] :
( class_Fields_Ofield(T_c)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_r_2)),V_A_2) ),
file('theBenchmark.p',fact_setsum__divide__distrib) ).
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_c_2,T_c] :
( class_Rings_Odivision__ring(T_c)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) = V_a_2
<=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2) ) ) ),
file('theBenchmark.p',fact_nonzero__divide__eq__eq) ).
fof(fact_nonzero__eq__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_c] :
( class_Rings_Odivision__ring(T_c)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c)
=> ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_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_c] :
( class_Rings_Odivision__ring(T_c)
=> ( V_b_2 != c_Groups_Ozero__class_Ozero(T_c)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_c)
<=> 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_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_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_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_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_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_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_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_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_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_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_setprod__dividef,axiom,
! [V_g_2,V_f_2,V_A_2,T_c,T_d] :
( class_Fields_Ofield__inverse__zero(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Rings_Oinverse__class_Odivide(T_d)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)) ) ),
file('theBenchmark.p',fact_setprod__dividef) ).
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_transfer__nat__int__sum__prod_I2_J,axiom,
! [V_A_2,V_f_2,T_c] :
( ( class_Groups_Ocomm__monoid__mult(T_c)
& class_Groups_Ocomm__monoid__add(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_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__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__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_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_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_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_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_transfer__nat__int__sum__prod_I1_J,axiom,
! [V_A_2,V_f_2,T_c] :
( ( class_Groups_Ocomm__monoid__mult(T_c)
& class_Groups_Ocomm__monoid__add(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_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_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_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_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_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_transfer__nat__int__sum__prod2_I1_J,axiom,
! [V_A_2,V_f_2,T_c] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_c),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_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_transfer__nat__int__sum__prod2_I2_J,axiom,
! [V_A_2,V_f_2,T_c] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_c),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_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_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_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_geometric__sum,axiom,
! [V_n_2,V_x_2,T_c] :
( class_Fields_Ofield(T_c)
=> ( V_x_2 != c_Groups_Oone__class_Oone(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(c_Power_Opower__class_Opower(T_c),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_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_c))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_x_2),c_Groups_Oone__class_Oone(T_c))) ) ),
file('theBenchmark.p',fact_geometric__sum) ).
fof(fact_le__divide__eq,axiom,
! [V_c_2,V_b_2,V_a_2,T_c] :
( class_Fields_Olinordered__field__inverse__zero(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq) ).
fof(fact_divide__le__eq,axiom,
! [V_a_2,V_c_2,V_b_2,T_c] :
( class_Fields_Olinordered__field__inverse__zero(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq) ).
fof(fact_pos__le__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_c] :
( class_Fields_Olinordered__field(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_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_c_2,T_c] :
( class_Fields_Olinordered__field(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_pos__divide__le__eq) ).
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_zero__le__divide__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Fields_Olinordered__field__inverse__zero(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_zero__le__divide__iff) ).
fof(fact_divide__le__0__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Fields_Olinordered__field__inverse__zero(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__le__0__iff) ).
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__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_zero__less__divide__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Fields_Olinordered__field__inverse__zero(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_zero__less__divide__iff) ).
fof(fact_divide__less__0__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Fields_Olinordered__field__inverse__zero(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__less__0__iff) ).
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__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__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__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__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__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_frac__eq__eq,axiom,
! [V_w_2,V_x_2,V_z_2,V_y_2,T_c] :
( class_Fields_Ofield(T_c)
=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_c)
=> ( V_z_2 != c_Groups_Ozero__class_Ozero(T_c)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_w_2),V_z_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_w_2),V_y_2) ) ) ) ),
file('theBenchmark.p',fact_frac__eq__eq) ).
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_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_divide__eq__eq,axiom,
! [V_a_2,V_c_2,V_b_2,T_c] :
( class_Fields_Ofield__inverse__zero(T_c)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) = V_a_2
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_c)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c)
=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq) ).
fof(fact_eq__divide__eq,axiom,
! [V_c_2,V_b_2,V_a_2,T_c] :
( class_Fields_Ofield__inverse__zero(T_c)
=> ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_c)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__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_less__divide__eq,axiom,
! [V_c_2,V_b_2,V_a_2,T_c] :
( class_Fields_Olinordered__field__inverse__zero(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq) ).
fof(fact_divide__less__eq,axiom,
! [V_a_2,V_c_2,V_b_2,T_c] :
( class_Fields_Olinordered__field__inverse__zero(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq) ).
fof(fact_pos__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_c] :
( class_Fields_Olinordered__field(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_pos__less__divide__eq) ).
fof(fact_pos__divide__less__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_c] :
( class_Fields_Olinordered__field(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_pos__divide__less__eq) ).
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_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_neg__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_c] :
( class_Fields_Olinordered__field(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_neg__less__divide__eq) ).
fof(fact_neg__divide__less__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_c] :
( class_Fields_Olinordered__field(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_neg__divide__less__eq) ).
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_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_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_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__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_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__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_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_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_c_2,T_c] :
( class_Fields_Olinordered__field(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_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_c_2,T_c] :
( class_Fields_Olinordered__field(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_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_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_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_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_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_transfer__int__nat__sum__prod_I2_J,axiom,
! [V_f_2,V_A_2,T_c] :
( ( class_Groups_Ocomm__monoid__mult(T_c)
& class_Groups_Ocomm__monoid__add(T_c) )
=> ( c_Nat__Transfer_Onat__set(V_A_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_c,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_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_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__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_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_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__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_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_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_transfer__int__nat__sum__prod_I1_J,axiom,
! [V_f_2,V_A_2,T_c] :
( ( class_Groups_Ocomm__monoid__mult(T_c)
& class_Groups_Ocomm__monoid__add(T_c) )
=> ( c_Nat__Transfer_Onat__set(V_A_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_c,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_setprod__Un,axiom,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( class_Fields_Ofield(T_d)
=> ( 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_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_d) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_Rings_Oinverse__class_Odivide(T_d),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ),
file('theBenchmark.p',fact_setprod__Un) ).
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__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_setsum__nonneg__leq__bound,axiom,
! [V_i_2,V_B_2,V_f_2,V_s_2,T_c,T_d] :
( class_Groups_Oordered__ab__group__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_s_2))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_i))) )
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_s_2) = V_B_2
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_setsum__nonneg__leq__bound) ).
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_greaterThan__eq__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_greaterThan__eq__iff) ).
fof(fact_of__int__eq__iff,axiom,
! [V_z_2,V_w_2,T_c] :
( class_Int_Oring__char__0(T_c)
=> ( hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)
<=> V_w_2 = V_z_2 ) ),
file('theBenchmark.p',fact_of__int__eq__iff) ).
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_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_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_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_of__int__0__eq__iff,axiom,
! [V_z_2,T_c] :
( class_Int_Oring__char__0(T_c)
=> ( c_Groups_Ozero__class_Ozero(T_c) = hAPP(c_Int_Oring__1__class_Oof__int(T_c),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__eq__0__iff,axiom,
! [V_z_2,T_c] :
( class_Int_Oring__char__0(T_c)
=> ( hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2) = c_Groups_Ozero__class_Ozero(T_c)
<=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_of__int__eq__0__iff) ).
fof(fact_of__int__le__iff,axiom,
! [V_z_2,V_w_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),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_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),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__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_c] :
( class_Rings_Oring__1(T_c)
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)),c_Int_Oring__1__class_OInts(T_c))) ),
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_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_greaterThan__iff,axiom,
! [V_k_2,V_i_2,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_greaterThan__iff) ).
fof(fact_greaterThan__subset__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_greaterThan__subset__iff) ).
fof(fact_of__int__setsum,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( class_Rings_Oring__1(T_c)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_c,T_d),c_Int_Oring__1__class_Oof__int(T_c)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_of__int__setsum) ).
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_of__int__setprod,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( ( class_Rings_Oring__1(T_c)
& class_Groups_Ocomm__monoid__mult(T_c) )
=> hAPP(c_Int_Oring__1__class_Oof__int(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_c,T_d),c_Int_Oring__1__class_Oof__int(T_c)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_of__int__setprod) ).
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_of__int__0__le__iff,axiom,
! [V_z_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),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_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> 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_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),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_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> 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_ivl__disj__un_I11_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_l_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I11_J) ).
fof(fact_image__uminus__lessThan,axiom,
! [V_x_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__lessThan) ).
fof(fact_image__uminus__greaterThan,axiom,
! [V_x_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__greaterThan) ).
fof(fact_ivl__disj__int_I5_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I5_J) ).
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_transfer__int__nat__sum__prod2_I2_J,axiom,
! [V_f_2,V_A_2,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),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_c,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_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_c),c_Int_Onat),V_f_2)),V_A_2)) ),
file('theBenchmark.p',fact_transfer__int__nat__sum__prod2_I2_J) ).
fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
! [V_f_2,V_A_2,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),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_c,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_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_c),c_Int_Onat),V_f_2)),V_A_2)) ),
file('theBenchmark.p',fact_transfer__int__nat__sum__prod2_I1_J) ).
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_setsum__natinterval__difff,axiom,
! [V_f_2,V_n_2,V_m_2,T_c] :
( class_Groups_Oab__group__add(T_c)
=> ( ( ~ 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_c),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_c) )
& ( 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_c),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_c),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_gauss__sum,axiom,
! [V_n_2,T_c] :
( class_Rings_Ocomm__semiring__1(T_c)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),c_Groups_Oone__class_Oone(T_c))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_c)),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_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),c_Groups_Oone__class_Oone(T_c))) ),
file('theBenchmark.p',fact_gauss__sum) ).
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_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,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_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_atLeastatMost__empty__iff2,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_atLeastatMost__empty__iff2) ).
fof(fact_atLeastatMost__empty__iff,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_atLeastatMost__empty__iff) ).
fof(fact_atLeastatMost__empty,axiom,
! [V_a_2,V_b_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2))
=> c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_atLeastatMost__empty) ).
fof(fact_atLeastatMost__subset__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),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_c] :
( class_Orderings_Oorder(T_c)
=> ( V_a_2 = V_b_2
=> c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_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_atLeastAtMost__singleton_H) ).
fof(fact_atLeastAtMost__singleton__iff,axiom,
! [V_c_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
<=> ( V_b_2 = V_c_2
& V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).
fof(fact_atLeastAtMost__singleton,axiom,
! [V_a_2,T_c] :
( class_Orderings_Oorder(T_c)
=> c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_a_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_atLeastAtMost__singleton) ).
fof(fact_image__uminus__atLeastAtMost,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__atLeastAtMost) ).
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_setsum__shift__bounds__cl__Suc__ivl,axiom,
! [V_n_2,V_m_2,V_f_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_setsum__shift__bounds__cl__nat__ivl,axiom,
! [V_n_2,V_k_2,V_m_2,V_f_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_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_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_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_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_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_ivl__disj__un_I21_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,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_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I15_J) ).
fof(fact_Int__atLeastAtMost,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastAtMost) ).
fof(fact_atLeastatMost__psubset__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_d_2))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_d_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_atLeastatMost__psubset__iff) ).
fof(fact_ivl__disj__un_I22_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,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_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I7_J) ).
fof(fact_setsum__head__Suc,axiom,
! [V_f_2,V_n_2,V_m_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( 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_c),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_c),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_setsum__cl__ivl__Suc,axiom,
! [V_f_2,V_m_2,V_n_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( ( ~ 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_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_c) ) ) ),
file('theBenchmark.p',fact_setsum__cl__ivl__Suc) ).
fof(fact_setsum__head,axiom,
! [V_Pa_2,V_n_2,V_m_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( 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_c),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_c),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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__ub__add__nat,axiom,
! [V_p_2,V_f_2,V_n_2,V_m_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( 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_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_ivl__disj__un_I6_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I6_J) ).
fof(fact_ivl__disj__un_I5_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I5_J) ).
fof(fact_ivl__disj__un_I18_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I18_J) ).
fof(fact_ivl__disj__un_I19_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I19_J) ).
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_UN__le__eq__Un0,axiom,
! [V_M_2,V_n_2,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_ivl__disj__un_I12_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_l_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I12_J) ).
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_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_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__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_atMost__eq__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_atMost__eq__iff) ).
fof(fact_atLeast__eq__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_atLeast__eq__iff) ).
fof(fact_image__uminus__atMost,axiom,
! [V_x_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__atMost) ).
fof(fact_image__uminus__atLeast,axiom,
! [V_x_2,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__atLeast) ).
fof(fact_atMost__Int__atLeast,axiom,
! [V_n_2,T_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_atMost__Int__atLeast) ).
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_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_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_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_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_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_atMost__iff,axiom,
! [V_k_2,V_i_2,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_i_2),V_k_2)) ) ),
file('theBenchmark.p',fact_atMost__iff) ).
fof(fact_atLeast__iff,axiom,
! [V_k_2,V_i_2,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_atLeast__iff) ).
fof(fact_atLeast__subset__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_atLeast__subset__iff) ).
fof(fact_atMost__subset__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Orderings_Oorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_atMost__subset__iff) ).
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_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_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_Compl__atLeast,axiom,
! [V_k_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2) ),
file('theBenchmark.p',fact_Compl__atLeast) ).
fof(fact_Compl__lessThan,axiom,
! [V_k_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_k_2) ),
file('theBenchmark.p',fact_Compl__lessThan) ).
fof(fact_Compl__greaterThan,axiom,
! [V_k_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_k_2) ),
file('theBenchmark.p',fact_Compl__greaterThan) ).
fof(fact_Compl__atMost,axiom,
! [V_k_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_k_2) ),
file('theBenchmark.p',fact_Compl__atMost) ).
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_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_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_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_setsum__atMost__Suc,axiom,
! [V_n_2,V_f_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_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_ivl__disj__un_I14_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_l_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I14_J) ).
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_ivl__disj__int_I8_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I8_J) ).
fof(fact_Int__atLeastAtMostR1,axiom,
! [V_d_2,V_c_2,V_b_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastAtMostR1) ).
fof(fact_Int__atLeastAtMostL1,axiom,
! [V_d_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastAtMostL1) ).
fof(fact_Int__atLeastAtMostR2,axiom,
! [V_d_2,V_c_2,V_a_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),V_d_2) ),
file('theBenchmark.p',fact_Int__atLeastAtMostR2) ).
fof(fact_Int__atLeastAtMostL2,axiom,
! [V_c_2,V_b_2,V_a_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),V_b_2) ),
file('theBenchmark.p',fact_Int__atLeastAtMostL2) ).
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_ivl__disj__un_I9_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I9_J) ).
fof(fact_UN__le__add__shift,axiom,
! [V_k_2,V_M_2,V_n_2,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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_c,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_ivl__disj__int_I3_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I1_J) ).
fof(fact_ivl__disj__int_I6_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Oorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I6_J) ).
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_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_ivl__disj__un_I2_J,axiom,
! [V_u_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_u_2) ),
file('theBenchmark.p',fact_ivl__disj__un_I2_J) ).
fof(fact_ivl__disj__un_I10_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I10_J) ).
fof(fact_ivl__disj__un_I1_J,axiom,
! [V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_l_2) ),
file('theBenchmark.p',fact_ivl__disj__un_I1_J) ).
fof(fact_ivl__disj__un_I13_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_l_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I13_J) ).
fof(fact_ivl__disj__un_I7_J,axiom,
! [V_u_2,V_l_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I7_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_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_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_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_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_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_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_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_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_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_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_setsum__mono__zero__right,axiom,
! [V_f_2,V_S_2,V_T_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_T_2),V_S_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_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_T_2),V_S_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_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_T_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__mono__zero__left) ).
fof(fact_card__Pow,axiom,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(c_Finite__Set_Ocard(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),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_c),V_A_2)) ),
file('theBenchmark.p',fact_card__Pow) ).
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_PowI,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_B_2))) ),
file('theBenchmark.p',fact_PowI) ).
fof(fact_finite__Pow__iff,axiom,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
file('theBenchmark.p',fact_finite__Pow__iff) ).
fof(fact_image__Pow__surj,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) = V_B_2
=> hAPP(c_Set_Oimage(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),c_Set_Oimage(T_d,T_c,V_f_2)),hAPP(c_Set_OPow(T_d),V_A_2)) = hAPP(c_Set_OPow(T_c),V_B_2) ),
file('theBenchmark.p',fact_image__Pow__surj) ).
fof(fact_Pow__top,axiom,
! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_A_2))),
file('theBenchmark.p',fact_Pow__top) ).
fof(fact_Cantors__paradox,axiom,
! [V_A_2,T_c] :
~ ? [B_f] : hAPP(c_Set_Oimage(T_c,tc_fun(T_c,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_c),V_A_2),
file('theBenchmark.p',fact_Cantors__paradox) ).
fof(fact_Pow__not__empty,axiom,
! [V_A_2,T_c] : hAPP(c_Set_OPow(T_c),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),
file('theBenchmark.p',fact_Pow__not__empty) ).
fof(fact_Pow__INT__eq,axiom,
! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Set_OPow(T_c),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(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_d),c_Set_OPow(T_c)),V_B_2)),
file('theBenchmark.p',fact_Pow__INT__eq) ).
fof(fact_Pow__bottom,axiom,
! [V_B_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),hAPP(c_Set_OPow(T_c),V_B_2))),
file('theBenchmark.p',fact_Pow__bottom) ).
fof(fact_PowD,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_B_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_PowD) ).
fof(fact_Pow__iff,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_B_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_Pow__iff) ).
fof(fact_nat__case__0,axiom,
! [V_f2_2,V_f1_2,T_c] : c_Nat_Onat_Onat__case(T_c,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_c] : c_Nat_Onat_Onat__case(T_c,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_Pow__mono,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)),hAPP(c_Set_OPow(T_c),V_B_2))) ),
file('theBenchmark.p',fact_Pow__mono) ).
fof(fact_Pow__insert,axiom,
! [V_A_2,V_a_2,T_c] : hAPP(c_Set_OPow(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_c),V_a_2)),hAPP(c_Set_OPow(T_c),V_A_2))),
file('theBenchmark.p',fact_Pow__insert) ).
fof(fact_Pow__UNIV,axiom,
! [T_c] : hAPP(c_Set_OPow(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),
file('theBenchmark.p',fact_Pow__UNIV) ).
fof(fact_UN__Pow__subset,axiom,
! [V_B_2,V_A_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_d),c_Set_OPow(T_c)),V_B_2))),hAPP(c_Set_OPow(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_UN__Pow__subset) ).
fof(fact_Pow__Int__eq,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(c_Set_OPow(T_c),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(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)),hAPP(c_Set_OPow(T_c),V_B_2)),
file('theBenchmark.p',fact_Pow__Int__eq) ).
fof(fact_image__Pow__mono,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),c_Set_Oimage(T_d,T_c,V_f_2)),hAPP(c_Set_OPow(T_d),V_A_2))),hAPP(c_Set_OPow(T_c),V_B_2))) ),
file('theBenchmark.p',fact_image__Pow__mono) ).
fof(fact_Pow__empty,axiom,
! [T_c] : hAPP(c_Set_OPow(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))),
file('theBenchmark.p',fact_Pow__empty) ).
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_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_Un__Pow__subset,axiom,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)),hAPP(c_Set_OPow(T_c),V_B_2))),hAPP(c_Set_OPow(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_Un__Pow__subset) ).
fof(fact_Powp__Pow__eq,axiom,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Predicate_OPowp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_c),V_A_2))) ),
file('theBenchmark.p',fact_Powp__Pow__eq) ).
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_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_transfer__nat__int__sum__prod__cong_I2_J,axiom,
! [V_g_2,V_f_2,V_B_2,V_A_2,T_c] :
( ( class_Groups_Ocomm__monoid__mult(T_c)
& class_Groups_Ocomm__monoid__add(T_c) )
=> ( 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_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_c),V_g_2),V_B_2) ) ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).
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_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_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_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_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_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_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_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__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_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_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_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_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_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__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__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__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__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_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__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_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__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__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__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_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__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_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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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_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_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_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_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_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_sgn__1__neg,axiom,
! [V_a_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( c_Groups_Osgn__class_Osgn(T_c,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Groups_Oone__class_Oone(T_c))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ),
file('theBenchmark.p',fact_sgn__1__neg) ).
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_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_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__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_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_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_sgn__0__0,axiom,
! [V_a_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( c_Groups_Osgn__class_Osgn(T_c,V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ),
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_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_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__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__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__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_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_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_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_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__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_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_sgn__greater,axiom,
! [V_a_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Osgn__class_Osgn(T_c,V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ),
file('theBenchmark.p',fact_sgn__greater) ).
fof(fact_sgn__less,axiom,
! [V_a_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Osgn__class_Osgn(T_c,V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) ) ),
file('theBenchmark.p',fact_sgn__less) ).
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_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_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_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_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_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_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( c_Groups_Osgn__class_Osgn(T_c,V_a_2) = c_Groups_Oone__class_Oone(T_c)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ),
file('theBenchmark.p',fact_sgn__1__pos) ).
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_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_transfer__nat__int__sum__prod__cong_I1_J,axiom,
! [V_g_2,V_f_2,V_B_2,V_A_2,T_c] :
( ( class_Groups_Ocomm__monoid__mult(T_c)
& class_Groups_Ocomm__monoid__add(T_c) )
=> ( 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_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),V_g_2),V_B_2) ) ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I1_J) ).
fof(fact_Sup__fold__sup,axiom,
! [V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_Sup__fold__sup) ).
fof(fact_UnionI,axiom,
! [V_A_2,V_C_2,V_X_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),V_X_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2))) ) ),
file('theBenchmark.p',fact_UnionI) ).
fof(fact_setsum__abs,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( class_Groups_Oordered__ab__group__add__abs(T_c)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),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_d,T_c] :
( class_Groups_Oordered__ab__group__add__abs(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__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2))) ),
file('theBenchmark.p',fact_setsum__abs__ge__zero) ).
fof(fact_Union__Pow__eq,axiom,
! [V_A_2,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_OPow(T_c),V_A_2)) = V_A_2,
file('theBenchmark.p',fact_Union__Pow__eq) ).
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__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__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__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__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_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__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__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__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__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__eq__0,axiom,
! [V_a_2,T_c] :
( class_Groups_Oordered__ab__group__add__abs(T_c)
=> ( hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_abs__eq__0) ).
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__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_abs__setsum__abs,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( class_Groups_Oordered__ab__group__add__abs(T_c)
=> hAPP(c_Groups_Oabs__class_Oabs(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_abs__setsum__abs) ).
fof(fact_abs__setprod,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( class_Fields_Olinordered__field(T_c)
=> hAPP(c_Groups_Oabs__class_Oabs(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_abs__setprod) ).
fof(fact_image__Union,axiom,
! [V_S_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_d,T_c,V_f_2)),
file('theBenchmark.p',fact_image__Union) ).
fof(fact_Int__Union2,axiom,
! [V_A_2,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),
file('theBenchmark.p',fact_Int__Union2) ).
fof(fact_Int__Union,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),
file('theBenchmark.p',fact_Int__Union) ).
fof(fact_UN__extend__simps_I8_J,axiom,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,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_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),
file('theBenchmark.p',fact_UN__simps_I8_J) ).
fof(fact_Sup__le__iff,axiom,
! [V_b_2,V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2)),V_b_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_c),B_x),V_b_2)) ) ) ),
file('theBenchmark.p',fact_Sup__le__iff) ).
fof(fact_less__Sup__iff,axiom,
! [V_S_2,V_a_2,T_c] :
( ( class_Orderings_Olinorder(T_c)
& class_Complete__Lattice_Ocomplete__lattice(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_S_2)))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) ) ) ),
file('theBenchmark.p',fact_less__Sup__iff) ).
fof(fact_vimage__Union,axiom,
! [V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_c,T_d,V_f_2)),
file('theBenchmark.p',fact_vimage__Union) ).
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_c] :
( class_Groups_Oordered__ab__group__add__abs(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ),
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_c] :
( class_Groups_Oordered__ab__group__add__abs(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_c) ) ),
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__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__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__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__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_c] :
( class_Groups_Oordered__ab__group__add__abs(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)),V_b_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),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_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)),V_b_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),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_Union__disjoint,axiom,
! [V_A_2,V_C_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_x),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_Union__disjoint) ).
fof(fact_Union__upper,axiom,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),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),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2))) ),
file('theBenchmark.p',fact_Union__upper) ).
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_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_Union__empty,axiom,
! [T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Union__empty) ).
fof(fact_Union__mono,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),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)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2))) ),
file('theBenchmark.p',fact_Union__mono) ).
fof(fact_Union__insert,axiom,
! [V_B_2,V_a_2,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(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),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)),
file('theBenchmark.p',fact_Union__insert) ).
fof(fact_finite__UnionD,axiom,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) ),
file('theBenchmark.p',fact_finite__UnionD) ).
fof(fact_subset__Pow__Union,axiom,
! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)))),
file('theBenchmark.p',fact_subset__Pow__Union) ).
fof(fact_Union__UNIV,axiom,
! [T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Union__UNIV) ).
fof(fact_Union__Un__distrib,axiom,
! [V_B_2,V_A_2,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)),
file('theBenchmark.p',fact_Union__Un__distrib) ).
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__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_UNION__eq__Union__image,axiom,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_A_2)),
file('theBenchmark.p',fact_UNION__eq__Union__image) ).
fof(fact_Union__image__eq,axiom,
! [V_A_2,V_B_2,T_d,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_A_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),
file('theBenchmark.p',fact_Union__image__eq) ).
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__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__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__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_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_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_Sup__upper,axiom,
! [V_A_2,V_x_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2))) ) ),
file('theBenchmark.p',fact_Sup__upper) ).
fof(fact_Sup__empty,axiom,
! [T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OSup__class_OSup(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_c) ),
file('theBenchmark.p',fact_Sup__empty) ).
fof(fact_Sup__singleton,axiom,
! [V_a_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_a_2 ),
file('theBenchmark.p',fact_Sup__singleton) ).
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_Sup__insert,axiom,
! [V_A_2,V_a_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2)) ),
file('theBenchmark.p',fact_Sup__insert) ).
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_Sup__UNIV,axiom,
! [T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OSup__class_OSup(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_c) ),
file('theBenchmark.p',fact_Sup__UNIV) ).
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_INT__simps_I8_J,axiom,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,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_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)),V_B_2),
file('theBenchmark.p',fact_INT__extend__simps_I8_J) ).
fof(fact_Un__eq__Union,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))))),
file('theBenchmark.p',fact_Un__eq__Union) ).
fof(fact_Un__Union__image,axiom,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_d,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_d),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)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_C_2))),
file('theBenchmark.p',fact_Un__Union__image) ).
fof(fact_Union__Int__subset,axiom,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)))),
file('theBenchmark.p',fact_Union__Int__subset) ).
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_Sup__binary,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),V_b_2) ),
file('theBenchmark.p',fact_Sup__binary) ).
fof(fact_sup__Sup__fold__sup,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_B_2),V_A_2) ) ),
file('theBenchmark.p',fact_sup__Sup__fold__sup) ).
fof(fact_Sup__fin__Sup,axiom,
! [V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2) ) ) ),
file('theBenchmark.p',fact_Sup__fin__Sup) ).
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_inj__on__Inter,axiom,
! [V_f_2,T_d,T_c,V_S_2] :
( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))
=> ( ! [B_A] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_A),V_S_2))
=> c_Fun_Oinj__on(T_c,T_d,V_f_2,B_A) )
=> c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_S_2)) ) ),
file('theBenchmark.p',fact_inj__on__Inter) ).
fof(fact_Inter__subset,axiom,
! [V_B_2,V_A_2,T_c] :
( ! [B_X] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_X),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_X),V_B_2)) )
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2)) ) ),
file('theBenchmark.p',fact_Inter__subset) ).
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_Union__def,axiom,
! [V_S_2,T_c] : 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_c,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_c,tc_HOL_Obool))),
file('theBenchmark.p',fact_Union__def) ).
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_finite__Union,axiom,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),V_A_2))
=> ( ! [B_M] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_M),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_M)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2))) ) ),
file('theBenchmark.p',fact_finite__Union) ).
fof(fact_insert__partition,axiom,
! [V_F_2,V_x_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_x_2),V_F_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_x_2),V_F_2)))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_x_2),V_F_2)))
=> ( B_x != B_xa
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_insert__partition) ).
fof(fact_card__partition,axiom,
! [V_k_2,V_C_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),V_C_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2)))
=> ( ! [B_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_c),V_C_2))
=> hAPP(c_Finite__Set_Ocard(T_c),B_c) = V_k_2 )
=> ( ! [B_c1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_c1),V_C_2))
=> ! [B_c2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_c2),V_C_2))
=> ( B_c1 != B_c2
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_c,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2)) ) ) ) ),
file('theBenchmark.p',fact_card__partition) ).
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_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_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_setprod__pos__nat,axiom,
! [V_f_2,V_S_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),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_c,tc_Nat_Onat),V_f_2),V_S_2))) ) ),
file('theBenchmark.p',fact_setprod__pos__nat) ).
fof(fact_inj__on__INTER,axiom,
! [V_A_2,V_f_2,T_e,T_d,T_c,V_I_2] :
( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_I_2))
=> c_Fun_Oinj__on(T_d,T_e,V_f_2,hAPP(V_A_2,B_i)) )
=> c_Fun_Oinj__on(T_d,T_e,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)) ) ),
file('theBenchmark.p',fact_inj__on__INTER) ).
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_d,T_c] :
( c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_d,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_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_CollectI,axiom,
! [T_c,V_a_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,V_a_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),V_Pa_2))) ),
file('theBenchmark.p',fact_CollectI) ).
fof(fact_finite__Collect__conjI,axiom,
! [V_Qa_2,V_Pa_2,T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Qa_2)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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),V_Pa_2)),V_Qa_2)))) ),
file('theBenchmark.p',fact_finite__Collect__conjI) ).
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_Collect__disj__eq,axiom,
! [V_Qa_2,V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),V_Pa_2)),hAPP(c_Set_OCollect(T_c),V_Qa_2)),
file('theBenchmark.p',fact_Collect__disj__eq) ).
fof(fact_Collect__conj__eq,axiom,
! [V_Qa_2,V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(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),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),V_Pa_2)),hAPP(c_Set_OCollect(T_c),V_Qa_2)),
file('theBenchmark.p',fact_Collect__conj__eq) ).
fof(fact_CollectE,axiom,
! [V_Pa_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),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_c] : hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)) = V_A_2,
file('theBenchmark.p',fact_Collect__mem__eq) ).
fof(fact_empty__def,axiom,
! [T_c] : c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_c),hAPP(c_COMBK(tc_HOL_Obool,T_c),c_fFalse)),
file('theBenchmark.p',fact_empty__def) ).
fof(fact_empty__Collect__eq,axiom,
! [V_Pa_2,T_c] :
( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_c),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_c] :
( hAPP(c_Set_OCollect(T_c),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
<=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ),
file('theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_Collect__def,axiom,
! [V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),V_Pa_2) = V_Pa_2,
file('theBenchmark.p',fact_Collect__def) ).
fof(fact_UNIV__def,axiom,
! [T_c] : c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_c),hAPP(c_COMBK(tc_HOL_Obool,T_c),c_fTrue)),
file('theBenchmark.p',fact_UNIV__def) ).
fof(fact_insert__Collect,axiom,
! [V_Pa_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(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_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)),
file('theBenchmark.p',fact_insert__Collect) ).
fof(fact_finite__Collect__disjI,axiom,
! [V_Qa_2,V_Pa_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),V_Pa_2)),V_Qa_2))))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Qa_2)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) ) ),
file('theBenchmark.p',fact_finite__Collect__disjI) ).
fof(fact_Collect__neg__eq,axiom,
! [V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),V_Pa_2)),
file('theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_vimage__Collect__eq,axiom,
! [V_Pa_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(c_Set_OCollect(T_d),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_d,tc_HOL_Obool,T_c),V_Pa_2),V_f_2)),
file('theBenchmark.p',fact_vimage__Collect__eq) ).
fof(fact_insert__compr,axiom,
! [V_B_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),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_insert__compr) ).
fof(fact_insert__compr__raw,axiom,
! [V_B_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),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_insert__compr__raw) ).
fof(fact_Un__def,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),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_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),
file('theBenchmark.p',fact_Un__def) ).
fof(fact_Int__def,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),
file('theBenchmark.p',fact_Int__def) ).
fof(fact_Int__Collect,axiom,
! [V_Pa_2,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_c),V_Pa_2))))
<=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Int__Collect) ).
fof(fact_singleton__conv2,axiom,
! [V_a_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(c_fequal,V_a_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_singleton__conv2) ).
fof(fact_singleton__conv,axiom,
! [V_a_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_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_singleton__conv) ).
fof(fact_Collect__conv__if2,axiom,
! [T_c,V_a_2,V_Pa_2] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
=> hAPP(c_Set_OCollect(T_c),hAPP(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(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hBOOL(hAPP(V_Pa_2,V_a_2))
=> hAPP(c_Set_OCollect(T_c),hAPP(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(c_fequal,V_a_2))),V_Pa_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_Collect__conv__if2) ).
fof(fact_Collect__conv__if,axiom,
! [T_c,V_a_2,V_Pa_2] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
=> hAPP(c_Set_OCollect(T_c),hAPP(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,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hBOOL(hAPP(V_Pa_2,V_a_2))
=> hAPP(c_Set_OCollect(T_c),hAPP(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,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_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_Collect__conv__if) ).
fof(fact_set__diff__eq,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),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_set__diff__eq) ).
fof(fact_finite__Collect__not,axiom,
! [V_Pa_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))))
<=> 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__Collect__not) ).
fof(fact_insert__def,axiom,
! [V_B_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2),
file('theBenchmark.p',fact_insert__def) ).
fof(fact_Compl__eq,axiom,
! [V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2))),
file('theBenchmark.p',fact_Compl__eq) ).
fof(fact_vimage__def,axiom,
! [V_B_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(T_d)),V_f_2)),V_B_2)),
file('theBenchmark.p',fact_vimage__def) ).
fof(fact_Collect__imp__eq,axiom,
! [V_Qa_2,V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(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),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),V_Pa_2))),hAPP(c_Set_OCollect(T_c),V_Qa_2)),
file('theBenchmark.p',fact_Collect__imp__eq) ).
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_setsum__setsum__restrict,axiom,
! [V_R_2,V_f_2,V_T_2,T_d,V_S_2,T_c,T_e] :
( class_Groups_Ocomm__monoid__add(T_e)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_T_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),T_e),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_e),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_e),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_OCollect(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e),hAPP(hAPP(c_COMBS(T_d,tc_fun(T_c,tc_HOL_Obool),T_e),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_e),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_e),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e)),hAPP(c_COMBC(T_c,T_d,T_e),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),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_S_2)))),hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ),
file('theBenchmark.p',fact_setsum__setsum__restrict) ).
fof(fact_if__image__distrib,axiom,
! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBS(T_d,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_d),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_d),V_Pa_2)))),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d),c_fNot),V_Pa_2))))),
file('theBenchmark.p',fact_if__image__distrib) ).
fof(fact_nat__seg__image__imp__finite,axiom,
! [V_n_2,V_f_2,T_c,V_A_2] :
( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_c,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_c),V_A_2)) ),
file('theBenchmark.p',fact_nat__seg__image__imp__finite) ).
fof(fact_setsum__restrict__set_H,axiom,
! [V_B_2,V_f_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(c_Set_OCollect(T_c),hAPP(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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_d))),V_A_2) ) ),
file('theBenchmark.p',fact_setsum__restrict__set_H) ).
fof(fact_setsum__image__gen,axiom,
! [V_f_2,T_e,V_g_2,V_S_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_e),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),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_S_2)))),hAPP(c_COMBC(T_c,T_e,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_e,tc_HOL_Obool),T_c),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_c,T_e,V_f_2),V_S_2)) ) ),
file('theBenchmark.p',fact_setsum__image__gen) ).
fof(fact_setsum__cases,axiom,
! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_Set_OCollect(T_c),V_Pa_2))))) ) ),
file('theBenchmark.p',fact_setsum__cases) ).
fof(fact_setsum__multicount,axiom,
! [V_k_2,V_R_2,V_T_2,T_d,V_S_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_T_2))
=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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_S_2))),hAPP(hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_Nat_Onat,T_c),c_Finite__Set_Ocard(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_OCollect(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),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_d),V_T_2)) ) ) ),
file('theBenchmark.p',fact_setsum__multicount) ).
fof(fact_min__max_Osup__Inf1__distrib,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2))))) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).
fof(fact_min__max_Oinf__Sup1__distrib,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2))))) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).
fof(fact_min__max_Osup__Inf2__distrib,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBS(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_c),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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal))),c_Orderings_Oord__class_Omax(T_c)))))),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).
fof(fact_finite__Collect__subsets,axiom,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),V_A_2)))) ),
file('theBenchmark.p',fact_finite__Collect__subsets) ).
fof(fact_Pow__Compl,axiom,
! [V_A_2,T_c] : hAPP(c_Set_OPow(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBS(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_c))))),
file('theBenchmark.p',fact_Pow__Compl) ).
fof(fact_Pow__def,axiom,
! [V_A_2,T_c] : hAPP(c_Set_OPow(T_c),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),
file('theBenchmark.p',fact_Pow__def) ).
fof(fact_finite__image__set,axiom,
! [V_f_2,T_d,V_Pa_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_d),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_d),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_c,T_d),tc_fun(T_c,tc_HOL_Obool)),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)),V_f_2)))),V_Pa_2))))) ),
file('theBenchmark.p',fact_finite__image__set) ).
fof(fact_finite__Collect__bounded__ex,axiom,
! [V_Qa_2,T_d,V_Pa_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),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),V_Pa_2))),V_Qa_2)))))
<=> ! [B_y] :
( hBOOL(hAPP(V_Pa_2,B_y))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBC(T_d,T_c,tc_HOL_Obool),V_Qa_2),B_y)))) ) ) ),
file('theBenchmark.p',fact_finite__Collect__bounded__ex) ).
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_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_add__Min__commute,axiom,
! [V_k_2,V_N_2,T_c] :
( class_Groups_Olinordered__ab__semigroup__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_c,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_c),V_k_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_N_2))))) ) ) ),
file('theBenchmark.p',fact_add__Min__commute) ).
fof(fact_add__Max__commute,axiom,
! [V_k_2,V_N_2,T_c] :
( class_Groups_Olinordered__ab__semigroup__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_c),V_k_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_N_2))))) ) ) ),
file('theBenchmark.p',fact_add__Max__commute) ).
fof(fact_sup__Inf2__distrib,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Lattices_Odistrib__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBS(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_c),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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_c)))))),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ) ) ),
file('theBenchmark.p',fact_sup__Inf2__distrib) ).
fof(fact_sup__Inf1__distrib,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Odistrib__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2))))) ) ) ),
file('theBenchmark.p',fact_sup__Inf1__distrib) ).
fof(fact_inf__Sup2__distrib,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Lattices_Odistrib__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBS(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_c),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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_c)))))),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ) ) ),
file('theBenchmark.p',fact_inf__Sup2__distrib) ).
fof(fact_inf__Sup1__distrib,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Lattices_Odistrib__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2))))) ) ) ),
file('theBenchmark.p',fact_inf__Sup1__distrib) ).
fof(fact_min__max_Oinf__Sup2__distrib,axiom,
! [V_B_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBS(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_c),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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal))),c_Orderings_Oord__class_Omin(T_c)))))),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).
fof(fact_setsum__multicount__gen,axiom,
! [V_k_2,V_R_2,V_t_2,T_d,V_s_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_s_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_t_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_t_2))
=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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_s_2))),hAPP(hAPP(c_COMBC(T_c,T_d,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_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_Nat_Onat,T_c),c_Finite__Set_Ocard(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_OCollect(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,tc_Nat_Onat),V_k_2),V_t_2) ) ) ),
file('theBenchmark.p',fact_setsum__multicount__gen) ).
fof(fact_finite__conv__nat__seg__image,axiom,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
<=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_c,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_pigeonhole__infinite,axiom,
! [V_f_2,T_d,V_A_2,T_c] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
=> ? [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_f_2,B_x))))))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_pigeonhole__infinite) ).
fof(fact_card__quotient__disjoint,axiom,
! [V_r_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( c_Fun_Oinj__on(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),T_c),c_Equiv__Relations_Oquotient(T_c)),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))))),V_r_2),V_A_2)
=> hAPP(c_Finite__Set_Ocard(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ) ),
file('theBenchmark.p',fact_card__quotient__disjoint) ).
fof(fact_quotient__is__empty,axiom,
! [V_r_2,V_A_2,T_c] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_quotient__is__empty) ).
fof(fact_quotient__is__empty2,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_quotient__is__empty2) ).
fof(fact_quotient__empty,axiom,
! [V_r_2,T_c] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),
file('theBenchmark.p',fact_quotient__empty) ).
fof(fact_quotient__diff1,axiom,
! [V_a_2,V_A_2,V_r_2,T_c] :
( c_Fun_Oinj__on(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),T_c),c_Equiv__Relations_Oquotient(T_c)),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))))),V_r_2),V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_r_2)) ) ),
file('theBenchmark.p',fact_quotient__diff1) ).
fof(fact_quotient__def,axiom,
! [V_r_2,V_A_2,T_c] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_c,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)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)))),
file('theBenchmark.p',fact_quotient__def) ).
fof(fact_singleton__quotient,axiom,
! [V_r_2,V_x_2,T_c] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))),
file('theBenchmark.p',fact_singleton__quotient) ).
fof(fact_finite__UN__I,axiom,
! [V_B_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ! [B_a] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_a),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_a))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,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_quotientI,axiom,
! [V_r_2,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) ),
file('theBenchmark.p',fact_quotientI) ).
fof(fact_Image__eq__UN,axiom,
! [V_B_2,V_r_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Relation_OImage(T_d,T_c,V_r_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),c_Set_Oinsert(T_d)),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))),
file('theBenchmark.p',fact_Image__eq__UN) ).
fof(fact_Image__INT__subset,axiom,
! [V_B_2,V_A_2,T_e,V_r_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Relation_OImage(T_d,T_c,V_r_2)),V_B_2)))),
file('theBenchmark.p',fact_Image__INT__subset) ).
fof(fact_Image__Int__subset,axiom,
! [V_B_2,V_A_2,V_R_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_Relation_OImage(T_d,T_c,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),V_B_2)))),
file('theBenchmark.p',fact_Image__Int__subset) ).
fof(fact_Image__UN,axiom,
! [V_B_2,V_A_2,T_e,V_r_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Relation_OImage(T_d,T_c,V_r_2)),V_B_2)),
file('theBenchmark.p',fact_Image__UN) ).
fof(fact_Image__empty,axiom,
! [V_R_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Image__empty) ).
fof(fact_Image__mono,axiom,
! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_H_2),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_d,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_c,T_d,V_r_2),V_A_2))) ) ),
file('theBenchmark.p',fact_Image__mono) ).
fof(fact_Image__Un,axiom,
! [V_B_2,V_A_2,V_R_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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(c_Relation_OImage(T_d,T_c,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),V_B_2)),
file('theBenchmark.p',fact_Image__Un) ).
fof(fact_Un__Image,axiom,
! [V_A_2,V_S_2,V_R_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_d,T_c,V_S_2),V_A_2)),
file('theBenchmark.p',fact_Un__Image) ).
fof(fact_quotientE,axiom,
! [V_r_2,V_A_2,V_X_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
=> ~ ! [B_x] :
( V_X_2 = hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_quotientE) ).
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_setsum__SucD,axiom,
! [V_n_2,V_A_2,V_f_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_setsum__SucD) ).
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_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_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_less__by__empty,axiom,
! [V_B_2,T_c,V_A_2] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_less__by__empty) ).
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__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__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_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_com_Osize_I5_J,axiom,
! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_com_Osize_I5_J) ).
fof(fact_com_Osize_I13_J,axiom,
! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_com_Osize_I13_J) ).
fof(fact_fold__image__1,axiom,
! [V_f_2,V_S_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_d) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_f_2),c_Groups_Oone__class_Oone(T_d)),V_S_2) = c_Groups_Oone__class_Oone(T_d) ) ) ),
file('theBenchmark.p',fact_fold__image__1) ).
fof(fact_card_Oneutral,axiom,
! [V_A_2,T_c] :
( 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))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_card_Oneutral) ).
fof(fact_com_Osimps_I4_J,axiom,
! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)
<=> ( V_com2_2 = V_com2_H_2
& V_com1_2 = V_com1_H_2
& V_fun_2 = V_fun_H_2 ) ),
file('theBenchmark.p',fact_com_Osimps_I4_J) ).
fof(fact_com_Osimps_I52_J,axiom,
! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
file('theBenchmark.p',fact_com_Osimps_I52_J) ).
fof(fact_com_Osimps_I53_J,axiom,
! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2),
file('theBenchmark.p',fact_com_Osimps_I53_J) ).
fof(fact_com_Osimps_I45_J,axiom,
! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
file('theBenchmark.p',fact_com_Osimps_I45_J) ).
fof(fact_com_Osimps_I44_J,axiom,
! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
file('theBenchmark.p',fact_com_Osimps_I44_J) ).
fof(fact_com_Osimps_I15_J,axiom,
! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP,
file('theBenchmark.p',fact_com_Osimps_I15_J) ).
fof(fact_com_Osimps_I14_J,axiom,
! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
file('theBenchmark.p',fact_com_Osimps_I14_J) ).
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_InterI,axiom,
! [V_A_2,V_C_2,T_c] :
( ! [B_X] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_X),V_C_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),B_X)) )
=> hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_C_2))) ),
file('theBenchmark.p',fact_InterI) ).
fof(fact_fold__image__cong,axiom,
! [V_z_2,V_h_2,V_g_2,V_A_2,T_c,T_d] :
( class_Groups_Oab__semigroup__mult(T_d)
=> ( 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(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_h_2),V_z_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_fold__image__cong) ).
fof(fact_inf__le__fold__inf,axiom,
! [V_c_2,V_b_2,V_A_2,T_c] :
( class_Lattices_Osemilattice__inf(T_c)
=> ( 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))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),B_x)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_c_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_inf__le__fold__inf) ).
fof(fact_fold__sup__le__sup,axiom,
! [V_c_2,V_b_2,V_A_2,T_c] :
( class_Lattices_Osemilattice__sup(T_c)
=> ( 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))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),V_b_2)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_b_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_fold__sup__le__sup) ).
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_quotient__disj,axiom,
! [V_Y_2,V_X_2,V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_X_2 = V_Y_2 ) ) ) ),
file('theBenchmark.p',fact_quotient__disj) ).
fof(fact_com_Osize_I3_J,axiom,
! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_com_Osize_I3_J) ).
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_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_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_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_com_Osimps_I2_J,axiom,
! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2)
<=> ( V_com_2 = V_com_H_2
& V_fun_2 = V_fun_H_2
& V_loc_2 = V_loc_H_2 ) ),
file('theBenchmark.p',fact_com_Osimps_I2_J) ).
fof(fact_number__of__reorient,axiom,
! [V_x_2,V_w_2,T_c] :
( class_Int_Onumber(T_c)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = V_x_2
<=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) ) ),
file('theBenchmark.p',fact_number__of__reorient) ).
fof(fact_eq__number__of,axiom,
! [V_y_2,V_x_2,T_c] :
( ( class_Int_Oring__char__0(T_c)
& class_Int_Onumber__ring(T_c) )
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_eq__number__of) ).
fof(fact_com_Osimps_I39_J,axiom,
! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
file('theBenchmark.p',fact_com_Osimps_I39_J) ).
fof(fact_com_Osimps_I38_J,axiom,
! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
file('theBenchmark.p',fact_com_Osimps_I38_J) ).
fof(fact_com_Osimps_I37_J,axiom,
! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
file('theBenchmark.p',fact_com_Osimps_I37_J) ).
fof(fact_com_Osimps_I36_J,axiom,
! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
file('theBenchmark.p',fact_com_Osimps_I36_J) ).
fof(fact_com_Osimps_I34_J,axiom,
! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2),
file('theBenchmark.p',fact_com_Osimps_I34_J) ).
fof(fact_com_Osimps_I35_J,axiom,
! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
file('theBenchmark.p',fact_com_Osimps_I35_J) ).
fof(fact_com_Osimps_I11_J,axiom,
! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP,
file('theBenchmark.p',fact_com_Osimps_I11_J) ).
fof(fact_com_Osimps_I10_J,axiom,
! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2),
file('theBenchmark.p',fact_com_Osimps_I10_J) ).
fof(fact_le__number__of__eq__not__less,axiom,
! [V_w_2,V_v_2,T_c] :
( ( class_Orderings_Olinorder(T_c)
& class_Int_Onumber(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2))) ) ),
file('theBenchmark.p',fact_le__number__of__eq__not__less) ).
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_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__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_le__number__of,axiom,
! [V_y_2,V_x_2,T_c] :
( ( class_Rings_Olinordered__idom(T_c)
& class_Int_Onumber__ring(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c] :
( ( class_Rings_Olinordered__idom(T_c)
& class_Int_Onumber__ring(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_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_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_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_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_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_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_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_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_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_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_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_Ints__number__of,axiom,
! [V_w_2,T_c] :
( class_Int_Onumber__ring(T_c)
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Int_Oring__1__class_OInts(T_c))) ),
file('theBenchmark.p',fact_Ints__number__of) ).
fof(fact_Union__quotient,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)) = V_A_2 ),
file('theBenchmark.p',fact_Union__quotient) ).
fof(fact_divide__eq__eq__number__of1,axiom,
! [V_a_2,V_w_2,V_b_2,T_c] :
( ( class_Int_Onumber(T_c)
& class_Fields_Ofield__inverse__zero(T_c) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) = V_a_2
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) != c_Groups_Ozero__class_Ozero(T_c)
=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq__number__of1) ).
fof(fact_divide__eq__eq__number__of,axiom,
! [V_w_2,V_c_2,V_b_2,T_c] :
( ( class_Int_Onumber(T_c)
& class_Fields_Ofield__inverse__zero(T_c) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_c)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c)
=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq__number__of) ).
fof(fact_eq__divide__eq__number__of,axiom,
! [V_c_2,V_b_2,V_w_2,T_c] :
( ( class_Int_Onumber(T_c)
& class_Fields_Ofield__inverse__zero(T_c) )
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_c)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq__number__of) ).
fof(fact_eq__divide__eq__number__of1,axiom,
! [V_w_2,V_b_2,V_a_2,T_c] :
( ( class_Int_Onumber(T_c)
& class_Fields_Ofield__inverse__zero(T_c) )
=> ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) != c_Groups_Ozero__class_Ozero(T_c)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq__number__of1) ).
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_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_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_divide__less__eq__number__of1,axiom,
! [V_a_2,V_w_2,V_b_2,T_c] :
( ( class_Int_Onumber(T_c)
& class_Fields_Olinordered__field__inverse__zero(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_a_2))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq__number__of1) ).
fof(fact_divide__less__eq__number__of,axiom,
! [V_w_2,V_c_2,V_b_2,T_c] :
( ( class_Int_Onumber(T_c)
& class_Fields_Olinordered__field__inverse__zero(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq__number__of) ).
fof(fact_less__divide__eq__number__of,axiom,
! [V_c_2,V_b_2,V_w_2,T_c] :
( ( class_Int_Onumber(T_c)
& class_Fields_Olinordered__field__inverse__zero(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq__number__of) ).
fof(fact_less__divide__eq__number__of1,axiom,
! [V_w_2,V_b_2,V_a_2,T_c] :
( ( class_Int_Onumber(T_c)
& class_Fields_Olinordered__field__inverse__zero(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq__number__of1) ).
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_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_le__divide__eq__number__of1,axiom,
! [V_w_2,V_b_2,V_a_2,T_c] :
( ( class_Int_Onumber(T_c)
& class_Fields_Olinordered__field__inverse__zero(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq__number__of1) ).
fof(fact_le__divide__eq__number__of,axiom,
! [V_c_2,V_b_2,V_w_2,T_c] :
( ( class_Int_Onumber(T_c)
& class_Fields_Olinordered__field__inverse__zero(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq__number__of) ).
fof(fact_divide__le__eq__number__of,axiom,
! [V_w_2,V_c_2,V_b_2,T_c] :
( ( class_Int_Onumber(T_c)
& class_Fields_Olinordered__field__inverse__zero(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq__number__of) ).
fof(fact_divide__le__eq__number__of1,axiom,
! [V_a_2,V_w_2,V_b_2,T_c] :
( ( class_Int_Onumber(T_c)
& class_Fields_Olinordered__field__inverse__zero(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_a_2))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq__number__of1) ).
fof(fact_equiv__class__self,axiom,
! [V_a_2,V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Relation_OImage(T_c,T_c,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)))))) ) ),
file('theBenchmark.p',fact_equiv__class__self) ).
fof(fact_com_Osize_I11_J,axiom,
! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_com_Osize_I11_J) ).
fof(fact_UN__equiv__class,axiom,
! [V_a_2,V_f_2,T_d,V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> ( c_Equiv__Relations_Ocongruent(T_c,tc_fun(T_d,tc_HOL_Obool),V_r_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(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_r_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) = 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_e,V_r2_2,V_A2_2,T_d,V_r1_2,V_A1_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A1_2,V_r1_2)
=> ( c_Equiv__Relations_Oequiv(T_d,V_A2_2,V_r2_2)
=> ( c_Equiv__Relations_Ocongruent2(T_c,T_d,tc_fun(T_e,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a1_2),V_A1_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_a2_2),V_A2_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_e,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_d,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,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_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_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_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_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_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_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_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_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_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_congruent2__implies__congruent,axiom,
! [V_a_2,V_f_2,V_r2_2,T_e,T_d,V_r1_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r1_2)
=> ( c_Equiv__Relations_Ocongruent2(T_c,T_d,T_e,V_r1_2,V_r2_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> c_Equiv__Relations_Ocongruent(T_d,T_e,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ),
file('theBenchmark.p',fact_congruent2__implies__congruent) ).
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_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__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_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_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_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_congruent2__implies__congruent__UN,axiom,
! [V_a_2,V_f_2,T_e,V_r2_2,V_A2_2,T_d,V_r1_2,V_A1_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A1_2,V_r1_2)
=> ( c_Equiv__Relations_Oequiv(T_d,V_A2_2,V_r2_2)
=> ( c_Equiv__Relations_Ocongruent2(T_c,T_d,tc_fun(T_e,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),V_A2_2))
=> c_Equiv__Relations_Ocongruent(T_c,tc_fun(T_e,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_d,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))),V_f_2)) ) ) ) ),
file('theBenchmark.p',fact_congruent2__implies__congruent__UN) ).
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_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_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_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_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_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_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_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_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_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_succ__pred,axiom,
! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
file('theBenchmark.p',fact_succ__pred) ).
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_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_Pls__def) ).
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_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_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_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_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_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_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_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_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__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_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_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_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_le__special_I1_J,axiom,
! [V_y_2,T_c] :
( ( class_Rings_Olinordered__idom(T_c)
& class_Int_Onumber__ring(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c] :
( ( class_Rings_Olinordered__idom(T_c)
& class_Int_Onumber__ring(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> 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_I3_J,axiom,
! [V_x_2,T_c] :
( ( class_Rings_Olinordered__idom(T_c)
& class_Int_Onumber__ring(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Ozero__class_Ozero(T_c)))
<=> 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__special_I1_J,axiom,
! [V_y_2,T_c] :
( ( class_Rings_Olinordered__idom(T_c)
& class_Int_Onumber__ring(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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__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_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_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_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_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_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__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_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_nat__case__number__of,axiom,
! [V_v_2,V_f_2,V_a_2,T_c] : c_Nat_Onat_Onat__case(T_c,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_c),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_c)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,tc_Int_Oint),V_f_2),c_Int_Onat))),
file('theBenchmark.p',fact_nat__case__number__of) ).
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_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_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_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_nat__case__add__eq__if,axiom,
! [V_n_2,V_v_2,V_f_2,V_a_2,T_c] : c_Nat_Onat_Onat__case(T_c,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_c),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_c)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_c,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_nat__rec__add__eq__if,axiom,
! [V_n_2,V_v_2,V_f_2,V_a_2,T_c] : hAPP(c_Nat_Onat_Onat__rec(T_c,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_c),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_c)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_c,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_c,T_c),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_c,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_c,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__number__of,axiom,
! [V_v_2,V_f_2,V_a_2,T_c] : hAPP(c_Nat_Onat_Onat__rec(T_c,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_c),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_c)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_c,T_c),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_c,V_a_2,V_f_2)),c_Int_Onat)))),
file('theBenchmark.p',fact_nat__rec__number__of) ).
fof(fact_UN__equiv__class__type2,axiom,
! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_e,V_r2_2,V_A2_2,T_d,V_r1_2,V_A1_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A1_2,V_r1_2)
=> ( c_Equiv__Relations_Oequiv(T_d,V_A2_2,V_r2_2)
=> ( c_Equiv__Relations_Ocongruent2(T_c,T_d,tc_fun(T_e,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A1_2),V_r1_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_d),V_A2_2),V_r2_2)))
=> ( ! [B_x1] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x1),V_A1_2))
=> ! [B_x2] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x2),V_A2_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_e,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,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_d,V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> ( c_Equiv__Relations_Ocongruent(T_c,tc_fun(T_d,tc_HOL_Obool),V_r_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_f_2,B_x)),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_c,tc_fun(T_d,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_UN__equiv__class__type) ).
fof(fact_nat__rec__0,axiom,
! [V_f2_2,V_f1_2,T_c] : hAPP(c_Nat_Onat_Onat__rec(T_c,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_c] : hAPP(c_Nat_Onat_Onat__rec(T_c,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_c,V_f1_2,V_f2_2),V_nat_2)),
file('theBenchmark.p',fact_nat__rec__Suc) ).
fof(fact_eq__special_I3_J,axiom,
! [V_x_2,T_c] :
( class_Int_Onumber__ring(T_c)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) = c_Groups_Ozero__class_Ozero(T_c)
<=> c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c] :
( class_Int_Onumber__ring(T_c)
=> ( c_Groups_Ozero__class_Ozero(T_c) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2)
<=> c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_power__number__of__odd__number__of,axiom,
! [V_v_2,V_w_2,T_c] :
( class_Int_Onumber__ring(T_c)
=> ( ( ~ 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_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c) )
& ( 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_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c,T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_c),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)))),c_COMBI(T_c))) ) ) ),
file('theBenchmark.p',fact_power__number__of__odd__number__of) ).
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_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_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_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_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_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_I46_J,axiom,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
file('theBenchmark.p',fact_rel__simps_I46_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_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_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_iszero__def,axiom,
! [V_z_2,T_c] :
( class_Rings_Osemiring__1(T_c)
=> ( c_Int_Oiszero(T_c,V_z_2)
<=> V_z_2 = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_iszero__def) ).
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_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_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_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_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_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_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_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_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_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_eq__special_I2_J,axiom,
! [V_y_2,T_c] :
( class_Int_Onumber__ring(T_c)
=> ( c_Groups_Oone__class_Oone(T_c) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2)
<=> c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_eq__special_I4_J,axiom,
! [V_x_2,T_c] :
( class_Int_Onumber__ring(T_c)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) = c_Groups_Oone__class_Oone(T_c)
<=> c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_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_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_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__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_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_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_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_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_c] :
( ( class_Rings_Olinordered__idom(T_c)
& class_Int_Onumber__ring(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Oone__class_Oone(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c] :
( ( class_Rings_Olinordered__idom(T_c)
& class_Int_Onumber__ring(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Oone__class_Oone(T_c)))
<=> 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_I4_J,axiom,
! [V_x_2,T_c] :
( ( class_Rings_Olinordered__idom(T_c)
& class_Int_Onumber__ring(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Oone__class_Oone(T_c)))
<=> 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_less__special_I2_J,axiom,
! [V_y_2,T_c] :
( ( class_Rings_Olinordered__idom(T_c)
& class_Int_Onumber__ring(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Oone__class_Oone(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_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_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_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_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_eq__number__of__eq,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Int_Onumber__ring(T_c)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2)
<=> c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_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_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_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_power__number__of__odd,axiom,
! [V_z_2,V_w_2,T_c] :
( class_Int_Onumber__ring(T_c)
=> ( ( ~ 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_c),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_c) )
& ( 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_c),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_c,T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_c),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Groups_Otimes__class_Otimes(T_c),V_z_2))),c_COMBI(T_c))) ) ) ),
file('theBenchmark.p',fact_power__number__of__odd) ).
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_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_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_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_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_Bit0__Pls,axiom,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
file('theBenchmark.p',fact_Bit0__Pls) ).
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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_iszero__number__of__Bit0,axiom,
! [V_w_2,T_c] :
( ( class_Int_Oring__char__0(T_c)
& class_Int_Onumber__ring(T_c) )
=> ( c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),c_Int_OBit0(V_w_2)))
<=> c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) ) ),
file('theBenchmark.p',fact_iszero__number__of__Bit0) ).
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_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_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_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_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_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__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_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_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_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_power__number__of__even,axiom,
! [V_w_2,V_z_2,T_c] :
( class_Int_Onumber__ring(T_c)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c,T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),c_Groups_Otimes__class_Otimes(T_c)),c_COMBI(T_c))) ),
file('theBenchmark.p',fact_power__number__of__even) ).
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_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_power__number__of__even__number__of,axiom,
! [V_w_2,V_v_2,T_c] :
( class_Int_Onumber__ring(T_c)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c,T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),c_Groups_Otimes__class_Otimes(T_c)),c_COMBI(T_c))) ),
file('theBenchmark.p',fact_power__number__of__even__number__of) ).
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_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_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__eq__power2,axiom,
! [V_a_2,T_c] :
( class_Rings_Oring__1__no__zero__divisors(T_c)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_zero__eq__power2) ).
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_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,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_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_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,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_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_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_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_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_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__iff,axiom,
! [V_r_2,T_c] :
( ( class_Int_Onumber__ring(T_c)
& class_Fields_Olinordered__field__inverse__zero(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_r_2)) ) ),
file('theBenchmark.p',fact_half__gt__zero__iff) ).
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_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_zero__less__power2,axiom,
! [V_a_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c) ) ),
file('theBenchmark.p',fact_zero__less__power2) ).
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_sum__power2__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),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_c)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_c)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
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_c] :
( class_Rings_Oring__1__no__zero__divisors(T_c)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c)
<=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Groups_Oone__class_Oone(T_c))
| V_a_2 = c_Groups_Oone__class_Oone(T_c) ) ) ),
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__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__le__zero__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),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_c)))
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_c)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
file('theBenchmark.p',fact_sum__power2__le__zero__iff) ).
fof(fact_sum__power2__gt__zero__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Rings_Olinordered__idom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),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_c)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_c) ) ) ),
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_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_of__int__num,axiom,
! [V_k_2,T_c] :
( class_Rings_Oring__1(T_c)
=> ( ( 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_c),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_c,T_c)),tc_fun(tc_Int_Oint,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),T_c),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_c,T_c)),tc_fun(tc_Int_Oint,T_c)),tc_Int_Oint),c_COMBB(tc_fun(T_c,T_c),T_c,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,T_c),T_c),tc_Int_Oint),c_HOL_OLet(T_c,T_c)),c_Int_Oring__1__class_Oof__int(T_c)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_c,T_c),tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,T_c)),tc_Int_Oint),c_COMBS(T_c,T_c,T_c)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_c,T_c),tc_fun(T_c,tc_fun(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_fun(T_c,T_c))),tc_Int_Oint),c_COMBB(T_c,tc_fun(T_c,T_c),T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),tc_Int_Oint),c_If(T_c)),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_c,T_c,T_c),c_Groups_Oplus__class_Oplus(T_c)),c_COMBI(T_c))))),hAPP(hAPP(c_COMBC(T_c,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_c),c_Groups_Oplus__class_Oplus(T_c)),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),c_Groups_Oplus__class_Oplus(T_c)),c_COMBI(T_c)))),c_Groups_Oone__class_Oone(T_c))))),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_c),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),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_c),V_k_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
file('theBenchmark.p',fact_of__int__num) ).
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_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_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_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_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_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_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_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_Bit1__Min,axiom,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
file('theBenchmark.p',fact_Bit1__Min) ).
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_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_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_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_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_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_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_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_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_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_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_pred__Pls,axiom,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
file('theBenchmark.p',fact_pred__Pls) ).
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_pred__Min,axiom,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
file('theBenchmark.p',fact_pred__Min) ).
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_succ__Min,axiom,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
file('theBenchmark.p',fact_succ__Min) ).
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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_inj__graph,axiom,
! [T_d,T_c] : c_Fun_Oinj__on(tc_fun(T_c,T_d),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,T_d)),c_Set_OCollect(tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,T_d)),c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool)),hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBC(T_d,T_d,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,T_d),tc_HOL_Obool))),
file('theBenchmark.p',fact_inj__graph) ).
fof(fact_Nitpick_Oprod__def,axiom,
! [V_B_2,V_A_2,T_d,T_c] : c_Nitpick_Oprod(T_c,T_d,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),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(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2)))),
file('theBenchmark.p',fact_Nitpick_Oprod__def) ).
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_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_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_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_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_Nats__number__of,axiom,
! [V_w_2,T_c] :
( class_Int_Onumber__ring(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_c))) ) ),
file('theBenchmark.p',fact_Nats__number__of) ).
fof(fact_sup__Un__eq2,axiom,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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_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_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_R_2),V_S_2))) ),
file('theBenchmark.p',fact_sup__Un__eq2) ).
fof(fact_pred__subset__eq2,axiom,
! [V_S_2,V_R_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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_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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_R_2),V_S_2)) ),
file('theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact_bot__empty__eq2,axiom,
! [V_y_2,V_x_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_bot__empty__eq2) ).
fof(fact_pred__equals__eq2,axiom,
! [V_S_2,V_R_2,T_d,T_c] :
( 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_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_R_2 = V_S_2 ),
file('theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_inf__Int__eq2,axiom,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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_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_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_R_2),V_S_2))) ),
file('theBenchmark.p',fact_inf__Int__eq2) ).
fof(fact_congruentD,axiom,
! [V_z_2,V_y_2,V_f_2,V_r_2,T_d,T_c] :
( c_Equiv__Relations_Ocongruent(T_c,T_d,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),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_congruent2D,axiom,
! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_e,T_d,T_c] :
( c_Equiv__Relations_Ocongruent2(T_c,T_d,T_e,V_r1_2,V_r2_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),V_y1_2),V_z1_2)),V_r1_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_d),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_Image__iff,axiom,
! [V_A_2,V_r_2,T_d,V_b_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),V_A_2)))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_x),V_b_2)),V_r_2))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_Image__iff) ).
fof(fact_rev__ImageI,axiom,
! [V_r_2,V_b_2,T_d,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(c_Relation_OImage(T_c,T_d,V_r_2),V_A_2))) ) ),
file('theBenchmark.p',fact_rev__ImageI) ).
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_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_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_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_INF__INT__eq2,axiom,
! [V_y_2,V_x_2,V_r_2,T_e,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),T_c),hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_d),c_COMBC(T_e,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),T_d),hAPP(c_COMBB(tc_prod(T_d,T_e),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_d,T_e)))),c_Product__Type_OPair(T_d,T_e))))),V_r_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,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_e,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),T_c),hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_d),c_COMBC(T_e,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),T_d),hAPP(c_COMBB(tc_prod(T_d,T_e),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_d,T_e)))),c_Product__Type_OPair(T_d,T_e))))),V_r_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2))) ),
file('theBenchmark.p',fact_SUP__UN__eq2) ).
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_Nats__0,axiom,
! [T_c] :
( class_Rings_Osemiring__1(T_c)
=> hBOOL(hAPP(hAPP(c_member(T_c),c_Groups_Ozero__class_Ozero(T_c)),c_Nat_Osemiring__1__class_ONats(T_c))) ),
file('theBenchmark.p',fact_Nats__0) ).
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_Nats__add,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Rings_Osemiring__1(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Nat_Osemiring__1__class_ONats(T_c)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Nat_Osemiring__1__class_ONats(T_c)))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_c))) ) ) ),
file('theBenchmark.p',fact_Nats__add) ).
fof(fact_Nats__mult,axiom,
! [V_b_2,V_a_2,T_c] :
( class_Rings_Osemiring__1(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Nat_Osemiring__1__class_ONats(T_c)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Nat_Osemiring__1__class_ONats(T_c)))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_c))) ) ) ),
file('theBenchmark.p',fact_Nats__mult) ).
fof(fact_Nats__1,axiom,
! [T_c] :
( class_Rings_Osemiring__1(T_c)
=> hBOOL(hAPP(hAPP(c_member(T_c),c_Groups_Oone__class_Oone(T_c)),c_Nat_Osemiring__1__class_ONats(T_c))) ),
file('theBenchmark.p',fact_Nats__1) ).
fof(fact_of__nat__in__Nats,axiom,
! [V_n_2,T_c] :
( class_Rings_Osemiring__1(T_c)
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_c))) ),
file('theBenchmark.p',fact_of__nat__in__Nats) ).
fof(fact_Image__singleton__iff,axiom,
! [V_a_2,V_r_2,T_d,V_b_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_a_2),V_b_2)),V_r_2)) ),
file('theBenchmark.p',fact_Image__singleton__iff) ).
fof(fact_equiv__class__eq,axiom,
! [V_b_2,V_a_2,V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_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_a_2),V_b_2)),V_r_2))
=> hAPP(c_Relation_OImage(T_c,T_c,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_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_equiv__class__eq) ).
fof(fact_quotient__eqI,axiom,
! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_Y_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2))
=> V_X_2 = V_Y_2 ) ) ) ) ) ),
file('theBenchmark.p',fact_quotient__eqI) ).
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_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_Y_2))
=> ( V_X_2 = V_Y_2
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_quotient__eq__iff) ).
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_Image__singleton,axiom,
! [V_a_2,V_r_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_c),c_member(tc_prod(T_d,T_c))),hAPP(c_Product__Type_OPair(T_d,T_c),V_a_2))),V_r_2)),
file('theBenchmark.p',fact_Image__singleton) ).
fof(fact_eq__equiv__class,axiom,
! [V_A_2,V_b_2,V_a_2,V_r_2,T_c] :
( hAPP(c_Relation_OImage(T_c,T_c,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_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
=> ( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_eq__equiv__class) ).
fof(fact_eq__equiv__class__iff,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_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(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) ) ) ) ),
file('theBenchmark.p',fact_eq__equiv__class__iff) ).
fof(fact_equiv__class__eq__iff,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_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_x_2),V_y_2)),V_r_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))
& hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) ) ),
file('theBenchmark.p',fact_equiv__class__eq__iff) ).
fof(fact_equiv__class__subset,axiom,
! [V_b_2,V_a_2,V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_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_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,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_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_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(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),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_x_2),V_y_2)),V_r_2)) ) ) ) ),
file('theBenchmark.p',fact_eq__equiv__class__iff2) ).
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_subset__equiv__class,axiom,
! [V_a_2,V_b_2,V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_c,T_c,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(T_c),V_b_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_subset__equiv__class) ).
fof(fact_equiv__class__nondisjoint,axiom,
! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,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_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_equiv__class__nondisjoint) ).
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_pair__imageI,axiom,
! [V_f_2,T_e,V_A_2,V_b_2,V_a_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_e),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),T_e,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_f_2)),V_A_2))) ),
file('theBenchmark.p',fact_pair__imageI) ).
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_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_sup2CI,axiom,
! [T_d,T_c,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_c,tc_fun(T_d,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_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,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_inf2E,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,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_inf2I,axiom,
! [T_d,T_c,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_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_inf2I) ).
fof(fact_mem__splitI,axiom,
! [T_e,T_d,V_b_2,V_a_2,V_c_2,V_z_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(T_c,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)))) ),
file('theBenchmark.p',fact_mem__splitI) ).
fof(fact_splitI,axiom,
! [T_d,T_c,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_c,T_d,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))) ),
file('theBenchmark.p',fact_splitI) ).
fof(fact_prod__caseI,axiom,
! [T_d,T_c,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_c,T_d,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))) ),
file('theBenchmark.p',fact_prod__caseI) ).
fof(fact_bot2E,axiom,
! [V_y_2,V_x_2,T_d,T_c] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_x_2),V_y_2)),
file('theBenchmark.p',fact_bot2E) ).
fof(fact_splitD_H,axiom,
! [V_c_2,V_b_2,V_a_2,V_R_2,T_e,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_e,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_c_2))
=> hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ),
file('theBenchmark.p',fact_splitD_H) ).
fof(fact_swap__inj__on,axiom,
! [V_A_2,T_d,T_c] : c_Fun_Oinj__on(tc_prod(T_c,T_d),tc_prod(T_d,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,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_A_2),
file('theBenchmark.p',fact_swap__inj__on) ).
fof(fact_sup2I2,axiom,
! [V_A_2,T_d,T_c,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_c,tc_fun(T_d,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_d,T_c,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_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_sup2I1) ).
fof(fact_rev__predicate2D,axiom,
! [V_Qa_2,T_d,T_c,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_c,tc_fun(T_d,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_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_fun(T_d,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_inf2D2,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,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_inf2D1,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,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_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_Pair__eq,axiom,
! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_d,T_c] :
( hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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_split__paired__All,axiom,
! [T_d,T_c,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_c,T_d),B_a),B_b))) ),
file('theBenchmark.p',fact_split__paired__All) ).
fof(fact_split__weak__cong,axiom,
! [V_c_2,T_e,T_d,T_c,V_q_2,V_p_2] :
( V_p_2 = V_q_2
=> hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_c_2),V_q_2) ),
file('theBenchmark.p',fact_split__weak__cong) ).
fof(fact_split__twice,axiom,
! [V_p_2,V_g_2,T_g,T_f,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_f,T_g,tc_prod(T_d,T_e)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_f,T_g,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(T_g,T_c),T_f),hAPP(c_COMBB(tc_prod(T_d,T_e),T_c,T_g),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2))),V_g_2)),V_p_2),
file('theBenchmark.p',fact_split__twice) ).
fof(fact_split__conv,axiom,
! [V_b_2,V_a_2,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),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_prod_Osimps_I2_J,axiom,
! [V_b_2,V_a_2,V_f1_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),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_splitD,axiom,
! [V_b_2,V_a_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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_split__eta,axiom,
! [V_f_2,T_e,T_d,T_c] : hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_e),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_e,T_d),V_f_2)),c_Product__Type_OPair(T_c,T_d))) = V_f_2,
file('theBenchmark.p',fact_split__eta) ).
fof(fact_The__split__eq,axiom,
! [V_y_2,V_x_2,T_d,T_c] : c_HOL_OThe(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2),
file('theBenchmark.p',fact_The__split__eq) ).
fof(fact_split__paired__The,axiom,
! [V_Pa_2,T_d,T_c] : c_HOL_OThe(tc_prod(T_c,T_d),V_Pa_2) = c_HOL_OThe(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_HOL_Obool,T_d),V_Pa_2)),c_Product__Type_OPair(T_c,T_d)))),
file('theBenchmark.p',fact_split__paired__The) ).
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_in__rel__def,axiom,
! [V_y_2,V_x_2,V_R_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(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)),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_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_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_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_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_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_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_Nitpick_Orefl_H__def,axiom,
! [V_r_2,T_c] :
( c_Nitpick_Orefl_H(T_c,V_r_2)
<=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) ),
file('theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
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_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_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_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_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_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_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__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_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_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_apsnd__conv,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_d,T_e] : hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_e),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),hAPP(V_f_2,V_y_2)),
file('theBenchmark.p',fact_apsnd__conv) ).
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_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_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_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__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_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_UN__equiv__class__inject,axiom,
! [V_Y_2,V_X_2,V_f_2,T_d,V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> ( c_Equiv__Relations_Ocongruent(T_c,tc_fun(T_d,tc_HOL_Obool),V_r_2,V_f_2)
=> ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_Y_2),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_c),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_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_r_2)) ) ) )
=> V_X_2 = V_Y_2 ) ) ) ) ) ),
file('theBenchmark.p',fact_UN__equiv__class__inject) ).
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_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_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_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_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_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_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_apsnd__eq__conv,axiom,
! [V_g_2,V_x_2,V_f_2,T_c,T_d,T_e] :
( hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_g_2),V_x_2)
<=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_e),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_e),V_x_2)) ),
file('theBenchmark.p',fact_apsnd__eq__conv) ).
fof(fact_snd__apsnd,axiom,
! [V_x_2,V_f_2,T_e,T_c,T_d] : hAPP(c_Product__Type_Osnd(T_d,T_c),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)),
file('theBenchmark.p',fact_snd__apsnd) ).
fof(fact_snd__def,axiom,
! [V_p_2,T_c,T_d] : hAPP(c_Product__Type_Osnd(T_d,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_c),hAPP(c_COMBK(tc_fun(T_c,T_c),T_d),c_COMBI(T_c))),V_p_2),
file('theBenchmark.p',fact_snd__def) ).
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_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_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_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_accp__subset,axiom,
! [V_R2_2,V_R1_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),V_R1_2),V_R2_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_c,V_R2_2)),c_Wellfounded_Oaccp(T_c,V_R1_2))) ),
file('theBenchmark.p',fact_accp__subset) ).
fof(fact_irrefl__def,axiom,
! [V_r_2,T_c] :
( c_Relation_Oirrefl(T_c,V_r_2)
<=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) ),
file('theBenchmark.p',fact_irrefl__def) ).
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_accp_Osimps,axiom,
! [V_a_2,V_r_2,T_c] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,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_c,V_r_2),B_x)) ) ),
file('theBenchmark.p',fact_accp_Osimps) ).
fof(fact_accp_Oequations,axiom,
! [V_a_2,V_r_2,T_c] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,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_c,V_r_2),B_x)) ) ),
file('theBenchmark.p',fact_accp_Oequations) ).
fof(fact_accp__downward,axiom,
! [V_a_2,V_b_2,V_r_2,T_c] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,V_r_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,V_r_2),V_a_2)) ) ),
file('theBenchmark.p',fact_accp__downward) ).
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_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_in__measure,axiom,
! [V_f_2,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_c),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_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_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_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_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_fst__apsnd,axiom,
! [V_x_2,V_f_2,T_e,T_d,T_c] : hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_c,T_e),V_x_2),
file('theBenchmark.p',fact_fst__apsnd) ).
fof(fact_fst__def,axiom,
! [V_p_2,T_d,T_c] : hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_c),c_COMBK(T_c,T_d)),V_p_2),
file('theBenchmark.p',fact_fst__def) ).
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_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__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_Pair__fst__snd__eq,axiom,
! [T_d,T_c,V_t_2,V_s_2] :
( V_s_2 = V_t_2
<=> ( hAPP(c_Product__Type_Osnd(T_c,T_d),V_s_2) = hAPP(c_Product__Type_Osnd(T_c,T_d),V_t_2)
& hAPP(c_Product__Type_Ofst(T_c,T_d),V_s_2) = hAPP(c_Product__Type_Ofst(T_c,T_d),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_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_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_prod__case__beta,axiom,
! [V_p_2,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_p_2)),hAPP(c_Product__Type_Osnd(T_d,T_e),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_split__comp__eq,axiom,
! [V_g_2,V_f_2,T_f,T_e,T_d,T_c] : hAPP(hAPP(c_COMBS(tc_prod(T_c,T_d),T_d,T_e),hAPP(hAPP(c_COMBB(T_f,tc_fun(T_d,T_e),tc_prod(T_c,T_d)),V_f_2),hAPP(hAPP(c_COMBB(T_c,T_f,tc_prod(T_c,T_d)),V_g_2),c_Product__Type_Ofst(T_c,T_d)))),c_Product__Type_Osnd(T_c,T_d)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),hAPP(hAPP(c_COMBB(T_f,tc_fun(T_d,T_e),T_c),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_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_z_2)),hAPP(c_Product__Type_Osnd(T_d,T_e),V_z_2)),
file('theBenchmark.p',fact_split__beta) ).
fof(fact_split__def,axiom,
! [V_p_2,V_c_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_p_2)),hAPP(c_Product__Type_Osnd(T_d,T_e),V_p_2)),
file('theBenchmark.p',fact_split__def) ).
fof(fact_The__split,axiom,
! [V_Pa_2,T_d,T_c] : c_HOL_OThe(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_c,T_d),hAPP(hAPP(c_COMBS(tc_prod(T_c,T_d),T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_HOL_Obool),tc_prod(T_c,T_d)),V_Pa_2),c_Product__Type_Ofst(T_c,T_d))),c_Product__Type_Osnd(T_c,T_d))),
file('theBenchmark.p',fact_The__split) ).
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_d,T_c] : c_Product__Type_Oprod_Oprod__size(T_c,T_d,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_c,T_d),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_d),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_c,T_d,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_d,T_c),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_d,T_c),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)))) ),
file('theBenchmark.p',fact_exI__realizer) ).
fof(fact_conjI__realizer,axiom,
! [T_d,T_c,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_c,T_d),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_p_2),V_q_2))))
& hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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_inv__image__def,axiom,
! [V_f_2,V_r_2,T_c,T_d] : hAPP(hAPP(c_Relation_Oinv__image(T_d,T_c),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_d),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_d,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_d,T_d)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_d),tc_fun(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_d,T_d)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_d),tc_fun(T_c,tc_prod(T_d,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_d)),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_prod(T_d,T_d))),T_c),c_COMBB(T_d,tc_prod(T_d,T_d),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_prod(T_d,T_d)),T_c),c_Product__Type_OPair(T_d,T_d)),V_f_2))),V_f_2)))),V_r_2))),
file('theBenchmark.p',fact_inv__image__def) ).
fof(fact_mlex__leq,axiom,
! [V_R_2,T_c,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_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_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),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_c,V_f_2,V_R_2))) ) ),
file('theBenchmark.p',fact_mlex__leq) ).
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_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_in__inv__image,axiom,
! [V_f_2,V_r_2,T_d,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_d,T_c),V_r_2),V_f_2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_d),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_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_mlex__less,axiom,
! [V_R_2,T_c,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_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_c,V_f_2,V_R_2))) ),
file('theBenchmark.p',fact_mlex__less) ).
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_rp__inv__image__def,axiom,
! [T_d,T_c] : c_FunDef_Orp__inv__image(T_c,T_d) = hAPP(c_Product__Type_Oprod_Oprod__case(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(T_d,T_c),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(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_fun(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)),tc_fun(tc_fun(T_d,T_c),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool))))),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)),tc_fun(tc_fun(T_d,T_c),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool))),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)),tc_fun(tc_fun(T_d,T_c),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_COMBS(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)),tc_fun(tc_fun(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool))),tc_fun(T_d,T_c)),c_Product__Type_OPair(tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)))),c_Relation_Oinv__image(T_c,T_d))))),c_Relation_Oinv__image(T_c,T_d))),
file('theBenchmark.p',fact_rp__inv__image__def) ).
fof(fact_finite__psubset__def,axiom,
! [T_c] : c_Wellfounded_Ofinite__psubset(T_c) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBS(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_c)))),
file('theBenchmark.p',fact_finite__psubset__def) ).
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_in__finite__psubset,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_c)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_in__finite__psubset) ).
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_c,T_e,T_d] : c_Product__Type_Oprod_Oprod__rec(T_d,T_e,T_c,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),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_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_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_c,T_d,V_r_2,V_s_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_d),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_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_a_H_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_in__lex__prod) ).
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_same__fstI,axiom,
! [T_c,V_R_2,V_y_2,V_y_H_2,T_d,V_x_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,V_x_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_d),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_c,T_d,V_Pa_2,V_R_2))) ) ),
file('theBenchmark.p',fact_same__fstI) ).
fof(fact_equivp__equiv,axiom,
! [V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_A_2)
<=> c_Equiv__Relations_Oequivp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_A_2)) ),
file('theBenchmark.p',fact_equivp__equiv) ).
fof(fact_apsnd__apfst,axiom,
! [V_x_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e] : hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_f,T_c,T_e,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_f,T_e),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_f,T_e),V_x_2))),
file('theBenchmark.p',fact_apsnd__apfst) ).
fof(fact_apfst__conv,axiom,
! [V_y_2,V_x_2,V_f_2,T_d,T_c,T_e] : hAPP(c_Product__Type_Oapfst(T_e,T_c,T_d,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_e,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,V_x_2)),V_y_2),
file('theBenchmark.p',fact_apfst__conv) ).
fof(fact_apfst__eq__conv,axiom,
! [V_g_2,V_x_2,V_f_2,T_d,T_c,T_e] :
( hAPP(c_Product__Type_Oapfst(T_e,T_c,T_d,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_e,T_c,T_d,V_g_2),V_x_2)
<=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2)) ),
file('theBenchmark.p',fact_apfst__eq__conv) ).
fof(fact_fst__apfst,axiom,
! [V_x_2,V_f_2,T_e,T_d,T_c] : hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(c_Product__Type_Oapfst(T_e,T_c,T_d,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2)),
file('theBenchmark.p',fact_fst__apfst) ).
fof(fact_snd__apfst,axiom,
! [V_x_2,V_f_2,T_e,T_c,T_d] : hAPP(c_Product__Type_Osnd(T_d,T_c),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_e,T_c),V_x_2),
file('theBenchmark.p',fact_snd__apfst) ).
fof(fact_identity__equivp,axiom,
! [T_c] : c_Equiv__Relations_Oequivp(T_c,c_fequal),
file('theBenchmark.p',fact_identity__equivp) ).
fof(fact_equivp__def,axiom,
! [V_R_2,T_c] :
( c_Equiv__Relations_Oequivp(T_c,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_equivp__reflp,axiom,
! [V_x_2,V_R_2,T_c] :
( c_Equiv__Relations_Oequivp(T_c,V_R_2)
=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
file('theBenchmark.p',fact_equivp__reflp) ).
fof(fact_equivp__symp,axiom,
! [V_y_2,V_x_2,V_R_2,T_c] :
( c_Equiv__Relations_Oequivp(T_c,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__transp,axiom,
! [V_z_2,V_y_2,V_x_2,V_R_2,T_c] :
( c_Equiv__Relations_Oequivp(T_c,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_apsnd__apfst__commute,axiom,
! [V_p_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e] : hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_f,T_c,T_e,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_f,T_c,T_d,V_g_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_f,V_f_2),V_p_2)),
file('theBenchmark.p',fact_apsnd__apfst__commute) ).
fof(fact_apfst__apsnd,axiom,
! [V_x_2,V_g_2,T_f,V_f_2,T_d,T_c,T_e] : hAPP(c_Product__Type_Oapfst(T_e,T_c,T_d,V_f_2),hAPP(c_Product__Type_Oapsnd(T_f,T_d,T_e,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_e,T_f),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_e,T_f),V_x_2))),
file('theBenchmark.p',fact_apfst__apsnd) ).
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_ImageE,axiom,
! [V_A_2,V_r_2,T_d,V_b_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),V_A_2)))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_x),V_b_2)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_ImageE) ).
fof(fact_mlex__prod__def,axiom,
! [V_R_2,V_f_2,T_c] : c_Wellfounded_Omlex__prod(T_c,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_c),T_c),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_c,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_c,T_c,tc_prod(tc_Nat_Onat,T_c)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_c,tc_prod(tc_Nat_Onat,T_c)),T_c),c_Product__Type_OPair(tc_Nat_Onat,T_c)),V_f_2)),c_COMBI(T_c))),
file('theBenchmark.p',fact_mlex__prod__def) ).
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_measure__def,axiom,
! [T_c] : c_Wellfounded_Omeasure(T_c) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_c),c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_measure__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_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_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_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_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_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_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_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_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_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_Field__insert,axiom,
! [V_r_2,V_b_2,V_a_2,T_c] : hAPP(c_Relation_OField(T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_c),V_r_2)),
file('theBenchmark.p',fact_Field__insert) ).
fof(fact_Field__Union,axiom,
! [V_R_2,T_c] : hAPP(c_Relation_OField(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),c_Relation_OField(T_c)),V_R_2)),
file('theBenchmark.p',fact_Field__Union) ).
fof(fact_Field__empty,axiom,
! [T_c] : hAPP(c_Relation_OField(T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Field__empty) ).
fof(fact_mono__Field,axiom,
! [V_s_2,V_r_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OField(T_c),V_r_2)),hAPP(c_Relation_OField(T_c),V_s_2))) ),
file('theBenchmark.p',fact_mono__Field) ).
fof(fact_Field__Un,axiom,
! [V_s_2,V_r_2,T_c] : hAPP(c_Relation_OField(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OField(T_c),V_r_2)),hAPP(c_Relation_OField(T_c),V_s_2)),
file('theBenchmark.p',fact_Field__Un) ).
fof(fact_finite__Field,axiom,
! [V_r_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),V_r_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_OField(T_c),V_r_2))) ),
file('theBenchmark.p',fact_finite__Field) ).
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_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_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_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_Id__on__def,axiom,
! [V_A_2,T_c] : c_Relation_OId__on(T_c,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,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_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBS(T_c,T_c,tc_prod(T_c,T_c)),c_Product__Type_OPair(T_c,T_c)),c_COMBI(T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),
file('theBenchmark.p',fact_Id__on__def) ).
fof(fact_Id__on__def_H,axiom,
! [V_A_2,T_c] : c_Relation_OId__on(T_c,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),c_fequal))),V_A_2)),
file('theBenchmark.p',fact_Id__on__def_H) ).
fof(fact_Id__on__empty,axiom,
! [T_c] : c_Relation_OId__on(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),
file('theBenchmark.p',fact_Id__on__empty) ).
fof(fact_Image__Id__on,axiom,
! [V_B_2,V_A_2,T_c] : hAPP(c_Relation_OImage(T_c,T_c,c_Relation_OId__on(T_c,V_A_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),
file('theBenchmark.p',fact_Image__Id__on) ).
fof(fact_Id__on__eqI,axiom,
! [V_A_2,T_c,V_b_2,V_a_2] :
( V_a_2 = V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Relation_OId__on(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Relation_OId__on(T_c,V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
& V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_Id__on__iff) ).
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_max__ext__additive,axiom,
! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_c,V_R_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_c,V_R_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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))),c_Wellfounded_Omax__ext(T_c,V_R_2))) ) ),
file('theBenchmark.p',fact_max__ext__additive) ).
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_max__extp__max__ext__eq,axiom,
! [V_xa_2,V_x_2,V_R_2,T_c] :
( c_Wellfounded_Omax__extp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_R_2),V_x_2,V_xa_2)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_c,V_R_2))) ),
file('theBenchmark.p',fact_max__extp__max__ext__eq) ).
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_rp__inv__image__rp,axiom,
! [V_f_2,T_d,V_Pa_2,T_c] :
( c_FunDef_Oreduction__pair(T_c,V_Pa_2)
=> c_FunDef_Oreduction__pair(T_d,hAPP(hAPP(c_FunDef_Orp__inv__image(T_c,T_d),V_Pa_2),V_f_2)) ),
file('theBenchmark.p',fact_rp__inv__image__rp) ).
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_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_Id__onE,axiom,
! [V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_c_2),c_Relation_OId__on(T_c,V_A_2)))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x) ) ),
file('theBenchmark.p',fact_Id__onE) ).
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_of__int,axiom,
! [V_j_2,V_i_2,T_c] :
( class_Rings_Oring__1(T_c)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_c),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_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),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_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_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_code__numeral_Osimps_I5_J,axiom,
! [V_code__numeral_2,V_f2_2,V_f1_2,T_c] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_c,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_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_code__numeral_Osimps_I4_J,axiom,
! [V_f2_2,V_f1_2,T_c] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_c,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_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_accp__acc__eq,axiom,
! [V_x_2,V_r_2,T_c] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Wellfounded_Oacc(T_c,V_r_2))) ),
file('theBenchmark.p',fact_accp__acc__eq) ).
fof(fact_rel__comp__def,axiom,
! [V_s_2,V_r_2,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_e))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_e,tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_c),c_COMBS(T_e,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(T_e,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_e),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_c),c_COMBC(T_e,tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_e)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_e),tc_fun(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_c,T_e)))),c_Product__Type_OPair(T_c,T_e)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_d),c_COMBC(T_e,tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_e,T_d)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_d),hAPP(c_COMBB(tc_prod(T_e,T_d),tc_fun(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_e,T_d)))),hAPP(c_COMBC(T_e,T_d,tc_prod(T_e,T_d)),c_Product__Type_OPair(T_e,T_d))))),V_s_2))))),
file('theBenchmark.p',fact_rel__comp__def) ).
fof(fact_rel__compI,axiom,
! [V_s_2,V_c_2,T_e,V_r_2,V_b_2,V_a_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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),V_b_2),V_c_2)),V_s_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_e),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_e),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_f,V_s_2,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_f,tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_f,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),T_f),hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),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_f,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_f,tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_f,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),T_f),c_Relation_Orel__comp(T_c,T_e,T_d)),V_r_2)),V_s_2)),
file('theBenchmark.p',fact_rel__comp__UNION__distrib2) ).
fof(fact_rel__comp__empty1,axiom,
! [V_R_2,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),
file('theBenchmark.p',fact_rel__comp__empty1) ).
fof(fact_rel__comp__empty2,axiom,
! [V_R_2,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),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_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_e,T_d),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),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_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_e),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_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_T_2),V_R_2)),
file('theBenchmark.p',fact_rel__comp__distrib2) ).
fof(fact_rel__comp__mono,axiom,
! [V_s_2,V_s_H_2,T_e,V_r_2,V_r_H_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_H_2),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool)),V_s_H_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_e),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_e),V_r_2),V_s_2))) ) ),
file('theBenchmark.p',fact_rel__comp__mono) ).
fof(fact_O__assoc,axiom,
! [V_T_2,V_S_2,V_R_2,T_f,T_d,T_e,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_f,T_e),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_f,T_d),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_f,T_e,T_d),V_S_2),V_T_2)),
file('theBenchmark.p',fact_O__assoc) ).
fof(fact_union__comp__emptyL,axiom,
! [V_B_2,V_C_2,V_A_2,T_c] :
( hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))
=> ( hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))
=> hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_union__comp__emptyL) ).
fof(fact_union__comp__emptyR,axiom,
! [V_C_2,V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))
=> ( hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))
=> hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_union__comp__emptyR) ).
fof(fact_acc__subset,axiom,
! [V_R2_2,V_R1_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R1_2),V_R2_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Wellfounded_Oacc(T_c,V_R2_2)),c_Wellfounded_Oacc(T_c,V_R1_2))) ),
file('theBenchmark.p',fact_acc__subset) ).
fof(fact_acc_Osimps,axiom,
! [V_r_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Wellfounded_Oacc(T_c,V_r_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),V_a_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Wellfounded_Oacc(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_acc_Osimps) ).
fof(fact_acc__downward,axiom,
! [V_a_2,V_r_2,V_b_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Wellfounded_Oacc(T_c,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_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Wellfounded_Oacc(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downward) ).
fof(fact_max__ext__compat,axiom,
! [V_S_2,V_R_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),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_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_c,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_c,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_c,V_R_2))) ),
file('theBenchmark.p',fact_max__ext__compat) ).
fof(fact_min__ext__compat,axiom,
! [V_S_2,V_R_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),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_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_c,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_c,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_c,V_R_2))) ),
file('theBenchmark.p',fact_min__ext__compat) ).
fof(fact_type__definition_OAbs__image,axiom,
! [V_A_2,V_Abs_2,V_Rep_2,T_d,T_c] :
( c_Typedef_Otype__definition(T_c,T_d,V_Rep_2,V_Abs_2,V_A_2)
=> hAPP(c_Set_Oimage(T_d,T_c,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,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_d,T_c] :
( c_Typedef_Otype__definition(T_c,T_d,V_Rep_2,V_Abs_2,V_A_2)
=> hAPP(c_Set_Oimage(T_c,T_d,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = V_A_2 ),
file('theBenchmark.p',fact_type__definition_ORep__range) ).
fof(fact_type__definition_OAbs__inject,axiom,
! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_d,T_c] :
( c_Typedef_Otype__definition(T_c,T_d,V_Rep_2,V_Abs_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_d),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_ORep__inject,axiom,
! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_d,T_c] :
( c_Typedef_Otype__definition(T_c,T_d,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_d,T_c] :
( c_Typedef_Otype__definition(T_c,T_d,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_type__definition_ORep,axiom,
! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_d,T_c] :
( c_Typedef_Otype__definition(T_c,T_d,V_Rep_2,V_Abs_2,V_A_2)
=> hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_Rep_2,V_x_2)),V_A_2)) ),
file('theBenchmark.p',fact_type__definition_ORep) ).
fof(fact_type__definition_OAbs__inverse,axiom,
! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_d,T_c] :
( c_Typedef_Otype__definition(T_c,T_d,V_Rep_2,V_Abs_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_d),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_pred__comp__rel__comp__eq,axiom,
! [V_y_2,V_x_2,V_s_2,V_r_2,T_e,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_c,T_d,T_e,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_r_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_d),c_COMBC(T_e,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),T_d),hAPP(c_COMBB(tc_prod(T_d,T_e),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_d,T_e)))),c_Product__Type_OPair(T_d,T_e)))),V_s_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_e),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_e),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_c] :
( c_Wellfounded_Owf(T_c,V_R_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),V_S_2)),V_R_2))
=> c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(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)),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_c] :
( c_Wellfounded_Omax__extp(T_c,V_R_2,V_a1_2,V_a2_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_a1_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_a2_2)) ) )
& V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_a2_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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_e,T_d,T_c,V_c_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_c_2))
=> hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_c,T_d,T_e,V_r_2,V_s_2),V_a_2),V_c_2)) ) ),
file('theBenchmark.p',fact_pred__comp_Ointros) ).
fof(fact_wf__empty,axiom,
! [T_c] : c_Wellfounded_Owf(T_c,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),
file('theBenchmark.p',fact_wf__empty) ).
fof(fact_wf__inv__image,axiom,
! [V_f_2,T_d,V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> c_Wellfounded_Owf(T_d,hAPP(hAPP(c_Relation_Oinv__image(T_c,T_d),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_wf__inv__image) ).
fof(fact_wf__lex__prod,axiom,
! [V_rb_2,T_d,V_ra_2,T_c] :
( c_Wellfounded_Owf(T_c,V_ra_2)
=> ( c_Wellfounded_Owf(T_d,V_rb_2)
=> c_Wellfounded_Owf(tc_prod(T_c,T_d),c_Wellfounded_Olex__prod(T_c,T_d,V_ra_2,V_rb_2)) ) ),
file('theBenchmark.p',fact_wf__lex__prod) ).
fof(fact_wf__measure,axiom,
! [V_f_2,T_c] : c_Wellfounded_Owf(T_c,hAPP(c_Wellfounded_Omeasure(T_c),V_f_2)),
file('theBenchmark.p',fact_wf__measure) ).
fof(fact_wf__comp__self,axiom,
! [V_R_2,T_c] :
( c_Wellfounded_Owf(T_c,V_R_2)
<=> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),V_R_2)) ),
file('theBenchmark.p',fact_wf__comp__self) ).
fof(fact_wf__subset,axiom,
! [V_p_2,V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_p_2),V_r_2))
=> c_Wellfounded_Owf(T_c,V_p_2) ) ),
file('theBenchmark.p',fact_wf__subset) ).
fof(fact_min__ext__wf,axiom,
! [V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> c_Wellfounded_Owf(tc_fun(T_c,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_c,V_r_2)) ),
file('theBenchmark.p',fact_min__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__finite__psubset,axiom,
! [T_c] : c_Wellfounded_Owf(tc_fun(T_c,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_c)),
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_e,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_c,T_d,T_e,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__Int2,axiom,
! [V_r_H_2,V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),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_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),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_c] :
( c_Wellfounded_Owf(T_c,V_R_2)
=> c_Wellfounded_Owf(T_c,c_Wellfounded_Omlex__prod(T_c,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_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> c_Wellfounded_Owf(tc_fun(T_c,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_c,V_r_2)) ),
file('theBenchmark.p',fact_max__ext__wf) ).
fof(fact_wf__irrefl,axiom,
! [V_a_2,V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,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_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_c] :
( c_Wellfounded_Owf(T_c,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_a_2),V_x_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_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_c] :
( c_Wellfounded_Owf(T_c,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_a_2),V_x_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_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_c] :
( c_Wellfounded_Owf(T_c,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_a_2),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_wf__not__refl) ).
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_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__acc__iff,axiom,
! [V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
<=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Wellfounded_Oacc(T_c,V_r_2))) ),
file('theBenchmark.p',fact_wf__acc__iff) ).
fof(fact_acc__wfD,axiom,
! [V_x_2,V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Wellfounded_Oacc(T_c,V_r_2))) ),
file('theBenchmark.p',fact_acc__wfD) ).
fof(fact_wf__no__loop,axiom,
! [V_R_2,T_c] :
( hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))
=> c_Wellfounded_Owf(T_c,V_R_2) ),
file('theBenchmark.p',fact_wf__no__loop) ).
fof(fact_wf__union__merge,axiom,
! [V_S_2,V_R_2,T_c] :
( c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),V_S_2))
<=> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),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_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
<=> ~ ? [B_f] :
! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),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_c] :
( c_Wellfounded_Owf(T_c,V_R_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_c,T_c,V_R_2),V_A_2)))
=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_wfE__pf) ).
fof(fact_wf__union__compatible,axiom,
! [V_S_2,V_R_2,T_c] :
( c_Wellfounded_Owf(T_c,V_R_2)
=> ( c_Wellfounded_Owf(T_c,V_S_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),V_S_2)),V_R_2))
=> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ),
file('theBenchmark.p',fact_wf__union__compatible) ).
fof(fact_wf,axiom,
! [T_c] :
( class_Orderings_Owellorder(T_c)
=> c_Wellfounded_Owf(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_c)))) ),
file('theBenchmark.p',fact_wf) ).
fof(fact_reduction__pair__def,axiom,
! [V_Pa_2,T_c] :
( c_FunDef_Oreduction__pair(T_c,V_Pa_2)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2)))
& c_Wellfounded_Owf(T_c,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),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_c] :
( c_FunDef_Oreduction__pair(T_c,V_Pa_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2)))
=> ( c_Wellfounded_Owf(T_c,V_S_2)
=> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),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_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> c_Wellfounded_Owf(tc_List_Olist(T_c),c_List_Olenlex(T_c,V_r_2)) ),
file('theBenchmark.p',fact_wf__lenlex) ).
fof(fact_wf__if__measure,axiom,
! [T_c,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_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_c),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),V_Pa_2))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),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_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_X_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Y_2))
=> ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_X_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_xa)),V_R_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_Y_2)) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_c,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_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> c_Wellfounded_Owf(tc_List_Olist(T_c),c_List_Olex(T_c,V_r_2)) ),
file('theBenchmark.p',fact_wf__lex) ).
fof(fact_wf__lexn,axiom,
! [V_n_2,V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> c_Wellfounded_Owf(tc_List_Olist(T_c),hAPP(c_List_Olexn(T_c,V_r_2),V_n_2)) ),
file('theBenchmark.p',fact_wf__lexn) ).
fof(fact_lex__def,axiom,
! [V_r_2,T_c] : c_List_Olex(T_c,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_c,V_r_2)),
file('theBenchmark.p',fact_lex__def) ).
fof(fact_lexn_Osimps_I1_J,axiom,
! [V_r_2,T_c] : hAPP(c_List_Olexn(T_c,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),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_c,V_R_2,T_d,V_Pa_2] :
( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
=> c_Wellfounded_Owf(T_d,hAPP(V_R_2,B_x)) )
=> c_Wellfounded_Owf(tc_prod(T_c,T_d),c_Recdef_Osame__fst(T_c,T_d,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_Range__Collect__split,axiom,
! [V_Pa_2,T_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),hAPP(c_Set_OCollect(tc_prod(T_d,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d)),hAPP(c_COMBC(T_d,T_c,tc_HOL_Obool),V_Pa_2))),
file('theBenchmark.p',fact_Range__Collect__split) ).
fof(fact_RangeI,axiom,
! [V_r_2,V_b_2,V_a_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(c_Relation_ORange(T_c,T_d),V_r_2))) ),
file('theBenchmark.p',fact_RangeI) ).
fof(fact_Range__Id__on,axiom,
! [V_A_2,T_c] : hAPP(c_Relation_ORange(T_c,T_c),c_Relation_OId__on(T_c,V_A_2)) = V_A_2,
file('theBenchmark.p',fact_Range__Id__on) ).
fof(fact_Range__Diff__subset,axiom,
! [V_B_2,V_A_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_d,T_c),V_A_2)),hAPP(c_Relation_ORange(T_d,T_c),V_B_2))),hAPP(c_Relation_ORange(T_d,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_d,T_c),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_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_d,T_c)),
file('theBenchmark.p',fact_Range__Union) ).
fof(fact_Range__empty__iff,axiom,
! [V_r_2,T_c,T_d] :
( hAPP(c_Relation_ORange(T_d,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
<=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)) ),
file('theBenchmark.p',fact_Range__empty__iff) ).
fof(fact_Range__empty,axiom,
! [T_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Range__empty) ).
fof(fact_Range__Un__eq,axiom,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,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(c_Relation_ORange(T_d,T_c),V_A_2)),hAPP(c_Relation_ORange(T_d,T_c),V_B_2)),
file('theBenchmark.p',fact_Range__Un__eq) ).
fof(fact_finite__Range,axiom,
! [V_r_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),V_r_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Relation_ORange(T_c,T_d),V_r_2))) ),
file('theBenchmark.p',fact_finite__Range) ).
fof(fact_snd__eq__Range,axiom,
! [V_R_2,T_c,T_d] : hAPP(c_Set_Oimage(tc_prod(T_d,T_c),T_c,c_Product__Type_Osnd(T_d,T_c)),V_R_2) = hAPP(c_Relation_ORange(T_d,T_c),V_R_2),
file('theBenchmark.p',fact_snd__eq__Range) ).
fof(fact_Range__iff,axiom,
! [V_r_2,T_d,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Relation_ORange(T_d,T_c),V_r_2)))
<=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_Range__iff) ).
fof(fact_Range__insert,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),hAPP(c_Relation_ORange(T_d,T_c),V_r_2)),
file('theBenchmark.p',fact_Range__insert) ).
fof(fact_Range__Int__subset,axiom,
! [V_B_2,V_A_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_d,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(c_Relation_ORange(T_d,T_c),V_A_2)),hAPP(c_Relation_ORange(T_d,T_c),V_B_2)))),
file('theBenchmark.p',fact_Range__Int__subset) ).
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_RangeP__Range__eq,axiom,
! [V_x_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(c_Predicate_ORangeP(T_c,T_d,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_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(c_Relation_ORange(T_c,T_d),V_r_2))) ),
file('theBenchmark.p',fact_RangeP__Range__eq) ).
fof(fact_RangeP_Ointros,axiom,
! [T_d,T_c,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_c,T_d,V_r_2),V_b_2)) ),
file('theBenchmark.p',fact_RangeP_Ointros) ).
fof(fact_RangeP_Oequations,axiom,
! [V_a2_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(c_Predicate_ORangeP(T_c,T_d,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_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_RangeE,axiom,
! [V_r_2,T_d,V_b_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_d,T_c),V_r_2)))
=> ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_x),V_b_2)),V_r_2)) ),
file('theBenchmark.p',fact_RangeE) ).
fof(fact_wf__Un,axiom,
! [V_s_2,V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> ( c_Wellfounded_Owf(T_c,V_s_2)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_c,T_c),V_r_2)),hAPP(c_Relation_ORange(T_c,T_c),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ),
file('theBenchmark.p',fact_wf__Un) ).
fof(fact_DomainI,axiom,
! [V_r_2,V_b_2,V_a_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2))) ),
file('theBenchmark.p',fact_DomainI) ).
fof(fact_Domain__Id__on,axiom,
! [V_A_2,T_c] : hAPP(c_Relation_ODomain(T_c,T_c),c_Relation_OId__on(T_c,V_A_2)) = V_A_2,
file('theBenchmark.p',fact_Domain__Id__on) ).
fof(fact_Domain__empty__iff,axiom,
! [V_r_2,T_d,T_c] :
( hAPP(c_Relation_ODomain(T_c,T_d),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
<=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)) ),
file('theBenchmark.p',fact_Domain__empty__iff) ).
fof(fact_Domain__empty,axiom,
! [T_d,T_c] : hAPP(c_Relation_ODomain(T_c,T_d),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Domain__empty) ).
fof(fact_Domain__mono,axiom,
! [V_s_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2)),hAPP(c_Relation_ODomain(T_c,T_d),V_s_2))) ),
file('theBenchmark.p',fact_Domain__mono) ).
fof(fact_Domain__Un__eq,axiom,
! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Relation_ODomain(T_c,T_d),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),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(c_Relation_ODomain(T_c,T_d),V_A_2)),hAPP(c_Relation_ODomain(T_c,T_d),V_B_2)),
file('theBenchmark.p',fact_Domain__Un__eq) ).
fof(fact_finite__Domain,axiom,
! [V_r_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),V_r_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2))) ),
file('theBenchmark.p',fact_finite__Domain) ).
fof(fact_fst__eq__Domain,axiom,
! [V_R_2,T_d,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_d),T_c,c_Product__Type_Ofst(T_c,T_d)),V_R_2) = hAPP(c_Relation_ODomain(T_c,T_d),V_R_2),
file('theBenchmark.p',fact_fst__eq__Domain) ).
fof(fact_Domain__iff,axiom,
! [V_r_2,T_d,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2)))
<=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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_d,T_c] : hAPP(c_Relation_ODomain(T_c,T_d),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2)),
file('theBenchmark.p',fact_Domain__insert) ).
fof(fact_Domain__Int__subset,axiom,
! [V_B_2,V_A_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_c,T_d),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_d),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_Relation_ODomain(T_c,T_d),V_A_2)),hAPP(c_Relation_ODomain(T_c,T_d),V_B_2)))),
file('theBenchmark.p',fact_Domain__Int__subset) ).
fof(fact_Domain__Diff__subset,axiom,
! [V_B_2,V_A_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_c,T_d),V_A_2)),hAPP(c_Relation_ODomain(T_c,T_d),V_B_2))),hAPP(c_Relation_ODomain(T_c,T_d),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_d),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_c] : hAPP(c_Relation_OField(T_c),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_c,T_c),V_r_2)),hAPP(c_Relation_ORange(T_c,T_c),V_r_2)),
file('theBenchmark.p',fact_Field__def) ).
fof(fact_Domain__Union,axiom,
! [V_S_2,T_d,T_c] : hAPP(c_Relation_ODomain(T_c,T_d),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_c,T_d)),
file('theBenchmark.p',fact_Domain__Union) ).
fof(fact_Domain__Collect__split,axiom,
! [V_Pa_2,T_d,T_c] : hAPP(c_Relation_ODomain(T_c,T_d),hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d)),V_Pa_2)),
file('theBenchmark.p',fact_Domain__Collect__split) ).
fof(fact_DomainP__Domain__eq,axiom,
! [V_x_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(c_Predicate_ODomainP(T_c,T_d,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_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2))) ),
file('theBenchmark.p',fact_DomainP__Domain__eq) ).
fof(fact_DomainE,axiom,
! [V_r_2,T_d,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Relation_ODomain(T_c,T_d),V_r_2)))
=> ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),B_y)),V_r_2)) ),
file('theBenchmark.p',fact_DomainE) ).
fof(fact_image__split__eq__Sigma,axiom,
! [V_A_2,V_g_2,V_f_2,T_d,T_c,T_e] : hAPP(c_Set_Oimage(T_e,tc_prod(T_c,T_d),hAPP(hAPP(c_COMBS(T_e,T_d,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(c_Set_Oimage(T_e,T_c,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_Oimage(T_e,T_d,V_g_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(tc_fun(T_e,tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_e,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool),T_c),c_Set_Ovimage(T_e,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)))))),V_A_2))),
file('theBenchmark.p',fact_image__split__eq__Sigma) ).
fof(fact_DomainP_Ointros,axiom,
! [T_d,T_c,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_c,T_d,V_r_2),V_a_2)) ),
file('theBenchmark.p',fact_DomainP_Ointros) ).
fof(fact_SigmaI,axiom,
! [V_B_2,V_b_2,T_d,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(V_B_2,V_a_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_SigmaI) ).
fof(fact_Sigma__empty1,axiom,
! [V_B_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),
file('theBenchmark.p',fact_Sigma__empty1) ).
fof(fact_Times__eq__cancel2,axiom,
! [V_B_2,V_A_2,T_d,V_C_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_C_2))
=> ( hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_C_2))
<=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_Times__eq__cancel2) ).
fof(fact_Sigma__Union,axiom,
! [V_B_2,V_X_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Product__Type_OSigma(T_c,T_d)),V_B_2)),
file('theBenchmark.p',fact_Sigma__Union) ).
fof(fact_card__cartesian__product,axiom,
! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Finite__Set_Ocard(tc_prod(T_c,T_d)),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_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),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_e,T_d,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),tc_fun(tc_fun(T_e,tc_HOL_Obool),T_c),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_d,T_e),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2)),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))) ),
file('theBenchmark.p',fact_setsum__cartesian__product) ).
fof(fact_Times__empty,axiom,
! [V_B_2,V_A_2,T_d,T_c] :
( 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)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))
<=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_Times__empty) ).
fof(fact_Sigma__empty2,axiom,
! [V_A_2,T_d,T_c] : 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),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),
file('theBenchmark.p',fact_Sigma__empty2) ).
fof(fact_Compl__Times__UNIV2,axiom,
! [V_A_2,T_d,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),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),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))),
file('theBenchmark.p',fact_Compl__Times__UNIV2) ).
fof(fact_Compl__Times__UNIV1,axiom,
! [V_A_2,T_d,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,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_e,T_d,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),tc_fun(tc_fun(T_e,tc_HOL_Obool),T_c),T_d),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_e,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_d,T_e),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2)),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))) ),
file('theBenchmark.p',fact_setprod__cartesian__product) ).
fof(fact_Sigma__Un__distrib2,axiom,
! [V_B_2,V_A_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),hAPP(hAPP(c_COMBS(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_B_2)),
file('theBenchmark.p',fact_Sigma__Un__distrib2) ).
fof(fact_Times__Un__distrib1,axiom,
! [V_C_2,V_B_2,V_A_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),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_C_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))),
file('theBenchmark.p',fact_Times__Un__distrib1) ).
fof(fact_Sigma__Un__distrib1,axiom,
! [V_C_2,V_J_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_J_2),V_C_2)),
file('theBenchmark.p',fact_Sigma__Un__distrib1) ).
fof(fact_rel__comp__subset__Sigma,axiom,
! [V_C_2,V_s_2,T_e,V_B_2,V_A_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_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))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_B_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_C_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_e),V_r_2),V_s_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_C_2)))) ) ),
file('theBenchmark.p',fact_rel__comp__subset__Sigma) ).
fof(fact_swap__product,axiom,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(c_Set_Oimage(tc_prod(T_d,T_c),tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_c,T_d)),hAPP(c_COMBC(T_c,T_d,tc_prod(T_c,T_d)),c_Product__Type_OPair(T_c,T_d)))),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_B_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_A_2)),
file('theBenchmark.p',fact_swap__product) ).
fof(fact_finite__cartesian__product,axiom,
! [V_B_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),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_finite__cartesian__product) ).
fof(fact_equiv__type,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) ),
file('theBenchmark.p',fact_equiv__type) ).
fof(fact_Sigma__Int__distrib1,axiom,
! [V_C_2,V_J_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_J_2),V_C_2)),
file('theBenchmark.p',fact_Sigma__Int__distrib1) ).
fof(fact_Times__Int__distrib1,axiom,
! [V_C_2,V_B_2,V_A_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),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_C_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))),
file('theBenchmark.p',fact_Times__Int__distrib1) ).
fof(fact_Sigma__Int__distrib2,axiom,
! [V_B_2,V_A_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),hAPP(hAPP(c_COMBS(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_B_2)),
file('theBenchmark.p',fact_Sigma__Int__distrib2) ).
fof(fact_Id__on__subset__Times,axiom,
! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Relation_OId__on(T_c,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))),
file('theBenchmark.p',fact_Id__on__subset__Times) ).
fof(fact_Sigma__Diff__distrib1,axiom,
! [V_C_2,V_J_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_J_2),V_C_2)),
file('theBenchmark.p',fact_Sigma__Diff__distrib1) ).
fof(fact_Times__Diff__distrib1,axiom,
! [V_C_2,V_B_2,V_A_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),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_C_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))),
file('theBenchmark.p',fact_Times__Diff__distrib1) ).
fof(fact_Sigma__Diff__distrib2,axiom,
! [V_B_2,V_A_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),hAPP(hAPP(c_COMBS(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_I_2),V_B_2)),
file('theBenchmark.p',fact_Sigma__Diff__distrib2) ).
fof(fact_DomainP_Oequations,axiom,
! [V_a1_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(c_Predicate_ODomainP(T_c,T_d,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_UNIV__Times__UNIV,axiom,
! [T_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_d),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_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_d),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_mem__Sigma__iff) ).
fof(fact_SigmaD1,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),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_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_d),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_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),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_d),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_d,T_c] : hAPP(c_Finite__Set_Ocard(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_d),V_A_2),
file('theBenchmark.p',fact_card__cartesian__product__singleton) ).
fof(fact_Times__subset__cancel2,axiom,
! [V_B_2,V_A_2,T_d,V_C_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_C_2))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,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_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_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))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_d,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_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),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))))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__cartesian__productD1) ).
fof(fact_finite__cartesian__productD2,axiom,
! [V_B_2,V_A_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),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))))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) ) ),
file('theBenchmark.p',fact_finite__cartesian__productD2) ).
fof(fact_Collect__split,axiom,
! [V_Qa_2,V_Pa_2,T_d,T_c] : hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(c_Set_OCollect(T_c),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_OCollect(T_d),V_Qa_2))),
file('theBenchmark.p',fact_Collect__split) ).
fof(fact_SetCompr__Sigma__eq,axiom,
! [V_Qa_2,V_Pa_2,T_d,T_c] : hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(c_Set_OCollect(T_c),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_OCollect(T_d)),V_Qa_2)),
file('theBenchmark.p',fact_SetCompr__Sigma__eq) ).
fof(fact_fst__image__times,axiom,
! [V_A_2,T_d,T_c,V_B_2] :
( ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_d,T_c),T_d,c_Product__Type_Ofst(T_d,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_B_2))) = V_A_2 )
& ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_d,T_c),T_d,c_Product__Type_Ofst(T_d,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_fst__image__times) ).
fof(fact_snd__image__times,axiom,
! [V_B_2,T_d,T_c,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_c,T_d),T_d,c_Product__Type_Osnd(T_c,T_d)),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))) = V_B_2 )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_c,T_d),T_d,c_Product__Type_Osnd(T_c,T_d)),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))) = c_Orderings_Obot__class_Obot(tc_fun(T_d,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_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(hAPP(c_Set_Oinsert(T_d),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),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),hAPP(hAPP(c_Set_Oinsert(T_d),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),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_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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_d,T_c,T_f,T_e] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_e,T_f),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_e,T_f),V_A_2),hAPP(c_COMBK(tc_fun(T_f,tc_HOL_Obool),T_e),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_f,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),tc_fun(T_f,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),tc_fun(tc_fun(T_f,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),tc_fun(T_f,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))),T_e),c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),T_f)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),T_e),c_Product__Type_OSigma(T_c,T_d)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_f),c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_f,tc_fun(T_d,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_d,T_c] : hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_prod(T_c,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_fun(tc_prod(T_c,T_d),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),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_fun(tc_prod(T_c,T_d),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_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),T_d),c_Set_Oinsert(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))))),
file('theBenchmark.p',fact_Sigma__def) ).
fof(fact_finite__quotient,axiom,
! [V_r_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),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_d,T_c,T_e] :
( class_Rings_Osemiring__0(T_e)
=> ( c_Fun_Oinj__on(tc_prod(T_c,T_d),T_e,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_e),tc_fun(T_d,T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_e),tc_fun(tc_fun(T_d,T_e),tc_fun(T_d,T_e)),T_c),c_COMBB(T_e,T_e,T_d)),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_e,T_e),T_c),c_Groups_Otimes__class_Otimes(T_e)),V_f_2))),V_g_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_Groups_Otimes__class_Otimes(T_e),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_e),c_Fun_Oid(T_e)),hAPP(c_Set_OCollect(T_e),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_e),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_e),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_e,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(T_c,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_e),c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool))),T_e),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_c),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_e),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,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_d),c_fconj))),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_c,tc_fun(T_d,T_e)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_e),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,T_e)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_e),c_COMBB(tc_fun(T_d,T_e),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_e),tc_fun(T_d,tc_HOL_Obool)),T_e),c_COMBB(T_e,tc_HOL_Obool,T_d)),c_fequal))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_e),tc_fun(T_d,T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_e),tc_fun(tc_fun(T_d,T_e),tc_fun(T_d,T_e)),T_c),c_COMBB(T_e,T_e,T_d)),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_e,T_e),T_c),c_Groups_Otimes__class_Otimes(T_e)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),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(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),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_d,T_c] :
? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,tc_prod(T_d,T_c),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_c),V_I_2),V_A_2)))
& c_Fun_Oinj__on(T_c,tc_prod(T_d,T_c),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,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_d,V_A_2,T_c,T_e] :
( class_Groups_Ocomm__monoid__mult(T_e)
=> ( 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))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_x))) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,T_c,c_Groups_Otimes__class_Otimes(T_e)),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),T_e),hAPP(hAPP(c_COMBC(T_c,T_e,tc_fun(tc_fun(T_d,tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_e),tc_fun(T_e,tc_fun(tc_fun(T_d,tc_HOL_Obool),T_e)),T_c),c_Finite__Set_Ofold__image(T_e,T_d,c_Groups_Otimes__class_Otimes(T_e))),V_g_2)),c_Groups_Oone__class_Oone(T_e))),V_B_2)),c_Groups_Oone__class_Oone(T_e)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,tc_prod(T_c,T_d),c_Groups_Otimes__class_Otimes(T_e)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_g_2)),c_Groups_Oone__class_Oone(T_e)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_fold__image__Sigma) ).
fof(fact_image__id,axiom,
! [V_Y_2,T_c] : hAPP(c_Set_Oimage(T_c,T_c,c_Fun_Oid(T_c)),V_Y_2) = V_Y_2,
file('theBenchmark.p',fact_image__id) ).
fof(fact_inj__on__id,axiom,
! [V_A_2,T_c] : c_Fun_Oinj__on(T_c,T_c,c_Fun_Oid(T_c),V_A_2),
file('theBenchmark.p',fact_inj__on__id) ).
fof(fact_vimage__id,axiom,
! [V_A_2,T_c] : hAPP(c_Set_Ovimage(T_c,T_c,c_Fun_Oid(T_c)),V_A_2) = V_A_2,
file('theBenchmark.p',fact_vimage__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_apsnd__id,axiom,
! [T_c,T_d] : c_Product__Type_Oapsnd(T_d,T_d,T_c,c_Fun_Oid(T_d)) = c_Fun_Oid(tc_prod(T_c,T_d)),
file('theBenchmark.p',fact_apsnd__id) ).
fof(fact_apfst__id,axiom,
! [T_d,T_c] : c_Product__Type_Oapfst(T_c,T_c,T_d,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_c,T_d)),
file('theBenchmark.p',fact_apfst__id) ).
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_c] : hAPP(c_Set_Oimage(T_c,T_c,c_Fun_Oid(T_c)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_surj__id) ).
fof(fact_split__Pair,axiom,
! [T_d,T_c] : hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_c,T_d)),c_Product__Type_OPair(T_c,T_d)) = c_Fun_Oid(tc_prod(T_c,T_d)),
file('theBenchmark.p',fact_split__Pair) ).
fof(fact_setsum__reindex__id,axiom,
! [V_B_2,V_f_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_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_Oimage(T_c,T_d,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_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_Oimage(T_c,T_d,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_d,V_A_2,T_c,T_e] :
( class_Groups_Ocomm__monoid__mult(T_e)
=> ( 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))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_x))) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_e),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),T_e),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_e),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_e),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_e)),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_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_setprod__Sigma) ).
fof(fact_setsum__Sigma,axiom,
! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_e] :
( class_Groups_Ocomm__monoid__add(T_e)
=> ( 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))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_x))) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),T_e),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_e),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_e),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e)),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_e),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_setsum__Sigma) ).
fof(fact_card__SigmaI,axiom,
! [V_B_2,T_d,V_A_2,T_c] :
( 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))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_x))) )
=> hAPP(c_Finite__Set_Ocard(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_Nat_Onat,T_c),c_Finite__Set_Ocard(T_d)),V_B_2)),V_A_2) ) ),
file('theBenchmark.p',fact_card__SigmaI) ).
fof(fact_finite__SigmaI,axiom,
! [V_B_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ! [B_a] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_a),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_a))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_finite__SigmaI) ).
fof(fact_SigmaE,axiom,
! [V_B_2,V_A_2,V_c_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_y),hAPP(V_B_2,B_x)))
=> V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) ) ) ),
file('theBenchmark.p',fact_SigmaE) ).
fof(fact_map__pair__surj,axiom,
! [V_g_2,T_e,T_f,V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
=> ( hAPP(c_Set_Oimage(T_f,T_e,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_f,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_d,T_f),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_d,T_c,T_f,T_e,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_d,T_f),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_map__pair__surj) ).
fof(fact_map__pair__imageI,axiom,
! [V_g_2,V_f_2,T_f,T_e,V_R_2,V_b_2,V_a_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_e,T_f)),hAPP(hAPP(c_Product__Type_OPair(T_e,T_f),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),tc_prod(T_e,T_f),c_Product__Type_Omap__pair(T_c,T_e,T_d,T_f,V_f_2,V_g_2)),V_R_2))) ),
file('theBenchmark.p',fact_map__pair__imageI) ).
fof(fact_map__pair__simp,axiom,
! [V_b_2,V_a_2,V_g_2,V_f_2,T_d,T_f,T_c,T_e] : hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_e,T_f),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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_d,T_c] : hAPP(c_Product__Type_Omap__pair(T_c,T_c,T_d,T_d,c_COMBI(T_c),c_COMBI(T_d)),V_z_2) = V_z_2,
file('theBenchmark.p',fact_map__pair__ident) ).
fof(fact_snd__prod__fun,axiom,
! [V_x_2,V_g_2,V_f_2,T_f,T_e,T_c,T_d] : hAPP(c_Product__Type_Osnd(T_d,T_c),hAPP(c_Product__Type_Omap__pair(T_e,T_d,T_f,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_e,T_f),V_x_2)),
file('theBenchmark.p',fact_snd__prod__fun) ).
fof(fact_fst__map__pair,axiom,
! [V_x_2,V_g_2,V_f_2,T_f,T_e,T_d,T_c] : hAPP(c_Product__Type_Ofst(T_c,T_d),hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_e,T_f),V_x_2)),
file('theBenchmark.p',fact_fst__map__pair) ).
fof(fact_map__pair_Oidentity,axiom,
! [T_d,T_c] : c_Product__Type_Omap__pair(T_c,T_c,T_d,T_d,c_COMBI(T_c),c_COMBI(T_d)) = c_Fun_Oid(tc_prod(T_c,T_d)),
file('theBenchmark.p',fact_map__pair_Oidentity) ).
fof(fact_apsnd__def,axiom,
! [V_f_2,T_c,T_e,T_d] : c_Product__Type_Oapsnd(T_d,T_e,T_c,V_f_2) = c_Product__Type_Omap__pair(T_c,T_c,T_d,T_e,c_Fun_Oid(T_c),V_f_2),
file('theBenchmark.p',fact_apsnd__def) ).
fof(fact_apfst__def,axiom,
! [V_f_2,T_d,T_e,T_c] : c_Product__Type_Oapfst(T_c,T_e,T_d,V_f_2) = c_Product__Type_Omap__pair(T_c,T_e,T_d,T_d,V_f_2,c_Fun_Oid(T_d)),
file('theBenchmark.p',fact_apfst__def) ).
fof(fact_map__pair_Oid,axiom,
! [T_d,T_c] : c_Product__Type_Omap__pair(T_c,T_c,T_d,T_d,c_Fun_Oid(T_c),c_Fun_Oid(T_d)) = c_Fun_Oid(tc_prod(T_c,T_d)),
file('theBenchmark.p',fact_map__pair_Oid) ).
fof(fact_map__pair__def,axiom,
! [V_g_2,V_f_2,T_f,T_d,T_e,T_c] : c_Product__Type_Omap__pair(T_c,T_e,T_d,T_f,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(T_e,T_f)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_f),tc_fun(T_d,tc_prod(T_e,T_f))),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_e,T_f)),tc_fun(tc_fun(T_d,T_f),tc_fun(T_d,tc_prod(T_e,T_f))),T_c),c_COMBB(T_f,tc_prod(T_e,T_f),T_d)),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_f,tc_prod(T_e,T_f)),T_c),c_Product__Type_OPair(T_e,T_f)),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_e,T_f,V_A_H_2,V_A_2,V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) = V_A_H_2
=> ( hAPP(c_Set_Oimage(T_f,T_e,V_g_2),V_B_2) = V_B_H_2
=> hAPP(c_Set_Oimage(tc_prod(T_d,T_f),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_d,T_c,T_f,T_e,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_f),V_A_2),hAPP(c_COMBK(tc_fun(T_f,tc_HOL_Obool),T_d),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_H_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_H_2)) ) ),
file('theBenchmark.p',fact_map__pair__surj__on) ).
fof(fact_wf__map__pair__image,axiom,
! [V_f_2,T_d,V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> c_Wellfounded_Owf(T_d,hAPP(c_Set_Oimage(tc_prod(T_c,T_c),tc_prod(T_d,T_d),c_Product__Type_Omap__pair(T_c,T_d,T_c,T_d,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_f,T_e,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( c_Fun_Oinj__on(T_e,T_f,V_g_2,V_B_2)
=> c_Fun_Oinj__on(tc_prod(T_c,T_e),tc_prod(T_d,T_f),c_Product__Type_Omap__pair(T_c,T_d,T_e,T_f,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))) ) ),
file('theBenchmark.p',fact_map__pair__inj__on) ).
fof(fact_prod__fun__imageE,axiom,
! [V_R_2,V_g_2,V_f_2,T_f,T_e,V_c_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_e,T_f),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2)),V_R_2)))
=> ~ ! [B_x,B_y] :
( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_e,T_f)),hAPP(hAPP(c_Product__Type_OPair(T_e,T_f),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_c] :
( c_Relation_Orefl__on(T_c,V_A_2,V_r_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) ) ),
file('theBenchmark.p',fact_refl__on__def) ).
fof(fact_wfP__def,axiom,
! [V_r_2,T_c] :
( c_Wellfounded_OwfP(T_c,V_r_2)
<=> c_Wellfounded_Owf(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_wfP__def) ).
fof(fact_wfP__empty,axiom,
! [T_c] : c_Wellfounded_OwfP(T_c,hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBK(tc_HOL_Obool,T_c),c_fFalse))),
file('theBenchmark.p',fact_wfP__empty) ).
fof(fact_refl__on__Id__on,axiom,
! [V_A_2,T_c] : c_Relation_Orefl__on(T_c,V_A_2,c_Relation_OId__on(T_c,V_A_2)),
file('theBenchmark.p',fact_refl__on__Id__on) ).
fof(fact_wfP__accp__iff,axiom,
! [V_r_2,T_c] :
( c_Wellfounded_OwfP(T_c,V_r_2)
<=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,V_r_2),B_x1)) ),
file('theBenchmark.p',fact_wfP__accp__iff) ).
fof(fact_accp__wfPD,axiom,
! [V_x_2,V_r_2,T_c] :
( c_Wellfounded_OwfP(T_c,V_r_2)
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_c,V_r_2),V_x_2)) ),
file('theBenchmark.p',fact_accp__wfPD) ).
fof(fact_wfP__subset,axiom,
! [V_p_2,V_r_2,T_c] :
( c_Wellfounded_OwfP(T_c,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),V_p_2),V_r_2))
=> c_Wellfounded_OwfP(T_c,V_p_2) ) ),
file('theBenchmark.p',fact_wfP__subset) ).
fof(fact_refl__on__empty,axiom,
! [T_c] : c_Relation_Orefl__on(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),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_c] :
( c_Relation_Orefl__on(T_c,V_A_2,V_r_2)
=> ( c_Relation_Orefl__on(T_c,V_B_2,V_s_2)
=> c_Relation_Orefl__on(T_c,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(tc_prod(T_c,T_c),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_c] :
( c_Relation_Orefl__on(T_c,V_A_2,V_r_2)
=> ( c_Relation_Orefl__on(T_c,V_B_2,V_s_2)
=> c_Relation_Orefl__on(T_c,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(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_refl__on__Int) ).
fof(fact_refl__onD,axiom,
! [V_a_2,V_r_2,V_A_2,T_c] :
( c_Relation_Orefl__on(T_c,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_a_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_refl__onD) ).
fof(fact_refl__onD1,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_c] :
( c_Relation_Orefl__on(T_c,V_A_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_x_2),V_y_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_refl__onD1) ).
fof(fact_refl__onD2,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_c] :
( c_Relation_Orefl__on(T_c,V_A_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_x_2),V_y_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2)) ) ),
file('theBenchmark.p',fact_refl__onD2) ).
fof(fact_wf__in__rel,axiom,
! [V_R_2,T_c] :
( c_Wellfounded_Owf(T_c,V_R_2)
=> c_Wellfounded_OwfP(T_c,c_FunDef_Oin__rel(T_c,T_c,V_R_2)) ),
file('theBenchmark.p',fact_wf__in__rel) ).
fof(fact_wfP__wf__eq,axiom,
! [V_r_2,T_c] :
( c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_r_2))
<=> c_Wellfounded_Owf(T_c,V_r_2) ),
file('theBenchmark.p',fact_wfP__wf__eq) ).
fof(fact_reflp__def,axiom,
! [V_r_2,T_c] :
( c_Predicate_Oreflp(T_c,V_r_2)
<=> c_Relation_Orefl__on(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_reflp__def) ).
fof(fact_refl__onI,axiom,
! [V_A_2,V_r_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2))))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) )
=> c_Relation_Orefl__on(T_c,V_A_2,V_r_2) ) ),
file('theBenchmark.p',fact_refl__onI) ).
fof(fact_wfP__acyclicP,axiom,
! [V_r_2,T_c] :
( c_Wellfounded_OwfP(T_c,V_r_2)
=> c_Wellfounded_Oacyclic(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_wfP__acyclicP) ).
fof(fact_acyclic__subset,axiom,
! [V_r_2,V_s_2,T_c] :
( c_Wellfounded_Oacyclic(T_c,V_s_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
=> c_Wellfounded_Oacyclic(T_c,V_r_2) ) ),
file('theBenchmark.p',fact_acyclic__subset) ).
fof(fact_reflpE,axiom,
! [V_x_2,V_r_2,T_c] :
( c_Predicate_Oreflp(T_c,V_r_2)
=> hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ),
file('theBenchmark.p',fact_reflpE) ).
fof(fact_wf__acyclic,axiom,
! [V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> c_Wellfounded_Oacyclic(T_c,V_r_2) ),
file('theBenchmark.p',fact_wf__acyclic) ).
fof(fact_wf__iff__acyclic__if__finite,axiom,
! [V_r_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),V_r_2))
=> ( c_Wellfounded_Owf(T_c,V_r_2)
<=> c_Wellfounded_Oacyclic(T_c,V_r_2) ) ),
file('theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).
fof(fact_finite__acyclic__wf,axiom,
! [V_r_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),V_r_2))
=> ( c_Wellfounded_Oacyclic(T_c,V_r_2)
=> c_Wellfounded_Owf(T_c,V_r_2) ) ),
file('theBenchmark.p',fact_finite__acyclic__wf) ).
fof(fact_Nitpick_Owf_H__def,axiom,
! [V_r_2,T_c] :
( c_Nitpick_Owf_H(T_c,V_r_2)
<=> ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),V_r_2)) )
& c_Wellfounded_Oacyclic(T_c,V_r_2) ) ),
file('theBenchmark.p',fact_Nitpick_Owf_H__def) ).
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_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_refl__on__def_H,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Relation_Orefl__on(T_c,V_A_2,V_r_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) )
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),B_x),V_r_2))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),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_c] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_HOL_Obool) = c_Set_OBall(T_c),
file('theBenchmark.p',fact_INFI__bool__eq) ).
fof(fact_ball__empty,axiom,
! [V_Pa_2,T_c,B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c] :
( hBOOL(hAPP(c_Predicate_OPowp(T_c,V_A_2),V_B_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),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_d,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OAll(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fimplies),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_A_2)))),V_Pa_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_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_OCollect(T_c)),hAPP(c_COMBC(T_c,T_d,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_d,T_c] :
( c_Equiv__Relations_Ocongruent(T_c,T_d,V_r_2,V_f_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),B_x),V_r_2))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),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_c),c_COMBB(T_d,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),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_c,T_d] : 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(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OAll(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fimplies),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d)),c_member(T_c))),V_B_2)))),
file('theBenchmark.p',fact_INTER__def) ).
fof(fact_Sup__Inf,axiom,
! [V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_c),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(c_COMBC(T_c,T_c,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_c)))))) ),
file('theBenchmark.p',fact_Sup__Inf) ).
fof(fact_Inf__Sup,axiom,
! [V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_c),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)))),c_Orderings_Oord__class_Oless__eq(T_c))))) ),
file('theBenchmark.p',fact_Inf__Sup) ).
fof(fact_wfP__SUP,axiom,
! [T_c,V_r_2,T_d] :
( ! [B_i] : c_Wellfounded_OwfP(T_d,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_d,tc_HOL_Obool)),c_Predicate_ODomainP(T_d,T_d,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_d,T_d,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) )
=> c_Wellfounded_OwfP(T_d,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2)) ) ),
file('theBenchmark.p',fact_wfP__SUP) ).
fof(fact_mem__splitI2,axiom,
! [V_c_2,V_z_2,T_e,T_d,T_c,V_p_2] :
( ! [B_a,B_b] :
( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b)
=> hBOOL(hAPP(hAPP(c_member(T_e),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
=> hBOOL(hAPP(hAPP(c_member(T_e),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_e,tc_HOL_Obool)),V_c_2),V_p_2))) ),
file('theBenchmark.p',fact_mem__splitI2) ).
fof(fact_mem__splitE,axiom,
! [V_p_2,V_c_2,T_e,T_d,V_z_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(T_c,tc_HOL_Obool)),V_c_2),V_p_2)))
=> ~ ! [B_x,B_y] :
( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ),
file('theBenchmark.p',fact_mem__splitE) ).
fof(fact_Inter__eq,axiom,
! [V_A_2,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OAll(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_c,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_c,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,tc_HOL_Obool))),V_A_2)))),c_member(T_c)))),
file('theBenchmark.p',fact_Inter__eq) ).
fof(fact_vimage__Times,axiom,
! [V_B_2,V_A_2,V_f_2,T_e,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,tc_prod(T_d,T_e),V_f_2),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(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,T_c,c_Product__Type_Ofst(T_d,T_e)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_e,hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_e,T_c,c_Product__Type_Osnd(T_d,T_e)),V_f_2)),V_B_2)),
file('theBenchmark.p',fact_vimage__Times) ).
fof(fact_Eps__split,axiom,
! [V_Pa_2,T_d,T_c] : c_Hilbert__Choice_OEps(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_c,T_d),hAPP(hAPP(c_COMBS(tc_prod(T_c,T_d),T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_HOL_Obool),tc_prod(T_c,T_d)),V_Pa_2),c_Product__Type_Ofst(T_c,T_d))),c_Product__Type_Osnd(T_c,T_d))),
file('theBenchmark.p',fact_Eps__split) ).
fof(fact_wfI__pf,axiom,
! [V_R_2,T_c] :
( ! [B_A] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_c,T_c,V_R_2),B_A)))
=> B_A = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
=> c_Wellfounded_Owf(T_c,V_R_2) ),
file('theBenchmark.p',fact_wfI__pf) ).
fof(fact_id__o,axiom,
! [V_g_2,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_d,T_c,c_Fun_Oid(T_d)),V_g_2) = V_g_2,
file('theBenchmark.p',fact_id__o) ).
fof(fact_o__id,axiom,
! [V_f_2,T_d,T_c] : hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_f_2),c_Fun_Oid(T_c)) = V_f_2,
file('theBenchmark.p',fact_o__id) ).
fof(fact_o__eq__id__dest,axiom,
! [V_v_2,V_c_2,V_b_2,V_a_2,T_c,T_d,T_e] :
( hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_d,T_c,c_Fun_Oid(T_d)),V_c_2)
=> hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ),
file('theBenchmark.p',fact_o__eq__id__dest) ).
fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
! [V_x_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2)
=> hAPP(c_Fun_Ocomp(T_d,T_d,T_d,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__upd__comp,axiom,
! [V_y_2,V_x_2,V_g_2,V_f_2,T_c,T_d,T_e] : hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),c_Fun_Ofun__upd(T_c,T_e,V_g_2,V_x_2,V_y_2)) = c_Fun_Ofun__upd(T_c,T_d,hAPP(c_Fun_Ocomp(T_e,T_d,T_c,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_vimage__compose,axiom,
! [V_x_2,V_f_2,V_g_2,T_e,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_c,T_e,V_f_2),hAPP(c_Set_Ovimage(T_e,T_d,V_g_2),V_x_2)),
file('theBenchmark.p',fact_vimage__compose) ).
fof(fact_o__assoc,axiom,
! [V_h_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e] : hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),hAPP(c_Fun_Ocomp(T_f,T_e,T_c,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_d,T_f,V_f_2),V_g_2)),V_h_2),
file('theBenchmark.p',fact_o__assoc) ).
fof(fact_o__apply,axiom,
! [V_x_2,V_g_2,V_f_2,T_e,T_c,T_d] : hAPP(hAPP(c_Fun_Ocomp(T_d,T_c,T_e,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__eq__dest,axiom,
! [V_v_2,V_d_2,V_c_2,T_f,V_b_2,V_a_2,T_c,T_d,T_e] :
( hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,V_c_2),V_d_2)
=> hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ),
file('theBenchmark.p',fact_o__eq__dest) ).
fof(fact_o__eq__elim,axiom,
! [V_d_2,V_c_2,T_f,V_b_2,V_a_2,T_c,T_d,T_e] :
( hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_f,T_d,T_c,V_c_2),V_d_2)
=> ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ),
file('theBenchmark.p',fact_o__eq__elim) ).
fof(fact_tfl__some,axiom,
! [T_c,B_P] :
( ? [B_x] : hBOOL(hAPP(B_P,B_x))
=> hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_c,B_P))) ),
file('theBenchmark.p',fact_tfl__some) ).
fof(fact_someI,axiom,
! [T_c,V_x_2,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,V_x_2))
=> hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_c,V_Pa_2))) ),
file('theBenchmark.p',fact_someI) ).
fof(fact_comp__cong,axiom,
! [T_g,T_f,T_e,T_c,T_d,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_d,T_c,T_e,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_f,T_c,T_g,V_f_H_2),V_g_H_2),V_x_H_2) ),
file('theBenchmark.p',fact_comp__cong) ).
fof(fact_o__eq__dest__lhs,axiom,
! [V_v_2,V_c_2,V_b_2,V_a_2,T_c,T_d,T_e] :
( hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_a_2),V_b_2) = V_c_2
=> hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ),
file('theBenchmark.p',fact_o__eq__dest__lhs) ).
fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
! [V_y_2,V_x_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2)
=> hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_d,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_someI__ex,axiom,
! [T_c,V_Pa_2] :
( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
=> hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_c,V_Pa_2))) ),
file('theBenchmark.p',fact_someI__ex) ).
fof(fact_some__eq__ex,axiom,
! [T_c,V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_c,V_Pa_2)))
<=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ),
file('theBenchmark.p',fact_some__eq__ex) ).
fof(fact_some__eq__trivial,axiom,
! [V_x_2,T_c] : c_Hilbert__Choice_OEps(T_c,hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2,
file('theBenchmark.p',fact_some__eq__trivial) ).
fof(fact_some__sym__eq__trivial,axiom,
! [V_x_2,T_c] : c_Hilbert__Choice_OEps(T_c,hAPP(c_fequal,V_x_2)) = V_x_2,
file('theBenchmark.p',fact_some__sym__eq__trivial) ).
fof(fact_K__record__comp,axiom,
! [V_x_2,V_f_2,V_c_2,T_e,T_c,T_d] : hAPP(hAPP(c_Fun_Ocomp(T_d,T_c,T_e,hAPP(c_COMBK(T_c,T_d),V_c_2)),V_f_2),V_x_2) = V_c_2,
file('theBenchmark.p',fact_K__record__comp) ).
fof(fact_o__def,axiom,
! [V_x_2,V_g_2,V_f_2,T_e,T_c,T_d] : hAPP(hAPP(c_Fun_Ocomp(T_d,T_c,T_e,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_exE__some,axiom,
! [T_c,V_c_2,V_Pa_2] :
( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
=> ( V_c_2 = c_Hilbert__Choice_OEps(T_c,V_Pa_2)
=> hBOOL(hAPP(V_Pa_2,V_c_2)) ) ),
file('theBenchmark.p',fact_exE__some) ).
fof(fact_apsnd__compose,axiom,
! [V_x_2,V_g_2,T_f,V_f_2,T_c,T_d,T_e] : hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_f,T_e,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_f,T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_d,T_f,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_f,V_f_2,T_d,T_c,T_e] : hAPP(c_Product__Type_Oapfst(T_e,T_c,T_d,V_f_2),hAPP(c_Product__Type_Oapfst(T_f,T_e,T_d,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_f,T_c,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_f,V_f_2),V_g_2)),V_x_2),
file('theBenchmark.p',fact_apfst__compose) ).
fof(fact_inj__on__imageI2,axiom,
! [V_A_2,V_f_2,V_f_H_2,T_e,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_H_2),V_f_2),V_A_2)
=> c_Fun_Oinj__on(T_c,T_e,V_f_2,V_A_2) ),
file('theBenchmark.p',fact_inj__on__imageI2) ).
fof(fact_inj__comp,axiom,
! [V_g_2,T_e,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(T_e,T_c,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool)))
=> c_Fun_Oinj__on(T_e,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_e,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_inj__comp) ).
fof(fact_comp__surj,axiom,
! [V_g_2,T_e,V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
=> ( hAPP(c_Set_Oimage(T_c,T_e,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_d,T_e,hAPP(c_Fun_Ocomp(T_c,T_e,T_d,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_comp__surj) ).
fof(fact_comp__inj__on__iff,axiom,
! [V_f_H_2,T_e,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( c_Fun_Oinj__on(T_d,T_e,V_f_H_2,hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))
<=> c_Fun_Oinj__on(T_c,T_e,hAPP(c_Fun_Ocomp(T_d,T_e,T_c,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_e,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( c_Fun_Oinj__on(T_d,T_e,V_g_2,hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))
=> c_Fun_Oinj__on(T_c,T_e,hAPP(c_Fun_Ocomp(T_d,T_e,T_c,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_e,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_g_2),V_f_2),V_A_2)
=> c_Fun_Oinj__on(T_e,T_d,V_g_2,hAPP(c_Set_Oimage(T_c,T_e,V_f_2),V_A_2)) ),
file('theBenchmark.p',fact_inj__on__imageI) ).
fof(fact_image__compose,axiom,
! [V_r_2,V_g_2,V_f_2,T_e,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,hAPP(c_Fun_Ocomp(T_e,T_c,T_d,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_e,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_e,V_g_2),V_r_2)),
file('theBenchmark.p',fact_image__compose) ).
fof(fact_map__pair_Ocompositionality,axiom,
! [V_prod_2,V_i_2,V_h_2,T_h,T_g,V_g_2,V_f_2,T_d,T_f,T_c,T_e] : hAPP(c_Product__Type_Omap__pair(T_e,T_c,T_f,T_d,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_g,T_e,T_h,T_f,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_g,T_c,T_h,T_d,hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_f,T_d,T_h,V_g_2),V_i_2)),V_prod_2),
file('theBenchmark.p',fact_map__pair_Ocompositionality) ).
fof(fact_map__pair__compose,axiom,
! [V_g2_2,V_g1_2,T_h,V_f2_2,V_f1_2,T_g,T_f,T_d,T_e,T_c] : c_Product__Type_Omap__pair(T_c,T_e,T_d,T_f,hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_h,T_f,T_d,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_g,T_h),tc_prod(T_e,T_f),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_g,T_e,T_h,T_f,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_c,T_g,T_d,T_h,V_f2_2,V_g2_2)),
file('theBenchmark.p',fact_map__pair__compose) ).
fof(fact_map__pair_Ocomp,axiom,
! [V_i_2,V_h_2,V_g_2,V_f_2,T_d,T_c,T_f,T_e,T_h,T_g] : hAPP(c_Fun_Ocomp(tc_prod(T_g,T_h),tc_prod(T_e,T_f),tc_prod(T_c,T_d),c_Product__Type_Omap__pair(T_g,T_e,T_h,T_f,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_c,T_g,T_d,T_h,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_c,T_e,T_d,T_f,hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_h,T_f,T_d,V_g_2),V_i_2)),
file('theBenchmark.p',fact_map__pair_Ocomp) ).
fof(fact_setsum__reindex,axiom,
! [V_h_2,V_B_2,V_f_2,T_d,T_c,T_e] :
( class_Groups_Ocomm__monoid__add(T_e)
=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e),V_h_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),hAPP(c_Fun_Ocomp(T_d,T_e,T_c,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_d,T_c,T_e] :
( class_Groups_Ocomm__monoid__mult(T_e)
=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_e),V_h_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_e),hAPP(c_Fun_Ocomp(T_d,T_e,T_c,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_d,T_c,T_e] :
( class_Groups_Ocomm__monoid__mult(T_e)
=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( V_B_2 = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)
=> ( V_g_2 = hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_h_2),V_f_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_e),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_e),V_g_2),V_A_2) ) ) ) ),
file('theBenchmark.p',fact_setprod__reindex__cong) ).
fof(fact_Eps__split__eq,axiom,
! [V_y_2,V_x_2,T_d,T_c] : c_Hilbert__Choice_OEps(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2),
file('theBenchmark.p',fact_Eps__split__eq) ).
fof(fact_split__paired__Eps,axiom,
! [V_Pa_2,T_d,T_c] : c_Hilbert__Choice_OEps(tc_prod(T_c,T_d),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_HOL_Obool,T_d),V_Pa_2)),c_Product__Type_OPair(T_c,T_d)))),
file('theBenchmark.p',fact_split__paired__Eps) ).
fof(fact_setsum_Oreindex,axiom,
! [V_g_2,V_h_2,V_A_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( 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(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_c,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_c,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( 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(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_c,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_e,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(c_Set_Oimage(T_e,T_c,V_g_2),V_A_2))
=> ( c_Fun_Oinj__on(T_e,T_c,V_g_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(c_Set_Oimage(T_e,T_c,V_g_2),V_A_2))))
=> hAPP(c_Fun_Othe__inv__into(T_e,T_d,V_A_2,hAPP(c_Fun_Ocomp(T_c,T_d,T_e,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_e,T_d,c_Fun_Othe__inv__into(T_e,T_c,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_c,T_d,hAPP(c_Set_Oimage(T_e,T_c,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_d,V_A_2,T_c,T_e] :
( class_Groups_Oab__semigroup__mult(T_e)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( c_Fun_Oinj__on(T_c,T_d,V_h_2,V_A_2)
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,T_d,c_Groups_Otimes__class_Otimes(T_e)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_c,T_d,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,T_c,c_Groups_Otimes__class_Otimes(T_e)),hAPP(c_Fun_Ocomp(T_d,T_e,T_c,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_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_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(c_Fun_Ocomp(T_d,T_d,T_d,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)))))),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_d,T_c] :
( c_Finite__Set_Ofolding__image(T_c,T_d,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> ( c_Fun_Oinj__on(T_d,T_d,V_h_2,V_A_2)
=> hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_d,T_d,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_d,T_c,T_d,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_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_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(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_folding_Ounion) ).
fof(fact_folding_Ocommute__comps_I1_J,axiom,
! [V_h_2,V_g_2,T_h,V_f_2,T_e,T_f,T_g,V_F_2,V_fa_2,T_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_fa_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_g,T_f,T_e,V_f_2),hAPP(c_Fun_Ocomp(T_h,T_g,T_e,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_h,T_f,T_e,hAPP(c_Fun_Ocomp(T_g,T_f,T_h,V_f_2),V_g_2)),V_h_2) ),
file('theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).
fof(fact_folding_Ocommute__comp,axiom,
! [V_x_2,V_y_2,V_F_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_d,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__left__comp,axiom,
! [V_g_2,V_x_2,V_y_2,T_e,V_F_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_y_2)),V_g_2)) ),
file('theBenchmark.p',fact_folding_Ocommute__left__comp) ).
fof(fact_UN__o,axiom,
! [V_f_2,V_g_2,T_e,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_c,tc_HOL_Obool),T_d,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_e,V_f_2),V_A_2)),V_g_2),
file('theBenchmark.p',fact_UN__o) ).
fof(fact_fst__comp__map__pair,axiom,
! [V_g_2,V_f_2,T_d,T_c,T_f,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_f),T_e,tc_prod(T_c,T_d),c_Product__Type_Ofst(T_e,T_f)),c_Product__Type_Omap__pair(T_c,T_e,T_d,T_f,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_e,tc_prod(T_c,T_d),V_f_2),c_Product__Type_Ofst(T_c,T_d)),
file('theBenchmark.p',fact_fst__comp__map__pair) ).
fof(fact_snd__comp__map__pair,axiom,
! [V_g_2,V_f_2,T_d,T_c,T_e,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_e),T_e,tc_prod(T_c,T_d),c_Product__Type_Osnd(T_f,T_e)),c_Product__Type_Omap__pair(T_c,T_f,T_d,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_d,T_e,tc_prod(T_c,T_d),V_g_2),c_Product__Type_Osnd(T_c,T_d)),
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_d,T_c] :
( c_Finite__Set_Ofolding__image(T_c,T_d,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),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_f,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),hAPP(c_Fun_Ocomp(T_f,tc_fun(T_e,T_c),T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)),
file('theBenchmark.p',fact_split__comp) ).
fof(fact_folding_Ocommute__comp_H,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_d,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_Ocommute__left__comp_H,axiom,
! [V_g_2,V_x_2,T_e,V_A_2,V_F_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,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_H,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_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(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_d,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_H,axiom,
! [V_g_2,T_e,V_B_2,V_A_2,V_F_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_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(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ),
file('theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).
fof(fact_folding_Oempty,axiom,
! [V_F_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2)
=> hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Fun_Oid(T_d) ),
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_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,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_d,T_c] :
( c_Finite__Set_Ofolding__image(T_c,T_d,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_d,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_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_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(c_Fun_Ocomp(T_d,T_d,T_d,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_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_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(c_Fun_Ocomp(T_d,T_d,T_d,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(c_Fun_Ocomp(T_d,T_d,T_d,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_d,T_c] :
( c_Finite__Set_Ofolding(T_c,T_d,V_f_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(c_Fun_Ocomp(T_d,T_d,T_d,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)))))),hAPP(V_f_2,V_x_2)) ) ),
file('theBenchmark.p',fact_folding_Oinsert__remove) ).
fof(fact_hoare__derivs_OIf,axiom,
! [V_d_2,V_Qa_2,V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),c_Hoare__Mirabelle_Opeek__and(T_c,V_Pa_2,V_b_2)),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),c_Hoare__Mirabelle_Opeek__and(T_c,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_hoare__derivs_OIf) ).
fof(fact_Loop,axiom,
! [V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),c_Hoare__Mirabelle_Opeek__and(T_c,V_Pa_2,V_b_2)),V_c_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_c,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_Loop) ).
fof(fact_setsum__reindex__nonzero,axiom,
! [T_d,V_h_2,V_f_2,V_S_2,T_c,T_e] :
( class_Groups_Ocomm__monoid__add(T_e)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_c),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_e) ) ) ) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e),V_h_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_h_2),V_f_2)),V_S_2) ) ) ),
file('theBenchmark.p',fact_setsum__reindex__nonzero) ).
fof(fact_peek__and__def,axiom,
! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_c] :
( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_c,V_Pa_2,V_p_2),V_Z_2),V_s_2))
<=> ( hBOOL(hAPP(V_p_2,V_s_2))
& hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) ) ),
file('theBenchmark.p',fact_peek__and__def) ).
fof(fact_folding__idem_Ounion__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding__idem(T_c,T_d,V_f_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(c_Fun_Ocomp(T_d,T_d,T_d,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_d,T_c] :
( c_Finite__Set_Ofolding__idem(T_c,T_d,V_f_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(c_Fun_Ocomp(T_d,T_d,T_d,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_Oinsert__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding__idem(T_c,T_d,V_f_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(c_Fun_Ocomp(T_d,T_d,T_d,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ),
file('theBenchmark.p',fact_folding__idem_Oinsert__idem) ).
fof(fact_folding__idem_Oidem__left__comp,axiom,
! [V_g_2,V_x_2,T_e,V_F_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofolding__idem(T_c,T_d,V_f_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_d,T_d,T_e,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_d,T_d,T_e,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_d,T_c] :
( c_Finite__Set_Ofolding__idem(T_c,T_d,V_f_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_d,T_d,T_d,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_d,T_c] :
( c_Finite__Set_Ofolding__idem(T_c,T_d,V_f_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(c_Fun_Ocomp(T_d,T_d,T_d,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_strong__setprod__reindex__cong,axiom,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_d,T_c,T_e] :
( class_Groups_Ocomm__monoid__mult(T_e)
=> ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( V_B_2 = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_h_2),V_f_2),B_x) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_e),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_e),V_g_2),V_A_2) ) ) ) ),
file('theBenchmark.p',fact_strong__setprod__reindex__cong) ).
fof(fact_Sigma__mono,axiom,
! [V_D_2,V_B_2,T_d,V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,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_c,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),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_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Wellfounded_Oacc(T_c,V_R_2)))
=> ~ ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_z),V_x_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),B_z),c_Wellfounded_Oacc(T_c,V_R_2))) ) ),
file('theBenchmark.p',fact_not__acc__down) ).
fof(fact_acc_OaccI,axiom,
! [V_r_2,V_x_2,T_c] :
( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),V_x_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),B_y),c_Wellfounded_Oacc(T_c,V_r_2))) )
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Wellfounded_Oacc(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_c,V_R_2)))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_a1_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_xa)),V_R_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_a2_2)) ) )
& V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_a2_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> ~ ! [B_k] : 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,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_scomp__unfold,axiom,
! [V_x_2,V_g_2,V_f_2,T_c,T_f,T_e,T_d] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_d,T_e,T_f,T_c),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_f),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_e,T_f),hAPP(V_f_2,V_x_2))),
file('theBenchmark.p',fact_scomp__unfold) ).
fof(fact_setsum__ivl__cong,axiom,
! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_c,T_d] :
( ( class_Orderings_Oord(T_c)
& class_Groups_Ocomm__monoid__add(T_d) )
=> ( V_a_2 = V_c_2
=> ( V_b_2 = V_d_2
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),B_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),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_c,T_d),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum__ivl__cong) ).
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_Pair__scomp,axiom,
! [V_f_2,V_x_2,T_d,T_e,T_c] : hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_e,T_c,T_d),hAPP(c_Product__Type_OPair(T_e,T_c),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2),
file('theBenchmark.p',fact_Pair__scomp) ).
fof(fact_scomp__Pair,axiom,
! [V_x_2,T_e,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,tc_prod(T_d,T_e)),V_x_2),c_Product__Type_OPair(T_d,T_e)) = V_x_2,
file('theBenchmark.p',fact_scomp__Pair) ).
fof(fact_scomp__scomp,axiom,
! [V_h_2,V_g_2,V_f_2,T_h,T_g,T_d,T_f,T_e,T_c] : hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_e,T_f,T_d),hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_g,T_h,tc_prod(T_e,T_f)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_g,T_h,T_d),V_f_2),hAPP(hAPP(c_COMBC(T_g,tc_fun(T_e,tc_fun(T_f,T_d)),tc_fun(T_h,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_h,tc_prod(T_e,T_f)),tc_fun(tc_fun(T_e,tc_fun(T_f,T_d)),tc_fun(T_h,T_d)),T_g),c_Product__Type_Oscomp(T_h,T_e,T_f,T_d)),V_g_2)),V_h_2)),
file('theBenchmark.p',fact_scomp__scomp) ).
fof(fact_wf__trancl,axiom,
! [V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
=> c_Wellfounded_Owf(T_c,c_Transitive__Closure_Otrancl(T_c,V_r_2)) ),
file('theBenchmark.p',fact_wf__trancl) ).
fof(fact_scomp__apply,axiom,
! [V_x_2,V_g_2,V_f_2,T_c,T_f,T_e,T_d] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_d,T_e,T_f,T_c),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_c),V_g_2),hAPP(V_f_2,V_x_2)),
file('theBenchmark.p',fact_scomp__apply) ).
fof(fact_scomp__def,axiom,
! [V_x_2,V_g_2,V_f_2,T_c,T_f,T_e,T_d] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_d,T_e,T_f,T_c),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_c),V_g_2),hAPP(V_f_2,V_x_2)),
file('theBenchmark.p',fact_scomp__def) ).
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_c] :
( c_Wellfounded_Oacyclic(T_c,V_r_2)
<=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),c_Transitive__Closure_Otrancl(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_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_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ),
file('theBenchmark.p',fact_trancl_Or__into__trancl) ).
fof(fact_trancl__subset__Field2,axiom,
! [V_r_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_c,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),hAPP(c_Relation_OField(T_c),V_r_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_Relation_OField(T_c),V_r_2))))),
file('theBenchmark.p',fact_trancl__subset__Field2) ).
fof(fact_trancl__Int__subset,axiom,
! [V_s_2,V_r_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,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_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_c,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_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_c,V_r_2)),V_s_2)) ) ),
file('theBenchmark.p',fact_trancl__Int__subset) ).
fof(fact_r__into__trancl_H,axiom,
! [V_r_2,V_p_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ),
file('theBenchmark.p',fact_r__into__trancl_H) ).
fof(fact_trancl__empty,axiom,
! [T_c] : c_Transitive__Closure_Otrancl(T_c,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),
file('theBenchmark.p',fact_trancl__empty) ).
fof(fact_trancl__domain,axiom,
! [V_r_2,T_c] : hAPP(c_Relation_ODomain(T_c,T_c),c_Transitive__Closure_Otrancl(T_c,V_r_2)) = hAPP(c_Relation_ODomain(T_c,T_c),V_r_2),
file('theBenchmark.p',fact_trancl__domain) ).
fof(fact_trancl__range,axiom,
! [V_r_2,T_c] : hAPP(c_Relation_ORange(T_c,T_c),c_Transitive__Closure_Otrancl(T_c,V_r_2)) = hAPP(c_Relation_ORange(T_c,T_c),V_r_2),
file('theBenchmark.p',fact_trancl__range) ).
fof(fact_finite__trancl,axiom,
! [V_r_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),c_Transitive__Closure_Otrancl(T_c,V_r_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),V_r_2)) ),
file('theBenchmark.p',fact_finite__trancl) ).
fof(fact_trancl__trans,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_c,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_c_2)),c_Transitive__Closure_Otrancl(T_c,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_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__trans) ).
fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_c,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_c_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_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
fof(fact_trancl__into__trancl2,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_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_c_2)),c_Transitive__Closure_Otrancl(T_c,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_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__into__trancl2) ).
fof(fact_r__r__into__trancl,axiom,
! [V_c_2,V_R_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_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_c_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_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_R_2))) ) ),
file('theBenchmark.p',fact_r__r__into__trancl) ).
fof(fact_trancl__mono,axiom,
! [V_s_2,V_r_2,V_p_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Otrancl(T_c,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Otrancl(T_c,V_s_2))) ) ),
file('theBenchmark.p',fact_trancl__mono) ).
fof(fact_trancl__unfold,axiom,
! [V_r_2,T_c] : c_Transitive__Closure_Otrancl(T_c,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),c_Transitive__Closure_Otrancl(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_c,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2)))) ),
file('theBenchmark.p',fact_trancl__subset__Sigma) ).
fof(fact_iterate_Osimps,axiom,
! [V_x_2,V_f_2,T_c,T_d,V_k_2] :
( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Random_Oiterate(T_d,T_c,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_c,tc_prod(T_d,T_c)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_d,T_c,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_d,T_c,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2) ) ),
file('theBenchmark.p',fact_iterate_Osimps) ).
fof(fact_trancl__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_c] : c_Transitive__Closure_Otrancl(T_c,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_c,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,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_c),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_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_c),c_member(tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBC(T_c,T_c,tc_prod(T_c,T_c)),c_Product__Type_OPair(T_c,T_c)),V_y_2))),c_Transitive__Closure_Ortrancl(T_c,V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_c),c_member(tc_prod(T_c,T_c))),hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2))),c_Transitive__Closure_Ortrancl(T_c,V_r_2)))))),
file('theBenchmark.p',fact_trancl__insert) ).
fof(fact_r__into__rtrancl,axiom,
! [V_r_2,V_p_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ),
file('theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [V_r_2,V_a_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))),
file('theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(fact_trancl__into__rtrancl,axiom,
! [V_r_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_c,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_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ),
file('theBenchmark.p',fact_trancl__into__rtrancl) ).
fof(fact_trancl__rtrancl__absorb,axiom,
! [V_R_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,c_Transitive__Closure_Otrancl(T_c,V_R_2)) = c_Transitive__Closure_Ortrancl(T_c,V_R_2),
file('theBenchmark.p',fact_trancl__rtrancl__absorb) ).
fof(fact_rtrancl__trancl__absorb,axiom,
! [V_R_2,T_c] : c_Transitive__Closure_Otrancl(T_c,c_Transitive__Closure_Ortrancl(T_c,V_R_2)) = c_Transitive__Closure_Ortrancl(T_c,V_R_2),
file('theBenchmark.p',fact_rtrancl__trancl__absorb) ).
fof(fact_trancl__unfold__right,axiom,
! [V_r_2,T_c] : c_Transitive__Closure_Otrancl(T_c,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),V_r_2),
file('theBenchmark.p',fact_trancl__unfold__right) ).
fof(fact_trancl__unfold__left,axiom,
! [V_r_2,T_c] : c_Transitive__Closure_Otrancl(T_c,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_r_2),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),
file('theBenchmark.p',fact_trancl__unfold__left) ).
fof(fact_Domain__rtrancl,axiom,
! [V_R_2,T_c] : hAPP(c_Relation_ODomain(T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Domain__rtrancl) ).
fof(fact_Range__rtrancl,axiom,
! [V_R_2,T_c] : hAPP(c_Relation_ORange(T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Range__rtrancl) ).
fof(fact_in__rtrancl__UnI,axiom,
! [V_S_2,V_R_2,V_x_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_x_2),c_Transitive__Closure_Ortrancl(T_c,V_S_2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_x_2),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_x_2),c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),V_S_2)))) ),
file('theBenchmark.p',fact_in__rtrancl__UnI) ).
fof(fact_r__comp__rtrancl__eq,axiom,
! [V_r_2,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_r_2),c_Transitive__Closure_Ortrancl(T_c,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,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_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_R_2)),c_Transitive__Closure_Ortrancl(T_c,V_R_2)) = c_Transitive__Closure_Ortrancl(T_c,V_R_2),
file('theBenchmark.p',fact_rtrancl__idemp__self__comp) ).
fof(fact_rtrancl__subset__rtrancl,axiom,
! [V_s_2,V_r_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_c,V_s_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),c_Transitive__Closure_Ortrancl(T_c,V_s_2))) ),
file('theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(fact_rtrancl__subset,axiom,
! [V_S_2,V_R_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,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_c,T_c),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_c,V_R_2)))
=> c_Transitive__Closure_Ortrancl(T_c,V_S_2) = c_Transitive__Closure_Ortrancl(T_c,V_R_2) ) ),
file('theBenchmark.p',fact_rtrancl__subset) ).
fof(fact_rtrancl__mono,axiom,
! [V_s_2,V_r_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,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_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),c_Transitive__Closure_Ortrancl(T_c,V_s_2))) ),
file('theBenchmark.p',fact_rtrancl__mono) ).
fof(fact_rtrancl__Un__subset,axiom,
! [V_S_2,V_R_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_R_2)),c_Transitive__Closure_Ortrancl(T_c,V_S_2))),c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),V_S_2)))),
file('theBenchmark.p',fact_rtrancl__Un__subset) ).
fof(fact_rtrancl__Un__rtrancl,axiom,
! [V_S_2,V_R_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_R_2)),c_Transitive__Closure_Ortrancl(T_c,V_S_2))) = c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),V_S_2)),
file('theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
fof(fact_Image__closed__trancl,axiom,
! [V_X_2,V_r_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r_2),V_X_2)),V_X_2))
=> hAPP(c_Relation_OImage(T_c,T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)),V_X_2) = V_X_2 ),
file('theBenchmark.p',fact_Image__closed__trancl) ).
fof(fact_rtrancl__idemp,axiom,
! [V_r_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)) = c_Transitive__Closure_Ortrancl(T_c,V_r_2),
file('theBenchmark.p',fact_rtrancl__idemp) ).
fof(fact_rtrancl__trans,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,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_c_2)),c_Transitive__Closure_Ortrancl(T_c,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_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__trans) ).
fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,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_c_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_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(fact_converse__rtrancl__into__rtrancl,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_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_c_2)),c_Transitive__Closure_Ortrancl(T_c,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_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(fact_refl__rtrancl,axiom,
! [V_r_2,T_c] : c_Relation_Orefl__on(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),
file('theBenchmark.p',fact_refl__rtrancl) ).
fof(fact_rtrancl__trancl__trancl,axiom,
! [V_z_2,V_r_2,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,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_2),V_z_2)),c_Transitive__Closure_Otrancl(T_c,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_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__trancl__trancl) ).
fof(fact_trancl__rtrancl__trancl,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_c,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_c_2)),c_Transitive__Closure_Ortrancl(T_c,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_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__rtrancl__trancl) ).
fof(fact_rtrancl__into__trancl1,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,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_c_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_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__into__trancl1) ).
fof(fact_rtranclD,axiom,
! [V_R_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,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_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_c,V_R_2)))
& V_a_2 != V_b_2 )
| V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_rtranclD) ).
fof(fact_rtrancl__into__trancl2,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_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_c_2)),c_Transitive__Closure_Ortrancl(T_c,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_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__into__trancl2) ).
fof(fact_rtrancl__eq__or__trancl,axiom,
! [V_R_2,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,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_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_c,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_Not__Domain__rtrancl,axiom,
! [V_y_2,V_R_2,V_x_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ODomain(T_c,T_c),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_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_R_2)))
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(fact_acc__downwards,axiom,
! [V_b_2,V_r_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Wellfounded_Oacc(T_c,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_a_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Wellfounded_Oacc(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downwards) ).
fof(fact_acc__downwards__aux,axiom,
! [V_r_2,V_a_2,V_b_2,T_c] :
( 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_a_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Wellfounded_Oacc(T_c,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Wellfounded_Oacc(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downwards__aux) ).
fof(fact_wf__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_c] :
( c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_x_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_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)))
& c_Wellfounded_Owf(T_c,V_r_2) ) ),
file('theBenchmark.p',fact_wf__insert) ).
fof(fact_acyclic__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_c] :
( c_Wellfounded_Oacyclic(T_c,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_x_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_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)))
& c_Wellfounded_Oacyclic(T_c,V_r_2) ) ),
file('theBenchmark.p',fact_acyclic__insert) ).
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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2))))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
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_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_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_irrefl__tranclI,axiom,
! [V_x_2,V_r_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_c,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_c] :
( ! [B_i] : 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,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_c,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,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_c,V_r_2))) ),
file('theBenchmark.p',fact_sequence__trans) ).
fof(fact_acyclic__converse,axiom,
! [V_r_2,T_c] :
( c_Wellfounded_Oacyclic(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2))
<=> c_Wellfounded_Oacyclic(T_c,V_r_2) ),
file('theBenchmark.p',fact_acyclic__converse) ).
fof(fact_converse__UNION,axiom,
! [V_r_2,V_S_2,T_e,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),T_e),c_Relation_Oconverse(T_d,T_c)),V_r_2)),
file('theBenchmark.p',fact_converse__UNION) ).
fof(fact_converse__rel__comp,axiom,
! [V_s_2,V_r_2,T_e,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_d,T_e,T_c),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),hAPP(c_Relation_Oconverse(T_e,T_c),V_s_2)),hAPP(c_Relation_Oconverse(T_d,T_e),V_r_2)),
file('theBenchmark.p',fact_converse__rel__comp) ).
fof(fact_converse__Un,axiom,
! [V_s_2,V_r_2,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)),hAPP(c_Relation_Oconverse(T_d,T_c),V_s_2)),
file('theBenchmark.p',fact_converse__Un) ).
fof(fact_converse__Id__on,axiom,
! [V_A_2,T_c] : hAPP(c_Relation_Oconverse(T_c,T_c),c_Relation_OId__on(T_c,V_A_2)) = c_Relation_OId__on(T_c,V_A_2),
file('theBenchmark.p',fact_converse__Id__on) ).
fof(fact_converse__inv__image,axiom,
! [V_f_2,V_R_2,T_d,T_c] : hAPP(c_Relation_Oconverse(T_c,T_c),hAPP(hAPP(c_Relation_Oinv__image(T_d,T_c),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_d),V_R_2)),V_f_2),
file('theBenchmark.p',fact_converse__inv__image) ).
fof(fact_converse__Int,axiom,
! [V_s_2,V_r_2,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)),hAPP(c_Relation_Oconverse(T_d,T_c),V_s_2)),
file('theBenchmark.p',fact_converse__Int) ).
fof(fact_converse__converse,axiom,
! [V_r_2,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)) = V_r_2,
file('theBenchmark.p',fact_converse__converse) ).
fof(fact_finite__converse,axiom,
! [V_r_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_d,T_c)),V_r_2)) ),
file('theBenchmark.p',fact_finite__converse) ).
fof(fact_Field__converse,axiom,
! [V_r_2,T_c] : hAPP(c_Relation_OField(T_c),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) = hAPP(c_Relation_OField(T_c),V_r_2),
file('theBenchmark.p',fact_Field__converse) ).
fof(fact_converse__iff,axiom,
! [V_r_2,V_b_2,V_a_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),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_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2))) ),
file('theBenchmark.p',fact_converseI) ).
fof(fact_converseD,axiom,
! [V_r_2,V_b_2,V_a_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_b_2),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_converseD) ).
fof(fact_refl__on__converse,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Relation_Orefl__on(T_c,V_A_2,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2))
<=> c_Relation_Orefl__on(T_c,V_A_2,V_r_2) ),
file('theBenchmark.p',fact_refl__on__converse) ).
fof(fact_converse__INTER,axiom,
! [V_r_2,V_S_2,T_e,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),T_e),c_Relation_Oconverse(T_d,T_c)),V_r_2)),
file('theBenchmark.p',fact_converse__INTER) ).
fof(fact_trancl__converse,axiom,
! [V_r_2,T_c] : c_Transitive__Closure_Otrancl(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) = hAPP(c_Relation_Oconverse(T_c,T_c),c_Transitive__Closure_Otrancl(T_c,V_r_2)),
file('theBenchmark.p',fact_trancl__converse) ).
fof(fact_rtrancl__converse,axiom,
! [V_r_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) = hAPP(c_Relation_Oconverse(T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),
file('theBenchmark.p',fact_rtrancl__converse) ).
fof(fact_wf__converse__trancl,axiom,
! [V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2))
=> c_Wellfounded_Owf(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),c_Transitive__Closure_Otrancl(T_c,V_r_2))) ),
file('theBenchmark.p',fact_wf__converse__trancl) ).
fof(fact_equiv__comp__eq,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(c_Relation_Oconverse(T_c,T_c),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_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)) = hAPP(c_Relation_ODomain(T_c,T_d),V_r_2),
file('theBenchmark.p',fact_Range__converse) ).
fof(fact_Domain__converse,axiom,
! [V_r_2,T_d,T_c] : hAPP(c_Relation_ODomain(T_c,T_d),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)) = hAPP(c_Relation_ORange(T_d,T_c),V_r_2),
file('theBenchmark.p',fact_Domain__converse) ).
fof(fact_Range__def,axiom,
! [V_r_2,T_c,T_d] : hAPP(c_Relation_ORange(T_d,T_c),V_r_2) = hAPP(c_Relation_ODomain(T_c,T_d),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)),
file('theBenchmark.p',fact_Range__def) ).
fof(fact_rtrancl__converseI,axiom,
! [V_r_2,V_x_2,V_y_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_c,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_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)))) ),
file('theBenchmark.p',fact_rtrancl__converseI) ).
fof(fact_rtrancl__converseD,axiom,
! [V_r_2,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),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_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2))) ),
file('theBenchmark.p',fact_rtrancl__converseD) ).
fof(fact_trancl__converseI,axiom,
! [V_r_2,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_c,T_c),c_Transitive__Closure_Otrancl(T_c,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_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)))) ),
file('theBenchmark.p',fact_trancl__converseI) ).
fof(fact_trancl__converseD,axiom,
! [V_r_2,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),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_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_c,T_c),c_Transitive__Closure_Otrancl(T_c,V_r_2)))) ),
file('theBenchmark.p',fact_trancl__converseD) ).
fof(fact_Image__subset__eq,axiom,
! [V_B_2,V_A_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),V_A_2)),V_B_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_d,hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,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_c] :
( c_Relation_Orefl__on(T_c,V_A_2,V_r_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(c_Relation_Oconverse(T_c,T_c),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_c] :
( hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)),V_r_2) = V_r_2
=> ( hAPP(c_Relation_ODomain(T_c,T_c),V_r_2) = V_A_2
=> c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ) ),
file('theBenchmark.p',fact_comp__equivI) ).
fof(fact_finite__acyclic__wf__converse,axiom,
! [V_r_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_c)),V_r_2))
=> ( c_Wellfounded_Oacyclic(T_c,V_r_2)
=> c_Wellfounded_Owf(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) ) ),
file('theBenchmark.p',fact_finite__acyclic__wf__converse) ).
fof(fact_converse__def,axiom,
! [V_r_2,T_c,T_d] : hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),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_r_2))),
file('theBenchmark.p',fact_converse__def) ).
fof(fact_Image__INT__eq,axiom,
! [V_B_2,T_e,V_A_2,V_r_2,T_d,T_c] :
( c_Relation_Osingle__valued(T_c,T_d,hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_e,tc_HOL_Obool))
=> hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Relation_OImage(T_d,T_c,V_r_2)),V_B_2)) ) ),
file('theBenchmark.p',fact_Image__INT__eq) ).
fof(fact_reflcl__set__eq,axiom,
! [V_y_2,V_x_2,V_r_2,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_r_2)),c_fequal),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c)))) ),
file('theBenchmark.p',fact_reflcl__set__eq) ).
fof(fact_IdI,axiom,
! [V_a_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_a_2)),c_Relation_OId(T_c))),
file('theBenchmark.p',fact_IdI) ).
fof(fact_converse__Id,axiom,
! [T_c] : hAPP(c_Relation_Oconverse(T_c,T_c),c_Relation_OId(T_c)) = c_Relation_OId(T_c),
file('theBenchmark.p',fact_converse__Id) ).
fof(fact_single__valued__subset,axiom,
! [V_s_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_2),V_s_2))
=> ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
=> c_Relation_Osingle__valued(T_c,T_d,V_r_2) ) ),
file('theBenchmark.p',fact_single__valued__subset) ).
fof(fact_single__valued__rel__comp,axiom,
! [V_s_2,T_e,V_r_2,T_d,T_c] :
( c_Relation_Osingle__valued(T_c,T_d,V_r_2)
=> ( c_Relation_Osingle__valued(T_d,T_e,V_s_2)
=> c_Relation_Osingle__valued(T_c,T_e,hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_e),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_single__valued__rel__comp) ).
fof(fact_single__valued__Id,axiom,
! [T_c] : c_Relation_Osingle__valued(T_c,T_c,c_Relation_OId(T_c)),
file('theBenchmark.p',fact_single__valued__Id) ).
fof(fact_Image__Id,axiom,
! [V_A_2,T_c] : hAPP(c_Relation_OImage(T_c,T_c,c_Relation_OId(T_c)),V_A_2) = V_A_2,
file('theBenchmark.p',fact_Image__Id) ).
fof(fact_Id__O__R,axiom,
! [V_R_2,T_d,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_d),c_Relation_OId(T_c)),V_R_2) = V_R_2,
file('theBenchmark.p',fact_Id__O__R) ).
fof(fact_R__O__Id,axiom,
! [V_R_2,T_d,T_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_d),V_R_2),c_Relation_OId(T_d)) = V_R_2,
file('theBenchmark.p',fact_R__O__Id) ).
fof(fact_single__valued__Id__on,axiom,
! [V_A_2,T_c] : c_Relation_Osingle__valued(T_c,T_c,c_Relation_OId__on(T_c,V_A_2)),
file('theBenchmark.p',fact_single__valued__Id__on) ).
fof(fact_pair__in__Id__conv,axiom,
! [V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Relation_OId(T_c)))
<=> V_a_2 = V_b_2 ),
file('theBenchmark.p',fact_pair__in__Id__conv) ).
fof(fact_Domain__Id,axiom,
! [T_c] : hAPP(c_Relation_ODomain(T_c,T_c),c_Relation_OId(T_c)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Domain__Id) ).
fof(fact_rtrancl__empty,axiom,
! [T_c] : c_Transitive__Closure_Ortrancl(T_c,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))) = c_Relation_OId(T_c),
file('theBenchmark.p',fact_rtrancl__empty) ).
fof(fact_Range__Id,axiom,
! [T_c] : hAPP(c_Relation_ORange(T_c,T_c),c_Relation_OId(T_c)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_Range__Id) ).
fof(fact_rtrancl__reflcl,axiom,
! [V_R_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_c))) = c_Transitive__Closure_Ortrancl(T_c,V_R_2),
file('theBenchmark.p',fact_rtrancl__reflcl) ).
fof(fact_rtrancl__reflcl__absorb,axiom,
! [V_R_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_R_2)),c_Relation_OId(T_c)) = c_Transitive__Closure_Ortrancl(T_c,V_R_2),
file('theBenchmark.p',fact_rtrancl__reflcl__absorb) ).
fof(fact_refl__Id,axiom,
! [T_c] : c_Relation_Orefl__on(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Relation_OId(T_c)),
file('theBenchmark.p',fact_refl__Id) ).
fof(fact_rtrancl__r__diff__Id,axiom,
! [V_r_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))) = c_Transitive__Closure_Ortrancl(T_c,V_r_2),
file('theBenchmark.p',fact_rtrancl__r__diff__Id) ).
fof(fact_single__valuedD,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_d,T_c] :
( c_Relation_Osingle__valued(T_c,T_d,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)),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_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_d,T_c] :
( c_Relation_Osingle__valued(T_c,T_d,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)),V_r_2))
=> ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_z)),V_r_2))
=> B_y = B_z ) ) ),
file('theBenchmark.p',fact_single__valued__def) ).
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_reflcl__trancl,axiom,
! [V_r_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_c,V_r_2)),c_Relation_OId(T_c)) = c_Transitive__Closure_Ortrancl(T_c,V_r_2),
file('theBenchmark.p',fact_reflcl__trancl) ).
fof(fact_trancl__reflcl,axiom,
! [V_r_2,T_c] : c_Transitive__Closure_Otrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))) = c_Transitive__Closure_Ortrancl(T_c,V_r_2),
file('theBenchmark.p',fact_trancl__reflcl) ).
fof(fact_rtrancl__unfold,axiom,
! [V_r_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Relation_OId(T_c)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),V_r_2)),
file('theBenchmark.p',fact_rtrancl__unfold) ).
fof(fact_refl__reflcl,axiom,
! [V_r_2,T_c] : c_Relation_Orefl__on(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))),
file('theBenchmark.p',fact_refl__reflcl) ).
fof(fact_Id__def,axiom,
! [T_c] : c_Relation_OId(T_c) = hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_c,T_c)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(tc_prod(T_c,T_c),tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_HOL_Obool)),tc_prod(T_c,T_c)),c_COMBB(tc_prod(T_c,T_c),tc_HOL_Obool,T_c)),c_fequal)),hAPP(hAPP(c_COMBS(T_c,T_c,tc_prod(T_c,T_c)),c_Product__Type_OPair(T_c,T_c)),c_COMBI(T_c))))),
file('theBenchmark.p',fact_Id__def) ).
fof(fact_irrefl__diff__Id,axiom,
! [V_r_2,T_c] : c_Relation_Oirrefl(T_c,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))),
file('theBenchmark.p',fact_irrefl__diff__Id) ).
fof(fact_single__valued__confluent,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_c] :
( c_Relation_Osingle__valued(T_c,T_c,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_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,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_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_c,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_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,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_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_c,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_d,T_c] :
( c_Relation_Osingle__valued(T_c,T_d,hAPP(c_Relation_Oconverse(T_d,T_c),V_R_2))
=> hAPP(c_Relation_OImage(T_d,T_c,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_Relation_OImage(T_d,T_c,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),V_B_2)) ),
file('theBenchmark.p',fact_Image__Int__eq) ).
fof(fact_rtrancl__Int__subset,axiom,
! [V_r_2,V_s_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Relation_OId(T_c)),V_s_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,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_c,T_c),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)),V_s_2)) ) ),
file('theBenchmark.p',fact_rtrancl__Int__subset) ).
fof(fact_total__on__diff__Id,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Relation_Ototal__on(T_c,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c)))
<=> c_Relation_Ototal__on(T_c,V_A_2,V_r_2) ),
file('theBenchmark.p',fact_total__on__diff__Id) ).
fof(fact_rtrancl__imp__UN__rel__pow,axiom,
! [V_R_2,V_p_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Ortrancl(T_c,V_R_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_c,T_c),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_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2)))) ),
file('theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).
fof(fact_single__valued__rel__pow,axiom,
! [V_n_2,V_R_2,T_c] :
( c_Relation_Osingle__valued(T_c,T_c,V_R_2)
=> c_Relation_Osingle__valued(T_c,T_c,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2)) ),
file('theBenchmark.p',fact_single__valued__rel__pow) ).
fof(fact_comp__funpow,axiom,
! [V_f_2,V_n_2,T_d,T_c] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),V_n_2),c_Fun_Ocomp(T_d,T_d,T_c,V_f_2)) = c_Fun_Ocomp(T_d,T_d,T_c,hAPP(hAPP(c_Nat_Ocompow(T_d,T_d),V_n_2),V_f_2)),
file('theBenchmark.p',fact_comp__funpow) ).
fof(fact_wf__exp,axiom,
! [V_R_2,V_n_2,T_c] :
( c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2))
=> c_Wellfounded_Owf(T_c,V_R_2) ),
file('theBenchmark.p',fact_wf__exp) ).
fof(fact_funpow__mult,axiom,
! [V_f_2,V_m_2,V_n_2,T_c] : hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),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_funpow__swap1,axiom,
! [V_x_2,V_n_2,T_c,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)),
file('theBenchmark.p',fact_funpow__swap1) ).
fof(fact_rel__pow__1,axiom,
! [V_R_2,T_c] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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_c] : hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
file('theBenchmark.p',fact_rel__pow__commute) ).
fof(fact_rel__pow__imp__rtrancl,axiom,
! [V_R_2,V_n_2,V_p_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) ),
file('theBenchmark.p',fact_rel__pow__imp__rtrancl) ).
fof(fact_rtrancl__power,axiom,
! [V_R_2,V_p_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Ortrancl(T_c,V_R_2)))
<=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),B_n),V_R_2))) ),
file('theBenchmark.p',fact_rtrancl__power) ).
fof(fact_relpow_Osimps_I2_J,axiom,
! [V_R_2,V_n_2,T_c] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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_c] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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_c,T_c,T_c),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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_c] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_c),
file('theBenchmark.p',fact_relpow_Osimps_I1_J) ).
fof(fact_total__on__empty,axiom,
! [V_r_2,T_c] : c_Relation_Ototal__on(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c] :
( c_Relation_Ototal__on(T_c,V_A_2,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2))
<=> c_Relation_Ototal__on(T_c,V_A_2,V_r_2) ),
file('theBenchmark.p',fact_total__on__converse) ).
fof(fact_rel__pow__0__I,axiom,
! [V_R_2,V_x_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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__0__E,axiom,
! [V_R_2,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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__Suc__I2,axiom,
! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_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),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_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_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_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_2),V_z_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_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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_c] : hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),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_c] : hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)),
file('theBenchmark.p',fact_funpow__add) ).
fof(fact_funpow_Osimps_I1_J,axiom,
! [V_f_2,T_c] : hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_c),
file('theBenchmark.p',fact_funpow_Osimps_I1_J) ).
fof(fact_trancl__power,axiom,
! [V_R_2,V_p_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Transitive__Closure_Otrancl(T_c,V_R_2)))
<=> ? [B_n] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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_total__on__def,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Relation_Ototal__on(T_c,V_A_2,V_r_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_A_2))
=> ( B_x != B_xa
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_xa),B_x)),V_r_2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_xa)),V_r_2)) ) ) ) ) ),
file('theBenchmark.p',fact_total__on__def) ).
fof(fact_rtrancl__is__UN__rel__pow,axiom,
! [V_R_2,T_c] : c_Transitive__Closure_Ortrancl(T_c,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_c,T_c),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_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool)),V_R_2)),
file('theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).
fof(fact_funpow__code__def,axiom,
! [T_c] : c_Nat_Ofunpow(T_c) = c_Nat_Ocompow(T_c,T_c),
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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),B_y)),V_R_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),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_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),B_m),V_R_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),V_z_2)),V_R_2)) ) ) ) ),
file('theBenchmark.p',fact_rel__pow__E) ).
fof(fact_acyclicI,axiom,
! [V_r_2,T_c] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),c_Transitive__Closure_Otrancl(T_c,V_r_2)))
=> c_Wellfounded_Oacyclic(T_c,V_r_2) ),
file('theBenchmark.p',fact_acyclicI) ).
fof(fact_rtrancl__Un__separator__converseE,axiom,
! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2),V_Qa_2))))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_Pa_2)))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),B_x)),V_Qa_2))
=> B_y = B_x ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_Pa_2))) ) ),
file('theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
fof(fact_rtrancl__Un__separatorE,axiom,
! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_Pa_2),V_Qa_2))))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_c,V_Pa_2)))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_Qa_2))
=> B_x = B_y ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_c,V_Pa_2))) ) ),
file('theBenchmark.p',fact_rtrancl__Un__separatorE) ).
fof(fact_rel__pow__Suc__D2,axiom,
! [V_R_2,V_n_2,V_z_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
=> ? [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_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_x_2),B_y)),V_R_2)) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__D2) ).
fof(fact_rel__pow__Suc__E2,axiom,
! [V_R_2,V_n_2,V_z_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
=> ~ ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),B_y)),V_R_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_2),V_R_2))) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__E2) ).
fof(fact_rel__pow__Suc__E,axiom,
! [V_R_2,V_n_2,V_z_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
=> ~ ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_c,T_c),tc_HOL_Obool),V_n_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),B_y),V_z_2)),V_R_2)) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__E) ).
fof(fact_tranclD2,axiom,
! [V_R_2,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_c,V_R_2)))
=> ? [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_z),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),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_c,V_R_2))) ) ),
file('theBenchmark.p',fact_tranclD2) ).
fof(fact_tranclD,axiom,
! [V_R_2,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_c,V_R_2)))
=> ? [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,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_x_2),B_z)),V_R_2)) ) ),
file('theBenchmark.p',fact_tranclD) ).
fof(fact_IdE,axiom,
! [V_p_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),V_p_2),c_Relation_OId(T_c)))
=> ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x) ),
file('theBenchmark.p',fact_IdE) ).
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_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_wf__eq__minimal,axiom,
! [V_r_2,T_c] :
( c_Wellfounded_Owf(T_c,V_r_2)
<=> ! [B_Q] :
( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_c),B_x),B_Q))
=> ? [B_x] :
( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),B_x)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),B_y),B_Q)) )
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),B_Q)) ) ) ),
file('theBenchmark.p',fact_wf__eq__minimal) ).
fof(fact_transfer__nat__int__set__cong,axiom,
! [V_P_Ha_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_Ha_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_Ha_2)) ),
file('theBenchmark.p',fact_transfer__nat__int__set__cong) ).
fof(fact_Int__Collect__mono,axiom,
! [V_Qa_2,V_Pa_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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(V_Pa_2,B_x))
=> hBOOL(hAPP(V_Qa_2,B_x)) ) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_c),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_c),V_Qa_2)))) ) ),
file('theBenchmark.p',fact_Int__Collect__mono) ).
fof(fact_UnionE,axiom,
! [V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2)))
=> ~ ! [B_X] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),B_X))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_X),V_C_2)) ) ),
file('theBenchmark.p',fact_UnionE) ).
fof(fact_rel__compE,axiom,
! [V_s_2,V_r_2,T_e,V_xz_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_e,T_d),V_r_2),V_s_2)))
=> ~ ! [B_x,B_y,B_z] :
( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_z)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_e),B_x),B_y)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_e,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_e,T_d),B_y),B_z)),V_s_2)) ) ) ),
file('theBenchmark.p',fact_rel__compE) ).
fof(fact_converseE,axiom,
! [V_r_2,V_yx_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),V_yx_2),hAPP(c_Relation_Oconverse(T_d,T_c),V_r_2)))
=> ~ ! [B_x,B_y] :
( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_y),B_x)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_x),B_y)),V_r_2)) ) ),
file('theBenchmark.p',fact_converseE) ).
fof(fact_Nitpick_Oplus__frac__def,axiom,
! [V_r_2,V_q_2,T_c] : c_Nitpick_Oplus__frac(T_c,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_c),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_c),V_q_2),hAPP(c_Nitpick_Odenom(T_c),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_c),tc_Int_Oint),c_Nitpick_Ofrac(T_c)),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_c),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_c),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_c),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_c),V_r_2)))))),c_COMBI(tc_Int_Oint))),
file('theBenchmark.p',fact_Nitpick_Oplus__frac__def) ).
fof(fact_setprod__pos,axiom,
! [V_f_2,V_A_2,T_c,T_d] :
( class_Rings_Olinordered__semidom(T_d)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_setprod__pos) ).
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_c] :
( c_Nitpick_Oless__frac(T_c,V_q_2,V_r_2)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_c),c_Nitpick_Oplus__frac(T_c,V_q_2,c_Nitpick_Ouminus__frac(T_c,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_c] :
( c_Nitpick_Oless__eq__frac(T_c,V_q_2,V_r_2)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_c),c_Nitpick_Oplus__frac(T_c,V_q_2,c_Nitpick_Ouminus__frac(T_c,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_Nitpick_Oless__eq__frac__def) ).
fof(fact_Nitpick_Onum__def,axiom,
! [T_c] : c_Nitpick_Onum(T_c) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_c,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_c)),
file('theBenchmark.p',fact_Nitpick_Onum__def) ).
fof(fact_Nitpick_Odenom__def,axiom,
! [T_c] : c_Nitpick_Odenom(T_c) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_c,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_c)),
file('theBenchmark.p',fact_Nitpick_Odenom__def) ).
fof(fact_internal__split__def,axiom,
! [T_e,T_d,T_c] : c_Product__Type_Ointernal__split(T_c,T_d,T_e) = c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),
file('theBenchmark.p',fact_internal__split__def) ).
fof(fact_setprod__nonneg,axiom,
! [V_f_2,V_A_2,T_c,T_d] :
( class_Rings_Olinordered__semidom(T_d)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_setprod__nonneg) ).
fof(fact_internal__split__conv,axiom,
! [V_b_2,V_a_2,V_c_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_d,T_e,T_c),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2),
file('theBenchmark.p',fact_internal__split__conv) ).
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_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_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_c] : c_List_Olenlex(T_c,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_c)),tc_List_Olist(T_c)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_c),c_Wellfounded_Oless__than,c_List_Olex(T_c,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_prod(tc_Nat_Onat,tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_c),tc_prod(tc_Nat_Onat,tc_List_Olist(T_c))),tc_List_Olist(T_c)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_c))),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),c_COMBI(tc_List_Olist(T_c)))),
file('theBenchmark.p',fact_lenlex__def) ).
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_lexn__length,axiom,
! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_c,V_r_2),V_n_2)))
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) = V_n_2
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = V_n_2 ) ),
file('theBenchmark.p',fact_lexn__length) ).
fof(fact_lenlex__conv,axiom,
! [V_r_2,T_c] : c_List_Olenlex(T_c,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBS(tc_List_Olist(T_c),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_c)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_c)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBS(tc_List_Olist(T_c),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_c)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBC(tc_List_Olist(T_c),tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(tc_List_Olist(T_c),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))))),c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c))))),c_List_Olex(T_c,V_r_2)))))),
file('theBenchmark.p',fact_lenlex__conv) ).
fof(fact_length__sublist,axiom,
! [V_I_2,V_xs_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Osublist(T_c,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_c)),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_c] : hAPP(c_List_Olexn(T_c,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_c),tc_List_Olist(T_c)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_c,tc_List_Olist(T_c)),tc_prod(T_c,tc_List_Olist(T_c))),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_Product__Type_Omap__pair(tc_prod(T_c,tc_List_Olist(T_c)),tc_List_Olist(T_c),tc_prod(T_c,tc_List_Olist(T_c)),tc_List_Olist(T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)))),c_Wellfounded_Olex__prod(T_c,tc_List_Olist(T_c),V_r_2,hAPP(c_List_Olexn(T_c,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),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_c] :
( hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))),c_List_Olex(T_c,V_r_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olex(T_c,V_r_2)))
& V_x_2 = V_y_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_c)),V_ys_2)
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),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_c] : c_List_Oset__Cons(T_c,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_c)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_List_Olist(T_c)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),tc_List_Olist(T_c)),c_COMBS(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),T_c),c_COMBS(tc_List_Olist(T_c),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_c)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),tc_List_Olist(T_c)),c_COMBB(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBB(tc_List_Olist(T_c),tc_HOL_Obool,tc_List_Olist(T_c))),c_fequal))),c_List_Olist_OCons(T_c)))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),T_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c))),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_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_c))),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_c] : c_Random_Oselect__weight(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_c),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_y_2))),c_List_Olexord(T_c,V_r_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olexord(T_c,V_r_2)))
& V_a_2 = V_b_2 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olex(T_c,V_r_2)))
<=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_y_2)
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olexord(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_c,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,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_c] : c_List_Olist_Olist__size(T_c,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),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_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Wellfounded_Oacc(T_c,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) ) ),
file('theBenchmark.p',fact_Cons__acc__listrel1I) ).
fof(fact_listrel1__mono,axiom,
! [V_s_2,V_r_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),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_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_List_Olistrel1(T_c,V_r_2)),c_List_Olistrel1(T_c,V_s_2))) ),
file('theBenchmark.p',fact_listrel1__mono) ).
fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
! [V_r_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_List_Olistrel1(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))),
file('theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).
fof(fact_listrel1__converse,axiom,
! [V_r_2,T_c] : c_List_Olistrel1(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olistrel1(T_c,V_r_2)),
file('theBenchmark.p',fact_listrel1__converse) ).
fof(fact_rtrancl__listrel1__ConsI1,axiom,
! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_ys_2))),c_List_Olistrel1(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2))))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_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_c)),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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olistrel1(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olistrel1(T_c,V_r_2)))) ),
file('theBenchmark.p',fact_in__listrel1__converse) ).
fof(fact_listrel1I1,axiom,
! [V_xs_2,V_r_2,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_xs_2))),c_List_Olistrel1(T_c,V_r_2))) ),
file('theBenchmark.p',fact_listrel1I1) ).
fof(fact_Cons__listrel1__Cons,axiom,
! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))),c_List_Olistrel1(T_c,V_r_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2)))
& V_x_2 = V_y_2 )
| ( V_xs_2 = V_ys_2
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_Cons__listrel1__Cons) ).
fof(fact_listrel__Cons,axiom,
! [V_xs_2,V_x_2,V_r_2,T_c] : hAPP(c_Relation_OImage(tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Olistrel(T_c,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)))) = c_List_Oset__Cons(T_c,hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Olistrel(T_c,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))))),
file('theBenchmark.p',fact_listrel__Cons) ).
fof(fact_lexord__irreflexive,axiom,
! [V_y_2,V_r_2,T_c] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_y_2),V_y_2)),c_List_Olexord(T_c,V_r_2))) ),
file('theBenchmark.p',fact_lexord__irreflexive) ).
fof(fact_listrel__rtrancl__refl,axiom,
! [V_r_2,V_xs_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_xs_2)),c_List_Olistrel(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)))),
file('theBenchmark.p',fact_listrel__rtrancl__refl) ).
fof(fact_listrel__mono,axiom,
! [V_s_2,V_r_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),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_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_List_Olistrel(T_c,V_r_2)),c_List_Olistrel(T_c,V_s_2))) ),
file('theBenchmark.p',fact_listrel__mono) ).
fof(fact_listrel__subset__rtrancl__listrel1,axiom,
! [V_r_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_List_Olistrel(T_c,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,V_r_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_c)),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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_ys_2),V_zs_2)),c_List_Olistrel(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_zs_2)),c_List_Olistrel(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)))) ) ),
file('theBenchmark.p',fact_listrel__rtrancl__trans) ).
fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
! [V_r_2,T_c] : c_List_Olistrel(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,c_Transitive__Closure_Ortrancl(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_r_H_2))
=> ( c_Relation_Orefl__on(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_r_H_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_List_Olistrel1(T_c,V_r_2)),c_List_Olistrel(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_c),c_List_Olistrel1(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))),c_List_Olistrel(T_c,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_c] :
( c_List_Olistrelp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_r_2),V_x_2,V_xa_2)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_xa_2)),c_List_Olistrel(T_c,V_r_2))) ),
file('theBenchmark.p',fact_listrelp__listrel__eq) ).
fof(fact_listrel__Cons2,axiom,
! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))),c_List_Olistrel(T_c,V_r_2)))
=> ~ ! [B_x,B_xs] :
( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),B_x),B_xs)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),V_y_2)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),B_xs),V_ys_2)),c_List_Olistrel(T_c,V_r_2))) ) ) ),
file('theBenchmark.p',fact_listrel__Cons2) ).
fof(fact_listrelp_OCons,axiom,
! [V_ys_2,V_xs_2,T_c,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_c,V_r_2,V_xs_2,V_ys_2)
=> c_List_Olistrelp(T_c,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),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_c] :
( c_List_Olistrelp(T_c,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a2_2),V_a4_2))
<=> ( c_List_Olistrelp(T_c,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__Cons1,axiom,
! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_c,V_r_2)))
=> ~ ! [B_y,B_ys] :
( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),B_y),B_ys)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),B_y)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_ys_2),B_ys)),c_List_Olistrel(T_c,V_r_2))) ) ) ),
file('theBenchmark.p',fact_listrel__Cons1) ).
fof(fact_listrel__subset,axiom,
! [V_A_2,V_r_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_c),V_A_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_HOL_Obool)),c_List_Olistrel(T_c,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olists(T_c,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_List_Olist(T_c)),c_List_Olists(T_c,V_A_2))))) ),
file('theBenchmark.p',fact_listrel__subset) ).
fof(fact_lists__UNIV,axiom,
! [T_c] : c_List_Olists(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),
file('theBenchmark.p',fact_lists__UNIV) ).
fof(fact_lists__mono,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),c_List_Olists(T_c,V_A_2)),c_List_Olists(T_c,V_B_2))) ),
file('theBenchmark.p',fact_lists__mono) ).
fof(fact_equiv__listrel,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> c_Equiv__Relations_Oequiv(tc_List_Olist(T_c),c_List_Olists(T_c,V_A_2),c_List_Olistrel(T_c,V_r_2)) ),
file('theBenchmark.p',fact_equiv__listrel) ).
fof(fact_listrel__refl__on,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Relation_Orefl__on(T_c,V_A_2,V_r_2)
=> c_Relation_Orefl__on(tc_List_Olist(T_c),c_List_Olists(T_c,V_A_2),c_List_Olistrel(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),c_List_Olists(T_c,V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_List_Olists(T_c,V_A_2)))
& hBOOL(hAPP(hAPP(c_member(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_List_Olists(T_c,c_Wellfounded_Oacc(T_c,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2)))) ),
file('theBenchmark.p',fact_lists__accD) ).
fof(fact_lists__accI,axiom,
! [V_r_2,V_xs_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_c),c_List_Olistrel1(T_c,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_List_Olists(T_c,c_Wellfounded_Oacc(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,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_c)),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_n))),V_r_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_c)),V_ys_2) ) ),
file('theBenchmark.p',fact_listrel__iff__nth) ).
fof(fact_lexord__linear,axiom,
! [V_y_2,V_x_2,V_r_2,T_c] :
( ! [B_a,B_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_b),B_a)),V_r_2))
| B_a = B_b
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_a),B_b)),V_r_2)) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_y_2),V_x_2)),c_List_Olexord(T_c,V_r_2)))
| V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olexord(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_lexord__linear) ).
fof(fact_infinite__UNIV__listI,axiom,
! [T_c] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)))),
file('theBenchmark.p',fact_infinite__UNIV__listI) ).
fof(fact_list__eq__iff__nth__eq,axiom,
! [T_c,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_c)),V_xs_2)))
=> hAPP(hAPP(c_List_Onth(T_c),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_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ),
file('theBenchmark.p',fact_list__eq__iff__nth__eq) ).
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__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_Osimps,axiom,
! [V_n_2,V_xs_2,V_x_2,T_c] : hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_c,V_x_2,hAPP(c_List_Onth(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olexord(T_c,V_r_2)))
<=> ( ? [B_i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(hAPP(c_List_Onth(T_c),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_y_2),B_i))),V_r_2))
& hAPP(hAPP(c_List_Otake(T_c),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_c),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_c)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_y_2)))) )
| ( hAPP(hAPP(c_List_Otake(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),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_c)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_y_2))) ) ) ),
file('theBenchmark.p',fact_lexord__take__index__conv) ).
fof(fact_set__sublist,axiom,
! [V_I_2,V_xs_2,T_c] : hAPP(c_List_Oset(T_c),c_List_Osublist(T_c,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(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)),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)),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(T_c,tc_fun(tc_Nat_Onat,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_c),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_c)),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_c] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_List_Oset(T_c),V_xs_2))),
file('theBenchmark.p',fact_finite__set) ).
fof(fact_set__subset__Cons,axiom,
! [V_x_2,V_xs_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),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,axiom,
! [V_xs_2,V_n_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_c),V_xs_2))),
file('theBenchmark.p',fact_set__take__subset) ).
fof(fact_set__take__subset__set__take,axiom,
! [V_xs_2,T_c,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_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Otake(T_c),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)))) ),
file('theBenchmark.p',fact_set__take__subset__set__take) ).
fof(fact_set__sublist__subset,axiom,
! [V_I_2,V_xs_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),c_List_Osublist(T_c,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_c),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_notin__set__sublistI,axiom,
! [V_I_2,V_xs_2,V_x_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Osublist(T_c,V_xs_2,V_I_2)))) ),
file('theBenchmark.p',fact_notin__set__sublistI) ).
fof(fact_in__set__takeD,axiom,
! [V_xs_2,V_n_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ),
file('theBenchmark.p',fact_in__set__takeD) ).
fof(fact_in__set__sublistD,axiom,
! [V_I_2,V_xs_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Osublist(T_c,V_xs_2,V_I_2))))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ),
file('theBenchmark.p',fact_in__set__sublistD) ).
fof(fact_set__ConsD,axiom,
! [V_xs_2,V_x_2,V_y_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_xs_2)))
| V_y_2 = V_x_2 ) ),
file('theBenchmark.p',fact_set__ConsD) ).
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_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_c] : hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(c_List_Oset(T_c),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_c] : c_List_Osublist(T_c,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_l_2),
file('theBenchmark.p',fact_sublist__upt__eq__take) ).
fof(fact_card__length,axiom,
! [V_xs_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_List_Oset(T_c),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),
file('theBenchmark.p',fact_card__length) ).
fof(fact_all__set__conv__all__nth,axiom,
! [V_Pa_2,V_xs_2,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),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_c)),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),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_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),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_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_List_Olists(T_c,V_A_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),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_c)),V_xs_2))) ),
file('theBenchmark.p',fact_length__pos__if__in__set) ).
fof(fact_nth__mem,axiom,
! [V_xs_2,T_c,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_c)),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_c),V_xs_2))) ),
file('theBenchmark.p',fact_nth__mem) ).
fof(fact_in__set__conv__nth,axiom,
! [V_xs_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
<=> ? [B_i] :
( hAPP(hAPP(c_List_Onth(T_c),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_c)),V_xs_2))) ) ),
file('theBenchmark.p',fact_in__set__conv__nth) ).
fof(fact_lists__eq__set,axiom,
! [V_A_2,T_c] : c_List_Olists(T_c,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_c)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),c_List_Oset(T_c))),V_A_2)),
file('theBenchmark.p',fact_lists__eq__set) ).
fof(fact_set__conv__nth,axiom,
! [V_xs_2,T_c] : hAPP(c_List_Oset(T_c),V_xs_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(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)),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)),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(T_c,tc_fun(tc_Nat_Onat,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_c),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_c)),V_xs_2))))),
file('theBenchmark.p',fact_set__conv__nth) ).
fof(fact_finite__lists__length__eq,axiom,
! [V_n_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_c)),hAPP(c_Set_OCollect(tc_List_Olist(T_c)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),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_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),c_List_Oset(T_c))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),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_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_c)),hAPP(c_Set_OCollect(tc_List_Olist(T_c)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),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_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),c_List_Oset(T_c))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel(T_c,V_r_2)))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_c,T_c)),hAPP(hAPP(c_List_Ozip(T_c,T_c),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,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_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_c,tc_HOL_Obool)),T_c),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),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_c),c_member(tc_prod(T_c,T_c)))),c_Product__Type_OPair(T_c,T_c)))),V_r_2)),B_x)) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ),
file('theBenchmark.p',fact_listrel__iff__zip) ).
fof(fact_set__zip,axiom,
! [V_ys_2,V_xs_2,T_d,T_c] : hAPP(c_List_Oset(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_c,T_d)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_c,T_d),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_c,T_d)),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_c,T_d)),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_c,T_d),tc_fun(tc_Nat_Onat,tc_prod(T_c,T_d)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_c,T_d)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_c,T_d)),c_COMBB(tc_prod(T_c,T_d),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_d,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),tc_Nat_Onat),c_Product__Type_OPair(T_c,T_d)),hAPP(c_List_Onth(T_c),V_xs_2))),hAPP(c_List_Onth(T_d),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_c)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),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_c,V_ys_2,V_xs_2] :
( V_xs_2 = V_ys_2
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_c,T_c)),hAPP(hAPP(c_List_Ozip(T_c,T_c),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),c_fequal),B_x)) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ),
file('theBenchmark.p',fact_list__eq__iff__zip__eq) ).
fof(fact_zip__same,axiom,
! [V_xs_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_c,T_c)),hAPP(hAPP(c_List_Ozip(T_c,T_c),V_xs_2),V_xs_2))))
<=> ( V_a_2 = V_b_2
& hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ),
file('theBenchmark.p',fact_zip__same) ).
fof(fact_set__zip__leftD,axiom,
! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_d,T_c] :
( 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(c_List_Oset(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ),
file('theBenchmark.p',fact_set__zip__leftD) ).
fof(fact_set__zip__rightD,axiom,
! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_d,T_c] :
( 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(c_List_Oset(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),hAPP(c_List_Oset(T_d),V_ys_2))) ),
file('theBenchmark.p',fact_set__zip__rightD) ).
fof(fact_in__set__zipE,axiom,
! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_d,T_c] :
( 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(c_List_Oset(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2))))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),hAPP(c_List_Oset(T_d),V_ys_2))) ) ),
file('theBenchmark.p',fact_in__set__zipE) ).
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_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(c_List_Onth(T_c),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_c)),V_xs_2))) ),
file('theBenchmark.p',fact_listsum__setsum__nth) ).
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_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_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_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),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_c,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_c,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_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_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_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_c] : hAPP(hAPP(c_List_Olist__update(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_c),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_c,tc_List_Olist(T_c)),c_List_Olist__update(T_c,V_xs_2)),V_v_2)),V_i_2),
file('theBenchmark.p',fact_list__update_Osimps_I2_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_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_in__set__butlastD,axiom,
! [V_xs_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Obutlast(T_c,V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist__update(T_c,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_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))),
file('theBenchmark.p',fact_set__update__subset__insert) ).
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_list__update__same__conv,axiom,
! [V_x_2,V_xs_2,T_c,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_c)),V_xs_2)))
=> ( hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_i_2),V_x_2) = V_xs_2
<=> hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_i_2) = V_x_2 ) ),
file('theBenchmark.p',fact_list__update__same__conv) ).
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_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_c,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_c)),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist__update(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2)))
<=> ? [B_y,B_n] :
( V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_c,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_c)),V_xs_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(hAPP(c_List_Onth(T_c),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_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
=> hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Olist__update(T_c,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_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_c),c_List_Osublist(T_c,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_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)))
<=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ),
file('theBenchmark.p',fact_distinct_Osimps_I2_J) ).
fof(fact_card__distinct,axiom,
! [V_xs_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
=> hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ),
file('theBenchmark.p',fact_card__distinct) ).
fof(fact_distinct__card,axiom,
! [V_xs_2,T_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ),
file('theBenchmark.p',fact_distinct__card) ).
fof(fact_distinct__conv__nth,axiom,
! [V_xs_2,T_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),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_c)),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_c)),V_xs_2)))
=> ( B_i != B_j
=> hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_j) ) ) ) ),
file('theBenchmark.p',fact_distinct__conv__nth) ).
fof(fact_nth__eq__iff__index__eq,axiom,
! [V_j_2,V_i_2,V_xs_2,T_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),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_c)),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_c)),V_xs_2)))
=> ( hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_j_2)
<=> V_i_2 = V_j_2 ) ) ) ),
file('theBenchmark.p',fact_nth__eq__iff__index__eq) ).
fof(fact_distinct__listsum__conv__Setsum,axiom,
! [V_xs_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_COMBI(T_c)),hAPP(c_List_Oset(T_c),V_xs_2)) ) ),
file('theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).
fof(fact_Nitpick_Ocard_H__def,axiom,
! [V_A_2,T_c] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Nitpick_Ocard_H(T_c,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Nitpick_Ocard_H(T_c,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_Hilbert__Choice_OEps(tc_List_Olist(T_c),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),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_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_fequal),c_List_Oset(T_c))),V_A_2))),c_List_Odistinct(T_c)))) ) ),
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_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> hAPP(c_List_Oset(T_c),c_List_Oremove1(T_c,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_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_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_c] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_List_Olists(T_c,V_A_2))),
file('theBenchmark.p',fact_lists_ONil) ).
fof(fact_listrel__Nil1,axiom,
! [V_r_2,V_xs_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),V_xs_2)),c_List_Olistrel(T_c,V_r_2)))
=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_listrel__Nil1) ).
fof(fact_listrel__Nil2,axiom,
! [V_r_2,V_xs_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),c_List_Olist_ONil(T_c))),c_List_Olistrel(T_c,V_r_2)))
=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_listrel__Nil2) ).
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__eq__Nil,axiom,
! [V_xs_2,V_n_2,T_c] :
( hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2) = c_List_Olist_ONil(T_c)
<=> ( V_xs_2 = c_List_Olist_ONil(T_c)
| 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_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_sublist__nil,axiom,
! [V_A_2,T_c] : c_List_Osublist(T_c,c_List_Olist_ONil(T_c),V_A_2) = c_List_Olist_ONil(T_c),
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_c] : c_List_Olistrelp(T_c,V_r_2,c_List_Olist_ONil(T_c),c_List_Olist_ONil(T_c)),
file('theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
fof(fact_listrelp_ONil,axiom,
! [V_r_2,T_c] : c_List_Olistrelp(T_c,V_r_2,c_List_Olist_ONil(T_c),c_List_Olist_ONil(T_c)),
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_c] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
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_set__empty,axiom,
! [V_xs_2,T_c] :
( hAPP(c_List_Oset(T_c),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_set__empty) ).
fof(fact_set__empty2,axiom,
! [V_xs_2,T_c] :
( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_List_Oset(T_c),V_xs_2)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_set__empty2) ).
fof(fact_List_Oset_Osimps_I1_J,axiom,
! [T_c] : hAPP(c_List_Oset(T_c),c_List_Olist_ONil(T_c)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
file('theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).
fof(fact_list_Osize_I1_J,axiom,
! [V_fa_2,T_c] : c_List_Olist_Olist__size(T_c,V_fa_2,c_List_Olist_ONil(T_c)) = 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_c] :
( hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_c)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_list__update__nonempty) ).
fof(fact_remove1__idem,axiom,
! [V_xs_2,V_x_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_Oremove1(T_c,V_x_2,V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_remove1__idem) ).
fof(fact_notin__set__remove1,axiom,
! [V_y_2,V_xs_2,V_x_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Oremove1(T_c,V_y_2,V_xs_2)))) ),
file('theBenchmark.p',fact_notin__set__remove1) ).
fof(fact_in__set__remove1,axiom,
! [V_xs_2,T_c,V_b_2,V_a_2] :
( V_a_2 != V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_List_Oset(T_c),c_List_Oremove1(T_c,V_b_2,V_xs_2))))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ),
file('theBenchmark.p',fact_in__set__remove1) ).
fof(fact_sublist__empty,axiom,
! [V_xs_2,T_c] : c_List_Osublist(T_c,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_c),
file('theBenchmark.p',fact_sublist__empty) ).
fof(fact_set__remove1__subset,axiom,
! [V_xs_2,V_x_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),c_List_Oremove1(T_c,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_c),V_xs_2))),
file('theBenchmark.p',fact_set__remove1__subset) ).
fof(fact_length__greater__0__conv,axiom,
! [V_xs_2,T_c] :
( 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_c)),V_xs_2)))
<=> V_xs_2 != c_List_Olist_ONil(T_c) ),
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__Nil__listrel1,axiom,
! [V_r_2,V_xs_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),V_xs_2)),c_List_Olistrel1(T_c,V_r_2))),
file('theBenchmark.p',fact_not__Nil__listrel1) ).
fof(fact_not__listrel1__Nil,axiom,
! [V_r_2,V_xs_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),c_List_Olist_ONil(T_c))),c_List_Olistrel1(T_c,V_r_2))),
file('theBenchmark.p',fact_not__listrel1__Nil) ).
fof(fact_listrel_ONil,axiom,
! [V_r_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_List_Olist_ONil(T_c))),c_List_Olistrel(T_c,V_r_2))),
file('theBenchmark.p',fact_listrel_ONil) ).
fof(fact_lexord__Nil__right,axiom,
! [V_r_2,V_x_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),c_List_Olist_ONil(T_c))),c_List_Olexord(T_c,V_r_2))),
file('theBenchmark.p',fact_lexord__Nil__right) ).
fof(fact_Nil__notin__lex,axiom,
! [V_r_2,V_ys_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),V_ys_2)),c_List_Olex(T_c,V_r_2))),
file('theBenchmark.p',fact_Nil__notin__lex) ).
fof(fact_Nil2__notin__lex,axiom,
! [V_r_2,V_xs_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),c_List_Olist_ONil(T_c))),c_List_Olex(T_c,V_r_2))),
file('theBenchmark.p',fact_Nil2__notin__lex) ).
fof(fact_take__Cons,axiom,
! [V_xs_2,V_x_2,V_n_2,T_c] : hAPP(hAPP(c_List_Otake(T_c),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_c),c_List_Olist_ONil(T_c),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_c),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Otake(T_c)),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_c,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_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)),V_A_2) = c_List_Olist_ONil(T_c) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
=> c_List_Osublist(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)) ) ),
file('theBenchmark.p',fact_sublist__singleton) ).
fof(fact_lists__empty,axiom,
! [T_c] : c_List_Olists(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),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_c] : hAPP(c_Relation_OImage(tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Olistrel(T_c,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),
file('theBenchmark.p',fact_listrel__Nil) ).
fof(fact_set__Cons__sing__Nil,axiom,
! [V_A_2,T_c] : c_List_Oset__Cons(T_c,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_c,tc_List_Olist(T_c),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),c_List_Olist_ONil(T_c))),V_A_2),
file('theBenchmark.p',fact_set__Cons__sing__Nil) ).
fof(fact_length__remove1,axiom,
! [V_xs_2,V_x_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Oremove1(T_c,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Oremove1(T_c,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_c)),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_c,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_c)
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Product__Type_Ofst(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_c,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_c),V_xs_2))) ),
file('theBenchmark.p',fact_select) ).
fof(fact_listset_Osimps_I1_J,axiom,
! [T_c] : c_List_Olistset(T_c,c_List_Olist_ONil(tc_fun(T_c,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))),
file('theBenchmark.p',fact_listset_Osimps_I1_J) ).
fof(fact_zip__Cons,axiom,
! [V_ys_2,V_y_2,V_xs_2,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_c,T_d)),T_c,c_List_Olist_ONil(tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_c,T_d))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_c,T_d)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(tc_prod(T_c,T_d))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_c,T_d))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_c,T_d)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(tc_prod(T_c,T_d))),T_c),c_List_Olist_OCons(tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBC(T_c,T_d,tc_prod(T_c,T_d)),c_Product__Type_OPair(T_c,T_d)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_d),tc_List_Olist(tc_prod(T_c,T_d))),c_List_Ozip(T_c,T_d)),V_ys_2))),V_xs_2),
file('theBenchmark.p',fact_zip__Cons) ).
fof(fact_list_Osimps_I5_J,axiom,
! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_d,T_c] : hAPP(c_List_Olist_Olist__case(T_c,T_d,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_d),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_d,T_c] : hAPP(c_List_Olist_Olist__case(T_c,T_d,V_f1_2,V_f2_2),c_List_Olist_ONil(T_d)) = 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_c] : c_List_Olistset(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_c,V_A_2,c_List_Olistset(T_c,V_As_2)),
file('theBenchmark.p',fact_listset_Osimps_I2_J) ).
fof(fact_zip__Cons1,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_c,T_d)),T_d,c_List_Olist_ONil(tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_List_Olist(T_d),tc_List_Olist(tc_prod(T_c,T_d))),tc_fun(tc_List_Olist(T_d),tc_List_Olist(tc_prod(T_c,T_d)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(tc_prod(T_c,T_d))),tc_fun(tc_fun(tc_List_Olist(T_d),tc_List_Olist(tc_prod(T_c,T_d))),tc_fun(tc_List_Olist(T_d),tc_List_Olist(tc_prod(T_c,T_d)))),T_d),c_COMBB(tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(T_d))),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_List_Olist(tc_prod(T_c,T_d)),tc_List_Olist(tc_prod(T_c,T_d))),T_d),c_List_Olist_OCons(tc_prod(T_c,T_d))),hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2)))),hAPP(c_List_Ozip(T_c,T_d),V_xs_2))),V_ys_2),
file('theBenchmark.p',fact_zip__Cons1) ).
fof(fact_sorted__list__of__set__remove,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_List_Olinorder__class_Osorted__list__of__set(T_c,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))))) = c_List_Oremove1(T_c,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_c,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_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osorted__list__of__set(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_sorted__list__of__set__empty) ).
fof(fact_anamorph_Osimps,axiom,
! [V_x_2,V_f_2,T_c,T_d,V_k_2] :
( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_d,T_c,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_c),T_d),tc_prod(T_c,T_d),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),T_d),c_List_Olist_ONil(T_c)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_prod(tc_List_Olist(T_c),T_d)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d)),tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_c),T_d),tc_prod(tc_List_Olist(T_c),T_d)),tc_fun(tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d)),tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d))),T_c),c_COMBB(tc_prod(tc_List_Olist(T_c),T_d),tc_prod(tc_List_Olist(T_c),T_d),T_d)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d))),tc_fun(tc_prod(tc_List_Olist(T_c),T_d),tc_prod(tc_List_Olist(T_c),T_d)),T_c),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_c),T_d,tc_prod(tc_List_Olist(T_c),T_d))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d))),T_c),hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(T_d,tc_prod(tc_List_Olist(T_c),T_d)),tc_List_Olist(T_c)),c_Product__Type_OPair(tc_List_Olist(T_c),T_d))),c_List_Olist_OCons(T_c))))),hAPP(c_Lazy__Sequence_Oanamorph(T_d,T_c,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_d,T_c,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),T_d),c_List_Olist_ONil(T_c)),V_x_2) ) ),
file('theBenchmark.p',fact_anamorph_Osimps) ).
fof(fact_sublist__Cons,axiom,
! [V_A_2,V_l_2,V_x_2,T_c] : c_List_Osublist(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_c),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_c)),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_c),V_x_2),c_List_Olist_ONil(T_c))),c_List_Olist_ONil(T_c))),c_List_Osublist(T_c,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_c] :
( hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)
<=> ( ? [B_ys_H] :
( hAPP(hAPP(c_List_Oappend(T_c),B_ys_H),V_zs_2) = V_xs_2
& V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),B_ys_H) )
| ( V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)
& V_ys_2 = c_List_Olist_ONil(T_c) ) ) ),
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_c] :
( hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2)
<=> ( ? [B_ys_H] :
( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),B_ys_H),V_zs_2)
& hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),B_ys_H) = V_ys_2 )
| ( hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) = V_zs_2
& V_ys_2 = c_List_Olist_ONil(T_c) ) ) ),
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_c] :
( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c))) = hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),c_List_Olist_ONil(T_c)))
<=> ( 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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)),c_List_Olists(T_c,V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_ys_2),c_List_Olists(T_c,V_A_2)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_xs_2),c_List_Olists(T_c,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_c] :
( hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_c),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_c] :
( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_c),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_c] :
( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_c),V_zs_2),V_ts_2)
<=> ? [B_us] :
( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_c),B_us),V_ts_2)
& hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),B_us) = V_zs_2 )
| ( hAPP(hAPP(c_List_Oappend(T_c),B_us),V_ys_2) = V_ts_2
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),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_c] : hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_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)),
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_c] :
( c_List_Olist_ONil(T_c) = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)
<=> ( V_ys_2 = c_List_Olist_ONil(T_c)
& V_xs_2 = c_List_Olist_ONil(T_c) ) ),
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_c,V_xs_2] :
( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)
<=> V_ys_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_self__append__conv) ).
fof(fact_self__append__conv2,axiom,
! [V_xs_2,T_c,V_ys_2] :
( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_self__append__conv2) ).
fof(fact_append__is__Nil__conv,axiom,
! [V_ys_2,V_xs_2,T_c] :
( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_c)
<=> ( V_ys_2 = c_List_Olist_ONil(T_c)
& V_xs_2 = c_List_Olist_ONil(T_c) ) ),
file('theBenchmark.p',fact_append__is__Nil__conv) ).
fof(fact_append__self__conv,axiom,
! [V_ys_2,V_xs_2,T_c] :
( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) = V_xs_2
<=> V_ys_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_append__self__conv) ).
fof(fact_append__self__conv2,axiom,
! [V_ys_2,V_xs_2,T_c] :
( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) = V_ys_2
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
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_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_Oremove1(T_c,V_x_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),c_List_Oremove1(T_c,V_x_2,V_ys_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_Oremove1(T_c,V_x_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_c),c_List_Oremove1(T_c,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_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Obutlast(T_c,V_ys_2))))
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Obutlast(T_c,V_xs_2)))) )
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Obutlast(T_c,hAPP(hAPP(c_List_Oappend(T_c),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_c] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_us_2),V_vs_2)),c_List_Olistrel1(T_c,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_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2))) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))),c_List_Olistrel1(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_u_2),V_v_2)),c_List_Olexord(T_c,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Oappend(T_c),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_c),V_x_2),V_v_2))),c_List_Olexord(T_c,V_r_2))) ),
file('theBenchmark.p',fact_lexord__append__leftI) ).
fof(fact_distinct__append,axiom,
! [V_ys_2,V_xs_2,T_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)))
<=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& hBOOL(hAPP(c_List_Odistinct(T_c),V_ys_2))
& hBOOL(hAPP(c_List_Odistinct(T_c),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_c] : c_List_Osublist(T_c,hAPP(hAPP(c_List_Oappend(T_c),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_c),c_List_Osublist(T_c,V_l_2,V_A_2)),c_List_Osublist(T_c,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_c)),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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2))
=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_vs_2))
=> ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_c),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_vs_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Oappend(T_c),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_c),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_y_2)))),c_List_Olexord(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)))),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),c_List_Olist_ONil(T_c))))),c_List_Olistrel1(T_c,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_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_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_c,V_r_2)))
=> ~ ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_r_2))
=> ! [B_us,B_vs] :
( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),B_us),hAPP(hAPP(c_List_Olist_OCons(T_c),B_x),B_vs))
=> V_ys_2 != hAPP(hAPP(c_List_Oappend(T_c),B_us),hAPP(hAPP(c_List_Olist_OCons(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_List_Oappend(T_c),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_c),V_x_2),V_v_2))),c_List_Olexord(T_c,V_r_2)))
=> ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_a),B_a)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_u_2),V_v_2)),c_List_Olexord(T_c,V_r_2))) ) ),
file('theBenchmark.p',fact_lexord__append__leftD) ).
fof(fact_rotate1__def,axiom,
! [V_xs_2,T_c] : hAPP(c_List_Orotate1(T_c),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_c),T_c,c_List_Olist_ONil(T_c),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),T_c),hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Oappend(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),c_List_Olist_ONil(T_c)))),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_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(c_List_Orotate1(T_c),V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_c),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__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__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__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__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_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_set__rotate1,axiom,
! [V_xs_2,T_c] : hAPP(c_List_Oset(T_c),hAPP(c_List_Orotate1(T_c),V_xs_2)) = hAPP(c_List_Oset(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ),
file('theBenchmark.p',fact_in__set__dropD) ).
fof(fact_set__drop__subset,axiom,
! [V_xs_2,V_n_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_c),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_c] :
( hAPP(c_List_Orotate1(T_c),V_xs_2) = c_List_Olist_ONil(T_c)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_rotate1__is__Nil__conv) ).
fof(fact_set__drop__subset__set__drop,axiom,
! [V_xs_2,T_c,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_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Odrop(T_c),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Odrop(T_c),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_c] :
( hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2) = c_List_Olist_ONil(T_c)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),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_c] :
( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2) = V_zs_2
<=> ( V_ys_2 = hAPP(hAPP(c_List_Odrop(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)),V_zs_2)
& V_xs_2 = hAPP(hAPP(c_List_Otake(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),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_c] : hAPP(hAPP(c_List_Odrop(T_c),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Odrop(T_c)),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_c] :
( hAPP(hAPP(c_List_Oappend(T_c),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_c),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_c)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_092_060_094isub_0621_2)))
=> ( hAPP(hAPP(c_List_Oappend(T_c),hAPP(hAPP(c_List_Odrop(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),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_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),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_c)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_092_060_094isub_0621_2)))
=> ( V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_c),hAPP(hAPP(c_List_Odrop(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),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_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),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__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_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_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_c,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_c)
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_List_Ohd(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),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_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ),
file('theBenchmark.p',fact_distinct__rotate) ).
fof(fact_rotate__add,axiom,
! [V_n_2,V_m_2,T_c] : c_List_Orotate(T_c,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Orotate(T_c,V_m_2)),c_List_Orotate(T_c,V_n_2)),
file('theBenchmark.p',fact_rotate__add) ).
fof(fact_rotate0,axiom,
! [T_c] : c_List_Orotate(T_c,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_c)),
file('theBenchmark.p',fact_rotate0) ).
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_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_c] : hAPP(c_List_Oset(T_c),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_c),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_c] :
( hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2) = c_List_Olist_ONil(T_c)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
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_c] : c_List_Orotate(T_c,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_n_2),c_List_Orotate1(T_c)),
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_c] : hAPP(c_List_Otl(T_c),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_c),T_c,hAPP(c_List_Otl(T_c),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),T_c),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Oappend(T_c)),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_c] :
( class_Lattices_Oab__semigroup__idem__mult(T_c)
=> ( V_xs_2 != c_List_Olist_ONil(T_c)
=> hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),hAPP(c_List_Ohd(T_c),V_xs_2)),hAPP(c_List_Otl(T_c),V_xs_2)) ) ),
file('theBenchmark.p',fact_fold1__set) ).
fof(fact_lexord__append__rightI,axiom,
! [V_r_2,V_x_2,T_c,V_y_2] :
( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),B_b),B_z)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),hAPP(hAPP(c_List_Oappend(T_c),V_x_2),V_y_2))),c_List_Olexord(T_c,V_r_2))) ),
file('theBenchmark.p',fact_lexord__append__rightI) ).
fof(fact_foldl__Nil,axiom,
! [V_a_2,V_f_2,T_d,T_c] : hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,V_a_2),c_List_Olist_ONil(T_d)) = V_a_2,
file('theBenchmark.p',fact_foldl__Nil) ).
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__assoc,axiom,
! [V_zs_2,V_y_2,V_x_2,T_c] :
( class_Groups_Osemigroup__add(T_c)
=> hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_x_2),hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_y_2),V_zs_2)) ),
file('theBenchmark.p',fact_foldl__assoc) ).
fof(fact_foldl__absorb0,axiom,
! [V_zs_2,V_x_2,T_c] :
( class_Groups_Omonoid__add(T_c)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_x_2),hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_zs_2)) = hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_x_2),V_zs_2) ),
file('theBenchmark.p',fact_foldl__absorb0) ).
fof(fact_foldl__Cons,axiom,
! [V_xs_2,V_x_2,V_a_2,V_f_2,T_d,T_c] : hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_d,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_foldl__append,axiom,
! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_d,T_c] : hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_d),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,V_a_2),V_xs_2)),V_ys_2),
file('theBenchmark.p',fact_foldl__append) ).
fof(fact_listsum__foldl,axiom,
! [T_c] :
( class_Groups_Omonoid__add(T_c)
=> c_List_Omonoid__add__class_Olistsum(T_c) = c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),c_Groups_Ozero__class_Ozero(T_c)) ),
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_fun__left__comm__idem_Ofold__set,axiom,
! [V_xs_2,V_y_2,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2)
=> hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_y_2),hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_List_Ofoldl(T_d,T_c,hAPP(c_COMBC(T_c,T_d,T_d),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_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c),c_Orderings_Obot__class_Obot(T_c)),V_xs_2) ),
file('theBenchmark.p',fact_Sup__set__fold) ).
fof(fact_Inf__set__fold,axiom,
! [V_xs_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c),c_Orderings_Otop__class_Otop(T_c)),V_xs_2) ),
file('theBenchmark.p',fact_Inf__set__fold) ).
fof(fact_Sup__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_c] :
( class_Lattices_Olattice(T_c)
=> c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c),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_c] :
( class_Lattices_Olattice(T_c)
=> c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_c,T_c,c_Orderings_Oord__class_Omin(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_c,T_c,c_Orderings_Oord__class_Omax(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_c,T_c,c_Orderings_Oord__class_Omin(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_c,T_c,c_Orderings_Oord__class_Omax(T_c),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_d,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),hAPP(c_List_Oset(T_d),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_c,T_d,hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_xs_2) ),
file('theBenchmark.p',fact_SUPR__set__fold) ).
fof(fact_INFI__set__fold,axiom,
! [V_f_2,V_xs_2,T_d,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),hAPP(c_List_Oset(T_d),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_c,T_d,hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),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_sorted__list__of__set__insert,axiom,
! [V_x_2,V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_List_Olinorder__class_Osorted__list__of__set(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_c,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_sorted__list__of__set__insert) ).
fof(fact_lexord__Nil__left,axiom,
! [V_r_2,V_y_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),V_y_2)),c_List_Olexord(T_c,V_r_2)))
<=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),B_a),B_x) ),
file('theBenchmark.p',fact_lexord__Nil__left) ).
fof(fact_insort__key_Osimps_I1_J,axiom,
! [V_x_2,V_f_2,T_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_x_2),c_List_Olist_ONil(T_c)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)) ),
file('theBenchmark.p',fact_insort__key_Osimps_I1_J) ).
fof(fact_insort__key_Osimps_I2_J,axiom,
! [V_ys_2,T_d,V_y_2,V_x_2,V_f_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_d),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),V_ys_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_d),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_y_2),V_ys_2)) ) ) ),
file('theBenchmark.p',fact_insort__key_Osimps_I2_J) ).
fof(fact_set__insort,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)) ),
file('theBenchmark.p',fact_set__insort) ).
fof(fact_length__insort,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)) ),
file('theBenchmark.p',fact_length__insort) ).
fof(fact_fun__left__comm__insort,axiom,
! [T_c] :
( class_Orderings_Olinorder(T_c)
=> c_Finite__Set_Ofun__left__comm(T_c,tc_List_Olist(T_c),c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c))) ),
file('theBenchmark.p',fact_fun__left__comm__insort) ).
fof(fact_insort__left__comm,axiom,
! [V_xs_2,V_y_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_x_2),V_xs_2)) ),
file('theBenchmark.p',fact_insort__left__comm) ).
fof(fact_insort__key__left__comm,axiom,
! [V_xs_2,T_d,V_y_2,V_x_2,V_f_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_y_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_insort__key__left__comm) ).
fof(fact_remove1__insort,axiom,
! [V_xs_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Oremove1(T_c,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_x_2),V_xs_2)) = V_xs_2 ),
file('theBenchmark.p',fact_remove1__insort) ).
fof(fact_insort__not__Nil,axiom,
! [V_xs_2,V_a_2,V_f_2,T_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_insort__not__Nil) ).
fof(fact_distinct__insort,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_x_2),V_xs_2)))
<=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ) ),
file('theBenchmark.p',fact_distinct__insort) ).
fof(fact_insort__insert__insort__key,axiom,
! [V_xs_2,T_d,V_x_2,V_f_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_List_Oset(T_d),V_xs_2))))
=> c_List_Olinorder__class_Oinsort__insert__key(T_d,T_c,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),V_xs_2) ) ),
file('theBenchmark.p',fact_insort__insert__insort__key) ).
fof(fact_insort__insert__insort,axiom,
! [V_xs_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_Olinorder__class_Oinsort__insert__key(T_c,T_c,c_COMBI(T_c),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_x_2),V_xs_2) ) ),
file('theBenchmark.p',fact_insort__insert__insort) ).
fof(fact_distinct__insort__insert,axiom,
! [V_x_2,V_f_2,V_xs_2,T_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_c),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_d,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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_Olinorder__class_Oinsort__insert__key(T_c,T_c,c_COMBI(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_List_Oset(T_c),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_c,c_COMBI(T_c),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)) ),
file('theBenchmark.p',fact_set__insort__insert) ).
fof(fact_insort__insert__key__triv,axiom,
! [V_xs_2,T_d,V_x_2,V_f_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_List_Oset(T_d),V_xs_2))))
=> c_List_Olinorder__class_Oinsort__insert__key(T_d,T_c,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ),
file('theBenchmark.p',fact_insort__insert__key__triv) ).
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__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_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__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__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__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__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__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__in__set,axiom,
! [T_c,V_as_2] :
( V_as_2 != c_List_Olist_ONil(T_c)
=> hBOOL(hAPP(hAPP(c_member(T_c),c_List_Olast(T_c,V_as_2)),hAPP(c_List_Oset(T_c),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_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_snoc__eq__iff__butlast,axiom,
! [V_ys_2,V_x_2,V_xs_2,T_c] :
( hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c))) = V_ys_2
<=> ( c_List_Olast(T_c,V_ys_2) = V_x_2
& c_List_Obutlast(T_c,V_ys_2) = V_xs_2
& V_ys_2 != c_List_Olist_ONil(T_c) ) ),
file('theBenchmark.p',fact_snoc__eq__iff__butlast) ).
fof(fact_lists_Osimps,axiom,
! [V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_a_2),c_List_Olists(T_c,V_A_2)))
<=> ( ? [B_a,B_l] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_l),c_List_Olists(T_c,V_A_2)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_a),V_A_2))
& V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),B_a),B_l) )
| V_a_2 = c_List_Olist_ONil(T_c) ) ),
file('theBenchmark.p',fact_lists_Osimps) ).
fof(fact_select__weigth__select,axiom,
! [T_c,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_c)
=> c_Random_Oselect__weight(T_c,hAPP(hAPP(c_List_Omap(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,T_c)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_c),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_c,V_xs_2) ),
file('theBenchmark.p',fact_select__weigth__select) ).
fof(fact_inj__mapI,axiom,
! [V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> c_Fun_Oinj__on(tc_List_Olist(T_c),tc_List_Olist(T_d),hAPP(c_List_Omap(T_c,T_d),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__mapI) ).
fof(fact_last__map,axiom,
! [V_f_2,T_d,T_c,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_c)
=> c_List_Olast(T_d,hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_c,V_xs_2)) ),
file('theBenchmark.p',fact_last__map) ).
fof(fact_foldl__map,axiom,
! [V_xs_2,V_f_2,T_e,V_a_2,V_g_2,T_d,T_c] : hAPP(c_List_Ofoldl(T_c,T_d,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_e,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,T_c)),T_c),c_COMBB(T_d,T_c,T_e)),V_g_2)),V_f_2),V_a_2),V_xs_2),
file('theBenchmark.p',fact_foldl__map) ).
fof(fact_rotate__map,axiom,
! [V_xs_2,V_f_2,T_d,V_n_2,T_c] : hAPP(c_List_Orotate(T_c,V_n_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(c_List_Orotate(T_d,V_n_2),V_xs_2)),
file('theBenchmark.p',fact_rotate__map) ).
fof(fact_map__tl,axiom,
! [V_xs_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(c_List_Otl(T_d),V_xs_2)) = hAPP(c_List_Otl(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_map__tl) ).
fof(fact_zip__map2,axiom,
! [V_ys_2,V_f_2,T_e,V_xs_2,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,tc_prod(T_c,T_d)),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_f_2))),hAPP(hAPP(c_List_Ozip(T_c,T_e),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_f,V_xs_2,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),T_c),V_f_2),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),hAPP(hAPP(c_List_Omap(T_f,T_e),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_f),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_f,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_d,T_e)),tc_fun(T_f,T_c),T_d),hAPP(c_COMBB(tc_prod(T_d,T_e),T_c,T_f),V_f_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_f,T_e),tc_fun(T_f,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_f,T_e),tc_fun(T_f,tc_prod(T_d,T_e))),T_d),c_COMBB(T_e,tc_prod(T_d,T_e),T_f)),c_Product__Type_OPair(T_d,T_e))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_d,T_f),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_f,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),T_c),V_f_2),hAPP(hAPP(c_List_Ozip(T_d,T_e),hAPP(hAPP(c_List_Omap(T_f,T_d),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_f,T_e),T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_f,T_e,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(T_e,T_c),T_f),hAPP(c_COMBB(tc_prod(T_d,T_e),T_c,T_e),V_f_2)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_f),c_Product__Type_OPair(T_d,T_e)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_f,T_e),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_e,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_e,T_d),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_f,V_xs_2,V_f_2,T_e,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_f,T_d),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_f),tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_f,T_d),tc_fun(T_f,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_f,T_d),tc_fun(T_f,tc_prod(T_c,T_d))),T_e),c_COMBB(T_d,tc_prod(T_c,T_d),T_f)),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_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_e,T_f),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__map__map) ).
fof(fact_zip__same__conv__map,axiom,
! [V_xs_2,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_c),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_c,T_c)),hAPP(hAPP(c_COMBS(T_c,T_c,tc_prod(T_c,T_c)),c_Product__Type_OPair(T_c,T_c)),c_COMBI(T_c))),V_xs_2),
file('theBenchmark.p',fact_zip__same__conv__map) ).
fof(fact_map__is__Nil__conv,axiom,
! [V_xs_2,V_f_2,T_c,T_d] :
( hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2) = c_List_Olist_ONil(T_c)
<=> V_xs_2 = c_List_Olist_ONil(T_d) ),
file('theBenchmark.p',fact_map__is__Nil__conv) ).
fof(fact_map_Osimps_I1_J,axiom,
! [V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Olist_ONil(T_d)) = c_List_Olist_ONil(T_c),
file('theBenchmark.p',fact_map_Osimps_I1_J) ).
fof(fact_Nil__is__map__conv,axiom,
! [V_xs_2,V_f_2,T_d,T_c] :
( c_List_Olist_ONil(T_c) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)
<=> V_xs_2 = c_List_Olist_ONil(T_d) ),
file('theBenchmark.p',fact_Nil__is__map__conv) ).
fof(fact_map__update,axiom,
! [V_y_2,V_k_2,V_xs_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Olist__update(T_d,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)),
file('theBenchmark.p',fact_map__update) ).
fof(fact_map__eq__conv,axiom,
! [V_g_2,V_xs_2,V_f_2,T_c,T_d] :
( hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),hAPP(c_List_Oset(T_d),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__eq__imp__length__eq,axiom,
! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_c,T_d] :
( hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_e)),V_ys_2) ),
file('theBenchmark.p',fact_map__eq__imp__length__eq) ).
fof(fact_length__map,axiom,
! [V_xs_2,V_f_2,T_d,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_xs_2),
file('theBenchmark.p',fact_length__map) ).
fof(fact_listsum__addf,axiom,
! [V_xs_2,V_g_2,V_f_2,T_d,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Oplus__class_Oplus(T_c)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2))) ),
file('theBenchmark.p',fact_listsum__addf) ).
fof(fact_listsum__subtractf,axiom,
! [V_xs_2,V_g_2,V_f_2,T_d,T_c] :
( class_Groups_Oab__group__add(T_c)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Ominus__class_Ominus(T_c)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2))) ),
file('theBenchmark.p',fact_listsum__subtractf) ).
fof(fact_listsum__0,axiom,
! [V_xs_2,T_d,T_c] :
( class_Groups_Omonoid__add(T_c)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(c_COMBK(T_c,T_d),c_Groups_Ozero__class_Ozero(T_c))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_c) ),
file('theBenchmark.p',fact_listsum__0) ).
fof(fact_listsum__const__mult,axiom,
! [V_xs_2,V_f_2,V_c_2,T_d,T_c] :
( class_Rings_Osemiring__0(T_c)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))) ),
file('theBenchmark.p',fact_listsum__const__mult) ).
fof(fact_listsum__mult__const,axiom,
! [V_xs_2,V_c_2,V_f_2,T_d,T_c] :
( class_Rings_Osemiring__0(T_c)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Otimes__class_Otimes(T_c)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))),V_c_2) ),
file('theBenchmark.p',fact_listsum__mult__const) ).
fof(fact_inj__map__eq__map,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> ( hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_d),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_c,T_d] :
( hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)
=> ( c_Fun_Oinj__on(T_d,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_map__injective) ).
fof(fact_map__ident,axiom,
! [V_xs_2,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_c),c_COMBI(T_c)),V_xs_2) = V_xs_2,
file('theBenchmark.p',fact_map__ident) ).
fof(fact_take__map,axiom,
! [V_xs_2,V_f_2,T_d,V_n_2,T_c] : hAPP(hAPP(c_List_Otake(T_c),V_n_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Otake(T_d),V_n_2),V_xs_2)),
file('theBenchmark.p',fact_take__map) ).
fof(fact_map__butlast,axiom,
! [V_xs_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Obutlast(T_d,V_xs_2)) = c_List_Obutlast(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_map__butlast) ).
fof(fact_set__map,axiom,
! [V_xs_2,V_f_2,T_d,T_c] : hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_List_Oset(T_d),V_xs_2)),
file('theBenchmark.p',fact_set__map) ).
fof(fact_map_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_map_Osimps_I2_J) ).
fof(fact_map__append,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Oappend(T_d),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)),
file('theBenchmark.p',fact_map__append) ).
fof(fact_hd__map,axiom,
! [V_f_2,T_d,T_c,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_c)
=> hAPP(c_List_Ohd(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_c),V_xs_2)) ),
file('theBenchmark.p',fact_hd__map) ).
fof(fact_drop__map,axiom,
! [V_xs_2,V_f_2,T_d,V_n_2,T_c] : hAPP(hAPP(c_List_Odrop(T_c),V_n_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Odrop(T_d),V_n_2),V_xs_2)),
file('theBenchmark.p',fact_drop__map) ).
fof(fact_List_Omap_Ocomp,axiom,
! [V_g_2,V_f_2,T_c,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_e),tc_List_Olist(T_d),tc_List_Olist(T_c),hAPP(c_List_Omap(T_e,T_d),V_f_2)),hAPP(c_List_Omap(T_c,T_e),V_g_2)) = hAPP(c_List_Omap(T_c,T_d),hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),V_g_2)),
file('theBenchmark.p',fact_List_Omap_Ocomp) ).
fof(fact_map__comp__map,axiom,
! [V_g_2,V_f_2,T_c,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_e),tc_List_Olist(T_d),tc_List_Olist(T_c),hAPP(c_List_Omap(T_e,T_d),V_f_2)),hAPP(c_List_Omap(T_c,T_e),V_g_2)) = hAPP(c_List_Omap(T_c,T_d),hAPP(c_Fun_Ocomp(T_e,T_d,T_c,V_f_2),V_g_2)),
file('theBenchmark.p',fact_map__comp__map) ).
fof(fact_List_Omap_Ocompositionality,axiom,
! [V_list_2,V_g_2,T_e,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_e,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_list_2),
file('theBenchmark.p',fact_List_Omap_Ocompositionality) ).
fof(fact_map__map,axiom,
! [V_xs_2,V_g_2,T_e,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_e,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_xs_2),
file('theBenchmark.p',fact_map__map) ).
fof(fact_List_Omap_Oidentity,axiom,
! [T_c] : hAPP(c_List_Omap(T_c,T_c),c_COMBI(T_c)) = c_Fun_Oid(tc_List_Olist(T_c)),
file('theBenchmark.p',fact_List_Omap_Oidentity) ).
fof(fact_List_Omap_Oid,axiom,
! [T_c] : hAPP(c_List_Omap(T_c,T_c),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_List_Olist(T_c)),
file('theBenchmark.p',fact_List_Omap_Oid) ).
fof(fact_list__size__map,axiom,
! [V_xs_2,V_g_2,T_d,V_f_2,T_c] : c_List_Olist_Olist__size(T_c,V_f_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_d,hAPP(c_Fun_Ocomp(T_c,tc_Nat_Onat,T_d,V_f_2),V_g_2),V_xs_2),
file('theBenchmark.p',fact_list__size__map) ).
fof(fact_inj__on__map__eq__map,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,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)))
=> ( hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_d),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_c,T_d] :
( hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)
=> ( c_Fun_Oinj__on(T_d,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_List_Oset(T_d),V_xs_2)),hAPP(c_List_Oset(T_d),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_d,V_xs_2,T_c,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_c)),V_xs_2)))
=> hAPP(hAPP(c_List_Onth(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_c),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_d,V_xs_2,V_y_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hAPP(hAPP(c_List_Omap(T_c,T_d),c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_y_2,V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_d),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_d,T_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)))
<=> ( c_Fun_Oinj__on(T_d,T_c,V_f_2,hAPP(c_List_Oset(T_d),V_xs_2))
& hBOOL(hAPP(c_List_Odistinct(T_d),V_xs_2)) ) ),
file('theBenchmark.p',fact_distinct__map) ).
fof(fact_listsum__abs,axiom,
! [V_xs_2,T_c] :
( class_Groups_Oordered__ab__group__add__abs(T_c)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_c,T_c),c_Groups_Oabs__class_Oabs(T_c)),V_xs_2)))) ),
file('theBenchmark.p',fact_listsum__abs) ).
fof(fact_uminus__listsum__map,axiom,
! [V_xs_2,V_f_2,T_d,T_c] :
( class_Groups_Oab__group__add(T_c)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,c_Groups_Ouminus__class_Ouminus(T_c)),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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),c_List_Oset(T_c)),V_A_2)))
=> c_Fun_Oinj__on(tc_List_Olist(T_c),tc_List_Olist(T_d),hAPP(c_List_Omap(T_c,T_d),V_f_2),V_A_2) ),
file('theBenchmark.p',fact_inj__on__mapI) ).
fof(fact_inj__mapD,axiom,
! [V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(tc_List_Olist(T_c),tc_List_Olist(T_d),hAPP(c_List_Omap(T_c,T_d),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)))
=> c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__mapD) ).
fof(fact_inj__map,axiom,
! [V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(tc_List_Olist(T_c),tc_List_Olist(T_d),hAPP(c_List_Omap(T_c,T_d),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)))
<=> c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__map) ).
fof(fact_listsum__distinct__conv__setsum__set,axiom,
! [V_f_2,V_xs_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)) ) ),
file('theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).
fof(fact_listsum__triv,axiom,
! [V_xs_2,V_r_2,T_d,T_c] :
( class_Rings_Osemiring__1(T_c)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(c_COMBK(T_c,T_d),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),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_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),c_List_Oremove1(T_c,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_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Nitpick_Osetsum_H(T_c,T_d,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_d) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> c_Nitpick_Osetsum_H(T_c,T_d,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_c),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),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_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_fequal),c_List_Oset(T_c))),V_A_2))),c_List_Odistinct(T_c))))) ) ) ),
file('theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).
fof(fact_pick__same,axiom,
! [V_xs_2,T_c,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_c)),V_xs_2)))
=> hAPP(c_Random_Opick(T_c,hAPP(hAPP(c_List_Omap(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,T_c)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_c),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_c),V_xs_2),V_l_2) ),
file('theBenchmark.p',fact_pick__same) ).
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_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_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_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_d,V_xs_2,T_c] :
( 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)
=> hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_c),c_Product__Type_Ofst(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),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_d,V_xs_2,T_c] :
( 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)
=> hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_d),c_Product__Type_Osnd(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),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_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_c),c_Product__Type_Ofst(T_c,T_d)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_d),c_Product__Type_Osnd(T_c,T_d)),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_pick__member,axiom,
! [V_xs_2,T_c,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_c),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_c)),V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Random_Opick(T_c,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_c),T_c),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_c)),V_xs_2)))) ),
file('theBenchmark.p',fact_pick__member) ).
fof(fact_zip__eq__conv,axiom,
! [V_zs_2,V_ys_2,T_d,V_xs_2,T_c] :
( 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)
=> ( hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2) = V_zs_2
<=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_d),c_Product__Type_Osnd(T_c,T_d)),V_zs_2) = V_ys_2
& hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_c),c_Product__Type_Ofst(T_c,T_d)),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_c] : c_List_Olist_Olist__size(T_c,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_c,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),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_setsum__set__upto__conv__listsum__int,axiom,
! [V_j_2,V_i_2,V_f_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),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_c),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_c),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ),
file('theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).
fof(fact_interv__listsum__conv__setsum__set__int,axiom,
! [V_l_2,V_k_2,V_f_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_c),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_c),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_select__weight__member,axiom,
! [V_s_2,V_xs_2,T_c] :
( 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_c),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_c)),V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Product__Type_Ofst(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_c,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_c),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_c),T_c),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_c)),V_xs_2)))) ),
file('theBenchmark.p',fact_select__weight__member) ).
fof(fact_select__weight__def,axiom,
! [V_xs_2,T_c] : c_Random_Oselect__weight(T_c,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_c,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_c),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_c)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_c,V_xs_2))),
file('theBenchmark.p',fact_select__weight__def) ).
fof(fact_select__def,axiom,
! [V_xs_2,T_c] : c_Random_Oselect(T_c,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_c,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_c)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_c),V_xs_2)),c_Code__Numeral_Onat__of))),
file('theBenchmark.p',fact_select__def) ).
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_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__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_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__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_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_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_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_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_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_listsum__mono,axiom,
! [V_g_2,V_f_2,V_xs_2,T_c,T_d] :
( ( class_Groups_Oordered__ab__semigroup__add(T_d)
& class_Groups_Omonoid__add(T_d) )
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_g_2),V_xs_2)))) ) ),
file('theBenchmark.p',fact_listsum__mono) ).
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_c] :
( c_List_Opartition(T_c,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_yes_2),V_no_2)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_yes_2)),hAPP(c_List_Oset(T_c),V_no_2)) = hAPP(c_List_Oset(T_c),V_xs_2) ),
file('theBenchmark.p',fact_partition__set) ).
fof(fact_lists__IntI,axiom,
! [V_B_2,V_A_2,V_l_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_l_2),c_List_Olists(T_c,V_A_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_l_2),c_List_Olists(T_c,V_B_2)))
=> hBOOL(hAPP(c_List_Olistsp(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_l_2)) ) ),
file('theBenchmark.p',fact_lists__IntI) ).
fof(fact_listsp_ONil,axiom,
! [V_A_2,T_c] : hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),c_List_Olist_ONil(T_c))),
file('theBenchmark.p',fact_listsp_ONil) ).
fof(fact_listsp_Oequations_I1_J,axiom,
! [V_A_2,T_c] : hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),c_List_Olist_ONil(T_c))),
file('theBenchmark.p',fact_listsp_Oequations_I1_J) ).
fof(fact_in__listsp__conv__set,axiom,
! [V_xs_2,V_A_2,T_c] :
( hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),V_xs_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(V_A_2,B_x)) ) ),
file('theBenchmark.p',fact_in__listsp__conv__set) ).
fof(fact_listsp__conj__eq,axiom,
! [V_x_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(c_List_Olistsp(T_c,hAPP(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),V_A_2)),V_B_2)),V_x_2))
<=> ( hBOOL(hAPP(c_List_Olistsp(T_c,V_B_2),V_x_2))
& hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),V_x_2)) ) ),
file('theBenchmark.p',fact_listsp__conj__eq) ).
fof(fact_listsp__infI,axiom,
! [V_B_2,V_l_2,V_A_2,T_c] :
( hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),V_l_2))
=> ( hBOOL(hAPP(c_List_Olistsp(T_c,V_B_2),V_l_2))
=> hBOOL(hAPP(c_List_Olistsp(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_c] : c_List_Olistsp(T_c,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(tc_List_Olist(T_c),tc_HOL_Obool)),c_List_Olistsp(T_c,V_A_2)),c_List_Olistsp(T_c,V_B_2)),
file('theBenchmark.p',fact_listsp__inf__eq) ).
fof(fact_listsp_Oequations_I2_J,axiom,
! [V_a2_2,V_a1_2,V_A_2,T_c] :
( hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a1_2),V_a2_2)))
<=> ( hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),V_a2_2))
& hBOOL(hAPP(V_A_2,V_a1_2)) ) ),
file('theBenchmark.p',fact_listsp_Oequations_I2_J) ).
fof(fact_append__in__listsp__conv,axiom,
! [V_ys_2,V_xs_2,V_A_2,T_c] :
( hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)))
<=> ( hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),V_ys_2))
& hBOOL(hAPP(c_List_Olistsp(T_c,V_A_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_append__in__listsp__conv) ).
fof(fact_listsp__mono,axiom,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),c_List_Olistsp(T_c,V_A_2)),c_List_Olistsp(T_c,V_B_2))) ),
file('theBenchmark.p',fact_listsp__mono) ).
fof(fact_partition__P,axiom,
! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_c] :
( c_List_Opartition(T_c,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_yes_2),V_no_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_no_2)))
=> ~ hBOOL(hAPP(V_Pa_2,B_x)) )
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),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_c] : c_List_Opartition(T_c,V_Pa_2,c_List_Olist_ONil(T_c)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),c_List_Olist_ONil(T_c)),
file('theBenchmark.p',fact_partition_Osimps_I1_J) ).
fof(fact_listsp__lists__eq,axiom,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(c_List_Olistsp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_x_2),c_List_Olists(T_c,V_A_2))) ),
file('theBenchmark.p',fact_listsp__lists__eq) ).
fof(fact_partition_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,V_Pa_2,T_c] : c_List_Opartition(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),tc_List_Olist(T_c)),c_COMBS(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(tc_List_Olist(T_c),tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),tc_List_Olist(T_c)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_List_Olist(T_c)),hAPP(c_If(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_List_Olist(T_c)),c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(c_List_Olist_OCons(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)))),tc_List_Olist(T_c)),c_COMBB(tc_List_Olist(T_c),tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_List_Olist(T_c))),c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)))),hAPP(c_List_Olist_OCons(T_c),V_x_2)))),c_List_Opartition(T_c,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_c] : c_List_Olistsp(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_c))),c_List_Olists(T_c,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_c))),c_List_Olists(T_c,V_B_2))),
file('theBenchmark.p',fact_lists__Int__eq) ).
fof(fact_product_Osimps_I2_J,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_d,T_c] : c_Enum_Oproduct(T_c,T_d,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Omap(T_d,tc_prod(T_c,T_d)),hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_c,T_d,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_d,T_c] :
( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),B_x),hAPP(c_List_Oset(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_Pa_2),B_x)) )
& 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_list__all2__def) ).
fof(fact_list__all2__map1,axiom,
! [V_bs_2,V_as_2,V_f_2,T_e,V_Pa_2,T_d,T_c] :
( c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Omap(T_e,T_c),V_f_2),V_as_2),V_bs_2)
<=> c_List_Olist__all2(T_e,T_d,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_HOL_Obool),T_e),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_e,V_as_2,V_Pa_2,T_d,T_c] :
( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_as_2,hAPP(hAPP(c_List_Omap(T_e,T_d),V_f_2),V_bs_2))
<=> c_List_Olist__all2(T_c,T_e,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_HOL_Obool)),T_c),c_COMBB(T_d,tc_HOL_Obool,T_e)),V_Pa_2)),V_f_2),V_as_2,V_bs_2) ),
file('theBenchmark.p',fact_list__all2__map2) ).
fof(fact_list__all2__dropI,axiom,
! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_d,T_c] :
( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_as_2,V_bs_2)
=> c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_d),V_n_2),V_bs_2)) ),
file('theBenchmark.p',fact_list__all2__dropI) ).
fof(fact_list__all2__appendI,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,V_Pa_2,T_d,T_c] :
( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_a_2,V_b_2)
=> ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_c_2,V_d_2)
=> c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_d),V_b_2),V_d_2)) ) ),
file('theBenchmark.p',fact_list__all2__appendI) ).
fof(fact_list__all2__append,axiom,
! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_d,V_xs_2,T_c] :
( 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)
=> ( c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_d),V_ys_2),V_vs_2))
<=> ( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_us_2,V_vs_2)
& c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) ) ) ),
file('theBenchmark.p',fact_list__all2__append) ).
fof(fact_list__all2__Cons,axiom,
! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_d,T_c] :
( c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_d),V_y_2),V_ys_2))
<=> ( c_List_Olist__all2(T_c,T_d,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__takeI,axiom,
! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] :
( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2)
=> c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_d),V_n_2),V_ys_2)) ),
file('theBenchmark.p',fact_list__all2__takeI) ).
fof(fact_list__all2__eq,axiom,
! [T_c,V_ys_2,V_xs_2] :
( V_xs_2 = V_ys_2
<=> c_List_Olist__all2(T_c,T_c,c_fequal,V_xs_2,V_ys_2) ),
file('theBenchmark.p',fact_list__all2__eq) ).
fof(fact_list__all2__lengthD,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] :
( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_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_list__all2__lengthD) ).
fof(fact_list__all2__Nil,axiom,
! [V_ys_2,V_Pa_2,T_d,T_c] :
( c_List_Olist__all2(T_c,T_d,V_Pa_2,c_List_Olist_ONil(T_c),V_ys_2)
<=> V_ys_2 = c_List_Olist_ONil(T_d) ),
file('theBenchmark.p',fact_list__all2__Nil) ).
fof(fact_list__all2__Nil2,axiom,
! [V_xs_2,V_Pa_2,T_d,T_c] :
( c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_d))
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_list__all2__Nil2) ).
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_d,T_c] :
( c_List_Olist__all2(T_c,T_d,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_c)),V_xs_2)))
=> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_d),V_ys_2),B_i))) )
& 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_list__all2__conv__all__nth) ).
fof(fact_list__all2__nthD,axiom,
! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] :
( c_List_Olist__all2(T_c,T_d,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_xs_2)))
=> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_d),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_d,T_c] :
( c_List_Olist__all2(T_c,T_d,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_d)),V_ys_2)))
=> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_d),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_d,V_xs_2,T_c,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_c)),V_xs_2)))
=> ( c_List_Olist__all2(T_c,T_d,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_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_d,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_d,T_c] :
( c_List_Olist__all2(T_c,T_d,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_d)),V_ys_2)))
=> c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_d,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_d,T_c] : hAPP(c_List_Oset(tc_prod(T_c,T_d)),c_Enum_Oproduct(T_c,T_d,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_List_Oset(T_d),V_ys_2))),
file('theBenchmark.p',fact_product__list__set) ).
fof(fact_sublists__powset,axiom,
! [V_xs_2,T_c] : hAPP(c_Set_Oimage(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),c_List_Oset(T_c)),hAPP(c_List_Oset(tc_List_Olist(T_c)),c_Enum_Osublists(T_c,V_xs_2))) = hAPP(c_Set_OPow(T_c),hAPP(c_List_Oset(T_c),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_c] : c_Enum_Osublists(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c))),c_Enum_Osublists(T_c,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_c)),tc_fun(tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c))),tc_List_Olist(tc_List_Olist(T_c))),c_List_Oappend(tc_List_Olist(T_c))),hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(c_List_Olist_OCons(T_c),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_c))))),
file('theBenchmark.p',fact_sublists_Osimps_I2_J) ).
fof(fact_distinct__set__sublists,axiom,
! [V_xs_2,T_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool)),c_List_Oset(T_c)),c_Enum_Osublists(T_c,V_xs_2)))) ),
file('theBenchmark.p',fact_distinct__set__sublists) ).
fof(fact_set__n__lists,axiom,
! [V_xs_2,V_n_2,T_c] : hAPP(c_List_Oset(tc_List_Olist(T_c)),c_Enum_On__lists(T_c,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_c)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_c),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_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_c)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),c_List_Oset(T_c))),hAPP(c_List_Oset(T_c),V_xs_2)))),
file('theBenchmark.p',fact_set__n__lists) ).
fof(fact_enum__the__def,axiom,
! [V_Pa_2,T_c] : c_Enum_Oenum__the(T_c,V_Pa_2) = c_HOL_OThe(T_c,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__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_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_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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_c)),c_Enum_On__lists(T_c,V_n_2,V_xs_2))))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),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_d,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),B_x),hAPP(c_List_Oset(tc_prod(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_a_2),V_b_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_Pa_2),B_x)) )
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_b_2)
=> c_List_Olist__all2(T_c,T_d,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_c] :
( ! [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_c)),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i))) )
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),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_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2)
=> hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_y_2),hAPP(c_List_Oset(T_c),V_xs_2)) = hAPP(c_List_Ofoldl(T_d,T_c,hAPP(c_COMBC(T_c,T_d,T_d),V_f_2),V_y_2),c_List_Oremdups(T_c,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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),hAPP(c_List_OremoveAll(T_c,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_d,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_d),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_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_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_remdups__id__iff__distinct,axiom,
! [V_xs_2,T_c] :
( c_List_Oremdups(T_c,V_xs_2) = V_xs_2
<=> hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ),
file('theBenchmark.p',fact_remdups__id__iff__distinct) ).
fof(fact_set__remdups,axiom,
! [V_xs_2,T_c] : hAPP(c_List_Oset(T_c),c_List_Oremdups(T_c,V_xs_2)) = hAPP(c_List_Oset(T_c),V_xs_2),
file('theBenchmark.p',fact_set__remdups) ).
fof(fact_length__remdups__eq,axiom,
! [V_xs_2,T_c] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Oremdups(T_c,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
<=> c_List_Oremdups(T_c,V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_length__remdups__eq) ).
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_remdups__eq__nil__iff,axiom,
! [V_x_2,T_c] :
( c_List_Oremdups(T_c,V_x_2) = c_List_Olist_ONil(T_c)
<=> V_x_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_remdups__eq__nil__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__right__iff,axiom,
! [V_x_2,T_c] :
( c_List_Olist_ONil(T_c) = c_List_Oremdups(T_c,V_x_2)
<=> V_x_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_remdups__eq__nil__right__iff) ).
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_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_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_remdups__map__remdups,axiom,
! [V_xs_2,V_f_2,T_d,T_c] : c_List_Oremdups(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Oremdups(T_d,V_xs_2))) = c_List_Oremdups(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),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_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hAPP(c_List_OremoveAll(T_c,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_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_Oremdups(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Oremdups(T_c,V_xs_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_Oremdups(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = c_List_Oremdups(T_c,V_xs_2) ) ),
file('theBenchmark.p',fact_remdups_Osimps_I2_J) ).
fof(fact_length__remdups__card__conv,axiom,
! [V_xs_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Oremdups(T_c,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_List_Oset(T_c),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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),hAPP(c_List_OremoveAll(T_c,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_d,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_d),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_c] : hAPP(c_List_Oset(T_c),hAPP(c_List_OremoveAll(T_c,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_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_set__removeAll) ).
fof(fact_length__remdups__concat,axiom,
! [V_xss_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Oremdups(T_c,c_List_Oconcat(T_c,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xss_2)),c_List_Oset(T_c))),
file('theBenchmark.p',fact_length__remdups__concat) ).
fof(fact_sorted__list__of__set__sort__remdups,axiom,
! [V_xs_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osorted__list__of__set(T_c,hAPP(c_List_Oset(T_c),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_c,T_c,c_COMBI(T_c),c_List_Oremdups(T_c,V_xs_2)) ),
file('theBenchmark.p',fact_sorted__list__of__set__sort__remdups) ).
fof(fact_sort__key__simps_I1_J,axiom,
! [V_f_2,T_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_sort__key__simps_I1_J) ).
fof(fact_foldl__conv__concat,axiom,
! [V_xss_2,V_xs_2,T_c] : hAPP(c_List_Ofoldl(tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Oappend(T_c),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),c_List_Oconcat(T_c,V_xss_2)),
file('theBenchmark.p',fact_foldl__conv__concat) ).
fof(fact_concat__conv__foldl,axiom,
! [V_xss_2,T_c] : c_List_Oconcat(T_c,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Oappend(T_c),c_List_Olist_ONil(T_c)),V_xss_2),
file('theBenchmark.p',fact_concat__conv__foldl) ).
fof(fact_length__sort,axiom,
! [V_xs_2,V_f_2,T_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Olinorder__class_Osort__key(T_c,T_d,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__sort) ).
fof(fact_set__sort,axiom,
! [V_xs_2,V_f_2,T_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> hAPP(c_List_Oset(T_c),c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_c),V_xs_2) ),
file('theBenchmark.p',fact_set__sort) ).
fof(fact_distinct__sort,axiom,
! [V_xs_2,V_f_2,T_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_c),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_concat__eq__Nil__conv,axiom,
! [V_xss_2,T_c] :
( c_List_Oconcat(T_c,V_xss_2) = c_List_Olist_ONil(T_c)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xss_2)))
=> B_x = c_List_Olist_ONil(T_c) ) ),
file('theBenchmark.p',fact_concat__eq__Nil__conv) ).
fof(fact_Nil__eq__concat__conv,axiom,
! [V_xss_2,T_c] :
( c_List_Olist_ONil(T_c) = c_List_Oconcat(T_c,V_xss_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xss_2)))
=> B_x = c_List_Olist_ONil(T_c) ) ),
file('theBenchmark.p',fact_Nil__eq__concat__conv) ).
fof(fact_map__concat,axiom,
! [V_xs_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Oconcat(T_d,V_xs_2)) = c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_d),tc_List_Olist(T_c)),hAPP(c_List_Omap(T_d,T_c),V_f_2)),V_xs_2)),
file('theBenchmark.p',fact_map__concat) ).
fof(fact_length__concat,axiom,
! [V_xss_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_Oconcat(T_c,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2)),
file('theBenchmark.p',fact_length__concat) ).
fof(fact_set__concat,axiom,
! [V_xs_2,T_c] : hAPP(c_List_Oset(T_c),c_List_Oconcat(T_c,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xs_2)),c_List_Oset(T_c)),
file('theBenchmark.p',fact_set__concat) ).
fof(fact_sort__key__simps_I2_J,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_c,T_d,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_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osort__key(T_c,T_c,c_COMBI(T_c),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_c),T_c,hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c))),c_List_Olist_ONil(T_c)),V_xs_2) ),
file('theBenchmark.p',fact_sort__foldl__insort) ).
fof(fact_concat__injective,axiom,
! [V_ys_2,V_xs_2,T_c] :
( c_List_Oconcat(T_c,V_xs_2) = c_List_Oconcat(T_c,V_ys_2)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),V_ys_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),B_x)) )
=> V_xs_2 = V_ys_2 ) ) ),
file('theBenchmark.p',fact_concat__injective) ).
fof(fact_concat__eq__concat__iff,axiom,
! [V_ys_2,V_xs_2,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_c),tc_Nat_Onat),tc_fun(tc_List_Olist(T_c),tc_HOL_Obool)),tc_List_Olist(T_c)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_c)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),B_x)) )
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),V_ys_2)
=> ( c_List_Oconcat(T_c,V_xs_2) = c_List_Oconcat(T_c,V_ys_2)
<=> V_xs_2 = V_ys_2 ) ) ),
file('theBenchmark.p',fact_concat__eq__concat__iff) ).
fof(fact_concat__map__singleton,axiom,
! [V_xs_2,V_f_2,T_d,T_c] : c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(T_d,tc_List_Olist(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),T_d),c_List_Olist_OCons(T_c)),V_f_2)),c_List_Olist_ONil(T_c))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),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_c] : c_Enum_On__lists(T_c,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_c),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),tc_List_Olist(T_c)),c_List_Omap(T_c,tc_List_Olist(T_c))),hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)))),V_xs_2)),c_Enum_On__lists(T_c,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_c] : c_List_Otranspose(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_Olist__case(tc_List_Olist(T_c),T_c,c_List_Olist_ONil(T_c),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),T_c),c_COMBK(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),c_List_Olist_ONil(T_c))))),V_xss_2)))),c_List_Otranspose(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_c),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_c)),T_c,c_List_Olist_ONil(tc_List_Olist(T_c)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),T_c),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c))),c_List_Olist_OCons(tc_List_Olist(T_c))),c_List_Olist_ONil(tc_List_Olist(T_c)))))),V_xss_2))))),
file('theBenchmark.p',fact_transpose_Osimps_I3_J) ).
fof(fact_transpose__aux__filter__head,axiom,
! [V_xss_2,T_c] : c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_Olist__case(tc_List_Olist(T_c),T_c,c_List_Olist_ONil(T_c),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),T_c),c_COMBK(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),c_List_Olist_ONil(T_c))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),T_c),c_List_Ohd(T_c)),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)),
file('theBenchmark.p',fact_transpose__aux__filter__head) ).
fof(fact_filter__concat,axiom,
! [V_xs_2,V_p_2,T_c] : hAPP(c_List_Ofilter(T_c,V_p_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Ofilter(T_c,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_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> hAPP(c_List_Ofilter(T_c,V_Pa_2),c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_c,T_d,V_f_2,hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ),
file('theBenchmark.p',fact_filter__sort) ).
fof(fact_distinct__filter,axiom,
! [V_Pa_2,V_xs_2,T_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) ),
file('theBenchmark.p',fact_distinct__filter) ).
fof(fact_filter__is__subset,axiom,
! [V_xs_2,V_Pa_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_c),V_xs_2))),
file('theBenchmark.p',fact_filter__is__subset) ).
fof(fact_filter__id__conv,axiom,
! [V_xs_2,V_Pa_2,T_c] :
( hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) = V_xs_2
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_filter__id__conv) ).
fof(fact_sum__length__filter__compl,axiom,
! [V_xs_2,V_Pa_2,T_c] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2),
file('theBenchmark.p',fact_sum__length__filter__compl) ).
fof(fact_length__filter__le,axiom,
! [V_xs_2,V_Pa_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),
file('theBenchmark.p',fact_length__filter__le) ).
fof(fact_partition__filter1,axiom,
! [V_xs_2,V_Pa_2,T_c] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Opartition(T_c,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2),
file('theBenchmark.p',fact_partition__filter1) ).
fof(fact_filter__filter,axiom,
! [V_xs_2,V_Qa_2,V_Pa_2,T_c] : hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(c_List_Ofilter(T_c,V_Qa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,hAPP(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),V_Qa_2)),V_Pa_2)),V_xs_2),
file('theBenchmark.p',fact_filter__filter) ).
fof(fact_filter__remove1,axiom,
! [V_xs_2,V_x_2,V_Qa_2,T_c] : hAPP(c_List_Ofilter(T_c,V_Qa_2),c_List_Oremove1(T_c,V_x_2,V_xs_2)) = c_List_Oremove1(T_c,V_x_2,hAPP(c_List_Ofilter(T_c,V_Qa_2),V_xs_2)),
file('theBenchmark.p',fact_filter__remove1) ).
fof(fact_remove1__filter__not,axiom,
! [V_xs_2,T_c,V_x_2,V_Pa_2] :
( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_Oremove1(T_c,V_x_2,hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) ),
file('theBenchmark.p',fact_remove1__filter__not) ).
fof(fact_filter__insort__triv,axiom,
! [V_xs_2,V_f_2,T_c,V_x_2,V_Pa_2,T_d] :
( class_Orderings_Olinorder(T_d)
=> ( ~ 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_d,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) ) ),
file('theBenchmark.p',fact_filter__insort__triv) ).
fof(fact_filter__map,axiom,
! [V_xs_2,V_f_2,T_d,V_Pa_2,T_c] : hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(c_List_Ofilter(T_d,hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,T_d,V_Pa_2),V_f_2)),V_xs_2)),
file('theBenchmark.p',fact_filter__map) ).
fof(fact_filter_Osimps_I1_J,axiom,
! [V_Pa_2,T_c] : hAPP(c_List_Ofilter(T_c,V_Pa_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_c),
file('theBenchmark.p',fact_filter_Osimps_I1_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_I2_J,axiom,
! [V_xs_2,T_c,V_x_2,V_Pa_2] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_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_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_filter_Osimps_I2_J) ).
fof(fact_filter__append,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_c] : hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_c),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_ys_2)),
file('theBenchmark.p',fact_filter__append) ).
fof(fact_filter__empty__conv,axiom,
! [V_xs_2,V_Pa_2,T_c] :
( hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_c)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_filter__empty__conv) ).
fof(fact_remdups__filter,axiom,
! [V_xs_2,V_Pa_2,T_c] : c_List_Oremdups(T_c,hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),c_List_Oremdups(T_c,V_xs_2)),
file('theBenchmark.p',fact_remdups__filter) ).
fof(fact_removeAll__filter__not,axiom,
! [V_xs_2,T_c,V_x_2,V_Pa_2] :
( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> hAPP(c_List_OremoveAll(T_c,V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2) ),
file('theBenchmark.p',fact_removeAll__filter__not) ).
fof(fact_removeAll__filter__not__eq,axiom,
! [V_x_2,T_c] : c_List_OremoveAll(T_c,V_x_2) = c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(c_fequal,V_x_2))),
file('theBenchmark.p',fact_removeAll__filter__not__eq) ).
fof(fact_partition__filter2,axiom,
! [V_xs_2,V_Pa_2,T_c] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Opartition(T_c,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_c,c_fNot),V_Pa_2)),V_xs_2),
file('theBenchmark.p',fact_partition__filter2) ).
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_c,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_c))),c_List_Otranspose(T_c,V_xs_2))))
=> hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),c_List_Otranspose(T_c,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),T_c),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,T_c),c_List_Onth(T_c)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),V_xs_2)) ),
file('theBenchmark.p',fact_nth__transpose) ).
fof(fact_transpose__map__map,axiom,
! [V_xs_2,V_f_2,T_d,T_c] : c_List_Otranspose(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_d),tc_List_Olist(T_c)),hAPP(c_List_Omap(T_d,T_c),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_d),tc_List_Olist(T_c)),hAPP(c_List_Omap(T_d,T_c),V_f_2)),c_List_Otranspose(T_d,V_xs_2)),
file('theBenchmark.p',fact_transpose__map__map) ).
fof(fact_set__filter,axiom,
! [V_xs_2,V_Pa_2,T_c] : hAPP(c_List_Oset(T_c),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_c),hAPP(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)),hAPP(c_List_Oset(T_c),V_xs_2)))),V_Pa_2)),
file('theBenchmark.p',fact_set__filter) ).
fof(fact_length__filter__map,axiom,
! [V_xs_2,V_f_2,T_d,V_Pa_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),hAPP(c_List_Ofilter(T_d,hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,T_d,V_Pa_2),V_f_2)),V_xs_2)),
file('theBenchmark.p',fact_length__filter__map) ).
fof(fact_length__filter__less,axiom,
! [V_Pa_2,V_xs_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),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_c)),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) ) ),
file('theBenchmark.p',fact_length__filter__less) ).
fof(fact_partition__filter__conv,axiom,
! [V_xs_2,V_f_2,T_c] : c_List_Opartition(T_c,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_c,c_fNot),V_f_2)),V_xs_2)),
file('theBenchmark.p',fact_partition__filter__conv) ).
fof(fact_set__minus__filter__out,axiom,
! [V_y_2,V_xs_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_c),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,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_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),hAPP(c_List_Oset(T_c),c_List_Osublist(T_c,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_c,V_xs_2,V_s_2) ),
file('theBenchmark.p',fact_filter__in__sublist) ).
fof(fact_transpose__empty,axiom,
! [V_xs_2,T_c] :
( c_List_Otranspose(T_c,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_c))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xs_2)))
=> B_x = c_List_Olist_ONil(T_c) ) ),
file('theBenchmark.p',fact_transpose__empty) ).
fof(fact_length__filter__conv__card,axiom,
! [V_xs_2,V_p_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,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_c)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_c),V_xs_2))))),
file('theBenchmark.p',fact_length__filter__conv__card) ).
fof(fact_transpose__aux__filter__tail,axiom,
! [V_xss_2,T_c] : c_List_Oconcat(tc_List_Olist(T_c),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_c)),T_c,c_List_Olist_ONil(tc_List_Olist(T_c)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),T_c),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c))),c_List_Olist_OCons(tc_List_Olist(T_c))),c_List_Olist_ONil(tc_List_Olist(T_c)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Otl(T_c)),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)),
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_c] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_c)),c_List_Otranspose__rel(T_c)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_xss_2)))
=> c_List_Otranspose(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_Olist__case(tc_List_Olist(T_c),T_c,c_List_Olist_ONil(T_c),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),T_c),c_COMBK(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),c_List_Olist_ONil(T_c))))),V_xss_2)))),c_List_Otranspose(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_c),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_c)),T_c,c_List_Olist_ONil(tc_List_Olist(T_c)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c))),T_c),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(tc_List_Olist(T_c)),tc_List_Olist(tc_List_Olist(T_c))),c_List_Olist_OCons(tc_List_Olist(T_c))),c_List_Olist_ONil(tc_List_Olist(T_c)))))),V_xss_2))))) ),
file('theBenchmark.p',fact_transpose_Opsimps_I3_J) ).
fof(fact_transpose_Opsimps_I2_J,axiom,
! [V_xss_2,T_c] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_c)),c_List_Otranspose__rel(T_c)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),V_xss_2)))
=> c_List_Otranspose(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),V_xss_2)) = c_List_Otranspose(T_c,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_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,tc_Nat_Onat),T_c),c_Product__Type_Ofst(T_c,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_c,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_c,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_c,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_c,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,tc_Nat_Onat),T_c),c_Product__Type_Ofst(T_c,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_c,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_c,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_c,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_select__weigth__drop__zero,axiom,
! [V_xs_2,T_c] : c_Random_Oselect__weight(T_c,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_c)),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_c,V_xs_2),
file('theBenchmark.p',fact_select__weigth__drop__zero) ).
fof(fact_pick__drop__zero,axiom,
! [V_xs_2,T_c] : c_Random_Opick(T_c,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_c)),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_c,V_xs_2),
file('theBenchmark.p',fact_pick__drop__zero) ).
fof(fact_transpose_Opsimps_I1_J,axiom,
! [T_c] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_c)),c_List_Otranspose__rel(T_c)),c_List_Olist_ONil(tc_List_Olist(T_c))))
=> c_List_Otranspose(T_c,c_List_Olist_ONil(tc_List_Olist(T_c))) = c_List_Olist_ONil(tc_List_Olist(T_c)) ),
file('theBenchmark.p',fact_transpose_Opsimps_I1_J) ).
fof(fact_transpose__max__length,axiom,
! [V_xs_2,T_c] : 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))),c_List_Otranspose(T_c,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),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_xs_2)),
file('theBenchmark.p',fact_transpose__max__length) ).
fof(fact_transpose__aux__max,axiom,
! [V_xss_2,T_d,V_xs_2,T_c] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_d),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_d)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_d))),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_c)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_d),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_d)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_d),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_d)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_d)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_d),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_d)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_d),tc_List_Olist(T_d),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_d)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
file('theBenchmark.p',fact_transpose__aux__max) ).
fof(fact_foldr_Osimps_I1_J,axiom,
! [V_a_2,V_f_2,T_c,T_d] : c_List_Ofoldr(T_d,T_c,V_f_2,c_List_Olist_ONil(T_d),V_a_2) = V_a_2,
file('theBenchmark.p',fact_foldr_Osimps_I1_J) ).
fof(fact_foldr_Osimps_I2_J,axiom,
! [V_a_2,V_xs_2,V_x_2,V_f_2,T_c,T_d] : c_List_Ofoldr(T_d,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_d),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_d,T_c,V_f_2,V_xs_2,V_a_2)),
file('theBenchmark.p',fact_foldr_Osimps_I2_J) ).
fof(fact_foldr__append,axiom,
! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_c,T_d] : c_List_Ofoldr(T_d,T_c,V_f_2,hAPP(hAPP(c_List_Oappend(T_d),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_d,T_c,V_f_2,V_xs_2,c_List_Ofoldr(T_d,T_c,V_f_2,V_ys_2,V_a_2)),
file('theBenchmark.p',fact_foldr__append) ).
fof(fact_foldr__conv__foldl,axiom,
! [V_a_2,V_xs_2,T_c] :
( class_Groups_Oab__semigroup__add(T_c)
=> c_List_Ofoldr(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),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_e,V_g_2,T_c,T_d] : c_List_Ofoldr(T_d,T_c,V_g_2,hAPP(hAPP(c_List_Omap(T_e,T_d),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_e,T_c,hAPP(c_Fun_Ocomp(T_d,tc_fun(T_c,T_c),T_e,V_g_2),V_f_2),V_xs_2,V_a_2),
file('theBenchmark.p',fact_foldr__map) ).
fof(fact_foldl__foldr1,axiom,
! [V_xs_2,T_c] :
( class_Groups_Omonoid__add(T_c)
=> hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_xs_2) = c_List_Ofoldr(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_xs_2,c_Groups_Ozero__class_Ozero(T_c)) ),
file('theBenchmark.p',fact_foldl__foldr1) ).
fof(fact_foldl__foldr1__lemma,axiom,
! [V_xs_2,V_a_2,T_c] :
( class_Groups_Omonoid__add(T_c)
=> hAPP(c_List_Ofoldl(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),c_List_Ofoldr(T_c,T_c,c_Groups_Oplus__class_Oplus(T_c),V_xs_2,c_Groups_Ozero__class_Ozero(T_c))) ),
file('theBenchmark.p',fact_foldl__foldr1__lemma) ).
fof(fact_length__transpose,axiom,
! [V_xs_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),c_List_Otranspose(T_c,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_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_c] : c_List_Osublist(T_c,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,tc_Nat_Onat),T_c),c_Product__Type_Ofst(T_c,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_c,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_c,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_c,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_c,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_c)),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_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,tc_Nat_Onat),T_c),c_Product__Type_Ofst(T_c,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_c,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_c,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_c,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_c,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_c)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,tc_Nat_Onat),T_c),c_Product__Type_Ofst(T_c,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_c,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_c,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_c,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_c,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_c,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_c,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_c)),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__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_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__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__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__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__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__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_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_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_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_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_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_c] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_c),hAPP(c_List_Onth(T_c),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))) = V_xs_2,
file('theBenchmark.p',fact_map__nth) ).
fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
! [V_n_2,V_m_2,V_f_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_c),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ),
file('theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).
fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
! [V_n_2,V_m_2,V_f_2,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_c),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_c),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_nth__map__upt,axiom,
! [V_f_2,T_c,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_c),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_c),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_c,V_xs_2] :
( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_c))
=> 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_c))),V_xs_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),V_xs_2),B_i)) = V_n_2 )
=> c_List_Otranspose(T_c,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_c)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_c),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_c)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_c)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBB(tc_List_Olist(T_c),tc_fun(tc_Nat_Onat,T_c),tc_Nat_Onat),c_List_Onth(T_c)),hAPP(c_List_Onth(tc_List_Olist(T_c)),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_c))),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_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> ( c_List_Olinorder__class_Osorted(T_d,hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2))
=> ( hAPP(c_List_Ohd(T_c),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_d,tc_HOL_Obool,T_c),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_c,T_d,V_f_2),V_a_2),c_List_Oremove1(T_c,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_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osorted(T_c,c_List_Olinorder__class_Osort__key(T_c,T_c,c_COMBI(T_c),V_xs_2)) ),
file('theBenchmark.p',fact_sorted__sort) ).
fof(fact_sorted__insort__insert,axiom,
! [V_x_2,V_xs_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_c,c_List_Olinorder__class_Oinsort__insert__key(T_c,T_c,c_COMBI(T_c),V_x_2,V_xs_2)) ) ),
file('theBenchmark.p',fact_sorted__insort__insert) ).
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__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__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__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__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__insort,axiom,
! [V_xs_2,V_x_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_x_2),V_xs_2))
<=> c_List_Olinorder__class_Osorted(T_c,V_xs_2) ) ),
file('theBenchmark.p',fact_sorted__insort) ).
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_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__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_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_zs_2)))
<=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_zs_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_sorted__many__eq) ).
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_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,V_xs_2)
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> ( c_List_Olinorder__class_Osorted(T_c,V_ys_2)
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_ys_2))
=> ( 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_sorted__distinct__set__unique) ).
fof(fact_sorted__sort__key,axiom,
! [V_xs_2,V_f_2,T_d,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Olinorder__class_Osort__key(T_d,T_c,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_d,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))
=> c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_d,T_c,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_d,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))
=> c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Oremove1(T_d,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_d,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),V_xs_2)))
<=> c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_sorted__insort__key) ).
fof(fact_sorted__filter,axiom,
! [V_Pa_2,V_xs_2,V_f_2,T_d,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))
=> c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(c_List_Ofilter(T_d,V_Pa_2),V_xs_2))) ) ),
file('theBenchmark.p',fact_sorted__filter) ).
fof(fact_sorted__map__same,axiom,
! [V_xs_2,V_g_2,V_f_2,T_d,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(c_List_Ofilter(T_d,hAPP(hAPP(c_COMBC(T_d,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_d),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__same,axiom,
! [V_xs_2,V_g_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osorted(T_c,hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_c,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_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),B_x)) )
& c_List_Olinorder__class_Osorted(T_c,V_xs_2) ) ) ),
file('theBenchmark.p',fact_sorted__Cons) ).
fof(fact_sorted__append,axiom,
! [V_ys_2,V_xs_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),hAPP(c_List_Oset(T_c),V_ys_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),B_xa)) ) )
& c_List_Olinorder__class_Osorted(T_c,V_ys_2)
& c_List_Olinorder__class_Osorted(T_c,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_d,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2))
=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> hAPP(c_List_Ofilter(T_d,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_d,T_c,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_d,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_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),V_a2_2),V_a1_2))
<=> ( c_List_Olinorder__class_Osorted(T_c,V_a1_2)
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_a1_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a2_2),B_x)) ) ) ) ),
file('theBenchmark.p',fact_sorted_Oequations_I2_J) ).
fof(fact_sorted__list__of__set,axiom,
! [V_A_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),c_List_Olinorder__class_Osorted__list__of__set(T_c,V_A_2)))
& c_List_Olinorder__class_Osorted(T_c,c_List_Olinorder__class_Osorted__list__of__set(T_c,V_A_2))
& hAPP(c_List_Oset(T_c),c_List_Olinorder__class_Osorted__list__of__set(T_c,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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> ( c_List_Olinorder__class_Osorted(T_c,V_xs_2)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_c,c_COMBI(T_c)),V_a_2),c_List_Oremove1(T_c,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_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,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_c)),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_c),hAPP(hAPP(c_List_Onth(T_c),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),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_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> ( c_Fun_Oinj__on(T_c,T_d,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)))
=> ( c_List_Olinorder__class_Osorted(T_d,hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2))
=> ( hBOOL(hAPP(c_List_Odistinct(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_xs_2)))
=> ( c_List_Olinorder__class_Osorted(T_d,hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_ys_2))
=> ( hBOOL(hAPP(c_List_Odistinct(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),V_ys_2)))
=> ( 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__sorted__distinct__set__unique) ).
fof(fact_transpose__column,axiom,
! [V_i_2,V_xs_2,T_c] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),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_c))),V_xs_2)))
=> hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),T_c),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,T_c),c_List_Onth(T_c)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),c_List_Otranspose(T_c,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),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_c] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),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_c))),c_List_Otranspose(T_c,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_c))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),V_xs_2))))
=> hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),c_List_Otranspose(T_c,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),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_c] : c_Fun_Oinj__on(tc_List_Olist(T_c),tc_List_Olist(T_c),c_List_Orev(T_c),V_A_2),
file('theBenchmark.p',fact_inj__on__rev) ).
fof(fact_distinct__rev,axiom,
! [V_xs_2,T_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(c_List_Orev(T_c),V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ),
file('theBenchmark.p',fact_distinct__rev) ).
fof(fact_rev__is__Nil__conv,axiom,
! [V_xs_2,T_c] :
( hAPP(c_List_Orev(T_c),V_xs_2) = c_List_Olist_ONil(T_c)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_rev__is__Nil__conv) ).
fof(fact_Nil__is__rev__conv,axiom,
! [V_xs_2,T_c] :
( c_List_Olist_ONil(T_c) = hAPP(c_List_Orev(T_c),V_xs_2)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_Nil__is__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_singleton__rev__conv,axiom,
! [V_xs_2,V_x_2,T_c] :
( hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)) = hAPP(c_List_Orev(T_c),V_xs_2)
<=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)) ),
file('theBenchmark.p',fact_singleton__rev__conv) ).
fof(fact_rev__singleton__conv,axiom,
! [V_x_2,V_xs_2,T_c] :
( hAPP(c_List_Orev(T_c),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c))
<=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_Olist_ONil(T_c)) ),
file('theBenchmark.p',fact_rev__singleton__conv) ).
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__concat,axiom,
! [V_xs_2,T_c] : hAPP(c_List_Orev(T_c),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Orev(T_c)),hAPP(c_List_Orev(tc_List_Olist(T_c)),V_xs_2))),
file('theBenchmark.p',fact_rev__concat) ).
fof(fact_rev__map,axiom,
! [V_xs_2,V_f_2,T_d,T_c] : hAPP(c_List_Orev(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),hAPP(c_List_Orev(T_d),V_xs_2)),
file('theBenchmark.p',fact_rev__map) ).
fof(fact_rev__filter,axiom,
! [V_xs_2,V_Pa_2,T_c] : hAPP(c_List_Orev(T_c),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(c_List_Orev(T_c),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_c] : hAPP(c_List_Oset(T_c),hAPP(c_List_Orev(T_c),V_xs_2)) = hAPP(c_List_Oset(T_c),V_xs_2),
file('theBenchmark.p',fact_set__rev) ).
fof(fact_list__all2__rev,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] :
( c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(c_List_Orev(T_c),V_xs_2),hAPP(c_List_Orev(T_d),V_ys_2))
<=> c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,V_ys_2) ),
file('theBenchmark.p',fact_list__all2__rev) ).
fof(fact_list__all2__rev1,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] :
( c_List_Olist__all2(T_c,T_d,V_Pa_2,hAPP(c_List_Orev(T_c),V_xs_2),V_ys_2)
<=> c_List_Olist__all2(T_c,T_d,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_d),V_ys_2)) ),
file('theBenchmark.p',fact_list__all2__rev1) ).
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_rev__swap,axiom,
! [V_ys_2,V_xs_2,T_c] :
( hAPP(c_List_Orev(T_c),V_xs_2) = V_ys_2
<=> V_xs_2 = hAPP(c_List_Orev(T_c),V_ys_2) ),
file('theBenchmark.p',fact_rev__swap) ).
fof(fact_rev__is__rev__conv,axiom,
! [V_ys_2,V_xs_2,T_c] :
( hAPP(c_List_Orev(T_c),V_xs_2) = hAPP(c_List_Orev(T_c),V_ys_2)
<=> V_xs_2 = V_ys_2 ),
file('theBenchmark.p',fact_rev__is__rev__conv) ).
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_c,T_d] : c_List_Ofoldr(T_d,T_c,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_c,T_d,hAPP(c_COMBC(T_d,T_c,T_c),V_f_2),V_a_2),hAPP(c_List_Orev(T_d),V_xs_2)),
file('theBenchmark.p',fact_foldr__foldl) ).
fof(fact_foldl__foldr,axiom,
! [V_xs_2,V_a_2,V_f_2,T_d,T_c] : hAPP(c_List_Ofoldl(T_c,T_d,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_d,T_c,hAPP(c_COMBC(T_c,T_d,T_c),V_f_2),hAPP(c_List_Orev(T_d),V_xs_2),V_a_2),
file('theBenchmark.p',fact_foldl__foldr) ).
fof(fact_rev__eq__Cons__iff,axiom,
! [V_ys_2,V_y_2,V_xs_2,T_c] :
( hAPP(c_List_Orev(T_c),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)
<=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),hAPP(c_List_Orev(T_c),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),c_List_Olist_ONil(T_c))) ),
file('theBenchmark.p',fact_rev__eq__Cons__iff) ).
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_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_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_sorted__transpose,axiom,
! [V_xs_2,T_c] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),c_List_Otranspose(T_c,V_xs_2)))),
file('theBenchmark.p',fact_sorted__transpose) ).
fof(fact_rev__foldl__cons,axiom,
! [V_xs_2,T_c] : hAPP(c_List_Orev(T_c),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_c),T_c,hAPP(c_COMBC(T_c,tc_List_Olist(T_c),tc_List_Olist(T_c)),c_List_Olist_OCons(T_c)),c_List_Olist_ONil(T_c)),V_xs_2),
file('theBenchmark.p',fact_rev__foldl__cons) ).
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_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_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_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(c_List_Orev(T_c),V_xs_2))
=> ( ( V_xs_2 != c_List_Olist_ONil(T_c)
=> c_List_Ofoldr(T_c,T_c,c_Orderings_Oord__class_Omax(T_c),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_List_Onth(T_c),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) )
& ( V_xs_2 = c_List_Olist_ONil(T_c)
=> c_List_Ofoldr(T_c,T_c,c_Orderings_Oord__class_Omax(T_c),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_c] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xs_2)))
=> ( ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_c))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),c_List_Otranspose(T_c,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_c))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),c_List_Otranspose(T_c,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_c] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),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_c))),V_xs_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_c))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_c)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),c_List_Otranspose(T_c,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_c)),V_xs_2),V_i_2)) ) ),
file('theBenchmark.p',fact_transpose__column__length) ).
fof(fact_transpose__transpose,axiom,
! [V_xs_2,T_c] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xs_2)))
=> c_List_Otranspose(T_c,c_List_Otranspose(T_c,V_xs_2)) = c_List_OtakeWhile(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_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_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_c,c_List_OtakeWhile(T_c,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_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),
file('theBenchmark.p',fact_length__takeWhile__le) ).
fof(fact_set__takeWhileD,axiom,
! [V_xs_2,V_Pa_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2))))
=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ) ),
file('theBenchmark.p',fact_set__takeWhileD) ).
fof(fact_takeWhile__eq__all__conv,axiom,
! [V_xs_2,V_Pa_2,T_c] :
( c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2) = V_xs_2
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_takeWhile__eq__all__conv) ).
fof(fact_zip__takeWhile__snd,axiom,
! [V_ys_2,V_Pa_2,V_xs_2,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),c_List_OtakeWhile(T_d,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_c,T_d),hAPP(c_Fun_Ocomp(T_d,tc_HOL_Obool,tc_prod(T_c,T_d),V_Pa_2),c_Product__Type_Osnd(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__takeWhile__snd) ).
fof(fact_zip__takeWhile__fst,axiom,
! [V_ys_2,V_xs_2,V_Pa_2,T_d,T_c] : hAPP(hAPP(c_List_Ozip(T_c,T_d),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_c,T_d),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_c,T_d),V_Pa_2),c_Product__Type_Ofst(T_c,T_d)),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__takeWhile__fst) ).
fof(fact_takeWhile__map,axiom,
! [V_xs_2,V_f_2,T_d,V_Pa_2,T_c] : c_List_OtakeWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_OtakeWhile(T_d,hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,T_d,V_Pa_2),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_takeWhile__map) ).
fof(fact_takeWhile__tail,axiom,
! [V_l_2,V_xs_2,T_c,V_x_2,V_Pa_2] :
( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OtakeWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_l_2))) = c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2) ),
file('theBenchmark.p',fact_takeWhile__tail) ).
fof(fact_takeWhile_Osimps_I2_J,axiom,
! [V_xs_2,T_c,V_x_2,V_Pa_2] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OtakeWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_c) )
& ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OtakeWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)) ) ),
file('theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).
fof(fact_takeWhile_Osimps_I1_J,axiom,
! [V_Pa_2,T_c] : c_List_OtakeWhile(T_c,V_Pa_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_c),
file('theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
fof(fact_takeWhile__eq__take,axiom,
! [V_xs_2,V_Pa_2,T_c] : c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OtakeWhile(T_c,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_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_c),c_List_OtakeWhile(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OtakeWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2) ) ),
file('theBenchmark.p',fact_takeWhile__append1) ).
fof(fact_takeWhile__nth,axiom,
! [V_xs_2,V_Pa_2,T_c,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_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2))))
=> hAPP(hAPP(c_List_Onth(T_c),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)))
=> ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2))))) ),
file('theBenchmark.p',fact_nth__length__takeWhile) ).
fof(fact_takeWhile__not__last,axiom,
! [T_c,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),c_List_Olast(T_c,V_xs_2))),V_xs_2) = c_List_Obutlast(T_c,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_d,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(c_List_Orev(T_c),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)))
=> hAPP(c_List_Ofilter(T_d,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_d),hAPP(c_Orderings_Oord__class_Oless(T_c),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_d,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_d),hAPP(c_Orderings_Oord__class_Oless(T_c),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_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_c),V_xs_2)) = hAPP(c_List_Orev(T_c),hAPP(c_List_Otl(T_c),c_List_OdropWhile(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,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_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_OdropWhile(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_c),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(c_List_Orev(T_c),c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,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_c] : hAPP(hAPP(c_List_Oappend(T_c),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_c,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_c] :
( c_List_OdropWhile(T_c,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_c)
=> ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_c),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2)))) ),
file('theBenchmark.p',fact_hd__dropWhile) ).
fof(fact_sorted__dropWhile,axiom,
! [V_Pa_2,V_xs_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_c,c_List_OdropWhile(T_c,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_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),
file('theBenchmark.p',fact_length__dropWhile__le) ).
fof(fact_dropWhile__eq__Nil__conv,axiom,
! [V_xs_2,V_Pa_2,T_c] :
( c_List_OdropWhile(T_c,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_c)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).
fof(fact_dropWhile_Osimps_I2_J,axiom,
! [V_xs_2,T_c,V_x_2,V_Pa_2] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OdropWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) )
& ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OdropWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = c_List_OdropWhile(T_c,V_Pa_2,V_xs_2) ) ),
file('theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).
fof(fact_dropWhile_Osimps_I1_J,axiom,
! [V_Pa_2,T_c] : c_List_OdropWhile(T_c,V_Pa_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_c),
file('theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).
fof(fact_distinct__dropWhile,axiom,
! [V_Pa_2,V_xs_2,T_c] :
( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_c),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2))) ),
file('theBenchmark.p',fact_distinct__dropWhile) ).
fof(fact_dropWhile__map,axiom,
! [V_xs_2,V_f_2,T_d,V_Pa_2,T_c] : c_List_OdropWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_OdropWhile(T_d,hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,T_d,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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_OdropWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_c),c_List_OdropWhile(T_c,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_c] :
( c_List_OdropWhile(T_c,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)
<=> ( ~ hBOOL(hAPP(V_Pa_2,V_y_2))
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_c),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_c] : c_List_OdropWhile(T_c,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_c),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),c_List_OtakeWhile(T_c,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_c,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_c)),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2))))
=> hAPP(hAPP(c_List_Onth(T_c),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_c),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_c)),c_List_OtakeWhile(T_c,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_c,T_d] :
( class_Groups_Omonoid__add(T_d)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_Pa_2,B_x))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_d) ) )
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_d),hAPP(hAPP(c_List_Omap(T_c,T_d),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_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),c_List_OdropWhile(T_c,V_Pa_2,V_xs_2))))
=> ~ hBOOL(hAPP(V_Pa_2,B_x)) )
=> c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_c,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_c,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_c)),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),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_c)),V_xs_2)))
=> ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_xs_2),V_n_2))) )
=> c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_c),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_c,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_c),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_c)),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_c)),c_List_OtakeWhile(T_c,V_Pa_2,V_xs_2)))) ) ),
file('theBenchmark.p',fact_length__takeWhile__less__P__nth) ).
fof(fact_sorted_Osimps,axiom,
! [V_a_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_List_Olinorder__class_Osorted(T_c,V_a_2)
<=> ( ? [B_xs,B_x] :
( c_List_Olinorder__class_Osorted(T_c,B_xs)
& ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),hAPP(c_List_Oset(T_c),B_xs)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),B_xa)) )
& V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_c),B_x),B_xs) )
| V_a_2 = c_List_Olist_ONil(T_c) ) ) ),
file('theBenchmark.p',fact_sorted_Osimps) ).
fof(fact_List_Oinsert__def,axiom,
! [V_xs_2,V_x_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_Oinsert(T_c,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_Oinsert(T_c,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_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_Oinsert(T_c,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
=> c_List_Oinsert(T_c,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_c] : hAPP(c_List_Oset(T_c),c_List_Oinsert(T_c,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(c_List_Oset(T_c),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_maps__def,axiom,
! [V_xs_2,V_f_2,T_c,T_d] : c_List_Omaps(T_d,T_c,V_f_2,V_xs_2) = c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(T_d,tc_List_Olist(T_c)),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_maps__def) ).
fof(fact_concat__map__maps,axiom,
! [V_xs_2,V_f_2,T_d,T_c] : c_List_Oconcat(T_c,hAPP(hAPP(c_List_Omap(T_d,tc_List_Olist(T_c)),V_f_2),V_xs_2)) = c_List_Omaps(T_d,T_c,V_f_2,V_xs_2),
file('theBenchmark.p',fact_concat__map__maps) ).
fof(fact_maps__simps_I2_J,axiom,
! [V_f_2,T_c,T_d] : c_List_Omaps(T_d,T_c,V_f_2,c_List_Olist_ONil(T_d)) = c_List_Olist_ONil(T_c),
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_c,T_d] : c_List_Omaps(T_d,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_d),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_c),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_d,T_c,V_f_2,V_xs_2)),
file('theBenchmark.p',fact_maps__simps_I1_J) ).
fof(fact_distinct__concat,axiom,
! [V_xs_2,T_c] :
( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_c)),V_xs_2))
=> ( ! [B_ys] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xs_2)))
=> hBOOL(hAPP(c_List_Odistinct(T_c),B_ys)) )
=> ( ! [B_ys] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xs_2)))
=> ! [B_zs] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_c)),V_xs_2)))
=> ( B_ys != B_zs
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),B_ys)),hAPP(c_List_Oset(T_c),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) )
=> hBOOL(hAPP(c_List_Odistinct(T_c),c_List_Oconcat(T_c,V_xs_2))) ) ) ),
file('theBenchmark.p',fact_distinct__concat) ).
fof(fact_measures__lesseq,axiom,
! [V_fs_2,T_c,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_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_List_Omeasures(T_c,V_fs_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_List_Omeasures(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_c,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ),
file('theBenchmark.p',fact_measures__lesseq) ).
fof(fact_wf__measures,axiom,
! [V_fs_2,T_c] : c_Wellfounded_Owf(T_c,c_List_Omeasures(T_c,V_fs_2)),
file('theBenchmark.p',fact_wf__measures) ).
fof(fact_in__measures_I1_J,axiom,
! [V_y_2,V_x_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_List_Omeasures(T_c,c_List_Olist_ONil(tc_fun(T_c,tc_Nat_Onat))))),
file('theBenchmark.p',fact_in__measures_I1_J) ).
fof(fact_measures__def,axiom,
! [V_fs_2,T_c] : c_List_Omeasures(T_c,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_c),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(tc_fun(T_c,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_c,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_c),c_List_Omap(tc_fun(T_c,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_c,tc_Nat_Onat),T_c,tc_Nat_Onat),c_COMBI(tc_fun(T_c,tc_Nat_Onat))))),V_fs_2)),
file('theBenchmark.p',fact_measures__def) ).
fof(fact_in__measures_I2_J,axiom,
! [V_fs_2,V_f_2,V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_List_Omeasures(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_c,tc_Nat_Onat)),V_f_2),V_fs_2))))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_List_Omeasures(T_c,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_measures__less,axiom,
! [V_fs_2,T_c,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_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),c_List_Omeasures(T_c,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_c,tc_Nat_Onat)),V_f_2),V_fs_2)))) ),
file('theBenchmark.p',fact_measures__less) ).
fof(fact_foldl__apply,axiom,
! [V_s_2,V_g_2,V_h_2,V_f_2,T_d,T_e,V_xs_2,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hAPP(c_Fun_Ocomp(T_e,T_e,T_d,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_d,T_e,T_d,V_h_2),hAPP(V_g_2,B_x)) )
=> hAPP(c_List_Ofoldl(T_e,T_c,hAPP(c_COMBC(T_c,T_e,T_e),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_d,T_c,hAPP(c_COMBC(T_c,T_d,T_d),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_c,T_d] :
( ( class_Enum_Oenum(T_c)
& class_Orderings_Oorder(T_d) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,T_d)),V_f_2),V_g_2))
<=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBS(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),V_g_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),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_c,T_d] :
( ( class_Enum_Oenum(T_c)
& class_Enum_Oenum(T_d) )
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_c,T_d)),V_Pa_2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_Enum_Oenum__class_Oenum__ex(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_HOL_Obool,T_d),V_Pa_2)),c_Product__Type_OPair(T_c,T_d))))) ) ),
file('theBenchmark.p',fact_enum__ex__prod__def) ).
fof(fact_enum__ex,axiom,
! [V_Pa_2,T_c] :
( class_Enum_Oenum(T_c)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_c),V_Pa_2))
<=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
file('theBenchmark.p',fact_enum__ex) ).
fof(fact_exists__code,axiom,
! [V_Pa_2,T_c] :
( class_Enum_Oenum(T_c)
=> ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_c),V_Pa_2)) ) ),
file('theBenchmark.p',fact_exists__code) ).
fof(fact_zip__obtain__same__length,axiom,
! [V_Pa_2,V_ys_2,T_d,V_xs_2,T_c] :
( ( 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_c)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),hAPP(hAPP(c_List_Otake(T_d),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),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))),V_ys_2))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_c,T_d),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_c)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_d),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),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))),V_ys_2)))) )
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_c,T_d),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_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
=> c_List_OdropWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_c,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_d,V_a_2,T_c] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),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_c)),V_a_2)))
=> hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_d),V_b_2),B_n))) )
=> c_List_Olist__all2(T_c,T_d,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_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ? [B_x] :
( ! [B_y] :
( ( hBOOL(hAPP(c_List_Odistinct(T_c),B_y))
& c_List_Olinorder__class_Osorted(T_c,B_y)
& hAPP(c_List_Oset(T_c),B_y) = V_A_2 )
=> B_y = B_x )
& hBOOL(hAPP(c_List_Odistinct(T_c),B_x))
& c_List_Olinorder__class_Osorted(T_c,B_x)
& hAPP(c_List_Oset(T_c),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_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
=> c_List_OtakeWhile(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),c_List_OtakeWhile(T_c,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_c,T_d] :
( class_Orderings_Olinorder(T_d)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_d,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_xs_2) ) ),
file('theBenchmark.p',fact_insort__is__Cons) ).
fof(fact_Cons__eq__filter__iff,axiom,
! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_c] :
( hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_c,V_Pa_2),V_ys_2)
<=> ? [B_us,B_vs] :
( V_xs_2 = hAPP(c_List_Ofilter(T_c,V_Pa_2),B_vs)
& hBOOL(hAPP(V_Pa_2,V_x_2))
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),B_us)))
=> ~ hBOOL(hAPP(V_Pa_2,B_x)) )
& V_ys_2 = hAPP(hAPP(c_List_Oappend(T_c),B_us),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),B_vs)) ) ),
file('theBenchmark.p',fact_Cons__eq__filter__iff) ).
fof(fact_filter__eq__Cons__iff,axiom,
! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_c] :
( hAPP(c_List_Ofilter(T_c,V_Pa_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)
<=> ? [B_us,B_vs] :
( V_xs_2 = hAPP(c_List_Ofilter(T_c,V_Pa_2),B_vs)
& hBOOL(hAPP(V_Pa_2,V_x_2))
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),B_us)))
=> ~ hBOOL(hAPP(V_Pa_2,B_x)) )
& V_ys_2 = hAPP(hAPP(c_List_Oappend(T_c),B_us),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),B_vs)) ) ),
file('theBenchmark.p',fact_filter__eq__Cons__iff) ).
fof(fact_order__fun_I1_J,axiom,
! [V_g_2,V_f_2,T_c,T_d] :
( ( class_Enum_Oenum(T_c)
& class_Orderings_Oorder(T_d) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_c),hAPP(hAPP(c_COMBS(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_Orderings_Oord__class_Oless__eq(T_d)),V_f_2)),V_g_2))) ) ),
file('theBenchmark.p',fact_order__fun_I1_J) ).
fof(fact_all__code,axiom,
! [V_Pa_2,T_c] :
( class_Enum_Oenum(T_c)
=> ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_c),V_Pa_2)) ) ),
file('theBenchmark.p',fact_all__code) ).
fof(fact_enum__all,axiom,
! [V_Pa_2,T_c] :
( class_Enum_Oenum(T_c)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_c),V_Pa_2))
<=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
file('theBenchmark.p',fact_enum__all) ).
fof(fact_enum__all__prod__def,axiom,
! [V_Pa_2,T_c,T_d] :
( ( class_Enum_Oenum(T_c)
& class_Enum_Oenum(T_d) )
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_c,T_d)),V_Pa_2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_Enum_Oenum__class_Oenum__all(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_HOL_Obool,T_d),V_Pa_2)),c_Product__Type_OPair(T_c,T_d))))) ) ),
file('theBenchmark.p',fact_enum__all__prod__def) ).
fof(fact_list__ball__nth,axiom,
! [V_Pa_2,V_xs_2,T_c,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_c)),V_xs_2)))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),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_c] :
( class_Orderings_Olinorder(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),B_x)) )
=> ( c_List_Olinorder__class_Osorted(T_c,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Olist_OCons(T_c),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_c] :
( c_List_Olist__ex(T_c,V_Pa_2,V_xs_2)
<=> ? [B_n] :
( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),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_c)),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex__length) ).
fof(fact_in__set__conv__decomp,axiom,
! [V_xs_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
<=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_c),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_c] : ~ c_List_Olist__ex(T_c,V_Pa_2,c_List_Olist_ONil(T_c)),
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_c] :
( c_List_Olist__ex(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2))
<=> ( c_List_Olist__ex(T_c,V_Pa_2,V_ys_2)
| c_List_Olist__ex(T_c,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_c] :
( c_List_Olist__ex(T_c,V_Pa_2,V_xs_2)
<=> ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex__iff) ).
fof(fact_list__ex__rev,axiom,
! [V_xs_2,V_Pa_2,T_c] :
( c_List_Olist__ex(T_c,V_Pa_2,hAPP(c_List_Orev(T_c),V_xs_2))
<=> c_List_Olist__ex(T_c,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_c] :
( c_List_Olist__ex(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))
<=> ( c_List_Olist__ex(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
<=> ? [B_ys] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),B_ys)))
& ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_c),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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
<=> ? [B_ys,B_zs] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),B_zs)))
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_c),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_c),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_c] :
( c_List_Olist__all(T_c,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_c)),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_c),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_c] : c_List_Olist__all(T_c,V_Pa_2,c_List_Olist_ONil(T_c)),
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_c] :
( c_List_Olist__all(T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2))
<=> ( c_List_Olist__all(T_c,V_Pa_2,V_ys_2)
& c_List_Olist__all(T_c,V_Pa_2,V_xs_2) ) ),
file('theBenchmark.p',fact_list__all__append) ).
fof(fact_measure__size,axiom,
! [T_c] :
( class_Nat_Osize(T_c)
=> c_FunDef_Ois__measure(T_c,c_Nat_Osize__class_Osize(T_c)) ),
file('theBenchmark.p',fact_measure__size) ).
fof(fact_is__measure_Osimps,axiom,
! [V_a_2,T_c] : c_FunDef_Ois__measure(T_c,V_a_2),
file('theBenchmark.p',fact_is__measure_Osimps) ).
fof(fact_is__measure_Oequations,axiom,
! [V_a_2,T_c] : c_FunDef_Ois__measure(T_c,V_a_2),
file('theBenchmark.p',fact_is__measure_Oequations) ).
fof(fact_is__measure_Ointros,axiom,
! [V_f_2,T_c] : c_FunDef_Ois__measure(T_c,V_f_2),
file('theBenchmark.p',fact_is__measure_Ointros) ).
fof(fact_list__all__iff,axiom,
! [V_xs_2,V_Pa_2,T_c] :
( c_List_Olist__all(T_c,V_Pa_2,V_xs_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) ) ),
file('theBenchmark.p',fact_list__all__iff) ).
fof(fact_measure__fst,axiom,
! [T_d,V_f_2,T_c] :
( c_FunDef_Ois__measure(T_c,V_f_2)
=> c_FunDef_Ois__measure(tc_prod(T_c,T_d),hAPP(hAPP(c_COMBB(T_c,tc_Nat_Onat,tc_prod(T_c,T_d)),V_f_2),c_Product__Type_Ofst(T_c,T_d))) ),
file('theBenchmark.p',fact_measure__fst) ).
fof(fact_measure__snd,axiom,
! [T_d,V_f_2,T_c] :
( c_FunDef_Ois__measure(T_c,V_f_2)
=> c_FunDef_Ois__measure(tc_prod(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_Nat_Onat,tc_prod(T_d,T_c)),V_f_2),c_Product__Type_Osnd(T_d,T_c))) ),
file('theBenchmark.p',fact_measure__snd) ).
fof(fact_list__all__rev,axiom,
! [V_xs_2,V_Pa_2,T_c] :
( c_List_Olist__all(T_c,V_Pa_2,hAPP(c_List_Orev(T_c),V_xs_2))
<=> c_List_Olist__all(T_c,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_c] :
( c_List_Olist__all(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))
<=> ( c_List_Olist__all(T_c,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_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hBOOL(hAPP(V_Pa_2,B_x)) )
<=> c_List_Olist__all(T_c,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_c] :
( c_List_Olist__all(T_c,V_Pa_2,V_xs_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),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_c] :
( c_List_Olist__ex1(T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2))
<=> ( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_Olist__ex1(T_c,V_Pa_2,V_xs_2) )
& ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> c_List_Olist__all(T_c,hAPP(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_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),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_c] : ~ c_List_Olist__ex1(T_c,V_Pa_2,c_List_Olist_ONil(T_c)),
file('theBenchmark.p',fact_list__ex1__simps_I1_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_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_list__ex1__iff,axiom,
! [V_xs_2,V_Pa_2,T_c] :
( c_List_Olist__ex1(T_c,V_Pa_2,V_xs_2)
<=> ? [B_x] :
( ! [B_y] :
( ( hBOOL(hAPP(V_Pa_2,B_y))
& hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_List_Oset(T_c),V_xs_2))) )
=> B_y = B_x )
& hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),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_c,T_d,V_i_2] :
( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Oneg__decr__bind(T_d,T_c,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_d,T_c,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_d,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_c))),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_d,T_c,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_c) ) ),
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_c,T_d,V_i_2] :
( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Opos__decr__bind(T_d,T_c,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_d,T_c,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_d,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_c)),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_d,T_c,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_c) ) ),
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_c,T_d] : c_New__Random__Sequence_Oneg__decr__bind(T_d,T_c,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_d,T_c,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_d,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_c)))),hAPP(hAPP(c_COMBC(T_d,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_c))))),hAPP(hAPP(c_COMBC(T_d,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_c)))))),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_c,T_d] : c_New__Random__Sequence_Opos__decr__bind(T_d,T_c,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_d,T_c,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_d,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_c))),hAPP(hAPP(c_COMBC(T_d,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_c)))),hAPP(hAPP(c_COMBC(T_d,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_c))))),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_c,T_d] : hAPP(c_New__DSequence_Oneg__bind(T_d,T_c,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_d,T_c,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_d,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_c))),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_c] : c_New__Random__Sequence_Opos__empty(T_c,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_c),
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_c,T_d] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_d,T_c,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_d,T_c,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_d,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_c)))),hAPP(hAPP(c_COMBC(T_d,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_c))))),hAPP(hAPP(c_COMBC(T_d,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_c)))))),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_c,T_d] : hAPP(c_New__DSequence_Opos__bind(T_d,T_c,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_d,T_c,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_d,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_c)),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_c,T_d] : c_New__Random__Sequence_Oneg__map(T_d,T_c,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_d,T_c,V_Pa_2,hAPP(c_Fun_Ocomp(T_c,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_c)))))),T_d,c_New__Random__Sequence_Oneg__single(T_c)),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_c] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_c),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_c,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_c,T_d] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_d,T_c,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_d,T_c,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_d,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_c))),hAPP(hAPP(c_COMBC(T_d,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_c)))),hAPP(hAPP(c_COMBC(T_d,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_c))))),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_c,T_d] : c_New__Random__Sequence_Opos__map(T_d,T_c,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_d,T_c,V_Pa_2,hAPP(c_Fun_Ocomp(T_c,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_c))))),T_d,c_New__Random__Sequence_Opos__single(T_c)),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_c] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_c),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_c,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_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__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_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_c] :
( c_Wellfounded_Oacyclic(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),c_Predicate_Oconversep(T_c,T_c,V_r_2))))
<=> c_Wellfounded_Oacyclic(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_acyclicP__converse) ).
fof(fact_conversep__noteq,axiom,
! [V_y_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_c,T_c,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot)),c_fequal)),V_x_2),V_y_2))
<=> V_x_2 != V_y_2 ),
file('theBenchmark.p',fact_conversep__noteq) ).
fof(fact_conversepD,axiom,
! [V_b_2,V_a_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_c,T_d,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_Ointros,axiom,
! [T_d,T_c,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_c,T_d,V_r_2),V_b_2),V_a_2)) ),
file('theBenchmark.p',fact_conversep_Ointros) ).
fof(fact_conversep_Oequations,axiom,
! [V_a1_2,V_a2_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_c,T_d,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__iff,axiom,
! [V_b_2,V_a_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_c,T_d,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__conversep,axiom,
! [V_r_2,T_c,T_d] : c_Predicate_Oconversep(T_d,T_c,c_Predicate_Oconversep(T_c,T_d,V_r_2)) = V_r_2,
file('theBenchmark.p',fact_conversep__conversep) ).
fof(fact_conversep__eq,axiom,
! [T_c] : c_Predicate_Oconversep(T_c,T_c,c_fequal) = c_fequal,
file('theBenchmark.p',fact_conversep__eq) ).
fof(fact_converse__pred__comp,axiom,
! [V_s_2,V_r_2,T_e,T_c,T_d] : c_Predicate_Oconversep(T_d,T_c,c_Predicate_Opred__comp(T_d,T_e,T_c,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_c,T_e,T_d,c_Predicate_Oconversep(T_e,T_c,V_s_2),c_Predicate_Oconversep(T_d,T_e,V_r_2)),
file('theBenchmark.p',fact_converse__pred__comp) ).
fof(fact_converse__join,axiom,
! [V_s_2,V_r_2,T_c,T_d] : c_Predicate_Oconversep(T_d,T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Predicate_Oconversep(T_d,T_c,V_r_2)),c_Predicate_Oconversep(T_d,T_c,V_s_2)),
file('theBenchmark.p',fact_converse__join) ).
fof(fact_converse__meet,axiom,
! [V_s_2,V_r_2,T_c,T_d] : c_Predicate_Oconversep(T_d,T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Predicate_Oconversep(T_d,T_c,V_r_2)),c_Predicate_Oconversep(T_d,T_c,V_s_2)),
file('theBenchmark.p',fact_converse__meet) ).
fof(fact_conversep__converse__eq,axiom,
! [V_y_2,V_x_2,V_r_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_c,T_d,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_r_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2))) ),
file('theBenchmark.p',fact_conversep__converse__eq) ).
fof(fact_,axiom,
! [V_s2_2,V_s1_2,T_d,T_c] : c_Lazy__Sequence_Oproduct(T_c,T_d,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_c,tc_prod(T_c,T_d),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_c,T_d))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_c,T_d)),T_c),c_Lazy__Sequence_Obind(T_d,tc_prod(T_c,T_d),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_c,T_d))),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_c,T_d)),T_d),c_Lazy__Sequence_Osingle(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),
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_c] : c_List_Oreplicate(T_c,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_c,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_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),hAPP(c_COMBK(T_c,T_d),V_k_2)),V_lst_2) = c_List_Oreplicate(T_c,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),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_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_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_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_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_Bex__set__replicate,axiom,
! [V_Pa_2,V_a_2,V_n_2,T_c] :
( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,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_Ball__set__replicate,axiom,
! [V_Pa_2,V_a_2,V_n_2,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,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_replicate__eq__replicate,axiom,
! [V_y_2,V_n_2,V_x_2,V_m_2,T_c] :
( c_List_Oreplicate(T_c,V_m_2,V_x_2) = c_List_Oreplicate(T_c,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_c,V_x_2,V_Pa_2] :
( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
=> hAPP(c_List_Ofilter(T_c,V_Pa_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Olist_ONil(T_c) )
& ( hBOOL(hAPP(V_Pa_2,V_x_2))
=> hAPP(c_List_Ofilter(T_c,V_Pa_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_c,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__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_empty__replicate,axiom,
! [V_x_2,V_n_2,T_c] :
( c_List_Olist_ONil(T_c) = c_List_Oreplicate(T_c,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__empty,axiom,
! [V_x_2,V_n_2,T_c] :
( c_List_Oreplicate(T_c,V_n_2,V_x_2) = c_List_Olist_ONil(T_c)
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_replicate__empty) ).
fof(fact_map__replicate,axiom,
! [V_x_2,V_n_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),c_List_Oreplicate(T_d,V_n_2,V_x_2)) = c_List_Oreplicate(T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,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_c] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_c),hAPP(c_COMBK(T_c,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_c,V_i_2,V_x_2),
file('theBenchmark.p',fact_map__replicate__trivial) ).
fof(fact_set__replicate,axiom,
! [V_x_2,T_c,V_n_2] :
( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,V_n_2,V_x_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_set__replicate) ).
fof(fact_set__replicate__conv__if,axiom,
! [V_x_2,T_c,V_n_2] :
( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_set__replicate__conv__if) ).
fof(fact_set__replicate__Suc,axiom,
! [V_x_2,V_n_2,T_c] : hAPP(c_List_Oset(T_c),c_List_Oreplicate(T_c,hAPP(c_Nat_OSuc,V_n_2),V_x_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_set__replicate__Suc) ).
fof(fact_small__lazy__list_Osimps,axiom,
! [V_d_2,T_c] :
( class_Lazy__Sequence_Osmall__lazy(T_c)
=> c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_c),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_c),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_c)),c_List_Olist_ONil(T_c)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_c))),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_c,tc_List_Olist(T_c)),tc_List_Olist(T_c),c_Lazy__Sequence_Oproduct(T_c,tc_List_Olist(T_c),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_c,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_c),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_c,tc_List_Olist(T_c),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_c),tc_List_Olist(T_c)),tc_fun(tc_List_Olist(T_c),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_c))),T_c),hAPP(c_COMBB(tc_List_Olist(T_c),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_c)),tc_List_Olist(T_c)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_c)))),c_List_Olist_OCons(T_c))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_c)))) ),
file('theBenchmark.p',fact_small__lazy__list_Osimps) ).
fof(fact_eq__comp__r,axiom,
! [V_R_2,T_c] : c_Predicate_Opred__comp(T_c,T_c,T_c,c_fequal,c_Predicate_Opred__comp(T_c,T_c,T_c,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_c] : hAPP(c_New__DSequence_Opos__union(T_c,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_c,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_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_pos__union__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_c] : c_New__Random__Sequence_Opos__union(T_c,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_c,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_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__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_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_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_c] :
( c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,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_lazy__sequence_Osize_I2_J,axiom,
! [V_lazy__sequence_2,V_a_2,V_fa_2,T_c] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_c,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,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_c,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_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_c] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_c)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat),T_c),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_c),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_c)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_c)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)),
file('theBenchmark.p',fact_size__code) ).
fof(fact_lazy__sequence__size__code,axiom,
! [V_xq_2,V_s_2,T_c] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_c,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_c,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat)),T_c),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_c),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_c)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),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_c),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_c),tc_Nat_Onat)),T_c),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_c))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_c),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_c,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_c),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_d,T_c] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_c,T_d,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_c,tc_prod(T_d,tc_Lazy__Sequence_Olazy__sequence(T_d)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_d,tc_Lazy__Sequence_Olazy__sequence(T_d),T_c),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_d),V_xq_2)),
file('theBenchmark.p',fact_seq__case) ).
fof(fact_yieldn__def,axiom,
! [T_c] : c_Lazy__Sequence_Oyieldn(T_c) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_c),T_c,c_Lazy__Sequence_Oyield(T_c)),
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_d,T_c] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_c,T_d,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_d,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_d,V_S_2,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2))
=> c_Relation_Orefl__on(T_d,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
=> c_Relation_Orefl__on(T_d,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_d,T_d),tc_HOL_Obool)),V_S_2),V_r_2)) ),
file('theBenchmark.p',fact_refl__on__INTER) ).
fof(fact_in__set__member,axiom,
! [V_xs_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
<=> hBOOL(hAPP(hAPP(c_List_Omember(T_c),V_xs_2),V_x_2)) ),
file('theBenchmark.p',fact_in__set__member) ).
fof(fact_member__rec_I1_J,axiom,
! [V_y_2,V_xs_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_List_Omember(T_c),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)),V_y_2))
<=> ( hBOOL(hAPP(hAPP(c_List_Omember(T_c),V_xs_2),V_y_2))
| V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_member__rec_I1_J) ).
fof(fact_member__set,axiom,
! [T_c] : c_List_Omember(T_c) = c_List_Oset(T_c),
file('theBenchmark.p',fact_member__set) ).
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_List_Omember__def,axiom,
! [V_x_2,V_xs_2,T_c] :
( hBOOL(hAPP(hAPP(c_List_Omember(T_c),V_xs_2),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2))) ),
file('theBenchmark.p',fact_List_Omember__def) ).
fof(fact_pair__box_Osize_I1_J,axiom,
! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__size(T_c,T_d,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,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_list__ex1__iff__raw,axiom,
! [V_xs_2,V_Pa_2,T_c] :
( c_List_Olist__ex1(T_c,V_Pa_2,V_xs_2)
<=> ? [B_x] :
( ! [B_y] :
( ( hBOOL(hAPP(V_Pa_2,B_y))
& hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_List_Oset(T_c),V_xs_2))) )
=> B_y = B_x )
& hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex1__iff__raw) ).
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_pair__box_Oinject,axiom,
! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_d,T_c] :
( c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_c,T_d,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_pair__box_Osimps_I2_J,axiom,
! [V_b_2,V_a_2,V_f1_2,T_c,T_e,T_d] : c_Nitpick_Opair__box_Opair__box__case(T_d,T_e,T_c,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_d,T_e,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_pair__box_Orecs,axiom,
! [V_b_2,V_a_2,V_f1_2,T_c,T_e,T_d] : c_Nitpick_Opair__box_Opair__box__rec(T_d,T_e,T_c,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_d,T_e,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_THE__default__def,axiom,
! [V_d_2,T_c,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_c,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_c,V_d_2,V_Pa_2) = c_HOL_OThe(T_c,V_Pa_2) ) ),
file('theBenchmark.p',fact_THE__default__def) ).
fof(fact_setsum__UNION__zero,axiom,
! [V_f_2,V_S_2,T_c,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_x),V_S_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_x)) )
=> ( ! [B_T1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_T1),V_S_2))
=> ! [B_T2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_T2),V_S_2))
=> ( B_T1 != B_T2
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),B_T1))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),B_T2))
=> 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_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2)),V_S_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__UNION__zero) ).
fof(fact_INF2__I,axiom,
! [T_e,T_d,V_c_2,V_b_2,V_B_2,V_A_2,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) )
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
file('theBenchmark.p',fact_INF2__I) ).
fof(fact_SUP2__E,axiom,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_SUP2__E) ).
fof(fact_finite__maxlen,axiom,
! [V_M_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_c)),V_M_2))
=> ? [B_n] :
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_c)),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_c)),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_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_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__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_I4_J,axiom,
! [V_f2_2,V_f1_2,T_d,T_c] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_c,T_d,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_d)) = V_f1_2,
file('theBenchmark.p',fact_lazy__sequence_Osimps_I4_J) ).
fof(fact_lazy__sequence_Osize_I1_J,axiom,
! [V_fa_2,T_c] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_c,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_lazy__sequence_Osize_I1_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_c] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_c,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_c,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_c,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_c,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_c,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_c)))),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_c)))),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_c)))),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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_c,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_c)))),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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_c,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_c)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_c))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_c)))),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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_c,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_c)))),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_c)))),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_c))))),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_c)))),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_c)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_c)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_c))))),tc_prod(T_c,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_c)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_c)))),tc_prod(T_c,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_c)),c_Product__Type_Ofst(T_c,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_c,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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_c)) ) ),
file('theBenchmark.p',fact_Random_Osimps) ).
fof(fact_code__numeral_Orecs_I1_J,axiom,
! [V_f2_2,V_f1_2,T_c] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_c,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_c] : c_Random__Sequence_Oempty(T_c,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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_c)),
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_c] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_c),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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_c),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_c,T_d] : c_Random__Sequence_Omap(T_d,T_c,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_d,T_c,V_Pa_2,hAPP(c_Fun_Ocomp(T_c,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_c)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_d,c_Random__Sequence_Osingle(T_c)),V_f_2)),
file('theBenchmark.p',fact_Random__Sequence_Omap__def) ).
fof(fact_exE__realizer,axiom,
! [T_e,V_f_2,V_Qa_2,V_p_2,T_c,T_d,V_Pa_2] :
( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_d,T_c),V_p_2)),hAPP(c_Product__Type_Ofst(T_d,T_c),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_d,T_c,T_e),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_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,hAPP(c_Set_OCollect(tc_prod(T_d,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_HOL_Obool),V_Pa_2))),V_A_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_A_2)))),hAPP(c_COMBC(T_d,T_c,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_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_y_2)),c_List_Olexord(T_c,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_y_2),V_z_2)),c_List_Olexord(T_c,V_r_2)))
=> ( c_Relation_Otrans(T_c,V_r_2)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_c),tc_List_Olist(T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_c),tc_List_Olist(T_c)),V_x_2),V_z_2)),c_List_Olexord(T_c,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_d,V_R1_2,T_c] :
( c_Relation_Otrans(T_c,V_R1_2)
=> ( c_Relation_Otrans(T_d,V_R2_2)
=> c_Relation_Otrans(tc_prod(T_c,T_d),c_Wellfounded_Olex__prod(T_c,T_d,V_R1_2,V_R2_2)) ) ),
file('theBenchmark.p',fact_trans__lex__prod) ).
fof(fact_transD,axiom,
! [V_c_2,V_b_2,V_a_2,V_r_2,T_c] :
( c_Relation_Otrans(T_c,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_a_2),V_b_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_c_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_a_2),V_c_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_transD) ).
fof(fact_trans__def,axiom,
! [V_r_2,T_c] :
( c_Relation_Otrans(T_c,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_r_2))
=> ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),B_z)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_z)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_trans__def) ).
fof(fact_Union__eq,axiom,
! [V_A_2,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_c,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_c,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,tc_HOL_Obool))),V_A_2)))),c_member(T_c)))),
file('theBenchmark.p',fact_Union__eq) ).
fof(fact_trans__O__subset,axiom,
! [V_r_2,T_c] :
( c_Relation_Otrans(T_c,V_r_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),V_r_2),V_r_2)),V_r_2)) ),
file('theBenchmark.p',fact_trans__O__subset) ).
fof(fact_trans__Int,axiom,
! [V_s_2,V_r_2,T_c] :
( c_Relation_Otrans(T_c,V_r_2)
=> ( c_Relation_Otrans(T_c,V_s_2)
=> c_Relation_Otrans(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_trans__Int) ).
fof(fact_trans__rtrancl,axiom,
! [V_r_2,T_c] : c_Relation_Otrans(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)),
file('theBenchmark.p',fact_trans__rtrancl) ).
fof(fact_trans__Id,axiom,
! [T_c] : c_Relation_Otrans(T_c,c_Relation_OId(T_c)),
file('theBenchmark.p',fact_trans__Id) ).
fof(fact_trans__finite__psubset,axiom,
! [T_c] : c_Relation_Otrans(tc_fun(T_c,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_c)),
file('theBenchmark.p',fact_trans__finite__psubset) ).
fof(fact_trancl__id,axiom,
! [V_r_2,T_c] :
( c_Relation_Otrans(T_c,V_r_2)
=> c_Transitive__Closure_Otrancl(T_c,V_r_2) = V_r_2 ),
file('theBenchmark.p',fact_trancl__id) ).
fof(fact_trans__trancl,axiom,
! [V_r_2,T_c] : c_Relation_Otrans(T_c,c_Transitive__Closure_Otrancl(T_c,V_r_2)),
file('theBenchmark.p',fact_trans__trancl) ).
fof(fact_trans__Id__on,axiom,
! [V_A_2,T_c] : c_Relation_Otrans(T_c,c_Relation_OId__on(T_c,V_A_2)),
file('theBenchmark.p',fact_trans__Id__on) ).
fof(fact_lexord__transI,axiom,
! [V_r_2,T_c] :
( c_Relation_Otrans(T_c,V_r_2)
=> c_Relation_Otrans(tc_List_Olist(T_c),c_List_Olexord(T_c,V_r_2)) ),
file('theBenchmark.p',fact_lexord__transI) ).
fof(fact_bex__empty,axiom,
! [V_Pa_2,T_c] :
~ ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_bex__empty) ).
fof(fact_listrel__trans,axiom,
! [V_r_2,T_c] :
( c_Relation_Otrans(T_c,V_r_2)
=> c_Relation_Otrans(tc_List_Olist(T_c),c_List_Olistrel(T_c,V_r_2)) ),
file('theBenchmark.p',fact_listrel__trans) ).
fof(fact_trans__converse,axiom,
! [V_r_2,T_c] :
( c_Relation_Otrans(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2))
<=> c_Relation_Otrans(T_c,V_r_2) ),
file('theBenchmark.p',fact_trans__converse) ).
fof(fact_finite__Collect__bex,axiom,
! [V_Qa_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),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)))),V_Qa_2)))))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBC(T_d,T_c,tc_HOL_Obool),V_Qa_2),B_x)))) ) ) ),
file('theBenchmark.p',fact_finite__Collect__bex) ).
fof(fact_bex__UNIV,axiom,
! [V_Pa_2,T_c] :
( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) )
<=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ),
file('theBenchmark.p',fact_bex__UNIV) ).
fof(fact_SUPR__bool__eq,axiom,
! [T_c] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_HOL_Obool) = c_Set_OBex(T_c),
file('theBenchmark.p',fact_SUPR__bool__eq) ).
fof(fact_trans__reflclI,axiom,
! [V_r_2,T_c] :
( c_Relation_Otrans(T_c,V_r_2)
=> c_Relation_Otrans(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))) ),
file('theBenchmark.p',fact_trans__reflclI) ).
fof(fact_trans__inv__image,axiom,
! [V_f_2,T_d,V_r_2,T_c] :
( c_Relation_Otrans(T_c,V_r_2)
=> c_Relation_Otrans(T_d,hAPP(hAPP(c_Relation_Oinv__image(T_c,T_d),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_trans__inv__image) ).
fof(fact_Bex__set__list__ex,axiom,
! [V_Pa_2,V_xs_2,T_c] :
( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) )
<=> c_List_Olist__ex(T_c,V_Pa_2,V_xs_2) ),
file('theBenchmark.p',fact_Bex__set__list__ex) ).
fof(fact_list__ex__iff__raw,axiom,
! [V_xs_2,V_Pa_2,T_c] :
( c_List_Olist__ex(T_c,V_Pa_2,V_xs_2)
<=> ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex__iff__raw) ).
fof(fact_UN__eq,axiom,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),c_HOL_OEx(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d)),c_fequal)),V_B_2))))),
file('theBenchmark.p',fact_UN__eq) ).
fof(fact_INT__eq,axiom,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),c_HOL_OEx(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d)),c_fequal)),V_B_2))))),
file('theBenchmark.p',fact_INT__eq) ).
fof(fact_Sup__fun__def,axiom,
! [V_x_2,V_A_2,T_d,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,T_c),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_c,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_Sup__fun__def) ).
fof(fact_Sup__apply,axiom,
! [V_x_2,V_A_2,T_d,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,T_c),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_c,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_Sup__apply) ).
fof(fact_Inf__apply,axiom,
! [V_x_2,V_A_2,T_d,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_d,T_c),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_c,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_Inf__apply) ).
fof(fact_Inf__fun__def,axiom,
! [V_x_2,V_A_2,T_d,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_d,T_c),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_c,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_Inf__fun__def) ).
fof(fact_max__extp_Ointros,axiom,
! [V_R_2,V_Y_2,V_X_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_X_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Y_2))
=> ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_X_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_Y_2)) ) )
=> c_Wellfounded_Omax__extp(T_c,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_c] :
( c_Predicate_Otransp(T_c,V_r_2)
<=> c_Relation_Otrans(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,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_c] :
( c_Predicate_Otransp(T_c,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_equivpE,axiom,
! [V_R_2,T_c] :
( c_Equiv__Relations_Oequivp(T_c,V_R_2)
=> ~ ( c_Predicate_Oreflp(T_c,V_R_2)
=> ( c_Predicate_Osymp(T_c,V_R_2)
=> ~ c_Predicate_Otransp(T_c,V_R_2) ) ) ),
file('theBenchmark.p',fact_equivpE) ).
fof(fact_equivpI,axiom,
! [V_R_2,T_c] :
( c_Predicate_Oreflp(T_c,V_R_2)
=> ( c_Predicate_Osymp(T_c,V_R_2)
=> ( c_Predicate_Otransp(T_c,V_R_2)
=> c_Equiv__Relations_Oequivp(T_c,V_R_2) ) ) ),
file('theBenchmark.p',fact_equivpI) ).
fof(fact_sympE,axiom,
! [V_y_2,V_x_2,V_r_2,T_c] :
( c_Predicate_Osymp(T_c,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_equivp__reflp__symp__transp,axiom,
! [V_R_2,T_c] :
( c_Equiv__Relations_Oequivp(T_c,V_R_2)
<=> ( c_Predicate_Otransp(T_c,V_R_2)
& c_Predicate_Osymp(T_c,V_R_2)
& c_Predicate_Oreflp(T_c,V_R_2) ) ),
file('theBenchmark.p',fact_equivp__reflp__symp__transp) ).
fof(fact_max__extp_Osimps,axiom,
! [V_a2_2,V_a1_2,V_R_2,T_c] :
( c_Wellfounded_Omax__extp(T_c,V_R_2,V_a1_2,V_a2_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_a1_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_a2_2)) ) )
& V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_a2_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_a1_2)) ) ),
file('theBenchmark.p',fact_max__extp_Osimps) ).
fof(fact_trans__diff__Id,axiom,
! [V_r_2,T_c] :
( c_Relation_Otrans(T_c,V_r_2)
=> ( c_Relation_Oantisym(T_c,V_r_2)
=> c_Relation_Otrans(T_c,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c))) ) ),
file('theBenchmark.p',fact_trans__diff__Id) ).
fof(fact_antisym__converse,axiom,
! [V_r_2,T_c] :
( c_Relation_Oantisym(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2))
<=> c_Relation_Oantisym(T_c,V_r_2) ),
file('theBenchmark.p',fact_antisym__converse) ).
fof(fact_antisym__empty,axiom,
! [T_c] : c_Relation_Oantisym(T_c,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),
file('theBenchmark.p',fact_antisym__empty) ).
fof(fact_antisym__Id,axiom,
! [T_c] : c_Relation_Oantisym(T_c,c_Relation_OId(T_c)),
file('theBenchmark.p',fact_antisym__Id) ).
fof(fact_antisym__Id__on,axiom,
! [V_A_2,T_c] : c_Relation_Oantisym(T_c,c_Relation_OId__on(T_c,V_A_2)),
file('theBenchmark.p',fact_antisym__Id__on) ).
fof(fact_antisym__subset,axiom,
! [V_s_2,V_r_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
=> ( c_Relation_Oantisym(T_c,V_s_2)
=> c_Relation_Oantisym(T_c,V_r_2) ) ),
file('theBenchmark.p',fact_antisym__subset) ).
fof(fact_antisym__def,axiom,
! [V_r_2,T_c] :
( c_Relation_Oantisym(T_c,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),B_x)),V_r_2))
=> B_x = B_y ) ) ),
file('theBenchmark.p',fact_antisym__def) ).
fof(fact_antisymD,axiom,
! [V_b_2,V_a_2,V_r_2,T_c] :
( c_Relation_Oantisym(T_c,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_a_2),V_b_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_a_2)),V_r_2))
=> V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_antisymD) ).
fof(fact_antisym__reflcl,axiom,
! [V_r_2,T_c] :
( c_Relation_Oantisym(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_c)))
<=> c_Relation_Oantisym(T_c,V_r_2) ),
file('theBenchmark.p',fact_antisym__reflcl) ).
fof(fact_acyclic__impl__antisym__rtrancl,axiom,
! [V_r_2,T_c] :
( c_Wellfounded_Oacyclic(T_c,V_r_2)
=> c_Relation_Oantisym(T_c,c_Transitive__Closure_Ortrancl(T_c,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_e,T_c,T_d] : c_Partial__Function_Ofun__lub(T_d,T_c,T_e,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_e,T_d),tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(tc_fun(T_e,T_d))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_e,T_d),tc_HOL_Obool),tc_fun(tc_fun(T_e,T_d),tc_HOL_Obool),T_d),hAPP(c_COMBS(tc_fun(T_e,T_d),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_e,T_d)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_e,T_d),tc_fun(tc_fun(T_e,T_d),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_e,T_d))),V_A_2)))),hAPP(hAPP(c_COMBC(T_d,tc_fun(tc_fun(T_e,T_d),T_d),tc_fun(tc_fun(T_e,T_d),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_e,T_d),T_d),tc_fun(tc_fun(T_e,T_d),tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,tc_fun(T_e,T_d))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_e,T_d),T_e,T_d),c_COMBI(tc_fun(T_e,T_d))),V_x_2)))))),
file('theBenchmark.p',fact_fun__lub__def) ).
fof(fact_sym__trans__comp__subset,axiom,
! [V_r_2,T_c] :
( c_Relation_Osym(T_c,V_r_2)
=> ( c_Relation_Otrans(T_c,V_r_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_c,T_c),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2)),V_r_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_sym__trans__comp__subset) ).
fof(fact_symD,axiom,
! [V_b_2,V_a_2,V_r_2,T_c] :
( c_Relation_Osym(T_c,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_a_2),V_b_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_a_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_symD) ).
fof(fact_sym__def,axiom,
! [V_r_2,T_c] :
( c_Relation_Osym(T_c,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),B_x)),V_r_2)) ) ),
file('theBenchmark.p',fact_sym__def) ).
fof(fact_sym__Int,axiom,
! [V_s_2,V_r_2,T_c] :
( c_Relation_Osym(T_c,V_r_2)
=> ( c_Relation_Osym(T_c,V_s_2)
=> c_Relation_Osym(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_sym__Int) ).
fof(fact_sym__rtrancl,axiom,
! [V_r_2,T_c] :
( c_Relation_Osym(T_c,V_r_2)
=> c_Relation_Osym(T_c,c_Transitive__Closure_Ortrancl(T_c,V_r_2)) ),
file('theBenchmark.p',fact_sym__rtrancl) ).
fof(fact_sym__Id,axiom,
! [T_c] : c_Relation_Osym(T_c,c_Relation_OId(T_c)),
file('theBenchmark.p',fact_sym__Id) ).
fof(fact_sym__Un,axiom,
! [V_s_2,V_r_2,T_c] :
( c_Relation_Osym(T_c,V_r_2)
=> ( c_Relation_Osym(T_c,V_s_2)
=> c_Relation_Osym(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_sym__Un) ).
fof(fact_sym__trancl,axiom,
! [V_r_2,T_c] :
( c_Relation_Osym(T_c,V_r_2)
=> c_Relation_Osym(T_c,c_Transitive__Closure_Otrancl(T_c,V_r_2)) ),
file('theBenchmark.p',fact_sym__trancl) ).
fof(fact_sym__Id__on,axiom,
! [V_A_2,T_c] : c_Relation_Osym(T_c,c_Relation_OId__on(T_c,V_A_2)),
file('theBenchmark.p',fact_sym__Id__on) ).
fof(fact_listrel__sym,axiom,
! [V_r_2,T_c] :
( c_Relation_Osym(T_c,V_r_2)
=> c_Relation_Osym(tc_List_Olist(T_c),c_List_Olistrel(T_c,V_r_2)) ),
file('theBenchmark.p',fact_listrel__sym) ).
fof(fact_sym__conv__converse__eq,axiom,
! [V_r_2,T_c] :
( c_Relation_Osym(T_c,V_r_2)
<=> hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2) = V_r_2 ),
file('theBenchmark.p',fact_sym__conv__converse__eq) ).
fof(fact_sym__converse,axiom,
! [V_r_2,T_c] :
( c_Relation_Osym(T_c,hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2))
<=> c_Relation_Osym(T_c,V_r_2) ),
file('theBenchmark.p',fact_sym__converse) ).
fof(fact_sym__Un__converse,axiom,
! [V_r_2,T_c] : c_Relation_Osym(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2))),
file('theBenchmark.p',fact_sym__Un__converse) ).
fof(fact_sym__inv__image,axiom,
! [V_f_2,T_d,V_r_2,T_c] :
( c_Relation_Osym(T_c,V_r_2)
=> c_Relation_Osym(T_d,hAPP(hAPP(c_Relation_Oinv__image(T_c,T_d),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_sym__inv__image) ).
fof(fact_sym__Int__converse,axiom,
! [V_r_2,T_c] : c_Relation_Osym(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_c,T_c),V_r_2))),
file('theBenchmark.p',fact_sym__Int__converse) ).
fof(fact_equiv__def,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
<=> ( c_Relation_Otrans(T_c,V_r_2)
& c_Relation_Osym(T_c,V_r_2)
& c_Relation_Orefl__on(T_c,V_A_2,V_r_2) ) ),
file('theBenchmark.p',fact_equiv__def) ).
fof(fact_equivI,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Relation_Orefl__on(T_c,V_A_2,V_r_2)
=> ( c_Relation_Osym(T_c,V_r_2)
=> ( c_Relation_Otrans(T_c,V_r_2)
=> c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ) ) ),
file('theBenchmark.p',fact_equivI) ).
fof(fact_equivE,axiom,
! [V_r_2,V_A_2,T_c] :
( c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
=> ~ ( c_Relation_Orefl__on(T_c,V_A_2,V_r_2)
=> ( c_Relation_Osym(T_c,V_r_2)
=> ~ c_Relation_Otrans(T_c,V_r_2) ) ) ),
file('theBenchmark.p',fact_equivE) ).
fof(fact_symp__def,axiom,
! [V_r_2,T_c] :
( c_Predicate_Osymp(T_c,V_r_2)
<=> c_Relation_Osym(T_c,hAPP(c_Set_OCollect(tc_prod(T_c,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_c,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_symp__def) ).
fof(fact_part__equivpI,axiom,
! [T_c,V_R_2] :
( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
=> ( c_Predicate_Osymp(T_c,V_R_2)
=> ( c_Predicate_Otransp(T_c,V_R_2)
=> c_Equiv__Relations_Opart__equivp(T_c,V_R_2) ) ) ),
file('theBenchmark.p',fact_part__equivpI) ).
fof(fact_part__equivp__refl__symp__transp,axiom,
! [V_R_2,T_c] :
( c_Equiv__Relations_Opart__equivp(T_c,V_R_2)
<=> ( c_Predicate_Otransp(T_c,V_R_2)
& c_Predicate_Osymp(T_c,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_equivp__implies__part__equivp,axiom,
! [V_R_2,T_c] :
( c_Equiv__Relations_Oequivp(T_c,V_R_2)
=> c_Equiv__Relations_Opart__equivp(T_c,V_R_2) ),
file('theBenchmark.p',fact_equivp__implies__part__equivp) ).
fof(fact_part__equivp__transp,axiom,
! [V_z_2,V_y_2,V_x_2,V_R_2,T_c] :
( c_Equiv__Relations_Opart__equivp(T_c,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__equivp__symp,axiom,
! [V_y_2,V_x_2,V_R_2,T_c] :
( c_Equiv__Relations_Opart__equivp(T_c,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__def,axiom,
! [V_R_2,T_c] :
( c_Equiv__Relations_Opart__equivp(T_c,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__equivpE,axiom,
! [V_R_2,T_c] :
( c_Equiv__Relations_Opart__equivp(T_c,V_R_2)
=> ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
=> ( c_Predicate_Osymp(T_c,V_R_2)
=> ~ c_Predicate_Otransp(T_c,V_R_2) ) ) ),
file('theBenchmark.p',fact_part__equivpE) ).
fof(fact_part__equivp__typedef,axiom,
! [V_R_2,T_c] :
( c_Equiv__Relations_Opart__equivp(T_c,V_R_2)
=> ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,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_c,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_COMBS(T_c,T_c,tc_HOL_Obool),V_R_2),c_COMBI(T_c))))),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_R_2))))) ),
file('theBenchmark.p',fact_part__equivp__typedef) ).
fof(fact_inj__iff,axiom,
! [V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
<=> hAPP(c_Fun_Ocomp(T_d,T_c,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_c) ),
file('theBenchmark.p',fact_inj__iff) ).
fof(fact_inv__o__cancel,axiom,
! [V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Fun_Ocomp(T_d,T_c,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_c) ),
file('theBenchmark.p',fact_inv__o__cancel) ).
fof(fact_inv__def,axiom,
! [V_y_2,V_f_2,T_d,T_c] : hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(T_c,hAPP(hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),V_y_2)),
file('theBenchmark.p',fact_inv__def) ).
fof(fact_inv__id,axiom,
! [T_c] : c_Hilbert__Choice_Oinv__into(T_c,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Fun_Oid(T_c)) = c_Fun_Oid(T_c),
file('theBenchmark.p',fact_inv__id) ).
fof(fact_inv__f__eq,axiom,
! [V_y_2,V_x_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> ( hAPP(V_f_2,V_x_2) = V_y_2
=> hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,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__f__eq,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( hAPP(V_f_2,V_x_2) = V_y_2
=> hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ),
file('theBenchmark.p',fact_inv__into__f__eq) ).
fof(fact_inv__into__f__f,axiom,
! [V_x_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,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_f__inv__into__f,axiom,
! [V_A_2,V_f_2,T_d,V_y_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)))
=> hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ),
file('theBenchmark.p',fact_f__inv__into__f) ).
fof(fact_inv__into__into,axiom,
! [V_A_2,V_f_2,T_d,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)))
=> hBOOL(hAPP(hAPP(c_member(T_d),hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,V_f_2),V_x_2)),V_A_2)) ),
file('theBenchmark.p',fact_inv__into__into) ).
fof(fact_inv__into__injective,axiom,
! [V_y_2,V_x_2,V_f_2,V_A_2,T_d,T_c] :
( hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2),V_y_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_inv__into__injective) ).
fof(fact_image__surj__f__inv__f,axiom,
! [V_A_2,V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ),
file('theBenchmark.p',fact_image__surj__f__inv__f) ).
fof(fact_surj__f__inv__f,axiom,
! [V_y_2,V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ),
file('theBenchmark.p',fact_surj__f__inv__f) ).
fof(fact_surj__iff__all,axiom,
! [V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
<=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_f_2),B_x)) = B_x ),
file('theBenchmark.p',fact_surj__iff__all) ).
fof(fact_image__inv__into__cancel,axiom,
! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) = V_A_H_2
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
=> hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ),
file('theBenchmark.p',fact_image__inv__into__cancel) ).
fof(fact_inv__into__def,axiom,
! [V_x_2,V_f_2,V_A_2,T_d,T_c] : hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_c,hAPP(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(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),V_x_2))),
file('theBenchmark.p',fact_inv__into__def) ).
fof(fact_o__inv__o__cancel,axiom,
! [V_g_2,T_e,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Fun_Ocomp(T_d,T_e,T_c,hAPP(c_Fun_Ocomp(T_c,T_e,T_d,V_g_2),c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ),
file('theBenchmark.p',fact_o__inv__o__cancel) ).
fof(fact_inj__imp__surj__inv,axiom,
! [V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_c,T_d,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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_c,T_d,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_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
=> c_Fun_Oinj__on(T_c,T_d,c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_surj__imp__inj__inv) ).
fof(fact_inv__into__image__cancel,axiom,
! [V_S_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2))
=> hAPP(c_Set_Oimage(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_S_2)) = V_S_2 ) ),
file('theBenchmark.p',fact_inv__into__image__cancel) ).
fof(fact_inj__on__inv__into,axiom,
! [V_A_2,V_f_2,T_d,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)))
=> c_Fun_Oinj__on(T_c,T_d,c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,V_f_2),V_B_2) ),
file('theBenchmark.p',fact_inj__on__inv__into) ).
fof(fact_inv__into__comp,axiom,
! [V_x_2,V_A_2,V_g_2,T_e,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(c_Set_Oimage(T_e,T_c,V_g_2),V_A_2))
=> ( c_Fun_Oinj__on(T_e,T_c,V_g_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(c_Set_Oimage(T_e,T_c,V_g_2),V_A_2))))
=> hAPP(c_Hilbert__Choice_Oinv__into(T_e,T_d,V_A_2,hAPP(c_Fun_Ocomp(T_c,T_d,T_e,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_e,T_d,c_Hilbert__Choice_Oinv__into(T_e,T_c,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__into(T_c,T_d,hAPP(c_Set_Oimage(T_e,T_c,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_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
<=> hAPP(c_Fun_Ocomp(T_d,T_c,T_c,V_f_2),c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_c) ),
file('theBenchmark.p',fact_surj__iff) ).
fof(fact_inj__transfer,axiom,
! [V_x_2,V_Pa_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> ( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_y),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
=> hBOOL(hAPP(V_Pa_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,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_d,V_I_2,T_c,T_e] :
( class_Groups_Ocomm__monoid__mult(T_e)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_I_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_A_2,B_x))) )
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_I_2))
=> ( B_x != B_xa
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,T_d,c_Groups_Otimes__class_Otimes(T_e)),V_g_2),c_Groups_Oone__class_Oone(T_e)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,T_c,c_Groups_Otimes__class_Otimes(T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),T_e,T_c),hAPP(hAPP(c_Finite__Set_Ofold__image(T_e,T_d,c_Groups_Otimes__class_Otimes(T_e)),V_g_2),c_Groups_Oone__class_Oone(T_e))),V_A_2)),c_Groups_Oone__class_Oone(T_e)),V_I_2) ) ) ) ),
file('theBenchmark.p',fact_fold__image__UN__disjoint) ).
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_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_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_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_lazy__sequence_Orecs_I1_J,axiom,
! [V_f2_2,V_f1_2,T_d,T_c] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_c,T_d,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_d)) = 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_d,T_c] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_c,T_d,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_d,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_c,T_d,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_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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)))
=> hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_d),V_Pa_2),c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,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_c_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Ocurry(T_d,T_e,T_c,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_x_2),V_y_2)),
file('theBenchmark.p',fact_curry__def) ).
fof(fact_curryI,axiom,
! [V_b_2,V_a_2,T_d,T_c,V_f_2] :
( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))
=> hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,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_c] : c_Fun_Obij__betw(T_c,T_c,c_Fun_Oid(T_c),V_A_2,V_A_2),
file('theBenchmark.p',fact_bij__betw__id) ).
fof(fact_bij__betw__inv__into,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2)
=> c_Fun_Obij__betw(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,V_A_2,V_f_2),V_B_2,V_A_2) ),
file('theBenchmark.p',fact_bij__betw__inv__into) ).
fof(fact_inv__into__inv__into__eq,axiom,
! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_A_H_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_c,T_d,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_inv__inv__eq,axiom,
! [V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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)))
=> c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = V_f_2 ),
file('theBenchmark.p',fact_inv__inv__eq) ).
fof(fact_bij__imp__bij__inv,axiom,
! [V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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)))
=> c_Fun_Obij__betw(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_bij__imp__bij__inv) ).
fof(fact_o__inv__distrib,axiom,
! [V_g_2,T_e,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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)))
=> ( c_Fun_Obij__betw(T_e,T_c,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> c_Hilbert__Choice_Oinv__into(T_e,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_c,T_d,T_e,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_e,T_d,c_Hilbert__Choice_Oinv__into(T_e,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,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_e,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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)))
=> hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_e),c_Set_Oimage(T_c,T_d,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_e,V_A_H_H_2,V_A_H_2,V_f_H_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_e,T_c,V_f_2),V_A_2)),V_A_H_2))
=> ( c_Fun_Obij__betw(T_e,T_c,V_f_2,V_A_2,V_A_H_2)
<=> c_Fun_Obij__betw(T_e,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_e,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__betw__trans,axiom,
! [V_C_2,V_g_2,T_e,V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2)
=> ( c_Fun_Obij__betw(T_d,T_e,V_g_2,V_B_2,V_C_2)
=> c_Fun_Obij__betw(T_c,T_e,hAPP(c_Fun_Ocomp(T_d,T_e,T_c,V_g_2),V_f_2),V_A_2,V_C_2) ) ),
file('theBenchmark.p',fact_bij__betw__trans) ).
fof(fact_bij__betw__comp__iff,axiom,
! [V_A_H_H_2,V_f_H_2,T_e,V_A_H_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_A_H_2)
=> ( c_Fun_Obij__betw(T_d,T_e,V_f_H_2,V_A_H_2,V_A_H_H_2)
<=> c_Fun_Obij__betw(T_c,T_e,hAPP(c_Fun_Ocomp(T_d,T_e,T_c,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__comp,axiom,
! [V_g_2,T_e,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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)))
=> ( c_Fun_Obij__betw(T_d,T_e,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool)))
=> c_Fun_Obij__betw(T_c,T_e,hAPP(c_Fun_Ocomp(T_d,T_e,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_e,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_bij__comp) ).
fof(fact_curryE,axiom,
! [V_b_2,V_a_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
=> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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_d,T_c] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
=> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Ocurry(T_d,T_e,T_c,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)),
file('theBenchmark.p',fact_curry__conv) ).
fof(fact_split__curry,axiom,
! [V_f_2,T_e,T_d,T_c] : hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),c_Product__Type_Ocurry(T_c,T_d,T_e,V_f_2)) = V_f_2,
file('theBenchmark.p',fact_split__curry) ).
fof(fact_curry__split,axiom,
! [V_f_2,T_e,T_d,T_c] : c_Product__Type_Ocurry(T_c,T_d,T_e,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_f_2)) = V_f_2,
file('theBenchmark.p',fact_curry__split) ).
fof(fact_finite__vimage__iff,axiom,
! [V_F_2,V_h_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_h_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)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_d,V_h_2),V_F_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_F_2)) ) ),
file('theBenchmark.p',fact_finite__vimage__iff) ).
fof(fact_bij__image__Compl__eq,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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)))
=> hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) ),
file('theBenchmark.p',fact_bij__image__Compl__eq) ).
fof(fact_bij__betw__subset,axiom,
! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_A_H_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> ( hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2) = V_B_H_2
=> c_Fun_Obij__betw(T_c,T_d,V_f_2,V_B_2,V_B_H_2) ) ) ),
file('theBenchmark.p',fact_bij__betw__subset) ).
fof(fact_bij__is__surj,axiom,
! [V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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)))
=> hAPP(c_Set_Oimage(T_c,T_d,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_bij__is__surj) ).
fof(fact_bij__betw__imp__surj,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_c,T_d,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_bij__betw__imp__surj) ).
fof(fact_bij__betw__def,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2)
<=> ( hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) = V_B_2
& c_Fun_Oinj__on(T_c,T_d,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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) ),
file('theBenchmark.p',fact_inj__on__imp__bij__betw) ).
fof(fact_bij__betw__imp__inj__on,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2)
=> c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
file('theBenchmark.p',fact_bij__betw__imp__inj__on) ).
fof(fact_bij__is__inj,axiom,
! [V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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)))
=> c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_bij__is__inj) ).
fof(fact_bij__betw__the__inv__into,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2)
=> c_Fun_Obij__betw(T_d,T_c,c_Fun_Othe__inv__into(T_c,T_d,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__same__card,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2)
=> hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(c_Finite__Set_Ocard(T_d),V_B_2) ),
file('theBenchmark.p',fact_bij__betw__same__card) ).
fof(fact_bij__betw__empty2,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))
=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_bij__betw__empty2) ).
fof(fact_bij__betw__empty1,axiom,
! [V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),V_A_2)
=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_bij__betw__empty1) ).
fof(fact_BIJ,axiom,
! [V_B_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
=> ( ? [B_f] : c_Fun_Obij__betw(T_c,T_d,B_f,V_A_2,V_B_2)
<=> hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(c_Finite__Set_Ocard(T_d),V_B_2) ) ) ),
file('theBenchmark.p',fact_BIJ) ).
fof(fact_bij__betw__finite,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2)) ) ),
file('theBenchmark.p',fact_bij__betw__finite) ).
fof(fact_bij__betw__id__iff,axiom,
! [V_B_2,V_A_2,T_c] :
( c_Fun_Obij__betw(T_c,T_c,c_Fun_Oid(T_c),V_A_2,V_B_2)
<=> V_A_2 = V_B_2 ),
file('theBenchmark.p',fact_bij__betw__id__iff) ).
fof(fact_bij__id,axiom,
! [T_c] : c_Fun_Obij__betw(T_c,T_c,c_Fun_Oid(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),
file('theBenchmark.p',fact_bij__id) ).
fof(fact_bij__betw__combine,axiom,
! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_B_2)
=> ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_C_2,V_D_2)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
=> c_Fun_Obij__betw(T_c,T_d,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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_d,V_B_2,V_A_2,T_c] :
( 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(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
=> ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_A_2,V_A_H_2)
=> ( c_Fun_Obij__betw(T_c,T_d,V_f_2,V_B_2,V_B_H_2)
=> c_Fun_Obij__betw(T_c,T_d,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_d,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_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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)))
<=> ( hAPP(c_Set_Oimage(T_c,T_d,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))
& c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_bij__def) ).
fof(fact_bijI,axiom,
! [V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> ( hAPP(c_Set_Oimage(T_c,T_d,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))
=> c_Fun_Obij__betw(T_c,T_d,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_bijI) ).
fof(fact_vimage__subset__eq,axiom,
! [V_A_2,V_B_2,V_f_2,T_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)),V_A_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_d,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_d,T_c] :
( c_Fun_Obij__betw(T_c,T_d,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)))
=> hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_d,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,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_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_M_2))
=> ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_c,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),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_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2))
=> ( c_Fun_Oinj__on(T_d,T_c,V_g_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_d,T_c,V_g_2),V_B_2)),V_A_2))
=> ? [B_h] : c_Fun_Obij__betw(T_c,T_d,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_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_M_2))
=> ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_c,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_c),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_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_M_2))
=> ? [B_h] : c_Fun_Obij__betw(T_c,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_c),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_d,V_S_2,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2))
=> c_Relation_Orefl__on(T_d,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
=> c_Relation_Orefl__on(T_d,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_d,T_d),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_c] :
( c_Equiv__Relations_Oequivp(T_c,V_R_2)
=> ( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),c_Quotient_ORespects(T_c,V_R_2))) )
<=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
file('theBenchmark.p',fact_bex__reg__eqv) ).
fof(fact_in__respects,axiom,
! [V_R_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Quotient_ORespects(T_c,V_R_2)))
<=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
file('theBenchmark.p',fact_in__respects) ).
fof(fact_Respects__def,axiom,
! [V_x_2,V_R_2,T_c] :
( hBOOL(hAPP(c_Quotient_ORespects(T_c,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_bex__reg__right,axiom,
! [V_Pa_2,V_Qa_2,V_R_2,T_c] :
( c_Equiv__Relations_Oequivp(T_c,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_c),B_x),c_Quotient_ORespects(T_c,V_R_2))) ) ) ) ),
file('theBenchmark.p',fact_bex__reg__right) ).
fof(fact_babs__reg__eqv,axiom,
! [V_Pa_2,T_d,V_R_2,T_c] :
( c_Equiv__Relations_Oequivp(T_c,V_R_2)
=> c_Quotient_OBabs(T_c,T_d,c_Quotient_ORespects(T_c,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_d,V_p_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_p_2))
=> hAPP(c_Quotient_OBabs(T_c,T_d,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_c] :
( ! [B_i] : 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,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_c,V_r_2)))
=> ( c_Wellfounded_Owf(T_c,c_Transitive__Closure_Otrancl(T_c,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__greatest,axiom,
! [V_B_2,V_C_2,T_d,V_A_2,T_c] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_INT__greatest) ).
fof(fact_INT__anti__mono,axiom,
! [V_g_2,V_f_2,T_d,V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,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_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_g_2))) ) ),
file('theBenchmark.p',fact_INT__anti__mono) ).
fof(fact_rtrancl__induct2,axiom,
! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_c,T_d),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_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_c,T_d),V_r_2)))
=> ! [B_aa,B_ba] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_c,T_d),V_r_2)))
=> ( hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_za_2),V_zb_2)
=> ~ ! [B_a,B_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b))),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_c,T_d),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_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_c,T_d),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_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_aa),B_ba))),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_c,T_d),tc_prod(T_c,T_d))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_c,T_d),tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_c,T_d),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_congruent2I_H,axiom,
! [T_e,V_f_2,V_r2_2,T_d,V_r1_2,T_c] :
( ! [B_y1,B_z1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y1),B_z1)),V_r1_2))
=> ! [B_y2,B_z2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_d),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_c,T_d,T_e,V_r1_2,V_r2_2,V_f_2) ),
file('theBenchmark.p',fact_congruent2I_H) ).
fof(fact_congruentI,axiom,
! [T_d,V_f_2,V_r_2,T_c] :
( ! [B_y,B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y),B_z)),V_r_2))
=> hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
=> c_Equiv__Relations_Ocongruent(T_c,T_d,V_r_2,V_f_2) ),
file('theBenchmark.p',fact_congruentI) ).
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_c,T_d] : hAPP(c_Lazy__Sequence_Obind(T_d,T_c,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_c,c_Lazy__Sequence_Omap(T_d,tc_Lazy__Sequence_Olazy__sequence(T_c),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_d,T_c] :
( c_Finite__Set_Ofolding__image(T_c,T_d,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),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_c,T_d] : c_Lazy__Sequence_Omap(T_d,T_c,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_d,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_d,T_c,V_f_2,V_xq_2)),
file('theBenchmark.p',fact__06) ).
fof(fact__07,axiom,
! [V_f_2,T_c,T_d] : c_Lazy__Sequence_Omap(T_d,T_c,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_d)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c),
file('theBenchmark.p',fact__07) ).
fof(fact_New__DSequence_Opos__map__def,axiom,
! [V_i_2,V_xq_2,V_f_2,T_c,T_d] : c_New__DSequence_Opos__map(T_d,T_c,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_d,T_c,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_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_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_setprod__dvd__setprod__subset,axiom,
! [V_f_2,V_A_2,V_B_2,T_c,T_d] :
( ( class_Rings_Odvd(T_d)
& class_Groups_Ocomm__monoid__mult(T_d) )
=> ( 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_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_c] :
( ( class_Rings_Odvd(T_c)
& class_Rings_Ocomm__ring(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_d_2),V_D_2))
=> ! [B_x,B_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),B_x),V_t_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),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_c] :
( ( class_Rings_Odvd(T_c)
& class_Rings_Ocomm__ring(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_d_2),V_D_2))
=> ! [B_x,B_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),B_x),V_t_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),B_k),V_D_2))),V_t_2))) ) ) ),
file('theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_dvd__div__eq__mult,axiom,
! [V_c_2,V_b_2,V_a_2,T_c] :
( class_Divides_Osemiring__div(T_c)
=> ( V_a_2 != c_Groups_Ozero__class_Ozero(T_c)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_b_2))
=> ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_c),V_b_2),V_a_2) = V_c_2
<=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_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_c_2,V_a_2,T_c] :
( class_Divides_Osemiring__div(T_c)
=> ( V_a_2 != c_Groups_Ozero__class_Ozero(T_c)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_c)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_c_2),V_d_2))
=> ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_c),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_c),V_d_2),V_c_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_d_2) ) ) ) ) ) ),
file('theBenchmark.p',fact_dvd__div__div__eq__mult) ).
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_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__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_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_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__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__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__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__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_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_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_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_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__cancel__left,axiom,
! [V_b_2,V_a_2,V_c_2,T_c] :
( class_Rings_Oidom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_dvd__mult__cancel__right,axiom,
! [V_b_2,V_c_2,V_a_2,T_c] :
( class_Rings_Oidom(T_c)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_c_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel__right) ).
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_unity__coeff__ex,axiom,
! [V_l_2,V_Pa_2,T_c] :
( ( class_Rings_Osemiring__0(T_c)
& class_Rings_Odvd(T_c) )
=> ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_l_2),B_x)))
<=> ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),B_x),c_Groups_Ozero__class_Ozero(T_c)))) ) ) ),
file('theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
! [V_b_2,V_a_2] :
( V_a_2 = V_b_2
=> c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_dvd_OatLeastAtMost__singleton_H) ).
fof(fact_dvd_OatLeastAtMost__singleton,axiom,
! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('theBenchmark.p',fact_dvd_OatLeastAtMost__singleton) ).
fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
! [V_c_2,V_b_2,V_a_2] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
<=> ( V_b_2 = V_c_2
& V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_dvd_OatLeastAtMost__singleton__iff) ).
fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
! [V_b_2,V_a_2] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2)
<=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_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_OatLeastLessThan__empty__iff2) ).
fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2)
<=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) ) ),
file('theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff2) ).
fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
! [V_b_2,V_a_2] :
( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_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_OatLeastLessThan__empty__iff) ).
fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
! [V_l_2,V_k_2] :
( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) ) ),
file('theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff) ).
fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
! [V_k_2,V_l_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
=> c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_dvd_OgreaterThanLessThan__empty) ).
fof(fact_dvd_OatLeastLessThan__empty,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
=> c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_dvd_OatLeastLessThan__empty) ).
fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
! [V_k_2,V_l_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
=> c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty) ).
fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
! [V_b_2,V_a_2] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)
<=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ),
file('theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff2) ).
fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
! [V_b_2,V_a_2] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ),
file('theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff) ).
fof(fact_dvd_OatLeastatMost__empty,axiom,
! [V_a_2,V_b_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) )
=> c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_dvd_OatLeastatMost__empty) ).
fof(fact_dvd__div__neg,axiom,
! [V_x,V_y,T_a] :
( class_Divides_Oring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_dvd__div__neg) ).
fof(fact_dvd__neg__div,axiom,
! [V_x,V_y,T_a] :
( class_Divides_Oring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_dvd__neg__div) ).
fof(fact_minus__dvd__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Rings_Ocomm__ring__1(T_c)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)),V_y_2))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_minus__dvd__iff) ).
fof(fact_dvd__minus__iff,axiom,
! [V_y_2,V_x_2,T_c] :
( class_Rings_Ocomm__ring__1(T_c)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_dvd__minus__iff) ).
fof(fact_dvd__1__iff__1,axiom,
! [V_m_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('theBenchmark.p',fact_dvd__1__iff__1) ).
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_c] :
( class_Divides_Osemiring__div(T_c)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_b_2))
<=> c_Divides_Odiv__class_Omod(T_c,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
fof(fact_div__dvd__div,axiom,
! [V_c_2,V_b_2,V_a_2,T_c] :
( class_Divides_Osemiring__div(T_c)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_a_2),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_c),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_c),V_c_2),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_b_2),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_div__dvd__div) ).
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_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_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_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__iff,axiom,
! [V_m_2,V_n_2,V_k_2,T_c] :
( class_Divides_Osemiring__div(T_c)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_k_2),V_n_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_k_2),c_Divides_Odiv__class_Omod(T_c,V_m_2,V_n_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),V_k_2),V_m_2)) ) ) ),
file('theBenchmark.p',fact_dvd__mod__iff) ).
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__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_Oless__asym,axiom,
! [V_y,V_x] :
( ( ~ 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)) )
=> ~ ( ~ 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)) ) ),
file('theBenchmark.p',fact_dvd_Oless__asym) ).
fof(fact_dvd_Oless__trans,axiom,
! [V_z,V_y,V_x] :
( ( ~ 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)) )
=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_dvd_Oless__trans) ).
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__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__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_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__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__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__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__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__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__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__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__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__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__Nat_Osize,axiom,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
file('theBenchmark.p',arity_Code____Evaluation__Oterm__Nat_Osize) ).
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__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__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_e,T_c,T_d] : hAPP(hAPP(hAPP(c_COMBB(T_d,T_c,T_e),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_c,T_e,T_d] : hAPP(hAPP(hAPP(c_COMBC(T_d,T_e,T_c),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_c,T_e,T_d] : hAPP(hAPP(hAPP(c_COMBS(T_d,T_e,T_c),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_p] :
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,B_p)),hAPP(v_c0,B_p)),hAPP(v_Q_H,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,B_p)),hAPP(v_c0,B_p)),hAPP(v_Q,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
file('theBenchmark.p',conj_0) ).
fof(conj_1,hypothesis,
hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_F)),
file('theBenchmark.p',conj_1) ).
fof(conj_2,hypothesis,
~ hBOOL(hAPP(hAPP(c_member(t_a),v_x),v_F)),
file('theBenchmark.p',conj_2) ).
fof(conj_3,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F))
=> c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F)) ),
file('theBenchmark.p',conj_3) ).
fof(conj_4,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F))
& c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
file('theBenchmark.p',conj_4) ).
fof(conj_5,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))),
file('theBenchmark.p',conj_5) ).
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_Ga_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_empty]) ).
fof(f_2_2,plain,
! [U_4,U_3] : c_Hoare__Mirabelle_Ohoare__derivs(U_3,U_4,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_3),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_4] : c_Hoare__Mirabelle_Ohoare__derivs(U_3,U_4,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_3),tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
c_Hoare__Mirabelle_Ohoare__derivs(U_3,U_4,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_3),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [V_a_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oequations_I1_J]) ).
fof(f_3_2,plain,
! [U_6,U_5] : c_Hoare__Mirabelle_Ohoare__derivs(U_5,U_6,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_6,U_5] : c_Hoare__Mirabelle_Ohoare__derivs(U_5,U_6,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5),tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
c_Hoare__Mirabelle_Ohoare__derivs(U_5,U_6,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_5),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_c] :
( ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_H_2),V_com_H_2),V_fun2_H_2)
| V_fun2_2 != V_fun2_H_2
| V_com_2 != V_com_H_2
| V_fun1_2 != V_fun1_H_2 )
& ( ( V_fun2_2 = V_fun2_H_2
& V_com_2 = V_com_H_2
& V_fun1_2 = V_fun1_H_2 )
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_H_2),V_com_H_2),V_fun2_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_triple_Oinject]) ).
fof(f_4_2,plain,
! [U_13,U_12,U_11,U_10,U_9,U_8,U_7] :
( ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7),U_8),U_9),U_10) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7),U_11),U_12),U_13)
| U_10 != U_13
| U_9 != U_12
| U_8 != U_11 )
& ( ( U_10 = U_13
& U_9 = U_12
& U_8 = U_11 )
| hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7),U_8),U_9),U_10) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7),U_11),U_12),U_13) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_27,U_25,U_23,U_21,U_19,U_17] :
( ! [U_15] : hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15),U_17),U_19),U_21) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15),U_23),U_25),U_27)
| U_21 != U_27
| U_19 != U_25
| U_17 != U_23 )
& ! [U_26,U_24,U_22,U_20,U_18,U_16] :
( ! [U_14] : hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_16),U_18),U_20) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_22),U_24),U_26)
| ( U_20 = U_26
& U_18 = U_24
& U_16 = U_22 ) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_20,U_22,U_18,U_16,U_26,U_24] :
( U_20 = U_26
| ~ sP0(U_20,U_22,U_18,U_16,U_26,U_24) )
& ! [U_20,U_22,U_18,U_16,U_26,U_24] :
( U_18 = U_24
| ~ sP0(U_20,U_22,U_18,U_16,U_26,U_24) )
& ! [U_20,U_22,U_18,U_16,U_26,U_24] :
( U_16 = U_22
| ~ sP0(U_20,U_22,U_18,U_16,U_26,U_24) )
& ! [U_21,U_23,U_15,U_17,U_19,U_27,U_25] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15),U_17),U_19),U_21) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15),U_23),U_25),U_27)
| U_21 != U_27
| U_19 != U_25
| U_17 != U_23 )
& ! [U_20,U_22,U_14,U_18,U_16,U_26,U_24] :
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_16),U_18),U_20) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_22),U_24),U_26)
| sP0(U_20,U_22,U_18,U_16,U_26,U_24) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_4_3]) ).
cnf(f_4_5,plain,
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_16),U_18),U_20) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14),U_22),U_24),U_26)
| sP0(U_20,U_22,U_18,U_16,U_26,U_24) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15),U_17),U_19),U_21) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15),U_23),U_25),U_27)
| U_21 != U_27
| U_19 != U_25
| U_17 != U_23 ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( U_16 = U_22
| ~ sP0(U_20,U_22,U_18,U_16,U_26,U_24) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_8,plain,
( U_18 = U_24
| ~ sP0(U_20,U_22,U_18,U_16,U_26,U_24) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_9,plain,
( U_20 = U_26
| ~ sP0(U_20,U_22,U_18,U_16,U_26,U_24) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
! [V_Ga_2,V_ts_2,V_G_H_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_G_H_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_G_H_2,V_ts_2) ),
inference(fof_nnf,[status(thm)],[fact_cut]) ).
fof(f_5_2,plain,
! [U_31,U_30,U_29,U_28] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_30)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_29)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_29,U_30) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_29,U_28,U_30,U_31] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_30)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_29)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_29,U_30) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_30)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_31,U_29)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_28,U_29,U_30) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [V_ts_2,V_t_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),V_t_2),V_ts_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oinsert]) ).
fof(f_6_2,plain,
! [U_35,U_34,U_33,U_32] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),U_35))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,U_35)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_32),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_33,U_34,U_32,U_35] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),U_35))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,U_35)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_32),tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),U_35))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,U_35)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_32,U_33,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_32)),U_34),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_32),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [V_ts_2,V_t_2,V_Ga_2,T_c] :
( ( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2)
& c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),V_t_2),V_ts_2)) ),
inference(fof_nnf,[status(thm)],[fact_derivs__insertD]) ).
fof(f_7_2,plain,
! [U_39,U_38,U_37,U_36] :
( ( c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,U_39)
& c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_36)),U_38),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_36),tc_HOL_Obool)))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_36)),U_38),U_39)) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_36,U_37,U_38,U_39] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,U_39)
| ~ sP1(U_36,U_37,U_38,U_39) )
& ! [U_36,U_37,U_38,U_39] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_36)),U_38),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_36),tc_HOL_Obool))))
| ~ sP1(U_36,U_37,U_38,U_39) )
& ! [U_36,U_37,U_38,U_39] :
( sP1(U_36,U_37,U_38,U_39)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_36)),U_38),U_39)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_7_2]) ).
cnf(f_7_4,plain,
( sP1(U_36,U_37,U_38,U_39)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_36)),U_38),U_39)) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_36)),U_38),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_36),tc_HOL_Obool))))
| ~ sP1(U_36,U_37,U_38,U_39) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_36,U_37,U_39)
| ~ sP1(U_36,U_37,U_38,U_39) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [V_h_2,T_d,V_F_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__imageI]) ).
fof(f_8_2,plain,
! [U_43,U_42,U_41,U_40] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_42),hAPP(c_Set_Oimage(U_40,U_42,U_43),U_41)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_40),U_41)) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_41,U_40,U_42,U_43] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_42),hAPP(c_Set_Oimage(U_40,U_42,U_43),U_41)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_40),U_41)) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_42),hAPP(c_Set_Oimage(U_40,U_42,U_43),U_41)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_40),U_41)) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [V_a_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite_OinsertI]) ).
fof(f_9_2,plain,
! [U_46,U_45,U_44] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_44),hAPP(hAPP(c_Set_Oinsert(U_44),U_46),U_45)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_44),U_45)) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_44,U_45,U_46] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_44),hAPP(hAPP(c_Set_Oinsert(U_44),U_46),U_45)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_44),U_45)) ),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_44),hAPP(hAPP(c_Set_Oinsert(U_44),U_46),U_45)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_44),U_45)) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [T_c] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_finite_OemptyI]) ).
fof(f_10_2,plain,
! [U_47] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_47),c_Orderings_Obot__class_Obot(tc_fun(U_47,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_47] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_47),c_Orderings_Obot__class_Obot(tc_fun(U_47,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(U_47),c_Orderings_Obot__class_Obot(tc_fun(U_47,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [T_c,V_A_2,T_d,V_x_2,V_f_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),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_11_2,plain,
! [U_53,U_52,U_51,U_50,U_49,U_48] :
( hBOOL(hAPP(hAPP(c_member(U_53),U_48),hAPP(c_Set_Oimage(U_51,U_53,U_49),U_52)))
| ~ hBOOL(hAPP(hAPP(c_member(U_51),U_50),U_52))
| U_48 != hAPP(U_49,U_50) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_48,U_49,U_50,U_51,U_52,U_53] :
( hBOOL(hAPP(hAPP(c_member(U_53),U_48),hAPP(c_Set_Oimage(U_51,U_53,U_49),U_52)))
| ~ hBOOL(hAPP(hAPP(c_member(U_51),U_50),U_52))
| U_48 != hAPP(U_49,U_50) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_53),U_48),hAPP(c_Set_Oimage(U_51,U_53,U_49),U_52)))
| ~ hBOOL(hAPP(hAPP(c_member(U_51),U_50),U_52))
| U_48 != hAPP(U_49,U_50) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [V_A_2,V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| V_a_2 = V_b_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_insertE]) ).
fof(f_12_2,plain,
! [U_57,U_56,U_55,U_54] :
( hBOOL(hAPP(hAPP(c_member(U_54),U_55),U_57))
| U_55 = U_56
| ~ hBOOL(hAPP(hAPP(c_member(U_54),U_55),hAPP(hAPP(c_Set_Oinsert(U_54),U_56),U_57))) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_55,U_54,U_56,U_57] :
( hBOOL(hAPP(hAPP(c_member(U_54),U_55),U_57))
| U_55 = U_56
| ~ hBOOL(hAPP(hAPP(c_member(U_54),U_55),hAPP(hAPP(c_Set_Oinsert(U_54),U_56),U_57))) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_54),U_55),U_57))
| U_55 = U_56
| ~ hBOOL(hAPP(hAPP(c_member(U_54),U_55),hAPP(hAPP(c_Set_Oinsert(U_54),U_56),U_57))) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [V_b_2,V_B_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))
| ( V_a_2 != V_b_2
& ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insertCI]) ).
fof(f_13_2,plain,
! [U_61,U_60,U_59,U_58] :
( hBOOL(hAPP(hAPP(c_member(U_58),U_59),hAPP(hAPP(c_Set_Oinsert(U_58),U_61),U_60)))
| ( U_59 != U_61
& ~ hBOOL(hAPP(hAPP(c_member(U_58),U_59),U_60)) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_58,U_59,U_60,U_61] :
( U_59 != U_61
| ~ sP2(U_58,U_59,U_60,U_61) )
& ! [U_58,U_59,U_60,U_61] :
( ~ hBOOL(hAPP(hAPP(c_member(U_58),U_59),U_60))
| ~ sP2(U_58,U_59,U_60,U_61) )
& ! [U_58,U_59,U_60,U_61] :
( hBOOL(hAPP(hAPP(c_member(U_58),U_59),hAPP(hAPP(c_Set_Oinsert(U_58),U_61),U_60)))
| sP2(U_58,U_59,U_60,U_61) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_13_2]) ).
cnf(f_13_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_58),U_59),hAPP(hAPP(c_Set_Oinsert(U_58),U_61),U_60)))
| sP2(U_58,U_59,U_60,U_61) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_58),U_59),U_60))
| ~ sP2(U_58,U_59,U_60,U_61) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( U_59 != U_61
| ~ sP2(U_58,U_59,U_60,U_61) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [V_a_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_emptyE]) ).
fof(f_14_2,plain,
! [U_63,U_62] : ~ hBOOL(hAPP(hAPP(c_member(U_62),U_63),c_Orderings_Obot__class_Obot(tc_fun(U_62,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_63,U_62] : ~ hBOOL(hAPP(hAPP(c_member(U_62),U_63),c_Orderings_Obot__class_Obot(tc_fun(U_62,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
~ hBOOL(hAPP(hAPP(c_member(U_62),U_63),c_Orderings_Obot__class_Obot(tc_fun(U_62,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [V_c_2,T_d,V_A_2,V_x_2,T_c] :
( hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_COMBK(T_d,T_c),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_d),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__constant]) ).
fof(f_15_2,plain,
! [U_68,U_67,U_66,U_65,U_64] :
( hAPP(c_Set_Oimage(U_64,U_67,hAPP(c_COMBK(U_67,U_64),U_68)),U_66) = hAPP(hAPP(c_Set_Oinsert(U_67),U_68),c_Orderings_Obot__class_Obot(tc_fun(U_67,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(U_64),U_65),U_66)) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_64,U_65,U_66,U_67,U_68] :
( hAPP(c_Set_Oimage(U_64,U_67,hAPP(c_COMBK(U_67,U_64),U_68)),U_66) = hAPP(hAPP(c_Set_Oinsert(U_67),U_68),c_Orderings_Obot__class_Obot(tc_fun(U_67,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(U_64),U_65),U_66)) ),
inference(definitional_conversion,[status(esa)],[f_15_2]) ).
cnf(f_15_4,plain,
( hAPP(c_Set_Oimage(U_64,U_67,hAPP(c_COMBK(U_67,U_64),U_68)),U_66) = hAPP(hAPP(c_Set_Oinsert(U_67),U_68),c_Orderings_Obot__class_Obot(tc_fun(U_67,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(U_64),U_65),U_66)) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [V_c_2,T_d,T_c,V_A_2] :
( ( hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_COMBK(T_d,T_c),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_d),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,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_d,hAPP(c_COMBK(T_d,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_image__constant__conv]) ).
fof(f_16_2,plain,
! [U_72,U_71,U_70,U_69] :
( ( hAPP(c_Set_Oimage(U_70,U_71,hAPP(c_COMBK(U_71,U_70),U_72)),U_69) = hAPP(hAPP(c_Set_Oinsert(U_71),U_72),c_Orderings_Obot__class_Obot(tc_fun(U_71,tc_HOL_Obool)))
| U_69 = c_Orderings_Obot__class_Obot(tc_fun(U_70,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(U_70,U_71,hAPP(c_COMBK(U_71,U_70),U_72)),U_69) = c_Orderings_Obot__class_Obot(tc_fun(U_71,tc_HOL_Obool))
| U_69 != c_Orderings_Obot__class_Obot(tc_fun(U_70,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_80,U_78,U_76,U_74] :
( hAPP(c_Set_Oimage(U_76,U_78,hAPP(c_COMBK(U_78,U_76),U_80)),U_74) = hAPP(hAPP(c_Set_Oinsert(U_78),U_80),c_Orderings_Obot__class_Obot(tc_fun(U_78,tc_HOL_Obool)))
| U_74 = c_Orderings_Obot__class_Obot(tc_fun(U_76,tc_HOL_Obool)) )
& ! [U_79,U_77,U_75,U_73] :
( hAPP(c_Set_Oimage(U_75,U_77,hAPP(c_COMBK(U_77,U_75),U_79)),U_73) = c_Orderings_Obot__class_Obot(tc_fun(U_77,tc_HOL_Obool))
| U_73 != c_Orderings_Obot__class_Obot(tc_fun(U_75,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
( ! [U_80,U_74,U_76,U_78] :
( hAPP(c_Set_Oimage(U_76,U_78,hAPP(c_COMBK(U_78,U_76),U_80)),U_74) = hAPP(hAPP(c_Set_Oinsert(U_78),U_80),c_Orderings_Obot__class_Obot(tc_fun(U_78,tc_HOL_Obool)))
| U_74 = c_Orderings_Obot__class_Obot(tc_fun(U_76,tc_HOL_Obool)) )
& ! [U_77,U_75,U_79,U_73] :
( hAPP(c_Set_Oimage(U_75,U_77,hAPP(c_COMBK(U_77,U_75),U_79)),U_73) = c_Orderings_Obot__class_Obot(tc_fun(U_77,tc_HOL_Obool))
| U_73 != c_Orderings_Obot__class_Obot(tc_fun(U_75,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_16_3]) ).
cnf(f_16_5,plain,
( hAPP(c_Set_Oimage(U_75,U_77,hAPP(c_COMBK(U_77,U_75),U_79)),U_73) = c_Orderings_Obot__class_Obot(tc_fun(U_77,tc_HOL_Obool))
| U_73 != c_Orderings_Obot__class_Obot(tc_fun(U_75,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_16_4]) ).
cnf(f_16_6,plain,
( hAPP(c_Set_Oimage(U_76,U_78,hAPP(c_COMBK(U_78,U_76),U_80)),U_74) = hAPP(hAPP(c_Set_Oinsert(U_78),U_80),c_Orderings_Obot__class_Obot(tc_fun(U_78,tc_HOL_Obool)))
| U_74 = c_Orderings_Obot__class_Obot(tc_fun(U_76,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_17_1,plain,
! [V_f_2,T_d,V_A_2,V_x_2,T_c] :
( hAPP(hAPP(c_Set_Oinsert(T_d),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__image]) ).
fof(f_17_2,plain,
! [U_85,U_84,U_83,U_82,U_81] :
( hAPP(hAPP(c_Set_Oinsert(U_84),hAPP(U_85,U_82)),hAPP(c_Set_Oimage(U_81,U_84,U_85),U_83)) = hAPP(c_Set_Oimage(U_81,U_84,U_85),U_83)
| ~ hBOOL(hAPP(hAPP(c_member(U_81),U_82),U_83)) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_81,U_82,U_83,U_84,U_85] :
( hAPP(hAPP(c_Set_Oinsert(U_84),hAPP(U_85,U_82)),hAPP(c_Set_Oimage(U_81,U_84,U_85),U_83)) = hAPP(c_Set_Oimage(U_81,U_84,U_85),U_83)
| ~ hBOOL(hAPP(hAPP(c_member(U_81),U_82),U_83)) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( hAPP(hAPP(c_Set_Oinsert(U_84),hAPP(U_85,U_82)),hAPP(c_Set_Oimage(U_81,U_84,U_85),U_83)) = hAPP(c_Set_Oimage(U_81,U_84,U_85),U_83)
| ~ hBOOL(hAPP(hAPP(c_member(U_81),U_82),U_83)) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [V_a_2,V_b_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),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_b_2 != V_a_2 )
& ( V_b_2 = V_a_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),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))))) ) ),
inference(fof_nnf,[status(thm)],[fact_singleton__iff]) ).
fof(f_18_2,plain,
! [U_88,U_87,U_86] :
( ( hBOOL(hAPP(hAPP(c_member(U_86),U_87),hAPP(hAPP(c_Set_Oinsert(U_86),U_88),c_Orderings_Obot__class_Obot(tc_fun(U_86,tc_HOL_Obool)))))
| U_87 != U_88 )
& ( U_87 = U_88
| ~ hBOOL(hAPP(hAPP(c_member(U_86),U_87),hAPP(hAPP(c_Set_Oinsert(U_86),U_88),c_Orderings_Obot__class_Obot(tc_fun(U_86,tc_HOL_Obool))))) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_94,U_92] :
( ! [U_90] : hBOOL(hAPP(hAPP(c_member(U_90),U_92),hAPP(hAPP(c_Set_Oinsert(U_90),U_94),c_Orderings_Obot__class_Obot(tc_fun(U_90,tc_HOL_Obool)))))
| U_92 != U_94 )
& ! [U_93,U_91] :
( ! [U_89] : ~ hBOOL(hAPP(hAPP(c_member(U_89),U_91),hAPP(hAPP(c_Set_Oinsert(U_89),U_93),c_Orderings_Obot__class_Obot(tc_fun(U_89,tc_HOL_Obool)))))
| U_91 = U_93 ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_90,U_92,U_94] :
( hBOOL(hAPP(hAPP(c_member(U_90),U_92),hAPP(hAPP(c_Set_Oinsert(U_90),U_94),c_Orderings_Obot__class_Obot(tc_fun(U_90,tc_HOL_Obool)))))
| U_92 != U_94 )
& ! [U_93,U_91,U_89] :
( ~ hBOOL(hAPP(hAPP(c_member(U_89),U_91),hAPP(hAPP(c_Set_Oinsert(U_89),U_93),c_Orderings_Obot__class_Obot(tc_fun(U_89,tc_HOL_Obool)))))
| U_91 = U_93 ) ),
inference(definitional_conversion,[status(esa)],[f_18_3]) ).
cnf(f_18_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_89),U_91),hAPP(hAPP(c_Set_Oinsert(U_89),U_93),c_Orderings_Obot__class_Obot(tc_fun(U_89,tc_HOL_Obool)))))
| U_91 = U_93 ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_90),U_92),hAPP(hAPP(c_Set_Oinsert(U_90),U_94),c_Orderings_Obot__class_Obot(tc_fun(U_90,tc_HOL_Obool)))))
| U_92 != U_94 ),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
! [V_a_2,V_b_2,T_c] :
( V_b_2 = V_a_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),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))))) ),
inference(fof_nnf,[status(thm)],[fact_singletonE]) ).
fof(f_19_2,plain,
! [U_97,U_96,U_95] :
( U_96 = U_97
| ~ hBOOL(hAPP(hAPP(c_member(U_95),U_96),hAPP(hAPP(c_Set_Oinsert(U_95),U_97),c_Orderings_Obot__class_Obot(tc_fun(U_95,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_97,U_96] :
( ! [U_95] : ~ hBOOL(hAPP(hAPP(c_member(U_95),U_96),hAPP(hAPP(c_Set_Oinsert(U_95),U_97),c_Orderings_Obot__class_Obot(tc_fun(U_95,tc_HOL_Obool)))))
| U_96 = U_97 ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
! [U_95,U_96,U_97] :
( ~ hBOOL(hAPP(hAPP(c_member(U_95),U_96),hAPP(hAPP(c_Set_Oinsert(U_95),U_97),c_Orderings_Obot__class_Obot(tc_fun(U_95,tc_HOL_Obool)))))
| U_96 = U_97 ),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_95),U_96),hAPP(hAPP(c_Set_Oinsert(U_95),U_97),c_Orderings_Obot__class_Obot(tc_fun(U_95,tc_HOL_Obool)))))
| U_96 = U_97 ),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
! [V_c_2,T_c,V_B_2,V_A_2] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) )
| ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityCE]) ).
fof(f_20_2,plain,
! [U_101,U_100,U_99,U_98] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_100),U_101),U_99))
& ~ hBOOL(hAPP(hAPP(c_member(U_100),U_101),U_98)) )
| ( hBOOL(hAPP(hAPP(c_member(U_100),U_101),U_99))
& hBOOL(hAPP(hAPP(c_member(U_100),U_101),U_98)) )
| U_98 != U_99 ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_98,U_99,U_100,U_101] :
( ~ hBOOL(hAPP(hAPP(c_member(U_100),U_101),U_99))
| ~ sP4(U_98,U_99,U_100,U_101) )
& ! [U_98,U_99,U_100,U_101] :
( ~ hBOOL(hAPP(hAPP(c_member(U_100),U_101),U_98))
| ~ sP4(U_98,U_99,U_100,U_101) )
& ! [U_98,U_99,U_100,U_101] :
( hBOOL(hAPP(hAPP(c_member(U_100),U_101),U_99))
| ~ sP3(U_98,U_99,U_100,U_101) )
& ! [U_98,U_99,U_100,U_101] :
( hBOOL(hAPP(hAPP(c_member(U_100),U_101),U_98))
| ~ sP3(U_98,U_99,U_100,U_101) )
& ! [U_98,U_99,U_100,U_101] :
( sP4(U_98,U_99,U_100,U_101)
| sP3(U_98,U_99,U_100,U_101)
| U_98 != U_99 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3,sP4])],[f_20_2]) ).
cnf(f_20_4,plain,
( sP4(U_98,U_99,U_100,U_101)
| sP3(U_98,U_99,U_100,U_101)
| U_98 != U_99 ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_100),U_101),U_98))
| ~ sP3(U_98,U_99,U_100,U_101) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_100),U_101),U_99))
| ~ sP3(U_98,U_99,U_100,U_101) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_100),U_101),U_98))
| ~ sP4(U_98,U_99,U_100,U_101) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_100),U_101),U_99))
| ~ sP4(U_98,U_99,U_100,U_101) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [V_A_2,T_c,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_c),V_b_2),V_A_2))
| V_a_2 != V_b_2 ),
inference(fof_nnf,[status(thm)],[fact_eq__mem__trans]) ).
fof(f_21_2,plain,
! [U_105,U_104,U_103,U_102] :
( hBOOL(hAPP(hAPP(c_member(U_104),U_102),U_105))
| ~ hBOOL(hAPP(hAPP(c_member(U_104),U_103),U_105))
| U_102 != U_103 ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_103,U_105,U_104,U_102] :
( hBOOL(hAPP(hAPP(c_member(U_104),U_102),U_105))
| ~ hBOOL(hAPP(hAPP(c_member(U_104),U_103),U_105))
| U_102 != U_103 ),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_104),U_102),U_105))
| ~ hBOOL(hAPP(hAPP(c_member(U_104),U_103),U_105))
| U_102 != U_103 ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [V_A_2,T_c,V_y_2,V_x_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)) )
& ( 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)) ) )
| V_x_2 != V_y_2 ),
inference(fof_nnf,[status(thm)],[fact_eqelem__imp__iff]) ).
fof(f_22_2,plain,
! [U_109,U_108,U_107,U_106] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_108),U_106),U_109))
| ~ hBOOL(hAPP(hAPP(c_member(U_108),U_107),U_109)) )
& ( hBOOL(hAPP(hAPP(c_member(U_108),U_107),U_109))
| ~ hBOOL(hAPP(hAPP(c_member(U_108),U_106),U_109)) ) )
| U_106 != U_107 ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_106,U_107,U_108,U_109] :
( hBOOL(hAPP(hAPP(c_member(U_108),U_106),U_109))
| ~ hBOOL(hAPP(hAPP(c_member(U_108),U_107),U_109))
| ~ sP5(U_106,U_107,U_108,U_109) )
& ! [U_106,U_107,U_108,U_109] :
( hBOOL(hAPP(hAPP(c_member(U_108),U_107),U_109))
| ~ hBOOL(hAPP(hAPP(c_member(U_108),U_106),U_109))
| ~ sP5(U_106,U_107,U_108,U_109) )
& ! [U_106,U_107,U_108,U_109] :
( sP5(U_106,U_107,U_108,U_109)
| U_106 != U_107 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_22_2]) ).
cnf(f_22_4,plain,
( sP5(U_106,U_107,U_108,U_109)
| U_106 != U_107 ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_108),U_107),U_109))
| ~ hBOOL(hAPP(hAPP(c_member(U_108),U_106),U_109))
| ~ sP5(U_106,U_107,U_108,U_109) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_108),U_106),U_109))
| ~ hBOOL(hAPP(hAPP(c_member(U_108),U_107),U_109))
| ~ sP5(U_106,U_107,U_108,U_109) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [V_x_2,T_c,V_B_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_x_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_eqset__imp__iff]) ).
fof(f_23_2,plain,
! [U_113,U_112,U_111,U_110] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_112),U_113),U_110))
| ~ hBOOL(hAPP(hAPP(c_member(U_112),U_113),U_111)) )
& ( hBOOL(hAPP(hAPP(c_member(U_112),U_113),U_111))
| ~ hBOOL(hAPP(hAPP(c_member(U_112),U_113),U_110)) ) )
| U_110 != U_111 ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ! [U_111,U_112,U_110,U_113] :
( hBOOL(hAPP(hAPP(c_member(U_112),U_113),U_110))
| ~ hBOOL(hAPP(hAPP(c_member(U_112),U_113),U_111))
| ~ sP6(U_111,U_112,U_110,U_113) )
& ! [U_111,U_112,U_110,U_113] :
( hBOOL(hAPP(hAPP(c_member(U_112),U_113),U_111))
| ~ hBOOL(hAPP(hAPP(c_member(U_112),U_113),U_110))
| ~ sP6(U_111,U_112,U_110,U_113) )
& ! [U_111,U_112,U_110,U_113] :
( sP6(U_111,U_112,U_110,U_113)
| U_110 != U_111 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_23_2]) ).
cnf(f_23_4,plain,
( sP6(U_111,U_112,U_110,U_113)
| U_110 != U_111 ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_112),U_113),U_111))
| ~ hBOOL(hAPP(hAPP(c_member(U_112),U_113),U_110))
| ~ sP6(U_111,U_112,U_110,U_113) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_112),U_113),U_110))
| ~ hBOOL(hAPP(hAPP(c_member(U_112),U_113),U_111))
| ~ sP6(U_111,U_112,U_110,U_113) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [V_A_2,V_x_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),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_c),V_x_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mem__def]) ).
fof(f_24_2,plain,
! [U_116,U_115,U_114] :
( ( hBOOL(hAPP(hAPP(c_member(U_114),U_115),U_116))
| ~ hBOOL(hAPP(U_116,U_115)) )
& ( hBOOL(hAPP(U_116,U_115))
| ~ hBOOL(hAPP(hAPP(c_member(U_114),U_115),U_116)) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_122,U_120] :
( ! [U_118] : hBOOL(hAPP(hAPP(c_member(U_118),U_120),U_122))
| ~ hBOOL(hAPP(U_122,U_120)) )
& ! [U_121,U_119] :
( ! [U_117] : ~ hBOOL(hAPP(hAPP(c_member(U_117),U_119),U_121))
| hBOOL(hAPP(U_121,U_119)) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_122,U_118,U_120] :
( hBOOL(hAPP(hAPP(c_member(U_118),U_120),U_122))
| ~ hBOOL(hAPP(U_122,U_120)) )
& ! [U_119,U_117,U_121] :
( ~ hBOOL(hAPP(hAPP(c_member(U_117),U_119),U_121))
| hBOOL(hAPP(U_121,U_119)) ) ),
inference(definitional_conversion,[status(esa)],[f_24_3]) ).
cnf(f_24_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_117),U_119),U_121))
| hBOOL(hAPP(U_121,U_119)) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_118),U_120),U_122))
| ~ hBOOL(hAPP(U_122,U_120)) ),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Finite__Set_Ofinite(T_c) ),
inference(fof_nnf,[status(thm)],[fact_finite__code]) ).
fof(f_25_2,plain,
! [U_124,U_123] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_123),U_124))
| ~ class_Finite__Set_Ofinite(U_123) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_123,U_124] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_123),U_124))
| ~ class_Finite__Set_Ofinite(U_123) ),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_123),U_124))
| ~ class_Finite__Set_Ofinite(U_123) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Finite__Set_Ofinite(T_c) ),
inference(fof_nnf,[status(thm)],[fact_finite]) ).
fof(f_26_2,plain,
! [U_126,U_125] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_125),U_126))
| ~ class_Finite__Set_Ofinite(U_125) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_126,U_125] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_125),U_126))
| ~ class_Finite__Set_Ofinite(U_125) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_125),U_126))
| ~ class_Finite__Set_Ofinite(U_125) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [V_x_2,V_A_2,V_y_2,T_c] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_c),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_c),V_y_2),V_A_2),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__code]) ).
fof(f_27_2,plain,
! [U_130,U_129,U_128,U_127] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_127),U_128),U_129),U_130))
| ( ~ hBOOL(hAPP(U_129,U_130))
& U_128 != U_130 ) )
& ( hBOOL(hAPP(U_129,U_130))
| U_128 = U_130
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_127),U_128),U_129),U_130)) ) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_138,U_136,U_134] :
( ! [U_132] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_132),U_134),U_136),U_138))
| ( ~ hBOOL(hAPP(U_136,U_138))
& U_134 != U_138 ) )
& ! [U_137,U_135,U_133] :
( ! [U_131] : ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_131),U_133),U_135),U_137))
| hBOOL(hAPP(U_135,U_137))
| U_133 = U_137 ) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
( ! [U_138,U_136,U_134] :
( ~ hBOOL(hAPP(U_136,U_138))
| ~ sP7(U_138,U_136,U_134) )
& ! [U_138,U_136,U_134] :
( U_134 != U_138
| ~ sP7(U_138,U_136,U_134) )
& ! [U_138,U_136,U_132,U_134] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_132),U_134),U_136),U_138))
| sP7(U_138,U_136,U_134) )
& ! [U_135,U_137,U_133,U_131] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_131),U_133),U_135),U_137))
| hBOOL(hAPP(U_135,U_137))
| U_133 = U_137 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_27_3]) ).
cnf(f_27_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_131),U_133),U_135),U_137))
| hBOOL(hAPP(U_135,U_137))
| U_133 = U_137 ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_6,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_132),U_134),U_136),U_138))
| sP7(U_138,U_136,U_134) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_7,plain,
( U_134 != U_138
| ~ sP7(U_138,U_136,U_134) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_8,plain,
( ~ hBOOL(hAPP(U_136,U_138))
| ~ sP7(U_138,U_136,U_134) ),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
! [V_A_2,V_y_2,V_x_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_insert__commute]) ).
fof(f_28_2,plain,
! [U_142,U_141,U_140,U_139] : hAPP(hAPP(c_Set_Oinsert(U_139),U_140),hAPP(hAPP(c_Set_Oinsert(U_139),U_141),U_142)) = hAPP(hAPP(c_Set_Oinsert(U_139),U_141),hAPP(hAPP(c_Set_Oinsert(U_139),U_140),U_142)),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_140,U_139,U_141,U_142] : hAPP(hAPP(c_Set_Oinsert(U_139),U_140),hAPP(hAPP(c_Set_Oinsert(U_139),U_141),U_142)) = hAPP(hAPP(c_Set_Oinsert(U_139),U_141),hAPP(hAPP(c_Set_Oinsert(U_139),U_140),U_142)),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_139),U_140),hAPP(hAPP(c_Set_Oinsert(U_139),U_141),U_142)) = hAPP(hAPP(c_Set_Oinsert(U_139),U_141),hAPP(hAPP(c_Set_Oinsert(U_139),U_140),U_142)),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [V_A_2,V_x_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_insert__absorb2]) ).
fof(f_29_2,plain,
! [U_145,U_144,U_143] : hAPP(hAPP(c_Set_Oinsert(U_143),U_144),hAPP(hAPP(c_Set_Oinsert(U_143),U_144),U_145)) = hAPP(hAPP(c_Set_Oinsert(U_143),U_144),U_145),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_143,U_144,U_145] : hAPP(hAPP(c_Set_Oinsert(U_143),U_144),hAPP(hAPP(c_Set_Oinsert(U_143),U_144),U_145)) = hAPP(hAPP(c_Set_Oinsert(U_143),U_144),U_145),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_143),U_144),hAPP(hAPP(c_Set_Oinsert(U_143),U_144),U_145)) = hAPP(hAPP(c_Set_Oinsert(U_143),U_144),U_145),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [V_A_2,V_g_2,T_e,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_e,T_c,hAPP(hAPP(c_COMBB(T_d,T_c,T_e),V_f_2),V_g_2)),V_A_2),
inference(fof_nnf,[status(thm)],[fact_image__image]) ).
fof(f_30_2,plain,
! [U_151,U_150,U_149,U_148,U_147,U_146] : hAPP(c_Set_Oimage(U_146,U_147,U_148),hAPP(c_Set_Oimage(U_149,U_146,U_150),U_151)) = hAPP(c_Set_Oimage(U_149,U_147,hAPP(hAPP(c_COMBB(U_146,U_147,U_149),U_148),U_150)),U_151),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_146,U_147,U_148,U_149,U_150,U_151] : hAPP(c_Set_Oimage(U_146,U_147,U_148),hAPP(c_Set_Oimage(U_149,U_146,U_150),U_151)) = hAPP(c_Set_Oimage(U_149,U_147,hAPP(hAPP(c_COMBB(U_146,U_147,U_149),U_148),U_150)),U_151),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
hAPP(c_Set_Oimage(U_146,U_147,U_148),hAPP(c_Set_Oimage(U_149,U_146,U_150),U_151)) = hAPP(c_Set_Oimage(U_149,U_147,hAPP(hAPP(c_COMBB(U_146,U_147,U_149),U_148),U_150)),U_151),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [V_a_2,T_c,V_A_2] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_equals0D]) ).
fof(f_31_2,plain,
! [U_154,U_153,U_152] :
( ~ hBOOL(hAPP(hAPP(c_member(U_153),U_154),U_152))
| U_152 != c_Orderings_Obot__class_Obot(tc_fun(U_153,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_152,U_153,U_154] :
( ~ hBOOL(hAPP(hAPP(c_member(U_153),U_154),U_152))
| U_152 != c_Orderings_Obot__class_Obot(tc_fun(U_153,tc_HOL_Obool)) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_153),U_154),U_152))
| U_152 != c_Orderings_Obot__class_Obot(tc_fun(U_153,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [V_c_2,T_c] : ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_empty__iff]) ).
fof(f_32_2,plain,
! [U_156,U_155] : ~ hBOOL(hAPP(hAPP(c_member(U_155),U_156),c_Orderings_Obot__class_Obot(tc_fun(U_155,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_155,U_156] : ~ hBOOL(hAPP(hAPP(c_member(U_155),U_156),c_Orderings_Obot__class_Obot(tc_fun(U_155,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
~ hBOOL(hAPP(hAPP(c_member(U_155),U_156),c_Orderings_Obot__class_Obot(tc_fun(U_155,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [V_A_2,T_c] :
( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_c),B_x),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))
| ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_ex__in__conv]) ).
fof(f_33_2,plain,
! [U_160,U_159] :
( ( ? [U_158] : hBOOL(hAPP(hAPP(c_member(U_159),U_158),U_160))
| U_160 = c_Orderings_Obot__class_Obot(tc_fun(U_159,tc_HOL_Obool)) )
& ( U_160 != c_Orderings_Obot__class_Obot(tc_fun(U_159,tc_HOL_Obool))
| ! [U_157] : ~ hBOOL(hAPP(hAPP(c_member(U_159),U_157),U_160)) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_164,U_162] :
( ? [U_158] : hBOOL(hAPP(hAPP(c_member(U_162),U_158),U_164))
| U_164 = c_Orderings_Obot__class_Obot(tc_fun(U_162,tc_HOL_Obool)) )
& ! [U_163,U_161] :
( U_163 != c_Orderings_Obot__class_Obot(tc_fun(U_161,tc_HOL_Obool))
| ! [U_157] : ~ hBOOL(hAPP(hAPP(c_member(U_161),U_157),U_163)) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_164,U_162] :
( hBOOL(hAPP(hAPP(c_member(U_162),sK2(U_164,U_162)),U_164))
| U_164 = c_Orderings_Obot__class_Obot(tc_fun(U_162,tc_HOL_Obool)) )
& ! [U_163,U_161] :
( U_163 != c_Orderings_Obot__class_Obot(tc_fun(U_161,tc_HOL_Obool))
| ! [U_157] : ~ hBOOL(hAPP(hAPP(c_member(U_161),U_157),U_163)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_158,sK2(U_164,U_162))],[f_33_3]) ).
fof(f_33_5,plain,
( ! [U_162,U_164] :
( hBOOL(hAPP(hAPP(c_member(U_162),sK2(U_164,U_162)),U_164))
| U_164 = c_Orderings_Obot__class_Obot(tc_fun(U_162,tc_HOL_Obool)) )
& ! [U_163,U_157,U_161] :
( U_163 != c_Orderings_Obot__class_Obot(tc_fun(U_161,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_161),U_157),U_163)) ) ),
inference(definitional_conversion,[status(esa)],[f_33_4]) ).
cnf(f_33_6,plain,
( U_163 != c_Orderings_Obot__class_Obot(tc_fun(U_161,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_161),U_157),U_163)) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_162),sK2(U_164,U_162)),U_164))
| U_164 = c_Orderings_Obot__class_Obot(tc_fun(U_162,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_33_5]) ).
fof(f_34_1,plain,
! [V_A_2,T_c] :
( ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),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))
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_all__not__in__conv]) ).
fof(f_34_2,plain,
! [U_168,U_167] :
( ( ! [U_166] : ~ hBOOL(hAPP(hAPP(c_member(U_167),U_166),U_168))
| U_168 != c_Orderings_Obot__class_Obot(tc_fun(U_167,tc_HOL_Obool)) )
& ( U_168 = c_Orderings_Obot__class_Obot(tc_fun(U_167,tc_HOL_Obool))
| ? [U_165] : hBOOL(hAPP(hAPP(c_member(U_167),U_165),U_168)) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_172,U_170] :
( ! [U_166] : ~ hBOOL(hAPP(hAPP(c_member(U_170),U_166),U_172))
| U_172 != c_Orderings_Obot__class_Obot(tc_fun(U_170,tc_HOL_Obool)) )
& ! [U_171,U_169] :
( U_171 = c_Orderings_Obot__class_Obot(tc_fun(U_169,tc_HOL_Obool))
| ? [U_165] : hBOOL(hAPP(hAPP(c_member(U_169),U_165),U_171)) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
fof(f_34_4,plain,
( ! [U_172,U_170] :
( ! [U_166] : ~ hBOOL(hAPP(hAPP(c_member(U_170),U_166),U_172))
| U_172 != c_Orderings_Obot__class_Obot(tc_fun(U_170,tc_HOL_Obool)) )
& ! [U_171,U_169] :
( U_171 = c_Orderings_Obot__class_Obot(tc_fun(U_169,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_169),sK3(U_171,U_169)),U_171)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_165,sK3(U_171,U_169))],[f_34_3]) ).
fof(f_34_5,plain,
( ! [U_166,U_170,U_172] :
( ~ hBOOL(hAPP(hAPP(c_member(U_170),U_166),U_172))
| U_172 != c_Orderings_Obot__class_Obot(tc_fun(U_170,tc_HOL_Obool)) )
& ! [U_171,U_169] :
( U_171 = c_Orderings_Obot__class_Obot(tc_fun(U_169,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_169),sK3(U_171,U_169)),U_171)) ) ),
inference(definitional_conversion,[status(esa)],[f_34_4]) ).
cnf(f_34_6,plain,
( U_171 = c_Orderings_Obot__class_Obot(tc_fun(U_169,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_169),sK3(U_171,U_169)),U_171)) ),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_170),U_166),U_172))
| U_172 != c_Orderings_Obot__class_Obot(tc_fun(U_170,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_34_5]) ).
fof(f_35_1,plain,
! [V_A_2,V_a_2,T_c] :
( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__absorb]) ).
fof(f_35_2,plain,
! [U_175,U_174,U_173] :
( hAPP(hAPP(c_Set_Oinsert(U_173),U_174),U_175) = U_175
| ~ hBOOL(hAPP(hAPP(c_member(U_173),U_174),U_175)) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_173,U_174,U_175] :
( hAPP(hAPP(c_Set_Oinsert(U_173),U_174),U_175) = U_175
| ~ hBOOL(hAPP(hAPP(c_member(U_173),U_174),U_175)) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( hAPP(hAPP(c_Set_Oinsert(U_173),U_174),U_175) = U_175
| ~ hBOOL(hAPP(hAPP(c_member(U_173),U_174),U_175)) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [V_b_2,V_B_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_insertI2]) ).
fof(f_36_2,plain,
! [U_179,U_178,U_177,U_176] :
( hBOOL(hAPP(hAPP(c_member(U_176),U_177),hAPP(hAPP(c_Set_Oinsert(U_176),U_179),U_178)))
| ~ hBOOL(hAPP(hAPP(c_member(U_176),U_177),U_178)) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_176,U_177,U_178,U_179] :
( hBOOL(hAPP(hAPP(c_member(U_176),U_177),hAPP(hAPP(c_Set_Oinsert(U_176),U_179),U_178)))
| ~ hBOOL(hAPP(hAPP(c_member(U_176),U_177),U_178)) ),
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_176),U_177),hAPP(hAPP(c_Set_Oinsert(U_176),U_179),U_178)))
| ~ hBOOL(hAPP(hAPP(c_member(U_176),U_177),U_178)) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [V_B_2,V_A_2,V_x_2,T_c] :
( ( ( hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2)
| V_A_2 != V_B_2 )
& ( V_A_2 = V_B_2
| hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2) != hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2) ) )
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__ident]) ).
fof(f_37_2,plain,
! [U_183,U_182,U_181,U_180] :
( ( ( hAPP(hAPP(c_Set_Oinsert(U_180),U_181),U_182) = hAPP(hAPP(c_Set_Oinsert(U_180),U_181),U_183)
| U_182 != U_183 )
& ( U_182 = U_183
| hAPP(hAPP(c_Set_Oinsert(U_180),U_181),U_182) != hAPP(hAPP(c_Set_Oinsert(U_180),U_181),U_183) ) )
| hBOOL(hAPP(hAPP(c_member(U_180),U_181),U_183))
| hBOOL(hAPP(hAPP(c_member(U_180),U_181),U_182)) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_180,U_181,U_182,U_183] :
( hAPP(hAPP(c_Set_Oinsert(U_180),U_181),U_182) = hAPP(hAPP(c_Set_Oinsert(U_180),U_181),U_183)
| U_182 != U_183
| ~ sP8(U_180,U_181,U_182,U_183) )
& ! [U_180,U_181,U_182,U_183] :
( U_182 = U_183
| hAPP(hAPP(c_Set_Oinsert(U_180),U_181),U_182) != hAPP(hAPP(c_Set_Oinsert(U_180),U_181),U_183)
| ~ sP8(U_180,U_181,U_182,U_183) )
& ! [U_180,U_181,U_182,U_183] :
( sP8(U_180,U_181,U_182,U_183)
| hBOOL(hAPP(hAPP(c_member(U_180),U_181),U_183))
| hBOOL(hAPP(hAPP(c_member(U_180),U_181),U_182)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_37_2]) ).
cnf(f_37_4,plain,
( sP8(U_180,U_181,U_182,U_183)
| hBOOL(hAPP(hAPP(c_member(U_180),U_181),U_183))
| hBOOL(hAPP(hAPP(c_member(U_180),U_181),U_182)) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( U_182 = U_183
| hAPP(hAPP(c_Set_Oinsert(U_180),U_181),U_182) != hAPP(hAPP(c_Set_Oinsert(U_180),U_181),U_183)
| ~ sP8(U_180,U_181,U_182,U_183) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
( hAPP(hAPP(c_Set_Oinsert(U_180),U_181),U_182) = hAPP(hAPP(c_Set_Oinsert(U_180),U_181),U_183)
| U_182 != U_183
| ~ sP8(U_180,U_181,U_182,U_183) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [V_A_2,V_b_2,V_a_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_A_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
& V_a_2 != V_b_2 ) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| V_a_2 = V_b_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__iff]) ).
fof(f_38_2,plain,
! [U_187,U_186,U_185,U_184] :
( ( hBOOL(hAPP(hAPP(c_member(U_184),U_185),hAPP(hAPP(c_Set_Oinsert(U_184),U_186),U_187)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_184),U_185),U_187))
& U_185 != U_186 ) )
& ( hBOOL(hAPP(hAPP(c_member(U_184),U_185),U_187))
| U_185 = U_186
| ~ hBOOL(hAPP(hAPP(c_member(U_184),U_185),hAPP(hAPP(c_Set_Oinsert(U_184),U_186),U_187))) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_195,U_193,U_191,U_189] :
( hBOOL(hAPP(hAPP(c_member(U_189),U_191),hAPP(hAPP(c_Set_Oinsert(U_189),U_193),U_195)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_189),U_191),U_195))
& U_191 != U_193 ) )
& ! [U_194,U_192,U_190,U_188] :
( hBOOL(hAPP(hAPP(c_member(U_188),U_190),U_194))
| U_190 = U_192
| ~ hBOOL(hAPP(hAPP(c_member(U_188),U_190),hAPP(hAPP(c_Set_Oinsert(U_188),U_192),U_194))) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
( ! [U_193,U_191,U_195,U_189] :
( ~ hBOOL(hAPP(hAPP(c_member(U_189),U_191),U_195))
| ~ sP9(U_193,U_191,U_195,U_189) )
& ! [U_193,U_191,U_195,U_189] :
( U_191 != U_193
| ~ sP9(U_193,U_191,U_195,U_189) )
& ! [U_193,U_191,U_195,U_189] :
( hBOOL(hAPP(hAPP(c_member(U_189),U_191),hAPP(hAPP(c_Set_Oinsert(U_189),U_193),U_195)))
| sP9(U_193,U_191,U_195,U_189) )
& ! [U_190,U_188,U_192,U_194] :
( hBOOL(hAPP(hAPP(c_member(U_188),U_190),U_194))
| U_190 = U_192
| ~ hBOOL(hAPP(hAPP(c_member(U_188),U_190),hAPP(hAPP(c_Set_Oinsert(U_188),U_192),U_194))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_38_3]) ).
cnf(f_38_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_188),U_190),U_194))
| U_190 = U_192
| ~ hBOOL(hAPP(hAPP(c_member(U_188),U_190),hAPP(hAPP(c_Set_Oinsert(U_188),U_192),U_194))) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_189),U_191),hAPP(hAPP(c_Set_Oinsert(U_189),U_193),U_195)))
| sP9(U_193,U_191,U_195,U_189) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_7,plain,
( U_191 != U_193
| ~ sP9(U_193,U_191,U_195,U_189) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_189),U_191),U_195))
| ~ sP9(U_193,U_191,U_195,U_189) ),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_1,plain,
! [V_B_2,V_a_2,T_c] : hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_insertI1]) ).
fof(f_39_2,plain,
! [U_198,U_197,U_196] : hBOOL(hAPP(hAPP(c_member(U_196),U_197),hAPP(hAPP(c_Set_Oinsert(U_196),U_197),U_198))),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_197,U_196,U_198] : hBOOL(hAPP(hAPP(c_member(U_196),U_197),hAPP(hAPP(c_Set_Oinsert(U_196),U_197),U_198))),
inference(definitional_conversion,[status(esa)],[f_39_2]) ).
cnf(f_39_4,plain,
hBOOL(hAPP(hAPP(c_member(U_196),U_197),hAPP(hAPP(c_Set_Oinsert(U_196),U_197),U_198))),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [T_d,V_f_2,V_b_2,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
| V_b_2 != hAPP(V_f_2,V_x_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__image__eqI]) ).
fof(f_40_2,plain,
! [U_204,U_203,U_202,U_201,U_200,U_199] :
( hBOOL(hAPP(hAPP(c_member(U_204),U_202),hAPP(c_Set_Oimage(U_199,U_204,U_203),U_201)))
| U_202 != hAPP(U_203,U_200)
| ~ hBOOL(hAPP(hAPP(c_member(U_199),U_200),U_201)) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_199,U_200,U_201,U_202,U_203,U_204] :
( hBOOL(hAPP(hAPP(c_member(U_204),U_202),hAPP(c_Set_Oimage(U_199,U_204,U_203),U_201)))
| U_202 != hAPP(U_203,U_200)
| ~ hBOOL(hAPP(hAPP(c_member(U_199),U_200),U_201)) ),
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_204),U_202),hAPP(c_Set_Oimage(U_199,U_204,U_203),U_201)))
| U_202 != hAPP(U_203,U_200)
| ~ hBOOL(hAPP(hAPP(c_member(U_199),U_200),U_201)) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [V_f_2,T_d,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_imageI]) ).
fof(f_41_2,plain,
! [U_209,U_208,U_207,U_206,U_205] :
( hBOOL(hAPP(hAPP(c_member(U_208),hAPP(U_209,U_206)),hAPP(c_Set_Oimage(U_205,U_208,U_209),U_207)))
| ~ hBOOL(hAPP(hAPP(c_member(U_205),U_206),U_207)) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_209,U_208,U_205,U_206,U_207] :
( hBOOL(hAPP(hAPP(c_member(U_208),hAPP(U_209,U_206)),hAPP(c_Set_Oimage(U_205,U_208,U_209),U_207)))
| ~ hBOOL(hAPP(hAPP(c_member(U_205),U_206),U_207)) ),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_208),hAPP(U_209,U_206)),hAPP(c_Set_Oimage(U_205,U_208,U_209),U_207)))
| ~ hBOOL(hAPP(hAPP(c_member(U_205),U_206),U_207)) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [V_A_2,V_f_2,T_d,V_z_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)))
| ! [B_x] :
( V_z_2 != hAPP(V_f_2,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ? [B_x] :
( V_z_2 = hAPP(V_f_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_image__iff]) ).
fof(f_42_2,plain,
! [U_216,U_215,U_214,U_213,U_212] :
( ( hBOOL(hAPP(hAPP(c_member(U_212),U_213),hAPP(c_Set_Oimage(U_214,U_212,U_215),U_216)))
| ! [U_211] :
( U_213 != hAPP(U_215,U_211)
| ~ hBOOL(hAPP(hAPP(c_member(U_214),U_211),U_216)) ) )
& ( ? [U_210] :
( U_213 = hAPP(U_215,U_210)
& hBOOL(hAPP(hAPP(c_member(U_214),U_210),U_216)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_212),U_213),hAPP(c_Set_Oimage(U_214,U_212,U_215),U_216))) ) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( ! [U_226,U_224,U_222,U_220] :
( ! [U_218] : hBOOL(hAPP(hAPP(c_member(U_218),U_220),hAPP(c_Set_Oimage(U_222,U_218,U_224),U_226)))
| ! [U_211] :
( U_220 != hAPP(U_224,U_211)
| ~ hBOOL(hAPP(hAPP(c_member(U_222),U_211),U_226)) ) )
& ! [U_225,U_223,U_221,U_219] :
( ! [U_217] : ~ hBOOL(hAPP(hAPP(c_member(U_217),U_219),hAPP(c_Set_Oimage(U_221,U_217,U_223),U_225)))
| ? [U_210] :
( U_219 = hAPP(U_223,U_210)
& hBOOL(hAPP(hAPP(c_member(U_221),U_210),U_225)) ) ) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
( ! [U_226,U_224,U_222,U_220] :
( ! [U_218] : hBOOL(hAPP(hAPP(c_member(U_218),U_220),hAPP(c_Set_Oimage(U_222,U_218,U_224),U_226)))
| ! [U_211] :
( U_220 != hAPP(U_224,U_211)
| ~ hBOOL(hAPP(hAPP(c_member(U_222),U_211),U_226)) ) )
& ! [U_225,U_223,U_221,U_219] :
( ! [U_217] : ~ hBOOL(hAPP(hAPP(c_member(U_217),U_219),hAPP(c_Set_Oimage(U_221,U_217,U_223),U_225)))
| ( U_219 = hAPP(U_223,sK4(U_225,U_223,U_221,U_219))
& hBOOL(hAPP(hAPP(c_member(U_221),sK4(U_225,U_223,U_221,U_219)),U_225)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_210,sK4(U_225,U_223,U_221,U_219))],[f_42_3]) ).
fof(f_42_5,plain,
( ! [U_221,U_223,U_219,U_225] :
( U_219 = hAPP(U_223,sK4(U_225,U_223,U_221,U_219))
| ~ sP10(U_221,U_223,U_219,U_225) )
& ! [U_221,U_223,U_219,U_225] :
( hBOOL(hAPP(hAPP(c_member(U_221),sK4(U_225,U_223,U_221,U_219)),U_225))
| ~ sP10(U_221,U_223,U_219,U_225) )
& ! [U_211,U_226,U_220,U_218,U_224,U_222] :
( hBOOL(hAPP(hAPP(c_member(U_218),U_220),hAPP(c_Set_Oimage(U_222,U_218,U_224),U_226)))
| U_220 != hAPP(U_224,U_211)
| ~ hBOOL(hAPP(hAPP(c_member(U_222),U_211),U_226)) )
& ! [U_221,U_223,U_217,U_219,U_225] :
( ~ hBOOL(hAPP(hAPP(c_member(U_217),U_219),hAPP(c_Set_Oimage(U_221,U_217,U_223),U_225)))
| sP10(U_221,U_223,U_219,U_225) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_42_4]) ).
cnf(f_42_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_217),U_219),hAPP(c_Set_Oimage(U_221,U_217,U_223),U_225)))
| sP10(U_221,U_223,U_219,U_225) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_218),U_220),hAPP(c_Set_Oimage(U_222,U_218,U_224),U_226)))
| U_220 != hAPP(U_224,U_211)
| ~ hBOOL(hAPP(hAPP(c_member(U_222),U_211),U_226)) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_221),sK4(U_225,U_223,U_221,U_219)),U_225))
| ~ sP10(U_221,U_223,U_219,U_225) ),
inference(clausify,[status(thm)],[f_42_5]) ).
cnf(f_42_9,plain,
( U_219 = hAPP(U_223,sK4(U_225,U_223,U_221,U_219))
| ~ sP10(U_221,U_223,U_219,U_225) ),
inference(clausify,[status(thm)],[f_42_5]) ).
fof(f_43_1,plain,
! [T_c] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_finite_Oequations_I1_J]) ).
fof(f_43_2,plain,
! [U_227] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_227),c_Orderings_Obot__class_Obot(tc_fun(U_227,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_227] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_227),c_Orderings_Obot__class_Obot(tc_fun(U_227,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(U_227),c_Orderings_Obot__class_Obot(tc_fun(U_227,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [V_b_2,V_a_2,T_c] :
( V_a_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))) != hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_singleton__inject]) ).
fof(f_44_2,plain,
! [U_230,U_229,U_228] :
( U_229 = U_230
| hAPP(hAPP(c_Set_Oinsert(U_228),U_229),c_Orderings_Obot__class_Obot(tc_fun(U_228,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_228),U_230),c_Orderings_Obot__class_Obot(tc_fun(U_228,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_230,U_229] :
( ! [U_228] : hAPP(hAPP(c_Set_Oinsert(U_228),U_229),c_Orderings_Obot__class_Obot(tc_fun(U_228,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_228),U_230),c_Orderings_Obot__class_Obot(tc_fun(U_228,tc_HOL_Obool)))
| U_229 = U_230 ),
inference(miniscope,[status(thm)],[f_44_2]) ).
fof(f_44_4,plain,
! [U_230,U_229,U_228] :
( hAPP(hAPP(c_Set_Oinsert(U_228),U_229),c_Orderings_Obot__class_Obot(tc_fun(U_228,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_228),U_230),c_Orderings_Obot__class_Obot(tc_fun(U_228,tc_HOL_Obool)))
| U_229 = U_230 ),
inference(definitional_conversion,[status(esa)],[f_44_3]) ).
cnf(f_44_5,plain,
( hAPP(hAPP(c_Set_Oinsert(U_228),U_229),c_Orderings_Obot__class_Obot(tc_fun(U_228,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_228),U_230),c_Orderings_Obot__class_Obot(tc_fun(U_228,tc_HOL_Obool)))
| U_229 = U_230 ),
inference(clausify,[status(thm)],[f_44_4]) ).
fof(f_45_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( ( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
| ( ( V_b_2 != V_c_2
| V_a_2 != V_d_2 )
& ( V_b_2 != V_d_2
| V_a_2 != V_c_2 ) ) )
& ( ( V_b_2 = V_c_2
& V_a_2 = V_d_2 )
| ( V_b_2 = V_d_2
& V_a_2 = V_c_2 )
| hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff]) ).
fof(f_45_2,plain,
! [U_235,U_234,U_233,U_232,U_231] :
( ( hAPP(hAPP(c_Set_Oinsert(U_231),U_232),hAPP(hAPP(c_Set_Oinsert(U_231),U_233),c_Orderings_Obot__class_Obot(tc_fun(U_231,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_231),U_234),hAPP(hAPP(c_Set_Oinsert(U_231),U_235),c_Orderings_Obot__class_Obot(tc_fun(U_231,tc_HOL_Obool))))
| ( ( U_233 != U_234
| U_232 != U_235 )
& ( U_233 != U_235
| U_232 != U_234 ) ) )
& ( ( U_233 = U_234
& U_232 = U_235 )
| ( U_233 = U_235
& U_232 = U_234 )
| hAPP(hAPP(c_Set_Oinsert(U_231),U_232),hAPP(hAPP(c_Set_Oinsert(U_231),U_233),c_Orderings_Obot__class_Obot(tc_fun(U_231,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_231),U_234),hAPP(hAPP(c_Set_Oinsert(U_231),U_235),c_Orderings_Obot__class_Obot(tc_fun(U_231,tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( ! [U_245,U_243,U_241,U_239] :
( ! [U_237] : hAPP(hAPP(c_Set_Oinsert(U_237),U_239),hAPP(hAPP(c_Set_Oinsert(U_237),U_241),c_Orderings_Obot__class_Obot(tc_fun(U_237,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_237),U_243),hAPP(hAPP(c_Set_Oinsert(U_237),U_245),c_Orderings_Obot__class_Obot(tc_fun(U_237,tc_HOL_Obool))))
| ( ( U_241 != U_243
| U_239 != U_245 )
& ( U_241 != U_245
| U_239 != U_243 ) ) )
& ! [U_244,U_242,U_240,U_238] :
( ! [U_236] : hAPP(hAPP(c_Set_Oinsert(U_236),U_238),hAPP(hAPP(c_Set_Oinsert(U_236),U_240),c_Orderings_Obot__class_Obot(tc_fun(U_236,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_236),U_242),hAPP(hAPP(c_Set_Oinsert(U_236),U_244),c_Orderings_Obot__class_Obot(tc_fun(U_236,tc_HOL_Obool))))
| ( U_240 = U_242
& U_238 = U_244 )
| ( U_240 = U_244
& U_238 = U_242 ) ) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
( ! [U_243,U_239,U_241,U_245] :
( U_241 != U_243
| U_239 != U_245
| ~ sP13(U_243,U_239,U_241,U_245) )
& ! [U_243,U_239,U_241,U_245] :
( U_241 != U_245
| U_239 != U_243
| ~ sP13(U_243,U_239,U_241,U_245) )
& ! [U_238,U_240,U_242,U_244] :
( U_240 = U_242
| ~ sP12(U_238,U_240,U_242,U_244) )
& ! [U_238,U_240,U_242,U_244] :
( U_238 = U_244
| ~ sP12(U_238,U_240,U_242,U_244) )
& ! [U_238,U_240,U_242,U_244] :
( U_240 = U_244
| ~ sP11(U_238,U_240,U_242,U_244) )
& ! [U_238,U_240,U_242,U_244] :
( U_238 = U_242
| ~ sP11(U_238,U_240,U_242,U_244) )
& ! [U_237,U_243,U_239,U_241,U_245] :
( hAPP(hAPP(c_Set_Oinsert(U_237),U_239),hAPP(hAPP(c_Set_Oinsert(U_237),U_241),c_Orderings_Obot__class_Obot(tc_fun(U_237,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_237),U_243),hAPP(hAPP(c_Set_Oinsert(U_237),U_245),c_Orderings_Obot__class_Obot(tc_fun(U_237,tc_HOL_Obool))))
| sP13(U_243,U_239,U_241,U_245) )
& ! [U_238,U_236,U_240,U_242,U_244] :
( hAPP(hAPP(c_Set_Oinsert(U_236),U_238),hAPP(hAPP(c_Set_Oinsert(U_236),U_240),c_Orderings_Obot__class_Obot(tc_fun(U_236,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_236),U_242),hAPP(hAPP(c_Set_Oinsert(U_236),U_244),c_Orderings_Obot__class_Obot(tc_fun(U_236,tc_HOL_Obool))))
| sP12(U_238,U_240,U_242,U_244)
| sP11(U_238,U_240,U_242,U_244) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11,sP12,sP13])],[f_45_3]) ).
cnf(f_45_5,plain,
( hAPP(hAPP(c_Set_Oinsert(U_236),U_238),hAPP(hAPP(c_Set_Oinsert(U_236),U_240),c_Orderings_Obot__class_Obot(tc_fun(U_236,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_236),U_242),hAPP(hAPP(c_Set_Oinsert(U_236),U_244),c_Orderings_Obot__class_Obot(tc_fun(U_236,tc_HOL_Obool))))
| sP12(U_238,U_240,U_242,U_244)
| sP11(U_238,U_240,U_242,U_244) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_6,plain,
( hAPP(hAPP(c_Set_Oinsert(U_237),U_239),hAPP(hAPP(c_Set_Oinsert(U_237),U_241),c_Orderings_Obot__class_Obot(tc_fun(U_237,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_237),U_243),hAPP(hAPP(c_Set_Oinsert(U_237),U_245),c_Orderings_Obot__class_Obot(tc_fun(U_237,tc_HOL_Obool))))
| sP13(U_243,U_239,U_241,U_245) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_7,plain,
( U_238 = U_242
| ~ sP11(U_238,U_240,U_242,U_244) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_8,plain,
( U_240 = U_244
| ~ sP11(U_238,U_240,U_242,U_244) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_9,plain,
( U_238 = U_244
| ~ sP12(U_238,U_240,U_242,U_244) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_10,plain,
( U_240 = U_242
| ~ sP12(U_238,U_240,U_242,U_244) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_11,plain,
( U_241 != U_245
| U_239 != U_243
| ~ sP13(U_243,U_239,U_241,U_245) ),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_12,plain,
( U_241 != U_243
| U_239 != U_245
| ~ sP13(U_243,U_239,U_241,U_245) ),
inference(clausify,[status(thm)],[f_45_4]) ).
fof(f_46_1,plain,
! [V_A_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_insert__not__empty]) ).
fof(f_46_2,plain,
! [U_248,U_247,U_246] : hAPP(hAPP(c_Set_Oinsert(U_246),U_247),U_248) != c_Orderings_Obot__class_Obot(tc_fun(U_246,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_248,U_246,U_247] : hAPP(hAPP(c_Set_Oinsert(U_246),U_247),U_248) != c_Orderings_Obot__class_Obot(tc_fun(U_246,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_246),U_247),U_248) != c_Orderings_Obot__class_Obot(tc_fun(U_246,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [V_A_2,V_a_2,T_c] : c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_empty__not__insert]) ).
fof(f_47_2,plain,
! [U_251,U_250,U_249] : c_Orderings_Obot__class_Obot(tc_fun(U_249,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_249),U_250),U_251),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_249,U_250,U_251] : c_Orderings_Obot__class_Obot(tc_fun(U_249,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_249),U_250),U_251),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
c_Orderings_Obot__class_Obot(tc_fun(U_249,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_249),U_250),U_251),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [V_A_2,V_a_2,T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__insert]) ).
fof(f_48_2,plain,
! [U_254,U_253,U_252] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_252),hAPP(hAPP(c_Set_Oinsert(U_252),U_253),U_254)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_252),U_254)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_252),U_254))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_252),hAPP(hAPP(c_Set_Oinsert(U_252),U_253),U_254))) ) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
( ! [U_260,U_258,U_256] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_256),hAPP(hAPP(c_Set_Oinsert(U_256),U_258),U_260)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_256),U_260)) )
& ! [U_259,U_257,U_255] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_255),U_259))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_255),hAPP(hAPP(c_Set_Oinsert(U_255),U_257),U_259))) ) ),
inference(miniscope,[status(thm)],[f_48_2]) ).
fof(f_48_4,plain,
( ! [U_256,U_258,U_260] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_256),hAPP(hAPP(c_Set_Oinsert(U_256),U_258),U_260)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_256),U_260)) )
& ! [U_255,U_259,U_257] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_255),U_259))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_255),hAPP(hAPP(c_Set_Oinsert(U_255),U_257),U_259))) ) ),
inference(definitional_conversion,[status(esa)],[f_48_3]) ).
cnf(f_48_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_255),U_259))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_255),hAPP(hAPP(c_Set_Oinsert(U_255),U_257),U_259))) ),
inference(clausify,[status(thm)],[f_48_4]) ).
cnf(f_48_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_256),hAPP(hAPP(c_Set_Oinsert(U_256),U_258),U_260)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_256),U_260)) ),
inference(clausify,[status(thm)],[f_48_4]) ).
fof(f_49_1,plain,
! [V_A_2,V_f_2,T_c,T_d] :
( ( hAPP(c_Set_Oimage(T_d,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_d,tc_HOL_Obool)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_image__is__empty]) ).
fof(f_49_2,plain,
! [U_264,U_263,U_262,U_261] :
( ( hAPP(c_Set_Oimage(U_261,U_262,U_263),U_264) = c_Orderings_Obot__class_Obot(tc_fun(U_262,tc_HOL_Obool))
| U_264 != c_Orderings_Obot__class_Obot(tc_fun(U_261,tc_HOL_Obool)) )
& ( U_264 = c_Orderings_Obot__class_Obot(tc_fun(U_261,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_261,U_262,U_263),U_264) != c_Orderings_Obot__class_Obot(tc_fun(U_262,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_272,U_270,U_268,U_266] :
( hAPP(c_Set_Oimage(U_266,U_268,U_270),U_272) = c_Orderings_Obot__class_Obot(tc_fun(U_268,tc_HOL_Obool))
| U_272 != c_Orderings_Obot__class_Obot(tc_fun(U_266,tc_HOL_Obool)) )
& ! [U_271,U_269,U_267,U_265] :
( U_271 = c_Orderings_Obot__class_Obot(tc_fun(U_265,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_265,U_267,U_269),U_271) != c_Orderings_Obot__class_Obot(tc_fun(U_267,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
( ! [U_266,U_272,U_268,U_270] :
( hAPP(c_Set_Oimage(U_266,U_268,U_270),U_272) = c_Orderings_Obot__class_Obot(tc_fun(U_268,tc_HOL_Obool))
| U_272 != c_Orderings_Obot__class_Obot(tc_fun(U_266,tc_HOL_Obool)) )
& ! [U_267,U_271,U_269,U_265] :
( U_271 = c_Orderings_Obot__class_Obot(tc_fun(U_265,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_265,U_267,U_269),U_271) != c_Orderings_Obot__class_Obot(tc_fun(U_267,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_49_3]) ).
cnf(f_49_5,plain,
( U_271 = c_Orderings_Obot__class_Obot(tc_fun(U_265,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_265,U_267,U_269),U_271) != c_Orderings_Obot__class_Obot(tc_fun(U_267,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_49_6,plain,
( hAPP(c_Set_Oimage(U_266,U_268,U_270),U_272) = c_Orderings_Obot__class_Obot(tc_fun(U_268,tc_HOL_Obool))
| U_272 != c_Orderings_Obot__class_Obot(tc_fun(U_266,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_50_1,plain,
! [V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_image__empty]) ).
fof(f_50_2,plain,
! [U_275,U_274,U_273] : hAPP(c_Set_Oimage(U_273,U_274,U_275),c_Orderings_Obot__class_Obot(tc_fun(U_273,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_274,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_273,U_274,U_275] : hAPP(c_Set_Oimage(U_273,U_274,U_275),c_Orderings_Obot__class_Obot(tc_fun(U_273,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_274,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
hAPP(c_Set_Oimage(U_273,U_274,U_275),c_Orderings_Obot__class_Obot(tc_fun(U_273,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_274,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) != hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) ) ),
inference(fof_nnf,[status(thm)],[fact_empty__is__image]) ).
fof(f_51_2,plain,
! [U_279,U_278,U_277,U_276] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_276,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_277,U_276,U_278),U_279)
| U_279 != c_Orderings_Obot__class_Obot(tc_fun(U_277,tc_HOL_Obool)) )
& ( U_279 = c_Orderings_Obot__class_Obot(tc_fun(U_277,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(U_276,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_277,U_276,U_278),U_279) ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_287,U_285,U_283] :
( ! [U_281] : c_Orderings_Obot__class_Obot(tc_fun(U_281,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_283,U_281,U_285),U_287)
| U_287 != c_Orderings_Obot__class_Obot(tc_fun(U_283,tc_HOL_Obool)) )
& ! [U_286,U_284,U_282] :
( ! [U_280] : c_Orderings_Obot__class_Obot(tc_fun(U_280,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_282,U_280,U_284),U_286)
| U_286 = c_Orderings_Obot__class_Obot(tc_fun(U_282,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
( ! [U_287,U_285,U_281,U_283] :
( c_Orderings_Obot__class_Obot(tc_fun(U_281,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_283,U_281,U_285),U_287)
| U_287 != c_Orderings_Obot__class_Obot(tc_fun(U_283,tc_HOL_Obool)) )
& ! [U_284,U_282,U_280,U_286] :
( c_Orderings_Obot__class_Obot(tc_fun(U_280,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_282,U_280,U_284),U_286)
| U_286 = c_Orderings_Obot__class_Obot(tc_fun(U_282,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_51_3]) ).
cnf(f_51_5,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_280,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_282,U_280,U_284),U_286)
| U_286 = c_Orderings_Obot__class_Obot(tc_fun(U_282,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_281,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_283,U_281,U_285),U_287)
| U_287 != c_Orderings_Obot__class_Obot(tc_fun(U_283,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_51_4]) ).
fof(f_52_1,plain,
! [V_B_2,V_a_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_image__insert]) ).
fof(f_52_2,plain,
! [U_292,U_291,U_290,U_289,U_288] : hAPP(c_Set_Oimage(U_288,U_289,U_290),hAPP(hAPP(c_Set_Oinsert(U_288),U_291),U_292)) = hAPP(hAPP(c_Set_Oinsert(U_289),hAPP(U_290,U_291)),hAPP(c_Set_Oimage(U_288,U_289,U_290),U_292)),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_288,U_289,U_290,U_291,U_292] : hAPP(c_Set_Oimage(U_288,U_289,U_290),hAPP(hAPP(c_Set_Oinsert(U_288),U_291),U_292)) = hAPP(hAPP(c_Set_Oinsert(U_289),hAPP(U_290,U_291)),hAPP(c_Set_Oimage(U_288,U_289,U_290),U_292)),
inference(definitional_conversion,[status(esa)],[f_52_2]) ).
cnf(f_52_4,plain,
hAPP(c_Set_Oimage(U_288,U_289,U_290),hAPP(hAPP(c_Set_Oinsert(U_288),U_291),U_292)) = hAPP(hAPP(c_Set_Oinsert(U_289),hAPP(U_290,U_291)),hAPP(c_Set_Oimage(U_288,U_289,U_290),U_292)),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [V_x_2,T_c] : c_Set_Othe__elem(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2,
inference(fof_nnf,[status(thm)],[fact_the__elem__eq]) ).
fof(f_53_2,plain,
! [U_294,U_293] : c_Set_Othe__elem(U_293,hAPP(hAPP(c_Set_Oinsert(U_293),U_294),c_Orderings_Obot__class_Obot(tc_fun(U_293,tc_HOL_Obool)))) = U_294,
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_294,U_293] : c_Set_Othe__elem(U_293,hAPP(hAPP(c_Set_Oinsert(U_293),U_294),c_Orderings_Obot__class_Obot(tc_fun(U_293,tc_HOL_Obool)))) = U_294,
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
c_Set_Othe__elem(U_293,hAPP(hAPP(c_Set_Oinsert(U_293),U_294),c_Orderings_Obot__class_Obot(tc_fun(U_293,tc_HOL_Obool)))) = U_294,
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
! [V_x_2,T_d,T_c] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_d,T_c)),V_x_2) = c_Orderings_Obot__class_Obot(T_c)
| ~ class_Orderings_Obot(T_c) ),
inference(fof_nnf,[status(thm)],[fact_bot__fun__def]) ).
fof(f_54_2,plain,
! [U_297,U_296,U_295] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_296,U_295)),U_297) = c_Orderings_Obot__class_Obot(U_295)
| ~ class_Orderings_Obot(U_295) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_295,U_296,U_297] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_296,U_295)),U_297) = c_Orderings_Obot__class_Obot(U_295)
| ~ class_Orderings_Obot(U_295) ),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_296,U_295)),U_297) = c_Orderings_Obot__class_Obot(U_295)
| ~ class_Orderings_Obot(U_295) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [V_x_2,T_c] :
( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(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),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_bot__empty__eq]) ).
fof(f_55_2,plain,
! [U_299,U_298] :
( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_298,tc_HOL_Obool)),U_299))
| ~ hBOOL(hAPP(hAPP(c_member(U_298),U_299),c_Orderings_Obot__class_Obot(tc_fun(U_298,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(c_member(U_298),U_299),c_Orderings_Obot__class_Obot(tc_fun(U_298,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_298,tc_HOL_Obool)),U_299)) ) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( ! [U_303,U_301] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_301,tc_HOL_Obool)),U_303))
| ~ hBOOL(hAPP(hAPP(c_member(U_301),U_303),c_Orderings_Obot__class_Obot(tc_fun(U_301,tc_HOL_Obool)))) )
& ! [U_302,U_300] :
( hBOOL(hAPP(hAPP(c_member(U_300),U_302),c_Orderings_Obot__class_Obot(tc_fun(U_300,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_300,tc_HOL_Obool)),U_302)) ) ),
inference(miniscope,[status(thm)],[f_55_2]) ).
fof(f_55_4,plain,
( ! [U_301,U_303] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_301,tc_HOL_Obool)),U_303))
| ~ hBOOL(hAPP(hAPP(c_member(U_301),U_303),c_Orderings_Obot__class_Obot(tc_fun(U_301,tc_HOL_Obool)))) )
& ! [U_302,U_300] :
( hBOOL(hAPP(hAPP(c_member(U_300),U_302),c_Orderings_Obot__class_Obot(tc_fun(U_300,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_300,tc_HOL_Obool)),U_302)) ) ),
inference(definitional_conversion,[status(esa)],[f_55_3]) ).
cnf(f_55_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_300),U_302),c_Orderings_Obot__class_Obot(tc_fun(U_300,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_300,tc_HOL_Obool)),U_302)) ),
inference(clausify,[status(thm)],[f_55_4]) ).
cnf(f_55_6,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_301,tc_HOL_Obool)),U_303))
| ~ hBOOL(hAPP(hAPP(c_member(U_301),U_303),c_Orderings_Obot__class_Obot(tc_fun(U_301,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_55_4]) ).
fof(f_56_1,plain,
! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_c,T_d] : c_Hoare__Mirabelle_Otriple_Otriple__case(T_d,T_c,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_d),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2),
inference(fof_nnf,[status(thm)],[fact_triple_Osimps_I2_J]) ).
fof(f_56_2,plain,
! [U_309,U_308,U_307,U_306,U_305,U_304] : c_Hoare__Mirabelle_Otriple_Otriple__case(U_304,U_305,U_306,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_304),U_307),U_308),U_309)) = hAPP(hAPP(hAPP(U_306,U_307),U_308),U_309),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_306,U_305,U_304,U_307,U_308,U_309] : c_Hoare__Mirabelle_Otriple_Otriple__case(U_304,U_305,U_306,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_304),U_307),U_308),U_309)) = hAPP(hAPP(hAPP(U_306,U_307),U_308),U_309),
inference(definitional_conversion,[status(esa)],[f_56_2]) ).
cnf(f_56_4,plain,
c_Hoare__Mirabelle_Otriple_Otriple__case(U_304,U_305,U_306,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_304),U_307),U_308),U_309)) = hAPP(hAPP(hAPP(U_306,U_307),U_308),U_309),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
! [V_fun2_2,V_com_2,V_fun1_2,V_f1_2,T_c,T_d] : c_Hoare__Mirabelle_Otriple_Otriple__rec(T_d,T_c,V_f1_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_d),V_fun1_2),V_com_2),V_fun2_2)) = hAPP(hAPP(hAPP(V_f1_2,V_fun1_2),V_com_2),V_fun2_2),
inference(fof_nnf,[status(thm)],[fact_triple_Orecs]) ).
fof(f_57_2,plain,
! [U_315,U_314,U_313,U_312,U_311,U_310] : c_Hoare__Mirabelle_Otriple_Otriple__rec(U_310,U_311,U_312,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_310),U_313),U_314),U_315)) = hAPP(hAPP(hAPP(U_312,U_313),U_314),U_315),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_310,U_311,U_312,U_313,U_314,U_315] : c_Hoare__Mirabelle_Otriple_Otriple__rec(U_310,U_311,U_312,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_310),U_313),U_314),U_315)) = hAPP(hAPP(hAPP(U_312,U_313),U_314),U_315),
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
c_Hoare__Mirabelle_Otriple_Otriple__rec(U_310,U_311,U_312,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_310),U_313),U_314),U_315)) = hAPP(hAPP(hAPP(U_312,U_313),U_314),U_315),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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_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__one(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert]) ).
fof(f_58_2,plain,
! [U_320,U_319,U_318,U_317,U_316] :
( hAPP(U_318,hAPP(hAPP(c_Set_Oinsert(U_316),U_320),U_319)) = hAPP(hAPP(U_317,U_320),hAPP(U_318,U_319))
| U_319 = c_Orderings_Obot__class_Obot(tc_fun(U_316,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_316),U_320),U_319))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_316),U_319))
| ~ c_Finite__Set_Ofolding__one(U_316,U_317,U_318) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_316,U_317,U_318,U_319,U_320] :
( hAPP(U_318,hAPP(hAPP(c_Set_Oinsert(U_316),U_320),U_319)) = hAPP(hAPP(U_317,U_320),hAPP(U_318,U_319))
| U_319 = c_Orderings_Obot__class_Obot(tc_fun(U_316,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_316),U_320),U_319))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_316),U_319))
| ~ c_Finite__Set_Ofolding__one(U_316,U_317,U_318) ),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
( hAPP(U_318,hAPP(hAPP(c_Set_Oinsert(U_316),U_320),U_319)) = hAPP(hAPP(U_317,U_320),hAPP(U_318,U_319))
| U_319 = c_Orderings_Obot__class_Obot(tc_fun(U_316,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_316),U_320),U_319))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_316),U_319))
| ~ c_Finite__Set_Ofolding__one(U_316,U_317,U_318) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [V_x_2,T_d,T_c] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_d,T_c)),V_x_2) = c_Orderings_Obot__class_Obot(T_c)
| ~ class_Orderings_Obot(T_c) ),
inference(fof_nnf,[status(thm)],[fact_bot__apply]) ).
fof(f_59_2,plain,
! [U_323,U_322,U_321] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_322,U_321)),U_323) = c_Orderings_Obot__class_Obot(U_321)
| ~ class_Orderings_Obot(U_321) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_322,U_321,U_323] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_322,U_321)),U_323) = c_Orderings_Obot__class_Obot(U_321)
| ~ class_Orderings_Obot(U_321) ),
inference(definitional_conversion,[status(esa)],[f_59_2]) ).
cnf(f_59_4,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_322,U_321)),U_323) = c_Orderings_Obot__class_Obot(U_321)
| ~ class_Orderings_Obot(U_321) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [V_Qa_2,V_c_2,V_Ga_2,T_c,V_Pa_2] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
| ? [B_Z,B_s] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_c_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_c),hAPP(V_Qa_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) ) ),
inference(fof_nnf,[status(thm)],[fact_escape]) ).
fof(f_60_2,plain,
! [U_330,U_329,U_328,U_327,U_326] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_327,U_328,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_327)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_327),U_326),U_329),U_330)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_327),tc_HOL_Obool))))
| ? [U_325,U_324] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_327,U_328,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_327)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_327),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_327),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),U_324))),U_329),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_327),hAPP(U_330,U_325)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_327),tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(U_326,U_325),U_324)) ) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_330,U_329,U_328,U_327,U_326] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_327,U_328,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_327)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_327),U_326),U_329),U_330)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_327),tc_HOL_Obool))))
| ? [U_324] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_327,U_328,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_327)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_327),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_327),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),U_324))),U_329),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_327),hAPP(U_330,sK5(U_330,U_329,U_328,U_327,U_326))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_327),tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(U_326,sK5(U_330,U_329,U_328,U_327,U_326)),U_324)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_325,sK5(U_330,U_329,U_328,U_327,U_326))],[f_60_2]) ).
fof(f_60_4,plain,
! [U_330,U_329,U_328,U_327,U_326] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_327,U_328,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_327)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_327),U_326),U_329),U_330)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_327),tc_HOL_Obool))))
| ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_327,U_328,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_327)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_327),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_327),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK6(U_330,U_329,U_328,U_327,U_326)))),U_329),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_327),hAPP(U_330,sK5(U_330,U_329,U_328,U_327,U_326))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_327),tc_HOL_Obool))))
& hBOOL(hAPP(hAPP(U_326,sK5(U_330,U_329,U_328,U_327,U_326)),sK6(U_330,U_329,U_328,U_327,U_326))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_324,sK6(U_330,U_329,U_328,U_327,U_326))],[f_60_3]) ).
fof(f_60_5,plain,
( ! [U_326,U_327,U_328,U_329,U_330] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_327,U_328,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_327)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_327),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_327),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK6(U_330,U_329,U_328,U_327,U_326)))),U_329),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_327),hAPP(U_330,sK5(U_330,U_329,U_328,U_327,U_326))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_327),tc_HOL_Obool))))
| ~ sP14(U_326,U_327,U_328,U_329,U_330) )
& ! [U_326,U_327,U_328,U_329,U_330] :
( hBOOL(hAPP(hAPP(U_326,sK5(U_330,U_329,U_328,U_327,U_326)),sK6(U_330,U_329,U_328,U_327,U_326)))
| ~ sP14(U_326,U_327,U_328,U_329,U_330) )
& ! [U_326,U_327,U_328,U_329,U_330] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_327,U_328,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_327)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_327),U_326),U_329),U_330)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_327),tc_HOL_Obool))))
| sP14(U_326,U_327,U_328,U_329,U_330) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_60_4]) ).
cnf(f_60_6,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_327,U_328,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_327)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_327),U_326),U_329),U_330)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_327),tc_HOL_Obool))))
| sP14(U_326,U_327,U_328,U_329,U_330) ),
inference(clausify,[status(thm)],[f_60_5]) ).
cnf(f_60_7,plain,
( hBOOL(hAPP(hAPP(U_326,sK5(U_330,U_329,U_328,U_327,U_326)),sK6(U_330,U_329,U_328,U_327,U_326)))
| ~ sP14(U_326,U_327,U_328,U_329,U_330) ),
inference(clausify,[status(thm)],[f_60_5]) ).
cnf(f_60_8,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_327,U_328,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_327)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_327),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_327),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK6(U_330,U_329,U_328,U_327,U_326)))),U_329),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_327),hAPP(U_330,sK5(U_330,U_329,U_328,U_327,U_326))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_327),tc_HOL_Obool))))
| ~ sP14(U_326,U_327,U_328,U_329,U_330) ),
inference(clausify,[status(thm)],[f_60_5]) ).
fof(f_61_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem]) ).
fof(f_61_2,plain,
! [U_335,U_334,U_333,U_332,U_331] :
( hAPP(U_333,hAPP(hAPP(c_Set_Oinsert(U_331),U_335),U_334)) = hAPP(hAPP(U_332,U_335),hAPP(U_333,U_334))
| U_334 = c_Orderings_Obot__class_Obot(tc_fun(U_331,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_331),U_334))
| ~ c_Finite__Set_Ofolding__one__idem(U_331,U_332,U_333) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_332,U_331,U_333,U_335,U_334] :
( hAPP(U_333,hAPP(hAPP(c_Set_Oinsert(U_331),U_335),U_334)) = hAPP(hAPP(U_332,U_335),hAPP(U_333,U_334))
| U_334 = c_Orderings_Obot__class_Obot(tc_fun(U_331,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_331),U_334))
| ~ c_Finite__Set_Ofolding__one__idem(U_331,U_332,U_333) ),
inference(definitional_conversion,[status(esa)],[f_61_2]) ).
cnf(f_61_4,plain,
( hAPP(U_333,hAPP(hAPP(c_Set_Oinsert(U_331),U_335),U_334)) = hAPP(hAPP(U_332,U_335),hAPP(U_333,U_334))
| U_334 = c_Orderings_Obot__class_Obot(tc_fun(U_331,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_331),U_334))
| ~ c_Finite__Set_Ofolding__one__idem(U_331,U_332,U_333) ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
! [V_a2_2,V_a1_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_a1_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_a2_2),c_Com_Ocom_OSKIP),V_a2_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oequations_I7_J]) ).
fof(f_62_2,plain,
! [U_338,U_337,U_336] : c_Hoare__Mirabelle_Ohoare__derivs(U_336,U_337,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_336)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_336),U_338),c_Com_Ocom_OSKIP),U_338)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_336),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_336,U_337,U_338] : c_Hoare__Mirabelle_Ohoare__derivs(U_336,U_337,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_336)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_336),U_338),c_Com_Ocom_OSKIP),U_338)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_336),tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_62_2]) ).
cnf(f_62_4,plain,
c_Hoare__Mirabelle_Ohoare__derivs(U_336,U_337,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_336)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_336),U_338),c_Com_Ocom_OSKIP),U_338)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_336),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [V_Pa_2,V_Ga_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OSkip]) ).
fof(f_63_2,plain,
! [U_341,U_340,U_339] : c_Hoare__Mirabelle_Ohoare__derivs(U_339,U_340,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_339)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_339),U_341),c_Com_Ocom_OSKIP),U_341)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_339),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_339,U_340,U_341] : c_Hoare__Mirabelle_Ohoare__derivs(U_339,U_340,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_339)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_339),U_341),c_Com_Ocom_OSKIP),U_341)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_339),tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_63_2]) ).
cnf(f_63_4,plain,
c_Hoare__Mirabelle_Ohoare__derivs(U_339,U_340,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_339)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_339),U_341),c_Com_Ocom_OSKIP),U_341)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_339),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
! [V_Pa_2,V_Qa_2,V_c_2,V_P_Ha_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
| ? [B_Z,B_s] :
( ~ hBOOL(hAPP(hAPP(V_P_Ha_2,B_Z),B_s))
& hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_P_Ha_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_conseq1]) ).
fof(f_64_2,plain,
! [U_349,U_348,U_347,U_346,U_345,U_344] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_344,U_345,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_344)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_344),U_349),U_347),U_348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_344),tc_HOL_Obool))))
| ? [U_343,U_342] :
( ~ hBOOL(hAPP(hAPP(U_346,U_343),U_342))
& hBOOL(hAPP(hAPP(U_349,U_343),U_342)) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_344,U_345,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_344)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_344),U_346),U_347),U_348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_344),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_349,U_348,U_347,U_346,U_345,U_344] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_344,U_345,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_344)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_344),U_349),U_347),U_348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_344),tc_HOL_Obool))))
| ? [U_342] :
( ~ hBOOL(hAPP(hAPP(U_346,sK7(U_349,U_348,U_347,U_346,U_345,U_344)),U_342))
& hBOOL(hAPP(hAPP(U_349,sK7(U_349,U_348,U_347,U_346,U_345,U_344)),U_342)) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_344,U_345,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_344)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_344),U_346),U_347),U_348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_344),tc_HOL_Obool)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_343,sK7(U_349,U_348,U_347,U_346,U_345,U_344))],[f_64_2]) ).
fof(f_64_4,plain,
! [U_349,U_348,U_347,U_346,U_345,U_344] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_344,U_345,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_344)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_344),U_349),U_347),U_348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_344),tc_HOL_Obool))))
| ( ~ hBOOL(hAPP(hAPP(U_346,sK7(U_349,U_348,U_347,U_346,U_345,U_344)),sK8(U_349,U_348,U_347,U_346,U_345,U_344)))
& hBOOL(hAPP(hAPP(U_349,sK7(U_349,U_348,U_347,U_346,U_345,U_344)),sK8(U_349,U_348,U_347,U_346,U_345,U_344))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_344,U_345,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_344)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_344),U_346),U_347),U_348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_344),tc_HOL_Obool)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_342,sK8(U_349,U_348,U_347,U_346,U_345,U_344))],[f_64_3]) ).
fof(f_64_5,plain,
( ! [U_344,U_345,U_346,U_347,U_348,U_349] :
( ~ hBOOL(hAPP(hAPP(U_346,sK7(U_349,U_348,U_347,U_346,U_345,U_344)),sK8(U_349,U_348,U_347,U_346,U_345,U_344)))
| ~ sP15(U_344,U_345,U_346,U_347,U_348,U_349) )
& ! [U_344,U_345,U_346,U_347,U_348,U_349] :
( hBOOL(hAPP(hAPP(U_349,sK7(U_349,U_348,U_347,U_346,U_345,U_344)),sK8(U_349,U_348,U_347,U_346,U_345,U_344)))
| ~ sP15(U_344,U_345,U_346,U_347,U_348,U_349) )
& ! [U_344,U_345,U_346,U_347,U_348,U_349] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_344,U_345,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_344)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_344),U_349),U_347),U_348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_344),tc_HOL_Obool))))
| sP15(U_344,U_345,U_346,U_347,U_348,U_349)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_344,U_345,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_344)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_344),U_346),U_347),U_348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_344),tc_HOL_Obool)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_64_4]) ).
cnf(f_64_6,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_344,U_345,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_344)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_344),U_349),U_347),U_348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_344),tc_HOL_Obool))))
| sP15(U_344,U_345,U_346,U_347,U_348,U_349)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_344,U_345,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_344)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_344),U_346),U_347),U_348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_344),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_64_5]) ).
cnf(f_64_7,plain,
( hBOOL(hAPP(hAPP(U_349,sK7(U_349,U_348,U_347,U_346,U_345,U_344)),sK8(U_349,U_348,U_347,U_346,U_345,U_344)))
| ~ sP15(U_344,U_345,U_346,U_347,U_348,U_349) ),
inference(clausify,[status(thm)],[f_64_5]) ).
cnf(f_64_8,plain,
( ~ hBOOL(hAPP(hAPP(U_346,sK7(U_349,U_348,U_347,U_346,U_345,U_344)),sK8(U_349,U_348,U_347,U_346,U_345,U_344)))
| ~ sP15(U_344,U_345,U_346,U_347,U_348,U_349) ),
inference(clausify,[status(thm)],[f_64_5]) ).
fof(f_65_1,plain,
! [V_x_2,V_F_2,V_f_2,T_c] :
( hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2
| ~ c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem]) ).
fof(f_65_2,plain,
! [U_353,U_352,U_351,U_350] :
( hAPP(hAPP(U_351,U_353),U_353) = U_353
| ~ c_Finite__Set_Ofolding__one__idem(U_350,U_351,U_352) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_353,U_352,U_351] :
( ! [U_350] : ~ c_Finite__Set_Ofolding__one__idem(U_350,U_351,U_352)
| hAPP(hAPP(U_351,U_353),U_353) = U_353 ),
inference(miniscope,[status(thm)],[f_65_2]) ).
fof(f_65_4,plain,
! [U_353,U_350,U_351,U_352] :
( ~ c_Finite__Set_Ofolding__one__idem(U_350,U_351,U_352)
| hAPP(hAPP(U_351,U_353),U_353) = U_353 ),
inference(definitional_conversion,[status(esa)],[f_65_3]) ).
cnf(f_65_5,plain,
( ~ c_Finite__Set_Ofolding__one__idem(U_350,U_351,U_352)
| hAPP(hAPP(U_351,U_353),U_353) = U_353 ),
inference(clausify,[status(thm)],[f_65_4]) ).
fof(f_66_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),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_c),V_x_2),hAPP(c_fequal,V_y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__mem]) ).
fof(f_66_2,plain,
! [U_356,U_355,U_354] :
( ( hBOOL(hAPP(hAPP(c_member(U_354),U_355),hAPP(c_fequal,U_356)))
| U_355 != U_356 )
& ( U_355 = U_356
| ~ hBOOL(hAPP(hAPP(c_member(U_354),U_355),hAPP(c_fequal,U_356))) ) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
( ! [U_362,U_360] :
( ! [U_358] : hBOOL(hAPP(hAPP(c_member(U_358),U_360),hAPP(c_fequal,U_362)))
| U_360 != U_362 )
& ! [U_361,U_359] :
( ! [U_357] : ~ hBOOL(hAPP(hAPP(c_member(U_357),U_359),hAPP(c_fequal,U_361)))
| U_359 = U_361 ) ),
inference(miniscope,[status(thm)],[f_66_2]) ).
fof(f_66_4,plain,
( ! [U_362,U_358,U_360] :
( hBOOL(hAPP(hAPP(c_member(U_358),U_360),hAPP(c_fequal,U_362)))
| U_360 != U_362 )
& ! [U_359,U_357,U_361] :
( ~ hBOOL(hAPP(hAPP(c_member(U_357),U_359),hAPP(c_fequal,U_361)))
| U_359 = U_361 ) ),
inference(definitional_conversion,[status(esa)],[f_66_3]) ).
cnf(f_66_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_357),U_359),hAPP(c_fequal,U_361)))
| U_359 = U_361 ),
inference(clausify,[status(thm)],[f_66_4]) ).
cnf(f_66_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_358),U_360),hAPP(c_fequal,U_362)))
| U_360 != U_362 ),
inference(clausify,[status(thm)],[f_66_4]) ).
fof(f_67_1,plain,
! [V_x_2,V_F_2,V_f_2,T_c] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2
| ~ c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton]) ).
fof(f_67_2,plain,
! [U_366,U_365,U_364,U_363] :
( hAPP(U_365,hAPP(hAPP(c_Set_Oinsert(U_363),U_366),c_Orderings_Obot__class_Obot(tc_fun(U_363,tc_HOL_Obool)))) = U_366
| ~ c_Finite__Set_Ofolding__one(U_363,U_364,U_365) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_363,U_364,U_365,U_366] :
( hAPP(U_365,hAPP(hAPP(c_Set_Oinsert(U_363),U_366),c_Orderings_Obot__class_Obot(tc_fun(U_363,tc_HOL_Obool)))) = U_366
| ~ c_Finite__Set_Ofolding__one(U_363,U_364,U_365) ),
inference(definitional_conversion,[status(esa)],[f_67_2]) ).
cnf(f_67_4,plain,
( hAPP(U_365,hAPP(hAPP(c_Set_Oinsert(U_363),U_366),c_Orderings_Obot__class_Obot(tc_fun(U_363,tc_HOL_Obool)))) = U_366
| ~ c_Finite__Set_Ofolding__one(U_363,U_364,U_365) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] :
( 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_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem]) ).
fof(f_68_2,plain,
! [U_371,U_370,U_369,U_368,U_367] :
( hAPP(hAPP(U_368,U_371),hAPP(U_369,U_370)) = hAPP(U_369,U_370)
| ~ hBOOL(hAPP(hAPP(c_member(U_367),U_371),U_370))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_367),U_370))
| ~ c_Finite__Set_Ofolding__one__idem(U_367,U_368,U_369) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_367,U_368,U_369,U_370,U_371] :
( hAPP(hAPP(U_368,U_371),hAPP(U_369,U_370)) = hAPP(U_369,U_370)
| ~ hBOOL(hAPP(hAPP(c_member(U_367),U_371),U_370))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_367),U_370))
| ~ c_Finite__Set_Ofolding__one__idem(U_367,U_368,U_369) ),
inference(definitional_conversion,[status(esa)],[f_68_2]) ).
cnf(f_68_4,plain,
( hAPP(hAPP(U_368,U_371),hAPP(U_369,U_370)) = hAPP(U_369,U_370)
| ~ hBOOL(hAPP(hAPP(c_member(U_367),U_371),U_370))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_367),U_370))
| ~ c_Finite__Set_Ofolding__one__idem(U_367,U_368,U_369) ),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_1,plain,
! [V_S_2,V_R_2,T_c] :
( ( hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2) = hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2)
| V_R_2 != V_S_2 )
& ( V_R_2 = V_S_2
| hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2) != hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__equals__eq]) ).
fof(f_69_2,plain,
! [U_374,U_373,U_372] :
( ( hAPP(hAPP(c_COMBC(U_372,tc_fun(U_372,tc_HOL_Obool),tc_HOL_Obool),c_member(U_372)),U_373) = hAPP(hAPP(c_COMBC(U_372,tc_fun(U_372,tc_HOL_Obool),tc_HOL_Obool),c_member(U_372)),U_374)
| U_373 != U_374 )
& ( U_373 = U_374
| hAPP(hAPP(c_COMBC(U_372,tc_fun(U_372,tc_HOL_Obool),tc_HOL_Obool),c_member(U_372)),U_373) != hAPP(hAPP(c_COMBC(U_372,tc_fun(U_372,tc_HOL_Obool),tc_HOL_Obool),c_member(U_372)),U_374) ) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
( ! [U_380,U_378] :
( ! [U_376] : hAPP(hAPP(c_COMBC(U_376,tc_fun(U_376,tc_HOL_Obool),tc_HOL_Obool),c_member(U_376)),U_378) = hAPP(hAPP(c_COMBC(U_376,tc_fun(U_376,tc_HOL_Obool),tc_HOL_Obool),c_member(U_376)),U_380)
| U_378 != U_380 )
& ! [U_379,U_377] :
( ! [U_375] : hAPP(hAPP(c_COMBC(U_375,tc_fun(U_375,tc_HOL_Obool),tc_HOL_Obool),c_member(U_375)),U_377) != hAPP(hAPP(c_COMBC(U_375,tc_fun(U_375,tc_HOL_Obool),tc_HOL_Obool),c_member(U_375)),U_379)
| U_377 = U_379 ) ),
inference(miniscope,[status(thm)],[f_69_2]) ).
fof(f_69_4,plain,
( ! [U_376,U_380,U_378] :
( hAPP(hAPP(c_COMBC(U_376,tc_fun(U_376,tc_HOL_Obool),tc_HOL_Obool),c_member(U_376)),U_378) = hAPP(hAPP(c_COMBC(U_376,tc_fun(U_376,tc_HOL_Obool),tc_HOL_Obool),c_member(U_376)),U_380)
| U_378 != U_380 )
& ! [U_377,U_375,U_379] :
( hAPP(hAPP(c_COMBC(U_375,tc_fun(U_375,tc_HOL_Obool),tc_HOL_Obool),c_member(U_375)),U_377) != hAPP(hAPP(c_COMBC(U_375,tc_fun(U_375,tc_HOL_Obool),tc_HOL_Obool),c_member(U_375)),U_379)
| U_377 = U_379 ) ),
inference(definitional_conversion,[status(esa)],[f_69_3]) ).
cnf(f_69_5,plain,
( hAPP(hAPP(c_COMBC(U_375,tc_fun(U_375,tc_HOL_Obool),tc_HOL_Obool),c_member(U_375)),U_377) != hAPP(hAPP(c_COMBC(U_375,tc_fun(U_375,tc_HOL_Obool),tc_HOL_Obool),c_member(U_375)),U_379)
| U_377 = U_379 ),
inference(clausify,[status(thm)],[f_69_4]) ).
cnf(f_69_6,plain,
( hAPP(hAPP(c_COMBC(U_376,tc_fun(U_376,tc_HOL_Obool),tc_HOL_Obool),c_member(U_376)),U_378) = hAPP(hAPP(c_COMBC(U_376,tc_fun(U_376,tc_HOL_Obool),tc_HOL_Obool),c_member(U_376)),U_380)
| U_378 != U_380 ),
inference(clausify,[status(thm)],[f_69_4]) ).
fof(f_70_1,plain,
! [V_A_2,V_F_2,V_f_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_F_2,V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oclosed]) ).
fof(f_70_2,plain,
! [U_386,U_385,U_384,U_383] :
( hBOOL(hAPP(hAPP(c_member(U_383),hAPP(U_385,U_386)),U_386))
| ? [U_382,U_381] : ~ hBOOL(hAPP(hAPP(c_member(U_383),hAPP(hAPP(U_384,U_382),U_381)),hAPP(hAPP(c_Set_Oinsert(U_383),U_382),hAPP(hAPP(c_Set_Oinsert(U_383),U_381),c_Orderings_Obot__class_Obot(tc_fun(U_383,tc_HOL_Obool))))))
| U_386 = c_Orderings_Obot__class_Obot(tc_fun(U_383,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_383),U_386))
| ~ c_Finite__Set_Ofolding__one(U_383,U_384,U_385) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_386,U_385,U_384,U_383] :
( hBOOL(hAPP(hAPP(c_member(U_383),hAPP(U_385,U_386)),U_386))
| ? [U_381] : ~ hBOOL(hAPP(hAPP(c_member(U_383),hAPP(hAPP(U_384,sK9(U_386,U_385,U_384,U_383)),U_381)),hAPP(hAPP(c_Set_Oinsert(U_383),sK9(U_386,U_385,U_384,U_383)),hAPP(hAPP(c_Set_Oinsert(U_383),U_381),c_Orderings_Obot__class_Obot(tc_fun(U_383,tc_HOL_Obool))))))
| U_386 = c_Orderings_Obot__class_Obot(tc_fun(U_383,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_383),U_386))
| ~ c_Finite__Set_Ofolding__one(U_383,U_384,U_385) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_382,sK9(U_386,U_385,U_384,U_383))],[f_70_2]) ).
fof(f_70_4,plain,
! [U_386,U_385,U_384,U_383] :
( hBOOL(hAPP(hAPP(c_member(U_383),hAPP(U_385,U_386)),U_386))
| ~ hBOOL(hAPP(hAPP(c_member(U_383),hAPP(hAPP(U_384,sK9(U_386,U_385,U_384,U_383)),sK10(U_386,U_385,U_384,U_383))),hAPP(hAPP(c_Set_Oinsert(U_383),sK9(U_386,U_385,U_384,U_383)),hAPP(hAPP(c_Set_Oinsert(U_383),sK10(U_386,U_385,U_384,U_383)),c_Orderings_Obot__class_Obot(tc_fun(U_383,tc_HOL_Obool))))))
| U_386 = c_Orderings_Obot__class_Obot(tc_fun(U_383,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_383),U_386))
| ~ c_Finite__Set_Ofolding__one(U_383,U_384,U_385) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_381,sK10(U_386,U_385,U_384,U_383))],[f_70_3]) ).
fof(f_70_5,plain,
! [U_383,U_384,U_385,U_386] :
( hBOOL(hAPP(hAPP(c_member(U_383),hAPP(U_385,U_386)),U_386))
| ~ hBOOL(hAPP(hAPP(c_member(U_383),hAPP(hAPP(U_384,sK9(U_386,U_385,U_384,U_383)),sK10(U_386,U_385,U_384,U_383))),hAPP(hAPP(c_Set_Oinsert(U_383),sK9(U_386,U_385,U_384,U_383)),hAPP(hAPP(c_Set_Oinsert(U_383),sK10(U_386,U_385,U_384,U_383)),c_Orderings_Obot__class_Obot(tc_fun(U_383,tc_HOL_Obool))))))
| U_386 = c_Orderings_Obot__class_Obot(tc_fun(U_383,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_383),U_386))
| ~ c_Finite__Set_Ofolding__one(U_383,U_384,U_385) ),
inference(definitional_conversion,[status(esa)],[f_70_4]) ).
cnf(f_70_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_383),hAPP(U_385,U_386)),U_386))
| ~ hBOOL(hAPP(hAPP(c_member(U_383),hAPP(hAPP(U_384,sK9(U_386,U_385,U_384,U_383)),sK10(U_386,U_385,U_384,U_383))),hAPP(hAPP(c_Set_Oinsert(U_383),sK9(U_386,U_385,U_384,U_383)),hAPP(hAPP(c_Set_Oinsert(U_383),sK10(U_386,U_385,U_384,U_383)),c_Orderings_Obot__class_Obot(tc_fun(U_383,tc_HOL_Obool))))))
| U_386 = c_Orderings_Obot__class_Obot(tc_fun(U_383,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_383),U_386))
| ~ c_Finite__Set_Ofolding__one(U_383,U_384,U_385) ),
inference(clausify,[status(thm)],[f_70_5]) ).
fof(f_71_1,plain,
! [V_Qa_2,V_Q_Ha_2,V_c_2,V_Pa_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
| ? [B_Z,B_s] :
( ~ hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s))
& hBOOL(hAPP(hAPP(V_Q_Ha_2,B_Z),B_s)) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Q_Ha_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_conseq2]) ).
fof(f_71_2,plain,
! [U_394,U_393,U_392,U_391,U_390,U_389] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_389,U_390,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_389)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_389),U_391),U_392),U_394)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_389),tc_HOL_Obool))))
| ? [U_388,U_387] :
( ~ hBOOL(hAPP(hAPP(U_394,U_388),U_387))
& hBOOL(hAPP(hAPP(U_393,U_388),U_387)) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_389,U_390,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_389)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_389),U_391),U_392),U_393)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_389),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_394,U_393,U_392,U_391,U_390,U_389] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_389,U_390,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_389)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_389),U_391),U_392),U_394)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_389),tc_HOL_Obool))))
| ? [U_387] :
( ~ hBOOL(hAPP(hAPP(U_394,sK11(U_394,U_393,U_392,U_391,U_390,U_389)),U_387))
& hBOOL(hAPP(hAPP(U_393,sK11(U_394,U_393,U_392,U_391,U_390,U_389)),U_387)) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_389,U_390,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_389)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_389),U_391),U_392),U_393)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_389),tc_HOL_Obool)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_388,sK11(U_394,U_393,U_392,U_391,U_390,U_389))],[f_71_2]) ).
fof(f_71_4,plain,
! [U_394,U_393,U_392,U_391,U_390,U_389] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_389,U_390,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_389)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_389),U_391),U_392),U_394)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_389),tc_HOL_Obool))))
| ( ~ hBOOL(hAPP(hAPP(U_394,sK11(U_394,U_393,U_392,U_391,U_390,U_389)),sK12(U_394,U_393,U_392,U_391,U_390,U_389)))
& hBOOL(hAPP(hAPP(U_393,sK11(U_394,U_393,U_392,U_391,U_390,U_389)),sK12(U_394,U_393,U_392,U_391,U_390,U_389))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_389,U_390,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_389)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_389),U_391),U_392),U_393)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_389),tc_HOL_Obool)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_387,sK12(U_394,U_393,U_392,U_391,U_390,U_389))],[f_71_3]) ).
fof(f_71_5,plain,
( ! [U_389,U_390,U_391,U_392,U_393,U_394] :
( ~ hBOOL(hAPP(hAPP(U_394,sK11(U_394,U_393,U_392,U_391,U_390,U_389)),sK12(U_394,U_393,U_392,U_391,U_390,U_389)))
| ~ sP16(U_389,U_390,U_391,U_392,U_393,U_394) )
& ! [U_389,U_390,U_391,U_392,U_393,U_394] :
( hBOOL(hAPP(hAPP(U_393,sK11(U_394,U_393,U_392,U_391,U_390,U_389)),sK12(U_394,U_393,U_392,U_391,U_390,U_389)))
| ~ sP16(U_389,U_390,U_391,U_392,U_393,U_394) )
& ! [U_389,U_390,U_391,U_392,U_393,U_394] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_389,U_390,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_389)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_389),U_391),U_392),U_394)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_389),tc_HOL_Obool))))
| sP16(U_389,U_390,U_391,U_392,U_393,U_394)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_389,U_390,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_389)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_389),U_391),U_392),U_393)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_389),tc_HOL_Obool)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_71_4]) ).
cnf(f_71_6,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_389,U_390,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_389)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_389),U_391),U_392),U_394)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_389),tc_HOL_Obool))))
| sP16(U_389,U_390,U_391,U_392,U_393,U_394)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_389,U_390,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_389)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_389),U_391),U_392),U_393)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_389),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_7,plain,
( hBOOL(hAPP(hAPP(U_393,sK11(U_394,U_393,U_392,U_391,U_390,U_389)),sK12(U_394,U_393,U_392,U_391,U_390,U_389)))
| ~ sP16(U_389,U_390,U_391,U_392,U_393,U_394) ),
inference(clausify,[status(thm)],[f_71_5]) ).
cnf(f_71_8,plain,
( ~ hBOOL(hAPP(hAPP(U_394,sK11(U_394,U_393,U_392,U_391,U_390,U_389)),sK12(U_394,U_393,U_392,U_391,U_390,U_389)))
| ~ sP16(U_389,U_390,U_391,U_392,U_393,U_394) ),
inference(clausify,[status(thm)],[f_71_5]) ).
fof(f_72_1,plain,
! [V_R_2,V_d_2,V_Qa_2,V_c_2,V_Pa_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Qa_2),V_d_2),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_Comp]) ).
fof(f_72_2,plain,
! [U_401,U_400,U_399,U_398,U_397,U_396,U_395] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_395,U_396,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_395)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_395),U_397),c_Com_Ocom_OSemi(U_398,U_400)),U_401)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_395),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_395,U_396,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_395)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_395),U_399),U_400),U_401)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_395),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_395,U_396,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_395)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_395),U_397),U_398),U_399)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_395),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_395,U_397,U_396,U_398,U_399,U_400,U_401] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_395,U_396,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_395)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_395),U_397),c_Com_Ocom_OSemi(U_398,U_400)),U_401)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_395),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_395,U_396,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_395)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_395),U_399),U_400),U_401)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_395),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_395,U_396,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_395)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_395),U_397),U_398),U_399)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_395),tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_72_2]) ).
cnf(f_72_4,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_395,U_396,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_395)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_395),U_397),c_Com_Ocom_OSemi(U_398,U_400)),U_401)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_395),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_395,U_396,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_395)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_395),U_399),U_400),U_401)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_395),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_395,U_396,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_395)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_395),U_397),U_398),U_399)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_395),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_73_1,plain,
! [V_X_2,T_c] : c_Set_Othe__elem(T_c,V_X_2) = c_HOL_OThe(T_c,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),hAPP(c_fequal,V_X_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_the__elem__def]) ).
fof(f_73_2,plain,
! [U_403,U_402] : c_Set_Othe__elem(U_402,U_403) = c_HOL_OThe(U_402,hAPP(hAPP(c_COMBB(tc_fun(U_402,tc_HOL_Obool),tc_HOL_Obool,U_402),hAPP(c_fequal,U_403)),hAPP(hAPP(c_COMBC(U_402,tc_fun(U_402,tc_HOL_Obool),tc_fun(U_402,tc_HOL_Obool)),c_Set_Oinsert(U_402)),c_Orderings_Obot__class_Obot(tc_fun(U_402,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_403,U_402] : c_Set_Othe__elem(U_402,U_403) = c_HOL_OThe(U_402,hAPP(hAPP(c_COMBB(tc_fun(U_402,tc_HOL_Obool),tc_HOL_Obool,U_402),hAPP(c_fequal,U_403)),hAPP(hAPP(c_COMBC(U_402,tc_fun(U_402,tc_HOL_Obool),tc_fun(U_402,tc_HOL_Obool)),c_Set_Oinsert(U_402)),c_Orderings_Obot__class_Obot(tc_fun(U_402,tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_73_2]) ).
cnf(f_73_4,plain,
c_Set_Othe__elem(U_402,U_403) = c_HOL_OThe(U_402,hAPP(hAPP(c_COMBB(tc_fun(U_402,tc_HOL_Obool),tc_HOL_Obool,U_402),hAPP(c_fequal,U_403)),hAPP(hAPP(c_COMBC(U_402,tc_fun(U_402,tc_HOL_Obool),tc_fun(U_402,tc_HOL_Obool)),c_Set_Oinsert(U_402)),c_Orderings_Obot__class_Obot(tc_fun(U_402,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_73_3]) ).
fof(f_74_1,plain,
! [V_c_2,V_b_2,V_Pa_2,V_Ga_2,T_c] : c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_c),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_Pa_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_LoopF]) ).
fof(f_74_2,plain,
! [U_408,U_407,U_406,U_405,U_404] : c_Hoare__Mirabelle_Ohoare__derivs(U_404,U_405,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_404)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_404),hAPP(hAPP(c_COMBC(U_404,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_404),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_404),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_406))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_407))),c_Com_Ocom_OWhile(U_407,U_408)),U_406)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_404),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_404,U_405,U_406,U_407,U_408] : c_Hoare__Mirabelle_Ohoare__derivs(U_404,U_405,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_404)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_404),hAPP(hAPP(c_COMBC(U_404,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_404),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_404),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_406))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_407))),c_Com_Ocom_OWhile(U_407,U_408)),U_406)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_404),tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_74_2]) ).
cnf(f_74_4,plain,
c_Hoare__Mirabelle_Ohoare__derivs(U_404,U_405,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_404)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_404),hAPP(hAPP(c_COMBC(U_404,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),U_404),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_404),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_406))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_407))),c_Com_Ocom_OWhile(U_407,U_408)),U_406)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_404),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
! [V_N_2,V_h_2,V_F_2,V_f_2,T_c] :
( hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute]) ).
fof(f_75_2,plain,
! [U_415,U_414,U_413,U_412,U_411] :
( hAPP(U_414,hAPP(U_413,U_415)) = hAPP(U_413,hAPP(c_Set_Oimage(U_411,U_411,U_414),U_415))
| U_415 = c_Orderings_Obot__class_Obot(tc_fun(U_411,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_411),U_415))
| ? [U_410,U_409] : hAPP(U_414,hAPP(hAPP(U_412,U_410),U_409)) != hAPP(hAPP(U_412,hAPP(U_414,U_410)),hAPP(U_414,U_409))
| ~ c_Finite__Set_Ofolding__one__idem(U_411,U_412,U_413) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
! [U_415,U_414,U_413,U_412,U_411] :
( hAPP(U_414,hAPP(U_413,U_415)) = hAPP(U_413,hAPP(c_Set_Oimage(U_411,U_411,U_414),U_415))
| U_415 = c_Orderings_Obot__class_Obot(tc_fun(U_411,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_411),U_415))
| ? [U_409] : hAPP(U_414,hAPP(hAPP(U_412,sK13(U_415,U_414,U_413,U_412,U_411)),U_409)) != hAPP(hAPP(U_412,hAPP(U_414,sK13(U_415,U_414,U_413,U_412,U_411))),hAPP(U_414,U_409))
| ~ c_Finite__Set_Ofolding__one__idem(U_411,U_412,U_413) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_410,sK13(U_415,U_414,U_413,U_412,U_411))],[f_75_2]) ).
fof(f_75_4,plain,
! [U_415,U_414,U_413,U_412,U_411] :
( hAPP(U_414,hAPP(U_413,U_415)) = hAPP(U_413,hAPP(c_Set_Oimage(U_411,U_411,U_414),U_415))
| U_415 = c_Orderings_Obot__class_Obot(tc_fun(U_411,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_411),U_415))
| hAPP(U_414,hAPP(hAPP(U_412,sK13(U_415,U_414,U_413,U_412,U_411)),sK14(U_415,U_414,U_413,U_412,U_411))) != hAPP(hAPP(U_412,hAPP(U_414,sK13(U_415,U_414,U_413,U_412,U_411))),hAPP(U_414,sK14(U_415,U_414,U_413,U_412,U_411)))
| ~ c_Finite__Set_Ofolding__one__idem(U_411,U_412,U_413) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_409,sK14(U_415,U_414,U_413,U_412,U_411))],[f_75_3]) ).
fof(f_75_5,plain,
! [U_411,U_412,U_413,U_414,U_415] :
( hAPP(U_414,hAPP(U_413,U_415)) = hAPP(U_413,hAPP(c_Set_Oimage(U_411,U_411,U_414),U_415))
| U_415 = c_Orderings_Obot__class_Obot(tc_fun(U_411,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_411),U_415))
| hAPP(U_414,hAPP(hAPP(U_412,sK13(U_415,U_414,U_413,U_412,U_411)),sK14(U_415,U_414,U_413,U_412,U_411))) != hAPP(hAPP(U_412,hAPP(U_414,sK13(U_415,U_414,U_413,U_412,U_411))),hAPP(U_414,sK14(U_415,U_414,U_413,U_412,U_411)))
| ~ c_Finite__Set_Ofolding__one__idem(U_411,U_412,U_413) ),
inference(definitional_conversion,[status(esa)],[f_75_4]) ).
cnf(f_75_6,plain,
( hAPP(U_414,hAPP(U_413,U_415)) = hAPP(U_413,hAPP(c_Set_Oimage(U_411,U_411,U_414),U_415))
| U_415 = c_Orderings_Obot__class_Obot(tc_fun(U_411,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_411),U_415))
| hAPP(U_414,hAPP(hAPP(U_412,sK13(U_415,U_414,U_413,U_412,U_411)),sK14(U_415,U_414,U_413,U_412,U_411))) != hAPP(hAPP(U_412,hAPP(U_414,sK13(U_415,U_414,U_413,U_412,U_411))),hAPP(U_414,sK14(U_415,U_414,U_413,U_412,U_411)))
| ~ c_Finite__Set_Ofolding__one__idem(U_411,U_412,U_413) ),
inference(clausify,[status(thm)],[f_75_5]) ).
fof(f_76_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_d),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_d),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert]) ).
fof(f_76_2,plain,
! [U_423,U_422,U_421,U_420,U_419,U_418,U_417,U_416] :
( hAPP(U_421,hAPP(hAPP(c_Set_Oinsert(U_417),U_423),U_422)) = hAPP(hAPP(U_418,hAPP(U_420,U_423)),hAPP(U_421,U_422))
| hBOOL(hAPP(hAPP(c_member(U_417),U_423),U_422))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_417),U_422))
| ~ c_Finite__Set_Ofolding__image__simple(U_416,U_417,U_418,U_419,U_420,U_421) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
! [U_423,U_422,U_421,U_420,U_419,U_418,U_417] :
( ! [U_416] : ~ c_Finite__Set_Ofolding__image__simple(U_416,U_417,U_418,U_419,U_420,U_421)
| hAPP(U_421,hAPP(hAPP(c_Set_Oinsert(U_417),U_423),U_422)) = hAPP(hAPP(U_418,hAPP(U_420,U_423)),hAPP(U_421,U_422))
| hBOOL(hAPP(hAPP(c_member(U_417),U_423),U_422))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_417),U_422)) ),
inference(miniscope,[status(thm)],[f_76_2]) ).
fof(f_76_4,plain,
! [U_417,U_418,U_416,U_420,U_419,U_421,U_422,U_423] :
( ~ c_Finite__Set_Ofolding__image__simple(U_416,U_417,U_418,U_419,U_420,U_421)
| hAPP(U_421,hAPP(hAPP(c_Set_Oinsert(U_417),U_423),U_422)) = hAPP(hAPP(U_418,hAPP(U_420,U_423)),hAPP(U_421,U_422))
| hBOOL(hAPP(hAPP(c_member(U_417),U_423),U_422))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_417),U_422)) ),
inference(definitional_conversion,[status(esa)],[f_76_3]) ).
cnf(f_76_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_416,U_417,U_418,U_419,U_420,U_421)
| hAPP(U_421,hAPP(hAPP(c_Set_Oinsert(U_417),U_423),U_422)) = hAPP(hAPP(U_418,hAPP(U_420,U_423)),hAPP(U_421,U_422))
| hBOOL(hAPP(hAPP(c_member(U_417),U_423),U_422))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_417),U_422)) ),
inference(clausify,[status(thm)],[f_76_4]) ).
fof(f_77_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] :
( ( ( 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_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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(V_F_2,V_A_2) = V_x_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)))) != 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__one(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oremove]) ).
fof(f_77_2,plain,
! [U_428,U_427,U_426,U_425,U_424] :
( ( ( hAPP(U_426,U_427) = hAPP(hAPP(U_425,U_428),hAPP(U_426,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_424,tc_HOL_Obool)),U_427),hAPP(hAPP(c_Set_Oinsert(U_424),U_428),c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_424,tc_HOL_Obool)),U_427),hAPP(hAPP(c_Set_Oinsert(U_424),U_428),c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool)) )
& ( hAPP(U_426,U_427) = U_428
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_424,tc_HOL_Obool)),U_427),hAPP(hAPP(c_Set_Oinsert(U_424),U_428),c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_424),U_428),U_427))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_424),U_427))
| ~ c_Finite__Set_Ofolding__one(U_424,U_425,U_426) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
( ! [U_424,U_425,U_426,U_427,U_428] :
( hAPP(U_426,U_427) = hAPP(hAPP(U_425,U_428),hAPP(U_426,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_424,tc_HOL_Obool)),U_427),hAPP(hAPP(c_Set_Oinsert(U_424),U_428),c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_424,tc_HOL_Obool)),U_427),hAPP(hAPP(c_Set_Oinsert(U_424),U_428),c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool))
| ~ sP17(U_424,U_425,U_426,U_427,U_428) )
& ! [U_424,U_425,U_426,U_427,U_428] :
( hAPP(U_426,U_427) = U_428
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_424,tc_HOL_Obool)),U_427),hAPP(hAPP(c_Set_Oinsert(U_424),U_428),c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool))
| ~ sP17(U_424,U_425,U_426,U_427,U_428) )
& ! [U_424,U_425,U_426,U_427,U_428] :
( sP17(U_424,U_425,U_426,U_427,U_428)
| ~ hBOOL(hAPP(hAPP(c_member(U_424),U_428),U_427))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_424),U_427))
| ~ c_Finite__Set_Ofolding__one(U_424,U_425,U_426) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_77_2]) ).
cnf(f_77_4,plain,
( sP17(U_424,U_425,U_426,U_427,U_428)
| ~ hBOOL(hAPP(hAPP(c_member(U_424),U_428),U_427))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_424),U_427))
| ~ c_Finite__Set_Ofolding__one(U_424,U_425,U_426) ),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_5,plain,
( hAPP(U_426,U_427) = U_428
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_424,tc_HOL_Obool)),U_427),hAPP(hAPP(c_Set_Oinsert(U_424),U_428),c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool))
| ~ sP17(U_424,U_425,U_426,U_427,U_428) ),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_6,plain,
( hAPP(U_426,U_427) = hAPP(hAPP(U_425,U_428),hAPP(U_426,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_424,tc_HOL_Obool)),U_427),hAPP(hAPP(c_Set_Oinsert(U_424),U_428),c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_424,tc_HOL_Obool)),U_427),hAPP(hAPP(c_Set_Oinsert(U_424),U_428),c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_424,tc_HOL_Obool))
| ~ sP17(U_424,U_425,U_426,U_427,U_428) ),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_d),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_d),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,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_78_2,plain,
! [U_436,U_435,U_434,U_433,U_432,U_431,U_430,U_429] :
( hAPP(U_434,hAPP(hAPP(c_Set_Oinsert(U_430),U_436),U_435)) = hAPP(hAPP(U_431,hAPP(U_433,U_436)),hAPP(U_434,U_435))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_430),U_435))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_429,U_430,U_431,U_432,U_433,U_434) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_436,U_435,U_434,U_433,U_432,U_431,U_430] :
( ! [U_429] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_429,U_430,U_431,U_432,U_433,U_434)
| hAPP(U_434,hAPP(hAPP(c_Set_Oinsert(U_430),U_436),U_435)) = hAPP(hAPP(U_431,hAPP(U_433,U_436)),hAPP(U_434,U_435))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_430),U_435)) ),
inference(miniscope,[status(thm)],[f_78_2]) ).
fof(f_78_4,plain,
! [U_434,U_433,U_432,U_435,U_429,U_431,U_436,U_430] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_429,U_430,U_431,U_432,U_433,U_434)
| hAPP(U_434,hAPP(hAPP(c_Set_Oinsert(U_430),U_436),U_435)) = hAPP(hAPP(U_431,hAPP(U_433,U_436)),hAPP(U_434,U_435))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_430),U_435)) ),
inference(definitional_conversion,[status(esa)],[f_78_3]) ).
cnf(f_78_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_429,U_430,U_431,U_432,U_433,U_434)
| hAPP(U_434,hAPP(hAPP(c_Set_Oinsert(U_430),U_436),U_435)) = hAPP(hAPP(U_431,hAPP(U_433,U_436)),hAPP(U_434,U_435))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_430),U_435)) ),
inference(clausify,[status(thm)],[f_78_4]) ).
fof(f_79_1,plain,
! [V_Pa_2,V_F_2,T_c] :
( hBOOL(hAPP(V_Pa_2,V_F_2))
| ? [B_x,B_F] :
( ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_c),B_x),B_F)))
& hBOOL(hAPP(V_Pa_2,B_F))
& ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),B_F))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_F)) )
| ~ hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__induct]) ).
fof(f_79_2,plain,
! [U_441,U_440,U_439] :
( hBOOL(hAPP(U_441,U_440))
| ? [U_438,U_437] :
( ~ hBOOL(hAPP(U_441,hAPP(hAPP(c_Set_Oinsert(U_439),U_438),U_437)))
& hBOOL(hAPP(U_441,U_437))
& ~ hBOOL(hAPP(hAPP(c_member(U_439),U_438),U_437))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_439),U_437)) )
| ~ hBOOL(hAPP(U_441,c_Orderings_Obot__class_Obot(tc_fun(U_439,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_439),U_440)) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_441,U_440,U_439] :
( hBOOL(hAPP(U_441,U_440))
| ? [U_437] :
( ~ hBOOL(hAPP(U_441,hAPP(hAPP(c_Set_Oinsert(U_439),sK15(U_441,U_440,U_439)),U_437)))
& hBOOL(hAPP(U_441,U_437))
& ~ hBOOL(hAPP(hAPP(c_member(U_439),sK15(U_441,U_440,U_439)),U_437))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_439),U_437)) )
| ~ hBOOL(hAPP(U_441,c_Orderings_Obot__class_Obot(tc_fun(U_439,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_439),U_440)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_438,sK15(U_441,U_440,U_439))],[f_79_2]) ).
fof(f_79_4,plain,
! [U_441,U_440,U_439] :
( hBOOL(hAPP(U_441,U_440))
| ( ~ hBOOL(hAPP(U_441,hAPP(hAPP(c_Set_Oinsert(U_439),sK15(U_441,U_440,U_439)),sK16(U_441,U_440,U_439))))
& hBOOL(hAPP(U_441,sK16(U_441,U_440,U_439)))
& ~ hBOOL(hAPP(hAPP(c_member(U_439),sK15(U_441,U_440,U_439)),sK16(U_441,U_440,U_439)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_439),sK16(U_441,U_440,U_439))) )
| ~ hBOOL(hAPP(U_441,c_Orderings_Obot__class_Obot(tc_fun(U_439,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_439),U_440)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_437,sK16(U_441,U_440,U_439))],[f_79_3]) ).
fof(f_79_5,plain,
( ! [U_439,U_440,U_441] :
( ~ hBOOL(hAPP(U_441,hAPP(hAPP(c_Set_Oinsert(U_439),sK15(U_441,U_440,U_439)),sK16(U_441,U_440,U_439))))
| ~ sP18(U_439,U_440,U_441) )
& ! [U_439,U_440,U_441] :
( hBOOL(hAPP(U_441,sK16(U_441,U_440,U_439)))
| ~ sP18(U_439,U_440,U_441) )
& ! [U_439,U_440,U_441] :
( ~ hBOOL(hAPP(hAPP(c_member(U_439),sK15(U_441,U_440,U_439)),sK16(U_441,U_440,U_439)))
| ~ sP18(U_439,U_440,U_441) )
& ! [U_439,U_440,U_441] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_439),sK16(U_441,U_440,U_439)))
| ~ sP18(U_439,U_440,U_441) )
& ! [U_439,U_440,U_441] :
( hBOOL(hAPP(U_441,U_440))
| sP18(U_439,U_440,U_441)
| ~ hBOOL(hAPP(U_441,c_Orderings_Obot__class_Obot(tc_fun(U_439,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_439),U_440)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_79_4]) ).
cnf(f_79_6,plain,
( hBOOL(hAPP(U_441,U_440))
| sP18(U_439,U_440,U_441)
| ~ hBOOL(hAPP(U_441,c_Orderings_Obot__class_Obot(tc_fun(U_439,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_439),U_440)) ),
inference(clausify,[status(thm)],[f_79_5]) ).
cnf(f_79_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_439),sK16(U_441,U_440,U_439)))
| ~ sP18(U_439,U_440,U_441) ),
inference(clausify,[status(thm)],[f_79_5]) ).
cnf(f_79_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_439),sK15(U_441,U_440,U_439)),sK16(U_441,U_440,U_439)))
| ~ sP18(U_439,U_440,U_441) ),
inference(clausify,[status(thm)],[f_79_5]) ).
cnf(f_79_9,plain,
( hBOOL(hAPP(U_441,sK16(U_441,U_440,U_439)))
| ~ sP18(U_439,U_440,U_441) ),
inference(clausify,[status(thm)],[f_79_5]) ).
cnf(f_79_10,plain,
( ~ hBOOL(hAPP(U_441,hAPP(hAPP(c_Set_Oinsert(U_439),sK15(U_441,U_440,U_439)),sK16(U_441,U_440,U_439))))
| ~ sP18(U_439,U_440,U_441) ),
inference(clausify,[status(thm)],[f_79_5]) ).
fof(f_80_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( 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_d),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,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_80_2,plain,
! [U_449,U_448,U_447,U_446,U_445,U_444,U_443,U_442] :
( hAPP(hAPP(U_444,hAPP(U_446,U_449)),hAPP(U_447,U_448)) = hAPP(U_447,U_448)
| ~ hBOOL(hAPP(hAPP(c_member(U_443),U_449),U_448))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_443),U_448))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_442,U_443,U_444,U_445,U_446,U_447) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
! [U_449,U_448,U_447,U_446,U_445,U_444,U_443] :
( ! [U_442] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_442,U_443,U_444,U_445,U_446,U_447)
| hAPP(hAPP(U_444,hAPP(U_446,U_449)),hAPP(U_447,U_448)) = hAPP(U_447,U_448)
| ~ hBOOL(hAPP(hAPP(c_member(U_443),U_449),U_448))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_443),U_448)) ),
inference(miniscope,[status(thm)],[f_80_2]) ).
fof(f_80_4,plain,
! [U_449,U_446,U_442,U_444,U_443,U_447,U_445,U_448] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_442,U_443,U_444,U_445,U_446,U_447)
| hAPP(hAPP(U_444,hAPP(U_446,U_449)),hAPP(U_447,U_448)) = hAPP(U_447,U_448)
| ~ hBOOL(hAPP(hAPP(c_member(U_443),U_449),U_448))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_443),U_448)) ),
inference(definitional_conversion,[status(esa)],[f_80_3]) ).
cnf(f_80_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_442,U_443,U_444,U_445,U_446,U_447)
| hAPP(hAPP(U_444,hAPP(U_446,U_449)),hAPP(U_447,U_448)) = hAPP(U_447,U_448)
| ~ hBOOL(hAPP(hAPP(c_member(U_443),U_449),U_448))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_443),U_448)) ),
inference(clausify,[status(thm)],[f_80_4]) ).
fof(f_81_1,plain,
! [V_Y_2,T_c] : hAPP(c_Set_Oimage(T_c,T_c,c_COMBI(T_c)),V_Y_2) = V_Y_2,
inference(fof_nnf,[status(thm)],[fact_image__ident]) ).
fof(f_81_2,plain,
! [U_451,U_450] : hAPP(c_Set_Oimage(U_450,U_450,c_COMBI(U_450)),U_451) = U_451,
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_450,U_451] : hAPP(c_Set_Oimage(U_450,U_450,c_COMBI(U_450)),U_451) = U_451,
inference(definitional_conversion,[status(esa)],[f_81_2]) ).
cnf(f_81_4,plain,
hAPP(c_Set_Oimage(U_450,U_450,c_COMBI(U_450)),U_451) = U_451,
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_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_DiffE]) ).
fof(f_82_2,plain,
! [U_455,U_454,U_453,U_452] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_452),U_453),U_455))
& hBOOL(hAPP(hAPP(c_member(U_452),U_453),U_454)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_452),U_453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_452,tc_HOL_Obool)),U_454),U_455))) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
( ! [U_453,U_454,U_455,U_452] :
( ~ hBOOL(hAPP(hAPP(c_member(U_452),U_453),U_455))
| ~ sP19(U_453,U_454,U_455,U_452) )
& ! [U_453,U_454,U_455,U_452] :
( hBOOL(hAPP(hAPP(c_member(U_452),U_453),U_454))
| ~ sP19(U_453,U_454,U_455,U_452) )
& ! [U_453,U_454,U_455,U_452] :
( sP19(U_453,U_454,U_455,U_452)
| ~ hBOOL(hAPP(hAPP(c_member(U_452),U_453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_452,tc_HOL_Obool)),U_454),U_455))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_82_2]) ).
cnf(f_82_4,plain,
( sP19(U_453,U_454,U_455,U_452)
| ~ hBOOL(hAPP(hAPP(c_member(U_452),U_453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_452,tc_HOL_Obool)),U_454),U_455))) ),
inference(clausify,[status(thm)],[f_82_3]) ).
cnf(f_82_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_452),U_453),U_454))
| ~ sP19(U_453,U_454,U_455,U_452) ),
inference(clausify,[status(thm)],[f_82_3]) ).
cnf(f_82_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_452),U_453),U_455))
| ~ sP19(U_453,U_454,U_455,U_452) ),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_DiffI]) ).
fof(f_83_2,plain,
! [U_459,U_458,U_457,U_456] :
( hBOOL(hAPP(hAPP(c_member(U_456),U_457),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_456,tc_HOL_Obool)),U_458),U_459)))
| hBOOL(hAPP(hAPP(c_member(U_456),U_457),U_459))
| ~ hBOOL(hAPP(hAPP(c_member(U_456),U_457),U_458)) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_456,U_457,U_458,U_459] :
( hBOOL(hAPP(hAPP(c_member(U_456),U_457),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_456,tc_HOL_Obool)),U_458),U_459)))
| hBOOL(hAPP(hAPP(c_member(U_456),U_457),U_459))
| ~ hBOOL(hAPP(hAPP(c_member(U_456),U_457),U_458)) ),
inference(definitional_conversion,[status(esa)],[f_83_2]) ).
cnf(f_83_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_456),U_457),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_456,tc_HOL_Obool)),U_458),U_459)))
| hBOOL(hAPP(hAPP(c_member(U_456),U_457),U_459))
| ~ hBOOL(hAPP(hAPP(c_member(U_456),U_457),U_458)) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Diff]) ).
fof(f_84_2,plain,
! [U_462,U_461,U_460] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_460,tc_HOL_Obool)),U_461),U_462)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_460),U_461)) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
! [U_460,U_461,U_462] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_460,tc_HOL_Obool)),U_461),U_462)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_460),U_461)) ),
inference(definitional_conversion,[status(esa)],[f_84_2]) ).
cnf(f_84_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_460,tc_HOL_Obool)),U_461),U_462)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_460),U_461)) ),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_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_Diff__idemp]) ).
fof(f_85_2,plain,
! [U_465,U_464,U_463] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),U_464),U_465)),U_465) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),U_464),U_465),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_463,U_464,U_465] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),U_464),U_465)),U_465) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),U_464),U_465),
inference(definitional_conversion,[status(esa)],[f_85_2]) ).
cnf(f_85_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),U_464),U_465)),U_465) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_463,tc_HOL_Obool)),U_464),U_465),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,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_86_2,plain,
! [U_472,U_471,U_470,U_469,U_468,U_467,U_466] :
( hAPP(hAPP(U_468,U_472),U_472) = U_472
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_466,U_467,U_468,U_469,U_470,U_471) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_472,U_471,U_470,U_469,U_468] :
( ! [U_467,U_466] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_466,U_467,U_468,U_469,U_470,U_471)
| hAPP(hAPP(U_468,U_472),U_472) = U_472 ),
inference(miniscope,[status(thm)],[f_86_2]) ).
fof(f_86_4,plain,
! [U_466,U_468,U_467,U_469,U_470,U_471,U_472] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_466,U_467,U_468,U_469,U_470,U_471)
| hAPP(hAPP(U_468,U_472),U_472) = U_472 ),
inference(definitional_conversion,[status(esa)],[f_86_3]) ).
cnf(f_86_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_466,U_467,U_468,U_469,U_470,U_471)
| hAPP(hAPP(U_468,U_472),U_472) = U_472 ),
inference(clausify,[status(thm)],[f_86_4]) ).
fof(f_87_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_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_DiffD2]) ).
fof(f_87_2,plain,
! [U_476,U_475,U_474,U_473] :
( ~ hBOOL(hAPP(hAPP(c_member(U_473),U_474),U_476))
| ~ hBOOL(hAPP(hAPP(c_member(U_473),U_474),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_473,tc_HOL_Obool)),U_475),U_476))) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_473,U_474,U_475,U_476] :
( ~ hBOOL(hAPP(hAPP(c_member(U_473),U_474),U_476))
| ~ hBOOL(hAPP(hAPP(c_member(U_473),U_474),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_473,tc_HOL_Obool)),U_475),U_476))) ),
inference(definitional_conversion,[status(esa)],[f_87_2]) ).
cnf(f_87_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_473),U_474),U_476))
| ~ hBOOL(hAPP(hAPP(c_member(U_473),U_474),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_473,tc_HOL_Obool)),U_475),U_476))) ),
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_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_DiffD1]) ).
fof(f_88_2,plain,
! [U_480,U_479,U_478,U_477] :
( hBOOL(hAPP(hAPP(c_member(U_477),U_478),U_479))
| ~ hBOOL(hAPP(hAPP(c_member(U_477),U_478),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_477,tc_HOL_Obool)),U_479),U_480))) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_477,U_478,U_479,U_480] :
( hBOOL(hAPP(hAPP(c_member(U_477),U_478),U_479))
| ~ hBOOL(hAPP(hAPP(c_member(U_477),U_478),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_477,tc_HOL_Obool)),U_479),U_480))) ),
inference(definitional_conversion,[status(esa)],[f_88_2]) ).
cnf(f_88_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_477),U_478),U_479))
| ~ hBOOL(hAPP(hAPP(c_member(U_477),U_478),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_477,tc_HOL_Obool)),U_479),U_480))) ),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_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_Diff__iff]) ).
fof(f_89_2,plain,
! [U_484,U_483,U_482,U_481] :
( ( hBOOL(hAPP(hAPP(c_member(U_481),U_482),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_481,tc_HOL_Obool)),U_483),U_484)))
| hBOOL(hAPP(hAPP(c_member(U_481),U_482),U_484))
| ~ hBOOL(hAPP(hAPP(c_member(U_481),U_482),U_483)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(U_481),U_482),U_484))
& hBOOL(hAPP(hAPP(c_member(U_481),U_482),U_483)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_481),U_482),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_481,tc_HOL_Obool)),U_483),U_484))) ) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
( ! [U_492,U_490,U_488,U_486] :
( hBOOL(hAPP(hAPP(c_member(U_486),U_488),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_486,tc_HOL_Obool)),U_490),U_492)))
| hBOOL(hAPP(hAPP(c_member(U_486),U_488),U_492))
| ~ hBOOL(hAPP(hAPP(c_member(U_486),U_488),U_490)) )
& ! [U_491,U_489,U_487,U_485] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_485),U_487),U_491))
& hBOOL(hAPP(hAPP(c_member(U_485),U_487),U_489)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_485),U_487),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_485,tc_HOL_Obool)),U_489),U_491))) ) ),
inference(miniscope,[status(thm)],[f_89_2]) ).
fof(f_89_4,plain,
( ! [U_487,U_491,U_485,U_489] :
( ~ hBOOL(hAPP(hAPP(c_member(U_485),U_487),U_491))
| ~ sP20(U_487,U_491,U_485,U_489) )
& ! [U_487,U_491,U_485,U_489] :
( hBOOL(hAPP(hAPP(c_member(U_485),U_487),U_489))
| ~ sP20(U_487,U_491,U_485,U_489) )
& ! [U_488,U_486,U_492,U_490] :
( hBOOL(hAPP(hAPP(c_member(U_486),U_488),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_486,tc_HOL_Obool)),U_490),U_492)))
| hBOOL(hAPP(hAPP(c_member(U_486),U_488),U_492))
| ~ hBOOL(hAPP(hAPP(c_member(U_486),U_488),U_490)) )
& ! [U_487,U_491,U_485,U_489] :
( sP20(U_487,U_491,U_485,U_489)
| ~ hBOOL(hAPP(hAPP(c_member(U_485),U_487),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_485,tc_HOL_Obool)),U_489),U_491))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_89_3]) ).
cnf(f_89_5,plain,
( sP20(U_487,U_491,U_485,U_489)
| ~ hBOOL(hAPP(hAPP(c_member(U_485),U_487),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_485,tc_HOL_Obool)),U_489),U_491))) ),
inference(clausify,[status(thm)],[f_89_4]) ).
cnf(f_89_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_486),U_488),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_486,tc_HOL_Obool)),U_490),U_492)))
| hBOOL(hAPP(hAPP(c_member(U_486),U_488),U_492))
| ~ hBOOL(hAPP(hAPP(c_member(U_486),U_488),U_490)) ),
inference(clausify,[status(thm)],[f_89_4]) ).
cnf(f_89_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_485),U_487),U_489))
| ~ sP20(U_487,U_491,U_485,U_489) ),
inference(clausify,[status(thm)],[f_89_4]) ).
cnf(f_89_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_485),U_487),U_491))
| ~ sP20(U_487,U_491,U_485,U_489) ),
inference(clausify,[status(thm)],[f_89_4]) ).
fof(f_90_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Diff__cancel]) ).
fof(f_90_2,plain,
! [U_494,U_493] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_493,tc_HOL_Obool)),U_494),U_494) = c_Orderings_Obot__class_Obot(tc_fun(U_493,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_494,U_493] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_493,tc_HOL_Obool)),U_494),U_494) = c_Orderings_Obot__class_Obot(tc_fun(U_493,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_90_2]) ).
cnf(f_90_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_493,tc_HOL_Obool)),U_494),U_494) = c_Orderings_Obot__class_Obot(tc_fun(U_493,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Diff__empty]) ).
fof(f_91_2,plain,
! [U_496,U_495] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_495,tc_HOL_Obool)),U_496),c_Orderings_Obot__class_Obot(tc_fun(U_495,tc_HOL_Obool))) = U_496,
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
! [U_495,U_496] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_495,tc_HOL_Obool)),U_496),c_Orderings_Obot__class_Obot(tc_fun(U_495,tc_HOL_Obool))) = U_496,
inference(definitional_conversion,[status(esa)],[f_91_2]) ).
cnf(f_91_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_495,tc_HOL_Obool)),U_496),c_Orderings_Obot__class_Obot(tc_fun(U_495,tc_HOL_Obool))) = U_496,
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_92_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),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)),
inference(fof_nnf,[status(thm)],[fact_empty__Diff]) ).
fof(f_92_2,plain,
! [U_498,U_497] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_497,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_497,tc_HOL_Obool))),U_498) = c_Orderings_Obot__class_Obot(tc_fun(U_497,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_497,U_498] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_497,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_497,tc_HOL_Obool))),U_498) = c_Orderings_Obot__class_Obot(tc_fun(U_497,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_92_2]) ).
cnf(f_92_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_497,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_497,tc_HOL_Obool))),U_498) = c_Orderings_Obot__class_Obot(tc_fun(U_497,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
! [V_A_2,V_B_2,T_c] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Diff2]) ).
fof(f_93_2,plain,
! [U_501,U_500,U_499] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_499,tc_HOL_Obool)),U_501),U_500)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),U_501)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),U_501))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_499,tc_HOL_Obool)),U_501),U_500))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),U_500)) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
( ! [U_499,U_500,U_501] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_499,tc_HOL_Obool)),U_501),U_500)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),U_501))
| ~ sP21(U_499,U_500,U_501) )
& ! [U_499,U_500,U_501] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),U_501))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_499,tc_HOL_Obool)),U_501),U_500)))
| ~ sP21(U_499,U_500,U_501) )
& ! [U_499,U_500,U_501] :
( sP21(U_499,U_500,U_501)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),U_500)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_93_2]) ).
cnf(f_93_4,plain,
( sP21(U_499,U_500,U_501)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),U_500)) ),
inference(clausify,[status(thm)],[f_93_3]) ).
cnf(f_93_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),U_501))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_499,tc_HOL_Obool)),U_501),U_500)))
| ~ sP21(U_499,U_500,U_501) ),
inference(clausify,[status(thm)],[f_93_3]) ).
cnf(f_93_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_499,tc_HOL_Obool)),U_501),U_500)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_499),U_501))
| ~ sP21(U_499,U_500,U_501) ),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_d),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_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_c,T_d,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_94_2,plain,
! [U_509,U_508,U_507,U_506,U_505,U_504,U_503,U_502] :
( hAPP(U_507,hAPP(hAPP(c_Set_Oinsert(U_503),U_509),U_508)) = hAPP(hAPP(U_504,hAPP(U_506,U_509)),hAPP(U_507,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_503,tc_HOL_Obool)),U_508),hAPP(hAPP(c_Set_Oinsert(U_503),U_509),c_Orderings_Obot__class_Obot(tc_fun(U_503,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_503),U_508))
| ~ c_Finite__Set_Ofolding__image__simple(U_502,U_503,U_504,U_505,U_506,U_507) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_509,U_508,U_507,U_506,U_505,U_504,U_503] :
( ! [U_502] : ~ c_Finite__Set_Ofolding__image__simple(U_502,U_503,U_504,U_505,U_506,U_507)
| hAPP(U_507,hAPP(hAPP(c_Set_Oinsert(U_503),U_509),U_508)) = hAPP(hAPP(U_504,hAPP(U_506,U_509)),hAPP(U_507,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_503,tc_HOL_Obool)),U_508),hAPP(hAPP(c_Set_Oinsert(U_503),U_509),c_Orderings_Obot__class_Obot(tc_fun(U_503,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_503),U_508)) ),
inference(miniscope,[status(thm)],[f_94_2]) ).
fof(f_94_4,plain,
! [U_502,U_503,U_504,U_505,U_506,U_507,U_508,U_509] :
( ~ c_Finite__Set_Ofolding__image__simple(U_502,U_503,U_504,U_505,U_506,U_507)
| hAPP(U_507,hAPP(hAPP(c_Set_Oinsert(U_503),U_509),U_508)) = hAPP(hAPP(U_504,hAPP(U_506,U_509)),hAPP(U_507,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_503,tc_HOL_Obool)),U_508),hAPP(hAPP(c_Set_Oinsert(U_503),U_509),c_Orderings_Obot__class_Obot(tc_fun(U_503,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_503),U_508)) ),
inference(definitional_conversion,[status(esa)],[f_94_3]) ).
cnf(f_94_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_502,U_503,U_504,U_505,U_506,U_507)
| hAPP(U_507,hAPP(hAPP(c_Set_Oinsert(U_503),U_509),U_508)) = hAPP(hAPP(U_504,hAPP(U_506,U_509)),hAPP(U_507,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_503,tc_HOL_Obool)),U_508),hAPP(hAPP(c_Set_Oinsert(U_503),U_509),c_Orderings_Obot__class_Obot(tc_fun(U_503,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_503),U_508)) ),
inference(clausify,[status(thm)],[f_94_4]) ).
fof(f_95_1,plain,
! [V_A_2,V_B_2,V_x_2,T_c] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__Diff1]) ).
fof(f_95_2,plain,
! [U_513,U_512,U_511,U_510] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_510,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_510),U_511),U_513)),U_512) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_510,tc_HOL_Obool)),U_513),U_512)
| ~ hBOOL(hAPP(hAPP(c_member(U_510),U_511),U_512)) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_510,U_511,U_512,U_513] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_510,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_510),U_511),U_513)),U_512) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_510,tc_HOL_Obool)),U_513),U_512)
| ~ hBOOL(hAPP(hAPP(c_member(U_510),U_511),U_512)) ),
inference(definitional_conversion,[status(esa)],[f_95_2]) ).
cnf(f_95_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_510,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_510),U_511),U_513)),U_512) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_510,tc_HOL_Obool)),U_513),U_512)
| ~ hBOOL(hAPP(hAPP(c_member(U_510),U_511),U_512)) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_1,plain,
! [V_A_2,V_B_2,V_x_2,T_c] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__Diff__if]) ).
fof(f_96_2,plain,
! [U_517,U_516,U_515,U_514] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_514,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_514),U_515),U_517)),U_516) = hAPP(hAPP(c_Set_Oinsert(U_514),U_515),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_514,tc_HOL_Obool)),U_517),U_516))
| hBOOL(hAPP(hAPP(c_member(U_514),U_515),U_516)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_514,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_514),U_515),U_517)),U_516) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_514,tc_HOL_Obool)),U_517),U_516)
| ~ hBOOL(hAPP(hAPP(c_member(U_514),U_515),U_516)) ) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
( ! [U_525,U_523,U_521,U_519] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_519,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_519),U_521),U_525)),U_523) = hAPP(hAPP(c_Set_Oinsert(U_519),U_521),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_519,tc_HOL_Obool)),U_525),U_523))
| hBOOL(hAPP(hAPP(c_member(U_519),U_521),U_523)) )
& ! [U_524,U_522,U_520,U_518] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_518,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_518),U_520),U_524)),U_522) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_518,tc_HOL_Obool)),U_524),U_522)
| ~ hBOOL(hAPP(hAPP(c_member(U_518),U_520),U_522)) ) ),
inference(miniscope,[status(thm)],[f_96_2]) ).
fof(f_96_4,plain,
( ! [U_519,U_521,U_523,U_525] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_519,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_519),U_521),U_525)),U_523) = hAPP(hAPP(c_Set_Oinsert(U_519),U_521),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_519,tc_HOL_Obool)),U_525),U_523))
| hBOOL(hAPP(hAPP(c_member(U_519),U_521),U_523)) )
& ! [U_522,U_520,U_524,U_518] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_518,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_518),U_520),U_524)),U_522) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_518,tc_HOL_Obool)),U_524),U_522)
| ~ hBOOL(hAPP(hAPP(c_member(U_518),U_520),U_522)) ) ),
inference(definitional_conversion,[status(esa)],[f_96_3]) ).
cnf(f_96_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_518,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_518),U_520),U_524)),U_522) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_518,tc_HOL_Obool)),U_524),U_522)
| ~ hBOOL(hAPP(hAPP(c_member(U_518),U_520),U_522)) ),
inference(clausify,[status(thm)],[f_96_4]) ).
cnf(f_96_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_519,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_519),U_521),U_525)),U_523) = hAPP(hAPP(c_Set_Oinsert(U_519),U_521),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_519,tc_HOL_Obool)),U_525),U_523))
| hBOOL(hAPP(hAPP(c_member(U_519),U_521),U_523)) ),
inference(clausify,[status(thm)],[f_96_4]) ).
fof(f_97_1,plain,
! [V_A_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_insert__Diff__single]) ).
fof(f_97_2,plain,
! [U_528,U_527,U_526] : hAPP(hAPP(c_Set_Oinsert(U_526),U_527),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_526,tc_HOL_Obool)),U_528),hAPP(hAPP(c_Set_Oinsert(U_526),U_527),c_Orderings_Obot__class_Obot(tc_fun(U_526,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_526),U_527),U_528),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
! [U_526,U_527,U_528] : hAPP(hAPP(c_Set_Oinsert(U_526),U_527),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_526,tc_HOL_Obool)),U_528),hAPP(hAPP(c_Set_Oinsert(U_526),U_527),c_Orderings_Obot__class_Obot(tc_fun(U_526,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_526),U_527),U_528),
inference(definitional_conversion,[status(esa)],[f_97_2]) ).
cnf(f_97_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_526),U_527),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_526,tc_HOL_Obool)),U_528),hAPP(hAPP(c_Set_Oinsert(U_526),U_527),c_Orderings_Obot__class_Obot(tc_fun(U_526,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_526),U_527),U_528),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_1,plain,
! [V_B_2,V_a_2,V_A_2,T_c] : 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_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Diff__insert2]) ).
fof(f_98_2,plain,
! [U_532,U_531,U_530,U_529] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_529,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_529),U_531),U_532)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_529,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_529,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_529),U_531),c_Orderings_Obot__class_Obot(tc_fun(U_529,tc_HOL_Obool))))),U_532),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_529,U_530,U_531,U_532] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_529,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_529),U_531),U_532)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_529,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_529,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_529),U_531),c_Orderings_Obot__class_Obot(tc_fun(U_529,tc_HOL_Obool))))),U_532),
inference(definitional_conversion,[status(esa)],[f_98_2]) ).
cnf(f_98_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_529,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_529),U_531),U_532)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_529,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_529,tc_HOL_Obool)),U_530),hAPP(hAPP(c_Set_Oinsert(U_529),U_531),c_Orderings_Obot__class_Obot(tc_fun(U_529,tc_HOL_Obool))))),U_532),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_1,plain,
! [V_B_2,V_a_2,V_A_2,T_c] : 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_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_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)))),
inference(fof_nnf,[status(thm)],[fact_Diff__insert]) ).
fof(f_99_2,plain,
! [U_536,U_535,U_534,U_533] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_533,tc_HOL_Obool)),U_534),hAPP(hAPP(c_Set_Oinsert(U_533),U_535),U_536)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_533,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_533,tc_HOL_Obool)),U_534),U_536)),hAPP(hAPP(c_Set_Oinsert(U_533),U_535),c_Orderings_Obot__class_Obot(tc_fun(U_533,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_533,U_534,U_535,U_536] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_533,tc_HOL_Obool)),U_534),hAPP(hAPP(c_Set_Oinsert(U_533),U_535),U_536)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_533,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_533,tc_HOL_Obool)),U_534),U_536)),hAPP(hAPP(c_Set_Oinsert(U_533),U_535),c_Orderings_Obot__class_Obot(tc_fun(U_533,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_99_2]) ).
cnf(f_99_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_533,tc_HOL_Obool)),U_534),hAPP(hAPP(c_Set_Oinsert(U_533),U_535),U_536)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_533,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_533,tc_HOL_Obool)),U_534),U_536)),hAPP(hAPP(c_Set_Oinsert(U_533),U_535),c_Orderings_Obot__class_Obot(tc_fun(U_533,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
! [V_B_2,V_a_2,V_A_2,T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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_a_2),V_B_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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_a_2),V_B_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert]) ).
fof(f_100_2,plain,
! [U_540,U_539,U_538,U_537] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_537),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_537,tc_HOL_Obool)),U_538),hAPP(hAPP(c_Set_Oinsert(U_537),U_539),U_540))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_537),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_537,tc_HOL_Obool)),U_538),U_540))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_537),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_537,tc_HOL_Obool)),U_538),U_540)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_537),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_537,tc_HOL_Obool)),U_538),hAPP(hAPP(c_Set_Oinsert(U_537),U_539),U_540)))) ) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
( ! [U_548,U_546,U_544,U_542] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_542),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_542,tc_HOL_Obool)),U_544),hAPP(hAPP(c_Set_Oinsert(U_542),U_546),U_548))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_542),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_542,tc_HOL_Obool)),U_544),U_548))) )
& ! [U_547,U_545,U_543,U_541] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_541),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_541,tc_HOL_Obool)),U_543),U_547)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_541),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_541,tc_HOL_Obool)),U_543),hAPP(hAPP(c_Set_Oinsert(U_541),U_545),U_547)))) ) ),
inference(miniscope,[status(thm)],[f_100_2]) ).
fof(f_100_4,plain,
( ! [U_542,U_544,U_546,U_548] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_542),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_542,tc_HOL_Obool)),U_544),hAPP(hAPP(c_Set_Oinsert(U_542),U_546),U_548))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_542),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_542,tc_HOL_Obool)),U_544),U_548))) )
& ! [U_547,U_543,U_541,U_545] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_541),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_541,tc_HOL_Obool)),U_543),U_547)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_541),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_541,tc_HOL_Obool)),U_543),hAPP(hAPP(c_Set_Oinsert(U_541),U_545),U_547)))) ) ),
inference(definitional_conversion,[status(esa)],[f_100_3]) ).
cnf(f_100_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_541),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_541,tc_HOL_Obool)),U_543),U_547)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_541),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_541,tc_HOL_Obool)),U_543),hAPP(hAPP(c_Set_Oinsert(U_541),U_545),U_547)))) ),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_542),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_542,tc_HOL_Obool)),U_544),hAPP(hAPP(c_Set_Oinsert(U_542),U_546),U_548))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_542),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_542,tc_HOL_Obool)),U_544),U_548))) ),
inference(clausify,[status(thm)],[f_100_4]) ).
fof(f_101_1,plain,
! [V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = V_z_2
| ~ c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty]) ).
fof(f_101_2,plain,
! [U_554,U_553,U_552,U_551,U_550,U_549] :
( hAPP(U_554,c_Orderings_Obot__class_Obot(tc_fun(U_550,tc_HOL_Obool))) = U_552
| ~ c_Finite__Set_Ofolding__image__simple(U_549,U_550,U_551,U_552,U_553,U_554) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_554,U_553,U_552,U_551,U_550] :
( ! [U_549] : ~ c_Finite__Set_Ofolding__image__simple(U_549,U_550,U_551,U_552,U_553,U_554)
| hAPP(U_554,c_Orderings_Obot__class_Obot(tc_fun(U_550,tc_HOL_Obool))) = U_552 ),
inference(miniscope,[status(thm)],[f_101_2]) ).
fof(f_101_4,plain,
! [U_550,U_551,U_552,U_549,U_553,U_554] :
( ~ c_Finite__Set_Ofolding__image__simple(U_549,U_550,U_551,U_552,U_553,U_554)
| hAPP(U_554,c_Orderings_Obot__class_Obot(tc_fun(U_550,tc_HOL_Obool))) = U_552 ),
inference(definitional_conversion,[status(esa)],[f_101_3]) ).
cnf(f_101_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_549,U_550,U_551,U_552,U_553,U_554)
| hAPP(U_554,c_Orderings_Obot__class_Obot(tc_fun(U_550,tc_HOL_Obool))) = U_552 ),
inference(clausify,[status(thm)],[f_101_4]) ).
fof(f_102_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( 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_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_c,T_d,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove]) ).
fof(f_102_2,plain,
! [U_562,U_561,U_560,U_559,U_558,U_557,U_556,U_555] :
( hAPP(U_560,U_561) = hAPP(hAPP(U_557,hAPP(U_559,U_562)),hAPP(U_560,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_556,tc_HOL_Obool)),U_561),hAPP(hAPP(c_Set_Oinsert(U_556),U_562),c_Orderings_Obot__class_Obot(tc_fun(U_556,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_556),U_562),U_561))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_556),U_561))
| ~ c_Finite__Set_Ofolding__image__simple(U_555,U_556,U_557,U_558,U_559,U_560) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_562,U_561,U_560,U_559,U_558,U_557,U_556] :
( ! [U_555] : ~ c_Finite__Set_Ofolding__image__simple(U_555,U_556,U_557,U_558,U_559,U_560)
| hAPP(U_560,U_561) = hAPP(hAPP(U_557,hAPP(U_559,U_562)),hAPP(U_560,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_556,tc_HOL_Obool)),U_561),hAPP(hAPP(c_Set_Oinsert(U_556),U_562),c_Orderings_Obot__class_Obot(tc_fun(U_556,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_556),U_562),U_561))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_556),U_561)) ),
inference(miniscope,[status(thm)],[f_102_2]) ).
fof(f_102_4,plain,
! [U_556,U_555,U_557,U_558,U_559,U_560,U_561,U_562] :
( ~ c_Finite__Set_Ofolding__image__simple(U_555,U_556,U_557,U_558,U_559,U_560)
| hAPP(U_560,U_561) = hAPP(hAPP(U_557,hAPP(U_559,U_562)),hAPP(U_560,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_556,tc_HOL_Obool)),U_561),hAPP(hAPP(c_Set_Oinsert(U_556),U_562),c_Orderings_Obot__class_Obot(tc_fun(U_556,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_556),U_562),U_561))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_556),U_561)) ),
inference(definitional_conversion,[status(esa)],[f_102_3]) ).
cnf(f_102_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_555,U_556,U_557,U_558,U_559,U_560)
| hAPP(U_560,U_561) = hAPP(hAPP(U_557,hAPP(U_559,U_562)),hAPP(U_560,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_556,tc_HOL_Obool)),U_561),hAPP(hAPP(c_Set_Oinsert(U_556),U_562),c_Orderings_Obot__class_Obot(tc_fun(U_556,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_556),U_562),U_561))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_556),U_561)) ),
inference(clausify,[status(thm)],[f_102_4]) ).
fof(f_103_1,plain,
! [V_A_2,V_a_2,T_c] :
( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__Diff]) ).
fof(f_103_2,plain,
! [U_565,U_564,U_563] :
( hAPP(hAPP(c_Set_Oinsert(U_563),U_564),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_563,tc_HOL_Obool)),U_565),hAPP(hAPP(c_Set_Oinsert(U_563),U_564),c_Orderings_Obot__class_Obot(tc_fun(U_563,tc_HOL_Obool))))) = U_565
| ~ hBOOL(hAPP(hAPP(c_member(U_563),U_564),U_565)) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_563,U_564,U_565] :
( hAPP(hAPP(c_Set_Oinsert(U_563),U_564),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_563,tc_HOL_Obool)),U_565),hAPP(hAPP(c_Set_Oinsert(U_563),U_564),c_Orderings_Obot__class_Obot(tc_fun(U_563,tc_HOL_Obool))))) = U_565
| ~ hBOOL(hAPP(hAPP(c_member(U_563),U_564),U_565)) ),
inference(definitional_conversion,[status(esa)],[f_103_2]) ).
cnf(f_103_4,plain,
( hAPP(hAPP(c_Set_Oinsert(U_563),U_564),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_563,tc_HOL_Obool)),U_565),hAPP(hAPP(c_Set_Oinsert(U_563),U_564),c_Orderings_Obot__class_Obot(tc_fun(U_563,tc_HOL_Obool))))) = U_565
| ~ hBOOL(hAPP(hAPP(c_member(U_563),U_564),U_565)) ),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_1,plain,
! [V_A_2,V_x_2,T_c] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),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)))) = V_A_2
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Diff__insert__absorb]) ).
fof(f_104_2,plain,
! [U_568,U_567,U_566] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_566,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_566),U_567),U_568)),hAPP(hAPP(c_Set_Oinsert(U_566),U_567),c_Orderings_Obot__class_Obot(tc_fun(U_566,tc_HOL_Obool)))) = U_568
| hBOOL(hAPP(hAPP(c_member(U_566),U_567),U_568)) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_566,U_567,U_568] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_566,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_566),U_567),U_568)),hAPP(hAPP(c_Set_Oinsert(U_566),U_567),c_Orderings_Obot__class_Obot(tc_fun(U_566,tc_HOL_Obool)))) = U_568
| hBOOL(hAPP(hAPP(c_member(U_566),U_567),U_568)) ),
inference(definitional_conversion,[status(esa)],[f_104_2]) ).
cnf(f_104_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_566,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_566),U_567),U_568)),hAPP(hAPP(c_Set_Oinsert(U_566),U_567),c_Orderings_Obot__class_Obot(tc_fun(U_566,tc_HOL_Obool)))) = U_568
| hBOOL(hAPP(hAPP(c_member(U_566),U_567),U_568)) ),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] :
( ( ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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_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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_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)))) != 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__one(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove]) ).
fof(f_105_2,plain,
! [U_573,U_572,U_571,U_570,U_569] :
( ( ( hAPP(U_571,hAPP(hAPP(c_Set_Oinsert(U_569),U_573),U_572)) = hAPP(hAPP(U_570,U_573),hAPP(U_571,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_569,tc_HOL_Obool)),U_572),hAPP(hAPP(c_Set_Oinsert(U_569),U_573),c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_569,tc_HOL_Obool)),U_572),hAPP(hAPP(c_Set_Oinsert(U_569),U_573),c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool)) )
& ( hAPP(U_571,hAPP(hAPP(c_Set_Oinsert(U_569),U_573),U_572)) = U_573
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_569,tc_HOL_Obool)),U_572),hAPP(hAPP(c_Set_Oinsert(U_569),U_573),c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_569),U_572))
| ~ c_Finite__Set_Ofolding__one(U_569,U_570,U_571) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
( ! [U_569,U_570,U_571,U_572,U_573] :
( hAPP(U_571,hAPP(hAPP(c_Set_Oinsert(U_569),U_573),U_572)) = hAPP(hAPP(U_570,U_573),hAPP(U_571,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_569,tc_HOL_Obool)),U_572),hAPP(hAPP(c_Set_Oinsert(U_569),U_573),c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_569,tc_HOL_Obool)),U_572),hAPP(hAPP(c_Set_Oinsert(U_569),U_573),c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool))
| ~ sP22(U_569,U_570,U_571,U_572,U_573) )
& ! [U_569,U_570,U_571,U_572,U_573] :
( hAPP(U_571,hAPP(hAPP(c_Set_Oinsert(U_569),U_573),U_572)) = U_573
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_569,tc_HOL_Obool)),U_572),hAPP(hAPP(c_Set_Oinsert(U_569),U_573),c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool))
| ~ sP22(U_569,U_570,U_571,U_572,U_573) )
& ! [U_569,U_570,U_571,U_572,U_573] :
( sP22(U_569,U_570,U_571,U_572,U_573)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_569),U_572))
| ~ c_Finite__Set_Ofolding__one(U_569,U_570,U_571) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_105_2]) ).
cnf(f_105_4,plain,
( sP22(U_569,U_570,U_571,U_572,U_573)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_569),U_572))
| ~ c_Finite__Set_Ofolding__one(U_569,U_570,U_571) ),
inference(clausify,[status(thm)],[f_105_3]) ).
cnf(f_105_5,plain,
( hAPP(U_571,hAPP(hAPP(c_Set_Oinsert(U_569),U_573),U_572)) = U_573
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_569,tc_HOL_Obool)),U_572),hAPP(hAPP(c_Set_Oinsert(U_569),U_573),c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool))
| ~ sP22(U_569,U_570,U_571,U_572,U_573) ),
inference(clausify,[status(thm)],[f_105_3]) ).
cnf(f_105_6,plain,
( hAPP(U_571,hAPP(hAPP(c_Set_Oinsert(U_569),U_573),U_572)) = hAPP(hAPP(U_570,U_573),hAPP(U_571,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_569,tc_HOL_Obool)),U_572),hAPP(hAPP(c_Set_Oinsert(U_569),U_573),c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_569,tc_HOL_Obool)),U_572),hAPP(hAPP(c_Set_Oinsert(U_569),U_573),c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_569,tc_HOL_Obool))
| ~ sP22(U_569,U_570,U_571,U_572,U_573) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [V_x_2,V_B_2,V_A_2,T_d,T_c] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,T_c)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))
| ~ class_Groups_Ominus(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fun__diff__def]) ).
fof(f_106_2,plain,
! [U_578,U_577,U_576,U_575,U_574] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_575,U_574)),U_576),U_577),U_578) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_574),hAPP(U_576,U_578)),hAPP(U_577,U_578))
| ~ class_Groups_Ominus(U_574) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
! [U_575,U_574,U_577,U_576,U_578] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_575,U_574)),U_576),U_577),U_578) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_574),hAPP(U_576,U_578)),hAPP(U_577,U_578))
| ~ class_Groups_Ominus(U_574) ),
inference(definitional_conversion,[status(esa)],[f_106_2]) ).
cnf(f_106_4,plain,
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_575,U_574)),U_576),U_577),U_578) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_574),hAPP(U_576,U_578)),hAPP(U_577,U_578))
| ~ class_Groups_Ominus(U_574) ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_1,plain,
! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I12_J]) ).
fof(f_107_2,plain,
! [U_580,U_579] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_579,U_580),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_580,U_579] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_579,U_580),
inference(definitional_conversion,[status(esa)],[f_107_2]) ).
cnf(f_107_4,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_579,U_580),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP,
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I13_J]) ).
fof(f_108_2,plain,
! [U_582,U_581] : c_Com_Ocom_OSemi(U_581,U_582) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_581,U_582] : c_Com_Ocom_OSemi(U_581,U_582) != c_Com_Ocom_OSKIP,
inference(definitional_conversion,[status(esa)],[f_108_2]) ).
cnf(f_108_4,plain,
c_Com_Ocom_OSemi(U_581,U_582) != c_Com_Ocom_OSKIP,
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_1,plain,
! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I16_J]) ).
fof(f_109_2,plain,
! [U_584,U_583] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_583,U_584),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_583,U_584] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_583,U_584),
inference(definitional_conversion,[status(esa)],[f_109_2]) ).
cnf(f_109_4,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_583,U_584),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP,
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I17_J]) ).
fof(f_110_2,plain,
! [U_586,U_585] : c_Com_Ocom_OWhile(U_585,U_586) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_585,U_586] : c_Com_Ocom_OWhile(U_585,U_586) != c_Com_Ocom_OSKIP,
inference(definitional_conversion,[status(esa)],[f_110_2]) ).
cnf(f_110_4,plain,
c_Com_Ocom_OWhile(U_585,U_586) != c_Com_Ocom_OSKIP,
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I46_J]) ).
fof(f_111_2,plain,
! [U_590,U_589,U_588,U_587] : c_Com_Ocom_OSemi(U_587,U_588) != c_Com_Ocom_OWhile(U_589,U_590),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_587,U_588,U_589,U_590] : c_Com_Ocom_OSemi(U_587,U_588) != c_Com_Ocom_OWhile(U_589,U_590),
inference(definitional_conversion,[status(esa)],[f_111_2]) ).
cnf(f_111_4,plain,
c_Com_Ocom_OSemi(U_587,U_588) != c_Com_Ocom_OWhile(U_589,U_590),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
! [V_com2_2,V_com1_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I47_J]) ).
fof(f_112_2,plain,
! [U_594,U_593,U_592,U_591] : c_Com_Ocom_OWhile(U_591,U_592) != c_Com_Ocom_OSemi(U_593,U_594),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_591,U_592,U_593,U_594] : c_Com_Ocom_OWhile(U_591,U_592) != c_Com_Ocom_OSemi(U_593,U_594),
inference(definitional_conversion,[status(esa)],[f_112_2]) ).
cnf(f_112_4,plain,
c_Com_Ocom_OWhile(U_591,U_592) != c_Com_Ocom_OSemi(U_593,U_594),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [V_x_2,V_B_2,V_A_2,T_d,T_c] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,T_c)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))
| ~ class_Groups_Ominus(T_c) ),
inference(fof_nnf,[status(thm)],[fact_minus__apply]) ).
fof(f_113_2,plain,
! [U_599,U_598,U_597,U_596,U_595] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_596,U_595)),U_597),U_598),U_599) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_595),hAPP(U_597,U_599)),hAPP(U_598,U_599))
| ~ class_Groups_Ominus(U_595) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
! [U_595,U_596,U_597,U_598,U_599] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_596,U_595)),U_597),U_598),U_599) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_595),hAPP(U_597,U_599)),hAPP(U_598,U_599))
| ~ class_Groups_Ominus(U_595) ),
inference(definitional_conversion,[status(esa)],[f_113_2]) ).
cnf(f_113_4,plain,
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_596,U_595)),U_597),U_598),U_599) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_595),hAPP(U_597,U_599)),hAPP(U_598,U_599))
| ~ class_Groups_Ominus(U_595) ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_1,plain,
! [V_y_2,V_f_2,T_d,V_A_2,V_x_2,T_c] :
( ( hAPP(c_Set_Oimage(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) )
& ( hAPP(c_Set_Oimage(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_d),V_y_2),hAPP(c_Set_Oimage(T_c,T_d,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)) ) ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__image]) ).
fof(f_114_2,plain,
! [U_605,U_604,U_603,U_602,U_601,U_600] :
( ( hAPP(c_Set_Oimage(U_600,U_603,c_Fun_Ofun__upd(U_600,U_603,U_604,U_601,U_605)),U_602) = hAPP(c_Set_Oimage(U_600,U_603,U_604),U_602)
| hBOOL(hAPP(hAPP(c_member(U_600),U_601),U_602)) )
& ( hAPP(c_Set_Oimage(U_600,U_603,c_Fun_Ofun__upd(U_600,U_603,U_604,U_601,U_605)),U_602) = hAPP(hAPP(c_Set_Oinsert(U_603),U_605),hAPP(c_Set_Oimage(U_600,U_603,U_604),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_600,tc_HOL_Obool)),U_602),hAPP(hAPP(c_Set_Oinsert(U_600),U_601),c_Orderings_Obot__class_Obot(tc_fun(U_600,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_600),U_601),U_602)) ) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
( ! [U_617,U_615,U_613,U_611,U_609,U_607] :
( hAPP(c_Set_Oimage(U_607,U_613,c_Fun_Ofun__upd(U_607,U_613,U_615,U_609,U_617)),U_611) = hAPP(c_Set_Oimage(U_607,U_613,U_615),U_611)
| hBOOL(hAPP(hAPP(c_member(U_607),U_609),U_611)) )
& ! [U_616,U_614,U_612,U_610,U_608,U_606] :
( hAPP(c_Set_Oimage(U_606,U_612,c_Fun_Ofun__upd(U_606,U_612,U_614,U_608,U_616)),U_610) = hAPP(hAPP(c_Set_Oinsert(U_612),U_616),hAPP(c_Set_Oimage(U_606,U_612,U_614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_606,tc_HOL_Obool)),U_610),hAPP(hAPP(c_Set_Oinsert(U_606),U_608),c_Orderings_Obot__class_Obot(tc_fun(U_606,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_606),U_608),U_610)) ) ),
inference(miniscope,[status(thm)],[f_114_2]) ).
fof(f_114_4,plain,
( ! [U_607,U_609,U_611,U_613,U_615,U_617] :
( hAPP(c_Set_Oimage(U_607,U_613,c_Fun_Ofun__upd(U_607,U_613,U_615,U_609,U_617)),U_611) = hAPP(c_Set_Oimage(U_607,U_613,U_615),U_611)
| hBOOL(hAPP(hAPP(c_member(U_607),U_609),U_611)) )
& ! [U_612,U_608,U_606,U_614,U_616,U_610] :
( hAPP(c_Set_Oimage(U_606,U_612,c_Fun_Ofun__upd(U_606,U_612,U_614,U_608,U_616)),U_610) = hAPP(hAPP(c_Set_Oinsert(U_612),U_616),hAPP(c_Set_Oimage(U_606,U_612,U_614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_606,tc_HOL_Obool)),U_610),hAPP(hAPP(c_Set_Oinsert(U_606),U_608),c_Orderings_Obot__class_Obot(tc_fun(U_606,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_606),U_608),U_610)) ) ),
inference(definitional_conversion,[status(esa)],[f_114_3]) ).
cnf(f_114_5,plain,
( hAPP(c_Set_Oimage(U_606,U_612,c_Fun_Ofun__upd(U_606,U_612,U_614,U_608,U_616)),U_610) = hAPP(hAPP(c_Set_Oinsert(U_612),U_616),hAPP(c_Set_Oimage(U_606,U_612,U_614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_606,tc_HOL_Obool)),U_610),hAPP(hAPP(c_Set_Oinsert(U_606),U_608),c_Orderings_Obot__class_Obot(tc_fun(U_606,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_606),U_608),U_610)) ),
inference(clausify,[status(thm)],[f_114_4]) ).
cnf(f_114_6,plain,
( hAPP(c_Set_Oimage(U_607,U_613,c_Fun_Ofun__upd(U_607,U_613,U_615,U_609,U_617)),U_611) = hAPP(c_Set_Oimage(U_607,U_613,U_615),U_611)
| hBOOL(hAPP(hAPP(c_member(U_607),U_609),U_611)) ),
inference(clausify,[status(thm)],[f_114_4]) ).
fof(f_115_1,plain,
! [V_Pa_2,V_A_2,T_c] :
( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
| ? [B_a,B_A] :
( ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_c),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
& hBOOL(hAPP(V_Pa_2,B_A))
& hBOOL(hAPP(hAPP(c_member(T_c),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_A)) )
| ~ hBOOL(hAPP(V_Pa_2,V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__empty__induct]) ).
fof(f_115_2,plain,
! [U_622,U_621,U_620] :
( hBOOL(hAPP(U_622,c_Orderings_Obot__class_Obot(tc_fun(U_620,tc_HOL_Obool))))
| ? [U_619,U_618] :
( ~ hBOOL(hAPP(U_622,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_620,tc_HOL_Obool)),U_618),hAPP(hAPP(c_Set_Oinsert(U_620),U_619),c_Orderings_Obot__class_Obot(tc_fun(U_620,tc_HOL_Obool))))))
& hBOOL(hAPP(U_622,U_618))
& hBOOL(hAPP(hAPP(c_member(U_620),U_619),U_618))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_620),U_618)) )
| ~ hBOOL(hAPP(U_622,U_621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_620),U_621)) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_622,U_621,U_620] :
( hBOOL(hAPP(U_622,c_Orderings_Obot__class_Obot(tc_fun(U_620,tc_HOL_Obool))))
| ? [U_618] :
( ~ hBOOL(hAPP(U_622,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_620,tc_HOL_Obool)),U_618),hAPP(hAPP(c_Set_Oinsert(U_620),sK17(U_622,U_621,U_620)),c_Orderings_Obot__class_Obot(tc_fun(U_620,tc_HOL_Obool))))))
& hBOOL(hAPP(U_622,U_618))
& hBOOL(hAPP(hAPP(c_member(U_620),sK17(U_622,U_621,U_620)),U_618))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_620),U_618)) )
| ~ hBOOL(hAPP(U_622,U_621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_620),U_621)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_619,sK17(U_622,U_621,U_620))],[f_115_2]) ).
fof(f_115_4,plain,
! [U_622,U_621,U_620] :
( hBOOL(hAPP(U_622,c_Orderings_Obot__class_Obot(tc_fun(U_620,tc_HOL_Obool))))
| ( ~ hBOOL(hAPP(U_622,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_620,tc_HOL_Obool)),sK18(U_622,U_621,U_620)),hAPP(hAPP(c_Set_Oinsert(U_620),sK17(U_622,U_621,U_620)),c_Orderings_Obot__class_Obot(tc_fun(U_620,tc_HOL_Obool))))))
& hBOOL(hAPP(U_622,sK18(U_622,U_621,U_620)))
& hBOOL(hAPP(hAPP(c_member(U_620),sK17(U_622,U_621,U_620)),sK18(U_622,U_621,U_620)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_620),sK18(U_622,U_621,U_620))) )
| ~ hBOOL(hAPP(U_622,U_621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_620),U_621)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_618,sK18(U_622,U_621,U_620))],[f_115_3]) ).
fof(f_115_5,plain,
( ! [U_620,U_621,U_622] :
( ~ hBOOL(hAPP(U_622,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_620,tc_HOL_Obool)),sK18(U_622,U_621,U_620)),hAPP(hAPP(c_Set_Oinsert(U_620),sK17(U_622,U_621,U_620)),c_Orderings_Obot__class_Obot(tc_fun(U_620,tc_HOL_Obool))))))
| ~ sP23(U_620,U_621,U_622) )
& ! [U_620,U_621,U_622] :
( hBOOL(hAPP(U_622,sK18(U_622,U_621,U_620)))
| ~ sP23(U_620,U_621,U_622) )
& ! [U_620,U_621,U_622] :
( hBOOL(hAPP(hAPP(c_member(U_620),sK17(U_622,U_621,U_620)),sK18(U_622,U_621,U_620)))
| ~ sP23(U_620,U_621,U_622) )
& ! [U_620,U_621,U_622] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_620),sK18(U_622,U_621,U_620)))
| ~ sP23(U_620,U_621,U_622) )
& ! [U_620,U_621,U_622] :
( hBOOL(hAPP(U_622,c_Orderings_Obot__class_Obot(tc_fun(U_620,tc_HOL_Obool))))
| sP23(U_620,U_621,U_622)
| ~ hBOOL(hAPP(U_622,U_621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_620),U_621)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_115_4]) ).
cnf(f_115_6,plain,
( hBOOL(hAPP(U_622,c_Orderings_Obot__class_Obot(tc_fun(U_620,tc_HOL_Obool))))
| sP23(U_620,U_621,U_622)
| ~ hBOOL(hAPP(U_622,U_621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_620),U_621)) ),
inference(clausify,[status(thm)],[f_115_5]) ).
cnf(f_115_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_620),sK18(U_622,U_621,U_620)))
| ~ sP23(U_620,U_621,U_622) ),
inference(clausify,[status(thm)],[f_115_5]) ).
cnf(f_115_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_620),sK17(U_622,U_621,U_620)),sK18(U_622,U_621,U_620)))
| ~ sP23(U_620,U_621,U_622) ),
inference(clausify,[status(thm)],[f_115_5]) ).
cnf(f_115_9,plain,
( hBOOL(hAPP(U_622,sK18(U_622,U_621,U_620)))
| ~ sP23(U_620,U_621,U_622) ),
inference(clausify,[status(thm)],[f_115_5]) ).
cnf(f_115_10,plain,
( ~ hBOOL(hAPP(U_622,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_620,tc_HOL_Obool)),sK18(U_622,U_621,U_620)),hAPP(hAPP(c_Set_Oinsert(U_620),sK17(U_622,U_621,U_620)),c_Orderings_Obot__class_Obot(tc_fun(U_620,tc_HOL_Obool))))))
| ~ sP23(U_620,U_621,U_622) ),
inference(clausify,[status(thm)],[f_115_5]) ).
fof(f_116_1,plain,
! [T_c] : c_Finite__Set_Ofun__left__comm__idem(T_c,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_c),hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)))),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_fun__left__comm__idem__remove]) ).
fof(f_116_2,plain,
! [U_623] : c_Finite__Set_Ofun__left__comm__idem(U_623,tc_fun(U_623,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_623,tc_HOL_Obool),tc_fun(tc_fun(U_623,tc_HOL_Obool),tc_fun(U_623,tc_HOL_Obool)),U_623),hAPP(c_COMBC(tc_fun(U_623,tc_HOL_Obool),tc_fun(U_623,tc_HOL_Obool),tc_fun(U_623,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_623,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_623,tc_fun(U_623,tc_HOL_Obool),tc_fun(U_623,tc_HOL_Obool)),c_Set_Oinsert(U_623)),c_Orderings_Obot__class_Obot(tc_fun(U_623,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_623] : c_Finite__Set_Ofun__left__comm__idem(U_623,tc_fun(U_623,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_623,tc_HOL_Obool),tc_fun(tc_fun(U_623,tc_HOL_Obool),tc_fun(U_623,tc_HOL_Obool)),U_623),hAPP(c_COMBC(tc_fun(U_623,tc_HOL_Obool),tc_fun(U_623,tc_HOL_Obool),tc_fun(U_623,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_623,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_623,tc_fun(U_623,tc_HOL_Obool),tc_fun(U_623,tc_HOL_Obool)),c_Set_Oinsert(U_623)),c_Orderings_Obot__class_Obot(tc_fun(U_623,tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_116_2]) ).
cnf(f_116_4,plain,
c_Finite__Set_Ofun__left__comm__idem(U_623,tc_fun(U_623,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_623,tc_HOL_Obool),tc_fun(tc_fun(U_623,tc_HOL_Obool),tc_fun(U_623,tc_HOL_Obool)),U_623),hAPP(c_COMBC(tc_fun(U_623,tc_HOL_Obool),tc_fun(U_623,tc_HOL_Obool),tc_fun(U_623,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_623,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_623,tc_fun(U_623,tc_HOL_Obool),tc_fun(U_623,tc_HOL_Obool)),c_Set_Oinsert(U_623)),c_Orderings_Obot__class_Obot(tc_fun(U_623,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_1,plain,
! [V_x_2,T_c] : c_HOL_OThe(T_c,hAPP(c_fequal,V_x_2)) = V_x_2,
inference(fof_nnf,[status(thm)],[fact_the__sym__eq__trivial]) ).
fof(f_117_2,plain,
! [U_625,U_624] : c_HOL_OThe(U_624,hAPP(c_fequal,U_625)) = U_625,
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_624,U_625] : c_HOL_OThe(U_624,hAPP(c_fequal,U_625)) = U_625,
inference(definitional_conversion,[status(esa)],[f_117_2]) ).
cnf(f_117_4,plain,
c_HOL_OThe(U_624,hAPP(c_fequal,U_625)) = U_625,
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [V_x_2,V_f_2,T_d,T_c] : c_Fun_Ofun__upd(T_c,T_d,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_118_2,plain,
! [U_629,U_628,U_627,U_626] : c_Fun_Ofun__upd(U_626,U_627,U_628,U_629,hAPP(U_628,U_629)) = U_628,
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_627,U_628,U_626,U_629] : c_Fun_Ofun__upd(U_626,U_627,U_628,U_629,hAPP(U_628,U_629)) = U_628,
inference(definitional_conversion,[status(esa)],[f_118_2]) ).
cnf(f_118_4,plain,
c_Fun_Ofun__upd(U_626,U_627,U_628,U_629,hAPP(U_628,U_629)) = U_628,
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_1,plain,
! [V_y_2,V_x_2,V_f_2,T_d,T_c] :
( ( c_Fun_Ofun__upd(T_c,T_d,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_c,T_d,V_f_2,V_x_2,V_y_2) != V_f_2 ) ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff]) ).
fof(f_119_2,plain,
! [U_634,U_633,U_632,U_631,U_630] :
( ( c_Fun_Ofun__upd(U_630,U_631,U_632,U_633,U_634) = U_632
| hAPP(U_632,U_633) != U_634 )
& ( hAPP(U_632,U_633) = U_634
| c_Fun_Ofun__upd(U_630,U_631,U_632,U_633,U_634) != U_632 ) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
( ! [U_644,U_642,U_640] :
( ! [U_638,U_636] : c_Fun_Ofun__upd(U_636,U_638,U_640,U_642,U_644) = U_640
| hAPP(U_640,U_642) != U_644 )
& ! [U_643,U_641,U_639] :
( ! [U_637,U_635] : c_Fun_Ofun__upd(U_635,U_637,U_639,U_641,U_643) != U_639
| hAPP(U_639,U_641) = U_643 ) ),
inference(miniscope,[status(thm)],[f_119_2]) ).
fof(f_119_4,plain,
( ! [U_638,U_644,U_636,U_640,U_642] :
( c_Fun_Ofun__upd(U_636,U_638,U_640,U_642,U_644) = U_640
| hAPP(U_640,U_642) != U_644 )
& ! [U_635,U_637,U_639,U_641,U_643] :
( c_Fun_Ofun__upd(U_635,U_637,U_639,U_641,U_643) != U_639
| hAPP(U_639,U_641) = U_643 ) ),
inference(definitional_conversion,[status(esa)],[f_119_3]) ).
cnf(f_119_5,plain,
( c_Fun_Ofun__upd(U_635,U_637,U_639,U_641,U_643) != U_639
| hAPP(U_639,U_641) = U_643 ),
inference(clausify,[status(thm)],[f_119_4]) ).
cnf(f_119_6,plain,
( c_Fun_Ofun__upd(U_636,U_638,U_640,U_642,U_644) = U_640
| hAPP(U_640,U_642) != U_644 ),
inference(clausify,[status(thm)],[f_119_4]) ).
fof(f_120_1,plain,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_d,T_c] : c_Fun_Ofun__upd(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_z_2),
inference(fof_nnf,[status(thm)],[fact_fun__upd__upd]) ).
fof(f_120_2,plain,
! [U_650,U_649,U_648,U_647,U_646,U_645] : c_Fun_Ofun__upd(U_645,U_646,c_Fun_Ofun__upd(U_645,U_646,U_647,U_648,U_649),U_648,U_650) = c_Fun_Ofun__upd(U_645,U_646,U_647,U_648,U_650),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_645,U_646,U_647,U_648,U_649,U_650] : c_Fun_Ofun__upd(U_645,U_646,c_Fun_Ofun__upd(U_645,U_646,U_647,U_648,U_649),U_648,U_650) = c_Fun_Ofun__upd(U_645,U_646,U_647,U_648,U_650),
inference(definitional_conversion,[status(esa)],[f_120_2]) ).
cnf(f_120_4,plain,
c_Fun_Ofun__upd(U_645,U_646,c_Fun_Ofun__upd(U_645,U_646,U_647,U_648,U_649),U_648,U_650) = c_Fun_Ofun__upd(U_645,U_646,U_647,U_648,U_650),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
! [V_y_2,V_x_2,V_f_2,T_c,T_d] : hAPP(c_Fun_Ofun__upd(T_d,T_c,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_121_2,plain,
! [U_655,U_654,U_653,U_652,U_651] : hAPP(c_Fun_Ofun__upd(U_651,U_652,U_653,U_654,U_655),U_654) = U_655,
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
! [U_651,U_652,U_653,U_654,U_655] : hAPP(c_Fun_Ofun__upd(U_651,U_652,U_653,U_654,U_655),U_654) = U_655,
inference(definitional_conversion,[status(esa)],[f_121_2]) ).
cnf(f_121_4,plain,
hAPP(c_Fun_Ofun__upd(U_651,U_652,U_653,U_654,U_655),U_654) = U_655,
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
! [V_y_2,V_f_2,T_d,T_c,V_x_2,V_z_2] :
( ( hAPP(c_Fun_Ofun__upd(T_c,T_d,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_c,T_d,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_122_2,plain,
! [U_661,U_660,U_659,U_658,U_657,U_656] :
( ( hAPP(c_Fun_Ofun__upd(U_658,U_659,U_660,U_657,U_661),U_656) = hAPP(U_660,U_656)
| U_656 = U_657 )
& ( hAPP(c_Fun_Ofun__upd(U_658,U_659,U_660,U_657,U_661),U_656) = U_661
| U_656 != U_657 ) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
( ! [U_673,U_671,U_669,U_667,U_665,U_663] :
( hAPP(c_Fun_Ofun__upd(U_667,U_669,U_671,U_665,U_673),U_663) = hAPP(U_671,U_663)
| U_663 = U_665 )
& ! [U_672,U_670,U_668,U_666,U_664,U_662] :
( hAPP(c_Fun_Ofun__upd(U_666,U_668,U_670,U_664,U_672),U_662) = U_672
| U_662 != U_664 ) ),
inference(miniscope,[status(thm)],[f_122_2]) ).
fof(f_122_4,plain,
( ! [U_663,U_665,U_667,U_669,U_671,U_673] :
( hAPP(c_Fun_Ofun__upd(U_667,U_669,U_671,U_665,U_673),U_663) = hAPP(U_671,U_663)
| U_663 = U_665 )
& ! [U_668,U_666,U_662,U_664,U_670,U_672] :
( hAPP(c_Fun_Ofun__upd(U_666,U_668,U_670,U_664,U_672),U_662) = U_672
| U_662 != U_664 ) ),
inference(definitional_conversion,[status(esa)],[f_122_3]) ).
cnf(f_122_5,plain,
( hAPP(c_Fun_Ofun__upd(U_666,U_668,U_670,U_664,U_672),U_662) = U_672
| U_662 != U_664 ),
inference(clausify,[status(thm)],[f_122_4]) ).
cnf(f_122_6,plain,
( hAPP(c_Fun_Ofun__upd(U_667,U_669,U_671,U_665,U_673),U_663) = hAPP(U_671,U_663)
| U_663 = U_665 ),
inference(clausify,[status(thm)],[f_122_4]) ).
fof(f_123_1,plain,
! [V_d_2,V_b_2,V_m_2,T_d,T_c,V_c_2,V_a_2] :
( c_Fun_Ofun__upd(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_m_2,V_c_2,V_d_2),V_a_2,V_b_2)
| V_a_2 = V_c_2 ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__twist]) ).
fof(f_123_2,plain,
! [U_680,U_679,U_678,U_677,U_676,U_675,U_674] :
( c_Fun_Ofun__upd(U_676,U_677,c_Fun_Ofun__upd(U_676,U_677,U_678,U_674,U_679),U_675,U_680) = c_Fun_Ofun__upd(U_676,U_677,c_Fun_Ofun__upd(U_676,U_677,U_678,U_675,U_680),U_674,U_679)
| U_674 = U_675 ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_675,U_674,U_676,U_677,U_678,U_679,U_680] :
( c_Fun_Ofun__upd(U_676,U_677,c_Fun_Ofun__upd(U_676,U_677,U_678,U_674,U_679),U_675,U_680) = c_Fun_Ofun__upd(U_676,U_677,c_Fun_Ofun__upd(U_676,U_677,U_678,U_675,U_680),U_674,U_679)
| U_674 = U_675 ),
inference(definitional_conversion,[status(esa)],[f_123_2]) ).
cnf(f_123_4,plain,
( c_Fun_Ofun__upd(U_676,U_677,c_Fun_Ofun__upd(U_676,U_677,U_678,U_674,U_679),U_675,U_680) = c_Fun_Ofun__upd(U_676,U_677,c_Fun_Ofun__upd(U_676,U_677,U_678,U_675,U_680),U_674,U_679)
| U_674 = U_675 ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_1,plain,
! [V_y_2,V_f_2,T_d,T_c,V_x_2,V_z_2] :
( hAPP(c_Fun_Ofun__upd(T_c,T_d,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_124_2,plain,
! [U_686,U_685,U_684,U_683,U_682,U_681] :
( hAPP(c_Fun_Ofun__upd(U_683,U_684,U_685,U_682,U_686),U_681) = hAPP(U_685,U_681)
| U_681 = U_682 ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_682,U_683,U_681,U_684,U_685,U_686] :
( hAPP(c_Fun_Ofun__upd(U_683,U_684,U_685,U_682,U_686),U_681) = hAPP(U_685,U_681)
| U_681 = U_682 ),
inference(definitional_conversion,[status(esa)],[f_124_2]) ).
cnf(f_124_4,plain,
( hAPP(c_Fun_Ofun__upd(U_683,U_684,U_685,U_682,U_686),U_681) = hAPP(U_685,U_681)
| U_681 = U_682 ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
! [T_c,T_d,V_y_2,V_x_2,V_f_2] :
( c_Fun_Ofun__upd(T_d,T_c,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_125_2,plain,
! [U_691,U_690,U_689,U_688,U_687] :
( c_Fun_Ofun__upd(U_690,U_691,U_687,U_688,U_689) = U_687
| hAPP(U_687,U_688) != U_689 ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
! [U_688,U_687,U_689,U_690,U_691] :
( c_Fun_Ofun__upd(U_690,U_691,U_687,U_688,U_689) = U_687
| hAPP(U_687,U_688) != U_689 ),
inference(definitional_conversion,[status(esa)],[f_125_2]) ).
cnf(f_125_4,plain,
( c_Fun_Ofun__upd(U_690,U_691,U_687,U_688,U_689) = U_687
| hAPP(U_687,U_688) != U_689 ),
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [V_z_2,V_x_2,V_f_2,T_d,T_c] :
( 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_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem]) ).
fof(f_126_2,plain,
! [U_696,U_695,U_694,U_693,U_692] :
( hAPP(hAPP(U_694,U_695),hAPP(hAPP(U_694,U_695),U_696)) = hAPP(hAPP(U_694,U_695),U_696)
| ~ c_Finite__Set_Ofun__left__comm__idem(U_692,U_693,U_694) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_696,U_695,U_694] :
( ! [U_693,U_692] : ~ c_Finite__Set_Ofun__left__comm__idem(U_692,U_693,U_694)
| hAPP(hAPP(U_694,U_695),hAPP(hAPP(U_694,U_695),U_696)) = hAPP(hAPP(U_694,U_695),U_696) ),
inference(miniscope,[status(thm)],[f_126_2]) ).
fof(f_126_4,plain,
! [U_694,U_692,U_693,U_695,U_696] :
( ~ c_Finite__Set_Ofun__left__comm__idem(U_692,U_693,U_694)
| hAPP(hAPP(U_694,U_695),hAPP(hAPP(U_694,U_695),U_696)) = hAPP(hAPP(U_694,U_695),U_696) ),
inference(definitional_conversion,[status(esa)],[f_126_3]) ).
cnf(f_126_5,plain,
( ~ c_Finite__Set_Ofun__left__comm__idem(U_692,U_693,U_694)
| hAPP(hAPP(U_694,U_695),hAPP(hAPP(U_694,U_695),U_696)) = hAPP(hAPP(U_694,U_695),U_696) ),
inference(clausify,[status(thm)],[f_126_4]) ).
fof(f_127_1,plain,
! [V_b_2,V_f_2,T_d,T_c,V_a_2,V_x_2] :
( ( hAPP(c_Fun_Ofun__upd(T_c,T_d,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_c,T_d,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_127_2,plain,
! [U_702,U_701,U_700,U_699,U_698,U_697] :
( ( hAPP(c_Fun_Ofun__upd(U_699,U_700,U_701,U_698,U_702),U_697) = hAPP(U_701,U_697)
| U_697 = U_698 )
& ( hAPP(c_Fun_Ofun__upd(U_699,U_700,U_701,U_698,U_702),U_697) = U_702
| U_697 != U_698 ) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
( ! [U_714,U_712,U_710,U_708,U_706,U_704] :
( hAPP(c_Fun_Ofun__upd(U_708,U_710,U_712,U_706,U_714),U_704) = hAPP(U_712,U_704)
| U_704 = U_706 )
& ! [U_713,U_711,U_709,U_707,U_705,U_703] :
( hAPP(c_Fun_Ofun__upd(U_707,U_709,U_711,U_705,U_713),U_703) = U_713
| U_703 != U_705 ) ),
inference(miniscope,[status(thm)],[f_127_2]) ).
fof(f_127_4,plain,
( ! [U_704,U_706,U_708,U_710,U_712,U_714] :
( hAPP(c_Fun_Ofun__upd(U_708,U_710,U_712,U_706,U_714),U_704) = hAPP(U_712,U_704)
| U_704 = U_706 )
& ! [U_707,U_709,U_705,U_703,U_711,U_713] :
( hAPP(c_Fun_Ofun__upd(U_707,U_709,U_711,U_705,U_713),U_703) = U_713
| U_703 != U_705 ) ),
inference(definitional_conversion,[status(esa)],[f_127_3]) ).
cnf(f_127_5,plain,
( hAPP(c_Fun_Ofun__upd(U_707,U_709,U_711,U_705,U_713),U_703) = U_713
| U_703 != U_705 ),
inference(clausify,[status(thm)],[f_127_4]) ).
cnf(f_127_6,plain,
( hAPP(c_Fun_Ofun__upd(U_708,U_710,U_712,U_706,U_714),U_704) = hAPP(U_712,U_704)
| U_704 = U_706 ),
inference(clausify,[status(thm)],[f_127_4]) ).
fof(f_128_1,plain,
! [V_g_2,T_e,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm__idem(T_e,T_d,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_d),T_e),V_f_2),V_g_2))
| ~ c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply]) ).
fof(f_128_2,plain,
! [U_719,U_718,U_717,U_716,U_715] :
( c_Finite__Set_Ofun__left__comm__idem(U_718,U_716,hAPP(hAPP(c_COMBB(U_715,tc_fun(U_716,U_716),U_718),U_717),U_719))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_715,U_716,U_717) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
! [U_715,U_716,U_717,U_718,U_719] :
( c_Finite__Set_Ofun__left__comm__idem(U_718,U_716,hAPP(hAPP(c_COMBB(U_715,tc_fun(U_716,U_716),U_718),U_717),U_719))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_715,U_716,U_717) ),
inference(definitional_conversion,[status(esa)],[f_128_2]) ).
cnf(f_128_4,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_718,U_716,hAPP(hAPP(c_COMBB(U_715,tc_fun(U_716,U_716),U_718),U_717),U_719))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_715,U_716,U_717) ),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_1,plain,
! [T_c] : c_Finite__Set_Ofun__left__comm__idem(T_c,tc_fun(T_c,tc_HOL_Obool),c_Set_Oinsert(T_c)),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__insert]) ).
fof(f_129_2,plain,
! [U_720] : c_Finite__Set_Ofun__left__comm__idem(U_720,tc_fun(U_720,tc_HOL_Obool),c_Set_Oinsert(U_720)),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
! [U_720] : c_Finite__Set_Ofun__left__comm__idem(U_720,tc_fun(U_720,tc_HOL_Obool),c_Set_Oinsert(U_720)),
inference(definitional_conversion,[status(esa)],[f_129_2]) ).
cnf(f_129_4,plain,
c_Finite__Set_Ofun__left__comm__idem(U_720,tc_fun(U_720,tc_HOL_Obool),c_Set_Oinsert(U_720)),
inference(clausify,[status(thm)],[f_129_3]) ).
fof(f_130_1,plain,
! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
( ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
| V_com_2 != V_com_H_2
| V_fun_2 != V_fun_H_2 )
& ( ( V_com_2 = V_com_H_2
& V_fun_2 = V_fun_H_2 )
| c_Com_Ocom_OWhile(V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I5_J]) ).
fof(f_130_2,plain,
! [U_724,U_723,U_722,U_721] :
( ( c_Com_Ocom_OWhile(U_721,U_722) = c_Com_Ocom_OWhile(U_723,U_724)
| U_722 != U_724
| U_721 != U_723 )
& ( ( U_722 = U_724
& U_721 = U_723 )
| c_Com_Ocom_OWhile(U_721,U_722) != c_Com_Ocom_OWhile(U_723,U_724) ) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
( ! [U_732,U_730,U_728,U_726] :
( c_Com_Ocom_OWhile(U_726,U_728) = c_Com_Ocom_OWhile(U_730,U_732)
| U_728 != U_732
| U_726 != U_730 )
& ! [U_731,U_729,U_727,U_725] :
( ( U_727 = U_731
& U_725 = U_729 )
| c_Com_Ocom_OWhile(U_725,U_727) != c_Com_Ocom_OWhile(U_729,U_731) ) ),
inference(miniscope,[status(thm)],[f_130_2]) ).
fof(f_130_4,plain,
( ! [U_725,U_729,U_727,U_731] :
( U_727 = U_731
| ~ sP24(U_725,U_729,U_727,U_731) )
& ! [U_725,U_729,U_727,U_731] :
( U_725 = U_729
| ~ sP24(U_725,U_729,U_727,U_731) )
& ! [U_732,U_728,U_726,U_730] :
( c_Com_Ocom_OWhile(U_726,U_728) = c_Com_Ocom_OWhile(U_730,U_732)
| U_728 != U_732
| U_726 != U_730 )
& ! [U_725,U_729,U_727,U_731] :
( sP24(U_725,U_729,U_727,U_731)
| c_Com_Ocom_OWhile(U_725,U_727) != c_Com_Ocom_OWhile(U_729,U_731) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_130_3]) ).
cnf(f_130_5,plain,
( sP24(U_725,U_729,U_727,U_731)
| c_Com_Ocom_OWhile(U_725,U_727) != c_Com_Ocom_OWhile(U_729,U_731) ),
inference(clausify,[status(thm)],[f_130_4]) ).
cnf(f_130_6,plain,
( c_Com_Ocom_OWhile(U_726,U_728) = c_Com_Ocom_OWhile(U_730,U_732)
| U_728 != U_732
| U_726 != U_730 ),
inference(clausify,[status(thm)],[f_130_4]) ).
cnf(f_130_7,plain,
( U_725 = U_729
| ~ sP24(U_725,U_729,U_727,U_731) ),
inference(clausify,[status(thm)],[f_130_4]) ).
cnf(f_130_8,plain,
( U_727 = U_731
| ~ sP24(U_725,U_729,U_727,U_731) ),
inference(clausify,[status(thm)],[f_130_4]) ).
fof(f_131_1,plain,
! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
( ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
| V_com2_2 != V_com2_H_2
| V_com1_2 != V_com1_H_2 )
& ( ( V_com2_2 = V_com2_H_2
& V_com1_2 = V_com1_H_2 )
| c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I3_J]) ).
fof(f_131_2,plain,
! [U_736,U_735,U_734,U_733] :
( ( c_Com_Ocom_OSemi(U_733,U_734) = c_Com_Ocom_OSemi(U_735,U_736)
| U_734 != U_736
| U_733 != U_735 )
& ( ( U_734 = U_736
& U_733 = U_735 )
| c_Com_Ocom_OSemi(U_733,U_734) != c_Com_Ocom_OSemi(U_735,U_736) ) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
( ! [U_744,U_742,U_740,U_738] :
( c_Com_Ocom_OSemi(U_738,U_740) = c_Com_Ocom_OSemi(U_742,U_744)
| U_740 != U_744
| U_738 != U_742 )
& ! [U_743,U_741,U_739,U_737] :
( ( U_739 = U_743
& U_737 = U_741 )
| c_Com_Ocom_OSemi(U_737,U_739) != c_Com_Ocom_OSemi(U_741,U_743) ) ),
inference(miniscope,[status(thm)],[f_131_2]) ).
fof(f_131_4,plain,
( ! [U_739,U_741,U_743,U_737] :
( U_739 = U_743
| ~ sP25(U_739,U_741,U_743,U_737) )
& ! [U_739,U_741,U_743,U_737] :
( U_737 = U_741
| ~ sP25(U_739,U_741,U_743,U_737) )
& ! [U_742,U_740,U_738,U_744] :
( c_Com_Ocom_OSemi(U_738,U_740) = c_Com_Ocom_OSemi(U_742,U_744)
| U_740 != U_744
| U_738 != U_742 )
& ! [U_739,U_741,U_743,U_737] :
( sP25(U_739,U_741,U_743,U_737)
| c_Com_Ocom_OSemi(U_737,U_739) != c_Com_Ocom_OSemi(U_741,U_743) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25])],[f_131_3]) ).
cnf(f_131_5,plain,
( sP25(U_739,U_741,U_743,U_737)
| c_Com_Ocom_OSemi(U_737,U_739) != c_Com_Ocom_OSemi(U_741,U_743) ),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_6,plain,
( c_Com_Ocom_OSemi(U_738,U_740) = c_Com_Ocom_OSemi(U_742,U_744)
| U_740 != U_744
| U_738 != U_742 ),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_7,plain,
( U_737 = U_741
| ~ sP25(U_739,U_741,U_743,U_737) ),
inference(clausify,[status(thm)],[f_131_4]) ).
cnf(f_131_8,plain,
( U_739 = U_743
| ~ sP25(U_739,U_741,U_743,U_737) ),
inference(clausify,[status(thm)],[f_131_4]) ).
fof(f_132_1,plain,
! [V_a_2,T_c] : c_HOL_OThe(T_c,hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2,
inference(fof_nnf,[status(thm)],[fact_the__eq__trivial]) ).
fof(f_132_2,plain,
! [U_746,U_745] : c_HOL_OThe(U_745,hAPP(hAPP(c_COMBC(U_745,U_745,tc_HOL_Obool),c_fequal),U_746)) = U_746,
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_746,U_745] : c_HOL_OThe(U_745,hAPP(hAPP(c_COMBC(U_745,U_745,tc_HOL_Obool),c_fequal),U_746)) = U_746,
inference(definitional_conversion,[status(esa)],[f_132_2]) ).
cnf(f_132_4,plain,
c_HOL_OThe(U_745,hAPP(hAPP(c_COMBC(U_745,U_745,tc_HOL_Obool),c_fequal),U_746)) = U_746,
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_1,plain,
! [V_y_2,V_z_2,V_f_2,T_d,V_A_2,V_x_2,T_c] :
( c_Nitpick_Ofold__graph_H(T_c,T_d,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_c,T_d,V_f_2,V_z_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)))),V_y_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J]) ).
fof(f_133_2,plain,
! [U_753,U_752,U_751,U_750,U_749,U_748,U_747] :
( c_Nitpick_Ofold__graph_H(U_747,U_750,U_751,U_752,U_749,hAPP(hAPP(U_751,U_748),U_753))
| ~ c_Nitpick_Ofold__graph_H(U_747,U_750,U_751,U_752,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_747,tc_HOL_Obool)),U_749),hAPP(hAPP(c_Set_Oinsert(U_747),U_748),c_Orderings_Obot__class_Obot(tc_fun(U_747,tc_HOL_Obool)))),U_753)
| ~ hBOOL(hAPP(hAPP(c_member(U_747),U_748),U_749)) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_747,U_748,U_749,U_750,U_751,U_752,U_753] :
( c_Nitpick_Ofold__graph_H(U_747,U_750,U_751,U_752,U_749,hAPP(hAPP(U_751,U_748),U_753))
| ~ c_Nitpick_Ofold__graph_H(U_747,U_750,U_751,U_752,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_747,tc_HOL_Obool)),U_749),hAPP(hAPP(c_Set_Oinsert(U_747),U_748),c_Orderings_Obot__class_Obot(tc_fun(U_747,tc_HOL_Obool)))),U_753)
| ~ hBOOL(hAPP(hAPP(c_member(U_747),U_748),U_749)) ),
inference(definitional_conversion,[status(esa)],[f_133_2]) ).
cnf(f_133_4,plain,
( c_Nitpick_Ofold__graph_H(U_747,U_750,U_751,U_752,U_749,hAPP(hAPP(U_751,U_748),U_753))
| ~ c_Nitpick_Ofold__graph_H(U_747,U_750,U_751,U_752,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_747,tc_HOL_Obool)),U_749),hAPP(hAPP(c_Set_Oinsert(U_747),U_748),c_Orderings_Obot__class_Obot(tc_fun(U_747,tc_HOL_Obool)))),U_753)
| ~ hBOOL(hAPP(hAPP(c_member(U_747),U_748),U_749)) ),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_1,plain,
! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,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_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_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))))),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph]) ).
fof(f_134_2,plain,
! [U_760,U_759,U_758,U_757,U_756,U_755,U_754] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_754,U_755,U_756,U_757,U_758),hAPP(hAPP(U_756,U_759),U_760)))
| ~ hBOOL(hAPP(hAPP(c_member(U_754),U_759),U_758))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_754,U_755,U_756,U_757,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_754,tc_HOL_Obool)),U_758),hAPP(hAPP(c_Set_Oinsert(U_754),U_759),c_Orderings_Obot__class_Obot(tc_fun(U_754,tc_HOL_Obool))))),U_760)) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_754,U_755,U_756,U_757,U_758,U_759,U_760] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_754,U_755,U_756,U_757,U_758),hAPP(hAPP(U_756,U_759),U_760)))
| ~ hBOOL(hAPP(hAPP(c_member(U_754),U_759),U_758))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_754,U_755,U_756,U_757,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_754,tc_HOL_Obool)),U_758),hAPP(hAPP(c_Set_Oinsert(U_754),U_759),c_Orderings_Obot__class_Obot(tc_fun(U_754,tc_HOL_Obool))))),U_760)) ),
inference(definitional_conversion,[status(esa)],[f_134_2]) ).
cnf(f_134_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_754,U_755,U_756,U_757,U_758),hAPP(hAPP(U_756,U_759),U_760)))
| ~ hBOOL(hAPP(hAPP(c_member(U_754),U_759),U_758))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_754,U_755,U_756,U_757,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_754,tc_HOL_Obool)),U_758),hAPP(hAPP(c_Set_Oinsert(U_754),U_759),c_Orderings_Obot__class_Obot(tc_fun(U_754,tc_HOL_Obool))))),U_760)) ),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_1,plain,
! [V_A_2,V_a_2,V_f_2,T_d,T_c] :
( ( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_d,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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_d,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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))))
& c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) )
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__insert]) ).
fof(f_135_2,plain,
! [U_765,U_764,U_763,U_762,U_761] :
( ( c_Fun_Oinj__on(U_761,U_762,U_763,hAPP(hAPP(c_Set_Oinsert(U_761),U_764),U_765))
| hBOOL(hAPP(hAPP(c_member(U_762),hAPP(U_763,U_764)),hAPP(c_Set_Oimage(U_761,U_762,U_763),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_761,tc_HOL_Obool)),U_765),hAPP(hAPP(c_Set_Oinsert(U_761),U_764),c_Orderings_Obot__class_Obot(tc_fun(U_761,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(U_761,U_762,U_763,U_765) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(U_762),hAPP(U_763,U_764)),hAPP(c_Set_Oimage(U_761,U_762,U_763),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_761,tc_HOL_Obool)),U_765),hAPP(hAPP(c_Set_Oinsert(U_761),U_764),c_Orderings_Obot__class_Obot(tc_fun(U_761,tc_HOL_Obool)))))))
& c_Fun_Oinj__on(U_761,U_762,U_763,U_765) )
| ~ c_Fun_Oinj__on(U_761,U_762,U_763,hAPP(hAPP(c_Set_Oinsert(U_761),U_764),U_765)) ) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
( ! [U_775,U_773,U_771,U_769,U_767] :
( c_Fun_Oinj__on(U_767,U_769,U_771,hAPP(hAPP(c_Set_Oinsert(U_767),U_773),U_775))
| hBOOL(hAPP(hAPP(c_member(U_769),hAPP(U_771,U_773)),hAPP(c_Set_Oimage(U_767,U_769,U_771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_767,tc_HOL_Obool)),U_775),hAPP(hAPP(c_Set_Oinsert(U_767),U_773),c_Orderings_Obot__class_Obot(tc_fun(U_767,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(U_767,U_769,U_771,U_775) )
& ! [U_774,U_772,U_770,U_768,U_766] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_768),hAPP(U_770,U_772)),hAPP(c_Set_Oimage(U_766,U_768,U_770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_766,tc_HOL_Obool)),U_774),hAPP(hAPP(c_Set_Oinsert(U_766),U_772),c_Orderings_Obot__class_Obot(tc_fun(U_766,tc_HOL_Obool)))))))
& c_Fun_Oinj__on(U_766,U_768,U_770,U_774) )
| ~ c_Fun_Oinj__on(U_766,U_768,U_770,hAPP(hAPP(c_Set_Oinsert(U_766),U_772),U_774)) ) ),
inference(miniscope,[status(thm)],[f_135_2]) ).
fof(f_135_4,plain,
( ! [U_768,U_766,U_770,U_772,U_774] :
( ~ hBOOL(hAPP(hAPP(c_member(U_768),hAPP(U_770,U_772)),hAPP(c_Set_Oimage(U_766,U_768,U_770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_766,tc_HOL_Obool)),U_774),hAPP(hAPP(c_Set_Oinsert(U_766),U_772),c_Orderings_Obot__class_Obot(tc_fun(U_766,tc_HOL_Obool)))))))
| ~ sP26(U_768,U_766,U_770,U_772,U_774) )
& ! [U_768,U_766,U_770,U_772,U_774] :
( c_Fun_Oinj__on(U_766,U_768,U_770,U_774)
| ~ sP26(U_768,U_766,U_770,U_772,U_774) )
& ! [U_769,U_767,U_773,U_771,U_775] :
( c_Fun_Oinj__on(U_767,U_769,U_771,hAPP(hAPP(c_Set_Oinsert(U_767),U_773),U_775))
| hBOOL(hAPP(hAPP(c_member(U_769),hAPP(U_771,U_773)),hAPP(c_Set_Oimage(U_767,U_769,U_771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_767,tc_HOL_Obool)),U_775),hAPP(hAPP(c_Set_Oinsert(U_767),U_773),c_Orderings_Obot__class_Obot(tc_fun(U_767,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(U_767,U_769,U_771,U_775) )
& ! [U_768,U_766,U_770,U_772,U_774] :
( sP26(U_768,U_766,U_770,U_772,U_774)
| ~ c_Fun_Oinj__on(U_766,U_768,U_770,hAPP(hAPP(c_Set_Oinsert(U_766),U_772),U_774)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_135_3]) ).
cnf(f_135_5,plain,
( sP26(U_768,U_766,U_770,U_772,U_774)
| ~ c_Fun_Oinj__on(U_766,U_768,U_770,hAPP(hAPP(c_Set_Oinsert(U_766),U_772),U_774)) ),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_6,plain,
( c_Fun_Oinj__on(U_767,U_769,U_771,hAPP(hAPP(c_Set_Oinsert(U_767),U_773),U_775))
| hBOOL(hAPP(hAPP(c_member(U_769),hAPP(U_771,U_773)),hAPP(c_Set_Oimage(U_767,U_769,U_771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_767,tc_HOL_Obool)),U_775),hAPP(hAPP(c_Set_Oinsert(U_767),U_773),c_Orderings_Obot__class_Obot(tc_fun(U_767,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(U_767,U_769,U_771,U_775) ),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_7,plain,
( c_Fun_Oinj__on(U_766,U_768,U_770,U_774)
| ~ sP26(U_768,U_766,U_770,U_772,U_774) ),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_768),hAPP(U_770,U_772)),hAPP(c_Set_Oimage(U_766,U_768,U_770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_766,tc_HOL_Obool)),U_774),hAPP(hAPP(c_Set_Oinsert(U_766),U_772),c_Orderings_Obot__class_Obot(tc_fun(U_766,tc_HOL_Obool)))))))
| ~ sP26(U_768,U_766,U_770,U_772,U_774) ),
inference(clausify,[status(thm)],[f_135_4]) ).
fof(f_136_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,V_f_2),V_x_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__one(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold_H]) ).
fof(f_136_2,plain,
! [U_780,U_779,U_778,U_777,U_776] :
( hAPP(U_778,hAPP(hAPP(c_Set_Oinsert(U_776),U_780),U_779)) = hAPP(hAPP(c_Finite__Set_Ofold(U_776,U_776,U_777),U_780),U_779)
| hBOOL(hAPP(hAPP(c_member(U_776),U_780),U_779))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_776),U_779))
| ~ c_Finite__Set_Ofolding__one(U_776,U_777,U_778) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
! [U_779,U_776,U_777,U_778,U_780] :
( hAPP(U_778,hAPP(hAPP(c_Set_Oinsert(U_776),U_780),U_779)) = hAPP(hAPP(c_Finite__Set_Ofold(U_776,U_776,U_777),U_780),U_779)
| hBOOL(hAPP(hAPP(c_member(U_776),U_780),U_779))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_776),U_779))
| ~ c_Finite__Set_Ofolding__one(U_776,U_777,U_778) ),
inference(definitional_conversion,[status(esa)],[f_136_2]) ).
cnf(f_136_4,plain,
( hAPP(U_778,hAPP(hAPP(c_Set_Oinsert(U_776),U_780),U_779)) = hAPP(hAPP(c_Finite__Set_Ofold(U_776,U_776,U_777),U_780),U_779)
| hBOOL(hAPP(hAPP(c_member(U_776),U_780),U_779))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_776),U_779))
| ~ c_Finite__Set_Ofolding__one(U_776,U_777,U_778) ),
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,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_c),hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)))),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))))),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_minus__fold__remove]) ).
fof(f_137_2,plain,
! [U_783,U_782,U_781] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_781,tc_HOL_Obool)),U_783),U_782) = hAPP(hAPP(c_Finite__Set_Ofold(U_781,tc_fun(U_781,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_781,tc_HOL_Obool),tc_fun(tc_fun(U_781,tc_HOL_Obool),tc_fun(U_781,tc_HOL_Obool)),U_781),hAPP(c_COMBC(tc_fun(U_781,tc_HOL_Obool),tc_fun(U_781,tc_HOL_Obool),tc_fun(U_781,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_781,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_781,tc_fun(U_781,tc_HOL_Obool),tc_fun(U_781,tc_HOL_Obool)),c_Set_Oinsert(U_781)),c_Orderings_Obot__class_Obot(tc_fun(U_781,tc_HOL_Obool))))),U_783),U_782)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_781),U_782)) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_781,U_782,U_783] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_781,tc_HOL_Obool)),U_783),U_782) = hAPP(hAPP(c_Finite__Set_Ofold(U_781,tc_fun(U_781,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_781,tc_HOL_Obool),tc_fun(tc_fun(U_781,tc_HOL_Obool),tc_fun(U_781,tc_HOL_Obool)),U_781),hAPP(c_COMBC(tc_fun(U_781,tc_HOL_Obool),tc_fun(U_781,tc_HOL_Obool),tc_fun(U_781,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_781,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_781,tc_fun(U_781,tc_HOL_Obool),tc_fun(U_781,tc_HOL_Obool)),c_Set_Oinsert(U_781)),c_Orderings_Obot__class_Obot(tc_fun(U_781,tc_HOL_Obool))))),U_783),U_782)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_781),U_782)) ),
inference(definitional_conversion,[status(esa)],[f_137_2]) ).
cnf(f_137_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_781,tc_HOL_Obool)),U_783),U_782) = hAPP(hAPP(c_Finite__Set_Ofold(U_781,tc_fun(U_781,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_781,tc_HOL_Obool),tc_fun(tc_fun(U_781,tc_HOL_Obool),tc_fun(U_781,tc_HOL_Obool)),U_781),hAPP(c_COMBC(tc_fun(U_781,tc_HOL_Obool),tc_fun(U_781,tc_HOL_Obool),tc_fun(U_781,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_781,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_781,tc_fun(U_781,tc_HOL_Obool),tc_fun(U_781,tc_HOL_Obool)),c_Set_Oinsert(U_781)),c_Orderings_Obot__class_Obot(tc_fun(U_781,tc_HOL_Obool))))),U_783),U_782)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_781),U_782)) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_1,plain,
! [V_x_2,V_f_2,V_A_2,T_d,T_c] : hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_c,hAPP(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(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),V_x_2))),
inference(fof_nnf,[status(thm)],[fact_the__inv__into__def]) ).
fof(f_138_2,plain,
! [U_788,U_787,U_786,U_785,U_784] : hAPP(c_Fun_Othe__inv__into(U_784,U_785,U_786,U_787),U_788) = c_HOL_OThe(U_784,hAPP(hAPP(c_COMBS(U_784,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_784),c_fconj),hAPP(hAPP(c_COMBC(U_784,tc_fun(U_784,tc_HOL_Obool),tc_HOL_Obool),c_member(U_784)),U_786))),hAPP(hAPP(c_COMBC(U_784,U_785,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_785,tc_fun(U_785,tc_HOL_Obool),U_784),c_fequal),U_787)),U_788))),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_784,U_785,U_786,U_787,U_788] : hAPP(c_Fun_Othe__inv__into(U_784,U_785,U_786,U_787),U_788) = c_HOL_OThe(U_784,hAPP(hAPP(c_COMBS(U_784,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_784),c_fconj),hAPP(hAPP(c_COMBC(U_784,tc_fun(U_784,tc_HOL_Obool),tc_HOL_Obool),c_member(U_784)),U_786))),hAPP(hAPP(c_COMBC(U_784,U_785,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_785,tc_fun(U_785,tc_HOL_Obool),U_784),c_fequal),U_787)),U_788))),
inference(definitional_conversion,[status(esa)],[f_138_2]) ).
cnf(f_138_4,plain,
hAPP(c_Fun_Othe__inv__into(U_784,U_785,U_786,U_787),U_788) = c_HOL_OThe(U_784,hAPP(hAPP(c_COMBS(U_784,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_784),c_fconj),hAPP(hAPP(c_COMBC(U_784,tc_fun(U_784,tc_HOL_Obool),tc_HOL_Obool),c_member(U_784)),U_786))),hAPP(hAPP(c_COMBC(U_784,U_785,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_785,tc_fun(U_785,tc_HOL_Obool),U_784),c_fequal),U_787)),U_788))),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
! [V_B_2,V_x_2,V_A_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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))))),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ) )
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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))))),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__insert__iff]) ).
fof(f_139_2,plain,
! [U_792,U_791,U_790,U_789] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_789,tc_HOL_Obool)),U_790),hAPP(hAPP(c_Set_Oinsert(U_789),U_791),U_792)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_789,tc_HOL_Obool)),U_790),U_792))
& ~ hBOOL(hAPP(hAPP(c_member(U_789),U_791),U_790)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_789,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_789,tc_HOL_Obool)),U_790),hAPP(hAPP(c_Set_Oinsert(U_789),U_791),c_Orderings_Obot__class_Obot(tc_fun(U_789,tc_HOL_Obool))))),U_792))
& hBOOL(hAPP(hAPP(c_member(U_789),U_791),U_790)) ) )
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_789,tc_HOL_Obool)),U_790),U_792))
| hBOOL(hAPP(hAPP(c_member(U_789),U_791),U_790)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_789,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_789,tc_HOL_Obool)),U_790),hAPP(hAPP(c_Set_Oinsert(U_789),U_791),c_Orderings_Obot__class_Obot(tc_fun(U_789,tc_HOL_Obool))))),U_792))
| ~ hBOOL(hAPP(hAPP(c_member(U_789),U_791),U_790)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_789,tc_HOL_Obool)),U_790),hAPP(hAPP(c_Set_Oinsert(U_789),U_791),U_792))) ) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
( ! [U_800,U_798,U_796,U_794] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_794,tc_HOL_Obool)),U_796),hAPP(hAPP(c_Set_Oinsert(U_794),U_798),U_800)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_794,tc_HOL_Obool)),U_796),U_800))
& ~ hBOOL(hAPP(hAPP(c_member(U_794),U_798),U_796)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_794,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_794,tc_HOL_Obool)),U_796),hAPP(hAPP(c_Set_Oinsert(U_794),U_798),c_Orderings_Obot__class_Obot(tc_fun(U_794,tc_HOL_Obool))))),U_800))
& hBOOL(hAPP(hAPP(c_member(U_794),U_798),U_796)) ) )
& ! [U_799,U_797,U_795,U_793] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_793,tc_HOL_Obool)),U_795),U_799))
| hBOOL(hAPP(hAPP(c_member(U_793),U_797),U_795)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_793,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_793,tc_HOL_Obool)),U_795),hAPP(hAPP(c_Set_Oinsert(U_793),U_797),c_Orderings_Obot__class_Obot(tc_fun(U_793,tc_HOL_Obool))))),U_799))
| ~ hBOOL(hAPP(hAPP(c_member(U_793),U_797),U_795)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_793,tc_HOL_Obool)),U_795),hAPP(hAPP(c_Set_Oinsert(U_793),U_797),U_799))) ) ),
inference(miniscope,[status(thm)],[f_139_2]) ).
fof(f_139_4,plain,
( ! [U_800,U_796,U_794,U_798] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_794,tc_HOL_Obool)),U_796),U_800))
| ~ sP29(U_800,U_796,U_794,U_798) )
& ! [U_800,U_796,U_794,U_798] :
( ~ hBOOL(hAPP(hAPP(c_member(U_794),U_798),U_796))
| ~ sP29(U_800,U_796,U_794,U_798) )
& ! [U_800,U_796,U_794,U_798] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_794,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_794,tc_HOL_Obool)),U_796),hAPP(hAPP(c_Set_Oinsert(U_794),U_798),c_Orderings_Obot__class_Obot(tc_fun(U_794,tc_HOL_Obool))))),U_800))
| ~ sP28(U_800,U_796,U_794,U_798) )
& ! [U_800,U_796,U_794,U_798] :
( hBOOL(hAPP(hAPP(c_member(U_794),U_798),U_796))
| ~ sP28(U_800,U_796,U_794,U_798) )
& ! [U_797,U_799,U_793,U_795] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_793,tc_HOL_Obool)),U_795),U_799))
| hBOOL(hAPP(hAPP(c_member(U_793),U_797),U_795))
| ~ sP27(U_797,U_799,U_793,U_795) )
& ! [U_797,U_799,U_793,U_795] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_793,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_793,tc_HOL_Obool)),U_795),hAPP(hAPP(c_Set_Oinsert(U_793),U_797),c_Orderings_Obot__class_Obot(tc_fun(U_793,tc_HOL_Obool))))),U_799))
| ~ hBOOL(hAPP(hAPP(c_member(U_793),U_797),U_795))
| ~ sP27(U_797,U_799,U_793,U_795) )
& ! [U_800,U_796,U_794,U_798] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_794,tc_HOL_Obool)),U_796),hAPP(hAPP(c_Set_Oinsert(U_794),U_798),U_800)))
| sP29(U_800,U_796,U_794,U_798)
| sP28(U_800,U_796,U_794,U_798) )
& ! [U_797,U_799,U_793,U_795] :
( sP27(U_797,U_799,U_793,U_795)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_793,tc_HOL_Obool)),U_795),hAPP(hAPP(c_Set_Oinsert(U_793),U_797),U_799))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27,sP28,sP29])],[f_139_3]) ).
cnf(f_139_5,plain,
( sP27(U_797,U_799,U_793,U_795)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_793,tc_HOL_Obool)),U_795),hAPP(hAPP(c_Set_Oinsert(U_793),U_797),U_799))) ),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_794,tc_HOL_Obool)),U_796),hAPP(hAPP(c_Set_Oinsert(U_794),U_798),U_800)))
| sP29(U_800,U_796,U_794,U_798)
| sP28(U_800,U_796,U_794,U_798) ),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_793,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_793,tc_HOL_Obool)),U_795),hAPP(hAPP(c_Set_Oinsert(U_793),U_797),c_Orderings_Obot__class_Obot(tc_fun(U_793,tc_HOL_Obool))))),U_799))
| ~ hBOOL(hAPP(hAPP(c_member(U_793),U_797),U_795))
| ~ sP27(U_797,U_799,U_793,U_795) ),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_793,tc_HOL_Obool)),U_795),U_799))
| hBOOL(hAPP(hAPP(c_member(U_793),U_797),U_795))
| ~ sP27(U_797,U_799,U_793,U_795) ),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_794),U_798),U_796))
| ~ sP28(U_800,U_796,U_794,U_798) ),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_794,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_794,tc_HOL_Obool)),U_796),hAPP(hAPP(c_Set_Oinsert(U_794),U_798),c_Orderings_Obot__class_Obot(tc_fun(U_794,tc_HOL_Obool))))),U_800))
| ~ sP28(U_800,U_796,U_794,U_798) ),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_794),U_798),U_796))
| ~ sP29(U_800,U_796,U_794,U_798) ),
inference(clausify,[status(thm)],[f_139_4]) ).
cnf(f_139_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_794,tc_HOL_Obool)),U_796),U_800))
| ~ sP29(U_800,U_796,U_794,U_798) ),
inference(clausify,[status(thm)],[f_139_4]) ).
fof(f_140_1,plain,
! [V_B_2,V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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))))),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_diff__single__insert]) ).
fof(f_140_2,plain,
! [U_804,U_803,U_802,U_801] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_801,tc_HOL_Obool)),U_802),hAPP(hAPP(c_Set_Oinsert(U_801),U_803),U_804)))
| ~ hBOOL(hAPP(hAPP(c_member(U_801),U_803),U_802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_801,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_801,tc_HOL_Obool)),U_802),hAPP(hAPP(c_Set_Oinsert(U_801),U_803),c_Orderings_Obot__class_Obot(tc_fun(U_801,tc_HOL_Obool))))),U_804)) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
! [U_801,U_802,U_803,U_804] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_801,tc_HOL_Obool)),U_802),hAPP(hAPP(c_Set_Oinsert(U_801),U_803),U_804)))
| ~ hBOOL(hAPP(hAPP(c_member(U_801),U_803),U_802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_801,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_801,tc_HOL_Obool)),U_802),hAPP(hAPP(c_Set_Oinsert(U_801),U_803),c_Orderings_Obot__class_Obot(tc_fun(U_801,tc_HOL_Obool))))),U_804)) ),
inference(definitional_conversion,[status(esa)],[f_140_2]) ).
cnf(f_140_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_801,tc_HOL_Obool)),U_802),hAPP(hAPP(c_Set_Oinsert(U_801),U_803),U_804)))
| ~ hBOOL(hAPP(hAPP(c_member(U_801),U_803),U_802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_801,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_801,tc_HOL_Obool)),U_802),hAPP(hAPP(c_Set_Oinsert(U_801),U_803),c_Orderings_Obot__class_Obot(tc_fun(U_801,tc_HOL_Obool))))),U_804)) ),
inference(clausify,[status(thm)],[f_140_3]) ).
fof(f_141_1,plain,
! [V_f_2,V_a_2,V_A_2,T_c,T_d] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Oab__group__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff1]) ).
fof(f_141_2,plain,
! [U_809,U_808,U_807,U_806,U_805] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_806,U_805),U_809),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_806,tc_HOL_Obool)),U_807),hAPP(hAPP(c_Set_Oinsert(U_806),U_808),c_Orderings_Obot__class_Obot(tc_fun(U_806,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_806,U_805),U_809),U_807)
| hBOOL(hAPP(hAPP(c_member(U_806),U_808),U_807)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_806,U_805),U_809),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_806,tc_HOL_Obool)),U_807),hAPP(hAPP(c_Set_Oinsert(U_806),U_808),c_Orderings_Obot__class_Obot(tc_fun(U_806,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_805),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_806,U_805),U_809),U_807)),hAPP(U_809,U_808))
| ~ hBOOL(hAPP(hAPP(c_member(U_806),U_808),U_807)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_806),U_807))
| ~ class_Groups_Oab__group__add(U_805) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
( ! [U_806,U_805,U_807,U_808,U_809] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_806,U_805),U_809),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_806,tc_HOL_Obool)),U_807),hAPP(hAPP(c_Set_Oinsert(U_806),U_808),c_Orderings_Obot__class_Obot(tc_fun(U_806,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_806,U_805),U_809),U_807)
| hBOOL(hAPP(hAPP(c_member(U_806),U_808),U_807))
| ~ sP30(U_806,U_805,U_807,U_808,U_809) )
& ! [U_806,U_805,U_807,U_808,U_809] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_806,U_805),U_809),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_806,tc_HOL_Obool)),U_807),hAPP(hAPP(c_Set_Oinsert(U_806),U_808),c_Orderings_Obot__class_Obot(tc_fun(U_806,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_805),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_806,U_805),U_809),U_807)),hAPP(U_809,U_808))
| ~ hBOOL(hAPP(hAPP(c_member(U_806),U_808),U_807))
| ~ sP30(U_806,U_805,U_807,U_808,U_809) )
& ! [U_806,U_805,U_807,U_808,U_809] :
( sP30(U_806,U_805,U_807,U_808,U_809)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_806),U_807))
| ~ class_Groups_Oab__group__add(U_805) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30])],[f_141_2]) ).
cnf(f_141_4,plain,
( sP30(U_806,U_805,U_807,U_808,U_809)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_806),U_807))
| ~ class_Groups_Oab__group__add(U_805) ),
inference(clausify,[status(thm)],[f_141_3]) ).
cnf(f_141_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_806,U_805),U_809),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_806,tc_HOL_Obool)),U_807),hAPP(hAPP(c_Set_Oinsert(U_806),U_808),c_Orderings_Obot__class_Obot(tc_fun(U_806,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_805),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_806,U_805),U_809),U_807)),hAPP(U_809,U_808))
| ~ hBOOL(hAPP(hAPP(c_member(U_806),U_808),U_807))
| ~ sP30(U_806,U_805,U_807,U_808,U_809) ),
inference(clausify,[status(thm)],[f_141_3]) ).
cnf(f_141_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_806,U_805),U_809),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_806,tc_HOL_Obool)),U_807),hAPP(hAPP(c_Set_Oinsert(U_806),U_808),c_Orderings_Obot__class_Obot(tc_fun(U_806,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_806,U_805),U_809),U_807)
| hBOOL(hAPP(hAPP(c_member(U_806),U_808),U_807))
| ~ sP30(U_806,U_805,U_807,U_808,U_809) ),
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_1,plain,
! [V_f_2,V_a_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Rings_Oring(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring]) ).
fof(f_142_2,plain,
! [U_814,U_813,U_812,U_811,U_810] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_811,U_810),U_814),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_811,tc_HOL_Obool)),U_812),hAPP(hAPP(c_Set_Oinsert(U_811),U_813),c_Orderings_Obot__class_Obot(tc_fun(U_811,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_810),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_811,U_810),U_814),U_812)),hAPP(U_814,U_813))
| ~ hBOOL(hAPP(hAPP(c_member(U_811),U_813),U_812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_811),U_812))
| ~ class_Rings_Oring(U_810) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
! [U_811,U_810,U_814,U_813,U_812] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_811,U_810),U_814),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_811,tc_HOL_Obool)),U_812),hAPP(hAPP(c_Set_Oinsert(U_811),U_813),c_Orderings_Obot__class_Obot(tc_fun(U_811,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_810),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_811,U_810),U_814),U_812)),hAPP(U_814,U_813))
| ~ hBOOL(hAPP(hAPP(c_member(U_811),U_813),U_812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_811),U_812))
| ~ class_Rings_Oring(U_810) ),
inference(definitional_conversion,[status(esa)],[f_142_2]) ).
cnf(f_142_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_811,U_810),U_814),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_811,tc_HOL_Obool)),U_812),hAPP(hAPP(c_Set_Oinsert(U_811),U_813),c_Orderings_Obot__class_Obot(tc_fun(U_811,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_810),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_811,U_810),U_814),U_812)),hAPP(U_814,U_813))
| ~ hBOOL(hAPP(hAPP(c_member(U_811),U_813),U_812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_811),U_812))
| ~ class_Rings_Oring(U_810) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_1,plain,
! [V_g_2,V_f_2,T_d,V_A_2,V_a_2,T_c] :
( ( hAPP(c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) )
& ( hAPP(c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_override__on__def]) ).
fof(f_143_2,plain,
! [U_820,U_819,U_818,U_817,U_816,U_815] :
( ( hAPP(c_Fun_Ooverride__on(U_815,U_818,U_819,U_820,U_817),U_816) = hAPP(U_819,U_816)
| hBOOL(hAPP(hAPP(c_member(U_815),U_816),U_817)) )
& ( hAPP(c_Fun_Ooverride__on(U_815,U_818,U_819,U_820,U_817),U_816) = hAPP(U_820,U_816)
| ~ hBOOL(hAPP(hAPP(c_member(U_815),U_816),U_817)) ) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
( ! [U_832,U_830,U_828,U_826,U_824,U_822] :
( hAPP(c_Fun_Ooverride__on(U_822,U_828,U_830,U_832,U_826),U_824) = hAPP(U_830,U_824)
| hBOOL(hAPP(hAPP(c_member(U_822),U_824),U_826)) )
& ! [U_831,U_829,U_827,U_825,U_823,U_821] :
( hAPP(c_Fun_Ooverride__on(U_821,U_827,U_829,U_831,U_825),U_823) = hAPP(U_831,U_823)
| ~ hBOOL(hAPP(hAPP(c_member(U_821),U_823),U_825)) ) ),
inference(miniscope,[status(thm)],[f_143_2]) ).
fof(f_143_4,plain,
( ! [U_822,U_824,U_826,U_828,U_830,U_832] :
( hAPP(c_Fun_Ooverride__on(U_822,U_828,U_830,U_832,U_826),U_824) = hAPP(U_830,U_824)
| hBOOL(hAPP(hAPP(c_member(U_822),U_824),U_826)) )
& ! [U_823,U_827,U_821,U_825,U_829,U_831] :
( hAPP(c_Fun_Ooverride__on(U_821,U_827,U_829,U_831,U_825),U_823) = hAPP(U_831,U_823)
| ~ hBOOL(hAPP(hAPP(c_member(U_821),U_823),U_825)) ) ),
inference(definitional_conversion,[status(esa)],[f_143_3]) ).
cnf(f_143_5,plain,
( hAPP(c_Fun_Ooverride__on(U_821,U_827,U_829,U_831,U_825),U_823) = hAPP(U_831,U_823)
| ~ hBOOL(hAPP(hAPP(c_member(U_821),U_823),U_825)) ),
inference(clausify,[status(thm)],[f_143_4]) ).
cnf(f_143_6,plain,
( hAPP(c_Fun_Ooverride__on(U_822,U_828,U_830,U_832,U_826),U_824) = hAPP(U_830,U_824)
| hBOOL(hAPP(hAPP(c_member(U_822),U_824),U_826)) ),
inference(clausify,[status(thm)],[f_143_4]) ).
fof(f_144_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_144_2,plain,
! [U_834,U_833] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_833),U_834),U_834))
| ~ class_Orderings_Opreorder(U_833) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_833,U_834] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_833),U_834),U_834))
| ~ class_Orderings_Opreorder(U_833) ),
inference(definitional_conversion,[status(esa)],[f_144_2]) ).
cnf(f_144_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_833),U_834),U_834))
| ~ class_Orderings_Opreorder(U_833) ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [V_B_2,V_A_2,T_c] :
( V_A_2 = V_B_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(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_equalityI]) ).
fof(f_145_2,plain,
! [U_837,U_836,U_835] :
( U_836 = U_837
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_835,tc_HOL_Obool)),U_837),U_836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_835,tc_HOL_Obool)),U_836),U_837)) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_835,U_836,U_837] :
( U_836 = U_837
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_835,tc_HOL_Obool)),U_837),U_836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_835,tc_HOL_Obool)),U_836),U_837)) ),
inference(definitional_conversion,[status(esa)],[f_145_2]) ).
cnf(f_145_4,plain,
( U_836 = U_837
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_835,tc_HOL_Obool)),U_837),U_836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_835,tc_HOL_Obool)),U_836),U_837)) ),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_1,plain,
! [V_c_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_subsetD]) ).
fof(f_146_2,plain,
! [U_841,U_840,U_839,U_838] :
( hBOOL(hAPP(hAPP(c_member(U_838),U_841),U_840))
| ~ hBOOL(hAPP(hAPP(c_member(U_838),U_841),U_839))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_838,tc_HOL_Obool)),U_839),U_840)) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_838,U_839,U_840,U_841] :
( hBOOL(hAPP(hAPP(c_member(U_838),U_841),U_840))
| ~ hBOOL(hAPP(hAPP(c_member(U_838),U_841),U_839))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_838,tc_HOL_Obool)),U_839),U_840)) ),
inference(definitional_conversion,[status(esa)],[f_146_2]) ).
cnf(f_146_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_838),U_841),U_840))
| ~ hBOOL(hAPP(hAPP(c_member(U_838),U_841),U_839))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_838,tc_HOL_Obool)),U_839),U_840)) ),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_1,plain,
! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_empty__subsetI]) ).
fof(f_147_2,plain,
! [U_843,U_842] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_842,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_842,tc_HOL_Obool))),U_843)),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_843,U_842] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_842,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_842,tc_HOL_Obool))),U_843)),
inference(definitional_conversion,[status(esa)],[f_147_2]) ).
cnf(f_147_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_842,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_842,tc_HOL_Obool))),U_843)),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_1,plain,
! [V_f_2,T_d,T_c] : c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_inj__on__empty]) ).
fof(f_148_2,plain,
! [U_846,U_845,U_844] : c_Fun_Oinj__on(U_844,U_845,U_846,c_Orderings_Obot__class_Obot(tc_fun(U_844,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_844,U_845,U_846] : c_Fun_Oinj__on(U_844,U_845,U_846,c_Orderings_Obot__class_Obot(tc_fun(U_844,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_148_2]) ).
cnf(f_148_4,plain,
c_Fun_Oinj__on(U_844,U_845,U_846,c_Orderings_Obot__class_Obot(tc_fun(U_844,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_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_149_2,plain,
! [U_849,U_848,U_847] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_847),U_849),U_848))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_847),U_848),U_849))
| ~ class_Orderings_Olinorder(U_847) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_847,U_848,U_849] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_847),U_849),U_848))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_847),U_848),U_849))
| ~ class_Orderings_Olinorder(U_847) ),
inference(definitional_conversion,[status(esa)],[f_149_2]) ).
cnf(f_149_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_847),U_849),U_848))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_847),U_848),U_849))
| ~ class_Orderings_Olinorder(U_847) ),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_1,plain,
! [V_x_2,V_g_2,V_f_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),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_c,T_d)),V_f_2),V_g_2))
| ~ class_Orderings_Oord(T_d) ),
inference(fof_nnf,[status(thm)],[fact_le__funE]) ).
fof(f_150_2,plain,
! [U_854,U_853,U_852,U_851,U_850] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_850),hAPP(U_852,U_854)),hAPP(U_853,U_854)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_851,U_850)),U_852),U_853))
| ~ class_Orderings_Oord(U_850) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_850,U_851,U_852,U_853,U_854] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_850),hAPP(U_852,U_854)),hAPP(U_853,U_854)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_851,U_850)),U_852),U_853))
| ~ class_Orderings_Oord(U_850) ),
inference(definitional_conversion,[status(esa)],[f_150_2]) ).
cnf(f_150_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_850),hAPP(U_852,U_854)),hAPP(U_853,U_854)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_851,U_850)),U_852),U_853))
| ~ class_Orderings_Oord(U_850) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_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_151_2,plain,
! [U_858,U_857,U_856,U_855] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_855),U_858),U_857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_855),U_858),U_856))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_855),U_856),U_857))
| ~ class_Orderings_Oorder(U_855) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_855,U_856,U_857,U_858] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_855),U_858),U_857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_855),U_858),U_856))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_855),U_856),U_857))
| ~ class_Orderings_Oorder(U_855) ),
inference(definitional_conversion,[status(esa)],[f_151_2]) ).
cnf(f_151_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_855),U_858),U_857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_855),U_858),U_856))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_855),U_856),U_857))
| ~ class_Orderings_Oorder(U_855) ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_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_152_2,plain,
! [U_861,U_860,U_859] :
( U_861 = U_860
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_859),U_861),U_860))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_859),U_860),U_861))
| ~ class_Orderings_Oorder(U_859) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_859,U_860,U_861] :
( U_861 = U_860
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_859),U_861),U_860))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_859),U_860),U_861))
| ~ class_Orderings_Oorder(U_859) ),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
( U_861 = U_860
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_859),U_861),U_860))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_859),U_860),U_861))
| ~ class_Orderings_Oorder(U_859) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_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_153_2,plain,
! [U_865,U_864,U_863,U_862] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_862),U_863),U_865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_862),U_864),U_865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_862),U_863),U_864))
| ~ class_Orderings_Opreorder(U_862) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_862,U_863,U_864,U_865] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_862),U_863),U_865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_862),U_864),U_865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_862),U_863),U_864))
| ~ class_Orderings_Opreorder(U_862) ),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_862),U_863),U_865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_862),U_864),U_865))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_862),U_863),U_864))
| ~ class_Orderings_Opreorder(U_862) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_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_154_2,plain,
! [U_868,U_867,U_866] :
( U_867 = U_868
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_866),U_868),U_867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_866),U_867),U_868))
| ~ class_Orderings_Oorder(U_866) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
! [U_866,U_867,U_868] :
( U_867 = U_868
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_866),U_868),U_867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_866),U_867),U_868))
| ~ class_Orderings_Oorder(U_866) ),
inference(definitional_conversion,[status(esa)],[f_154_2]) ).
cnf(f_154_4,plain,
( U_867 = U_868
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_866),U_868),U_867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_866),U_867),U_868))
| ~ class_Orderings_Oorder(U_866) ),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_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_155_2,plain,
! [U_872,U_871,U_870,U_869] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_869),U_872),U_871))
| U_870 != U_872
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_869),U_870),U_871))
| ~ class_Orderings_Oorder(U_869) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_869,U_870,U_871,U_872] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_869),U_872),U_871))
| U_870 != U_872
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_869),U_870),U_871))
| ~ class_Orderings_Oorder(U_869) ),
inference(definitional_conversion,[status(esa)],[f_155_2]) ).
cnf(f_155_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_869),U_872),U_871))
| U_870 != U_872
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_869),U_870),U_871))
| ~ class_Orderings_Oorder(U_869) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_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_156_2,plain,
! [U_876,U_875,U_874,U_873] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_873),U_874),U_876))
| U_875 != U_876
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_873),U_874),U_875))
| ~ class_Orderings_Oord(U_873) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
! [U_873,U_874,U_875,U_876] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_873),U_874),U_876))
| U_875 != U_876
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_873),U_874),U_875))
| ~ class_Orderings_Oord(U_873) ),
inference(definitional_conversion,[status(esa)],[f_156_2]) ).
cnf(f_156_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_873),U_874),U_876))
| U_875 != U_876
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_873),U_874),U_875))
| ~ class_Orderings_Oord(U_873) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_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_157_2,plain,
! [U_880,U_879,U_878,U_877] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_877),U_880),U_878))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_877),U_880),U_879))
| U_878 != U_879
| ~ class_Orderings_Oorder(U_877) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
! [U_880,U_877,U_878,U_879] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_877),U_880),U_878))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_877),U_880),U_879))
| U_878 != U_879
| ~ class_Orderings_Oorder(U_877) ),
inference(definitional_conversion,[status(esa)],[f_157_2]) ).
cnf(f_157_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_877),U_880),U_878))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_877),U_880),U_879))
| U_878 != U_879
| ~ class_Orderings_Oorder(U_877) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_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_158_2,plain,
! [U_884,U_883,U_882,U_881] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_881),U_882),U_884))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_881),U_883),U_884))
| U_882 != U_883
| ~ class_Orderings_Oord(U_881) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_881,U_882,U_883,U_884] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_881),U_882),U_884))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_881),U_883),U_884))
| U_882 != U_883
| ~ class_Orderings_Oord(U_881) ),
inference(definitional_conversion,[status(esa)],[f_158_2]) ).
cnf(f_158_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_881),U_882),U_884))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_881),U_883),U_884))
| U_882 != U_883
| ~ class_Orderings_Oord(U_881) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_1,plain,
! [V_x_2,V_Qa_2,V_Pa_2,T_c] :
( 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_c,tc_HOL_Obool)),V_Pa_2),V_Qa_2)) ),
inference(fof_nnf,[status(thm)],[fact_predicate1D]) ).
fof(f_159_2,plain,
! [U_888,U_887,U_886,U_885] :
( hBOOL(hAPP(U_887,U_888))
| ~ hBOOL(hAPP(U_886,U_888))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_885,tc_HOL_Obool)),U_886),U_887)) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_888,U_887,U_886] :
( ! [U_885] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_885,tc_HOL_Obool)),U_886),U_887))
| hBOOL(hAPP(U_887,U_888))
| ~ hBOOL(hAPP(U_886,U_888)) ),
inference(miniscope,[status(thm)],[f_159_2]) ).
fof(f_159_4,plain,
! [U_886,U_887,U_885,U_888] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_885,tc_HOL_Obool)),U_886),U_887))
| hBOOL(hAPP(U_887,U_888))
| ~ hBOOL(hAPP(U_886,U_888)) ),
inference(definitional_conversion,[status(esa)],[f_159_3]) ).
cnf(f_159_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_885,tc_HOL_Obool)),U_886),U_887))
| hBOOL(hAPP(U_887,U_888))
| ~ hBOOL(hAPP(U_886,U_888)) ),
inference(clausify,[status(thm)],[f_159_4]) ).
fof(f_160_1,plain,
! [V_x_2,V_y_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),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_c),V_x_2),V_y_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).
fof(f_160_2,plain,
! [U_891,U_890,U_889] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_889),U_891),U_890))
| U_891 != U_890 )
& ( U_891 = U_890
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_889),U_891),U_890)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_889),U_890),U_891))
| ~ class_Orderings_Oorder(U_889) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
( ! [U_889,U_890,U_891] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_889),U_891),U_890))
| U_891 != U_890
| ~ sP31(U_889,U_890,U_891) )
& ! [U_889,U_890,U_891] :
( U_891 = U_890
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_889),U_891),U_890))
| ~ sP31(U_889,U_890,U_891) )
& ! [U_889,U_890,U_891] :
( sP31(U_889,U_890,U_891)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_889),U_890),U_891))
| ~ class_Orderings_Oorder(U_889) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31])],[f_160_2]) ).
cnf(f_160_4,plain,
( sP31(U_889,U_890,U_891)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_889),U_890),U_891))
| ~ class_Orderings_Oorder(U_889) ),
inference(clausify,[status(thm)],[f_160_3]) ).
cnf(f_160_5,plain,
( U_891 = U_890
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_889),U_891),U_890))
| ~ sP31(U_889,U_890,U_891) ),
inference(clausify,[status(thm)],[f_160_3]) ).
cnf(f_160_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_889),U_891),U_890))
| U_891 != U_890
| ~ sP31(U_889,U_890,U_891) ),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_1,plain,
! [V_x_2,V_g_2,V_f_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),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_c,T_d)),V_f_2),V_g_2))
| ~ class_Orderings_Oord(T_d) ),
inference(fof_nnf,[status(thm)],[fact_le__funD]) ).
fof(f_161_2,plain,
! [U_896,U_895,U_894,U_893,U_892] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_892),hAPP(U_894,U_896)),hAPP(U_895,U_896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_893,U_892)),U_894),U_895))
| ~ class_Orderings_Oord(U_892) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_895,U_894,U_893,U_892,U_896] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_892),hAPP(U_894,U_896)),hAPP(U_895,U_896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_893,U_892)),U_894),U_895))
| ~ class_Orderings_Oord(U_892) ),
inference(definitional_conversion,[status(esa)],[f_161_2]) ).
cnf(f_161_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_892),hAPP(U_894,U_896)),hAPP(U_895,U_896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_893,U_892)),U_894),U_895))
| ~ class_Orderings_Oord(U_892) ),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_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_162_2,plain,
! [U_899,U_898,U_897] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_897),U_898),U_899))
| U_898 != U_899
| ~ class_Orderings_Opreorder(U_897) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_898,U_897,U_899] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_897),U_898),U_899))
| U_898 != U_899
| ~ class_Orderings_Opreorder(U_897) ),
inference(definitional_conversion,[status(esa)],[f_162_2]) ).
cnf(f_162_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_897),U_898),U_899))
| U_898 != U_899
| ~ class_Orderings_Opreorder(U_897) ),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_1,plain,
! [V_Qa_2,T_c,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_c,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_163_2,plain,
! [U_903,U_902,U_901,U_900] :
( hBOOL(hAPP(U_903,U_901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_902,tc_HOL_Obool)),U_900),U_903))
| ~ hBOOL(hAPP(U_900,U_901)) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_901,U_900,U_902,U_903] :
( hBOOL(hAPP(U_903,U_901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_902,tc_HOL_Obool)),U_900),U_903))
| ~ hBOOL(hAPP(U_900,U_901)) ),
inference(definitional_conversion,[status(esa)],[f_163_2]) ).
cnf(f_163_4,plain,
( hBOOL(hAPP(U_903,U_901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_902,tc_HOL_Obool)),U_900),U_903))
| ~ hBOOL(hAPP(U_900,U_901)) ),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) )
| V_x_2 != V_y_2 ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).
fof(f_164_2,plain,
! [U_906,U_905,U_904] :
( ( ( U_905 = U_906
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_904),U_906),U_905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_904),U_905),U_906)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_904),U_906),U_905))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_904),U_905),U_906)) )
| U_905 != U_906 ) )
| ~ class_Orderings_Oorder(U_904) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
( ! [U_904,U_905,U_906] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_904),U_906),U_905))
| ~ sP32(U_904,U_905,U_906) )
& ! [U_904,U_905,U_906] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_904),U_905),U_906))
| ~ sP32(U_904,U_905,U_906) )
& ! [U_904,U_905,U_906] :
( U_905 = U_906
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_904),U_906),U_905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_904),U_905),U_906))
| ~ sP33(U_904,U_905,U_906) )
& ! [U_904,U_905,U_906] :
( sP32(U_904,U_905,U_906)
| U_905 != U_906
| ~ sP33(U_904,U_905,U_906) )
& ! [U_904,U_905,U_906] :
( sP33(U_904,U_905,U_906)
| ~ class_Orderings_Oorder(U_904) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32,sP33])],[f_164_2]) ).
cnf(f_164_4,plain,
( sP33(U_904,U_905,U_906)
| ~ class_Orderings_Oorder(U_904) ),
inference(clausify,[status(thm)],[f_164_3]) ).
cnf(f_164_5,plain,
( sP32(U_904,U_905,U_906)
| U_905 != U_906
| ~ sP33(U_904,U_905,U_906) ),
inference(clausify,[status(thm)],[f_164_3]) ).
cnf(f_164_6,plain,
( U_905 = U_906
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_904),U_906),U_905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_904),U_905),U_906))
| ~ sP33(U_904,U_905,U_906) ),
inference(clausify,[status(thm)],[f_164_3]) ).
cnf(f_164_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_904),U_905),U_906))
| ~ sP32(U_904,U_905,U_906) ),
inference(clausify,[status(thm)],[f_164_3]) ).
cnf(f_164_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_904),U_906),U_905))
| ~ sP32(U_904,U_905,U_906) ),
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_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_165_2,plain,
! [U_909,U_908,U_907] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_907),U_909),U_908))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_907),U_908),U_909))
| ~ class_Orderings_Olinorder(U_907) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
! [U_907,U_908,U_909] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_907),U_909),U_908))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_907),U_908),U_909))
| ~ class_Orderings_Olinorder(U_907) ),
inference(definitional_conversion,[status(esa)],[f_165_2]) ).
cnf(f_165_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_907),U_909),U_908))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_907),U_908),U_909))
| ~ class_Orderings_Olinorder(U_907) ),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_1,plain,
! [V_g_2,V_f_2,T_c,T_d] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2))
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
& ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),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,T_d)),V_f_2),V_g_2)) ) )
| ~ class_Orderings_Oord(T_d) ),
inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).
fof(f_166_2,plain,
! [U_915,U_914,U_913,U_912] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_913,U_912)),U_914),U_915))
| ? [U_911] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_912),hAPP(U_914,U_911)),hAPP(U_915,U_911))) )
& ( ! [U_910] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_912),hAPP(U_914,U_910)),hAPP(U_915,U_910)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_913,U_912)),U_914),U_915)) ) )
| ~ class_Orderings_Oord(U_912) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_915,U_914,U_913,U_912] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_913,U_912)),U_914),U_915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_912),hAPP(U_914,sK19(U_915,U_914,U_913,U_912))),hAPP(U_915,sK19(U_915,U_914,U_913,U_912)))) )
& ( ! [U_910] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_912),hAPP(U_914,U_910)),hAPP(U_915,U_910)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_913,U_912)),U_914),U_915)) ) )
| ~ class_Orderings_Oord(U_912) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_911,sK19(U_915,U_914,U_913,U_912))],[f_166_2]) ).
fof(f_166_4,plain,
( ! [U_910,U_912,U_913,U_914,U_915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_913,U_912)),U_914),U_915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_912),hAPP(U_914,sK19(U_915,U_914,U_913,U_912))),hAPP(U_915,sK19(U_915,U_914,U_913,U_912))))
| ~ sP34(U_910,U_912,U_913,U_914,U_915) )
& ! [U_910,U_912,U_913,U_914,U_915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_912),hAPP(U_914,U_910)),hAPP(U_915,U_910)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_913,U_912)),U_914),U_915))
| ~ sP34(U_910,U_912,U_913,U_914,U_915) )
& ! [U_910,U_912,U_913,U_914,U_915] :
( sP34(U_910,U_912,U_913,U_914,U_915)
| ~ class_Orderings_Oord(U_912) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP34])],[f_166_3]) ).
cnf(f_166_5,plain,
( sP34(U_910,U_912,U_913,U_914,U_915)
| ~ class_Orderings_Oord(U_912) ),
inference(clausify,[status(thm)],[f_166_4]) ).
cnf(f_166_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_912),hAPP(U_914,U_910)),hAPP(U_915,U_910)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_913,U_912)),U_914),U_915))
| ~ sP34(U_910,U_912,U_913,U_914,U_915) ),
inference(clausify,[status(thm)],[f_166_4]) ).
cnf(f_166_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_913,U_912)),U_914),U_915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_912),hAPP(U_914,sK19(U_915,U_914,U_913,U_912))),hAPP(U_915,sK19(U_915,U_914,U_913,U_912))))
| ~ sP34(U_910,U_912,U_913,U_914,U_915) ),
inference(clausify,[status(thm)],[f_166_4]) ).
fof(f_167_1,plain,
! [V_A_2,V_B_2,V_f_2,T_e,T_d,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),tc_fun(tc_fun(T_e,tc_HOL_Obool),T_c),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_c),T_e),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c)),hAPP(c_COMBC(T_d,T_e,T_c),V_f_2))),V_A_2)),V_B_2)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__commute]) ).
fof(f_167_2,plain,
! [U_921,U_920,U_919,U_918,U_917,U_916] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_917,U_916),hAPP(hAPP(c_COMBC(U_917,tc_fun(U_918,tc_HOL_Obool),U_916),hAPP(hAPP(c_COMBB(tc_fun(U_918,U_916),tc_fun(tc_fun(U_918,tc_HOL_Obool),U_916),U_917),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_918,U_916)),U_919)),U_920)),U_921) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_918,U_916),hAPP(hAPP(c_COMBC(U_918,tc_fun(U_917,tc_HOL_Obool),U_916),hAPP(hAPP(c_COMBB(tc_fun(U_917,U_916),tc_fun(tc_fun(U_917,tc_HOL_Obool),U_916),U_918),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_917,U_916)),hAPP(c_COMBC(U_917,U_918,U_916),U_919))),U_921)),U_920)
| ~ class_Groups_Ocomm__monoid__add(U_916) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
! [U_916,U_917,U_918,U_919,U_920,U_921] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_917,U_916),hAPP(hAPP(c_COMBC(U_917,tc_fun(U_918,tc_HOL_Obool),U_916),hAPP(hAPP(c_COMBB(tc_fun(U_918,U_916),tc_fun(tc_fun(U_918,tc_HOL_Obool),U_916),U_917),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_918,U_916)),U_919)),U_920)),U_921) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_918,U_916),hAPP(hAPP(c_COMBC(U_918,tc_fun(U_917,tc_HOL_Obool),U_916),hAPP(hAPP(c_COMBB(tc_fun(U_917,U_916),tc_fun(tc_fun(U_917,tc_HOL_Obool),U_916),U_918),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_917,U_916)),hAPP(c_COMBC(U_917,U_918,U_916),U_919))),U_921)),U_920)
| ~ class_Groups_Ocomm__monoid__add(U_916) ),
inference(definitional_conversion,[status(esa)],[f_167_2]) ).
cnf(f_167_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_917,U_916),hAPP(hAPP(c_COMBC(U_917,tc_fun(U_918,tc_HOL_Obool),U_916),hAPP(hAPP(c_COMBB(tc_fun(U_918,U_916),tc_fun(tc_fun(U_918,tc_HOL_Obool),U_916),U_917),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_918,U_916)),U_919)),U_920)),U_921) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_918,U_916),hAPP(hAPP(c_COMBC(U_918,tc_fun(U_917,tc_HOL_Obool),U_916),hAPP(hAPP(c_COMBB(tc_fun(U_917,U_916),tc_fun(tc_fun(U_917,tc_HOL_Obool),U_916),U_918),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_917,U_916)),hAPP(c_COMBC(U_917,U_918,U_916),U_919))),U_921)),U_920)
| ~ class_Groups_Ocomm__monoid__add(U_916) ),
inference(clausify,[status(thm)],[f_167_3]) ).
fof(f_168_1,plain,
! [T_c,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),V_A_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityE]) ).
fof(f_168_2,plain,
! [U_924,U_923,U_922] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_924,tc_HOL_Obool)),U_923),U_922))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_924,tc_HOL_Obool)),U_922),U_923)) )
| U_922 != U_923 ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
( ! [U_923,U_922,U_924] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_924,tc_HOL_Obool)),U_923),U_922))
| ~ sP35(U_923,U_922,U_924) )
& ! [U_923,U_922,U_924] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_924,tc_HOL_Obool)),U_922),U_923))
| ~ sP35(U_923,U_922,U_924) )
& ! [U_923,U_922,U_924] :
( sP35(U_923,U_922,U_924)
| U_922 != U_923 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35])],[f_168_2]) ).
cnf(f_168_4,plain,
( sP35(U_923,U_922,U_924)
| U_922 != U_923 ),
inference(clausify,[status(thm)],[f_168_3]) ).
cnf(f_168_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_924,tc_HOL_Obool)),U_922),U_923))
| ~ sP35(U_923,U_922,U_924) ),
inference(clausify,[status(thm)],[f_168_3]) ).
cnf(f_168_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_924,tc_HOL_Obool)),U_923),U_922))
| ~ sP35(U_923,U_922,U_924) ),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),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)) ),
inference(fof_nnf,[status(thm)],[fact_subset__trans]) ).
fof(f_169_2,plain,
! [U_928,U_927,U_926,U_925] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_925,tc_HOL_Obool)),U_926),U_928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_925,tc_HOL_Obool)),U_927),U_928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_925,tc_HOL_Obool)),U_926),U_927)) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
! [U_925,U_926,U_927,U_928] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_925,tc_HOL_Obool)),U_926),U_928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_925,tc_HOL_Obool)),U_927),U_928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_925,tc_HOL_Obool)),U_926),U_927)) ),
inference(definitional_conversion,[status(esa)],[f_169_2]) ).
cnf(f_169_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_925,tc_HOL_Obool)),U_926),U_928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_925,tc_HOL_Obool)),U_927),U_928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_925,tc_HOL_Obool)),U_926),U_927)) ),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_1,plain,
! [T_c,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),V_A_2))
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityD2]) ).
fof(f_170_2,plain,
! [U_931,U_930,U_929] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_931,tc_HOL_Obool)),U_930),U_929))
| U_929 != U_930 ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_930,U_929,U_931] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_931,tc_HOL_Obool)),U_930),U_929))
| U_929 != U_930 ),
inference(definitional_conversion,[status(esa)],[f_170_2]) ).
cnf(f_170_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_931,tc_HOL_Obool)),U_930),U_929))
| U_929 != U_930 ),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_1,plain,
! [T_c,V_B_2,V_A_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityD1]) ).
fof(f_171_2,plain,
! [U_934,U_933,U_932] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_934,tc_HOL_Obool)),U_932),U_933))
| U_932 != U_933 ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
! [U_932,U_933,U_934] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_934,tc_HOL_Obool)),U_932),U_933))
| U_932 != U_933 ),
inference(definitional_conversion,[status(esa)],[f_171_2]) ).
cnf(f_171_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_934,tc_HOL_Obool)),U_932),U_933))
| U_932 != U_933 ),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_1,plain,
! [T_c,V_B_2,V_A_2] :
( ( V_A_2 = V_B_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(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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)),V_B_2),V_A_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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_172_2,plain,
! [U_937,U_936,U_935] :
( ( U_935 = U_936
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_937,tc_HOL_Obool)),U_936),U_935))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_937,tc_HOL_Obool)),U_935),U_936)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_937,tc_HOL_Obool)),U_936),U_935))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_937,tc_HOL_Obool)),U_935),U_936)) )
| U_935 != U_936 ) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
( ! [U_943,U_941,U_939] :
( U_939 = U_941
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_943,tc_HOL_Obool)),U_941),U_939))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_943,tc_HOL_Obool)),U_939),U_941)) )
& ! [U_942,U_940,U_938] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_942,tc_HOL_Obool)),U_940),U_938))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_942,tc_HOL_Obool)),U_938),U_940)) )
| U_938 != U_940 ) ),
inference(miniscope,[status(thm)],[f_172_2]) ).
fof(f_172_4,plain,
( ! [U_940,U_938,U_942] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_942,tc_HOL_Obool)),U_940),U_938))
| ~ sP36(U_940,U_938,U_942) )
& ! [U_940,U_938,U_942] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_942,tc_HOL_Obool)),U_938),U_940))
| ~ sP36(U_940,U_938,U_942) )
& ! [U_941,U_939,U_943] :
( U_939 = U_941
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_943,tc_HOL_Obool)),U_941),U_939))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_943,tc_HOL_Obool)),U_939),U_941)) )
& ! [U_940,U_938,U_942] :
( sP36(U_940,U_938,U_942)
| U_938 != U_940 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36])],[f_172_3]) ).
cnf(f_172_5,plain,
( sP36(U_940,U_938,U_942)
| U_938 != U_940 ),
inference(clausify,[status(thm)],[f_172_4]) ).
cnf(f_172_6,plain,
( U_939 = U_941
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_943,tc_HOL_Obool)),U_941),U_939))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_943,tc_HOL_Obool)),U_939),U_941)) ),
inference(clausify,[status(thm)],[f_172_4]) ).
cnf(f_172_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_942,tc_HOL_Obool)),U_938),U_940))
| ~ sP36(U_940,U_938,U_942) ),
inference(clausify,[status(thm)],[f_172_4]) ).
cnf(f_172_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_942,tc_HOL_Obool)),U_940),U_938))
| ~ sP36(U_940,U_938,U_942) ),
inference(clausify,[status(thm)],[f_172_4]) ).
fof(f_173_1,plain,
! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_subset__refl]) ).
fof(f_173_2,plain,
! [U_945,U_944] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_944,tc_HOL_Obool)),U_945),U_945)),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_945,U_944] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_944,tc_HOL_Obool)),U_945),U_945)),
inference(definitional_conversion,[status(esa)],[f_173_2]) ).
cnf(f_173_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_944,tc_HOL_Obool)),U_945),U_945)),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_1,plain,
! [V_A_2,V_B_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_subset__inj__on]) ).
fof(f_174_2,plain,
! [U_950,U_949,U_948,U_947,U_946] :
( c_Fun_Oinj__on(U_946,U_947,U_948,U_950)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_946,tc_HOL_Obool)),U_950),U_949))
| ~ c_Fun_Oinj__on(U_946,U_947,U_948,U_949) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
! [U_946,U_947,U_948,U_949,U_950] :
( c_Fun_Oinj__on(U_946,U_947,U_948,U_950)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_946,tc_HOL_Obool)),U_950),U_949))
| ~ c_Fun_Oinj__on(U_946,U_947,U_948,U_949) ),
inference(definitional_conversion,[status(esa)],[f_174_2]) ).
cnf(f_174_4,plain,
( c_Fun_Oinj__on(U_946,U_947,U_948,U_950)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_946,tc_HOL_Obool)),U_950),U_949))
| ~ c_Fun_Oinj__on(U_946,U_947,U_948,U_949) ),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
| ? [B_x] :
( ? [B_xa] :
( B_x != B_xa
& hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
& hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_A_2)) )
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( ! [B_xa] :
( B_x = B_xa
| hAPP(V_f_2,B_x) != hAPP(V_f_2,B_xa)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__def]) ).
fof(f_175_2,plain,
! [U_958,U_957,U_956,U_955] :
( ( c_Fun_Oinj__on(U_955,U_956,U_957,U_958)
| ? [U_954] :
( ? [U_953] :
( U_954 != U_953
& hAPP(U_957,U_954) = hAPP(U_957,U_953)
& hBOOL(hAPP(hAPP(c_member(U_955),U_953),U_958)) )
& hBOOL(hAPP(hAPP(c_member(U_955),U_954),U_958)) ) )
& ( ! [U_952] :
( ! [U_951] :
( U_952 = U_951
| hAPP(U_957,U_952) != hAPP(U_957,U_951)
| ~ hBOOL(hAPP(hAPP(c_member(U_955),U_951),U_958)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_955),U_952),U_958)) )
| ~ c_Fun_Oinj__on(U_955,U_956,U_957,U_958) ) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
( ! [U_966,U_964,U_962,U_960] :
( c_Fun_Oinj__on(U_960,U_962,U_964,U_966)
| ? [U_954] :
( ? [U_953] :
( U_954 != U_953
& hAPP(U_964,U_954) = hAPP(U_964,U_953)
& hBOOL(hAPP(hAPP(c_member(U_960),U_953),U_966)) )
& hBOOL(hAPP(hAPP(c_member(U_960),U_954),U_966)) ) )
& ! [U_965,U_963,U_961,U_959] :
( ! [U_952] :
( ! [U_951] :
( U_952 = U_951
| hAPP(U_963,U_952) != hAPP(U_963,U_951)
| ~ hBOOL(hAPP(hAPP(c_member(U_959),U_951),U_965)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_959),U_952),U_965)) )
| ~ c_Fun_Oinj__on(U_959,U_961,U_963,U_965) ) ),
inference(miniscope,[status(thm)],[f_175_2]) ).
fof(f_175_4,plain,
( ! [U_966,U_964,U_962,U_960] :
( c_Fun_Oinj__on(U_960,U_962,U_964,U_966)
| ( ? [U_953] :
( sK20(U_966,U_964,U_962,U_960) != U_953
& hAPP(U_964,sK20(U_966,U_964,U_962,U_960)) = hAPP(U_964,U_953)
& hBOOL(hAPP(hAPP(c_member(U_960),U_953),U_966)) )
& hBOOL(hAPP(hAPP(c_member(U_960),sK20(U_966,U_964,U_962,U_960)),U_966)) ) )
& ! [U_965,U_963,U_961,U_959] :
( ! [U_952] :
( ! [U_951] :
( U_952 = U_951
| hAPP(U_963,U_952) != hAPP(U_963,U_951)
| ~ hBOOL(hAPP(hAPP(c_member(U_959),U_951),U_965)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_959),U_952),U_965)) )
| ~ c_Fun_Oinj__on(U_959,U_961,U_963,U_965) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_954,sK20(U_966,U_964,U_962,U_960))],[f_175_3]) ).
fof(f_175_5,plain,
( ! [U_966,U_964,U_962,U_960] :
( c_Fun_Oinj__on(U_960,U_962,U_964,U_966)
| ( sK20(U_966,U_964,U_962,U_960) != sK21(U_966,U_964,U_962,U_960)
& hAPP(U_964,sK20(U_966,U_964,U_962,U_960)) = hAPP(U_964,sK21(U_966,U_964,U_962,U_960))
& hBOOL(hAPP(hAPP(c_member(U_960),sK21(U_966,U_964,U_962,U_960)),U_966))
& hBOOL(hAPP(hAPP(c_member(U_960),sK20(U_966,U_964,U_962,U_960)),U_966)) ) )
& ! [U_965,U_963,U_961,U_959] :
( ! [U_952] :
( ! [U_951] :
( U_952 = U_951
| hAPP(U_963,U_952) != hAPP(U_963,U_951)
| ~ hBOOL(hAPP(hAPP(c_member(U_959),U_951),U_965)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_959),U_952),U_965)) )
| ~ c_Fun_Oinj__on(U_959,U_961,U_963,U_965) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_953,sK21(U_966,U_964,U_962,U_960))],[f_175_4]) ).
fof(f_175_6,plain,
( ! [U_962,U_966,U_960,U_964] :
( sK20(U_966,U_964,U_962,U_960) != sK21(U_966,U_964,U_962,U_960)
| ~ sP37(U_962,U_966,U_960,U_964) )
& ! [U_962,U_966,U_960,U_964] :
( hAPP(U_964,sK20(U_966,U_964,U_962,U_960)) = hAPP(U_964,sK21(U_966,U_964,U_962,U_960))
| ~ sP37(U_962,U_966,U_960,U_964) )
& ! [U_962,U_966,U_960,U_964] :
( hBOOL(hAPP(hAPP(c_member(U_960),sK21(U_966,U_964,U_962,U_960)),U_966))
| ~ sP37(U_962,U_966,U_960,U_964) )
& ! [U_962,U_966,U_960,U_964] :
( hBOOL(hAPP(hAPP(c_member(U_960),sK20(U_966,U_964,U_962,U_960)),U_966))
| ~ sP37(U_962,U_966,U_960,U_964) )
& ! [U_962,U_966,U_960,U_964] :
( c_Fun_Oinj__on(U_960,U_962,U_964,U_966)
| sP37(U_962,U_966,U_960,U_964) )
& ! [U_952,U_963,U_951,U_961,U_959,U_965] :
( U_952 = U_951
| hAPP(U_963,U_952) != hAPP(U_963,U_951)
| ~ hBOOL(hAPP(hAPP(c_member(U_959),U_951),U_965))
| ~ hBOOL(hAPP(hAPP(c_member(U_959),U_952),U_965))
| ~ c_Fun_Oinj__on(U_959,U_961,U_963,U_965) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP37])],[f_175_5]) ).
cnf(f_175_7,plain,
( U_952 = U_951
| hAPP(U_963,U_952) != hAPP(U_963,U_951)
| ~ hBOOL(hAPP(hAPP(c_member(U_959),U_951),U_965))
| ~ hBOOL(hAPP(hAPP(c_member(U_959),U_952),U_965))
| ~ c_Fun_Oinj__on(U_959,U_961,U_963,U_965) ),
inference(clausify,[status(thm)],[f_175_6]) ).
cnf(f_175_8,plain,
( c_Fun_Oinj__on(U_960,U_962,U_964,U_966)
| sP37(U_962,U_966,U_960,U_964) ),
inference(clausify,[status(thm)],[f_175_6]) ).
cnf(f_175_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_960),sK20(U_966,U_964,U_962,U_960)),U_966))
| ~ sP37(U_962,U_966,U_960,U_964) ),
inference(clausify,[status(thm)],[f_175_6]) ).
cnf(f_175_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_960),sK21(U_966,U_964,U_962,U_960)),U_966))
| ~ sP37(U_962,U_966,U_960,U_964) ),
inference(clausify,[status(thm)],[f_175_6]) ).
cnf(f_175_11,plain,
( hAPP(U_964,sK20(U_966,U_964,U_962,U_960)) = hAPP(U_964,sK21(U_966,U_964,U_962,U_960))
| ~ sP37(U_962,U_966,U_960,U_964) ),
inference(clausify,[status(thm)],[f_175_6]) ).
cnf(f_175_12,plain,
( sK20(U_966,U_964,U_962,U_960) != sK21(U_966,U_964,U_962,U_960)
| ~ sP37(U_962,U_966,U_960,U_964) ),
inference(clausify,[status(thm)],[f_175_6]) ).
fof(f_176_1,plain,
! [V_A_2,T_c] : c_Fun_Oinj__on(T_c,T_c,c_COMBI(T_c),V_A_2),
inference(fof_nnf,[status(thm)],[fact_inj__on__id2]) ).
fof(f_176_2,plain,
! [U_968,U_967] : c_Fun_Oinj__on(U_967,U_967,c_COMBI(U_967),U_968),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
! [U_967,U_968] : c_Fun_Oinj__on(U_967,U_967,c_COMBI(U_967),U_968),
inference(definitional_conversion,[status(esa)],[f_176_2]) ).
cnf(f_176_4,plain,
c_Fun_Oinj__on(U_967,U_967,c_COMBI(U_967),U_968),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_1,plain,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),V_y_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| hAPP(V_f_2,V_x_2) != V_y_2
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq]) ).
fof(f_177_2,plain,
! [U_974,U_973,U_972,U_971,U_970,U_969] :
( hAPP(c_Fun_Othe__inv__into(U_969,U_970,U_972,U_971),U_974) = U_973
| ~ hBOOL(hAPP(hAPP(c_member(U_969),U_973),U_972))
| hAPP(U_971,U_973) != U_974
| ~ c_Fun_Oinj__on(U_969,U_970,U_971,U_972) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
! [U_971,U_974,U_972,U_973,U_970,U_969] :
( hAPP(c_Fun_Othe__inv__into(U_969,U_970,U_972,U_971),U_974) = U_973
| ~ hBOOL(hAPP(hAPP(c_member(U_969),U_973),U_972))
| hAPP(U_971,U_973) != U_974
| ~ c_Fun_Oinj__on(U_969,U_970,U_971,U_972) ),
inference(definitional_conversion,[status(esa)],[f_177_2]) ).
cnf(f_177_4,plain,
( hAPP(c_Fun_Othe__inv__into(U_969,U_970,U_972,U_971),U_974) = U_973
| ~ hBOOL(hAPP(hAPP(c_member(U_969),U_973),U_972))
| hAPP(U_971,U_973) != U_974
| ~ c_Fun_Oinj__on(U_969,U_970,U_971,U_972) ),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_1,plain,
! [V_x_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f]) ).
fof(f_178_2,plain,
! [U_979,U_978,U_977,U_976,U_975] :
( hAPP(c_Fun_Othe__inv__into(U_975,U_976,U_978,U_977),hAPP(U_977,U_979)) = U_979
| ~ hBOOL(hAPP(hAPP(c_member(U_975),U_979),U_978))
| ~ c_Fun_Oinj__on(U_975,U_976,U_977,U_978) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_977,U_975,U_976,U_978,U_979] :
( hAPP(c_Fun_Othe__inv__into(U_975,U_976,U_978,U_977),hAPP(U_977,U_979)) = U_979
| ~ hBOOL(hAPP(hAPP(c_member(U_975),U_979),U_978))
| ~ c_Fun_Oinj__on(U_975,U_976,U_977,U_978) ),
inference(definitional_conversion,[status(esa)],[f_178_2]) ).
cnf(f_178_4,plain,
( hAPP(c_Fun_Othe__inv__into(U_975,U_976,U_978,U_977),hAPP(U_977,U_979)) = U_979
| ~ hBOOL(hAPP(hAPP(c_member(U_975),U_979),U_978))
| ~ c_Fun_Oinj__on(U_975,U_976,U_977,U_978) ),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Set_Oimage(T_d,T_c,c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = V_A_2
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto]) ).
fof(f_179_2,plain,
! [U_983,U_982,U_981,U_980] :
( hAPP(c_Set_Oimage(U_981,U_980,c_Fun_Othe__inv__into(U_980,U_981,U_983,U_982)),hAPP(c_Set_Oimage(U_980,U_981,U_982),U_983)) = U_983
| ~ c_Fun_Oinj__on(U_980,U_981,U_982,U_983) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_981,U_980,U_982,U_983] :
( hAPP(c_Set_Oimage(U_981,U_980,c_Fun_Othe__inv__into(U_980,U_981,U_983,U_982)),hAPP(c_Set_Oimage(U_980,U_981,U_982),U_983)) = U_983
| ~ c_Fun_Oinj__on(U_980,U_981,U_982,U_983) ),
inference(definitional_conversion,[status(esa)],[f_179_2]) ).
cnf(f_179_4,plain,
( hAPP(c_Set_Oimage(U_981,U_980,c_Fun_Othe__inv__into(U_980,U_981,U_983,U_982)),hAPP(c_Set_Oimage(U_980,U_981,U_982),U_983)) = U_983
| ~ c_Fun_Oinj__on(U_980,U_981,U_982,U_983) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_d,T_c,c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into]) ).
fof(f_180_2,plain,
! [U_987,U_986,U_985,U_984] :
( c_Fun_Oinj__on(U_985,U_984,c_Fun_Othe__inv__into(U_984,U_985,U_987,U_986),hAPP(c_Set_Oimage(U_984,U_985,U_986),U_987))
| ~ c_Fun_Oinj__on(U_984,U_985,U_986,U_987) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
! [U_985,U_984,U_986,U_987] :
( c_Fun_Oinj__on(U_985,U_984,c_Fun_Othe__inv__into(U_984,U_985,U_987,U_986),hAPP(c_Set_Oimage(U_984,U_985,U_986),U_987))
| ~ c_Fun_Oinj__on(U_984,U_985,U_986,U_987) ),
inference(definitional_conversion,[status(esa)],[f_180_2]) ).
cnf(f_180_4,plain,
( c_Fun_Oinj__on(U_985,U_984,c_Fun_Othe__inv__into(U_984,U_985,U_987,U_986),hAPP(c_Set_Oimage(U_984,U_985,U_986),U_987))
| ~ c_Fun_Oinj__on(U_984,U_985,U_986,U_987) ),
inference(clausify,[status(thm)],[f_180_3]) ).
fof(f_181_1,plain,
! [V_B_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),V_x_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_the__inv__into__into]) ).
fof(f_181_2,plain,
! [U_993,U_992,U_991,U_990,U_989,U_988] :
( hBOOL(hAPP(hAPP(c_member(U_988),hAPP(c_Fun_Othe__inv__into(U_988,U_989,U_991,U_990),U_992)),U_993))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_988,tc_HOL_Obool)),U_991),U_993))
| ~ hBOOL(hAPP(hAPP(c_member(U_989),U_992),hAPP(c_Set_Oimage(U_988,U_989,U_990),U_991)))
| ~ c_Fun_Oinj__on(U_988,U_989,U_990,U_991) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
! [U_988,U_989,U_990,U_991,U_992,U_993] :
( hBOOL(hAPP(hAPP(c_member(U_988),hAPP(c_Fun_Othe__inv__into(U_988,U_989,U_991,U_990),U_992)),U_993))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_988,tc_HOL_Obool)),U_991),U_993))
| ~ hBOOL(hAPP(hAPP(c_member(U_989),U_992),hAPP(c_Set_Oimage(U_988,U_989,U_990),U_991)))
| ~ c_Fun_Oinj__on(U_988,U_989,U_990,U_991) ),
inference(definitional_conversion,[status(esa)],[f_181_2]) ).
cnf(f_181_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_988),hAPP(c_Fun_Othe__inv__into(U_988,U_989,U_991,U_990),U_992)),U_993))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_988,tc_HOL_Obool)),U_991),U_993))
| ~ hBOOL(hAPP(hAPP(c_member(U_989),U_992),hAPP(c_Set_Oimage(U_988,U_989,U_990),U_991)))
| ~ c_Fun_Oinj__on(U_988,U_989,U_990,U_991) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_1,plain,
! [V_f_2,V_A_2,V_B_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),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_Nat_Onat),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,tc_Nat_Onat),V_f_2),V_B_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_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat]) ).
fof(f_182_2,plain,
! [U_997,U_996,U_995,U_994] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_994,tc_Nat_Onat),U_997),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_994,tc_HOL_Obool)),U_996),U_995)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_994,tc_Nat_Onat),U_997),U_996)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_994,tc_Nat_Onat),U_997),U_995))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_994,tc_HOL_Obool)),U_995),U_996))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_994),U_995)) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
! [U_995,U_994,U_996,U_997] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_994,tc_Nat_Onat),U_997),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_994,tc_HOL_Obool)),U_996),U_995)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_994,tc_Nat_Onat),U_997),U_996)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_994,tc_Nat_Onat),U_997),U_995))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_994,tc_HOL_Obool)),U_995),U_996))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_994),U_995)) ),
inference(definitional_conversion,[status(esa)],[f_182_2]) ).
cnf(f_182_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_994,tc_Nat_Onat),U_997),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_994,tc_HOL_Obool)),U_996),U_995)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_994,tc_Nat_Onat),U_997),U_996)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_994,tc_Nat_Onat),U_997),U_995))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_994,tc_HOL_Obool)),U_995),U_996))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_994),U_995)) ),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_1,plain,
! [V_A_2,V_g_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Ominus__class_Ominus(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_g_2),V_A_2))
| ~ class_Groups_Oab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__subtractf]) ).
fof(f_183_2,plain,
! [U_1002,U_1001,U_1000,U_999,U_998] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_999,U_998),hAPP(hAPP(c_COMBS(U_999,U_998,U_998),hAPP(hAPP(c_COMBB(U_998,tc_fun(U_998,U_998),U_999),c_Groups_Ominus__class_Ominus(U_998)),U_1000)),U_1001)),U_1002) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_998),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_999,U_998),U_1000),U_1002)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_999,U_998),U_1001),U_1002))
| ~ class_Groups_Oab__group__add(U_998) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_998,U_999,U_1000,U_1001,U_1002] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_999,U_998),hAPP(hAPP(c_COMBS(U_999,U_998,U_998),hAPP(hAPP(c_COMBB(U_998,tc_fun(U_998,U_998),U_999),c_Groups_Ominus__class_Ominus(U_998)),U_1000)),U_1001)),U_1002) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_998),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_999,U_998),U_1000),U_1002)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_999,U_998),U_1001),U_1002))
| ~ class_Groups_Oab__group__add(U_998) ),
inference(definitional_conversion,[status(esa)],[f_183_2]) ).
cnf(f_183_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_999,U_998),hAPP(hAPP(c_COMBS(U_999,U_998,U_998),hAPP(hAPP(c_COMBB(U_998,tc_fun(U_998,U_998),U_999),c_Groups_Ominus__class_Ominus(U_998)),U_1000)),U_1001)),U_1002) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_998),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_999,U_998),U_1000),U_1002)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_999,U_998),U_1001),U_1002))
| ~ class_Groups_Oab__group__add(U_998) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
! [V_A_2,V_z_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_Finite__Set_Ofold(T_d,T_c,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_c,c_Finite__Set_Ofold__graph(T_d,T_c,V_f_2,V_z_2,V_A_2)),
inference(fof_nnf,[status(thm)],[fact_fold__def]) ).
fof(f_184_2,plain,
! [U_1007,U_1006,U_1005,U_1004,U_1003] : hAPP(hAPP(c_Finite__Set_Ofold(U_1003,U_1004,U_1005),U_1006),U_1007) = c_HOL_OThe(U_1004,c_Finite__Set_Ofold__graph(U_1003,U_1004,U_1005,U_1006,U_1007)),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
! [U_1003,U_1004,U_1005,U_1006,U_1007] : hAPP(hAPP(c_Finite__Set_Ofold(U_1003,U_1004,U_1005),U_1006),U_1007) = c_HOL_OThe(U_1004,c_Finite__Set_Ofold__graph(U_1003,U_1004,U_1005,U_1006,U_1007)),
inference(definitional_conversion,[status(esa)],[f_184_2]) ).
cnf(f_184_4,plain,
hAPP(hAPP(c_Finite__Set_Ofold(U_1003,U_1004,U_1005),U_1006),U_1007) = c_HOL_OThe(U_1004,c_Finite__Set_Ofold__graph(U_1003,U_1004,U_1005,U_1006,U_1007)),
inference(clausify,[status(thm)],[f_184_3]) ).
fof(f_185_1,plain,
! [V_f_2,V_A_2,T_c] :
( hAPP(c_Set_Oimage(T_c,T_c,V_f_2),V_A_2) = V_A_2
| ~ c_Fun_Oinj__on(T_c,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_c,T_c,V_f_2),V_A_2)),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_endo__inj__surj]) ).
fof(f_185_2,plain,
! [U_1010,U_1009,U_1008] :
( hAPP(c_Set_Oimage(U_1008,U_1008,U_1010),U_1009) = U_1009
| ~ c_Fun_Oinj__on(U_1008,U_1008,U_1010,U_1009)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1008,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1008,U_1008,U_1010),U_1009)),U_1009))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1008),U_1009)) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
! [U_1008,U_1009,U_1010] :
( hAPP(c_Set_Oimage(U_1008,U_1008,U_1010),U_1009) = U_1009
| ~ c_Fun_Oinj__on(U_1008,U_1008,U_1010,U_1009)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1008,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1008,U_1008,U_1010),U_1009)),U_1009))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1008),U_1009)) ),
inference(definitional_conversion,[status(esa)],[f_185_2]) ).
cnf(f_185_4,plain,
( hAPP(c_Set_Oimage(U_1008,U_1008,U_1010),U_1009) = U_1009
| ~ c_Fun_Oinj__on(U_1008,U_1008,U_1010,U_1009)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1008,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1008,U_1008,U_1010),U_1009)),U_1009))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1008),U_1009)) ),
inference(clausify,[status(thm)],[f_185_3]) ).
fof(f_186_1,plain,
! [V_f_2,V_A_2,T_c] :
( c_Fun_Oinj__on(T_c,T_c,V_f_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_c,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__surj__inj]) ).
fof(f_186_2,plain,
! [U_1013,U_1012,U_1011] :
( c_Fun_Oinj__on(U_1011,U_1011,U_1013,U_1012)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1011,tc_HOL_Obool)),U_1012),hAPP(c_Set_Oimage(U_1011,U_1011,U_1013),U_1012)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1011),U_1012)) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
! [U_1011,U_1012,U_1013] :
( c_Fun_Oinj__on(U_1011,U_1011,U_1013,U_1012)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1011,tc_HOL_Obool)),U_1012),hAPP(c_Set_Oimage(U_1011,U_1011,U_1013),U_1012)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1011),U_1012)) ),
inference(definitional_conversion,[status(esa)],[f_186_2]) ).
cnf(f_186_4,plain,
( c_Fun_Oinj__on(U_1011,U_1011,U_1013,U_1012)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1011,tc_HOL_Obool)),U_1012),hAPP(c_Set_Oimage(U_1011,U_1011,U_1013),U_1012)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1011),U_1012)) ),
inference(clausify,[status(thm)],[f_186_3]) ).
fof(f_187_1,plain,
! [V_B_2,V_A_2,V_C_2,V_f_2,T_d,T_c] :
( hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_C_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__image__set__diff]) ).
fof(f_187_2,plain,
! [U_1019,U_1018,U_1017,U_1016,U_1015,U_1014] :
( hAPP(c_Set_Oimage(U_1014,U_1015,U_1016),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1014,tc_HOL_Obool)),U_1018),U_1019)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1015,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1014,U_1015,U_1016),U_1018)),hAPP(c_Set_Oimage(U_1014,U_1015,U_1016),U_1019))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1014,tc_HOL_Obool)),U_1019),U_1017))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1014,tc_HOL_Obool)),U_1018),U_1017))
| ~ c_Fun_Oinj__on(U_1014,U_1015,U_1016,U_1017) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
! [U_1014,U_1015,U_1016,U_1017,U_1018,U_1019] :
( hAPP(c_Set_Oimage(U_1014,U_1015,U_1016),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1014,tc_HOL_Obool)),U_1018),U_1019)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1015,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1014,U_1015,U_1016),U_1018)),hAPP(c_Set_Oimage(U_1014,U_1015,U_1016),U_1019))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1014,tc_HOL_Obool)),U_1019),U_1017))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1014,tc_HOL_Obool)),U_1018),U_1017))
| ~ c_Fun_Oinj__on(U_1014,U_1015,U_1016,U_1017) ),
inference(definitional_conversion,[status(esa)],[f_187_2]) ).
cnf(f_187_4,plain,
( hAPP(c_Set_Oimage(U_1014,U_1015,U_1016),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1014,tc_HOL_Obool)),U_1018),U_1019)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1015,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1014,U_1015,U_1016),U_1018)),hAPP(c_Set_Oimage(U_1014,U_1015,U_1016),U_1019))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1014,tc_HOL_Obool)),U_1019),U_1017))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1014,tc_HOL_Obool)),U_1018),U_1017))
| ~ c_Fun_Oinj__on(U_1014,U_1015,U_1016,U_1017) ),
inference(clausify,[status(thm)],[f_187_3]) ).
fof(f_188_1,plain,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( V_x_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))
| hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__onD]) ).
fof(f_188_2,plain,
! [U_1025,U_1024,U_1023,U_1022,U_1021,U_1020] :
( U_1024 = U_1025
| ~ hBOOL(hAPP(hAPP(c_member(U_1020),U_1025),U_1023))
| ~ hBOOL(hAPP(hAPP(c_member(U_1020),U_1024),U_1023))
| hAPP(U_1022,U_1024) != hAPP(U_1022,U_1025)
| ~ c_Fun_Oinj__on(U_1020,U_1021,U_1022,U_1023) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
! [U_1024,U_1023,U_1021,U_1020,U_1022,U_1025] :
( U_1024 = U_1025
| ~ hBOOL(hAPP(hAPP(c_member(U_1020),U_1025),U_1023))
| ~ hBOOL(hAPP(hAPP(c_member(U_1020),U_1024),U_1023))
| hAPP(U_1022,U_1024) != hAPP(U_1022,U_1025)
| ~ c_Fun_Oinj__on(U_1020,U_1021,U_1022,U_1023) ),
inference(definitional_conversion,[status(esa)],[f_188_2]) ).
cnf(f_188_4,plain,
( U_1024 = U_1025
| ~ hBOOL(hAPP(hAPP(c_member(U_1020),U_1025),U_1023))
| ~ hBOOL(hAPP(hAPP(c_member(U_1020),U_1024),U_1023))
| hAPP(U_1022,U_1024) != hAPP(U_1022,U_1025)
| ~ c_Fun_Oinj__on(U_1020,U_1021,U_1022,U_1023) ),
inference(clausify,[status(thm)],[f_188_3]) ).
fof(f_189_1,plain,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( ( ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(V_f_2,V_x_2) != hAPP(V_f_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_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__iff]) ).
fof(f_189_2,plain,
! [U_1031,U_1030,U_1029,U_1028,U_1027,U_1026] :
( ( ( hAPP(U_1028,U_1030) = hAPP(U_1028,U_1031)
| U_1030 != U_1031 )
& ( U_1030 = U_1031
| hAPP(U_1028,U_1030) != hAPP(U_1028,U_1031) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1026),U_1031),U_1029))
| ~ hBOOL(hAPP(hAPP(c_member(U_1026),U_1030),U_1029))
| ~ c_Fun_Oinj__on(U_1026,U_1027,U_1028,U_1029) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
( ! [U_1028,U_1030,U_1031] :
( hAPP(U_1028,U_1030) = hAPP(U_1028,U_1031)
| U_1030 != U_1031
| ~ sP38(U_1028,U_1030,U_1031) )
& ! [U_1028,U_1030,U_1031] :
( U_1030 = U_1031
| hAPP(U_1028,U_1030) != hAPP(U_1028,U_1031)
| ~ sP38(U_1028,U_1030,U_1031) )
& ! [U_1026,U_1027,U_1028,U_1030,U_1029,U_1031] :
( sP38(U_1028,U_1030,U_1031)
| ~ hBOOL(hAPP(hAPP(c_member(U_1026),U_1031),U_1029))
| ~ hBOOL(hAPP(hAPP(c_member(U_1026),U_1030),U_1029))
| ~ c_Fun_Oinj__on(U_1026,U_1027,U_1028,U_1029) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38])],[f_189_2]) ).
cnf(f_189_4,plain,
( sP38(U_1028,U_1030,U_1031)
| ~ hBOOL(hAPP(hAPP(c_member(U_1026),U_1031),U_1029))
| ~ hBOOL(hAPP(hAPP(c_member(U_1026),U_1030),U_1029))
| ~ c_Fun_Oinj__on(U_1026,U_1027,U_1028,U_1029) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_5,plain,
( U_1030 = U_1031
| hAPP(U_1028,U_1030) != hAPP(U_1028,U_1031)
| ~ sP38(U_1028,U_1030,U_1031) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_6,plain,
( hAPP(U_1028,U_1030) = hAPP(U_1028,U_1031)
| U_1030 != U_1031
| ~ sP38(U_1028,U_1030,U_1031) ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_1,plain,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(V_f_2,V_x_2) != hAPP(V_f_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))
| V_x_2 = V_y_2
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__contraD]) ).
fof(f_190_2,plain,
! [U_1037,U_1036,U_1035,U_1034,U_1033,U_1032] :
( hAPP(U_1034,U_1036) != hAPP(U_1034,U_1037)
| ~ hBOOL(hAPP(hAPP(c_member(U_1032),U_1037),U_1035))
| ~ hBOOL(hAPP(hAPP(c_member(U_1032),U_1036),U_1035))
| U_1036 = U_1037
| ~ c_Fun_Oinj__on(U_1032,U_1033,U_1034,U_1035) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_1037,U_1032,U_1036,U_1035,U_1033,U_1034] :
( hAPP(U_1034,U_1036) != hAPP(U_1034,U_1037)
| ~ hBOOL(hAPP(hAPP(c_member(U_1032),U_1037),U_1035))
| ~ hBOOL(hAPP(hAPP(c_member(U_1032),U_1036),U_1035))
| U_1036 = U_1037
| ~ c_Fun_Oinj__on(U_1032,U_1033,U_1034,U_1035) ),
inference(definitional_conversion,[status(esa)],[f_190_2]) ).
cnf(f_190_4,plain,
( hAPP(U_1034,U_1036) != hAPP(U_1034,U_1037)
| ~ hBOOL(hAPP(hAPP(c_member(U_1032),U_1037),U_1035))
| ~ hBOOL(hAPP(hAPP(c_member(U_1032),U_1036),U_1035))
| U_1036 = U_1037
| ~ c_Fun_Oinj__on(U_1032,U_1033,U_1034,U_1035) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__diff]) ).
fof(f_191_2,plain,
! [U_1042,U_1041,U_1040,U_1039,U_1038] :
( c_Fun_Oinj__on(U_1038,U_1039,U_1040,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1038,tc_HOL_Obool)),U_1041),U_1042))
| ~ c_Fun_Oinj__on(U_1038,U_1039,U_1040,U_1041) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
! [U_1042,U_1038,U_1039,U_1040,U_1041] :
( c_Fun_Oinj__on(U_1038,U_1039,U_1040,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1038,tc_HOL_Obool)),U_1041),U_1042))
| ~ c_Fun_Oinj__on(U_1038,U_1039,U_1040,U_1041) ),
inference(definitional_conversion,[status(esa)],[f_191_2]) ).
cnf(f_191_4,plain,
( c_Fun_Oinj__on(U_1038,U_1039,U_1040,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1038,tc_HOL_Obool)),U_1041),U_1042))
| ~ c_Fun_Oinj__on(U_1038,U_1039,U_1040,U_1041) ),
inference(clausify,[status(thm)],[f_191_3]) ).
fof(f_192_1,plain,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_B_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))
| ~ class_Groups_Oab__group__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff]) ).
fof(f_192_2,plain,
! [U_1047,U_1046,U_1045,U_1044,U_1043] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1044,U_1043),U_1047),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1044,tc_HOL_Obool)),U_1045),U_1046)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1043),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1044,U_1043),U_1047),U_1045)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1044,U_1043),U_1047),U_1046))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1044,tc_HOL_Obool)),U_1046),U_1045))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1044),U_1045))
| ~ class_Groups_Oab__group__add(U_1043) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
! [U_1044,U_1043,U_1045,U_1046,U_1047] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1044,U_1043),U_1047),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1044,tc_HOL_Obool)),U_1045),U_1046)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1043),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1044,U_1043),U_1047),U_1045)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1044,U_1043),U_1047),U_1046))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1044,tc_HOL_Obool)),U_1046),U_1045))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1044),U_1045))
| ~ class_Groups_Oab__group__add(U_1043) ),
inference(definitional_conversion,[status(esa)],[f_192_2]) ).
cnf(f_192_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1044,U_1043),U_1047),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1044,tc_HOL_Obool)),U_1045),U_1046)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1043),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1044,U_1043),U_1047),U_1045)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1044,U_1043),U_1047),U_1046))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1044,tc_HOL_Obool)),U_1046),U_1045))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1044),U_1045))
| ~ class_Groups_Oab__group__add(U_1043) ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_1,plain,
! [V_z_2,V_f_2,T_d,T_c] : c_Nitpick_Ofold__graph_H(T_c,T_d,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__graph_H_Ointros_I1_J]) ).
fof(f_193_2,plain,
! [U_1051,U_1050,U_1049,U_1048] : c_Nitpick_Ofold__graph_H(U_1048,U_1049,U_1050,U_1051,c_Orderings_Obot__class_Obot(tc_fun(U_1048,tc_HOL_Obool)),U_1051),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
! [U_1051,U_1049,U_1050,U_1048] : c_Nitpick_Ofold__graph_H(U_1048,U_1049,U_1050,U_1051,c_Orderings_Obot__class_Obot(tc_fun(U_1048,tc_HOL_Obool)),U_1051),
inference(definitional_conversion,[status(esa)],[f_193_2]) ).
cnf(f_193_4,plain,
c_Nitpick_Ofold__graph_H(U_1048,U_1049,U_1050,U_1051,c_Orderings_Obot__class_Obot(tc_fun(U_1048,tc_HOL_Obool)),U_1051),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_1,plain,
! [V_a2_2,V_a1_2,T_d,T_c] : c_Nitpick_Ofold__graph_H(T_c,T_d,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),V_a2_2),
inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).
fof(f_194_2,plain,
! [U_1055,U_1054,U_1053,U_1052] : c_Nitpick_Ofold__graph_H(U_1052,U_1053,U_1054,U_1055,c_Orderings_Obot__class_Obot(tc_fun(U_1052,tc_HOL_Obool)),U_1055),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
! [U_1053,U_1052,U_1054,U_1055] : c_Nitpick_Ofold__graph_H(U_1052,U_1053,U_1054,U_1055,c_Orderings_Obot__class_Obot(tc_fun(U_1052,tc_HOL_Obool)),U_1055),
inference(definitional_conversion,[status(esa)],[f_194_2]) ).
cnf(f_194_4,plain,
c_Nitpick_Ofold__graph_H(U_1052,U_1053,U_1054,U_1055,c_Orderings_Obot__class_Obot(tc_fun(U_1052,tc_HOL_Obool)),U_1055),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_1,plain,
! [V_z_2,V_f_2,T_c,T_d] : hAPP(hAPP(c_Finite__Set_Ofold(T_d,T_c,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = V_z_2,
inference(fof_nnf,[status(thm)],[fact_fold__empty]) ).
fof(f_195_2,plain,
! [U_1059,U_1058,U_1057,U_1056] : hAPP(hAPP(c_Finite__Set_Ofold(U_1056,U_1057,U_1058),U_1059),c_Orderings_Obot__class_Obot(tc_fun(U_1056,tc_HOL_Obool))) = U_1059,
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
! [U_1056,U_1057,U_1058,U_1059] : hAPP(hAPP(c_Finite__Set_Ofold(U_1056,U_1057,U_1058),U_1059),c_Orderings_Obot__class_Obot(tc_fun(U_1056,tc_HOL_Obool))) = U_1059,
inference(definitional_conversion,[status(esa)],[f_195_2]) ).
cnf(f_195_4,plain,
hAPP(hAPP(c_Finite__Set_Ofold(U_1056,U_1057,U_1058),U_1059),c_Orderings_Obot__class_Obot(tc_fun(U_1056,tc_HOL_Obool))) = U_1059,
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
! [V_y_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_c,T_d,V_A_2,V_f_2),V_y_2)) = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f]) ).
fof(f_196_2,plain,
! [U_1064,U_1063,U_1062,U_1061,U_1060] :
( hAPP(U_1062,hAPP(c_Fun_Othe__inv__into(U_1060,U_1061,U_1063,U_1062),U_1064)) = U_1064
| ~ hBOOL(hAPP(hAPP(c_member(U_1061),U_1064),hAPP(c_Set_Oimage(U_1060,U_1061,U_1062),U_1063)))
| ~ c_Fun_Oinj__on(U_1060,U_1061,U_1062,U_1063) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
! [U_1060,U_1061,U_1062,U_1063,U_1064] :
( hAPP(U_1062,hAPP(c_Fun_Othe__inv__into(U_1060,U_1061,U_1063,U_1062),U_1064)) = U_1064
| ~ hBOOL(hAPP(hAPP(c_member(U_1061),U_1064),hAPP(c_Set_Oimage(U_1060,U_1061,U_1062),U_1063)))
| ~ c_Fun_Oinj__on(U_1060,U_1061,U_1062,U_1063) ),
inference(definitional_conversion,[status(esa)],[f_196_2]) ).
cnf(f_196_4,plain,
( hAPP(U_1062,hAPP(c_Fun_Othe__inv__into(U_1060,U_1061,U_1063,U_1062),U_1064)) = U_1064
| ~ hBOOL(hAPP(hAPP(c_member(U_1061),U_1064),hAPP(c_Set_Oimage(U_1060,U_1061,U_1062),U_1063)))
| ~ c_Fun_Oinj__on(U_1060,U_1061,U_1062,U_1063) ),
inference(clausify,[status(thm)],[f_196_3]) ).
fof(f_197_1,plain,
! [V_x_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_set__mp]) ).
fof(f_197_2,plain,
! [U_1068,U_1067,U_1066,U_1065] :
( hBOOL(hAPP(hAPP(c_member(U_1065),U_1068),U_1067))
| ~ hBOOL(hAPP(hAPP(c_member(U_1065),U_1068),U_1066))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1065,tc_HOL_Obool)),U_1066),U_1067)) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
! [U_1066,U_1065,U_1067,U_1068] :
( hBOOL(hAPP(hAPP(c_member(U_1065),U_1068),U_1067))
| ~ hBOOL(hAPP(hAPP(c_member(U_1065),U_1068),U_1066))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1065,tc_HOL_Obool)),U_1066),U_1067)) ),
inference(definitional_conversion,[status(esa)],[f_197_2]) ).
cnf(f_197_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1065),U_1068),U_1067))
| ~ hBOOL(hAPP(hAPP(c_member(U_1065),U_1068),U_1066))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1065,tc_HOL_Obool)),U_1066),U_1067)) ),
inference(clausify,[status(thm)],[f_197_3]) ).
fof(f_198_1,plain,
! [V_B_2,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_set__rev__mp]) ).
fof(f_198_2,plain,
! [U_1072,U_1071,U_1070,U_1069] :
( hBOOL(hAPP(hAPP(c_member(U_1069),U_1070),U_1072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1069,tc_HOL_Obool)),U_1071),U_1072))
| ~ hBOOL(hAPP(hAPP(c_member(U_1069),U_1070),U_1071)) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
! [U_1069,U_1070,U_1071,U_1072] :
( hBOOL(hAPP(hAPP(c_member(U_1069),U_1070),U_1072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1069,tc_HOL_Obool)),U_1071),U_1072))
| ~ hBOOL(hAPP(hAPP(c_member(U_1069),U_1070),U_1071)) ),
inference(definitional_conversion,[status(esa)],[f_198_2]) ).
cnf(f_198_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1069),U_1070),U_1072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1069,tc_HOL_Obool)),U_1071),U_1072))
| ~ hBOOL(hAPP(hAPP(c_member(U_1069),U_1070),U_1071)) ),
inference(clausify,[status(thm)],[f_198_3]) ).
fof(f_199_1,plain,
! [V_x_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_in__mono]) ).
fof(f_199_2,plain,
! [U_1076,U_1075,U_1074,U_1073] :
( hBOOL(hAPP(hAPP(c_member(U_1073),U_1076),U_1075))
| ~ hBOOL(hAPP(hAPP(c_member(U_1073),U_1076),U_1074))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1073,tc_HOL_Obool)),U_1074),U_1075)) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
! [U_1073,U_1074,U_1075,U_1076] :
( hBOOL(hAPP(hAPP(c_member(U_1073),U_1076),U_1075))
| ~ hBOOL(hAPP(hAPP(c_member(U_1073),U_1076),U_1074))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1073,tc_HOL_Obool)),U_1074),U_1075)) ),
inference(definitional_conversion,[status(esa)],[f_199_2]) ).
cnf(f_199_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1073),U_1076),U_1075))
| ~ hBOOL(hAPP(hAPP(c_member(U_1073),U_1076),U_1074))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1073,tc_HOL_Obool)),U_1074),U_1075)) ),
inference(clausify,[status(thm)],[f_199_3]) ).
fof(f_200_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_200_2,plain,
! [U_1078,U_1077] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077),c_Orderings_Obot__class_Obot(U_1077)),U_1078))
| ~ class_Orderings_Obot(U_1077) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
fof(f_200_3,plain,
! [U_1077,U_1078] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077),c_Orderings_Obot__class_Obot(U_1077)),U_1078))
| ~ class_Orderings_Obot(U_1077) ),
inference(definitional_conversion,[status(esa)],[f_200_2]) ).
cnf(f_200_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077),c_Orderings_Obot__class_Obot(U_1077)),U_1078))
| ~ class_Orderings_Obot(U_1077) ),
inference(clausify,[status(thm)],[f_200_3]) ).
fof(f_201_1,plain,
! [V_A_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__empty]) ).
fof(f_201_2,plain,
! [U_1080,U_1079] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1079,tc_HOL_Obool)),U_1080),c_Orderings_Obot__class_Obot(tc_fun(U_1079,tc_HOL_Obool))))
| U_1080 != c_Orderings_Obot__class_Obot(tc_fun(U_1079,tc_HOL_Obool)) )
& ( U_1080 = c_Orderings_Obot__class_Obot(tc_fun(U_1079,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1079,tc_HOL_Obool)),U_1080),c_Orderings_Obot__class_Obot(tc_fun(U_1079,tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
( ! [U_1084,U_1082] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1082,tc_HOL_Obool)),U_1084),c_Orderings_Obot__class_Obot(tc_fun(U_1082,tc_HOL_Obool))))
| U_1084 != c_Orderings_Obot__class_Obot(tc_fun(U_1082,tc_HOL_Obool)) )
& ! [U_1083,U_1081] :
( U_1083 = c_Orderings_Obot__class_Obot(tc_fun(U_1081,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1081,tc_HOL_Obool)),U_1083),c_Orderings_Obot__class_Obot(tc_fun(U_1081,tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_201_2]) ).
fof(f_201_4,plain,
( ! [U_1082,U_1084] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1082,tc_HOL_Obool)),U_1084),c_Orderings_Obot__class_Obot(tc_fun(U_1082,tc_HOL_Obool))))
| U_1084 != c_Orderings_Obot__class_Obot(tc_fun(U_1082,tc_HOL_Obool)) )
& ! [U_1083,U_1081] :
( U_1083 = c_Orderings_Obot__class_Obot(tc_fun(U_1081,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1081,tc_HOL_Obool)),U_1083),c_Orderings_Obot__class_Obot(tc_fun(U_1081,tc_HOL_Obool)))) ) ),
inference(definitional_conversion,[status(esa)],[f_201_3]) ).
cnf(f_201_5,plain,
( U_1083 = c_Orderings_Obot__class_Obot(tc_fun(U_1081,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1081,tc_HOL_Obool)),U_1083),c_Orderings_Obot__class_Obot(tc_fun(U_1081,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_201_4]) ).
cnf(f_201_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1082,tc_HOL_Obool)),U_1084),c_Orderings_Obot__class_Obot(tc_fun(U_1082,tc_HOL_Obool))))
| U_1084 != c_Orderings_Obot__class_Obot(tc_fun(U_1082,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_201_4]) ).
fof(f_202_1,plain,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ 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_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__subset]) ).
fof(f_202_2,plain,
! [U_1087,U_1086,U_1085] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1085),U_1086))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1085),U_1087))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1085,tc_HOL_Obool)),U_1086),U_1087)) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
! [U_1085,U_1086,U_1087] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1085),U_1086))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1085),U_1087))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1085,tc_HOL_Obool)),U_1086),U_1087)) ),
inference(definitional_conversion,[status(esa)],[f_202_2]) ).
cnf(f_202_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1085),U_1086))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1085),U_1087))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1085,tc_HOL_Obool)),U_1086),U_1087)) ),
inference(clausify,[status(thm)],[f_202_3]) ).
fof(f_203_1,plain,
! [V_A_2,V_B_2,T_c] :
( 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_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__finite__subset]) ).
fof(f_203_2,plain,
! [U_1090,U_1089,U_1088] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1088),U_1090))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1088,tc_HOL_Obool)),U_1090),U_1089))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1088),U_1089)) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
! [U_1088,U_1089,U_1090] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1088),U_1090))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1088,tc_HOL_Obool)),U_1090),U_1089))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1088),U_1089)) ),
inference(definitional_conversion,[status(esa)],[f_203_2]) ).
cnf(f_203_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1088),U_1090))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1088,tc_HOL_Obool)),U_1090),U_1089))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1088),U_1089)) ),
inference(clausify,[status(thm)],[f_203_3]) ).
fof(f_204_1,plain,
! [V_a_2,V_D_2,V_C_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_D_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__mono]) ).
fof(f_204_2,plain,
! [U_1094,U_1093,U_1092,U_1091] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1091,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1091),U_1094),U_1092)),hAPP(hAPP(c_Set_Oinsert(U_1091),U_1094),U_1093)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1091,tc_HOL_Obool)),U_1092),U_1093)) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
! [U_1091,U_1092,U_1093,U_1094] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1091,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1091),U_1094),U_1092)),hAPP(hAPP(c_Set_Oinsert(U_1091),U_1094),U_1093)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1091,tc_HOL_Obool)),U_1092),U_1093)) ),
inference(definitional_conversion,[status(esa)],[f_204_2]) ).
cnf(f_204_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1091,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1091),U_1094),U_1092)),hAPP(hAPP(c_Set_Oinsert(U_1091),U_1094),U_1093)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1091,tc_HOL_Obool)),U_1092),U_1093)) ),
inference(clausify,[status(thm)],[f_204_3]) ).
fof(f_205_1,plain,
! [V_b_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_subset__insertI2]) ).
fof(f_205_2,plain,
! [U_1098,U_1097,U_1096,U_1095] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1095,tc_HOL_Obool)),U_1096),hAPP(hAPP(c_Set_Oinsert(U_1095),U_1098),U_1097)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1095,tc_HOL_Obool)),U_1096),U_1097)) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
! [U_1095,U_1096,U_1097,U_1098] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1095,tc_HOL_Obool)),U_1096),hAPP(hAPP(c_Set_Oinsert(U_1095),U_1098),U_1097)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1095,tc_HOL_Obool)),U_1096),U_1097)) ),
inference(definitional_conversion,[status(esa)],[f_205_2]) ).
cnf(f_205_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1095,tc_HOL_Obool)),U_1096),hAPP(hAPP(c_Set_Oinsert(U_1095),U_1098),U_1097)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1095,tc_HOL_Obool)),U_1096),U_1097)) ),
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_1,plain,
! [V_a_2,V_B_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_subset__insertI]) ).
fof(f_206_2,plain,
! [U_1101,U_1100,U_1099] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1099,tc_HOL_Obool)),U_1100),hAPP(hAPP(c_Set_Oinsert(U_1099),U_1101),U_1100))),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
! [U_1099,U_1100,U_1101] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1099,tc_HOL_Obool)),U_1100),hAPP(hAPP(c_Set_Oinsert(U_1099),U_1101),U_1100))),
inference(definitional_conversion,[status(esa)],[f_206_2]) ).
cnf(f_206_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1099,tc_HOL_Obool)),U_1100),hAPP(hAPP(c_Set_Oinsert(U_1099),U_1101),U_1100))),
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_1,plain,
! [V_f_2,T_d,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__mono]) ).
fof(f_207_2,plain,
! [U_1106,U_1105,U_1104,U_1103,U_1102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1105,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1102,U_1105,U_1106),U_1103)),hAPP(c_Set_Oimage(U_1102,U_1105,U_1106),U_1104)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1102,tc_HOL_Obool)),U_1103),U_1104)) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
! [U_1102,U_1103,U_1104,U_1105,U_1106] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1105,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1102,U_1105,U_1106),U_1103)),hAPP(c_Set_Oimage(U_1102,U_1105,U_1106),U_1104)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1102,tc_HOL_Obool)),U_1103),U_1104)) ),
inference(definitional_conversion,[status(esa)],[f_207_2]) ).
cnf(f_207_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1105,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1102,U_1105,U_1106),U_1103)),hAPP(c_Set_Oimage(U_1102,U_1105,U_1106),U_1104)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1102,tc_HOL_Obool)),U_1103),U_1104)) ),
inference(clausify,[status(thm)],[f_207_3]) ).
fof(f_208_1,plain,
! [V_A_2,V_f_2,T_d,V_B_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)))
| ! [B_AA] :
( V_B_2 != hAPP(c_Set_Oimage(T_d,T_c,V_f_2),B_AA)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),B_AA),V_A_2)) ) )
& ( ? [B_AA] :
( V_B_2 = hAPP(c_Set_Oimage(T_d,T_c,V_f_2),B_AA)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),B_AA),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_d,T_c,V_f_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__image__iff]) ).
fof(f_208_2,plain,
! [U_1113,U_1112,U_1111,U_1110,U_1109] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1109,tc_HOL_Obool)),U_1110),hAPP(c_Set_Oimage(U_1111,U_1109,U_1112),U_1113)))
| ! [U_1108] :
( U_1110 != hAPP(c_Set_Oimage(U_1111,U_1109,U_1112),U_1108)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1111,tc_HOL_Obool)),U_1108),U_1113)) ) )
& ( ? [U_1107] :
( U_1110 = hAPP(c_Set_Oimage(U_1111,U_1109,U_1112),U_1107)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1111,tc_HOL_Obool)),U_1107),U_1113)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1109,tc_HOL_Obool)),U_1110),hAPP(c_Set_Oimage(U_1111,U_1109,U_1112),U_1113))) ) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
( ! [U_1123,U_1121,U_1119,U_1117,U_1115] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1115,tc_HOL_Obool)),U_1117),hAPP(c_Set_Oimage(U_1119,U_1115,U_1121),U_1123)))
| ! [U_1108] :
( U_1117 != hAPP(c_Set_Oimage(U_1119,U_1115,U_1121),U_1108)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1119,tc_HOL_Obool)),U_1108),U_1123)) ) )
& ! [U_1122,U_1120,U_1118,U_1116,U_1114] :
( ? [U_1107] :
( U_1116 = hAPP(c_Set_Oimage(U_1118,U_1114,U_1120),U_1107)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1118,tc_HOL_Obool)),U_1107),U_1122)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1114,tc_HOL_Obool)),U_1116),hAPP(c_Set_Oimage(U_1118,U_1114,U_1120),U_1122))) ) ),
inference(miniscope,[status(thm)],[f_208_2]) ).
fof(f_208_4,plain,
( ! [U_1123,U_1121,U_1119,U_1117,U_1115] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1115,tc_HOL_Obool)),U_1117),hAPP(c_Set_Oimage(U_1119,U_1115,U_1121),U_1123)))
| ! [U_1108] :
( U_1117 != hAPP(c_Set_Oimage(U_1119,U_1115,U_1121),U_1108)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1119,tc_HOL_Obool)),U_1108),U_1123)) ) )
& ! [U_1122,U_1120,U_1118,U_1116,U_1114] :
( ( U_1116 = hAPP(c_Set_Oimage(U_1118,U_1114,U_1120),sK22(U_1122,U_1120,U_1118,U_1116,U_1114))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1118,tc_HOL_Obool)),sK22(U_1122,U_1120,U_1118,U_1116,U_1114)),U_1122)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1114,tc_HOL_Obool)),U_1116),hAPP(c_Set_Oimage(U_1118,U_1114,U_1120),U_1122))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_1107,sK22(U_1122,U_1120,U_1118,U_1116,U_1114))],[f_208_3]) ).
fof(f_208_5,plain,
( ! [U_1116,U_1118,U_1120,U_1114,U_1122] :
( U_1116 = hAPP(c_Set_Oimage(U_1118,U_1114,U_1120),sK22(U_1122,U_1120,U_1118,U_1116,U_1114))
| ~ sP39(U_1116,U_1118,U_1120,U_1114,U_1122) )
& ! [U_1116,U_1118,U_1120,U_1114,U_1122] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1118,tc_HOL_Obool)),sK22(U_1122,U_1120,U_1118,U_1116,U_1114)),U_1122))
| ~ sP39(U_1116,U_1118,U_1120,U_1114,U_1122) )
& ! [U_1108,U_1123,U_1117,U_1115,U_1121,U_1119] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1115,tc_HOL_Obool)),U_1117),hAPP(c_Set_Oimage(U_1119,U_1115,U_1121),U_1123)))
| U_1117 != hAPP(c_Set_Oimage(U_1119,U_1115,U_1121),U_1108)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1119,tc_HOL_Obool)),U_1108),U_1123)) )
& ! [U_1116,U_1118,U_1120,U_1114,U_1122] :
( sP39(U_1116,U_1118,U_1120,U_1114,U_1122)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1114,tc_HOL_Obool)),U_1116),hAPP(c_Set_Oimage(U_1118,U_1114,U_1120),U_1122))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39])],[f_208_4]) ).
cnf(f_208_6,plain,
( sP39(U_1116,U_1118,U_1120,U_1114,U_1122)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1114,tc_HOL_Obool)),U_1116),hAPP(c_Set_Oimage(U_1118,U_1114,U_1120),U_1122))) ),
inference(clausify,[status(thm)],[f_208_5]) ).
cnf(f_208_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1115,tc_HOL_Obool)),U_1117),hAPP(c_Set_Oimage(U_1119,U_1115,U_1121),U_1123)))
| U_1117 != hAPP(c_Set_Oimage(U_1119,U_1115,U_1121),U_1108)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1119,tc_HOL_Obool)),U_1108),U_1123)) ),
inference(clausify,[status(thm)],[f_208_5]) ).
cnf(f_208_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1118,tc_HOL_Obool)),sK22(U_1122,U_1120,U_1118,U_1116,U_1114)),U_1122))
| ~ sP39(U_1116,U_1118,U_1120,U_1114,U_1122) ),
inference(clausify,[status(thm)],[f_208_5]) ).
cnf(f_208_9,plain,
( U_1116 = hAPP(c_Set_Oimage(U_1118,U_1114,U_1120),sK22(U_1122,U_1120,U_1118,U_1116,U_1114))
| ~ sP39(U_1116,U_1118,U_1120,U_1114,U_1122) ),
inference(clausify,[status(thm)],[f_208_5]) ).
fof(f_209_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),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)) ),
inference(fof_nnf,[status(thm)],[fact_double__diff]) ).
fof(f_209_2,plain,
! [U_1127,U_1126,U_1125,U_1124] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1124,tc_HOL_Obool)),U_1126),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1124,tc_HOL_Obool)),U_1127),U_1125)) = U_1125
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1124,tc_HOL_Obool)),U_1126),U_1127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1124,tc_HOL_Obool)),U_1125),U_1126)) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
! [U_1125,U_1124,U_1126,U_1127] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1124,tc_HOL_Obool)),U_1126),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1124,tc_HOL_Obool)),U_1127),U_1125)) = U_1125
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1124,tc_HOL_Obool)),U_1126),U_1127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1124,tc_HOL_Obool)),U_1125),U_1126)) ),
inference(definitional_conversion,[status(esa)],[f_209_2]) ).
cnf(f_209_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1124,tc_HOL_Obool)),U_1126),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1124,tc_HOL_Obool)),U_1127),U_1125)) = U_1125
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1124,tc_HOL_Obool)),U_1126),U_1127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1124,tc_HOL_Obool)),U_1125),U_1126)) ),
inference(clausify,[status(thm)],[f_209_3]) ).
fof(f_210_1,plain,
! [V_B_2,V_D_2,V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_C_2),V_D_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_D_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Diff__mono]) ).
fof(f_210_2,plain,
! [U_1132,U_1131,U_1130,U_1129,U_1128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1128,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1128,tc_HOL_Obool)),U_1129),U_1132)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1128,tc_HOL_Obool)),U_1130),U_1131)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1128,tc_HOL_Obool)),U_1131),U_1132))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1128,tc_HOL_Obool)),U_1129),U_1130)) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
! [U_1128,U_1129,U_1130,U_1131,U_1132] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1128,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1128,tc_HOL_Obool)),U_1129),U_1132)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1128,tc_HOL_Obool)),U_1130),U_1131)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1128,tc_HOL_Obool)),U_1131),U_1132))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1128,tc_HOL_Obool)),U_1129),U_1130)) ),
inference(definitional_conversion,[status(esa)],[f_210_2]) ).
cnf(f_210_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1128,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1128,tc_HOL_Obool)),U_1129),U_1132)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1128,tc_HOL_Obool)),U_1130),U_1131)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1128,tc_HOL_Obool)),U_1131),U_1132))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1128,tc_HOL_Obool)),U_1129),U_1130)) ),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_1,plain,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Diff__subset]) ).
fof(f_211_2,plain,
! [U_1135,U_1134,U_1133] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1133,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1133,tc_HOL_Obool)),U_1134),U_1135)),U_1134)),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
! [U_1134,U_1133,U_1135] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1133,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1133,tc_HOL_Obool)),U_1134),U_1135)),U_1134)),
inference(definitional_conversion,[status(esa)],[f_211_2]) ).
cnf(f_211_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1133,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1133,tc_HOL_Obool)),U_1134),U_1135)),U_1134)),
inference(clausify,[status(thm)],[f_211_3]) ).
fof(f_212_1,plain,
! [V_Ga_2,V_ts_2,V_G_H_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_G_H_2,V_ts_2) ),
inference(fof_nnf,[status(thm)],[fact_thin]) ).
fof(f_212_2,plain,
! [U_1139,U_1138,U_1137,U_1136] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_1136,U_1139,U_1138)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1136),tc_HOL_Obool)),U_1137),U_1139))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1136,U_1137,U_1138) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
! [U_1136,U_1137,U_1138,U_1139] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_1136,U_1139,U_1138)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1136),tc_HOL_Obool)),U_1137),U_1139))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1136,U_1137,U_1138) ),
inference(definitional_conversion,[status(esa)],[f_212_2]) ).
cnf(f_212_4,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_1136,U_1139,U_1138)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1136),tc_HOL_Obool)),U_1137),U_1139))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1136,U_1137,U_1138) ),
inference(clausify,[status(thm)],[f_212_3]) ).
fof(f_213_1,plain,
! [V_ts_2,V_ts_H_2,V_Ga_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)),V_ts_2),V_ts_H_2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_H_2) ),
inference(fof_nnf,[status(thm)],[fact_weaken]) ).
fof(f_213_2,plain,
! [U_1143,U_1142,U_1141,U_1140] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_1140,U_1141,U_1143)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1140),tc_HOL_Obool)),U_1143),U_1142))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1140,U_1141,U_1142) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_1141,U_1140,U_1142,U_1143] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_1140,U_1141,U_1143)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1140),tc_HOL_Obool)),U_1143),U_1142))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1140,U_1141,U_1142) ),
inference(definitional_conversion,[status(esa)],[f_213_2]) ).
cnf(f_213_4,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_1140,U_1141,U_1143)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1140),tc_HOL_Obool)),U_1143),U_1142))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1140,U_1141,U_1142) ),
inference(clausify,[status(thm)],[f_213_3]) ).
fof(f_214_1,plain,
! [V_Ga_2,V_ts_2,T_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,V_ts_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)),V_ts_2),V_Ga_2)) ),
inference(fof_nnf,[status(thm)],[fact_asm]) ).
fof(f_214_2,plain,
! [U_1146,U_1145,U_1144] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_1144,U_1146,U_1145)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1144),tc_HOL_Obool)),U_1145),U_1146)) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
fof(f_214_3,plain,
! [U_1145,U_1144,U_1146] :
( c_Hoare__Mirabelle_Ohoare__derivs(U_1144,U_1146,U_1145)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1144),tc_HOL_Obool)),U_1145),U_1146)) ),
inference(definitional_conversion,[status(esa)],[f_214_2]) ).
cnf(f_214_4,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(U_1144,U_1146,U_1145)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1144),tc_HOL_Obool)),U_1145),U_1146)) ),
inference(clausify,[status(thm)],[f_214_3]) ).
fof(f_215_1,plain,
! [V_x_2,V_z_2,V_f_2,T_d,T_c] :
( V_x_2 = V_z_2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE]) ).
fof(f_215_2,plain,
! [U_1151,U_1150,U_1149,U_1148,U_1147] :
( U_1151 = U_1150
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1147,U_1148,U_1149,U_1150,c_Orderings_Obot__class_Obot(tc_fun(U_1147,tc_HOL_Obool))),U_1151)) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
! [U_1151,U_1150] :
( ! [U_1149,U_1148,U_1147] : ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1147,U_1148,U_1149,U_1150,c_Orderings_Obot__class_Obot(tc_fun(U_1147,tc_HOL_Obool))),U_1151))
| U_1151 = U_1150 ),
inference(miniscope,[status(thm)],[f_215_2]) ).
fof(f_215_4,plain,
! [U_1147,U_1148,U_1149,U_1150,U_1151] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1147,U_1148,U_1149,U_1150,c_Orderings_Obot__class_Obot(tc_fun(U_1147,tc_HOL_Obool))),U_1151))
| U_1151 = U_1150 ),
inference(definitional_conversion,[status(esa)],[f_215_3]) ).
cnf(f_215_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1147,U_1148,U_1149,U_1150,c_Orderings_Obot__class_Obot(tc_fun(U_1147,tc_HOL_Obool))),U_1151))
| U_1151 = U_1150 ),
inference(clausify,[status(thm)],[f_215_4]) ).
fof(f_216_1,plain,
! [V_z_2,V_f_2,T_d,T_c] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,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__graph_OemptyI]) ).
fof(f_216_2,plain,
! [U_1155,U_1154,U_1153,U_1152] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1152,U_1153,U_1154,U_1155,c_Orderings_Obot__class_Obot(tc_fun(U_1152,tc_HOL_Obool))),U_1155)),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_1152,U_1153,U_1154,U_1155] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1152,U_1153,U_1154,U_1155,c_Orderings_Obot__class_Obot(tc_fun(U_1152,tc_HOL_Obool))),U_1155)),
inference(definitional_conversion,[status(esa)],[f_216_2]) ).
cnf(f_216_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1152,U_1153,U_1154,U_1155,c_Orderings_Obot__class_Obot(tc_fun(U_1152,tc_HOL_Obool))),U_1155)),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_1,plain,
! [V_z_2,V_f_2,T_d,T_c] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,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__graph_Oequations_I1_J]) ).
fof(f_217_2,plain,
! [U_1159,U_1158,U_1157,U_1156] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1156,U_1157,U_1158,U_1159,c_Orderings_Obot__class_Obot(tc_fun(U_1156,tc_HOL_Obool))),U_1159)),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
! [U_1156,U_1157,U_1158,U_1159] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1156,U_1157,U_1158,U_1159,c_Orderings_Obot__class_Obot(tc_fun(U_1156,tc_HOL_Obool))),U_1159)),
inference(definitional_conversion,[status(esa)],[f_217_2]) ).
cnf(f_217_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1156,U_1157,U_1158,U_1159,c_Orderings_Obot__class_Obot(tc_fun(U_1156,tc_HOL_Obool))),U_1159)),
inference(clausify,[status(thm)],[f_217_3]) ).
fof(f_218_1,plain,
! [V_x_2,V_A_2,V_z_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite]) ).
fof(f_218_2,plain,
! [U_1165,U_1164,U_1163,U_1162,U_1161,U_1160] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1160),U_1164))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1160,U_1161,U_1162,U_1163,U_1164),U_1165)) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
! [U_1160,U_1161,U_1162,U_1163,U_1164,U_1165] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1160),U_1164))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1160,U_1161,U_1162,U_1163,U_1164),U_1165)) ),
inference(definitional_conversion,[status(esa)],[f_218_2]) ).
cnf(f_218_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1160),U_1164))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1160,U_1161,U_1162,U_1163,U_1164),U_1165)) ),
inference(clausify,[status(thm)],[f_218_3]) ).
fof(f_219_1,plain,
! [V_S_2,V_R_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_R_2),V_S_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_R_2),V_S_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__subset__eq]) ).
fof(f_219_2,plain,
! [U_1168,U_1167,U_1166] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1166,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1166,tc_fun(U_1166,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1166)),U_1167)),hAPP(hAPP(c_COMBC(U_1166,tc_fun(U_1166,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1166)),U_1168)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1166,tc_HOL_Obool)),U_1167),U_1168)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1166,tc_HOL_Obool)),U_1167),U_1168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1166,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1166,tc_fun(U_1166,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1166)),U_1167)),hAPP(hAPP(c_COMBC(U_1166,tc_fun(U_1166,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1166)),U_1168))) ) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
fof(f_219_3,plain,
( ! [U_1174,U_1172,U_1170] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1170,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1170,tc_fun(U_1170,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1170)),U_1172)),hAPP(hAPP(c_COMBC(U_1170,tc_fun(U_1170,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1170)),U_1174)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1170,tc_HOL_Obool)),U_1172),U_1174)) )
& ! [U_1173,U_1171,U_1169] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1169,tc_HOL_Obool)),U_1171),U_1173))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1169,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1169,tc_fun(U_1169,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1169)),U_1171)),hAPP(hAPP(c_COMBC(U_1169,tc_fun(U_1169,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1169)),U_1173))) ) ),
inference(miniscope,[status(thm)],[f_219_2]) ).
fof(f_219_4,plain,
( ! [U_1170,U_1172,U_1174] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1170,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1170,tc_fun(U_1170,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1170)),U_1172)),hAPP(hAPP(c_COMBC(U_1170,tc_fun(U_1170,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1170)),U_1174)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1170,tc_HOL_Obool)),U_1172),U_1174)) )
& ! [U_1171,U_1169,U_1173] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1169,tc_HOL_Obool)),U_1171),U_1173))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1169,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1169,tc_fun(U_1169,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1169)),U_1171)),hAPP(hAPP(c_COMBC(U_1169,tc_fun(U_1169,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1169)),U_1173))) ) ),
inference(definitional_conversion,[status(esa)],[f_219_3]) ).
cnf(f_219_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1169,tc_HOL_Obool)),U_1171),U_1173))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1169,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1169,tc_fun(U_1169,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1169)),U_1171)),hAPP(hAPP(c_COMBC(U_1169,tc_fun(U_1169,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1169)),U_1173))) ),
inference(clausify,[status(thm)],[f_219_4]) ).
cnf(f_219_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1170,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_1170,tc_fun(U_1170,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1170)),U_1172)),hAPP(hAPP(c_COMBC(U_1170,tc_fun(U_1170,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1170)),U_1174)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1170,tc_HOL_Obool)),U_1172),U_1174)) ),
inference(clausify,[status(thm)],[f_219_4]) ).
fof(f_220_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
| ~ c_Fun_Oinj__on(T_d,T_c,V_f_2,V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__imageD]) ).
fof(f_220_2,plain,
! [U_1178,U_1177,U_1176,U_1175] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1176),U_1178))
| ~ c_Fun_Oinj__on(U_1176,U_1175,U_1177,U_1178)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1175),hAPP(c_Set_Oimage(U_1176,U_1175,U_1177),U_1178))) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_1175,U_1176,U_1177,U_1178] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1176),U_1178))
| ~ c_Fun_Oinj__on(U_1176,U_1175,U_1177,U_1178)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1175),hAPP(c_Set_Oimage(U_1176,U_1175,U_1177),U_1178))) ),
inference(definitional_conversion,[status(esa)],[f_220_2]) ).
cnf(f_220_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1176),U_1178))
| ~ c_Fun_Oinj__on(U_1176,U_1175,U_1177,U_1178)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1175),hAPP(c_Set_Oimage(U_1176,U_1175,U_1177),U_1178))) ),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_1,plain,
! [V_B_2,V_A_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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)),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(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2))) ) )
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_subset__insert]) ).
fof(f_221_2,plain,
! [U_1182,U_1181,U_1180,U_1179] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1179,tc_HOL_Obool)),U_1181),hAPP(hAPP(c_Set_Oinsert(U_1179),U_1180),U_1182)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1179,tc_HOL_Obool)),U_1181),U_1182)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1179,tc_HOL_Obool)),U_1181),U_1182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1179,tc_HOL_Obool)),U_1181),hAPP(hAPP(c_Set_Oinsert(U_1179),U_1180),U_1182))) ) )
| hBOOL(hAPP(hAPP(c_member(U_1179),U_1180),U_1181)) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
( ! [U_1179,U_1180,U_1181,U_1182] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1179,tc_HOL_Obool)),U_1181),hAPP(hAPP(c_Set_Oinsert(U_1179),U_1180),U_1182)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1179,tc_HOL_Obool)),U_1181),U_1182))
| ~ sP40(U_1179,U_1180,U_1181,U_1182) )
& ! [U_1179,U_1180,U_1181,U_1182] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1179,tc_HOL_Obool)),U_1181),U_1182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1179,tc_HOL_Obool)),U_1181),hAPP(hAPP(c_Set_Oinsert(U_1179),U_1180),U_1182)))
| ~ sP40(U_1179,U_1180,U_1181,U_1182) )
& ! [U_1179,U_1180,U_1181,U_1182] :
( sP40(U_1179,U_1180,U_1181,U_1182)
| hBOOL(hAPP(hAPP(c_member(U_1179),U_1180),U_1181)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_221_2]) ).
cnf(f_221_4,plain,
( sP40(U_1179,U_1180,U_1181,U_1182)
| hBOOL(hAPP(hAPP(c_member(U_1179),U_1180),U_1181)) ),
inference(clausify,[status(thm)],[f_221_3]) ).
cnf(f_221_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1179,tc_HOL_Obool)),U_1181),U_1182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1179,tc_HOL_Obool)),U_1181),hAPP(hAPP(c_Set_Oinsert(U_1179),U_1180),U_1182)))
| ~ sP40(U_1179,U_1180,U_1181,U_1182) ),
inference(clausify,[status(thm)],[f_221_3]) ).
cnf(f_221_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1179,tc_HOL_Obool)),U_1181),hAPP(hAPP(c_Set_Oinsert(U_1179),U_1180),U_1182)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1179,tc_HOL_Obool)),U_1181),U_1182))
| ~ sP40(U_1179,U_1180,U_1181,U_1182) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_1,plain,
! [V_B_2,V_A_2,V_x_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_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),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__subset]) ).
fof(f_222_2,plain,
! [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_Set_Oinsert(U_1183),U_1184),U_1185)),U_1186))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1183,tc_HOL_Obool)),U_1185),U_1186))
| ~ hBOOL(hAPP(hAPP(c_member(U_1183),U_1184),U_1186)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1183,tc_HOL_Obool)),U_1185),U_1186))
& hBOOL(hAPP(hAPP(c_member(U_1183),U_1184),U_1186)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1183,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1183),U_1184),U_1185)),U_1186)) ) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
( ! [U_1194,U_1192,U_1190,U_1188] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1188),U_1190),U_1192)),U_1194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),U_1192),U_1194))
| ~ hBOOL(hAPP(hAPP(c_member(U_1188),U_1190),U_1194)) )
& ! [U_1193,U_1191,U_1189,U_1187] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1187,tc_HOL_Obool)),U_1191),U_1193))
& hBOOL(hAPP(hAPP(c_member(U_1187),U_1189),U_1193)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1187,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1187),U_1189),U_1191)),U_1193)) ) ),
inference(miniscope,[status(thm)],[f_222_2]) ).
fof(f_222_4,plain,
( ! [U_1189,U_1187,U_1191,U_1193] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1187,tc_HOL_Obool)),U_1191),U_1193))
| ~ sP41(U_1189,U_1187,U_1191,U_1193) )
& ! [U_1189,U_1187,U_1191,U_1193] :
( hBOOL(hAPP(hAPP(c_member(U_1187),U_1189),U_1193))
| ~ sP41(U_1189,U_1187,U_1191,U_1193) )
& ! [U_1192,U_1188,U_1194,U_1190] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1188),U_1190),U_1192)),U_1194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),U_1192),U_1194))
| ~ hBOOL(hAPP(hAPP(c_member(U_1188),U_1190),U_1194)) )
& ! [U_1189,U_1187,U_1191,U_1193] :
( sP41(U_1189,U_1187,U_1191,U_1193)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1187,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1187),U_1189),U_1191)),U_1193)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41])],[f_222_3]) ).
cnf(f_222_5,plain,
( sP41(U_1189,U_1187,U_1191,U_1193)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1187,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1187),U_1189),U_1191)),U_1193)) ),
inference(clausify,[status(thm)],[f_222_4]) ).
cnf(f_222_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1188),U_1190),U_1192)),U_1194))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1188,tc_HOL_Obool)),U_1192),U_1194))
| ~ hBOOL(hAPP(hAPP(c_member(U_1188),U_1190),U_1194)) ),
inference(clausify,[status(thm)],[f_222_4]) ).
cnf(f_222_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_1187),U_1189),U_1193))
| ~ sP41(U_1189,U_1187,U_1191,U_1193) ),
inference(clausify,[status(thm)],[f_222_4]) ).
cnf(f_222_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1187,tc_HOL_Obool)),U_1191),U_1193))
| ~ sP41(U_1189,U_1187,U_1191,U_1193) ),
inference(clausify,[status(thm)],[f_222_4]) ).
fof(f_223_1,plain,
! [V_x_2,V_A_2,T_c] :
( 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)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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))))) ),
inference(fof_nnf,[status(thm)],[fact_subset__singletonD]) ).
fof(f_223_2,plain,
! [U_1197,U_1196,U_1195] :
( U_1196 = hAPP(hAPP(c_Set_Oinsert(U_1195),U_1197),c_Orderings_Obot__class_Obot(tc_fun(U_1195,tc_HOL_Obool)))
| U_1196 = c_Orderings_Obot__class_Obot(tc_fun(U_1195,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1195,tc_HOL_Obool)),U_1196),hAPP(hAPP(c_Set_Oinsert(U_1195),U_1197),c_Orderings_Obot__class_Obot(tc_fun(U_1195,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_1196,U_1195,U_1197] :
( U_1196 = hAPP(hAPP(c_Set_Oinsert(U_1195),U_1197),c_Orderings_Obot__class_Obot(tc_fun(U_1195,tc_HOL_Obool)))
| U_1196 = c_Orderings_Obot__class_Obot(tc_fun(U_1195,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1195,tc_HOL_Obool)),U_1196),hAPP(hAPP(c_Set_Oinsert(U_1195),U_1197),c_Orderings_Obot__class_Obot(tc_fun(U_1195,tc_HOL_Obool))))) ),
inference(definitional_conversion,[status(esa)],[f_223_2]) ).
cnf(f_223_4,plain,
( U_1196 = hAPP(hAPP(c_Set_Oinsert(U_1195),U_1197),c_Orderings_Obot__class_Obot(tc_fun(U_1195,tc_HOL_Obool)))
| U_1196 = c_Orderings_Obot__class_Obot(tc_fun(U_1195,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1195,tc_HOL_Obool)),U_1196),hAPP(hAPP(c_Set_Oinsert(U_1195),U_1197),c_Orderings_Obot__class_Obot(tc_fun(U_1195,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_1,plain,
! [V_f_2,V_B_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__surj]) ).
fof(f_224_2,plain,
! [U_1202,U_1201,U_1200,U_1199,U_1198] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),U_1201))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1200,tc_HOL_Obool)),U_1201),hAPP(c_Set_Oimage(U_1198,U_1200,U_1202),U_1199)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1198),U_1199)) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
! [U_1198,U_1199,U_1200,U_1201,U_1202] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),U_1201))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1200,tc_HOL_Obool)),U_1201),hAPP(c_Set_Oimage(U_1198,U_1200,U_1202),U_1199)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1198),U_1199)) ),
inference(definitional_conversion,[status(esa)],[f_224_2]) ).
cnf(f_224_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1200),U_1201))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1200,tc_HOL_Obool)),U_1201),hAPP(c_Set_Oimage(U_1198,U_1200,U_1202),U_1199)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1198),U_1199)) ),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_image__diff__subset]) ).
fof(f_225_2,plain,
! [U_1207,U_1206,U_1205,U_1204,U_1203] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1203,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1203,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1204,U_1203,U_1205),U_1206)),hAPP(c_Set_Oimage(U_1204,U_1203,U_1205),U_1207))),hAPP(c_Set_Oimage(U_1204,U_1203,U_1205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1204,tc_HOL_Obool)),U_1206),U_1207)))),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
! [U_1203,U_1204,U_1205,U_1206,U_1207] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1203,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1203,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1204,U_1203,U_1205),U_1206)),hAPP(c_Set_Oimage(U_1204,U_1203,U_1205),U_1207))),hAPP(c_Set_Oimage(U_1204,U_1203,U_1205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1204,tc_HOL_Obool)),U_1206),U_1207)))),
inference(definitional_conversion,[status(esa)],[f_225_2]) ).
cnf(f_225_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1203,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1203,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1204,U_1203,U_1205),U_1206)),hAPP(c_Set_Oimage(U_1204,U_1203,U_1205),U_1207))),hAPP(c_Set_Oimage(U_1204,U_1203,U_1205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1204,tc_HOL_Obool)),U_1206),U_1207)))),
inference(clausify,[status(thm)],[f_225_3]) ).
fof(f_226_1,plain,
! [V_y_2,V_z_2,V_f_2,T_d,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_c),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_c,T_d,V_f_2,V_z_2,V_A_2),V_y_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph_OinsertI]) ).
fof(f_226_2,plain,
! [U_1214,U_1213,U_1212,U_1211,U_1210,U_1209,U_1208] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1208,U_1211,U_1212,U_1213,hAPP(hAPP(c_Set_Oinsert(U_1208),U_1209),U_1210)),hAPP(hAPP(U_1212,U_1209),U_1214)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1208,U_1211,U_1212,U_1213,U_1210),U_1214))
| hBOOL(hAPP(hAPP(c_member(U_1208),U_1209),U_1210)) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
! [U_1208,U_1209,U_1210,U_1211,U_1212,U_1213,U_1214] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1208,U_1211,U_1212,U_1213,hAPP(hAPP(c_Set_Oinsert(U_1208),U_1209),U_1210)),hAPP(hAPP(U_1212,U_1209),U_1214)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1208,U_1211,U_1212,U_1213,U_1210),U_1214))
| hBOOL(hAPP(hAPP(c_member(U_1208),U_1209),U_1210)) ),
inference(definitional_conversion,[status(esa)],[f_226_2]) ).
cnf(f_226_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1208,U_1211,U_1212,U_1213,hAPP(hAPP(c_Set_Oinsert(U_1208),U_1209),U_1210)),hAPP(hAPP(U_1212,U_1209),U_1214)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1208,U_1211,U_1212,U_1213,U_1210),U_1214))
| hBOOL(hAPP(hAPP(c_member(U_1208),U_1209),U_1210)) ),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_1,plain,
! [V_f_2,V_A_2,V_a_2,T_c] :
( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff1__nat]) ).
fof(f_227_2,plain,
! [U_1218,U_1217,U_1216,U_1215] :
( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1215,tc_Nat_Onat),U_1218),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1215,tc_HOL_Obool)),U_1217),hAPP(hAPP(c_Set_Oinsert(U_1215),U_1216),c_Orderings_Obot__class_Obot(tc_fun(U_1215,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1215,tc_Nat_Onat),U_1218),U_1217)
| hBOOL(hAPP(hAPP(c_member(U_1215),U_1216),U_1217)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1215,tc_Nat_Onat),U_1218),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1215,tc_HOL_Obool)),U_1217),hAPP(hAPP(c_Set_Oinsert(U_1215),U_1216),c_Orderings_Obot__class_Obot(tc_fun(U_1215,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1215,tc_Nat_Onat),U_1218),U_1217)),hAPP(U_1218,U_1216))
| ~ hBOOL(hAPP(hAPP(c_member(U_1215),U_1216),U_1217)) ) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
( ! [U_1226,U_1224,U_1222,U_1220] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1220,tc_Nat_Onat),U_1226),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1220,tc_HOL_Obool)),U_1224),hAPP(hAPP(c_Set_Oinsert(U_1220),U_1222),c_Orderings_Obot__class_Obot(tc_fun(U_1220,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1220,tc_Nat_Onat),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_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1219,tc_Nat_Onat),U_1225),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1219,tc_HOL_Obool)),U_1223),hAPP(hAPP(c_Set_Oinsert(U_1219),U_1221),c_Orderings_Obot__class_Obot(tc_fun(U_1219,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1219,tc_Nat_Onat),U_1225),U_1223)),hAPP(U_1225,U_1221))
| ~ hBOOL(hAPP(hAPP(c_member(U_1219),U_1221),U_1223)) ) ),
inference(miniscope,[status(thm)],[f_227_2]) ).
fof(f_227_4,plain,
( ! [U_1220,U_1222,U_1224,U_1226] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1220,tc_Nat_Onat),U_1226),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1220,tc_HOL_Obool)),U_1224),hAPP(hAPP(c_Set_Oinsert(U_1220),U_1222),c_Orderings_Obot__class_Obot(tc_fun(U_1220,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1220,tc_Nat_Onat),U_1226),U_1224)
| hBOOL(hAPP(hAPP(c_member(U_1220),U_1222),U_1224)) )
& ! [U_1219,U_1221,U_1225,U_1223] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1219,tc_Nat_Onat),U_1225),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1219,tc_HOL_Obool)),U_1223),hAPP(hAPP(c_Set_Oinsert(U_1219),U_1221),c_Orderings_Obot__class_Obot(tc_fun(U_1219,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1219,tc_Nat_Onat),U_1225),U_1223)),hAPP(U_1225,U_1221))
| ~ hBOOL(hAPP(hAPP(c_member(U_1219),U_1221),U_1223)) ) ),
inference(definitional_conversion,[status(esa)],[f_227_3]) ).
cnf(f_227_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1219,tc_Nat_Onat),U_1225),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1219,tc_HOL_Obool)),U_1223),hAPP(hAPP(c_Set_Oinsert(U_1219),U_1221),c_Orderings_Obot__class_Obot(tc_fun(U_1219,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1219,tc_Nat_Onat),U_1225),U_1223)),hAPP(U_1225,U_1221))
| ~ hBOOL(hAPP(hAPP(c_member(U_1219),U_1221),U_1223)) ),
inference(clausify,[status(thm)],[f_227_4]) ).
cnf(f_227_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1220,tc_Nat_Onat),U_1226),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1220,tc_HOL_Obool)),U_1224),hAPP(hAPP(c_Set_Oinsert(U_1220),U_1222),c_Orderings_Obot__class_Obot(tc_fun(U_1220,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1220,tc_Nat_Onat),U_1226),U_1224)
| hBOOL(hAPP(hAPP(c_member(U_1220),U_1222),U_1224)) ),
inference(clausify,[status(thm)],[f_227_4]) ).
fof(f_228_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( 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_d,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,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_228_2,plain,
! [U_1234,U_1233,U_1232,U_1231,U_1230,U_1229,U_1228,U_1227] :
( hAPP(hAPP(U_1229,hAPP(U_1232,U_1234)),hAPP(U_1232,U_1233)) = hAPP(U_1232,U_1233)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1228,tc_HOL_Obool)),U_1234),U_1233))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1228),U_1233))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_1227,U_1228,U_1229,U_1230,U_1231,U_1232) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
! [U_1234,U_1233,U_1232,U_1231,U_1230,U_1229,U_1228] :
( ! [U_1227] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_1227,U_1228,U_1229,U_1230,U_1231,U_1232)
| hAPP(hAPP(U_1229,hAPP(U_1232,U_1234)),hAPP(U_1232,U_1233)) = hAPP(U_1232,U_1233)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1228,tc_HOL_Obool)),U_1234),U_1233))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1228),U_1233)) ),
inference(miniscope,[status(thm)],[f_228_2]) ).
fof(f_228_4,plain,
! [U_1228,U_1227,U_1230,U_1229,U_1233,U_1231,U_1232,U_1234] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_1227,U_1228,U_1229,U_1230,U_1231,U_1232)
| hAPP(hAPP(U_1229,hAPP(U_1232,U_1234)),hAPP(U_1232,U_1233)) = hAPP(U_1232,U_1233)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1228,tc_HOL_Obool)),U_1234),U_1233))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1228),U_1233)) ),
inference(definitional_conversion,[status(esa)],[f_228_3]) ).
cnf(f_228_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_1227,U_1228,U_1229,U_1230,U_1231,U_1232)
| hAPP(hAPP(U_1229,hAPP(U_1232,U_1234)),hAPP(U_1232,U_1233)) = hAPP(U_1232,U_1233)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1228,tc_HOL_Obool)),U_1234),U_1233))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1228),U_1233)) ),
inference(clausify,[status(thm)],[f_228_4]) ).
fof(f_229_1,plain,
! [V_x_2,V_y_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,c_Fun_Ofun__upd(T_c,T_d,V_f_2,V_x_2,V_y_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_d),V_y_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__fun__updI]) ).
fof(f_229_2,plain,
! [U_1240,U_1239,U_1238,U_1237,U_1236,U_1235] :
( c_Fun_Oinj__on(U_1235,U_1236,c_Fun_Ofun__upd(U_1235,U_1236,U_1237,U_1240,U_1239),U_1238)
| hBOOL(hAPP(hAPP(c_member(U_1236),U_1239),hAPP(c_Set_Oimage(U_1235,U_1236,U_1237),U_1238)))
| ~ c_Fun_Oinj__on(U_1235,U_1236,U_1237,U_1238) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_1236,U_1235,U_1237,U_1238,U_1239,U_1240] :
( c_Fun_Oinj__on(U_1235,U_1236,c_Fun_Ofun__upd(U_1235,U_1236,U_1237,U_1240,U_1239),U_1238)
| hBOOL(hAPP(hAPP(c_member(U_1236),U_1239),hAPP(c_Set_Oimage(U_1235,U_1236,U_1237),U_1238)))
| ~ c_Fun_Oinj__on(U_1235,U_1236,U_1237,U_1238) ),
inference(definitional_conversion,[status(esa)],[f_229_2]) ).
cnf(f_229_4,plain,
( c_Fun_Oinj__on(U_1235,U_1236,c_Fun_Ofun__upd(U_1235,U_1236,U_1237,U_1240,U_1239),U_1238)
| hBOOL(hAPP(hAPP(c_member(U_1236),U_1239),hAPP(c_Set_Oimage(U_1235,U_1236,U_1237),U_1238)))
| ~ c_Fun_Oinj__on(U_1235,U_1236,U_1237,U_1238) ),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_1,plain,
! [V_g_2,V_f_2,T_d,V_A_2,V_a_2,T_c] :
( hAPP(c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_override__on__apply__in]) ).
fof(f_230_2,plain,
! [U_1246,U_1245,U_1244,U_1243,U_1242,U_1241] :
( hAPP(c_Fun_Ooverride__on(U_1241,U_1244,U_1245,U_1246,U_1243),U_1242) = hAPP(U_1246,U_1242)
| ~ hBOOL(hAPP(hAPP(c_member(U_1241),U_1242),U_1243)) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_1242,U_1241,U_1243,U_1244,U_1245,U_1246] :
( hAPP(c_Fun_Ooverride__on(U_1241,U_1244,U_1245,U_1246,U_1243),U_1242) = hAPP(U_1246,U_1242)
| ~ hBOOL(hAPP(hAPP(c_member(U_1241),U_1242),U_1243)) ),
inference(definitional_conversion,[status(esa)],[f_230_2]) ).
cnf(f_230_4,plain,
( hAPP(c_Fun_Ooverride__on(U_1241,U_1244,U_1245,U_1246,U_1243),U_1242) = hAPP(U_1246,U_1242)
| ~ hBOOL(hAPP(hAPP(c_member(U_1241),U_1242),U_1243)) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_1,plain,
! [V_g_2,V_f_2,T_d,V_A_2,V_a_2,T_c] :
( hAPP(c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_override__on__apply__notin]) ).
fof(f_231_2,plain,
! [U_1252,U_1251,U_1250,U_1249,U_1248,U_1247] :
( hAPP(c_Fun_Ooverride__on(U_1247,U_1250,U_1251,U_1252,U_1249),U_1248) = hAPP(U_1251,U_1248)
| hBOOL(hAPP(hAPP(c_member(U_1247),U_1248),U_1249)) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
! [U_1247,U_1248,U_1249,U_1250,U_1251,U_1252] :
( hAPP(c_Fun_Ooverride__on(U_1247,U_1250,U_1251,U_1252,U_1249),U_1248) = hAPP(U_1251,U_1248)
| hBOOL(hAPP(hAPP(c_member(U_1247),U_1248),U_1249)) ),
inference(definitional_conversion,[status(esa)],[f_231_2]) ).
cnf(f_231_4,plain,
( hAPP(c_Fun_Ooverride__on(U_1247,U_1250,U_1251,U_1252,U_1249),U_1248) = hAPP(U_1251,U_1248)
| hBOOL(hAPP(hAPP(c_member(U_1247),U_1248),U_1249)) ),
inference(clausify,[status(thm)],[f_231_3]) ).
fof(f_232_1,plain,
! [V_g_2,V_f_2,T_d,T_c] : c_Fun_Ooverride__on(T_c,T_d,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_f_2,
inference(fof_nnf,[status(thm)],[fact_override__on__emptyset]) ).
fof(f_232_2,plain,
! [U_1256,U_1255,U_1254,U_1253] : c_Fun_Ooverride__on(U_1253,U_1254,U_1255,U_1256,c_Orderings_Obot__class_Obot(tc_fun(U_1253,tc_HOL_Obool))) = U_1255,
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_1254,U_1253,U_1255,U_1256] : c_Fun_Ooverride__on(U_1253,U_1254,U_1255,U_1256,c_Orderings_Obot__class_Obot(tc_fun(U_1253,tc_HOL_Obool))) = U_1255,
inference(definitional_conversion,[status(esa)],[f_232_2]) ).
cnf(f_232_4,plain,
c_Fun_Ooverride__on(U_1253,U_1254,U_1255,U_1256,c_Orderings_Obot__class_Obot(tc_fun(U_1253,tc_HOL_Obool))) = U_1255,
inference(clausify,[status(thm)],[f_232_3]) ).
fof(f_233_1,plain,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2]) ).
fof(f_233_2,plain,
! [U_1262,U_1261,U_1260,U_1259,U_1258,U_1257] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1257,U_1258,U_1259),U_1261),hAPP(hAPP(c_Set_Oinsert(U_1257),U_1262),U_1260)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1257,U_1258,U_1259),hAPP(hAPP(U_1259,U_1262),U_1261)),U_1260)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1257),U_1260))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_1257,U_1258,U_1259) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
! [U_1257,U_1258,U_1259,U_1260,U_1261,U_1262] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1257,U_1258,U_1259),U_1261),hAPP(hAPP(c_Set_Oinsert(U_1257),U_1262),U_1260)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1257,U_1258,U_1259),hAPP(hAPP(U_1259,U_1262),U_1261)),U_1260)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1257),U_1260))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_1257,U_1258,U_1259) ),
inference(definitional_conversion,[status(esa)],[f_233_2]) ).
cnf(f_233_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_1257,U_1258,U_1259),U_1261),hAPP(hAPP(c_Set_Oinsert(U_1257),U_1262),U_1260)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1257,U_1258,U_1259),hAPP(hAPP(U_1259,U_1262),U_1261)),U_1260)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1257),U_1260))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_1257,U_1258,U_1259) ),
inference(clausify,[status(thm)],[f_233_3]) ).
fof(f_234_1,plain,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm__idem(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem]) ).
fof(f_234_2,plain,
! [U_1268,U_1267,U_1266,U_1265,U_1264,U_1263] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1263,U_1264,U_1265),U_1267),hAPP(hAPP(c_Set_Oinsert(U_1263),U_1268),U_1266)) = hAPP(hAPP(U_1265,U_1268),hAPP(hAPP(c_Finite__Set_Ofold(U_1263,U_1264,U_1265),U_1267),U_1266))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1263),U_1266))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_1263,U_1264,U_1265) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_1263,U_1264,U_1265,U_1266,U_1267,U_1268] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1263,U_1264,U_1265),U_1267),hAPP(hAPP(c_Set_Oinsert(U_1263),U_1268),U_1266)) = hAPP(hAPP(U_1265,U_1268),hAPP(hAPP(c_Finite__Set_Ofold(U_1263,U_1264,U_1265),U_1267),U_1266))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1263),U_1266))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_1263,U_1264,U_1265) ),
inference(definitional_conversion,[status(esa)],[f_234_2]) ).
cnf(f_234_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_1263,U_1264,U_1265),U_1267),hAPP(hAPP(c_Set_Oinsert(U_1263),U_1268),U_1266)) = hAPP(hAPP(U_1265,U_1268),hAPP(hAPP(c_Finite__Set_Ofold(U_1263,U_1264,U_1265),U_1267),U_1266))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1263),U_1266))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_1263,U_1264,U_1265) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_1,plain,
! [V_a_2,V_A_2,V_F_2,V_f_2,T_c] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,V_f_2),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H]) ).
fof(f_235_2,plain,
! [U_1273,U_1272,U_1271,U_1270,U_1269] :
( hAPP(U_1271,hAPP(hAPP(c_Set_Oinsert(U_1269),U_1273),U_1272)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1269,U_1269,U_1270),U_1273),U_1272)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1269),U_1272))
| ~ c_Finite__Set_Ofolding__one__idem(U_1269,U_1270,U_1271) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
! [U_1270,U_1269,U_1271,U_1272,U_1273] :
( hAPP(U_1271,hAPP(hAPP(c_Set_Oinsert(U_1269),U_1273),U_1272)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1269,U_1269,U_1270),U_1273),U_1272)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1269),U_1272))
| ~ c_Finite__Set_Ofolding__one__idem(U_1269,U_1270,U_1271) ),
inference(definitional_conversion,[status(esa)],[f_235_2]) ).
cnf(f_235_4,plain,
( hAPP(U_1271,hAPP(hAPP(c_Set_Oinsert(U_1269),U_1273),U_1272)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1269,U_1269,U_1270),U_1273),U_1272)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1269),U_1272))
| ~ c_Finite__Set_Ofolding__one__idem(U_1269,U_1270,U_1271) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c] :
( 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))
| V_B_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__one__idem(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem]) ).
fof(f_236_2,plain,
! [U_1278,U_1277,U_1276,U_1275,U_1274] :
( hAPP(hAPP(U_1275,hAPP(U_1276,U_1278)),hAPP(U_1276,U_1277)) = hAPP(U_1276,U_1277)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1274,tc_HOL_Obool)),U_1278),U_1277))
| U_1278 = c_Orderings_Obot__class_Obot(tc_fun(U_1274,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1274),U_1277))
| ~ c_Finite__Set_Ofolding__one__idem(U_1274,U_1275,U_1276) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_1274,U_1275,U_1276,U_1277,U_1278] :
( hAPP(hAPP(U_1275,hAPP(U_1276,U_1278)),hAPP(U_1276,U_1277)) = hAPP(U_1276,U_1277)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1274,tc_HOL_Obool)),U_1278),U_1277))
| U_1278 = c_Orderings_Obot__class_Obot(tc_fun(U_1274,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1274),U_1277))
| ~ c_Finite__Set_Ofolding__one__idem(U_1274,U_1275,U_1276) ),
inference(definitional_conversion,[status(esa)],[f_236_2]) ).
cnf(f_236_4,plain,
( hAPP(hAPP(U_1275,hAPP(U_1276,U_1278)),hAPP(U_1276,U_1277)) = hAPP(U_1276,U_1277)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1274,tc_HOL_Obool)),U_1278),U_1277))
| U_1278 = c_Orderings_Obot__class_Obot(tc_fun(U_1274,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1274),U_1277))
| ~ c_Finite__Set_Ofolding__one__idem(U_1274,U_1275,U_1276) ),
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_1,plain,
! [V_A_H_2,T_d,T_c,V_A_2] :
( ( ( ? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,B_f),V_A_2)),V_A_H_2))
& c_Fun_Oinj__on(T_c,T_d,B_f,V_A_2) )
| ! [B_g] : hAPP(c_Set_Oimage(T_d,T_c,B_g),V_A_H_2) != V_A_2 )
& ( ? [B_g] : hAPP(c_Set_Oimage(T_d,T_c,B_g),V_A_H_2) = V_A_2
| ! [B_f] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,B_f),V_A_2)),V_A_H_2))
| ~ c_Fun_Oinj__on(T_c,T_d,B_f,V_A_2) ) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__iff__surj]) ).
fof(f_237_2,plain,
! [U_1286,U_1285,U_1284,U_1283] :
( ( ( ? [U_1282] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1284,U_1285,U_1282),U_1283)),U_1286))
& c_Fun_Oinj__on(U_1284,U_1285,U_1282,U_1283) )
| ! [U_1281] : hAPP(c_Set_Oimage(U_1285,U_1284,U_1281),U_1286) != U_1283 )
& ( ? [U_1280] : hAPP(c_Set_Oimage(U_1285,U_1284,U_1280),U_1286) = U_1283
| ! [U_1279] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1284,U_1285,U_1279),U_1283)),U_1286))
| ~ c_Fun_Oinj__on(U_1284,U_1285,U_1279,U_1283) ) ) )
| U_1283 = c_Orderings_Obot__class_Obot(tc_fun(U_1284,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
! [U_1286,U_1285,U_1284,U_1283] :
( ( ( ? [U_1282] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1284,U_1285,U_1282),U_1283)),U_1286))
& c_Fun_Oinj__on(U_1284,U_1285,U_1282,U_1283) )
| ! [U_1281] : hAPP(c_Set_Oimage(U_1285,U_1284,U_1281),U_1286) != U_1283 )
& ( hAPP(c_Set_Oimage(U_1285,U_1284,sK23(U_1286,U_1285,U_1284,U_1283)),U_1286) = U_1283
| ! [U_1279] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1284,U_1285,U_1279),U_1283)),U_1286))
| ~ c_Fun_Oinj__on(U_1284,U_1285,U_1279,U_1283) ) ) )
| U_1283 = c_Orderings_Obot__class_Obot(tc_fun(U_1284,tc_HOL_Obool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_1280,sK23(U_1286,U_1285,U_1284,U_1283))],[f_237_2]) ).
fof(f_237_4,plain,
! [U_1286,U_1285,U_1284,U_1283] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1284,U_1285,sK24(U_1286,U_1285,U_1284,U_1283)),U_1283)),U_1286))
& c_Fun_Oinj__on(U_1284,U_1285,sK24(U_1286,U_1285,U_1284,U_1283),U_1283) )
| ! [U_1281] : hAPP(c_Set_Oimage(U_1285,U_1284,U_1281),U_1286) != U_1283 )
& ( hAPP(c_Set_Oimage(U_1285,U_1284,sK23(U_1286,U_1285,U_1284,U_1283)),U_1286) = U_1283
| ! [U_1279] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1284,U_1285,U_1279),U_1283)),U_1286))
| ~ c_Fun_Oinj__on(U_1284,U_1285,U_1279,U_1283) ) ) )
| U_1283 = c_Orderings_Obot__class_Obot(tc_fun(U_1284,tc_HOL_Obool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_1282,sK24(U_1286,U_1285,U_1284,U_1283))],[f_237_3]) ).
fof(f_237_5,plain,
( ! [U_1283,U_1284,U_1285,U_1286] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1284,U_1285,sK24(U_1286,U_1285,U_1284,U_1283)),U_1283)),U_1286))
| ~ sP42(U_1283,U_1284,U_1285,U_1286) )
& ! [U_1283,U_1284,U_1285,U_1286] :
( c_Fun_Oinj__on(U_1284,U_1285,sK24(U_1286,U_1285,U_1284,U_1283),U_1283)
| ~ sP42(U_1283,U_1284,U_1285,U_1286) )
& ! [U_1283,U_1279,U_1281,U_1284,U_1285,U_1286] :
( sP42(U_1283,U_1284,U_1285,U_1286)
| hAPP(c_Set_Oimage(U_1285,U_1284,U_1281),U_1286) != U_1283
| ~ sP43(U_1283,U_1279,U_1281,U_1284,U_1285,U_1286) )
& ! [U_1283,U_1279,U_1281,U_1284,U_1285,U_1286] :
( hAPP(c_Set_Oimage(U_1285,U_1284,sK23(U_1286,U_1285,U_1284,U_1283)),U_1286) = U_1283
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1284,U_1285,U_1279),U_1283)),U_1286))
| ~ c_Fun_Oinj__on(U_1284,U_1285,U_1279,U_1283)
| ~ sP43(U_1283,U_1279,U_1281,U_1284,U_1285,U_1286) )
& ! [U_1283,U_1279,U_1281,U_1284,U_1285,U_1286] :
( sP43(U_1283,U_1279,U_1281,U_1284,U_1285,U_1286)
| U_1283 = c_Orderings_Obot__class_Obot(tc_fun(U_1284,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42,sP43])],[f_237_4]) ).
cnf(f_237_6,plain,
( sP43(U_1283,U_1279,U_1281,U_1284,U_1285,U_1286)
| U_1283 = c_Orderings_Obot__class_Obot(tc_fun(U_1284,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_237_5]) ).
cnf(f_237_7,plain,
( hAPP(c_Set_Oimage(U_1285,U_1284,sK23(U_1286,U_1285,U_1284,U_1283)),U_1286) = U_1283
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1284,U_1285,U_1279),U_1283)),U_1286))
| ~ c_Fun_Oinj__on(U_1284,U_1285,U_1279,U_1283)
| ~ sP43(U_1283,U_1279,U_1281,U_1284,U_1285,U_1286) ),
inference(clausify,[status(thm)],[f_237_5]) ).
cnf(f_237_8,plain,
( sP42(U_1283,U_1284,U_1285,U_1286)
| hAPP(c_Set_Oimage(U_1285,U_1284,U_1281),U_1286) != U_1283
| ~ sP43(U_1283,U_1279,U_1281,U_1284,U_1285,U_1286) ),
inference(clausify,[status(thm)],[f_237_5]) ).
cnf(f_237_9,plain,
( c_Fun_Oinj__on(U_1284,U_1285,sK24(U_1286,U_1285,U_1284,U_1283),U_1283)
| ~ sP42(U_1283,U_1284,U_1285,U_1286) ),
inference(clausify,[status(thm)],[f_237_5]) ).
cnf(f_237_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1284,U_1285,sK24(U_1286,U_1285,U_1284,U_1283)),U_1283)),U_1286))
| ~ sP42(U_1283,U_1284,U_1285,U_1286) ),
inference(clausify,[status(thm)],[f_237_5]) ).
fof(f_238_1,plain,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_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_Ofun__left__comm(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__rec]) ).
fof(f_238_2,plain,
! [U_1292,U_1291,U_1290,U_1289,U_1288,U_1287] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1287,U_1288,U_1289),U_1292),U_1290) = hAPP(hAPP(U_1289,U_1291),hAPP(hAPP(c_Finite__Set_Ofold(U_1287,U_1288,U_1289),U_1292),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1287,tc_HOL_Obool)),U_1290),hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),c_Orderings_Obot__class_Obot(tc_fun(U_1287,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_1287),U_1291),U_1290))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1287),U_1290))
| ~ c_Finite__Set_Ofun__left__comm(U_1287,U_1288,U_1289) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_1288,U_1290,U_1289,U_1287,U_1291,U_1292] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1287,U_1288,U_1289),U_1292),U_1290) = hAPP(hAPP(U_1289,U_1291),hAPP(hAPP(c_Finite__Set_Ofold(U_1287,U_1288,U_1289),U_1292),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1287,tc_HOL_Obool)),U_1290),hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),c_Orderings_Obot__class_Obot(tc_fun(U_1287,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_1287),U_1291),U_1290))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1287),U_1290))
| ~ c_Finite__Set_Ofun__left__comm(U_1287,U_1288,U_1289) ),
inference(definitional_conversion,[status(esa)],[f_238_2]) ).
cnf(f_238_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_1287,U_1288,U_1289),U_1292),U_1290) = hAPP(hAPP(U_1289,U_1291),hAPP(hAPP(c_Finite__Set_Ofold(U_1287,U_1288,U_1289),U_1292),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1287,tc_HOL_Obool)),U_1290),hAPP(hAPP(c_Set_Oinsert(U_1287),U_1291),c_Orderings_Obot__class_Obot(tc_fun(U_1287,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_1287),U_1291),U_1290))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1287),U_1290))
| ~ c_Finite__Set_Ofun__left__comm(U_1287,U_1288,U_1289) ),
inference(clausify,[status(thm)],[f_238_3]) ).
fof(f_239_1,plain,
! [V_x_2,V_A_2,V_a_2,V_f_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_x_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,V_f_2,V_a_2,V_A_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold1Set_Ointros]) ).
fof(f_239_2,plain,
! [U_1297,U_1296,U_1295,U_1294,U_1293] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1293,U_1294,hAPP(hAPP(c_Set_Oinsert(U_1293),U_1295),U_1296)),U_1297))
| hBOOL(hAPP(hAPP(c_member(U_1293),U_1295),U_1296))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1293,U_1293,U_1294,U_1295,U_1296),U_1297)) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
fof(f_239_3,plain,
! [U_1294,U_1293,U_1295,U_1296,U_1297] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1293,U_1294,hAPP(hAPP(c_Set_Oinsert(U_1293),U_1295),U_1296)),U_1297))
| hBOOL(hAPP(hAPP(c_member(U_1293),U_1295),U_1296))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1293,U_1293,U_1294,U_1295,U_1296),U_1297)) ),
inference(definitional_conversion,[status(esa)],[f_239_2]) ).
cnf(f_239_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1293,U_1294,hAPP(hAPP(c_Set_Oinsert(U_1293),U_1295),U_1296)),U_1297))
| hBOOL(hAPP(hAPP(c_member(U_1293),U_1295),U_1296))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1293,U_1293,U_1294,U_1295,U_1296),U_1297)) ),
inference(clausify,[status(thm)],[f_239_3]) ).
fof(f_240_1,plain,
! [V_b_2,V_A_2,T_c] :
( ( c_Partial__Function_Oflat__lub(T_c,V_b_2,V_A_2) = c_HOL_OThe(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),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_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) )
& ( c_Partial__Function_Oflat__lub(T_c,V_b_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(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ) ),
inference(fof_nnf,[status(thm)],[fact_flat__lub__def]) ).
fof(f_240_2,plain,
! [U_1300,U_1299,U_1298] :
( ( c_Partial__Function_Oflat__lub(U_1298,U_1300,U_1299) = c_HOL_OThe(U_1298,hAPP(hAPP(c_COMBC(U_1298,tc_fun(U_1298,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1298)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1298,tc_HOL_Obool)),U_1299),hAPP(hAPP(c_Set_Oinsert(U_1298),U_1300),c_Orderings_Obot__class_Obot(tc_fun(U_1298,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1298,tc_HOL_Obool)),U_1299),hAPP(hAPP(c_Set_Oinsert(U_1298),U_1300),c_Orderings_Obot__class_Obot(tc_fun(U_1298,tc_HOL_Obool))))) )
& ( c_Partial__Function_Oflat__lub(U_1298,U_1300,U_1299) = U_1300
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1298,tc_HOL_Obool)),U_1299),hAPP(hAPP(c_Set_Oinsert(U_1298),U_1300),c_Orderings_Obot__class_Obot(tc_fun(U_1298,tc_HOL_Obool))))) ) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
( ! [U_1306,U_1304,U_1302] :
( c_Partial__Function_Oflat__lub(U_1302,U_1306,U_1304) = c_HOL_OThe(U_1302,hAPP(hAPP(c_COMBC(U_1302,tc_fun(U_1302,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1302)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1302,tc_HOL_Obool)),U_1304),hAPP(hAPP(c_Set_Oinsert(U_1302),U_1306),c_Orderings_Obot__class_Obot(tc_fun(U_1302,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1302,tc_HOL_Obool)),U_1304),hAPP(hAPP(c_Set_Oinsert(U_1302),U_1306),c_Orderings_Obot__class_Obot(tc_fun(U_1302,tc_HOL_Obool))))) )
& ! [U_1305,U_1303,U_1301] :
( c_Partial__Function_Oflat__lub(U_1301,U_1305,U_1303) = U_1305
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1301,tc_HOL_Obool)),U_1303),hAPP(hAPP(c_Set_Oinsert(U_1301),U_1305),c_Orderings_Obot__class_Obot(tc_fun(U_1301,tc_HOL_Obool))))) ) ),
inference(miniscope,[status(thm)],[f_240_2]) ).
fof(f_240_4,plain,
( ! [U_1302,U_1304,U_1306] :
( c_Partial__Function_Oflat__lub(U_1302,U_1306,U_1304) = c_HOL_OThe(U_1302,hAPP(hAPP(c_COMBC(U_1302,tc_fun(U_1302,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1302)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1302,tc_HOL_Obool)),U_1304),hAPP(hAPP(c_Set_Oinsert(U_1302),U_1306),c_Orderings_Obot__class_Obot(tc_fun(U_1302,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1302,tc_HOL_Obool)),U_1304),hAPP(hAPP(c_Set_Oinsert(U_1302),U_1306),c_Orderings_Obot__class_Obot(tc_fun(U_1302,tc_HOL_Obool))))) )
& ! [U_1303,U_1301,U_1305] :
( c_Partial__Function_Oflat__lub(U_1301,U_1305,U_1303) = U_1305
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1301,tc_HOL_Obool)),U_1303),hAPP(hAPP(c_Set_Oinsert(U_1301),U_1305),c_Orderings_Obot__class_Obot(tc_fun(U_1301,tc_HOL_Obool))))) ) ),
inference(definitional_conversion,[status(esa)],[f_240_3]) ).
cnf(f_240_5,plain,
( c_Partial__Function_Oflat__lub(U_1301,U_1305,U_1303) = U_1305
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1301,tc_HOL_Obool)),U_1303),hAPP(hAPP(c_Set_Oinsert(U_1301),U_1305),c_Orderings_Obot__class_Obot(tc_fun(U_1301,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_240_4]) ).
cnf(f_240_6,plain,
( c_Partial__Function_Oflat__lub(U_1302,U_1306,U_1304) = c_HOL_OThe(U_1302,hAPP(hAPP(c_COMBC(U_1302,tc_fun(U_1302,tc_HOL_Obool),tc_HOL_Obool),c_member(U_1302)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1302,tc_HOL_Obool)),U_1304),hAPP(hAPP(c_Set_Oinsert(U_1302),U_1306),c_Orderings_Obot__class_Obot(tc_fun(U_1302,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1302,tc_HOL_Obool)),U_1304),hAPP(hAPP(c_Set_Oinsert(U_1302),U_1306),c_Orderings_Obot__class_Obot(tc_fun(U_1302,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_240_4]) ).
fof(f_241_1,plain,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_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_Ofun__left__comm(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove]) ).
fof(f_241_2,plain,
! [U_1312,U_1311,U_1310,U_1309,U_1308,U_1307] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1307,U_1308,U_1309),U_1311),hAPP(hAPP(c_Set_Oinsert(U_1307),U_1312),U_1310)) = hAPP(hAPP(U_1309,U_1312),hAPP(hAPP(c_Finite__Set_Ofold(U_1307,U_1308,U_1309),U_1311),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1307,tc_HOL_Obool)),U_1310),hAPP(hAPP(c_Set_Oinsert(U_1307),U_1312),c_Orderings_Obot__class_Obot(tc_fun(U_1307,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1307),U_1310))
| ~ c_Finite__Set_Ofun__left__comm(U_1307,U_1308,U_1309) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
! [U_1307,U_1308,U_1309,U_1310,U_1311,U_1312] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1307,U_1308,U_1309),U_1311),hAPP(hAPP(c_Set_Oinsert(U_1307),U_1312),U_1310)) = hAPP(hAPP(U_1309,U_1312),hAPP(hAPP(c_Finite__Set_Ofold(U_1307,U_1308,U_1309),U_1311),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1307,tc_HOL_Obool)),U_1310),hAPP(hAPP(c_Set_Oinsert(U_1307),U_1312),c_Orderings_Obot__class_Obot(tc_fun(U_1307,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1307),U_1310))
| ~ c_Finite__Set_Ofun__left__comm(U_1307,U_1308,U_1309) ),
inference(definitional_conversion,[status(esa)],[f_241_2]) ).
cnf(f_241_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_1307,U_1308,U_1309),U_1311),hAPP(hAPP(c_Set_Oinsert(U_1307),U_1312),U_1310)) = hAPP(hAPP(U_1309,U_1312),hAPP(hAPP(c_Finite__Set_Ofold(U_1307,U_1308,U_1309),U_1311),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1307,tc_HOL_Obool)),U_1310),hAPP(hAPP(c_Set_Oinsert(U_1307),U_1312),c_Orderings_Obot__class_Obot(tc_fun(U_1307,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1307),U_1310))
| ~ c_Finite__Set_Ofun__left__comm(U_1307,U_1308,U_1309) ),
inference(clausify,[status(thm)],[f_241_3]) ).
fof(f_242_1,plain,
! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_d,T_c] :
( ( c_Nitpick_Ofold__graph_H(T_c,T_d,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_c,T_d,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),B_y)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),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_c,tc_HOL_Obool)) ) ) )
& ( ? [B_x,B_y] :
( c_Nitpick_Ofold__graph_H(T_c,T_d,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),B_y)
& hBOOL(hAPP(hAPP(c_member(T_c),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_c,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(T_c,T_d,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_242_2,plain,
! [U_1323,U_1322,U_1321,U_1320,U_1319,U_1318,U_1317] :
( ( c_Nitpick_Ofold__graph_H(U_1317,U_1318,U_1319,U_1320,U_1321,hAPP(hAPP(U_1319,U_1322),U_1323))
| ( ! [U_1316,U_1315] :
( ~ c_Nitpick_Ofold__graph_H(U_1317,U_1318,U_1319,U_1320,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1317,tc_HOL_Obool)),U_1321),hAPP(hAPP(c_Set_Oinsert(U_1317),U_1316),c_Orderings_Obot__class_Obot(tc_fun(U_1317,tc_HOL_Obool)))),U_1315)
| ~ hBOOL(hAPP(hAPP(c_member(U_1317),U_1316),U_1321))
| hAPP(hAPP(U_1319,U_1322),U_1323) != hAPP(hAPP(U_1319,U_1316),U_1315) )
& ( hAPP(hAPP(U_1319,U_1322),U_1323) != U_1320
| U_1321 != c_Orderings_Obot__class_Obot(tc_fun(U_1317,tc_HOL_Obool)) ) ) )
& ( ? [U_1314,U_1313] :
( c_Nitpick_Ofold__graph_H(U_1317,U_1318,U_1319,U_1320,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1317,tc_HOL_Obool)),U_1321),hAPP(hAPP(c_Set_Oinsert(U_1317),U_1314),c_Orderings_Obot__class_Obot(tc_fun(U_1317,tc_HOL_Obool)))),U_1313)
& hBOOL(hAPP(hAPP(c_member(U_1317),U_1314),U_1321))
& hAPP(hAPP(U_1319,U_1322),U_1323) = hAPP(hAPP(U_1319,U_1314),U_1313) )
| ( hAPP(hAPP(U_1319,U_1322),U_1323) = U_1320
& U_1321 = c_Orderings_Obot__class_Obot(tc_fun(U_1317,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_1317,U_1318,U_1319,U_1320,U_1321,hAPP(hAPP(U_1319,U_1322),U_1323)) ) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
( ! [U_1337,U_1335,U_1333,U_1331,U_1329,U_1327,U_1325] :
( c_Nitpick_Ofold__graph_H(U_1325,U_1327,U_1329,U_1331,U_1333,hAPP(hAPP(U_1329,U_1335),U_1337))
| ( ! [U_1316] :
( ! [U_1315] :
( ~ c_Nitpick_Ofold__graph_H(U_1325,U_1327,U_1329,U_1331,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1325,tc_HOL_Obool)),U_1333),hAPP(hAPP(c_Set_Oinsert(U_1325),U_1316),c_Orderings_Obot__class_Obot(tc_fun(U_1325,tc_HOL_Obool)))),U_1315)
| hAPP(hAPP(U_1329,U_1335),U_1337) != hAPP(hAPP(U_1329,U_1316),U_1315) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1325),U_1316),U_1333)) )
& ( hAPP(hAPP(U_1329,U_1335),U_1337) != U_1331
| U_1333 != c_Orderings_Obot__class_Obot(tc_fun(U_1325,tc_HOL_Obool)) ) ) )
& ! [U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324] :
( ? [U_1314] :
( ? [U_1313] :
( c_Nitpick_Ofold__graph_H(U_1324,U_1326,U_1328,U_1330,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1324,tc_HOL_Obool)),U_1332),hAPP(hAPP(c_Set_Oinsert(U_1324),U_1314),c_Orderings_Obot__class_Obot(tc_fun(U_1324,tc_HOL_Obool)))),U_1313)
& hAPP(hAPP(U_1328,U_1334),U_1336) = hAPP(hAPP(U_1328,U_1314),U_1313) )
& hBOOL(hAPP(hAPP(c_member(U_1324),U_1314),U_1332)) )
| ( hAPP(hAPP(U_1328,U_1334),U_1336) = U_1330
& U_1332 = c_Orderings_Obot__class_Obot(tc_fun(U_1324,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_1324,U_1326,U_1328,U_1330,U_1332,hAPP(hAPP(U_1328,U_1334),U_1336)) ) ),
inference(miniscope,[status(thm)],[f_242_2]) ).
fof(f_242_4,plain,
( ! [U_1337,U_1335,U_1333,U_1331,U_1329,U_1327,U_1325] :
( c_Nitpick_Ofold__graph_H(U_1325,U_1327,U_1329,U_1331,U_1333,hAPP(hAPP(U_1329,U_1335),U_1337))
| ( ! [U_1316] :
( ! [U_1315] :
( ~ c_Nitpick_Ofold__graph_H(U_1325,U_1327,U_1329,U_1331,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1325,tc_HOL_Obool)),U_1333),hAPP(hAPP(c_Set_Oinsert(U_1325),U_1316),c_Orderings_Obot__class_Obot(tc_fun(U_1325,tc_HOL_Obool)))),U_1315)
| hAPP(hAPP(U_1329,U_1335),U_1337) != hAPP(hAPP(U_1329,U_1316),U_1315) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1325),U_1316),U_1333)) )
& ( hAPP(hAPP(U_1329,U_1335),U_1337) != U_1331
| U_1333 != c_Orderings_Obot__class_Obot(tc_fun(U_1325,tc_HOL_Obool)) ) ) )
& ! [U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324] :
( ( ? [U_1313] :
( c_Nitpick_Ofold__graph_H(U_1324,U_1326,U_1328,U_1330,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1324,tc_HOL_Obool)),U_1332),hAPP(hAPP(c_Set_Oinsert(U_1324),sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324)),c_Orderings_Obot__class_Obot(tc_fun(U_1324,tc_HOL_Obool)))),U_1313)
& hAPP(hAPP(U_1328,U_1334),U_1336) = hAPP(hAPP(U_1328,sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324)),U_1313) )
& hBOOL(hAPP(hAPP(c_member(U_1324),sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324)),U_1332)) )
| ( hAPP(hAPP(U_1328,U_1334),U_1336) = U_1330
& U_1332 = c_Orderings_Obot__class_Obot(tc_fun(U_1324,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_1324,U_1326,U_1328,U_1330,U_1332,hAPP(hAPP(U_1328,U_1334),U_1336)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_1314,sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324))],[f_242_3]) ).
fof(f_242_5,plain,
( ! [U_1337,U_1335,U_1333,U_1331,U_1329,U_1327,U_1325] :
( c_Nitpick_Ofold__graph_H(U_1325,U_1327,U_1329,U_1331,U_1333,hAPP(hAPP(U_1329,U_1335),U_1337))
| ( ! [U_1316] :
( ! [U_1315] :
( ~ c_Nitpick_Ofold__graph_H(U_1325,U_1327,U_1329,U_1331,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1325,tc_HOL_Obool)),U_1333),hAPP(hAPP(c_Set_Oinsert(U_1325),U_1316),c_Orderings_Obot__class_Obot(tc_fun(U_1325,tc_HOL_Obool)))),U_1315)
| hAPP(hAPP(U_1329,U_1335),U_1337) != hAPP(hAPP(U_1329,U_1316),U_1315) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1325),U_1316),U_1333)) )
& ( hAPP(hAPP(U_1329,U_1335),U_1337) != U_1331
| U_1333 != c_Orderings_Obot__class_Obot(tc_fun(U_1325,tc_HOL_Obool)) ) ) )
& ! [U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324] :
( ( c_Nitpick_Ofold__graph_H(U_1324,U_1326,U_1328,U_1330,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1324,tc_HOL_Obool)),U_1332),hAPP(hAPP(c_Set_Oinsert(U_1324),sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324)),c_Orderings_Obot__class_Obot(tc_fun(U_1324,tc_HOL_Obool)))),sK26(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324))
& hAPP(hAPP(U_1328,U_1334),U_1336) = hAPP(hAPP(U_1328,sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324)),sK26(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324))
& hBOOL(hAPP(hAPP(c_member(U_1324),sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324)),U_1332)) )
| ( hAPP(hAPP(U_1328,U_1334),U_1336) = U_1330
& U_1332 = c_Orderings_Obot__class_Obot(tc_fun(U_1324,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_1324,U_1326,U_1328,U_1330,U_1332,hAPP(hAPP(U_1328,U_1334),U_1336)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_1313,sK26(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324))],[f_242_4]) ).
fof(f_242_6,plain,
( ! [U_1331,U_1327,U_1329,U_1315,U_1316,U_1337,U_1325,U_1333,U_1335] :
( ~ c_Nitpick_Ofold__graph_H(U_1325,U_1327,U_1329,U_1331,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1325,tc_HOL_Obool)),U_1333),hAPP(hAPP(c_Set_Oinsert(U_1325),U_1316),c_Orderings_Obot__class_Obot(tc_fun(U_1325,tc_HOL_Obool)))),U_1315)
| hAPP(hAPP(U_1329,U_1335),U_1337) != hAPP(hAPP(U_1329,U_1316),U_1315)
| ~ hBOOL(hAPP(hAPP(c_member(U_1325),U_1316),U_1333))
| ~ sP46(U_1331,U_1327,U_1329,U_1315,U_1316,U_1337,U_1325,U_1333,U_1335) )
& ! [U_1331,U_1327,U_1329,U_1315,U_1316,U_1337,U_1325,U_1333,U_1335] :
( hAPP(hAPP(U_1329,U_1335),U_1337) != U_1331
| U_1333 != c_Orderings_Obot__class_Obot(tc_fun(U_1325,tc_HOL_Obool))
| ~ sP46(U_1331,U_1327,U_1329,U_1315,U_1316,U_1337,U_1325,U_1333,U_1335) )
& ! [U_1334,U_1326,U_1324,U_1330,U_1328,U_1332,U_1336] :
( c_Nitpick_Ofold__graph_H(U_1324,U_1326,U_1328,U_1330,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1324,tc_HOL_Obool)),U_1332),hAPP(hAPP(c_Set_Oinsert(U_1324),sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324)),c_Orderings_Obot__class_Obot(tc_fun(U_1324,tc_HOL_Obool)))),sK26(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324))
| ~ sP45(U_1334,U_1326,U_1324,U_1330,U_1328,U_1332,U_1336) )
& ! [U_1334,U_1326,U_1324,U_1330,U_1328,U_1332,U_1336] :
( hAPP(hAPP(U_1328,U_1334),U_1336) = hAPP(hAPP(U_1328,sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324)),sK26(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324))
| ~ sP45(U_1334,U_1326,U_1324,U_1330,U_1328,U_1332,U_1336) )
& ! [U_1334,U_1326,U_1324,U_1330,U_1328,U_1332,U_1336] :
( hBOOL(hAPP(hAPP(c_member(U_1324),sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324)),U_1332))
| ~ sP45(U_1334,U_1326,U_1324,U_1330,U_1328,U_1332,U_1336) )
& ! [U_1334,U_1324,U_1330,U_1328,U_1332,U_1336] :
( hAPP(hAPP(U_1328,U_1334),U_1336) = U_1330
| ~ sP44(U_1334,U_1324,U_1330,U_1328,U_1332,U_1336) )
& ! [U_1334,U_1324,U_1330,U_1328,U_1332,U_1336] :
( U_1332 = c_Orderings_Obot__class_Obot(tc_fun(U_1324,tc_HOL_Obool))
| ~ sP44(U_1334,U_1324,U_1330,U_1328,U_1332,U_1336) )
& ! [U_1331,U_1327,U_1329,U_1315,U_1316,U_1337,U_1325,U_1333,U_1335] :
( c_Nitpick_Ofold__graph_H(U_1325,U_1327,U_1329,U_1331,U_1333,hAPP(hAPP(U_1329,U_1335),U_1337))
| sP46(U_1331,U_1327,U_1329,U_1315,U_1316,U_1337,U_1325,U_1333,U_1335) )
& ! [U_1334,U_1326,U_1324,U_1330,U_1328,U_1332,U_1336] :
( sP45(U_1334,U_1326,U_1324,U_1330,U_1328,U_1332,U_1336)
| sP44(U_1334,U_1324,U_1330,U_1328,U_1332,U_1336)
| ~ c_Nitpick_Ofold__graph_H(U_1324,U_1326,U_1328,U_1330,U_1332,hAPP(hAPP(U_1328,U_1334),U_1336)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44,sP45,sP46])],[f_242_5]) ).
cnf(f_242_7,plain,
( sP45(U_1334,U_1326,U_1324,U_1330,U_1328,U_1332,U_1336)
| sP44(U_1334,U_1324,U_1330,U_1328,U_1332,U_1336)
| ~ c_Nitpick_Ofold__graph_H(U_1324,U_1326,U_1328,U_1330,U_1332,hAPP(hAPP(U_1328,U_1334),U_1336)) ),
inference(clausify,[status(thm)],[f_242_6]) ).
cnf(f_242_8,plain,
( c_Nitpick_Ofold__graph_H(U_1325,U_1327,U_1329,U_1331,U_1333,hAPP(hAPP(U_1329,U_1335),U_1337))
| sP46(U_1331,U_1327,U_1329,U_1315,U_1316,U_1337,U_1325,U_1333,U_1335) ),
inference(clausify,[status(thm)],[f_242_6]) ).
cnf(f_242_9,plain,
( U_1332 = c_Orderings_Obot__class_Obot(tc_fun(U_1324,tc_HOL_Obool))
| ~ sP44(U_1334,U_1324,U_1330,U_1328,U_1332,U_1336) ),
inference(clausify,[status(thm)],[f_242_6]) ).
cnf(f_242_10,plain,
( hAPP(hAPP(U_1328,U_1334),U_1336) = U_1330
| ~ sP44(U_1334,U_1324,U_1330,U_1328,U_1332,U_1336) ),
inference(clausify,[status(thm)],[f_242_6]) ).
cnf(f_242_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_1324),sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324)),U_1332))
| ~ sP45(U_1334,U_1326,U_1324,U_1330,U_1328,U_1332,U_1336) ),
inference(clausify,[status(thm)],[f_242_6]) ).
cnf(f_242_12,plain,
( hAPP(hAPP(U_1328,U_1334),U_1336) = hAPP(hAPP(U_1328,sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324)),sK26(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324))
| ~ sP45(U_1334,U_1326,U_1324,U_1330,U_1328,U_1332,U_1336) ),
inference(clausify,[status(thm)],[f_242_6]) ).
cnf(f_242_13,plain,
( c_Nitpick_Ofold__graph_H(U_1324,U_1326,U_1328,U_1330,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1324,tc_HOL_Obool)),U_1332),hAPP(hAPP(c_Set_Oinsert(U_1324),sK25(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324)),c_Orderings_Obot__class_Obot(tc_fun(U_1324,tc_HOL_Obool)))),sK26(U_1336,U_1334,U_1332,U_1330,U_1328,U_1326,U_1324))
| ~ sP45(U_1334,U_1326,U_1324,U_1330,U_1328,U_1332,U_1336) ),
inference(clausify,[status(thm)],[f_242_6]) ).
cnf(f_242_14,plain,
( hAPP(hAPP(U_1329,U_1335),U_1337) != U_1331
| U_1333 != c_Orderings_Obot__class_Obot(tc_fun(U_1325,tc_HOL_Obool))
| ~ sP46(U_1331,U_1327,U_1329,U_1315,U_1316,U_1337,U_1325,U_1333,U_1335) ),
inference(clausify,[status(thm)],[f_242_6]) ).
cnf(f_242_15,plain,
( ~ c_Nitpick_Ofold__graph_H(U_1325,U_1327,U_1329,U_1331,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1325,tc_HOL_Obool)),U_1333),hAPP(hAPP(c_Set_Oinsert(U_1325),U_1316),c_Orderings_Obot__class_Obot(tc_fun(U_1325,tc_HOL_Obool)))),U_1315)
| hAPP(hAPP(U_1329,U_1335),U_1337) != hAPP(hAPP(U_1329,U_1316),U_1315)
| ~ hBOOL(hAPP(hAPP(c_member(U_1325),U_1316),U_1333))
| ~ sP46(U_1331,U_1327,U_1329,U_1315,U_1316,U_1337,U_1325,U_1333,U_1335) ),
inference(clausify,[status(thm)],[f_242_6]) ).
fof(f_243_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_c_2),V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq]) ).
fof(f_243_2,plain,
! [U_1342,U_1341,U_1340,U_1339,U_1338] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1338),U_1339),U_1340))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1338),U_1341),U_1342)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1338),U_1341),U_1342))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1338),U_1339),U_1340)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1338),U_1339),U_1340) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1338),U_1341),U_1342)
| ~ class_Groups_Oordered__ab__group__add(U_1338) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
( ! [U_1338,U_1339,U_1341,U_1340,U_1342] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1338),U_1339),U_1340))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1338),U_1341),U_1342))
| ~ sP47(U_1338,U_1339,U_1341,U_1340,U_1342) )
& ! [U_1338,U_1339,U_1341,U_1340,U_1342] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1338),U_1341),U_1342))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1338),U_1339),U_1340))
| ~ sP47(U_1338,U_1339,U_1341,U_1340,U_1342) )
& ! [U_1338,U_1339,U_1341,U_1340,U_1342] :
( sP47(U_1338,U_1339,U_1341,U_1340,U_1342)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1338),U_1339),U_1340) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1338),U_1341),U_1342)
| ~ class_Groups_Oordered__ab__group__add(U_1338) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_243_2]) ).
cnf(f_243_4,plain,
( sP47(U_1338,U_1339,U_1341,U_1340,U_1342)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1338),U_1339),U_1340) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1338),U_1341),U_1342)
| ~ class_Groups_Oordered__ab__group__add(U_1338) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1338),U_1341),U_1342))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1338),U_1339),U_1340))
| ~ sP47(U_1338,U_1339,U_1341,U_1340,U_1342) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1338),U_1339),U_1340))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1338),U_1341),U_1342))
| ~ sP47(U_1338,U_1339,U_1341,U_1340,U_1342) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_1,plain,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_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_Ofun__left__comm(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert2]) ).
fof(f_244_2,plain,
! [U_1348,U_1347,U_1346,U_1345,U_1344,U_1343] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1343,U_1344,U_1345),U_1348),hAPP(hAPP(c_Set_Oinsert(U_1343),U_1347),U_1346)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1343,U_1344,U_1345),hAPP(hAPP(U_1345,U_1347),U_1348)),U_1346)
| hBOOL(hAPP(hAPP(c_member(U_1343),U_1347),U_1346))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1343),U_1346))
| ~ c_Finite__Set_Ofun__left__comm(U_1343,U_1344,U_1345) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
! [U_1347,U_1348,U_1345,U_1343,U_1346,U_1344] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1343,U_1344,U_1345),U_1348),hAPP(hAPP(c_Set_Oinsert(U_1343),U_1347),U_1346)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1343,U_1344,U_1345),hAPP(hAPP(U_1345,U_1347),U_1348)),U_1346)
| hBOOL(hAPP(hAPP(c_member(U_1343),U_1347),U_1346))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1343),U_1346))
| ~ c_Finite__Set_Ofun__left__comm(U_1343,U_1344,U_1345) ),
inference(definitional_conversion,[status(esa)],[f_244_2]) ).
cnf(f_244_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_1343,U_1344,U_1345),U_1348),hAPP(hAPP(c_Set_Oinsert(U_1343),U_1347),U_1346)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1343,U_1344,U_1345),hAPP(hAPP(U_1345,U_1347),U_1348)),U_1346)
| hBOOL(hAPP(hAPP(c_member(U_1343),U_1347),U_1346))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1343),U_1346))
| ~ c_Finite__Set_Ofun__left__comm(U_1343,U_1344,U_1345) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_1,plain,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_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_Ofun__left__comm(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert]) ).
fof(f_245_2,plain,
! [U_1354,U_1353,U_1352,U_1351,U_1350,U_1349] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1349,U_1350,U_1351),U_1354),hAPP(hAPP(c_Set_Oinsert(U_1349),U_1353),U_1352)) = hAPP(hAPP(U_1351,U_1353),hAPP(hAPP(c_Finite__Set_Ofold(U_1349,U_1350,U_1351),U_1354),U_1352))
| hBOOL(hAPP(hAPP(c_member(U_1349),U_1353),U_1352))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1349),U_1352))
| ~ c_Finite__Set_Ofun__left__comm(U_1349,U_1350,U_1351) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
! [U_1351,U_1349,U_1350,U_1352,U_1353,U_1354] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1349,U_1350,U_1351),U_1354),hAPP(hAPP(c_Set_Oinsert(U_1349),U_1353),U_1352)) = hAPP(hAPP(U_1351,U_1353),hAPP(hAPP(c_Finite__Set_Ofold(U_1349,U_1350,U_1351),U_1354),U_1352))
| hBOOL(hAPP(hAPP(c_member(U_1349),U_1353),U_1352))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1349),U_1352))
| ~ c_Finite__Set_Ofun__left__comm(U_1349,U_1350,U_1351) ),
inference(definitional_conversion,[status(esa)],[f_245_2]) ).
cnf(f_245_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_1349,U_1350,U_1351),U_1354),hAPP(hAPP(c_Set_Oinsert(U_1349),U_1353),U_1352)) = hAPP(hAPP(U_1351,U_1353),hAPP(hAPP(c_Finite__Set_Ofold(U_1349,U_1350,U_1351),U_1354),U_1352))
| hBOOL(hAPP(hAPP(c_member(U_1349),U_1353),U_1352))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1349),U_1352))
| ~ c_Finite__Set_Ofun__left__comm(U_1349,U_1350,U_1351) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_1,plain,
! [V_Pa_2,V_A_2,V_F_2,T_c] :
( hBOOL(hAPP(V_Pa_2,V_F_2))
| ? [B_a,B_F] :
( ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_c),B_a),B_F)))
& hBOOL(hAPP(V_Pa_2,B_F))
& ~ hBOOL(hAPP(hAPP(c_member(T_c),B_a),B_F))
& hBOOL(hAPP(hAPP(c_member(T_c),B_a),V_A_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_F)) )
| ~ hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__subset__induct]) ).
fof(f_246_2,plain,
! [U_1360,U_1359,U_1358,U_1357] :
( hBOOL(hAPP(U_1360,U_1358))
| ? [U_1356,U_1355] :
( ~ hBOOL(hAPP(U_1360,hAPP(hAPP(c_Set_Oinsert(U_1357),U_1356),U_1355)))
& hBOOL(hAPP(U_1360,U_1355))
& ~ hBOOL(hAPP(hAPP(c_member(U_1357),U_1356),U_1355))
& hBOOL(hAPP(hAPP(c_member(U_1357),U_1356),U_1359))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_1357),U_1355)) )
| ~ hBOOL(hAPP(U_1360,c_Orderings_Obot__class_Obot(tc_fun(U_1357,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1357,tc_HOL_Obool)),U_1358),U_1359))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1357),U_1358)) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
! [U_1360,U_1359,U_1358,U_1357] :
( hBOOL(hAPP(U_1360,U_1358))
| ? [U_1355] :
( ~ hBOOL(hAPP(U_1360,hAPP(hAPP(c_Set_Oinsert(U_1357),sK27(U_1360,U_1359,U_1358,U_1357)),U_1355)))
& hBOOL(hAPP(U_1360,U_1355))
& ~ hBOOL(hAPP(hAPP(c_member(U_1357),sK27(U_1360,U_1359,U_1358,U_1357)),U_1355))
& hBOOL(hAPP(hAPP(c_member(U_1357),sK27(U_1360,U_1359,U_1358,U_1357)),U_1359))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_1357),U_1355)) )
| ~ hBOOL(hAPP(U_1360,c_Orderings_Obot__class_Obot(tc_fun(U_1357,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1357,tc_HOL_Obool)),U_1358),U_1359))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1357),U_1358)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_1356,sK27(U_1360,U_1359,U_1358,U_1357))],[f_246_2]) ).
fof(f_246_4,plain,
! [U_1360,U_1359,U_1358,U_1357] :
( hBOOL(hAPP(U_1360,U_1358))
| ( ~ hBOOL(hAPP(U_1360,hAPP(hAPP(c_Set_Oinsert(U_1357),sK27(U_1360,U_1359,U_1358,U_1357)),sK28(U_1360,U_1359,U_1358,U_1357))))
& hBOOL(hAPP(U_1360,sK28(U_1360,U_1359,U_1358,U_1357)))
& ~ hBOOL(hAPP(hAPP(c_member(U_1357),sK27(U_1360,U_1359,U_1358,U_1357)),sK28(U_1360,U_1359,U_1358,U_1357)))
& hBOOL(hAPP(hAPP(c_member(U_1357),sK27(U_1360,U_1359,U_1358,U_1357)),U_1359))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_1357),sK28(U_1360,U_1359,U_1358,U_1357))) )
| ~ hBOOL(hAPP(U_1360,c_Orderings_Obot__class_Obot(tc_fun(U_1357,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1357,tc_HOL_Obool)),U_1358),U_1359))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1357),U_1358)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_1355,sK28(U_1360,U_1359,U_1358,U_1357))],[f_246_3]) ).
fof(f_246_5,plain,
( ! [U_1357,U_1358,U_1359,U_1360] :
( ~ hBOOL(hAPP(U_1360,hAPP(hAPP(c_Set_Oinsert(U_1357),sK27(U_1360,U_1359,U_1358,U_1357)),sK28(U_1360,U_1359,U_1358,U_1357))))
| ~ sP48(U_1357,U_1358,U_1359,U_1360) )
& ! [U_1357,U_1358,U_1359,U_1360] :
( hBOOL(hAPP(U_1360,sK28(U_1360,U_1359,U_1358,U_1357)))
| ~ sP48(U_1357,U_1358,U_1359,U_1360) )
& ! [U_1357,U_1358,U_1359,U_1360] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1357),sK27(U_1360,U_1359,U_1358,U_1357)),sK28(U_1360,U_1359,U_1358,U_1357)))
| ~ sP48(U_1357,U_1358,U_1359,U_1360) )
& ! [U_1357,U_1358,U_1359,U_1360] :
( hBOOL(hAPP(hAPP(c_member(U_1357),sK27(U_1360,U_1359,U_1358,U_1357)),U_1359))
| ~ sP48(U_1357,U_1358,U_1359,U_1360) )
& ! [U_1357,U_1358,U_1359,U_1360] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1357),sK28(U_1360,U_1359,U_1358,U_1357)))
| ~ sP48(U_1357,U_1358,U_1359,U_1360) )
& ! [U_1357,U_1358,U_1359,U_1360] :
( hBOOL(hAPP(U_1360,U_1358))
| sP48(U_1357,U_1358,U_1359,U_1360)
| ~ hBOOL(hAPP(U_1360,c_Orderings_Obot__class_Obot(tc_fun(U_1357,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1357,tc_HOL_Obool)),U_1358),U_1359))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1357),U_1358)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_246_4]) ).
cnf(f_246_6,plain,
( hBOOL(hAPP(U_1360,U_1358))
| sP48(U_1357,U_1358,U_1359,U_1360)
| ~ hBOOL(hAPP(U_1360,c_Orderings_Obot__class_Obot(tc_fun(U_1357,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1357,tc_HOL_Obool)),U_1358),U_1359))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1357),U_1358)) ),
inference(clausify,[status(thm)],[f_246_5]) ).
cnf(f_246_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_1357),sK28(U_1360,U_1359,U_1358,U_1357)))
| ~ sP48(U_1357,U_1358,U_1359,U_1360) ),
inference(clausify,[status(thm)],[f_246_5]) ).
cnf(f_246_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_1357),sK27(U_1360,U_1359,U_1358,U_1357)),U_1359))
| ~ sP48(U_1357,U_1358,U_1359,U_1360) ),
inference(clausify,[status(thm)],[f_246_5]) ).
cnf(f_246_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1357),sK27(U_1360,U_1359,U_1358,U_1357)),sK28(U_1360,U_1359,U_1358,U_1357)))
| ~ sP48(U_1357,U_1358,U_1359,U_1360) ),
inference(clausify,[status(thm)],[f_246_5]) ).
cnf(f_246_10,plain,
( hBOOL(hAPP(U_1360,sK28(U_1360,U_1359,U_1358,U_1357)))
| ~ sP48(U_1357,U_1358,U_1359,U_1360) ),
inference(clausify,[status(thm)],[f_246_5]) ).
cnf(f_246_11,plain,
( ~ hBOOL(hAPP(U_1360,hAPP(hAPP(c_Set_Oinsert(U_1357),sK27(U_1360,U_1359,U_1358,U_1357)),sK28(U_1360,U_1359,U_1358,U_1357))))
| ~ sP48(U_1357,U_1358,U_1359,U_1360) ),
inference(clausify,[status(thm)],[f_246_5]) ).
fof(f_247_1,plain,
! [V_g_2,V_x_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oremove]) ).
fof(f_247_2,plain,
! [U_1365,U_1364,U_1363,U_1362,U_1361] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1362,U_1361),U_1365),U_1363) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1361),hAPP(U_1365,U_1364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1362,U_1361),U_1365),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1362,tc_HOL_Obool)),U_1363),hAPP(hAPP(c_Set_Oinsert(U_1362),U_1364),c_Orderings_Obot__class_Obot(tc_fun(U_1362,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_1362),U_1364),U_1363))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1362),U_1363))
| ~ class_Groups_Ocomm__monoid__add(U_1361) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_1362,U_1361,U_1364,U_1365,U_1363] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1362,U_1361),U_1365),U_1363) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1361),hAPP(U_1365,U_1364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1362,U_1361),U_1365),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1362,tc_HOL_Obool)),U_1363),hAPP(hAPP(c_Set_Oinsert(U_1362),U_1364),c_Orderings_Obot__class_Obot(tc_fun(U_1362,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_1362),U_1364),U_1363))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1362),U_1363))
| ~ class_Groups_Ocomm__monoid__add(U_1361) ),
inference(definitional_conversion,[status(esa)],[f_247_2]) ).
cnf(f_247_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1362,U_1361),U_1365),U_1363) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1361),hAPP(U_1365,U_1364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1362,U_1361),U_1365),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1362,tc_HOL_Obool)),U_1363),hAPP(hAPP(c_Set_Oinsert(U_1362),U_1364),c_Orderings_Obot__class_Obot(tc_fun(U_1362,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_1362),U_1364),U_1363))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1362),U_1363))
| ~ class_Groups_Ocomm__monoid__add(U_1361) ),
inference(clausify,[status(thm)],[f_247_3]) ).
fof(f_248_1,plain,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_d,T_c] :
( 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_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm]) ).
fof(f_248_2,plain,
! [U_1371,U_1370,U_1369,U_1368,U_1367,U_1366] :
( hAPP(hAPP(U_1368,U_1369),hAPP(hAPP(U_1368,U_1370),U_1371)) = hAPP(hAPP(U_1368,U_1370),hAPP(hAPP(U_1368,U_1369),U_1371))
| ~ c_Finite__Set_Ofun__left__comm(U_1366,U_1367,U_1368) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_1371,U_1370,U_1369,U_1368] :
( ! [U_1367,U_1366] : ~ c_Finite__Set_Ofun__left__comm(U_1366,U_1367,U_1368)
| hAPP(hAPP(U_1368,U_1369),hAPP(hAPP(U_1368,U_1370),U_1371)) = hAPP(hAPP(U_1368,U_1370),hAPP(hAPP(U_1368,U_1369),U_1371)) ),
inference(miniscope,[status(thm)],[f_248_2]) ).
fof(f_248_4,plain,
! [U_1369,U_1370,U_1368,U_1366,U_1367,U_1371] :
( ~ c_Finite__Set_Ofun__left__comm(U_1366,U_1367,U_1368)
| hAPP(hAPP(U_1368,U_1369),hAPP(hAPP(U_1368,U_1370),U_1371)) = hAPP(hAPP(U_1368,U_1370),hAPP(hAPP(U_1368,U_1369),U_1371)) ),
inference(definitional_conversion,[status(esa)],[f_248_3]) ).
cnf(f_248_5,plain,
( ~ c_Finite__Set_Ofun__left__comm(U_1366,U_1367,U_1368)
| hAPP(hAPP(U_1368,U_1369),hAPP(hAPP(U_1368,U_1370),U_1371)) = hAPP(hAPP(U_1368,U_1370),hAPP(hAPP(U_1368,U_1369),U_1371)) ),
inference(clausify,[status(thm)],[f_248_4]) ).
fof(f_249_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_249_2,plain,
! [U_1375,U_1374,U_1373,U_1372] :
( U_1373 = U_1375
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1372),U_1373),U_1374) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1372),U_1375),U_1374)
| ~ class_Groups_Ocancel__semigroup__add(U_1372) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
! [U_1372,U_1373,U_1374,U_1375] :
( U_1373 = U_1375
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1372),U_1373),U_1374) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1372),U_1375),U_1374)
| ~ class_Groups_Ocancel__semigroup__add(U_1372) ),
inference(definitional_conversion,[status(esa)],[f_249_2]) ).
cnf(f_249_4,plain,
( U_1373 = U_1375
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1372),U_1373),U_1374) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1372),U_1375),U_1374)
| ~ class_Groups_Ocancel__semigroup__add(U_1372) ),
inference(clausify,[status(thm)],[f_249_3]) ).
fof(f_250_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_250_2,plain,
! [U_1379,U_1378,U_1377,U_1376] :
( U_1378 = U_1379
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1376),U_1377),U_1378) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1376),U_1377),U_1379)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_1376) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
! [U_1376,U_1377,U_1378,U_1379] :
( U_1378 = U_1379
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1376),U_1377),U_1378) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1376),U_1377),U_1379)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_1376) ),
inference(definitional_conversion,[status(esa)],[f_250_2]) ).
cnf(f_250_4,plain,
( U_1378 = U_1379
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1376),U_1377),U_1378) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1376),U_1377),U_1379)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_1376) ),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_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_251_2,plain,
! [U_1383,U_1382,U_1381,U_1380] :
( U_1382 = U_1383
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1380),U_1381),U_1382) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1380),U_1381),U_1383)
| ~ class_Groups_Ocancel__semigroup__add(U_1380) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
! [U_1381,U_1380,U_1382,U_1383] :
( U_1382 = U_1383
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1380),U_1381),U_1382) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1380),U_1381),U_1383)
| ~ class_Groups_Ocancel__semigroup__add(U_1380) ),
inference(definitional_conversion,[status(esa)],[f_251_2]) ).
cnf(f_251_4,plain,
( U_1382 = U_1383
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1380),U_1381),U_1382) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1380),U_1381),U_1383)
| ~ class_Groups_Ocancel__semigroup__add(U_1380) ),
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_1,plain,
! [V_c_2,V_a_2,V_b_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_a_2)
| V_b_2 != V_c_2 )
& ( V_b_2 = V_c_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_a_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_a_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).
fof(f_252_2,plain,
! [U_1387,U_1386,U_1385,U_1384] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1384),U_1385),U_1386) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1384),U_1387),U_1386)
| U_1385 != U_1387 )
& ( U_1385 = U_1387
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1384),U_1385),U_1386) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1384),U_1387),U_1386) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_1384) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
( ! [U_1384,U_1385,U_1386,U_1387] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1384),U_1385),U_1386) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1384),U_1387),U_1386)
| U_1385 != U_1387
| ~ sP49(U_1384,U_1385,U_1386,U_1387) )
& ! [U_1384,U_1385,U_1386,U_1387] :
( U_1385 = U_1387
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1384),U_1385),U_1386) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1384),U_1387),U_1386)
| ~ sP49(U_1384,U_1385,U_1386,U_1387) )
& ! [U_1384,U_1385,U_1386,U_1387] :
( sP49(U_1384,U_1385,U_1386,U_1387)
| ~ class_Groups_Ocancel__semigroup__add(U_1384) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_252_2]) ).
cnf(f_252_4,plain,
( sP49(U_1384,U_1385,U_1386,U_1387)
| ~ class_Groups_Ocancel__semigroup__add(U_1384) ),
inference(clausify,[status(thm)],[f_252_3]) ).
cnf(f_252_5,plain,
( U_1385 = U_1387
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1384),U_1385),U_1386) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1384),U_1387),U_1386)
| ~ sP49(U_1384,U_1385,U_1386,U_1387) ),
inference(clausify,[status(thm)],[f_252_3]) ).
cnf(f_252_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1384),U_1385),U_1386) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1384),U_1387),U_1386)
| U_1385 != U_1387
| ~ sP49(U_1384,U_1385,U_1386,U_1387) ),
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_1,plain,
! [V_c_2,V_b_2,V_a_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_c_2)
| V_b_2 != V_c_2 )
& ( V_b_2 = V_c_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_c_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).
fof(f_253_2,plain,
! [U_1391,U_1390,U_1389,U_1388] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1388),U_1389),U_1390) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1388),U_1389),U_1391)
| U_1390 != U_1391 )
& ( U_1390 = U_1391
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1388),U_1389),U_1390) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1388),U_1389),U_1391) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_1388) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
( ! [U_1390,U_1391,U_1388,U_1389] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1388),U_1389),U_1390) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1388),U_1389),U_1391)
| U_1390 != U_1391
| ~ sP50(U_1390,U_1391,U_1388,U_1389) )
& ! [U_1390,U_1391,U_1388,U_1389] :
( U_1390 = U_1391
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1388),U_1389),U_1390) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1388),U_1389),U_1391)
| ~ sP50(U_1390,U_1391,U_1388,U_1389) )
& ! [U_1390,U_1391,U_1388,U_1389] :
( sP50(U_1390,U_1391,U_1388,U_1389)
| ~ class_Groups_Ocancel__semigroup__add(U_1388) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50])],[f_253_2]) ).
cnf(f_253_4,plain,
( sP50(U_1390,U_1391,U_1388,U_1389)
| ~ class_Groups_Ocancel__semigroup__add(U_1388) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_5,plain,
( U_1390 = U_1391
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1388),U_1389),U_1390) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1388),U_1389),U_1391)
| ~ sP50(U_1390,U_1391,U_1388,U_1389) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1388),U_1389),U_1390) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1388),U_1389),U_1391)
| U_1390 != U_1391
| ~ sP50(U_1390,U_1391,U_1388,U_1389) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_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_254_2,plain,
! [U_1395,U_1394,U_1393,U_1392] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1392),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1392),U_1393),U_1394)),U_1395) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1392),U_1393),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1392),U_1394),U_1395))
| ~ class_Groups_Oab__semigroup__add(U_1392) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_1393,U_1392,U_1394,U_1395] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1392),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1392),U_1393),U_1394)),U_1395) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1392),U_1393),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1392),U_1394),U_1395))
| ~ class_Groups_Oab__semigroup__add(U_1392) ),
inference(definitional_conversion,[status(esa)],[f_254_2]) ).
cnf(f_254_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1392),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1392),U_1393),U_1394)),U_1395) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1392),U_1393),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1392),U_1394),U_1395))
| ~ class_Groups_Oab__semigroup__add(U_1392) ),
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_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_255_2,plain,
! [U_1399,U_1398,U_1397,U_1396] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1396),U_1398),U_1399))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1396),U_1397),U_1398)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1396),U_1397),U_1399)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1396) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
! [U_1396,U_1397,U_1398,U_1399] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1396),U_1398),U_1399))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1396),U_1397),U_1398)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1396),U_1397),U_1399)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1396) ),
inference(definitional_conversion,[status(esa)],[f_255_2]) ).
cnf(f_255_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1396),U_1398),U_1399))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1396),U_1397),U_1398)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1396),U_1397),U_1399)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1396) ),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_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_256_2,plain,
! [U_1403,U_1402,U_1401,U_1400] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1400),U_1401),U_1403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1400),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1400),U_1401),U_1402)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1400),U_1403),U_1402)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1400) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_1400,U_1401,U_1402,U_1403] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1400),U_1401),U_1403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1400),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1400),U_1401),U_1402)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1400),U_1403),U_1402)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1400) ),
inference(definitional_conversion,[status(esa)],[f_256_2]) ).
cnf(f_256_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1400),U_1401),U_1403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1400),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1400),U_1401),U_1402)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1400),U_1403),U_1402)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1400) ),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_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_257_2,plain,
! [U_1408,U_1407,U_1406,U_1405,U_1404] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1404),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1404),U_1405),U_1407)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1404),U_1406),U_1408)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1404),U_1407),U_1408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1404),U_1405),U_1406))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1404) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
! [U_1404,U_1405,U_1406,U_1407,U_1408] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1404),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1404),U_1405),U_1407)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1404),U_1406),U_1408)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1404),U_1407),U_1408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1404),U_1405),U_1406))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1404) ),
inference(definitional_conversion,[status(esa)],[f_257_2]) ).
cnf(f_257_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1404),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1404),U_1405),U_1407)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1404),U_1406),U_1408)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1404),U_1407),U_1408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1404),U_1405),U_1406))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1404) ),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_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_258_2,plain,
! [U_1412,U_1411,U_1410,U_1409] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1409),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1409),U_1412),U_1410)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1409),U_1412),U_1411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1409),U_1410),U_1411))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1409) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
! [U_1410,U_1411,U_1412,U_1409] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1409),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1409),U_1412),U_1410)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1409),U_1412),U_1411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1409),U_1410),U_1411))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1409) ),
inference(definitional_conversion,[status(esa)],[f_258_2]) ).
cnf(f_258_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1409),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1409),U_1412),U_1410)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1409),U_1412),U_1411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1409),U_1410),U_1411))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1409) ),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_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_259_2,plain,
! [U_1416,U_1415,U_1414,U_1413] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1413),U_1414),U_1416)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1413),U_1415),U_1416)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),U_1414),U_1415))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1413) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
! [U_1413,U_1414,U_1415,U_1416] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1413),U_1414),U_1416)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1413),U_1415),U_1416)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),U_1414),U_1415))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1413) ),
inference(definitional_conversion,[status(esa)],[f_259_2]) ).
cnf(f_259_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1413),U_1414),U_1416)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1413),U_1415),U_1416)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1413),U_1414),U_1415))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1413) ),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
! [V_b_2,V_a_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_c) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left]) ).
fof(f_260_2,plain,
! [U_1420,U_1419,U_1418,U_1417] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1417),U_1418),U_1419)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1417),U_1418),U_1420)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1417),U_1419),U_1420)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1417),U_1419),U_1420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1417),U_1418),U_1419)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1417),U_1418),U_1420))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1417) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
( ! [U_1417,U_1418,U_1419,U_1420] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1417),U_1418),U_1419)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1417),U_1418),U_1420)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1417),U_1419),U_1420))
| ~ sP51(U_1417,U_1418,U_1419,U_1420) )
& ! [U_1417,U_1418,U_1419,U_1420] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1417),U_1419),U_1420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1417),U_1418),U_1419)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1417),U_1418),U_1420)))
| ~ sP51(U_1417,U_1418,U_1419,U_1420) )
& ! [U_1417,U_1418,U_1419,U_1420] :
( sP51(U_1417,U_1418,U_1419,U_1420)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1417) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_260_2]) ).
cnf(f_260_4,plain,
( sP51(U_1417,U_1418,U_1419,U_1420)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1417) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1417),U_1419),U_1420))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1417),U_1418),U_1419)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1417),U_1418),U_1420)))
| ~ sP51(U_1417,U_1418,U_1419,U_1420) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1417),U_1418),U_1419)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1417),U_1418),U_1420)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1417),U_1419),U_1420))
| ~ sP51(U_1417,U_1418,U_1419,U_1420) ),
inference(clausify,[status(thm)],[f_260_3]) ).
fof(f_261_1,plain,
! [V_b_2,V_c_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_c_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_c) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).
fof(f_261_2,plain,
! [U_1424,U_1423,U_1422,U_1421] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1421),U_1422),U_1423)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1421),U_1424),U_1423)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),U_1422),U_1424)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),U_1422),U_1424))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1421),U_1422),U_1423)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1421),U_1424),U_1423))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1421) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
( ! [U_1422,U_1423,U_1424,U_1421] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1421),U_1422),U_1423)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1421),U_1424),U_1423)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),U_1422),U_1424))
| ~ sP52(U_1422,U_1423,U_1424,U_1421) )
& ! [U_1422,U_1423,U_1424,U_1421] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),U_1422),U_1424))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1421),U_1422),U_1423)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1421),U_1424),U_1423)))
| ~ sP52(U_1422,U_1423,U_1424,U_1421) )
& ! [U_1422,U_1423,U_1424,U_1421] :
( sP52(U_1422,U_1423,U_1424,U_1421)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1421) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52])],[f_261_2]) ).
cnf(f_261_4,plain,
( sP52(U_1422,U_1423,U_1424,U_1421)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1421) ),
inference(clausify,[status(thm)],[f_261_3]) ).
cnf(f_261_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),U_1422),U_1424))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1421),U_1422),U_1423)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1421),U_1424),U_1423)))
| ~ sP52(U_1422,U_1423,U_1424,U_1421) ),
inference(clausify,[status(thm)],[f_261_3]) ).
cnf(f_261_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1421),U_1422),U_1423)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1421),U_1424),U_1423)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),U_1422),U_1424))
| ~ sP52(U_1422,U_1423,U_1424,U_1421) ),
inference(clausify,[status(thm)],[f_261_3]) ).
fof(f_262_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_262_2,plain,
! [U_1427,U_1426,U_1425] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1425),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1425),U_1426),U_1427)),U_1427) = U_1426
| ~ class_Groups_Ogroup__add(U_1425) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
! [U_1426,U_1427,U_1425] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1425),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1425),U_1426),U_1427)),U_1427) = U_1426
| ~ class_Groups_Ogroup__add(U_1425) ),
inference(definitional_conversion,[status(esa)],[f_262_2]) ).
cnf(f_262_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1425),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1425),U_1426),U_1427)),U_1427) = U_1426
| ~ class_Groups_Ogroup__add(U_1425) ),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_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_263_2,plain,
! [U_1430,U_1429,U_1428] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1428),U_1429),U_1430)),U_1430) = U_1429
| ~ class_Groups_Ogroup__add(U_1428) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
! [U_1428,U_1429,U_1430] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1428),U_1429),U_1430)),U_1430) = U_1429
| ~ class_Groups_Ogroup__add(U_1428) ),
inference(definitional_conversion,[status(esa)],[f_263_2]) ).
cnf(f_263_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1428),U_1429),U_1430)),U_1430) = U_1429
| ~ class_Groups_Ogroup__add(U_1428) ),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_1,plain,
! [V_g_2,T_e,V_f_2,T_d,T_c] :
( c_Finite__Set_Ofun__left__comm(T_e,T_d,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_d),T_e),V_f_2),V_g_2))
| ~ c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply]) ).
fof(f_264_2,plain,
! [U_1435,U_1434,U_1433,U_1432,U_1431] :
( c_Finite__Set_Ofun__left__comm(U_1434,U_1432,hAPP(hAPP(c_COMBB(U_1431,tc_fun(U_1432,U_1432),U_1434),U_1433),U_1435))
| ~ c_Finite__Set_Ofun__left__comm(U_1431,U_1432,U_1433) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
! [U_1431,U_1432,U_1433,U_1434,U_1435] :
( c_Finite__Set_Ofun__left__comm(U_1434,U_1432,hAPP(hAPP(c_COMBB(U_1431,tc_fun(U_1432,U_1432),U_1434),U_1433),U_1435))
| ~ c_Finite__Set_Ofun__left__comm(U_1431,U_1432,U_1433) ),
inference(definitional_conversion,[status(esa)],[f_264_2]) ).
cnf(f_264_4,plain,
( c_Finite__Set_Ofun__left__comm(U_1434,U_1432,hAPP(hAPP(c_COMBB(U_1431,tc_fun(U_1432,U_1432),U_1434),U_1433),U_1435))
| ~ c_Finite__Set_Ofun__left__comm(U_1431,U_1432,U_1433) ),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_1,plain,
! [V_A_2,V_g_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Oplus__class_Oplus(T_c)),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_d,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_g_2),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__addf]) ).
fof(f_265_2,plain,
! [U_1440,U_1439,U_1438,U_1437,U_1436] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1437,U_1436),hAPP(hAPP(c_COMBS(U_1437,U_1436,U_1436),hAPP(hAPP(c_COMBB(U_1436,tc_fun(U_1436,U_1436),U_1437),c_Groups_Oplus__class_Oplus(U_1436)),U_1438)),U_1439)),U_1440) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1436),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1437,U_1436),U_1438),U_1440)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1437,U_1436),U_1439),U_1440))
| ~ class_Groups_Ocomm__monoid__add(U_1436) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
! [U_1436,U_1437,U_1438,U_1439,U_1440] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1437,U_1436),hAPP(hAPP(c_COMBS(U_1437,U_1436,U_1436),hAPP(hAPP(c_COMBB(U_1436,tc_fun(U_1436,U_1436),U_1437),c_Groups_Oplus__class_Oplus(U_1436)),U_1438)),U_1439)),U_1440) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1436),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1437,U_1436),U_1438),U_1440)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1437,U_1436),U_1439),U_1440))
| ~ class_Groups_Ocomm__monoid__add(U_1436) ),
inference(definitional_conversion,[status(esa)],[f_265_2]) ).
cnf(f_265_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1437,U_1436),hAPP(hAPP(c_COMBS(U_1437,U_1436,U_1436),hAPP(hAPP(c_COMBB(U_1436,tc_fun(U_1436,U_1436),U_1437),c_Groups_Oplus__class_Oplus(U_1436)),U_1438)),U_1439)),U_1440) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1436),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1437,U_1436),U_1438),U_1440)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1437,U_1436),U_1439),U_1440))
| ~ class_Groups_Ocomm__monoid__add(U_1436) ),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_1,plain,
! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_d,T_c] :
( V_y_2 = V_x_2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_y_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_x_2))
| ~ c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ]) ).
fof(f_266_2,plain,
! [U_1447,U_1446,U_1445,U_1444,U_1443,U_1442,U_1441] :
( U_1447 = U_1446
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1441,U_1442,U_1443,U_1444,U_1445),U_1447))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1441,U_1442,U_1443,U_1444,U_1445),U_1446))
| ~ c_Finite__Set_Ofun__left__comm(U_1441,U_1442,U_1443) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
! [U_1441,U_1442,U_1443,U_1444,U_1445,U_1446,U_1447] :
( U_1447 = U_1446
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1441,U_1442,U_1443,U_1444,U_1445),U_1447))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1441,U_1442,U_1443,U_1444,U_1445),U_1446))
| ~ c_Finite__Set_Ofun__left__comm(U_1441,U_1442,U_1443) ),
inference(definitional_conversion,[status(esa)],[f_266_2]) ).
cnf(f_266_4,plain,
( U_1447 = U_1446
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1441,U_1442,U_1443,U_1444,U_1445),U_1447))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1441,U_1442,U_1443,U_1444,U_1445),U_1446))
| ~ c_Finite__Set_Ofun__left__comm(U_1441,U_1442,U_1443) ),
inference(clausify,[status(thm)],[f_266_3]) ).
fof(f_267_1,plain,
! [V_x_2,V_f_2,T_c] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_empty__fold1SetE]) ).
fof(f_267_2,plain,
! [U_1450,U_1449,U_1448] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1448,U_1449,c_Orderings_Obot__class_Obot(tc_fun(U_1448,tc_HOL_Obool))),U_1450)),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_1448,U_1449,U_1450] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1448,U_1449,c_Orderings_Obot__class_Obot(tc_fun(U_1448,tc_HOL_Obool))),U_1450)),
inference(definitional_conversion,[status(esa)],[f_267_2]) ).
cnf(f_267_4,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1448,U_1449,c_Orderings_Obot__class_Obot(tc_fun(U_1448,tc_HOL_Obool))),U_1450)),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_1,plain,
! [V_x_2,V_A_2,V_f_2,T_c] :
( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,V_A_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold1Set__nonempty]) ).
fof(f_268_2,plain,
! [U_1454,U_1453,U_1452,U_1451] :
( U_1453 != c_Orderings_Obot__class_Obot(tc_fun(U_1451,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1451,U_1452,U_1453),U_1454)) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
! [U_1451,U_1452,U_1453,U_1454] :
( U_1453 != c_Orderings_Obot__class_Obot(tc_fun(U_1451,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1451,U_1452,U_1453),U_1454)) ),
inference(definitional_conversion,[status(esa)],[f_268_2]) ).
cnf(f_268_4,plain,
( U_1453 != c_Orderings_Obot__class_Obot(tc_fun(U_1451,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1451,U_1452,U_1453),U_1454)) ),
inference(clausify,[status(thm)],[f_268_3]) ).
fof(f_269_1,plain,
! [V_h_2,V_g_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Groups_Oplus__class_Oplus(T_d)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Odistrib]) ).
fof(f_269_2,plain,
! [U_1459,U_1458,U_1457,U_1456,U_1455] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1456,U_1455),hAPP(hAPP(c_COMBS(U_1456,U_1455,U_1455),hAPP(hAPP(c_COMBB(U_1455,tc_fun(U_1455,U_1455),U_1456),c_Groups_Oplus__class_Oplus(U_1455)),U_1458)),U_1459)),U_1457) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1455),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1456,U_1455),U_1458),U_1457)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1456,U_1455),U_1459),U_1457))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1456),U_1457))
| ~ class_Groups_Ocomm__monoid__add(U_1455) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
! [U_1455,U_1456,U_1457,U_1458,U_1459] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1456,U_1455),hAPP(hAPP(c_COMBS(U_1456,U_1455,U_1455),hAPP(hAPP(c_COMBB(U_1455,tc_fun(U_1455,U_1455),U_1456),c_Groups_Oplus__class_Oplus(U_1455)),U_1458)),U_1459)),U_1457) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1455),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1456,U_1455),U_1458),U_1457)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1456,U_1455),U_1459),U_1457))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1456),U_1457))
| ~ class_Groups_Ocomm__monoid__add(U_1455) ),
inference(definitional_conversion,[status(esa)],[f_269_2]) ).
cnf(f_269_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1456,U_1455),hAPP(hAPP(c_COMBS(U_1456,U_1455,U_1455),hAPP(hAPP(c_COMBB(U_1455,tc_fun(U_1455,U_1455),U_1456),c_Groups_Oplus__class_Oplus(U_1455)),U_1458)),U_1459)),U_1457) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1455),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1456,U_1455),U_1458),U_1457)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1456,U_1455),U_1459),U_1457))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1456),U_1457))
| ~ class_Groups_Ocomm__monoid__add(U_1455) ),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( ( ( V_a_2 = V_b_2
| V_c_2 != V_d_2 )
& ( V_c_2 = V_d_2
| V_a_2 != V_b_2 ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_c_2),V_d_2)
| ~ class_Groups_Oab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).
fof(f_270_2,plain,
! [U_1464,U_1463,U_1462,U_1461,U_1460] :
( ( ( U_1461 = U_1462
| U_1463 != U_1464 )
& ( U_1463 = U_1464
| U_1461 != U_1462 ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1460),U_1461),U_1462) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1460),U_1463),U_1464)
| ~ class_Groups_Oab__group__add(U_1460) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
( ! [U_1462,U_1463,U_1461,U_1464] :
( U_1461 = U_1462
| U_1463 != U_1464
| ~ sP53(U_1462,U_1463,U_1461,U_1464) )
& ! [U_1462,U_1463,U_1461,U_1464] :
( U_1463 = U_1464
| U_1461 != U_1462
| ~ sP53(U_1462,U_1463,U_1461,U_1464) )
& ! [U_1462,U_1463,U_1460,U_1461,U_1464] :
( sP53(U_1462,U_1463,U_1461,U_1464)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1460),U_1461),U_1462) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1460),U_1463),U_1464)
| ~ class_Groups_Oab__group__add(U_1460) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53])],[f_270_2]) ).
cnf(f_270_4,plain,
( sP53(U_1462,U_1463,U_1461,U_1464)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1460),U_1461),U_1462) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1460),U_1463),U_1464)
| ~ class_Groups_Oab__group__add(U_1460) ),
inference(clausify,[status(thm)],[f_270_3]) ).
cnf(f_270_5,plain,
( U_1463 = U_1464
| U_1461 != U_1462
| ~ sP53(U_1462,U_1463,U_1461,U_1464) ),
inference(clausify,[status(thm)],[f_270_3]) ).
cnf(f_270_6,plain,
( U_1461 = U_1462
| U_1463 != U_1464
| ~ sP53(U_1462,U_1463,U_1461,U_1464) ),
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_1,plain,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm]) ).
fof(f_271_2,plain,
! [U_1470,U_1469,U_1468,U_1467,U_1466,U_1465] :
( hAPP(hAPP(U_1467,U_1469),hAPP(hAPP(c_Finite__Set_Ofold(U_1465,U_1466,U_1467),U_1470),U_1468)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1465,U_1466,U_1467),hAPP(hAPP(U_1467,U_1469),U_1470)),U_1468)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1465),U_1468))
| ~ c_Finite__Set_Ofun__left__comm(U_1465,U_1466,U_1467) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
! [U_1466,U_1465,U_1467,U_1469,U_1468,U_1470] :
( hAPP(hAPP(U_1467,U_1469),hAPP(hAPP(c_Finite__Set_Ofold(U_1465,U_1466,U_1467),U_1470),U_1468)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1465,U_1466,U_1467),hAPP(hAPP(U_1467,U_1469),U_1470)),U_1468)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1465),U_1468))
| ~ c_Finite__Set_Ofun__left__comm(U_1465,U_1466,U_1467) ),
inference(definitional_conversion,[status(esa)],[f_271_2]) ).
cnf(f_271_4,plain,
( hAPP(hAPP(U_1467,U_1469),hAPP(hAPP(c_Finite__Set_Ofold(U_1465,U_1466,U_1467),U_1470),U_1468)) = hAPP(hAPP(c_Finite__Set_Ofold(U_1465,U_1466,U_1467),hAPP(hAPP(U_1467,U_1469),U_1470)),U_1468)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1465),U_1468))
| ~ c_Finite__Set_Ofun__left__comm(U_1465,U_1466,U_1467) ),
inference(clausify,[status(thm)],[f_271_3]) ).
fof(f_272_1,plain,
! [V_y_2,V_A_2,V_z_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2) = V_y_2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_y_2))
| ~ c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__equality]) ).
fof(f_272_2,plain,
! [U_1476,U_1475,U_1474,U_1473,U_1472,U_1471] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1471,U_1472,U_1473),U_1474),U_1475) = U_1476
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1471,U_1472,U_1473,U_1474,U_1475),U_1476))
| ~ c_Finite__Set_Ofun__left__comm(U_1471,U_1472,U_1473) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
! [U_1471,U_1472,U_1473,U_1474,U_1475,U_1476] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_1471,U_1472,U_1473),U_1474),U_1475) = U_1476
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1471,U_1472,U_1473,U_1474,U_1475),U_1476))
| ~ c_Finite__Set_Ofun__left__comm(U_1471,U_1472,U_1473) ),
inference(definitional_conversion,[status(esa)],[f_272_2]) ).
cnf(f_272_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_1471,U_1472,U_1473),U_1474),U_1475) = U_1476
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1471,U_1472,U_1473,U_1474,U_1475),U_1476))
| ~ c_Finite__Set_Ofun__left__comm(U_1471,U_1472,U_1473) ),
inference(clausify,[status(thm)],[f_272_3]) ).
fof(f_273_1,plain,
! [V_b_2,V_a_2,V_f_2,T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(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)))),V_b_2))
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(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)))),V_b_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_fold1Set__sing]) ).
fof(f_273_2,plain,
! [U_1480,U_1479,U_1478,U_1477] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1477,U_1478,hAPP(hAPP(c_Set_Oinsert(U_1477),U_1479),c_Orderings_Obot__class_Obot(tc_fun(U_1477,tc_HOL_Obool)))),U_1480))
| U_1479 != U_1480 )
& ( U_1479 = U_1480
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1477,U_1478,hAPP(hAPP(c_Set_Oinsert(U_1477),U_1479),c_Orderings_Obot__class_Obot(tc_fun(U_1477,tc_HOL_Obool)))),U_1480)) ) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
( ! [U_1488,U_1486] :
( ! [U_1484,U_1482] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1482,U_1484,hAPP(hAPP(c_Set_Oinsert(U_1482),U_1486),c_Orderings_Obot__class_Obot(tc_fun(U_1482,tc_HOL_Obool)))),U_1488))
| U_1486 != U_1488 )
& ! [U_1487,U_1485] :
( ! [U_1483,U_1481] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1481,U_1483,hAPP(hAPP(c_Set_Oinsert(U_1481),U_1485),c_Orderings_Obot__class_Obot(tc_fun(U_1481,tc_HOL_Obool)))),U_1487))
| U_1485 = U_1487 ) ),
inference(miniscope,[status(thm)],[f_273_2]) ).
fof(f_273_4,plain,
( ! [U_1488,U_1482,U_1484,U_1486] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1482,U_1484,hAPP(hAPP(c_Set_Oinsert(U_1482),U_1486),c_Orderings_Obot__class_Obot(tc_fun(U_1482,tc_HOL_Obool)))),U_1488))
| U_1486 != U_1488 )
& ! [U_1485,U_1483,U_1481,U_1487] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1481,U_1483,hAPP(hAPP(c_Set_Oinsert(U_1481),U_1485),c_Orderings_Obot__class_Obot(tc_fun(U_1481,tc_HOL_Obool)))),U_1487))
| U_1485 = U_1487 ) ),
inference(definitional_conversion,[status(esa)],[f_273_3]) ).
cnf(f_273_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1481,U_1483,hAPP(hAPP(c_Set_Oinsert(U_1481),U_1485),c_Orderings_Obot__class_Obot(tc_fun(U_1481,tc_HOL_Obool)))),U_1487))
| U_1485 = U_1487 ),
inference(clausify,[status(thm)],[f_273_4]) ).
cnf(f_273_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1482,U_1484,hAPP(hAPP(c_Set_Oinsert(U_1482),U_1486),c_Orderings_Obot__class_Obot(tc_fun(U_1482,tc_HOL_Obool)))),U_1488))
| U_1486 != U_1488 ),
inference(clausify,[status(thm)],[f_273_4]) ).
fof(f_274_1,plain,
! [V_g_2,V_x_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert]) ).
fof(f_274_2,plain,
! [U_1493,U_1492,U_1491,U_1490,U_1489] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1490,U_1489),U_1493),hAPP(hAPP(c_Set_Oinsert(U_1490),U_1492),U_1491)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1489),hAPP(U_1493,U_1492)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1490,U_1489),U_1493),U_1491))
| hBOOL(hAPP(hAPP(c_member(U_1490),U_1492),U_1491))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1490),U_1491))
| ~ class_Groups_Ocomm__monoid__add(U_1489) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
! [U_1489,U_1490,U_1491,U_1492,U_1493] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1490,U_1489),U_1493),hAPP(hAPP(c_Set_Oinsert(U_1490),U_1492),U_1491)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1489),hAPP(U_1493,U_1492)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1490,U_1489),U_1493),U_1491))
| hBOOL(hAPP(hAPP(c_member(U_1490),U_1492),U_1491))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1490),U_1491))
| ~ class_Groups_Ocomm__monoid__add(U_1489) ),
inference(definitional_conversion,[status(esa)],[f_274_2]) ).
cnf(f_274_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1490,U_1489),U_1493),hAPP(hAPP(c_Set_Oinsert(U_1490),U_1492),U_1491)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1489),hAPP(U_1493,U_1492)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1490,U_1489),U_1493),U_1491))
| hBOOL(hAPP(hAPP(c_member(U_1490),U_1492),U_1491))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1490),U_1491))
| ~ class_Groups_Ocomm__monoid__add(U_1489) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_1,plain,
! [V_f_2,V_a_2,V_F_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_F_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_F_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__insert]) ).
fof(f_275_2,plain,
! [U_1498,U_1497,U_1496,U_1495,U_1494] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1495,U_1494),U_1498),hAPP(hAPP(c_Set_Oinsert(U_1495),U_1497),U_1496)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1494),hAPP(U_1498,U_1497)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1495,U_1494),U_1498),U_1496))
| hBOOL(hAPP(hAPP(c_member(U_1495),U_1497),U_1496))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1495),U_1496))
| ~ class_Groups_Ocomm__monoid__add(U_1494) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
! [U_1494,U_1495,U_1496,U_1497,U_1498] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1495,U_1494),U_1498),hAPP(hAPP(c_Set_Oinsert(U_1495),U_1497),U_1496)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1494),hAPP(U_1498,U_1497)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1495,U_1494),U_1498),U_1496))
| hBOOL(hAPP(hAPP(c_member(U_1495),U_1497),U_1496))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1495),U_1496))
| ~ class_Groups_Ocomm__monoid__add(U_1494) ),
inference(definitional_conversion,[status(esa)],[f_275_2]) ).
cnf(f_275_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1495,U_1494),U_1498),hAPP(hAPP(c_Set_Oinsert(U_1495),U_1497),U_1496)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1494),hAPP(U_1498,U_1497)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1495,U_1494),U_1498),U_1496))
| hBOOL(hAPP(hAPP(c_member(U_1495),U_1497),U_1496))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1495),U_1496))
| ~ class_Groups_Ocomm__monoid__add(U_1494) ),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_1,plain,
! [V_x_2,V_g_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert__remove]) ).
fof(f_276_2,plain,
! [U_1503,U_1502,U_1501,U_1500,U_1499] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1500,U_1499),U_1502),hAPP(hAPP(c_Set_Oinsert(U_1500),U_1503),U_1501)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1499),hAPP(U_1502,U_1503)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1500,U_1499),U_1502),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1500,tc_HOL_Obool)),U_1501),hAPP(hAPP(c_Set_Oinsert(U_1500),U_1503),c_Orderings_Obot__class_Obot(tc_fun(U_1500,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1500),U_1501))
| ~ class_Groups_Ocomm__monoid__add(U_1499) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
! [U_1500,U_1499,U_1501,U_1502,U_1503] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1500,U_1499),U_1502),hAPP(hAPP(c_Set_Oinsert(U_1500),U_1503),U_1501)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1499),hAPP(U_1502,U_1503)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1500,U_1499),U_1502),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1500,tc_HOL_Obool)),U_1501),hAPP(hAPP(c_Set_Oinsert(U_1500),U_1503),c_Orderings_Obot__class_Obot(tc_fun(U_1500,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1500),U_1501))
| ~ class_Groups_Ocomm__monoid__add(U_1499) ),
inference(definitional_conversion,[status(esa)],[f_276_2]) ).
cnf(f_276_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1500,U_1499),U_1502),hAPP(hAPP(c_Set_Oinsert(U_1500),U_1503),U_1501)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1499),hAPP(U_1502,U_1503)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1500,U_1499),U_1502),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1500,tc_HOL_Obool)),U_1501),hAPP(hAPP(c_Set_Oinsert(U_1500),U_1503),c_Orderings_Obot__class_Obot(tc_fun(U_1500,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1500),U_1501))
| ~ class_Groups_Ocomm__monoid__add(U_1499) ),
inference(clausify,[status(thm)],[f_276_3]) ).
fof(f_277_1,plain,
! [V_z_2,V_A_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,V_f_2),V_z_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold]) ).
fof(f_277_2,plain,
! [U_1508,U_1507,U_1506,U_1505,U_1504] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1504,U_1505,U_1506,U_1508,U_1507),hAPP(hAPP(c_Finite__Set_Ofold(U_1504,U_1505,U_1506),U_1508),U_1507)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1504),U_1507))
| ~ c_Finite__Set_Ofun__left__comm(U_1504,U_1505,U_1506) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
! [U_1505,U_1504,U_1506,U_1507,U_1508] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1504,U_1505,U_1506,U_1508,U_1507),hAPP(hAPP(c_Finite__Set_Ofold(U_1504,U_1505,U_1506),U_1508),U_1507)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1504),U_1507))
| ~ c_Finite__Set_Ofun__left__comm(U_1504,U_1505,U_1506) ),
inference(definitional_conversion,[status(esa)],[f_277_2]) ).
cnf(f_277_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1504,U_1505,U_1506,U_1508,U_1507),hAPP(hAPP(c_Finite__Set_Ofold(U_1504,U_1505,U_1506),U_1508),U_1507)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1504),U_1507))
| ~ c_Finite__Set_Ofun__left__comm(U_1504,U_1505,U_1506) ),
inference(clausify,[status(thm)],[f_277_3]) ).
fof(f_278_1,plain,
! [V_f_2,V_a_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H]) ).
fof(f_278_2,plain,
! [U_1513,U_1512,U_1511,U_1510,U_1509] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1510,U_1509),U_1513),U_1511) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1509),hAPP(U_1513,U_1512)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1510,U_1509),U_1513),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1510,tc_HOL_Obool)),U_1511),hAPP(hAPP(c_Set_Oinsert(U_1510),U_1512),c_Orderings_Obot__class_Obot(tc_fun(U_1510,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_1510),U_1512),U_1511))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1510),U_1511))
| ~ class_Groups_Ocomm__monoid__add(U_1509) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
! [U_1509,U_1510,U_1511,U_1512,U_1513] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1510,U_1509),U_1513),U_1511) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1509),hAPP(U_1513,U_1512)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1510,U_1509),U_1513),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1510,tc_HOL_Obool)),U_1511),hAPP(hAPP(c_Set_Oinsert(U_1510),U_1512),c_Orderings_Obot__class_Obot(tc_fun(U_1510,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_1510),U_1512),U_1511))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1510),U_1511))
| ~ class_Groups_Ocomm__monoid__add(U_1509) ),
inference(definitional_conversion,[status(esa)],[f_278_2]) ).
cnf(f_278_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1510,U_1509),U_1513),U_1511) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1509),hAPP(U_1513,U_1512)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1510,U_1509),U_1513),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1510,tc_HOL_Obool)),U_1511),hAPP(hAPP(c_Set_Oinsert(U_1510),U_1512),c_Orderings_Obot__class_Obot(tc_fun(U_1510,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_1510),U_1512),U_1511))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1510),U_1511))
| ~ class_Groups_Ocomm__monoid__add(U_1509) ),
inference(clausify,[status(thm)],[f_278_3]) ).
fof(f_279_1,plain,
! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_d,T_c] :
( ? [B_y_H] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,V_A_2),V_y_2))
| ~ c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE__aux]) ).
fof(f_279_2,plain,
! [U_1521,U_1520,U_1519,U_1518,U_1517,U_1516,U_1515] :
( ? [U_1514] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1515,U_1516,U_1517,U_1518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1515,tc_HOL_Obool)),U_1519),hAPP(hAPP(c_Set_Oinsert(U_1515),U_1521),c_Orderings_Obot__class_Obot(tc_fun(U_1515,tc_HOL_Obool))))),U_1514))
& U_1520 = hAPP(hAPP(U_1517,U_1521),U_1514) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1515),U_1521),U_1519))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1515,U_1516,U_1517,U_1518,U_1519),U_1520))
| ~ c_Finite__Set_Ofun__left__comm(U_1515,U_1516,U_1517) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
! [U_1521,U_1520,U_1519,U_1518,U_1517,U_1516,U_1515] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1515,U_1516,U_1517,U_1518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1515,tc_HOL_Obool)),U_1519),hAPP(hAPP(c_Set_Oinsert(U_1515),U_1521),c_Orderings_Obot__class_Obot(tc_fun(U_1515,tc_HOL_Obool))))),sK29(U_1521,U_1520,U_1519,U_1518,U_1517,U_1516,U_1515)))
& U_1520 = hAPP(hAPP(U_1517,U_1521),sK29(U_1521,U_1520,U_1519,U_1518,U_1517,U_1516,U_1515)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_1515),U_1521),U_1519))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1515,U_1516,U_1517,U_1518,U_1519),U_1520))
| ~ c_Finite__Set_Ofun__left__comm(U_1515,U_1516,U_1517) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1514,sK29(U_1521,U_1520,U_1519,U_1518,U_1517,U_1516,U_1515))],[f_279_2]) ).
fof(f_279_4,plain,
( ! [U_1515,U_1516,U_1517,U_1518,U_1519,U_1520,U_1521] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1515,U_1516,U_1517,U_1518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1515,tc_HOL_Obool)),U_1519),hAPP(hAPP(c_Set_Oinsert(U_1515),U_1521),c_Orderings_Obot__class_Obot(tc_fun(U_1515,tc_HOL_Obool))))),sK29(U_1521,U_1520,U_1519,U_1518,U_1517,U_1516,U_1515)))
| ~ sP54(U_1515,U_1516,U_1517,U_1518,U_1519,U_1520,U_1521) )
& ! [U_1515,U_1516,U_1517,U_1518,U_1519,U_1520,U_1521] :
( U_1520 = hAPP(hAPP(U_1517,U_1521),sK29(U_1521,U_1520,U_1519,U_1518,U_1517,U_1516,U_1515))
| ~ sP54(U_1515,U_1516,U_1517,U_1518,U_1519,U_1520,U_1521) )
& ! [U_1515,U_1516,U_1517,U_1518,U_1519,U_1520,U_1521] :
( sP54(U_1515,U_1516,U_1517,U_1518,U_1519,U_1520,U_1521)
| ~ hBOOL(hAPP(hAPP(c_member(U_1515),U_1521),U_1519))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1515,U_1516,U_1517,U_1518,U_1519),U_1520))
| ~ c_Finite__Set_Ofun__left__comm(U_1515,U_1516,U_1517) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54])],[f_279_3]) ).
cnf(f_279_5,plain,
( sP54(U_1515,U_1516,U_1517,U_1518,U_1519,U_1520,U_1521)
| ~ hBOOL(hAPP(hAPP(c_member(U_1515),U_1521),U_1519))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1515,U_1516,U_1517,U_1518,U_1519),U_1520))
| ~ c_Finite__Set_Ofun__left__comm(U_1515,U_1516,U_1517) ),
inference(clausify,[status(thm)],[f_279_4]) ).
cnf(f_279_6,plain,
( U_1520 = hAPP(hAPP(U_1517,U_1521),sK29(U_1521,U_1520,U_1519,U_1518,U_1517,U_1516,U_1515))
| ~ sP54(U_1515,U_1516,U_1517,U_1518,U_1519,U_1520,U_1521) ),
inference(clausify,[status(thm)],[f_279_4]) ).
cnf(f_279_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1515,U_1516,U_1517,U_1518,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1515,tc_HOL_Obool)),U_1519),hAPP(hAPP(c_Set_Oinsert(U_1515),U_1521),c_Orderings_Obot__class_Obot(tc_fun(U_1515,tc_HOL_Obool))))),sK29(U_1521,U_1520,U_1519,U_1518,U_1517,U_1516,U_1515)))
| ~ sP54(U_1515,U_1516,U_1517,U_1518,U_1519,U_1520,U_1521) ),
inference(clausify,[status(thm)],[f_279_4]) ).
fof(f_280_1,plain,
! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a1_2),V_a2_2)),V_a3_2))
| ! [B_a,B_A] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_a),B_A))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,V_f_2,B_a,B_A),V_a3_2))
| hAPP(hAPP(c_Set_Oinsert(T_c),V_a1_2),V_a2_2) != hAPP(hAPP(c_Set_Oinsert(T_c),B_a),B_A) ) )
& ( ? [B_a,B_A] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,V_f_2,B_a,B_A),V_a3_2))
& hAPP(hAPP(c_Set_Oinsert(T_c),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_c),B_a),B_A) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a1_2),V_a2_2)),V_a3_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_fold1Set_Oequations]) ).
fof(f_280_2,plain,
! [U_1530,U_1529,U_1528,U_1527,U_1526] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1526,U_1527,hAPP(hAPP(c_Set_Oinsert(U_1526),U_1528),U_1529)),U_1530))
| ! [U_1525,U_1524] :
( hBOOL(hAPP(hAPP(c_member(U_1526),U_1525),U_1524))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1526,U_1526,U_1527,U_1525,U_1524),U_1530))
| hAPP(hAPP(c_Set_Oinsert(U_1526),U_1528),U_1529) != hAPP(hAPP(c_Set_Oinsert(U_1526),U_1525),U_1524) ) )
& ( ? [U_1523,U_1522] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1526),U_1523),U_1522))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1526,U_1526,U_1527,U_1523,U_1522),U_1530))
& hAPP(hAPP(c_Set_Oinsert(U_1526),U_1528),U_1529) = hAPP(hAPP(c_Set_Oinsert(U_1526),U_1523),U_1522) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1526,U_1527,hAPP(hAPP(c_Set_Oinsert(U_1526),U_1528),U_1529)),U_1530)) ) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
fof(f_280_3,plain,
( ! [U_1540,U_1538,U_1536,U_1534,U_1532] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1532,U_1534,hAPP(hAPP(c_Set_Oinsert(U_1532),U_1536),U_1538)),U_1540))
| ! [U_1525,U_1524] :
( hBOOL(hAPP(hAPP(c_member(U_1532),U_1525),U_1524))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1532,U_1532,U_1534,U_1525,U_1524),U_1540))
| hAPP(hAPP(c_Set_Oinsert(U_1532),U_1536),U_1538) != hAPP(hAPP(c_Set_Oinsert(U_1532),U_1525),U_1524) ) )
& ! [U_1539,U_1537,U_1535,U_1533,U_1531] :
( ? [U_1523,U_1522] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1531),U_1523),U_1522))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1531,U_1531,U_1533,U_1523,U_1522),U_1539))
& hAPP(hAPP(c_Set_Oinsert(U_1531),U_1535),U_1537) = hAPP(hAPP(c_Set_Oinsert(U_1531),U_1523),U_1522) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1531,U_1533,hAPP(hAPP(c_Set_Oinsert(U_1531),U_1535),U_1537)),U_1539)) ) ),
inference(miniscope,[status(thm)],[f_280_2]) ).
fof(f_280_4,plain,
( ! [U_1540,U_1538,U_1536,U_1534,U_1532] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1532,U_1534,hAPP(hAPP(c_Set_Oinsert(U_1532),U_1536),U_1538)),U_1540))
| ! [U_1525,U_1524] :
( hBOOL(hAPP(hAPP(c_member(U_1532),U_1525),U_1524))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1532,U_1532,U_1534,U_1525,U_1524),U_1540))
| hAPP(hAPP(c_Set_Oinsert(U_1532),U_1536),U_1538) != hAPP(hAPP(c_Set_Oinsert(U_1532),U_1525),U_1524) ) )
& ! [U_1539,U_1537,U_1535,U_1533,U_1531] :
( ? [U_1522] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1531),sK30(U_1539,U_1537,U_1535,U_1533,U_1531)),U_1522))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1531,U_1531,U_1533,sK30(U_1539,U_1537,U_1535,U_1533,U_1531),U_1522),U_1539))
& hAPP(hAPP(c_Set_Oinsert(U_1531),U_1535),U_1537) = hAPP(hAPP(c_Set_Oinsert(U_1531),sK30(U_1539,U_1537,U_1535,U_1533,U_1531)),U_1522) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1531,U_1533,hAPP(hAPP(c_Set_Oinsert(U_1531),U_1535),U_1537)),U_1539)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_1523,sK30(U_1539,U_1537,U_1535,U_1533,U_1531))],[f_280_3]) ).
fof(f_280_5,plain,
( ! [U_1540,U_1538,U_1536,U_1534,U_1532] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1532,U_1534,hAPP(hAPP(c_Set_Oinsert(U_1532),U_1536),U_1538)),U_1540))
| ! [U_1525,U_1524] :
( hBOOL(hAPP(hAPP(c_member(U_1532),U_1525),U_1524))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1532,U_1532,U_1534,U_1525,U_1524),U_1540))
| hAPP(hAPP(c_Set_Oinsert(U_1532),U_1536),U_1538) != hAPP(hAPP(c_Set_Oinsert(U_1532),U_1525),U_1524) ) )
& ! [U_1539,U_1537,U_1535,U_1533,U_1531] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_1531),sK30(U_1539,U_1537,U_1535,U_1533,U_1531)),sK31(U_1539,U_1537,U_1535,U_1533,U_1531)))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1531,U_1531,U_1533,sK30(U_1539,U_1537,U_1535,U_1533,U_1531),sK31(U_1539,U_1537,U_1535,U_1533,U_1531)),U_1539))
& hAPP(hAPP(c_Set_Oinsert(U_1531),U_1535),U_1537) = hAPP(hAPP(c_Set_Oinsert(U_1531),sK30(U_1539,U_1537,U_1535,U_1533,U_1531)),sK31(U_1539,U_1537,U_1535,U_1533,U_1531)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1531,U_1533,hAPP(hAPP(c_Set_Oinsert(U_1531),U_1535),U_1537)),U_1539)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_1522,sK31(U_1539,U_1537,U_1535,U_1533,U_1531))],[f_280_4]) ).
fof(f_280_6,plain,
( ! [U_1537,U_1533,U_1531,U_1535,U_1539] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1531),sK30(U_1539,U_1537,U_1535,U_1533,U_1531)),sK31(U_1539,U_1537,U_1535,U_1533,U_1531)))
| ~ sP55(U_1537,U_1533,U_1531,U_1535,U_1539) )
& ! [U_1537,U_1533,U_1531,U_1535,U_1539] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1531,U_1531,U_1533,sK30(U_1539,U_1537,U_1535,U_1533,U_1531),sK31(U_1539,U_1537,U_1535,U_1533,U_1531)),U_1539))
| ~ sP55(U_1537,U_1533,U_1531,U_1535,U_1539) )
& ! [U_1537,U_1533,U_1531,U_1535,U_1539] :
( hAPP(hAPP(c_Set_Oinsert(U_1531),U_1535),U_1537) = hAPP(hAPP(c_Set_Oinsert(U_1531),sK30(U_1539,U_1537,U_1535,U_1533,U_1531)),sK31(U_1539,U_1537,U_1535,U_1533,U_1531))
| ~ sP55(U_1537,U_1533,U_1531,U_1535,U_1539) )
& ! [U_1524,U_1525,U_1538,U_1532,U_1534,U_1536,U_1540] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1532,U_1534,hAPP(hAPP(c_Set_Oinsert(U_1532),U_1536),U_1538)),U_1540))
| hBOOL(hAPP(hAPP(c_member(U_1532),U_1525),U_1524))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1532,U_1532,U_1534,U_1525,U_1524),U_1540))
| hAPP(hAPP(c_Set_Oinsert(U_1532),U_1536),U_1538) != hAPP(hAPP(c_Set_Oinsert(U_1532),U_1525),U_1524) )
& ! [U_1537,U_1533,U_1531,U_1535,U_1539] :
( sP55(U_1537,U_1533,U_1531,U_1535,U_1539)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1531,U_1533,hAPP(hAPP(c_Set_Oinsert(U_1531),U_1535),U_1537)),U_1539)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_280_5]) ).
cnf(f_280_7,plain,
( sP55(U_1537,U_1533,U_1531,U_1535,U_1539)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1531,U_1533,hAPP(hAPP(c_Set_Oinsert(U_1531),U_1535),U_1537)),U_1539)) ),
inference(clausify,[status(thm)],[f_280_6]) ).
cnf(f_280_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1532,U_1534,hAPP(hAPP(c_Set_Oinsert(U_1532),U_1536),U_1538)),U_1540))
| hBOOL(hAPP(hAPP(c_member(U_1532),U_1525),U_1524))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1532,U_1532,U_1534,U_1525,U_1524),U_1540))
| hAPP(hAPP(c_Set_Oinsert(U_1532),U_1536),U_1538) != hAPP(hAPP(c_Set_Oinsert(U_1532),U_1525),U_1524) ),
inference(clausify,[status(thm)],[f_280_6]) ).
cnf(f_280_9,plain,
( hAPP(hAPP(c_Set_Oinsert(U_1531),U_1535),U_1537) = hAPP(hAPP(c_Set_Oinsert(U_1531),sK30(U_1539,U_1537,U_1535,U_1533,U_1531)),sK31(U_1539,U_1537,U_1535,U_1533,U_1531))
| ~ sP55(U_1537,U_1533,U_1531,U_1535,U_1539) ),
inference(clausify,[status(thm)],[f_280_6]) ).
cnf(f_280_10,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1531,U_1531,U_1533,sK30(U_1539,U_1537,U_1535,U_1533,U_1531),sK31(U_1539,U_1537,U_1535,U_1533,U_1531)),U_1539))
| ~ sP55(U_1537,U_1533,U_1531,U_1535,U_1539) ),
inference(clausify,[status(thm)],[f_280_6]) ).
cnf(f_280_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1531),sK30(U_1539,U_1537,U_1535,U_1533,U_1531)),sK31(U_1539,U_1537,U_1535,U_1533,U_1531)))
| ~ sP55(U_1537,U_1533,U_1531,U_1535,U_1539) ),
inference(clausify,[status(thm)],[f_280_6]) ).
fof(f_281_1,plain,
! [V_x_2,V_X_2,V_a_2,V_f_2,T_c] :
( ? [B_a,B_A] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,V_f_2,B_a,B_A),V_x_2))
& hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_c),B_a),B_A) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_X_2)),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__fold1SetE]) ).
fof(f_281_2,plain,
! [U_1547,U_1546,U_1545,U_1544,U_1543] :
( ? [U_1542,U_1541] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1543),U_1542),U_1541))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1543,U_1543,U_1544,U_1542,U_1541),U_1547))
& hAPP(hAPP(c_Set_Oinsert(U_1543),U_1545),U_1546) = hAPP(hAPP(c_Set_Oinsert(U_1543),U_1542),U_1541) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1543,U_1544,hAPP(hAPP(c_Set_Oinsert(U_1543),U_1545),U_1546)),U_1547)) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
! [U_1547,U_1546,U_1545,U_1544,U_1543] :
( ? [U_1541] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1543),sK32(U_1547,U_1546,U_1545,U_1544,U_1543)),U_1541))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1543,U_1543,U_1544,sK32(U_1547,U_1546,U_1545,U_1544,U_1543),U_1541),U_1547))
& hAPP(hAPP(c_Set_Oinsert(U_1543),U_1545),U_1546) = hAPP(hAPP(c_Set_Oinsert(U_1543),sK32(U_1547,U_1546,U_1545,U_1544,U_1543)),U_1541) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1543,U_1544,hAPP(hAPP(c_Set_Oinsert(U_1543),U_1545),U_1546)),U_1547)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_1542,sK32(U_1547,U_1546,U_1545,U_1544,U_1543))],[f_281_2]) ).
fof(f_281_4,plain,
! [U_1547,U_1546,U_1545,U_1544,U_1543] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_1543),sK32(U_1547,U_1546,U_1545,U_1544,U_1543)),sK33(U_1547,U_1546,U_1545,U_1544,U_1543)))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1543,U_1543,U_1544,sK32(U_1547,U_1546,U_1545,U_1544,U_1543),sK33(U_1547,U_1546,U_1545,U_1544,U_1543)),U_1547))
& hAPP(hAPP(c_Set_Oinsert(U_1543),U_1545),U_1546) = hAPP(hAPP(c_Set_Oinsert(U_1543),sK32(U_1547,U_1546,U_1545,U_1544,U_1543)),sK33(U_1547,U_1546,U_1545,U_1544,U_1543)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1543,U_1544,hAPP(hAPP(c_Set_Oinsert(U_1543),U_1545),U_1546)),U_1547)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_1541,sK33(U_1547,U_1546,U_1545,U_1544,U_1543))],[f_281_3]) ).
fof(f_281_5,plain,
( ! [U_1543,U_1544,U_1545,U_1546,U_1547] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1543),sK32(U_1547,U_1546,U_1545,U_1544,U_1543)),sK33(U_1547,U_1546,U_1545,U_1544,U_1543)))
| ~ sP56(U_1543,U_1544,U_1545,U_1546,U_1547) )
& ! [U_1543,U_1544,U_1545,U_1546,U_1547] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1543,U_1543,U_1544,sK32(U_1547,U_1546,U_1545,U_1544,U_1543),sK33(U_1547,U_1546,U_1545,U_1544,U_1543)),U_1547))
| ~ sP56(U_1543,U_1544,U_1545,U_1546,U_1547) )
& ! [U_1543,U_1544,U_1545,U_1546,U_1547] :
( hAPP(hAPP(c_Set_Oinsert(U_1543),U_1545),U_1546) = hAPP(hAPP(c_Set_Oinsert(U_1543),sK32(U_1547,U_1546,U_1545,U_1544,U_1543)),sK33(U_1547,U_1546,U_1545,U_1544,U_1543))
| ~ sP56(U_1543,U_1544,U_1545,U_1546,U_1547) )
& ! [U_1543,U_1544,U_1545,U_1546,U_1547] :
( sP56(U_1543,U_1544,U_1545,U_1546,U_1547)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1543,U_1544,hAPP(hAPP(c_Set_Oinsert(U_1543),U_1545),U_1546)),U_1547)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56])],[f_281_4]) ).
cnf(f_281_6,plain,
( sP56(U_1543,U_1544,U_1545,U_1546,U_1547)
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1543,U_1544,hAPP(hAPP(c_Set_Oinsert(U_1543),U_1545),U_1546)),U_1547)) ),
inference(clausify,[status(thm)],[f_281_5]) ).
cnf(f_281_7,plain,
( hAPP(hAPP(c_Set_Oinsert(U_1543),U_1545),U_1546) = hAPP(hAPP(c_Set_Oinsert(U_1543),sK32(U_1547,U_1546,U_1545,U_1544,U_1543)),sK33(U_1547,U_1546,U_1545,U_1544,U_1543))
| ~ sP56(U_1543,U_1544,U_1545,U_1546,U_1547) ),
inference(clausify,[status(thm)],[f_281_5]) ).
cnf(f_281_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1543,U_1543,U_1544,sK32(U_1547,U_1546,U_1545,U_1544,U_1543),sK33(U_1547,U_1546,U_1545,U_1544,U_1543)),U_1547))
| ~ sP56(U_1543,U_1544,U_1545,U_1546,U_1547) ),
inference(clausify,[status(thm)],[f_281_5]) ).
cnf(f_281_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1543),sK32(U_1547,U_1546,U_1545,U_1544,U_1543)),sK33(U_1547,U_1546,U_1545,U_1544,U_1543)))
| ~ sP56(U_1543,U_1544,U_1545,U_1546,U_1547) ),
inference(clausify,[status(thm)],[f_281_5]) ).
fof(f_282_1,plain,
! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_d,T_c] :
( ? [B_y] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,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_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_d,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)),V_v_2))
| ~ c_Finite__Set_Ofun__left__comm(T_c,T_d,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE]) ).
fof(f_282_2,plain,
! [U_1555,U_1554,U_1553,U_1552,U_1551,U_1550,U_1549] :
( ? [U_1548] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1549,U_1550,U_1551,U_1552,U_1554),U_1548))
& U_1555 = hAPP(hAPP(U_1551,U_1553),U_1548) )
| hBOOL(hAPP(hAPP(c_member(U_1549),U_1553),U_1554))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1549,U_1550,U_1551,U_1552,hAPP(hAPP(c_Set_Oinsert(U_1549),U_1553),U_1554)),U_1555))
| ~ c_Finite__Set_Ofun__left__comm(U_1549,U_1550,U_1551) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
! [U_1555,U_1554,U_1553,U_1552,U_1551,U_1550,U_1549] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1549,U_1550,U_1551,U_1552,U_1554),sK34(U_1555,U_1554,U_1553,U_1552,U_1551,U_1550,U_1549)))
& U_1555 = hAPP(hAPP(U_1551,U_1553),sK34(U_1555,U_1554,U_1553,U_1552,U_1551,U_1550,U_1549)) )
| hBOOL(hAPP(hAPP(c_member(U_1549),U_1553),U_1554))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1549,U_1550,U_1551,U_1552,hAPP(hAPP(c_Set_Oinsert(U_1549),U_1553),U_1554)),U_1555))
| ~ c_Finite__Set_Ofun__left__comm(U_1549,U_1550,U_1551) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_1548,sK34(U_1555,U_1554,U_1553,U_1552,U_1551,U_1550,U_1549))],[f_282_2]) ).
fof(f_282_4,plain,
( ! [U_1550,U_1549,U_1551,U_1552,U_1553,U_1554,U_1555] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1549,U_1550,U_1551,U_1552,U_1554),sK34(U_1555,U_1554,U_1553,U_1552,U_1551,U_1550,U_1549)))
| ~ sP57(U_1550,U_1549,U_1551,U_1552,U_1553,U_1554,U_1555) )
& ! [U_1550,U_1549,U_1551,U_1552,U_1553,U_1554,U_1555] :
( U_1555 = hAPP(hAPP(U_1551,U_1553),sK34(U_1555,U_1554,U_1553,U_1552,U_1551,U_1550,U_1549))
| ~ sP57(U_1550,U_1549,U_1551,U_1552,U_1553,U_1554,U_1555) )
& ! [U_1550,U_1549,U_1551,U_1552,U_1553,U_1554,U_1555] :
( sP57(U_1550,U_1549,U_1551,U_1552,U_1553,U_1554,U_1555)
| hBOOL(hAPP(hAPP(c_member(U_1549),U_1553),U_1554))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1549,U_1550,U_1551,U_1552,hAPP(hAPP(c_Set_Oinsert(U_1549),U_1553),U_1554)),U_1555))
| ~ c_Finite__Set_Ofun__left__comm(U_1549,U_1550,U_1551) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57])],[f_282_3]) ).
cnf(f_282_5,plain,
( sP57(U_1550,U_1549,U_1551,U_1552,U_1553,U_1554,U_1555)
| hBOOL(hAPP(hAPP(c_member(U_1549),U_1553),U_1554))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1549,U_1550,U_1551,U_1552,hAPP(hAPP(c_Set_Oinsert(U_1549),U_1553),U_1554)),U_1555))
| ~ c_Finite__Set_Ofun__left__comm(U_1549,U_1550,U_1551) ),
inference(clausify,[status(thm)],[f_282_4]) ).
cnf(f_282_6,plain,
( U_1555 = hAPP(hAPP(U_1551,U_1553),sK34(U_1555,U_1554,U_1553,U_1552,U_1551,U_1550,U_1549))
| ~ sP57(U_1550,U_1549,U_1551,U_1552,U_1553,U_1554,U_1555) ),
inference(clausify,[status(thm)],[f_282_4]) ).
cnf(f_282_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1549,U_1550,U_1551,U_1552,U_1554),sK34(U_1555,U_1554,U_1553,U_1552,U_1551,U_1550,U_1549)))
| ~ sP57(U_1550,U_1549,U_1551,U_1552,U_1553,U_1554,U_1555) ),
inference(clausify,[status(thm)],[f_282_4]) ).
fof(f_283_1,plain,
! [V_a_2,V_x_2,V_A_2,V_b_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_b_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_x_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),V_b_2,V_A_2),V_x_2))
| ~ class_Groups_Oab__semigroup__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph__permute__diff]) ).
fof(f_283_2,plain,
! [U_1560,U_1559,U_1558,U_1557,U_1556] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1556,U_1556,c_Groups_Otimes__class_Otimes(U_1556),U_1560,hAPP(hAPP(c_Set_Oinsert(U_1556),U_1557),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1556,tc_HOL_Obool)),U_1558),hAPP(hAPP(c_Set_Oinsert(U_1556),U_1560),c_Orderings_Obot__class_Obot(tc_fun(U_1556,tc_HOL_Obool)))))),U_1559))
| hBOOL(hAPP(hAPP(c_member(U_1556),U_1557),U_1558))
| ~ hBOOL(hAPP(hAPP(c_member(U_1556),U_1560),U_1558))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1556,U_1556,c_Groups_Otimes__class_Otimes(U_1556),U_1557,U_1558),U_1559))
| ~ class_Groups_Oab__semigroup__mult(U_1556) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_1557,U_1556,U_1558,U_1559,U_1560] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1556,U_1556,c_Groups_Otimes__class_Otimes(U_1556),U_1560,hAPP(hAPP(c_Set_Oinsert(U_1556),U_1557),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1556,tc_HOL_Obool)),U_1558),hAPP(hAPP(c_Set_Oinsert(U_1556),U_1560),c_Orderings_Obot__class_Obot(tc_fun(U_1556,tc_HOL_Obool)))))),U_1559))
| hBOOL(hAPP(hAPP(c_member(U_1556),U_1557),U_1558))
| ~ hBOOL(hAPP(hAPP(c_member(U_1556),U_1560),U_1558))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1556,U_1556,c_Groups_Otimes__class_Otimes(U_1556),U_1557,U_1558),U_1559))
| ~ class_Groups_Oab__semigroup__mult(U_1556) ),
inference(definitional_conversion,[status(esa)],[f_283_2]) ).
cnf(f_283_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1556,U_1556,c_Groups_Otimes__class_Otimes(U_1556),U_1560,hAPP(hAPP(c_Set_Oinsert(U_1556),U_1557),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1556,tc_HOL_Obool)),U_1558),hAPP(hAPP(c_Set_Oinsert(U_1556),U_1560),c_Orderings_Obot__class_Obot(tc_fun(U_1556,tc_HOL_Obool)))))),U_1559))
| hBOOL(hAPP(hAPP(c_member(U_1556),U_1557),U_1558))
| ~ hBOOL(hAPP(hAPP(c_member(U_1556),U_1560),U_1558))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1556,U_1556,c_Groups_Otimes__class_Otimes(U_1556),U_1557,U_1558),U_1559))
| ~ class_Groups_Oab__semigroup__mult(U_1556) ),
inference(clausify,[status(thm)],[f_283_3]) ).
fof(f_284_1,plain,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_d,T_c,T_e] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),V_g_2),V_A_2)
| ? [B_a] :
( hAPP(V_g_2,B_a) != hAPP(V_h_2,hAPP(V_f_2,B_a))
& hBOOL(hAPP(hAPP(c_member(T_c),B_a),V_A_2)) )
| V_B_2 != hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
| ~ class_Groups_Ocomm__monoid__add(T_e) ),
inference(fof_nnf,[status(thm)],[fact_setsum__reindex__cong]) ).
fof(f_284_2,plain,
! [U_1569,U_1568,U_1567,U_1566,U_1565,U_1564,U_1563,U_1562] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1564,U_1562),U_1569),U_1567) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1563,U_1562),U_1568),U_1566)
| ? [U_1561] :
( hAPP(U_1568,U_1561) != hAPP(U_1569,hAPP(U_1565,U_1561))
& hBOOL(hAPP(hAPP(c_member(U_1563),U_1561),U_1566)) )
| U_1567 != hAPP(c_Set_Oimage(U_1563,U_1564,U_1565),U_1566)
| ~ c_Fun_Oinj__on(U_1563,U_1564,U_1565,U_1566)
| ~ class_Groups_Ocomm__monoid__add(U_1562) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
fof(f_284_3,plain,
! [U_1569,U_1568,U_1567,U_1566,U_1565,U_1564,U_1563,U_1562] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1564,U_1562),U_1569),U_1567) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1563,U_1562),U_1568),U_1566)
| ( hAPP(U_1568,sK35(U_1569,U_1568,U_1567,U_1566,U_1565,U_1564,U_1563,U_1562)) != hAPP(U_1569,hAPP(U_1565,sK35(U_1569,U_1568,U_1567,U_1566,U_1565,U_1564,U_1563,U_1562)))
& hBOOL(hAPP(hAPP(c_member(U_1563),sK35(U_1569,U_1568,U_1567,U_1566,U_1565,U_1564,U_1563,U_1562)),U_1566)) )
| U_1567 != hAPP(c_Set_Oimage(U_1563,U_1564,U_1565),U_1566)
| ~ c_Fun_Oinj__on(U_1563,U_1564,U_1565,U_1566)
| ~ class_Groups_Ocomm__monoid__add(U_1562) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_1561,sK35(U_1569,U_1568,U_1567,U_1566,U_1565,U_1564,U_1563,U_1562))],[f_284_2]) ).
fof(f_284_4,plain,
( ! [U_1563,U_1562,U_1564,U_1565,U_1566,U_1567,U_1568,U_1569] :
( hAPP(U_1568,sK35(U_1569,U_1568,U_1567,U_1566,U_1565,U_1564,U_1563,U_1562)) != hAPP(U_1569,hAPP(U_1565,sK35(U_1569,U_1568,U_1567,U_1566,U_1565,U_1564,U_1563,U_1562)))
| ~ sP58(U_1563,U_1562,U_1564,U_1565,U_1566,U_1567,U_1568,U_1569) )
& ! [U_1563,U_1562,U_1564,U_1565,U_1566,U_1567,U_1568,U_1569] :
( hBOOL(hAPP(hAPP(c_member(U_1563),sK35(U_1569,U_1568,U_1567,U_1566,U_1565,U_1564,U_1563,U_1562)),U_1566))
| ~ sP58(U_1563,U_1562,U_1564,U_1565,U_1566,U_1567,U_1568,U_1569) )
& ! [U_1563,U_1562,U_1564,U_1565,U_1566,U_1567,U_1568,U_1569] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1564,U_1562),U_1569),U_1567) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1563,U_1562),U_1568),U_1566)
| sP58(U_1563,U_1562,U_1564,U_1565,U_1566,U_1567,U_1568,U_1569)
| U_1567 != hAPP(c_Set_Oimage(U_1563,U_1564,U_1565),U_1566)
| ~ c_Fun_Oinj__on(U_1563,U_1564,U_1565,U_1566)
| ~ class_Groups_Ocomm__monoid__add(U_1562) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58])],[f_284_3]) ).
cnf(f_284_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1564,U_1562),U_1569),U_1567) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1563,U_1562),U_1568),U_1566)
| sP58(U_1563,U_1562,U_1564,U_1565,U_1566,U_1567,U_1568,U_1569)
| U_1567 != hAPP(c_Set_Oimage(U_1563,U_1564,U_1565),U_1566)
| ~ c_Fun_Oinj__on(U_1563,U_1564,U_1565,U_1566)
| ~ class_Groups_Ocomm__monoid__add(U_1562) ),
inference(clausify,[status(thm)],[f_284_4]) ).
cnf(f_284_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_1563),sK35(U_1569,U_1568,U_1567,U_1566,U_1565,U_1564,U_1563,U_1562)),U_1566))
| ~ sP58(U_1563,U_1562,U_1564,U_1565,U_1566,U_1567,U_1568,U_1569) ),
inference(clausify,[status(thm)],[f_284_4]) ).
cnf(f_284_7,plain,
( hAPP(U_1568,sK35(U_1569,U_1568,U_1567,U_1566,U_1565,U_1564,U_1563,U_1562)) != hAPP(U_1569,hAPP(U_1565,sK35(U_1569,U_1568,U_1567,U_1566,U_1565,U_1564,U_1563,U_1562)))
| ~ sP58(U_1563,U_1562,U_1564,U_1565,U_1566,U_1567,U_1568,U_1569) ),
inference(clausify,[status(thm)],[f_284_4]) ).
fof(f_285_1,plain,
! [V_B_2,V_x_2,V_A_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),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))))),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ) )
& ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),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))))),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ) )
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_B_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_psubset__insert__iff]) ).
fof(f_285_2,plain,
! [U_1573,U_1572,U_1571,U_1570] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1570,tc_HOL_Obool)),U_1571),hAPP(hAPP(c_Set_Oinsert(U_1570),U_1572),U_1573)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1570,tc_HOL_Obool)),U_1571),U_1573))
& ~ hBOOL(hAPP(hAPP(c_member(U_1570),U_1572),U_1571)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1570,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1570,tc_HOL_Obool)),U_1571),hAPP(hAPP(c_Set_Oinsert(U_1570),U_1572),c_Orderings_Obot__class_Obot(tc_fun(U_1570,tc_HOL_Obool))))),U_1573))
& hBOOL(hAPP(hAPP(c_member(U_1570),U_1572),U_1571)) ) )
& ~ hBOOL(hAPP(hAPP(c_member(U_1570),U_1572),U_1573)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1570,tc_HOL_Obool)),U_1571),U_1573))
& hBOOL(hAPP(hAPP(c_member(U_1570),U_1572),U_1573)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1570,tc_HOL_Obool)),U_1571),U_1573))
| hBOOL(hAPP(hAPP(c_member(U_1570),U_1572),U_1571)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1570,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1570,tc_HOL_Obool)),U_1571),hAPP(hAPP(c_Set_Oinsert(U_1570),U_1572),c_Orderings_Obot__class_Obot(tc_fun(U_1570,tc_HOL_Obool))))),U_1573))
| ~ hBOOL(hAPP(hAPP(c_member(U_1570),U_1572),U_1571)) ) )
| hBOOL(hAPP(hAPP(c_member(U_1570),U_1572),U_1573)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1570,tc_HOL_Obool)),U_1571),U_1573))
| ~ hBOOL(hAPP(hAPP(c_member(U_1570),U_1572),U_1573)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1570,tc_HOL_Obool)),U_1571),hAPP(hAPP(c_Set_Oinsert(U_1570),U_1572),U_1573))) ) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
( ! [U_1581,U_1579,U_1577,U_1575] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1575,tc_HOL_Obool)),U_1577),hAPP(hAPP(c_Set_Oinsert(U_1575),U_1579),U_1581)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1575,tc_HOL_Obool)),U_1577),U_1581))
& ~ hBOOL(hAPP(hAPP(c_member(U_1575),U_1579),U_1577)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1575,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1575,tc_HOL_Obool)),U_1577),hAPP(hAPP(c_Set_Oinsert(U_1575),U_1579),c_Orderings_Obot__class_Obot(tc_fun(U_1575,tc_HOL_Obool))))),U_1581))
& hBOOL(hAPP(hAPP(c_member(U_1575),U_1579),U_1577)) ) )
& ~ hBOOL(hAPP(hAPP(c_member(U_1575),U_1579),U_1581)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1575,tc_HOL_Obool)),U_1577),U_1581))
& hBOOL(hAPP(hAPP(c_member(U_1575),U_1579),U_1581)) ) )
& ! [U_1580,U_1578,U_1576,U_1574] :
( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1574,tc_HOL_Obool)),U_1576),U_1580))
| hBOOL(hAPP(hAPP(c_member(U_1574),U_1578),U_1576)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1574,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1574,tc_HOL_Obool)),U_1576),hAPP(hAPP(c_Set_Oinsert(U_1574),U_1578),c_Orderings_Obot__class_Obot(tc_fun(U_1574,tc_HOL_Obool))))),U_1580))
| ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1578),U_1576)) ) )
| hBOOL(hAPP(hAPP(c_member(U_1574),U_1578),U_1580)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1574,tc_HOL_Obool)),U_1576),U_1580))
| ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1578),U_1580)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1574,tc_HOL_Obool)),U_1576),hAPP(hAPP(c_Set_Oinsert(U_1574),U_1578),U_1580))) ) ),
inference(miniscope,[status(thm)],[f_285_2]) ).
fof(f_285_4,plain,
( ! [U_1581,U_1575,U_1577,U_1579] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1575,tc_HOL_Obool)),U_1577),U_1581))
| ~ sP63(U_1581,U_1575,U_1577,U_1579) )
& ! [U_1581,U_1575,U_1577,U_1579] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1575),U_1579),U_1577))
| ~ sP63(U_1581,U_1575,U_1577,U_1579) )
& ! [U_1581,U_1575,U_1577,U_1579] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1575,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1575,tc_HOL_Obool)),U_1577),hAPP(hAPP(c_Set_Oinsert(U_1575),U_1579),c_Orderings_Obot__class_Obot(tc_fun(U_1575,tc_HOL_Obool))))),U_1581))
| ~ sP62(U_1581,U_1575,U_1577,U_1579) )
& ! [U_1581,U_1575,U_1577,U_1579] :
( hBOOL(hAPP(hAPP(c_member(U_1575),U_1579),U_1577))
| ~ sP62(U_1581,U_1575,U_1577,U_1579) )
& ! [U_1581,U_1575,U_1577,U_1579] :
( sP63(U_1581,U_1575,U_1577,U_1579)
| sP62(U_1581,U_1575,U_1577,U_1579)
| ~ sP64(U_1581,U_1575,U_1577,U_1579) )
& ! [U_1581,U_1575,U_1577,U_1579] :
( ~ hBOOL(hAPP(hAPP(c_member(U_1575),U_1579),U_1581))
| ~ sP64(U_1581,U_1575,U_1577,U_1579) )
& ! [U_1581,U_1575,U_1577,U_1579] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1575,tc_HOL_Obool)),U_1577),U_1581))
| ~ sP61(U_1581,U_1575,U_1577,U_1579) )
& ! [U_1581,U_1575,U_1577,U_1579] :
( hBOOL(hAPP(hAPP(c_member(U_1575),U_1579),U_1581))
| ~ sP61(U_1581,U_1575,U_1577,U_1579) )
& ! [U_1574,U_1576,U_1578,U_1580] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1574,tc_HOL_Obool)),U_1576),U_1580))
| hBOOL(hAPP(hAPP(c_member(U_1574),U_1578),U_1576))
| ~ sP59(U_1574,U_1576,U_1578,U_1580) )
& ! [U_1574,U_1576,U_1578,U_1580] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1574,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1574,tc_HOL_Obool)),U_1576),hAPP(hAPP(c_Set_Oinsert(U_1574),U_1578),c_Orderings_Obot__class_Obot(tc_fun(U_1574,tc_HOL_Obool))))),U_1580))
| ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1578),U_1576))
| ~ sP59(U_1574,U_1576,U_1578,U_1580) )
& ! [U_1574,U_1576,U_1578,U_1580] :
( sP59(U_1574,U_1576,U_1578,U_1580)
| hBOOL(hAPP(hAPP(c_member(U_1574),U_1578),U_1580))
| ~ sP60(U_1574,U_1576,U_1578,U_1580) )
& ! [U_1574,U_1576,U_1578,U_1580] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1574,tc_HOL_Obool)),U_1576),U_1580))
| ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1578),U_1580))
| ~ sP60(U_1574,U_1576,U_1578,U_1580) )
& ! [U_1581,U_1575,U_1577,U_1579] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1575,tc_HOL_Obool)),U_1577),hAPP(hAPP(c_Set_Oinsert(U_1575),U_1579),U_1581)))
| sP64(U_1581,U_1575,U_1577,U_1579)
| sP61(U_1581,U_1575,U_1577,U_1579) )
& ! [U_1574,U_1576,U_1578,U_1580] :
( sP60(U_1574,U_1576,U_1578,U_1580)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1574,tc_HOL_Obool)),U_1576),hAPP(hAPP(c_Set_Oinsert(U_1574),U_1578),U_1580))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59,sP60,sP61,sP62,sP63,sP64])],[f_285_3]) ).
cnf(f_285_5,plain,
( sP60(U_1574,U_1576,U_1578,U_1580)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1574,tc_HOL_Obool)),U_1576),hAPP(hAPP(c_Set_Oinsert(U_1574),U_1578),U_1580))) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1575,tc_HOL_Obool)),U_1577),hAPP(hAPP(c_Set_Oinsert(U_1575),U_1579),U_1581)))
| sP64(U_1581,U_1575,U_1577,U_1579)
| sP61(U_1581,U_1575,U_1577,U_1579) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1574,tc_HOL_Obool)),U_1576),U_1580))
| ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1578),U_1580))
| ~ sP60(U_1574,U_1576,U_1578,U_1580) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_8,plain,
( sP59(U_1574,U_1576,U_1578,U_1580)
| hBOOL(hAPP(hAPP(c_member(U_1574),U_1578),U_1580))
| ~ sP60(U_1574,U_1576,U_1578,U_1580) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1574,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1574,tc_HOL_Obool)),U_1576),hAPP(hAPP(c_Set_Oinsert(U_1574),U_1578),c_Orderings_Obot__class_Obot(tc_fun(U_1574,tc_HOL_Obool))))),U_1580))
| ~ hBOOL(hAPP(hAPP(c_member(U_1574),U_1578),U_1576))
| ~ sP59(U_1574,U_1576,U_1578,U_1580) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1574,tc_HOL_Obool)),U_1576),U_1580))
| hBOOL(hAPP(hAPP(c_member(U_1574),U_1578),U_1576))
| ~ sP59(U_1574,U_1576,U_1578,U_1580) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_1575),U_1579),U_1581))
| ~ sP61(U_1581,U_1575,U_1577,U_1579) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1575,tc_HOL_Obool)),U_1577),U_1581))
| ~ sP61(U_1581,U_1575,U_1577,U_1579) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_13,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1575),U_1579),U_1581))
| ~ sP64(U_1581,U_1575,U_1577,U_1579) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_14,plain,
( sP63(U_1581,U_1575,U_1577,U_1579)
| sP62(U_1581,U_1575,U_1577,U_1579)
| ~ sP64(U_1581,U_1575,U_1577,U_1579) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_15,plain,
( hBOOL(hAPP(hAPP(c_member(U_1575),U_1579),U_1577))
| ~ sP62(U_1581,U_1575,U_1577,U_1579) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1575,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1575,tc_HOL_Obool)),U_1577),hAPP(hAPP(c_Set_Oinsert(U_1575),U_1579),c_Orderings_Obot__class_Obot(tc_fun(U_1575,tc_HOL_Obool))))),U_1581))
| ~ sP62(U_1581,U_1575,U_1577,U_1579) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_17,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_1575),U_1579),U_1577))
| ~ sP63(U_1581,U_1575,U_1577,U_1579) ),
inference(clausify,[status(thm)],[f_285_4]) ).
cnf(f_285_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1575,tc_HOL_Obool)),U_1577),U_1581))
| ~ sP63(U_1581,U_1575,U_1577,U_1579) ),
inference(clausify,[status(thm)],[f_285_4]) ).
fof(f_286_1,plain,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
| ~ c_Big__Operators_Ocomm__monoid__big(T_c,T_d,V_f_2,V_z_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_comm__monoid__big_Oinfinite]) ).
fof(f_286_2,plain,
! [U_1588,U_1587,U_1586,U_1585,U_1584,U_1583,U_1582] :
( hAPP(hAPP(U_1586,U_1588),U_1587) = U_1585
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_1583),U_1587))
| ~ c_Big__Operators_Ocomm__monoid__big(U_1582,U_1583,U_1584,U_1585,U_1586) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
! [U_1588,U_1587,U_1586,U_1585,U_1584,U_1583] :
( ! [U_1582] : ~ c_Big__Operators_Ocomm__monoid__big(U_1582,U_1583,U_1584,U_1585,U_1586)
| hAPP(hAPP(U_1586,U_1588),U_1587) = U_1585
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_1583),U_1587)) ),
inference(miniscope,[status(thm)],[f_286_2]) ).
fof(f_286_4,plain,
! [U_1585,U_1582,U_1584,U_1588,U_1586,U_1587,U_1583] :
( ~ c_Big__Operators_Ocomm__monoid__big(U_1582,U_1583,U_1584,U_1585,U_1586)
| hAPP(hAPP(U_1586,U_1588),U_1587) = U_1585
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_1583),U_1587)) ),
inference(definitional_conversion,[status(esa)],[f_286_3]) ).
cnf(f_286_5,plain,
( ~ c_Big__Operators_Ocomm__monoid__big(U_1582,U_1583,U_1584,U_1585,U_1586)
| hAPP(hAPP(U_1586,U_1588),U_1587) = U_1585
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_1583),U_1587)) ),
inference(clausify,[status(thm)],[f_286_4]) ).
fof(f_287_1,plain,
! [V_N_2,V_M_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_c,V_N_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
| V_M_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_M_2),V_N_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max__mono]) ).
fof(f_287_2,plain,
! [U_1591,U_1590,U_1589] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1589),c_Big__Operators_Olinorder__class_OMax(U_1589,U_1590)),c_Big__Operators_Olinorder__class_OMax(U_1589,U_1591)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1589),U_1591))
| U_1590 = c_Orderings_Obot__class_Obot(tc_fun(U_1589,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1589,tc_HOL_Obool)),U_1590),U_1591))
| ~ class_Orderings_Olinorder(U_1589) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
! [U_1591,U_1590,U_1589] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1589),c_Big__Operators_Olinorder__class_OMax(U_1589,U_1590)),c_Big__Operators_Olinorder__class_OMax(U_1589,U_1591)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1589),U_1591))
| U_1590 = c_Orderings_Obot__class_Obot(tc_fun(U_1589,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1589,tc_HOL_Obool)),U_1590),U_1591))
| ~ class_Orderings_Olinorder(U_1589) ),
inference(definitional_conversion,[status(esa)],[f_287_2]) ).
cnf(f_287_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1589),c_Big__Operators_Olinorder__class_OMax(U_1589,U_1590)),c_Big__Operators_Olinorder__class_OMax(U_1589,U_1591)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1589),U_1591))
| U_1590 = c_Orderings_Obot__class_Obot(tc_fun(U_1589,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1589,tc_HOL_Obool)),U_1590),U_1591))
| ~ class_Orderings_Olinorder(U_1589) ),
inference(clausify,[status(thm)],[f_287_3]) ).
fof(f_288_1,plain,
! [V_N_2,V_M_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_c,V_M_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
| V_M_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_M_2),V_N_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min__antimono]) ).
fof(f_288_2,plain,
! [U_1594,U_1593,U_1592] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1592),c_Big__Operators_Olinorder__class_OMin(U_1592,U_1594)),c_Big__Operators_Olinorder__class_OMin(U_1592,U_1593)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1592),U_1594))
| U_1593 = c_Orderings_Obot__class_Obot(tc_fun(U_1592,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1592,tc_HOL_Obool)),U_1593),U_1594))
| ~ class_Orderings_Olinorder(U_1592) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_1593,U_1592,U_1594] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1592),c_Big__Operators_Olinorder__class_OMin(U_1592,U_1594)),c_Big__Operators_Olinorder__class_OMin(U_1592,U_1593)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1592),U_1594))
| U_1593 = c_Orderings_Obot__class_Obot(tc_fun(U_1592,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1592,tc_HOL_Obool)),U_1593),U_1594))
| ~ class_Orderings_Olinorder(U_1592) ),
inference(definitional_conversion,[status(esa)],[f_288_2]) ).
cnf(f_288_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1592),c_Big__Operators_Olinorder__class_OMin(U_1592,U_1594)),c_Big__Operators_Olinorder__class_OMin(U_1592,U_1593)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1592),U_1594))
| U_1593 = c_Orderings_Obot__class_Obot(tc_fun(U_1592,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1592,tc_HOL_Obool)),U_1593),U_1594))
| ~ class_Orderings_Olinorder(U_1592) ),
inference(clausify,[status(thm)],[f_288_3]) ).
fof(f_289_1,plain,
! [V_f_2,V_A_2,T_c] :
( ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_c,V_f_2,V_A_2),B_x1))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__nonempty__imp__fold1Set]) ).
fof(f_289_2,plain,
! [U_1598,U_1597,U_1596] :
( ? [U_1595] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1596,U_1598,U_1597),U_1595))
| U_1597 = c_Orderings_Obot__class_Obot(tc_fun(U_1596,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1596),U_1597)) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
! [U_1598,U_1597,U_1596] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1596,U_1598,U_1597),sK36(U_1598,U_1597,U_1596)))
| U_1597 = c_Orderings_Obot__class_Obot(tc_fun(U_1596,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1596),U_1597)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_1595,sK36(U_1598,U_1597,U_1596))],[f_289_2]) ).
fof(f_289_4,plain,
! [U_1597,U_1598,U_1596] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1596,U_1598,U_1597),sK36(U_1598,U_1597,U_1596)))
| U_1597 = c_Orderings_Obot__class_Obot(tc_fun(U_1596,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1596),U_1597)) ),
inference(definitional_conversion,[status(esa)],[f_289_3]) ).
cnf(f_289_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_1596,U_1598,U_1597),sK36(U_1598,U_1597,U_1596)))
| U_1597 = c_Orderings_Obot__class_Obot(tc_fun(U_1596,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1596),U_1597)) ),
inference(clausify,[status(thm)],[f_289_4]) ).
fof(f_290_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_290_2,plain,
! [U_1602,U_1601,U_1600,U_1599] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1599),U_1600),U_1601)),U_1602) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1599),U_1600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1599),U_1601),U_1602))
| ~ class_Groups_Oab__semigroup__mult(U_1599) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
fof(f_290_3,plain,
! [U_1599,U_1600,U_1601,U_1602] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1599),U_1600),U_1601)),U_1602) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1599),U_1600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1599),U_1601),U_1602))
| ~ class_Groups_Oab__semigroup__mult(U_1599) ),
inference(definitional_conversion,[status(esa)],[f_290_2]) ).
cnf(f_290_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1599),U_1600),U_1601)),U_1602) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1599),U_1600),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1599),U_1601),U_1602))
| ~ class_Groups_Oab__semigroup__mult(U_1599) ),
inference(clausify,[status(thm)],[f_290_3]) ).
fof(f_291_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_291_2,plain,
! [U_1605,U_1604,U_1603] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1603),U_1604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1603),U_1604),U_1605)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1603),U_1604),U_1605)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1603) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
! [U_1603,U_1604,U_1605] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1603),U_1604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1603),U_1604),U_1605)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1603),U_1604),U_1605)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1603) ),
inference(definitional_conversion,[status(esa)],[f_291_2]) ).
cnf(f_291_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1603),U_1604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1603),U_1604),U_1605)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1603),U_1604),U_1605)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1603) ),
inference(clausify,[status(thm)],[f_291_3]) ).
fof(f_292_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_292_2,plain,
! [U_1607,U_1606] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1607),U_1607) = U_1607
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1606) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_1606,U_1607] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1607),U_1607) = U_1607
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1606) ),
inference(definitional_conversion,[status(esa)],[f_292_2]) ).
cnf(f_292_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1606),U_1607),U_1607) = U_1607
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1606) ),
inference(clausify,[status(thm)],[f_292_3]) ).
fof(f_293_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_293_2,plain,
! [U_1609,U_1608] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1608),U_1609),U_1609) = U_1609
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1608) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
! [U_1608,U_1609] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1608),U_1609),U_1609) = U_1609
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1608) ),
inference(definitional_conversion,[status(esa)],[f_293_2]) ).
cnf(f_293_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1608),U_1609),U_1609) = U_1609
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1608) ),
inference(clausify,[status(thm)],[f_293_3]) ).
fof(f_294_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_294_2,plain,
! [U_1612,U_1611,U_1610] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1610),U_1612),U_1611))
| U_1611 = U_1612
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1610),U_1611),U_1612))
| ~ class_Orderings_Olinorder(U_1610) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
! [U_1610,U_1611,U_1612] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1610),U_1612),U_1611))
| U_1611 = U_1612
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1610),U_1611),U_1612))
| ~ class_Orderings_Olinorder(U_1610) ),
inference(definitional_conversion,[status(esa)],[f_294_2]) ).
cnf(f_294_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1610),U_1612),U_1611))
| U_1611 = U_1612
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1610),U_1611),U_1612))
| ~ class_Orderings_Olinorder(U_1610) ),
inference(clausify,[status(thm)],[f_294_3]) ).
fof(f_295_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_295_2,plain,
! [U_1615,U_1614,U_1613] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1613),U_1615),U_1614))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1613),U_1614),U_1615))
| ~ class_Orderings_Opreorder(U_1613) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
! [U_1613,U_1614,U_1615] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1613),U_1615),U_1614))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1613),U_1614),U_1615))
| ~ class_Orderings_Opreorder(U_1613) ),
inference(definitional_conversion,[status(esa)],[f_295_2]) ).
cnf(f_295_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1613),U_1615),U_1614))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1613),U_1614),U_1615))
| ~ class_Orderings_Opreorder(U_1613) ),
inference(clausify,[status(thm)],[f_295_3]) ).
fof(f_296_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_296_2,plain,
! [U_1619,U_1618,U_1617,U_1616] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),U_1619),U_1618))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),U_1619),U_1617))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),U_1617),U_1618))
| ~ class_Orderings_Oorder(U_1616) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
! [U_1616,U_1617,U_1618,U_1619] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),U_1619),U_1618))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),U_1619),U_1617))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),U_1617),U_1618))
| ~ class_Orderings_Oorder(U_1616) ),
inference(definitional_conversion,[status(esa)],[f_296_2]) ).
cnf(f_296_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),U_1619),U_1618))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),U_1619),U_1617))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),U_1617),U_1618))
| ~ class_Orderings_Oorder(U_1616) ),
inference(clausify,[status(thm)],[f_296_3]) ).
fof(f_297_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_297_2,plain,
! [U_1623,U_1622,U_1621,U_1620] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1620),U_1621),U_1623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1620),U_1622),U_1623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1620),U_1621),U_1622))
| ~ class_Orderings_Opreorder(U_1620) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
! [U_1621,U_1620,U_1622,U_1623] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1620),U_1621),U_1623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1620),U_1622),U_1623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1620),U_1621),U_1622))
| ~ class_Orderings_Opreorder(U_1620) ),
inference(definitional_conversion,[status(esa)],[f_297_2]) ).
cnf(f_297_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1620),U_1621),U_1623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1620),U_1622),U_1623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1620),U_1621),U_1622))
| ~ class_Orderings_Opreorder(U_1620) ),
inference(clausify,[status(thm)],[f_297_3]) ).
fof(f_298_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_298_2,plain,
! [U_1627,U_1626,U_1625,U_1624] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1624),U_1627),U_1626))
| U_1625 != U_1627
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1624),U_1625),U_1626))
| ~ class_Orderings_Oorder(U_1624) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
! [U_1625,U_1626,U_1624,U_1627] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1624),U_1627),U_1626))
| U_1625 != U_1627
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1624),U_1625),U_1626))
| ~ class_Orderings_Oorder(U_1624) ),
inference(definitional_conversion,[status(esa)],[f_298_2]) ).
cnf(f_298_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1624),U_1627),U_1626))
| U_1625 != U_1627
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1624),U_1625),U_1626))
| ~ class_Orderings_Oorder(U_1624) ),
inference(clausify,[status(thm)],[f_298_3]) ).
fof(f_299_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_299_2,plain,
! [U_1631,U_1630,U_1629,U_1628] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1628),U_1629),U_1631))
| U_1630 != U_1631
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1628),U_1629),U_1630))
| ~ class_Orderings_Oord(U_1628) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
fof(f_299_3,plain,
! [U_1631,U_1629,U_1630,U_1628] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1628),U_1629),U_1631))
| U_1630 != U_1631
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1628),U_1629),U_1630))
| ~ class_Orderings_Oord(U_1628) ),
inference(definitional_conversion,[status(esa)],[f_299_2]) ).
cnf(f_299_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1628),U_1629),U_1631))
| U_1630 != U_1631
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1628),U_1629),U_1630))
| ~ class_Orderings_Oord(U_1628) ),
inference(clausify,[status(thm)],[f_299_3]) ).
fof(f_300_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_300_2,plain,
! [U_1635,U_1634,U_1633,U_1632] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1632),U_1635),U_1633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1632),U_1635),U_1634))
| U_1633 != U_1634
| ~ class_Orderings_Oorder(U_1632) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_1635,U_1634,U_1633,U_1632] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1632),U_1635),U_1633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1632),U_1635),U_1634))
| U_1633 != U_1634
| ~ class_Orderings_Oorder(U_1632) ),
inference(definitional_conversion,[status(esa)],[f_300_2]) ).
cnf(f_300_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1632),U_1635),U_1633))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1632),U_1635),U_1634))
| U_1633 != U_1634
| ~ class_Orderings_Oorder(U_1632) ),
inference(clausify,[status(thm)],[f_300_3]) ).
fof(f_301_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_301_2,plain,
! [U_1639,U_1638,U_1637,U_1636] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1636),U_1637),U_1639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1636),U_1638),U_1639))
| U_1637 != U_1638
| ~ class_Orderings_Oord(U_1636) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
! [U_1638,U_1636,U_1637,U_1639] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1636),U_1637),U_1639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1636),U_1638),U_1639))
| U_1637 != U_1638
| ~ class_Orderings_Oord(U_1636) ),
inference(definitional_conversion,[status(esa)],[f_301_2]) ).
cnf(f_301_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1636),U_1637),U_1639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1636),U_1638),U_1639))
| U_1637 != U_1638
| ~ class_Orderings_Oord(U_1636) ),
inference(clausify,[status(thm)],[f_301_3]) ).
fof(f_302_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_302_2,plain,
! [U_1642,U_1641,U_1640] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1640),U_1642),U_1641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1640),U_1641),U_1642))
| ~ class_Orderings_Oorder(U_1640) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
fof(f_302_3,plain,
! [U_1642,U_1641,U_1640] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1640),U_1642),U_1641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1640),U_1641),U_1642))
| ~ class_Orderings_Oorder(U_1640) ),
inference(definitional_conversion,[status(esa)],[f_302_2]) ).
cnf(f_302_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1640),U_1642),U_1641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1640),U_1641),U_1642))
| ~ class_Orderings_Oorder(U_1640) ),
inference(clausify,[status(thm)],[f_302_3]) ).
fof(f_303_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_303_2,plain,
! [U_1645,U_1644,U_1643] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),U_1645),U_1644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),U_1644),U_1645))
| ~ class_Orderings_Opreorder(U_1643) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
fof(f_303_3,plain,
! [U_1643,U_1644,U_1645] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),U_1645),U_1644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),U_1644),U_1645))
| ~ class_Orderings_Opreorder(U_1643) ),
inference(definitional_conversion,[status(esa)],[f_303_2]) ).
cnf(f_303_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),U_1645),U_1644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),U_1644),U_1645))
| ~ class_Orderings_Opreorder(U_1643) ),
inference(clausify,[status(thm)],[f_303_3]) ).
fof(f_304_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_304_2,plain,
! [U_1648,U_1647,U_1646] :
( U_1648 != U_1647
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1646),U_1647),U_1648))
| ~ class_Orderings_Oorder(U_1646) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
! [U_1646,U_1647,U_1648] :
( U_1648 != U_1647
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1646),U_1647),U_1648))
| ~ class_Orderings_Oorder(U_1646) ),
inference(definitional_conversion,[status(esa)],[f_304_2]) ).
cnf(f_304_4,plain,
( U_1648 != U_1647
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1646),U_1647),U_1648))
| ~ class_Orderings_Oorder(U_1646) ),
inference(clausify,[status(thm)],[f_304_3]) ).
fof(f_305_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_305_2,plain,
! [U_1651,U_1650,U_1649] :
( U_1650 != U_1651
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1649),U_1650),U_1651))
| ~ class_Orderings_Oorder(U_1649) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
! [U_1649,U_1650,U_1651] :
( U_1650 != U_1651
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1649),U_1650),U_1651))
| ~ class_Orderings_Oorder(U_1649) ),
inference(definitional_conversion,[status(esa)],[f_305_2]) ).
cnf(f_305_4,plain,
( U_1650 != U_1651
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1649),U_1650),U_1651))
| ~ class_Orderings_Oorder(U_1649) ),
inference(clausify,[status(thm)],[f_305_3]) ).
fof(f_306_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_306_2,plain,
! [U_1654,U_1653,U_1652] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1652),U_1654),U_1653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1652),U_1653),U_1654))
| ~ class_Orderings_Opreorder(U_1652) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
fof(f_306_3,plain,
! [U_1652,U_1653,U_1654] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1652),U_1654),U_1653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1652),U_1653),U_1654))
| ~ class_Orderings_Opreorder(U_1652) ),
inference(definitional_conversion,[status(esa)],[f_306_2]) ).
cnf(f_306_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1652),U_1654),U_1653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1652),U_1653),U_1654))
| ~ class_Orderings_Opreorder(U_1652) ),
inference(clausify,[status(thm)],[f_306_3]) ).
fof(f_307_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_307_2,plain,
! [U_1657,U_1656,U_1655] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1655),U_1657),U_1656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1655),U_1656),U_1657))
| ~ class_Orderings_Opreorder(U_1655) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
fof(f_307_3,plain,
! [U_1655,U_1656,U_1657] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1655),U_1657),U_1656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1655),U_1656),U_1657))
| ~ class_Orderings_Opreorder(U_1655) ),
inference(definitional_conversion,[status(esa)],[f_307_2]) ).
cnf(f_307_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1655),U_1657),U_1656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1655),U_1656),U_1657))
| ~ class_Orderings_Opreorder(U_1655) ),
inference(clausify,[status(thm)],[f_307_3]) ).
fof(f_308_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_308_2,plain,
! [U_1660,U_1659,U_1658] :
( U_1659 != U_1660
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1658),U_1659),U_1660))
| ~ class_Orderings_Oorder(U_1658) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
! [U_1658,U_1659,U_1660] :
( U_1659 != U_1660
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1658),U_1659),U_1660))
| ~ class_Orderings_Oorder(U_1658) ),
inference(definitional_conversion,[status(esa)],[f_308_2]) ).
cnf(f_308_4,plain,
( U_1659 != U_1660
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1658),U_1659),U_1660))
| ~ class_Orderings_Oorder(U_1658) ),
inference(clausify,[status(thm)],[f_308_3]) ).
fof(f_309_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_309_2,plain,
! [U_1663,U_1662,U_1661] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1663),U_1662))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1662),U_1663))
| U_1662 = U_1663
| ~ class_Orderings_Olinorder(U_1661) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
! [U_1661,U_1662,U_1663] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1663),U_1662))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1662),U_1663))
| U_1662 = U_1663
| ~ class_Orderings_Olinorder(U_1661) ),
inference(definitional_conversion,[status(esa)],[f_309_2]) ).
cnf(f_309_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1663),U_1662))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1661),U_1662),U_1663))
| U_1662 = U_1663
| ~ class_Orderings_Olinorder(U_1661) ),
inference(clausify,[status(thm)],[f_309_3]) ).
fof(f_310_1,plain,
! [V_x_2,V_y_2,T_c] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),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_c),V_x_2),V_y_2)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(f_310_2,plain,
! [U_1666,U_1665,U_1664] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1666),U_1665))
| U_1666 != U_1665 )
& ( U_1666 = U_1665
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1666),U_1665)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1665),U_1666))
| ~ class_Orderings_Olinorder(U_1664) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
( ! [U_1665,U_1664,U_1666] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1666),U_1665))
| U_1666 != U_1665
| ~ sP65(U_1665,U_1664,U_1666) )
& ! [U_1665,U_1664,U_1666] :
( U_1666 = U_1665
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1666),U_1665))
| ~ sP65(U_1665,U_1664,U_1666) )
& ! [U_1665,U_1664,U_1666] :
( sP65(U_1665,U_1664,U_1666)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1665),U_1666))
| ~ class_Orderings_Olinorder(U_1664) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_310_2]) ).
cnf(f_310_4,plain,
( sP65(U_1665,U_1664,U_1666)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1665),U_1666))
| ~ class_Orderings_Olinorder(U_1664) ),
inference(clausify,[status(thm)],[f_310_3]) ).
cnf(f_310_5,plain,
( U_1666 = U_1665
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1666),U_1665))
| ~ sP65(U_1665,U_1664,U_1666) ),
inference(clausify,[status(thm)],[f_310_3]) ).
cnf(f_310_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1664),U_1666),U_1665))
| U_1666 != U_1665
| ~ sP65(U_1665,U_1664,U_1666) ),
inference(clausify,[status(thm)],[f_310_3]) ).
fof(f_311_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_311_2,plain,
! [U_1669,U_1668,U_1667] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1667),U_1669),U_1668))
| U_1668 = U_1669
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1667),U_1668),U_1669))
| ~ class_Orderings_Olinorder(U_1667) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
fof(f_311_3,plain,
! [U_1669,U_1668,U_1667] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1667),U_1669),U_1668))
| U_1668 = U_1669
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1667),U_1668),U_1669))
| ~ class_Orderings_Olinorder(U_1667) ),
inference(definitional_conversion,[status(esa)],[f_311_2]) ).
cnf(f_311_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1667),U_1669),U_1668))
| U_1668 = U_1669
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1667),U_1668),U_1669))
| ~ class_Orderings_Olinorder(U_1667) ),
inference(clausify,[status(thm)],[f_311_3]) ).
fof(f_312_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
| ( V_x_2 != V_y_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2)) ) )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(f_312_2,plain,
! [U_1672,U_1671,U_1670] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1670),U_1671),U_1672))
| ( U_1671 != U_1672
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1670),U_1672),U_1671)) ) )
& ( U_1671 = U_1672
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1670),U_1672),U_1671))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1670),U_1671),U_1672)) ) )
| ~ class_Orderings_Olinorder(U_1670) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
fof(f_312_3,plain,
( ! [U_1670,U_1671,U_1672] :
( U_1671 != U_1672
| ~ sP66(U_1670,U_1671,U_1672) )
& ! [U_1670,U_1671,U_1672] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1670),U_1672),U_1671))
| ~ sP66(U_1670,U_1671,U_1672) )
& ! [U_1670,U_1671,U_1672] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1670),U_1671),U_1672))
| sP66(U_1670,U_1671,U_1672)
| ~ sP67(U_1670,U_1671,U_1672) )
& ! [U_1670,U_1671,U_1672] :
( U_1671 = U_1672
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1670),U_1672),U_1671))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1670),U_1671),U_1672))
| ~ sP67(U_1670,U_1671,U_1672) )
& ! [U_1670,U_1671,U_1672] :
( sP67(U_1670,U_1671,U_1672)
| ~ class_Orderings_Olinorder(U_1670) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66,sP67])],[f_312_2]) ).
cnf(f_312_4,plain,
( sP67(U_1670,U_1671,U_1672)
| ~ class_Orderings_Olinorder(U_1670) ),
inference(clausify,[status(thm)],[f_312_3]) ).
cnf(f_312_5,plain,
( U_1671 = U_1672
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1670),U_1672),U_1671))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1670),U_1671),U_1672))
| ~ sP67(U_1670,U_1671,U_1672) ),
inference(clausify,[status(thm)],[f_312_3]) ).
cnf(f_312_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1670),U_1671),U_1672))
| sP66(U_1670,U_1671,U_1672)
| ~ sP67(U_1670,U_1671,U_1672) ),
inference(clausify,[status(thm)],[f_312_3]) ).
cnf(f_312_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1670),U_1672),U_1671))
| ~ sP66(U_1670,U_1671,U_1672) ),
inference(clausify,[status(thm)],[f_312_3]) ).
cnf(f_312_8,plain,
( U_1671 != U_1672
| ~ sP66(U_1670,U_1671,U_1672) ),
inference(clausify,[status(thm)],[f_312_3]) ).
fof(f_313_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( V_x_2 != V_y_2
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
| V_x_2 = V_y_2 ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).
fof(f_313_2,plain,
! [U_1675,U_1674,U_1673] :
( ( ( U_1674 != U_1675
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1675),U_1674))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1674),U_1675)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1675),U_1674))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1674),U_1675))
| U_1674 = U_1675 ) )
| ~ class_Orderings_Olinorder(U_1673) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
fof(f_313_3,plain,
( ! [U_1675,U_1673,U_1674] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1675),U_1674))
| ~ sP68(U_1675,U_1673,U_1674) )
& ! [U_1675,U_1673,U_1674] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1674),U_1675))
| ~ sP68(U_1675,U_1673,U_1674) )
& ! [U_1675,U_1673,U_1674] :
( U_1674 != U_1675
| sP68(U_1675,U_1673,U_1674)
| ~ sP69(U_1675,U_1673,U_1674) )
& ! [U_1675,U_1673,U_1674] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1675),U_1674))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1674),U_1675))
| U_1674 = U_1675
| ~ sP69(U_1675,U_1673,U_1674) )
& ! [U_1675,U_1673,U_1674] :
( sP69(U_1675,U_1673,U_1674)
| ~ class_Orderings_Olinorder(U_1673) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68,sP69])],[f_313_2]) ).
cnf(f_313_4,plain,
( sP69(U_1675,U_1673,U_1674)
| ~ class_Orderings_Olinorder(U_1673) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1675),U_1674))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1674),U_1675))
| U_1674 = U_1675
| ~ sP69(U_1675,U_1673,U_1674) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_6,plain,
( U_1674 != U_1675
| sP68(U_1675,U_1673,U_1674)
| ~ sP69(U_1675,U_1673,U_1674) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1674),U_1675))
| ~ sP68(U_1675,U_1673,U_1674) ),
inference(clausify,[status(thm)],[f_313_3]) ).
cnf(f_313_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1673),U_1675),U_1674))
| ~ sP68(U_1675,U_1673,U_1674) ),
inference(clausify,[status(thm)],[f_313_3]) ).
fof(f_314_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_314_2,plain,
! [U_1677,U_1676] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1676),U_1677),U_1677))
| ~ class_Orderings_Opreorder(U_1676) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
fof(f_314_3,plain,
! [U_1676,U_1677] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1676),U_1677),U_1677))
| ~ class_Orderings_Opreorder(U_1676) ),
inference(definitional_conversion,[status(esa)],[f_314_2]) ).
cnf(f_314_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1676),U_1677),U_1677))
| ~ class_Orderings_Opreorder(U_1676) ),
inference(clausify,[status(thm)],[f_314_3]) ).
fof(f_315_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__trans]) ).
fof(f_315_2,plain,
! [U_1681,U_1680,U_1679,U_1678] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1678,tc_HOL_Obool)),U_1679),U_1681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1678,tc_HOL_Obool)),U_1680),U_1681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1678,tc_HOL_Obool)),U_1679),U_1680)) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
fof(f_315_3,plain,
! [U_1678,U_1680,U_1679,U_1681] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1678,tc_HOL_Obool)),U_1679),U_1681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1678,tc_HOL_Obool)),U_1680),U_1681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1678,tc_HOL_Obool)),U_1679),U_1680)) ),
inference(definitional_conversion,[status(esa)],[f_315_2]) ).
cnf(f_315_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1678,tc_HOL_Obool)),U_1679),U_1681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1678,tc_HOL_Obool)),U_1680),U_1681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1678,tc_HOL_Obool)),U_1679),U_1680)) ),
inference(clausify,[status(thm)],[f_315_3]) ).
fof(f_316_1,plain,
! [V_g_2,V_f_2,T_c,T_d] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,T_d)),V_f_2),V_g_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_g_2),V_f_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_g_2),V_f_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,T_d)),V_f_2),V_g_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,T_d)),V_f_2),V_g_2)) ) )
| ~ class_Orderings_Oord(T_d) ),
inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).
fof(f_316_2,plain,
! [U_1685,U_1684,U_1683,U_1682] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1683,U_1682)),U_1684),U_1685))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1683,U_1682)),U_1685),U_1684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1683,U_1682)),U_1684),U_1685)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1683,U_1682)),U_1685),U_1684))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1683,U_1682)),U_1684),U_1685)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1683,U_1682)),U_1684),U_1685)) ) )
| ~ class_Orderings_Oord(U_1682) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
fof(f_316_3,plain,
( ! [U_1683,U_1682,U_1684,U_1685] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1683,U_1682)),U_1685),U_1684))
| ~ sP70(U_1683,U_1682,U_1684,U_1685) )
& ! [U_1683,U_1682,U_1684,U_1685] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1683,U_1682)),U_1684),U_1685))
| ~ sP70(U_1683,U_1682,U_1684,U_1685) )
& ! [U_1683,U_1682,U_1684,U_1685] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1683,U_1682)),U_1684),U_1685))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1683,U_1682)),U_1685),U_1684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1683,U_1682)),U_1684),U_1685))
| ~ sP71(U_1683,U_1682,U_1684,U_1685) )
& ! [U_1683,U_1682,U_1684,U_1685] :
( sP70(U_1683,U_1682,U_1684,U_1685)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1683,U_1682)),U_1684),U_1685))
| ~ sP71(U_1683,U_1682,U_1684,U_1685) )
& ! [U_1683,U_1682,U_1684,U_1685] :
( sP71(U_1683,U_1682,U_1684,U_1685)
| ~ class_Orderings_Oord(U_1682) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP70,sP71])],[f_316_2]) ).
cnf(f_316_4,plain,
( sP71(U_1683,U_1682,U_1684,U_1685)
| ~ class_Orderings_Oord(U_1682) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_5,plain,
( sP70(U_1683,U_1682,U_1684,U_1685)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1683,U_1682)),U_1684),U_1685))
| ~ sP71(U_1683,U_1682,U_1684,U_1685) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1683,U_1682)),U_1684),U_1685))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1683,U_1682)),U_1685),U_1684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1683,U_1682)),U_1684),U_1685))
| ~ sP71(U_1683,U_1682,U_1684,U_1685) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1683,U_1682)),U_1684),U_1685))
| ~ sP70(U_1683,U_1682,U_1684,U_1685) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1683,U_1682)),U_1685),U_1684))
| ~ sP70(U_1683,U_1682,U_1684,U_1685) ),
inference(clausify,[status(thm)],[f_316_3]) ).
fof(f_317_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_317_2,plain,
! [U_1689,U_1688,U_1687,U_1686] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1686),U_1689),U_1688))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1686),U_1689),U_1687))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1686),U_1687),U_1688))
| ~ class_Orderings_Oorder(U_1686) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
fof(f_317_3,plain,
! [U_1689,U_1687,U_1686,U_1688] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1686),U_1689),U_1688))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1686),U_1689),U_1687))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1686),U_1687),U_1688))
| ~ class_Orderings_Oorder(U_1686) ),
inference(definitional_conversion,[status(esa)],[f_317_2]) ).
cnf(f_317_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1686),U_1689),U_1688))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1686),U_1689),U_1687))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1686),U_1687),U_1688))
| ~ class_Orderings_Oorder(U_1686) ),
inference(clausify,[status(thm)],[f_317_3]) ).
fof(f_318_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_318_2,plain,
! [U_1693,U_1692,U_1691,U_1690] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1691),U_1693))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1692),U_1693))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1690),U_1691),U_1692))
| ~ class_Orderings_Opreorder(U_1690) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
fof(f_318_3,plain,
! [U_1690,U_1691,U_1692,U_1693] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1691),U_1693))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1692),U_1693))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1690),U_1691),U_1692))
| ~ class_Orderings_Opreorder(U_1690) ),
inference(definitional_conversion,[status(esa)],[f_318_2]) ).
cnf(f_318_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1691),U_1693))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1692),U_1693))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1690),U_1691),U_1692))
| ~ class_Orderings_Opreorder(U_1690) ),
inference(clausify,[status(thm)],[f_318_3]) ).
fof(f_319_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_319_2,plain,
! [U_1697,U_1696,U_1695,U_1694] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1694),U_1697),U_1696))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1694),U_1697),U_1695))
| ~ 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_319_1]) ).
fof(f_319_3,plain,
! [U_1694,U_1695,U_1696,U_1697] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1694),U_1697),U_1696))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1694),U_1697),U_1695))
| ~ 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_319_2]) ).
cnf(f_319_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1694),U_1697),U_1696))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1694),U_1697),U_1695))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1694),U_1695),U_1696))
| ~ class_Orderings_Oorder(U_1694) ),
inference(clausify,[status(thm)],[f_319_3]) ).
fof(f_320_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_320_2,plain,
! [U_1701,U_1700,U_1699,U_1698] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1698),U_1699),U_1701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1698),U_1700),U_1701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1698),U_1699),U_1700))
| ~ class_Orderings_Opreorder(U_1698) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
fof(f_320_3,plain,
! [U_1699,U_1698,U_1700,U_1701] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1698),U_1699),U_1701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1698),U_1700),U_1701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1698),U_1699),U_1700))
| ~ class_Orderings_Opreorder(U_1698) ),
inference(definitional_conversion,[status(esa)],[f_320_2]) ).
cnf(f_320_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1698),U_1699),U_1701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1698),U_1700),U_1701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1698),U_1699),U_1700))
| ~ class_Orderings_Opreorder(U_1698) ),
inference(clausify,[status(thm)],[f_320_3]) ).
fof(f_321_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_321_2,plain,
! [U_1704,U_1703,U_1702] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1702),U_1703),U_1704))
| U_1704 = U_1703
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1702),U_1703),U_1704))
| ~ class_Orderings_Oorder(U_1702) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
fof(f_321_3,plain,
! [U_1702,U_1703,U_1704] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1702),U_1703),U_1704))
| U_1704 = U_1703
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1702),U_1703),U_1704))
| ~ class_Orderings_Oorder(U_1702) ),
inference(definitional_conversion,[status(esa)],[f_321_2]) ).
cnf(f_321_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1702),U_1703),U_1704))
| U_1704 = U_1703
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1702),U_1703),U_1704))
| ~ class_Orderings_Oorder(U_1702) ),
inference(clausify,[status(thm)],[f_321_3]) ).
fof(f_322_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_322_2,plain,
! [U_1707,U_1706,U_1705] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1705),U_1706),U_1707))
| U_1706 = U_1707
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1705),U_1706),U_1707))
| ~ class_Orderings_Oorder(U_1705) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
! [U_1705,U_1706,U_1707] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1705),U_1706),U_1707))
| U_1706 = U_1707
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1705),U_1706),U_1707))
| ~ class_Orderings_Oorder(U_1705) ),
inference(definitional_conversion,[status(esa)],[f_322_2]) ).
cnf(f_322_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1705),U_1706),U_1707))
| U_1706 = U_1707
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1705),U_1706),U_1707))
| ~ class_Orderings_Oorder(U_1705) ),
inference(clausify,[status(thm)],[f_322_3]) ).
fof(f_323_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_323_2,plain,
! [U_1710,U_1709,U_1708] :
( U_1709 = U_1710
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1708),U_1709),U_1710))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1708),U_1709),U_1710))
| ~ class_Orderings_Oorder(U_1708) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
fof(f_323_3,plain,
! [U_1708,U_1709,U_1710] :
( U_1709 = U_1710
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1708),U_1709),U_1710))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1708),U_1709),U_1710))
| ~ class_Orderings_Oorder(U_1708) ),
inference(definitional_conversion,[status(esa)],[f_323_2]) ).
cnf(f_323_4,plain,
( U_1709 = U_1710
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1708),U_1709),U_1710))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1708),U_1709),U_1710))
| ~ class_Orderings_Oorder(U_1708) ),
inference(clausify,[status(thm)],[f_323_3]) ).
fof(f_324_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),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_c),V_x_2),V_y_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(f_324_2,plain,
! [U_1713,U_1712,U_1711] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1711),U_1712),U_1713))
| U_1712 != U_1713 )
& ( U_1712 = U_1713
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1711),U_1712),U_1713)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1711),U_1712),U_1713))
| ~ class_Orderings_Olinorder(U_1711) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
( ! [U_1711,U_1712,U_1713] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1711),U_1712),U_1713))
| U_1712 != U_1713
| ~ sP72(U_1711,U_1712,U_1713) )
& ! [U_1711,U_1712,U_1713] :
( U_1712 = U_1713
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1711),U_1712),U_1713))
| ~ sP72(U_1711,U_1712,U_1713) )
& ! [U_1711,U_1712,U_1713] :
( sP72(U_1711,U_1712,U_1713)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1711),U_1712),U_1713))
| ~ class_Orderings_Olinorder(U_1711) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_324_2]) ).
cnf(f_324_4,plain,
( sP72(U_1711,U_1712,U_1713)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1711),U_1712),U_1713))
| ~ class_Orderings_Olinorder(U_1711) ),
inference(clausify,[status(thm)],[f_324_3]) ).
cnf(f_324_5,plain,
( U_1712 = U_1713
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1711),U_1712),U_1713))
| ~ sP72(U_1711,U_1712,U_1713) ),
inference(clausify,[status(thm)],[f_324_3]) ).
cnf(f_324_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1711),U_1712),U_1713))
| U_1712 != U_1713
| ~ sP72(U_1711,U_1712,U_1713) ),
inference(clausify,[status(thm)],[f_324_3]) ).
fof(f_325_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_325_2,plain,
! [U_1716,U_1715,U_1714] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1714),U_1715),U_1716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1714),U_1715),U_1716))
| ~ class_Orderings_Opreorder(U_1714) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
fof(f_325_3,plain,
! [U_1716,U_1715,U_1714] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1714),U_1715),U_1716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1714),U_1715),U_1716))
| ~ class_Orderings_Opreorder(U_1714) ),
inference(definitional_conversion,[status(esa)],[f_325_2]) ).
cnf(f_325_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1714),U_1715),U_1716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1714),U_1715),U_1716))
| ~ class_Orderings_Opreorder(U_1714) ),
inference(clausify,[status(thm)],[f_325_3]) ).
fof(f_326_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_326_2,plain,
! [U_1719,U_1718,U_1717] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1717),U_1719),U_1718))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1717),U_1718),U_1719))
| ~ class_Orderings_Olinorder(U_1717) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
! [U_1718,U_1717,U_1719] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1717),U_1719),U_1718))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1717),U_1718),U_1719))
| ~ class_Orderings_Olinorder(U_1717) ),
inference(definitional_conversion,[status(esa)],[f_326_2]) ).
cnf(f_326_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1717),U_1719),U_1718))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1717),U_1718),U_1719))
| ~ class_Orderings_Olinorder(U_1717) ),
inference(clausify,[status(thm)],[f_326_3]) ).
fof(f_327_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_327_2,plain,
! [U_1722,U_1721,U_1720] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1722),U_1721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1720),U_1722),U_1721))
| U_1721 = U_1722
| ~ class_Orderings_Oorder(U_1720) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
fof(f_327_3,plain,
! [U_1720,U_1721,U_1722] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1722),U_1721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1720),U_1722),U_1721))
| U_1721 = U_1722
| ~ class_Orderings_Oorder(U_1720) ),
inference(definitional_conversion,[status(esa)],[f_327_2]) ).
cnf(f_327_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1722),U_1721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1720),U_1722),U_1721))
| U_1721 = U_1722
| ~ class_Orderings_Oorder(U_1720) ),
inference(clausify,[status(thm)],[f_327_3]) ).
fof(f_328_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_328_2,plain,
! [U_1725,U_1724,U_1723] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1723),U_1724),U_1725))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1723),U_1724),U_1725))
| U_1724 = U_1725
| ~ class_Orderings_Oorder(U_1723) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
fof(f_328_3,plain,
! [U_1724,U_1723,U_1725] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1723),U_1724),U_1725))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1723),U_1724),U_1725))
| U_1724 = U_1725
| ~ class_Orderings_Oorder(U_1723) ),
inference(definitional_conversion,[status(esa)],[f_328_2]) ).
cnf(f_328_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1723),U_1724),U_1725))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1723),U_1724),U_1725))
| U_1724 = U_1725
| ~ class_Orderings_Oorder(U_1723) ),
inference(clausify,[status(thm)],[f_328_3]) ).
fof(f_329_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),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_c),V_x_2),V_y_2)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(f_329_2,plain,
! [U_1728,U_1727,U_1726] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1726),U_1727),U_1728))
| U_1727 != U_1728 )
& ( U_1727 = U_1728
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1726),U_1727),U_1728)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1726),U_1727),U_1728))
| ~ class_Orderings_Olinorder(U_1726) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
( ! [U_1726,U_1727,U_1728] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1726),U_1727),U_1728))
| U_1727 != U_1728
| ~ sP73(U_1726,U_1727,U_1728) )
& ! [U_1726,U_1727,U_1728] :
( U_1727 = U_1728
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1726),U_1727),U_1728))
| ~ sP73(U_1726,U_1727,U_1728) )
& ! [U_1726,U_1727,U_1728] :
( sP73(U_1726,U_1727,U_1728)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1726),U_1727),U_1728))
| ~ class_Orderings_Olinorder(U_1726) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_329_2]) ).
cnf(f_329_4,plain,
( sP73(U_1726,U_1727,U_1728)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1726),U_1727),U_1728))
| ~ class_Orderings_Olinorder(U_1726) ),
inference(clausify,[status(thm)],[f_329_3]) ).
cnf(f_329_5,plain,
( U_1727 = U_1728
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1726),U_1727),U_1728))
| ~ sP73(U_1726,U_1727,U_1728) ),
inference(clausify,[status(thm)],[f_329_3]) ).
cnf(f_329_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1726),U_1727),U_1728))
| U_1727 != U_1728
| ~ sP73(U_1726,U_1727,U_1728) ),
inference(clausify,[status(thm)],[f_329_3]) ).
fof(f_330_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_330_2,plain,
! [U_1731,U_1730,U_1729] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1729),U_1731),U_1730))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1729),U_1730),U_1731))
| ~ class_Orderings_Olinorder(U_1729) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
! [U_1731,U_1730,U_1729] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1729),U_1731),U_1730))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1729),U_1730),U_1731))
| ~ class_Orderings_Olinorder(U_1729) ),
inference(definitional_conversion,[status(esa)],[f_330_2]) ).
cnf(f_330_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1729),U_1731),U_1730))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1729),U_1730),U_1731))
| ~ class_Orderings_Olinorder(U_1729) ),
inference(clausify,[status(thm)],[f_330_3]) ).
fof(f_331_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_331_2,plain,
! [U_1734,U_1733,U_1732] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1732),U_1734),U_1733))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1732),U_1733),U_1734))
| ~ class_Orderings_Olinorder(U_1732) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
fof(f_331_3,plain,
! [U_1732,U_1733,U_1734] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1732),U_1734),U_1733))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1732),U_1733),U_1734))
| ~ class_Orderings_Olinorder(U_1732) ),
inference(definitional_conversion,[status(esa)],[f_331_2]) ).
cnf(f_331_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1732),U_1734),U_1733))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1732),U_1733),U_1734))
| ~ class_Orderings_Olinorder(U_1732) ),
inference(clausify,[status(thm)],[f_331_3]) ).
fof(f_332_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
| ( V_x_2 != V_y_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) ) )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).
fof(f_332_2,plain,
! [U_1737,U_1736,U_1735] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1735),U_1736),U_1737))
| ( U_1736 != U_1737
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1735),U_1736),U_1737)) ) )
& ( U_1736 = U_1737
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1735),U_1736),U_1737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1735),U_1736),U_1737)) ) )
| ~ class_Orderings_Oorder(U_1735) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
fof(f_332_3,plain,
( ! [U_1735,U_1736,U_1737] :
( U_1736 != U_1737
| ~ sP74(U_1735,U_1736,U_1737) )
& ! [U_1735,U_1736,U_1737] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1735),U_1736),U_1737))
| ~ sP74(U_1735,U_1736,U_1737) )
& ! [U_1735,U_1736,U_1737] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1735),U_1736),U_1737))
| sP74(U_1735,U_1736,U_1737)
| ~ sP75(U_1735,U_1736,U_1737) )
& ! [U_1735,U_1736,U_1737] :
( U_1736 = U_1737
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1735),U_1736),U_1737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1735),U_1736),U_1737))
| ~ sP75(U_1735,U_1736,U_1737) )
& ! [U_1735,U_1736,U_1737] :
( sP75(U_1735,U_1736,U_1737)
| ~ class_Orderings_Oorder(U_1735) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74,sP75])],[f_332_2]) ).
cnf(f_332_4,plain,
( sP75(U_1735,U_1736,U_1737)
| ~ class_Orderings_Oorder(U_1735) ),
inference(clausify,[status(thm)],[f_332_3]) ).
cnf(f_332_5,plain,
( U_1736 = U_1737
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1735),U_1736),U_1737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1735),U_1736),U_1737))
| ~ sP75(U_1735,U_1736,U_1737) ),
inference(clausify,[status(thm)],[f_332_3]) ).
cnf(f_332_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1735),U_1736),U_1737))
| sP74(U_1735,U_1736,U_1737)
| ~ sP75(U_1735,U_1736,U_1737) ),
inference(clausify,[status(thm)],[f_332_3]) ).
cnf(f_332_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1735),U_1736),U_1737))
| ~ sP74(U_1735,U_1736,U_1737) ),
inference(clausify,[status(thm)],[f_332_3]) ).
cnf(f_332_8,plain,
( U_1736 != U_1737
| ~ sP74(U_1735,U_1736,U_1737) ),
inference(clausify,[status(thm)],[f_332_3]) ).
fof(f_333_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Opreorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).
fof(f_333_2,plain,
! [U_1740,U_1739,U_1738] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1738),U_1739),U_1740))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1738),U_1740),U_1739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1738),U_1739),U_1740)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1738),U_1740),U_1739))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1738),U_1739),U_1740)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1738),U_1739),U_1740)) ) )
| ~ class_Orderings_Opreorder(U_1738) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
fof(f_333_3,plain,
( ! [U_1740,U_1739,U_1738] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1738),U_1740),U_1739))
| ~ sP76(U_1740,U_1739,U_1738) )
& ! [U_1740,U_1739,U_1738] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1738),U_1739),U_1740))
| ~ sP76(U_1740,U_1739,U_1738) )
& ! [U_1740,U_1739,U_1738] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1738),U_1739),U_1740))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1738),U_1740),U_1739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1738),U_1739),U_1740))
| ~ sP77(U_1740,U_1739,U_1738) )
& ! [U_1740,U_1739,U_1738] :
( sP76(U_1740,U_1739,U_1738)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1738),U_1739),U_1740))
| ~ sP77(U_1740,U_1739,U_1738) )
& ! [U_1740,U_1739,U_1738] :
( sP77(U_1740,U_1739,U_1738)
| ~ class_Orderings_Opreorder(U_1738) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76,sP77])],[f_333_2]) ).
cnf(f_333_4,plain,
( sP77(U_1740,U_1739,U_1738)
| ~ class_Orderings_Opreorder(U_1738) ),
inference(clausify,[status(thm)],[f_333_3]) ).
cnf(f_333_5,plain,
( sP76(U_1740,U_1739,U_1738)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1738),U_1739),U_1740))
| ~ sP77(U_1740,U_1739,U_1738) ),
inference(clausify,[status(thm)],[f_333_3]) ).
cnf(f_333_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1738),U_1739),U_1740))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1738),U_1740),U_1739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1738),U_1739),U_1740))
| ~ sP77(U_1740,U_1739,U_1738) ),
inference(clausify,[status(thm)],[f_333_3]) ).
cnf(f_333_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1738),U_1739),U_1740))
| ~ sP76(U_1740,U_1739,U_1738) ),
inference(clausify,[status(thm)],[f_333_3]) ).
cnf(f_333_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1738),U_1740),U_1739))
| ~ sP76(U_1740,U_1739,U_1738) ),
inference(clausify,[status(thm)],[f_333_3]) ).
fof(f_334_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
| V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) )
& ( ( V_x_2 != V_y_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).
fof(f_334_2,plain,
! [U_1743,U_1742,U_1741] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1741),U_1742),U_1743))
| U_1742 = U_1743
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1741),U_1742),U_1743)) )
& ( ( U_1742 != U_1743
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1741),U_1742),U_1743)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1741),U_1742),U_1743)) ) )
| ~ class_Orderings_Oorder(U_1741) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
( ! [U_1742,U_1741,U_1743] :
( U_1742 != U_1743
| ~ sP78(U_1742,U_1741,U_1743) )
& ! [U_1742,U_1741,U_1743] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1741),U_1742),U_1743))
| ~ sP78(U_1742,U_1741,U_1743) )
& ! [U_1742,U_1741,U_1743] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1741),U_1742),U_1743))
| U_1742 = U_1743
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1741),U_1742),U_1743))
| ~ sP79(U_1742,U_1741,U_1743) )
& ! [U_1742,U_1741,U_1743] :
( sP78(U_1742,U_1741,U_1743)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1741),U_1742),U_1743))
| ~ sP79(U_1742,U_1741,U_1743) )
& ! [U_1742,U_1741,U_1743] :
( sP79(U_1742,U_1741,U_1743)
| ~ class_Orderings_Oorder(U_1741) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78,sP79])],[f_334_2]) ).
cnf(f_334_4,plain,
( sP79(U_1742,U_1741,U_1743)
| ~ class_Orderings_Oorder(U_1741) ),
inference(clausify,[status(thm)],[f_334_3]) ).
cnf(f_334_5,plain,
( sP78(U_1742,U_1741,U_1743)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1741),U_1742),U_1743))
| ~ sP79(U_1742,U_1741,U_1743) ),
inference(clausify,[status(thm)],[f_334_3]) ).
cnf(f_334_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1741),U_1742),U_1743))
| U_1742 = U_1743
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1741),U_1742),U_1743))
| ~ sP79(U_1742,U_1741,U_1743) ),
inference(clausify,[status(thm)],[f_334_3]) ).
cnf(f_334_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1741),U_1742),U_1743))
| ~ sP78(U_1742,U_1741,U_1743) ),
inference(clausify,[status(thm)],[f_334_3]) ).
cnf(f_334_8,plain,
( U_1742 != U_1743
| ~ sP78(U_1742,U_1741,U_1743) ),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_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_335_2,plain,
! [U_1746,U_1745,U_1744] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1744),U_1746),U_1745))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1744),U_1745),U_1746))
| ~ class_Orderings_Olinorder(U_1744) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
fof(f_335_3,plain,
! [U_1746,U_1744,U_1745] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1744),U_1746),U_1745))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1744),U_1745),U_1746))
| ~ class_Orderings_Olinorder(U_1744) ),
inference(definitional_conversion,[status(esa)],[f_335_2]) ).
cnf(f_335_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1744),U_1746),U_1745))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1744),U_1745),U_1746))
| ~ class_Orderings_Olinorder(U_1744) ),
inference(clausify,[status(thm)],[f_335_3]) ).
fof(f_336_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).
fof(f_336_2,plain,
! [U_1749,U_1748,U_1747] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1747),U_1748),U_1749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1747),U_1749),U_1748)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1747),U_1749),U_1748))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1747),U_1748),U_1749)) ) )
| ~ class_Orderings_Olinorder(U_1747) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
fof(f_336_3,plain,
( ! [U_1747,U_1748,U_1749] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1747),U_1748),U_1749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1747),U_1749),U_1748))
| ~ sP80(U_1747,U_1748,U_1749) )
& ! [U_1747,U_1748,U_1749] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1747),U_1749),U_1748))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1747),U_1748),U_1749))
| ~ sP80(U_1747,U_1748,U_1749) )
& ! [U_1747,U_1748,U_1749] :
( sP80(U_1747,U_1748,U_1749)
| ~ class_Orderings_Olinorder(U_1747) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_336_2]) ).
cnf(f_336_4,plain,
( sP80(U_1747,U_1748,U_1749)
| ~ class_Orderings_Olinorder(U_1747) ),
inference(clausify,[status(thm)],[f_336_3]) ).
cnf(f_336_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1747),U_1749),U_1748))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1747),U_1748),U_1749))
| ~ sP80(U_1747,U_1748,U_1749) ),
inference(clausify,[status(thm)],[f_336_3]) ).
cnf(f_336_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1747),U_1748),U_1749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1747),U_1749),U_1748))
| ~ sP80(U_1747,U_1748,U_1749) ),
inference(clausify,[status(thm)],[f_336_3]) ).
fof(f_337_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).
fof(f_337_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_337_1]) ).
fof(f_337_3,plain,
( ! [U_1750,U_1751,U_1752] :
( ~ 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))
| ~ sP81(U_1750,U_1751,U_1752) )
& ! [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(U_1750),U_1751),U_1752))
| ~ sP81(U_1750,U_1751,U_1752) )
& ! [U_1750,U_1751,U_1752] :
( sP81(U_1750,U_1751,U_1752)
| ~ class_Orderings_Olinorder(U_1750) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81])],[f_337_2]) ).
cnf(f_337_4,plain,
( sP81(U_1750,U_1751,U_1752)
| ~ class_Orderings_Olinorder(U_1750) ),
inference(clausify,[status(thm)],[f_337_3]) ).
cnf(f_337_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))
| ~ sP81(U_1750,U_1751,U_1752) ),
inference(clausify,[status(thm)],[f_337_3]) ).
cnf(f_337_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))
| ~ sP81(U_1750,U_1751,U_1752) ),
inference(clausify,[status(thm)],[f_337_3]) ).
fof(f_338_1,plain,
! [V_c_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubsetD]) ).
fof(f_338_2,plain,
! [U_1756,U_1755,U_1754,U_1753] :
( hBOOL(hAPP(hAPP(c_member(U_1753),U_1756),U_1755))
| ~ hBOOL(hAPP(hAPP(c_member(U_1753),U_1756),U_1754))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1753,tc_HOL_Obool)),U_1754),U_1755)) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
! [U_1755,U_1754,U_1753,U_1756] :
( hBOOL(hAPP(hAPP(c_member(U_1753),U_1756),U_1755))
| ~ hBOOL(hAPP(hAPP(c_member(U_1753),U_1756),U_1754))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1753,tc_HOL_Obool)),U_1754),U_1755)) ),
inference(definitional_conversion,[status(esa)],[f_338_2]) ).
cnf(f_338_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1753),U_1756),U_1755))
| ~ hBOOL(hAPP(hAPP(c_member(U_1753),U_1756),U_1754))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1753,tc_HOL_Obool)),U_1754),U_1755)) ),
inference(clausify,[status(thm)],[f_338_3]) ).
fof(f_339_1,plain,
! [V_b_2,V_c_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_c_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_c) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).
fof(f_339_2,plain,
! [U_1760,U_1759,U_1758,U_1757] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1757),U_1758),U_1759)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1757),U_1760),U_1759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1757),U_1758),U_1760)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1757),U_1758),U_1760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1757),U_1758),U_1759)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1757),U_1760),U_1759))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1757) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
fof(f_339_3,plain,
( ! [U_1757,U_1758,U_1759,U_1760] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1757),U_1758),U_1759)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1757),U_1760),U_1759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1757),U_1758),U_1760))
| ~ sP82(U_1757,U_1758,U_1759,U_1760) )
& ! [U_1757,U_1758,U_1759,U_1760] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1757),U_1758),U_1760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1757),U_1758),U_1759)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1757),U_1760),U_1759)))
| ~ sP82(U_1757,U_1758,U_1759,U_1760) )
& ! [U_1757,U_1758,U_1759,U_1760] :
( sP82(U_1757,U_1758,U_1759,U_1760)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1757) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82])],[f_339_2]) ).
cnf(f_339_4,plain,
( sP82(U_1757,U_1758,U_1759,U_1760)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1757) ),
inference(clausify,[status(thm)],[f_339_3]) ).
cnf(f_339_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1757),U_1758),U_1760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1757),U_1758),U_1759)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1757),U_1760),U_1759)))
| ~ sP82(U_1757,U_1758,U_1759,U_1760) ),
inference(clausify,[status(thm)],[f_339_3]) ).
cnf(f_339_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1757),U_1758),U_1759)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1757),U_1760),U_1759)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1757),U_1758),U_1760))
| ~ sP82(U_1757,U_1758,U_1759,U_1760) ),
inference(clausify,[status(thm)],[f_339_3]) ).
fof(f_340_1,plain,
! [V_b_2,V_a_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_c_2),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_c) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left]) ).
fof(f_340_2,plain,
! [U_1764,U_1763,U_1762,U_1761] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1761),U_1762),U_1763)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1761),U_1762),U_1764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1761),U_1763),U_1764)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1761),U_1763),U_1764))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1761),U_1762),U_1763)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1761),U_1762),U_1764))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1761) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
fof(f_340_3,plain,
( ! [U_1762,U_1764,U_1763,U_1761] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1761),U_1762),U_1763)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1761),U_1762),U_1764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1761),U_1763),U_1764))
| ~ sP83(U_1762,U_1764,U_1763,U_1761) )
& ! [U_1762,U_1764,U_1763,U_1761] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1761),U_1763),U_1764))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1761),U_1762),U_1763)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1761),U_1762),U_1764)))
| ~ sP83(U_1762,U_1764,U_1763,U_1761) )
& ! [U_1762,U_1764,U_1763,U_1761] :
( sP83(U_1762,U_1764,U_1763,U_1761)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1761) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_340_2]) ).
cnf(f_340_4,plain,
( sP83(U_1762,U_1764,U_1763,U_1761)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1761) ),
inference(clausify,[status(thm)],[f_340_3]) ).
cnf(f_340_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1761),U_1763),U_1764))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1761),U_1762),U_1763)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1761),U_1762),U_1764)))
| ~ sP83(U_1762,U_1764,U_1763,U_1761) ),
inference(clausify,[status(thm)],[f_340_3]) ).
cnf(f_340_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1761),U_1762),U_1763)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1761),U_1762),U_1764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1761),U_1763),U_1764))
| ~ sP83(U_1762,U_1764,U_1763,U_1761) ),
inference(clausify,[status(thm)],[f_340_3]) ).
fof(f_341_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_341_2,plain,
! [U_1768,U_1767,U_1766,U_1765] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1765),U_1766),U_1768)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1765),U_1767),U_1768)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1765),U_1766),U_1767))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1765) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
fof(f_341_3,plain,
! [U_1767,U_1766,U_1765,U_1768] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1765),U_1766),U_1768)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1765),U_1767),U_1768)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1765),U_1766),U_1767))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1765) ),
inference(definitional_conversion,[status(esa)],[f_341_2]) ).
cnf(f_341_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1765),U_1766),U_1768)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1765),U_1767),U_1768)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1765),U_1766),U_1767))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1765) ),
inference(clausify,[status(thm)],[f_341_3]) ).
fof(f_342_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_342_2,plain,
! [U_1772,U_1771,U_1770,U_1769] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1769),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1769),U_1772),U_1770)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1769),U_1772),U_1771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1769),U_1770),U_1771))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1769) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
fof(f_342_3,plain,
! [U_1769,U_1770,U_1771,U_1772] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1769),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1769),U_1772),U_1770)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1769),U_1772),U_1771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1769),U_1770),U_1771))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1769) ),
inference(definitional_conversion,[status(esa)],[f_342_2]) ).
cnf(f_342_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1769),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1769),U_1772),U_1770)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1769),U_1772),U_1771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1769),U_1770),U_1771))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1769) ),
inference(clausify,[status(thm)],[f_342_3]) ).
fof(f_343_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_343_2,plain,
! [U_1777,U_1776,U_1775,U_1774,U_1773] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1773),U_1774),U_1776)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1773),U_1775),U_1777)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1773),U_1776),U_1777))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1773),U_1774),U_1775))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1773) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
fof(f_343_3,plain,
! [U_1773,U_1774,U_1775,U_1776,U_1777] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1773),U_1774),U_1776)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1773),U_1775),U_1777)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1773),U_1776),U_1777))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1773),U_1774),U_1775))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1773) ),
inference(definitional_conversion,[status(esa)],[f_343_2]) ).
cnf(f_343_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1773),U_1774),U_1776)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1773),U_1775),U_1777)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1773),U_1776),U_1777))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1773),U_1774),U_1775))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1773) ),
inference(clausify,[status(thm)],[f_343_3]) ).
fof(f_344_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_344_2,plain,
! [U_1781,U_1780,U_1779,U_1778] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1778),U_1779),U_1781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1778),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1778),U_1779),U_1780)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1778),U_1781),U_1780)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1778) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
fof(f_344_3,plain,
! [U_1780,U_1778,U_1779,U_1781] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1778),U_1779),U_1781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1778),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1778),U_1779),U_1780)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1778),U_1781),U_1780)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1778) ),
inference(definitional_conversion,[status(esa)],[f_344_2]) ).
cnf(f_344_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1778),U_1779),U_1781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1778),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1778),U_1779),U_1780)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1778),U_1781),U_1780)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1778) ),
inference(clausify,[status(thm)],[f_344_3]) ).
fof(f_345_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_345_2,plain,
! [U_1785,U_1784,U_1783,U_1782] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1782),U_1784),U_1785))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1782),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1782),U_1783),U_1784)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1782),U_1783),U_1785)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1782) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
fof(f_345_3,plain,
! [U_1782,U_1783,U_1784,U_1785] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1782),U_1784),U_1785))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1782),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1782),U_1783),U_1784)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1782),U_1783),U_1785)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1782) ),
inference(definitional_conversion,[status(esa)],[f_345_2]) ).
cnf(f_345_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1782),U_1784),U_1785))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1782),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1782),U_1783),U_1784)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1782),U_1783),U_1785)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1782) ),
inference(clausify,[status(thm)],[f_345_3]) ).
fof(f_346_1,plain,
! [V_A_2,T_c] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_not__psubset__empty]) ).
fof(f_346_2,plain,
! [U_1787,U_1786] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1786,tc_HOL_Obool)),U_1787),c_Orderings_Obot__class_Obot(tc_fun(U_1786,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_346_1]) ).
fof(f_346_3,plain,
! [U_1786,U_1787] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1786,tc_HOL_Obool)),U_1787),c_Orderings_Obot__class_Obot(tc_fun(U_1786,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_346_2]) ).
cnf(f_346_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1786,tc_HOL_Obool)),U_1787),c_Orderings_Obot__class_Obot(tc_fun(U_1786,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_346_3]) ).
fof(f_347_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_c_2),V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).
fof(f_347_2,plain,
! [U_1792,U_1791,U_1790,U_1789,U_1788] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1788),U_1789),U_1790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1788),U_1791),U_1792)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1788),U_1791),U_1792))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1788),U_1789),U_1790)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1788),U_1789),U_1790) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1788),U_1791),U_1792)
| ~ class_Groups_Oordered__ab__group__add(U_1788) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
fof(f_347_3,plain,
( ! [U_1788,U_1789,U_1790,U_1791,U_1792] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1788),U_1789),U_1790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1788),U_1791),U_1792))
| ~ sP84(U_1788,U_1789,U_1790,U_1791,U_1792) )
& ! [U_1788,U_1789,U_1790,U_1791,U_1792] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1788),U_1791),U_1792))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1788),U_1789),U_1790))
| ~ sP84(U_1788,U_1789,U_1790,U_1791,U_1792) )
& ! [U_1788,U_1789,U_1790,U_1791,U_1792] :
( sP84(U_1788,U_1789,U_1790,U_1791,U_1792)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1788),U_1789),U_1790) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1788),U_1791),U_1792)
| ~ class_Groups_Oordered__ab__group__add(U_1788) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84])],[f_347_2]) ).
cnf(f_347_4,plain,
( sP84(U_1788,U_1789,U_1790,U_1791,U_1792)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1788),U_1789),U_1790) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1788),U_1791),U_1792)
| ~ class_Groups_Oordered__ab__group__add(U_1788) ),
inference(clausify,[status(thm)],[f_347_3]) ).
cnf(f_347_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1788),U_1791),U_1792))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1788),U_1789),U_1790))
| ~ sP84(U_1788,U_1789,U_1790,U_1791,U_1792) ),
inference(clausify,[status(thm)],[f_347_3]) ).
cnf(f_347_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1788),U_1789),U_1790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1788),U_1791),U_1792))
| ~ sP84(U_1788,U_1789,U_1790,U_1791,U_1792) ),
inference(clausify,[status(thm)],[f_347_3]) ).
fof(f_348_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_B_2),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)) ),
inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans]) ).
fof(f_348_2,plain,
! [U_1796,U_1795,U_1794,U_1793] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1793,tc_HOL_Obool)),U_1794),U_1796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1793,tc_HOL_Obool)),U_1795),U_1796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1793,tc_HOL_Obool)),U_1794),U_1795)) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
fof(f_348_3,plain,
! [U_1795,U_1794,U_1796,U_1793] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1793,tc_HOL_Obool)),U_1794),U_1796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1793,tc_HOL_Obool)),U_1795),U_1796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1793,tc_HOL_Obool)),U_1794),U_1795)) ),
inference(definitional_conversion,[status(esa)],[f_348_2]) ).
cnf(f_348_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1793,tc_HOL_Obool)),U_1794),U_1796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1793,tc_HOL_Obool)),U_1795),U_1796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1793,tc_HOL_Obool)),U_1794),U_1795)) ),
inference(clausify,[status(thm)],[f_348_3]) ).
fof(f_349_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans]) ).
fof(f_349_2,plain,
! [U_1800,U_1799,U_1798,U_1797] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1797,tc_HOL_Obool)),U_1798),U_1800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1797,tc_HOL_Obool)),U_1799),U_1800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1797,tc_HOL_Obool)),U_1798),U_1799)) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
fof(f_349_3,plain,
! [U_1797,U_1798,U_1799,U_1800] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1797,tc_HOL_Obool)),U_1798),U_1800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1797,tc_HOL_Obool)),U_1799),U_1800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1797,tc_HOL_Obool)),U_1798),U_1799)) ),
inference(definitional_conversion,[status(esa)],[f_349_2]) ).
cnf(f_349_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1797,tc_HOL_Obool)),U_1798),U_1800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1797,tc_HOL_Obool)),U_1799),U_1800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1797,tc_HOL_Obool)),U_1798),U_1799)) ),
inference(clausify,[status(thm)],[f_349_3]) ).
fof(f_350_1,plain,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset]) ).
fof(f_350_2,plain,
! [U_1803,U_1802,U_1801] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1801,tc_HOL_Obool)),U_1802),U_1803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1801,tc_HOL_Obool)),U_1802),U_1803)) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
fof(f_350_3,plain,
! [U_1801,U_1802,U_1803] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1801,tc_HOL_Obool)),U_1802),U_1803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1801,tc_HOL_Obool)),U_1802),U_1803)) ),
inference(definitional_conversion,[status(esa)],[f_350_2]) ).
cnf(f_350_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1801,tc_HOL_Obool)),U_1802),U_1803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1801,tc_HOL_Obool)),U_1802),U_1803)) ),
inference(clausify,[status(thm)],[f_350_3]) ).
fof(f_351_1,plain,
! [V_B_2,V_A_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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_c,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_c,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)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq]) ).
fof(f_351_2,plain,
! [U_1806,U_1805,U_1804] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1804,tc_HOL_Obool)),U_1805),U_1806))
| ( U_1805 != U_1806
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1804,tc_HOL_Obool)),U_1805),U_1806)) ) )
& ( U_1805 = U_1806
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1804,tc_HOL_Obool)),U_1805),U_1806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1804,tc_HOL_Obool)),U_1805),U_1806)) ) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
fof(f_351_3,plain,
( ! [U_1812,U_1810,U_1808] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1808,tc_HOL_Obool)),U_1810),U_1812))
| ( U_1810 != U_1812
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1808,tc_HOL_Obool)),U_1810),U_1812)) ) )
& ! [U_1811,U_1809,U_1807] :
( U_1809 = U_1811
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1807,tc_HOL_Obool)),U_1809),U_1811))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1807,tc_HOL_Obool)),U_1809),U_1811)) ) ),
inference(miniscope,[status(thm)],[f_351_2]) ).
fof(f_351_4,plain,
( ! [U_1810,U_1808,U_1812] :
( U_1810 != U_1812
| ~ sP85(U_1810,U_1808,U_1812) )
& ! [U_1810,U_1808,U_1812] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1808,tc_HOL_Obool)),U_1810),U_1812))
| ~ sP85(U_1810,U_1808,U_1812) )
& ! [U_1810,U_1808,U_1812] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1808,tc_HOL_Obool)),U_1810),U_1812))
| sP85(U_1810,U_1808,U_1812) )
& ! [U_1809,U_1807,U_1811] :
( U_1809 = U_1811
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1807,tc_HOL_Obool)),U_1809),U_1811))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1807,tc_HOL_Obool)),U_1809),U_1811)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85])],[f_351_3]) ).
cnf(f_351_5,plain,
( U_1809 = U_1811
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1807,tc_HOL_Obool)),U_1809),U_1811))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1807,tc_HOL_Obool)),U_1809),U_1811)) ),
inference(clausify,[status(thm)],[f_351_4]) ).
cnf(f_351_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1808,tc_HOL_Obool)),U_1810),U_1812))
| sP85(U_1810,U_1808,U_1812) ),
inference(clausify,[status(thm)],[f_351_4]) ).
cnf(f_351_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1808,tc_HOL_Obool)),U_1810),U_1812))
| ~ sP85(U_1810,U_1808,U_1812) ),
inference(clausify,[status(thm)],[f_351_4]) ).
cnf(f_351_8,plain,
( U_1810 != U_1812
| ~ sP85(U_1810,U_1808,U_1812) ),
inference(clausify,[status(thm)],[f_351_4]) ).
fof(f_352_1,plain,
! [V_B_2,V_A_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,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_c,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_c,tc_HOL_Obool)),V_A_2),V_B_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_psubset__eq]) ).
fof(f_352_2,plain,
! [U_1815,U_1814,U_1813] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1813,tc_HOL_Obool)),U_1814),U_1815))
| U_1814 = U_1815
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1813,tc_HOL_Obool)),U_1814),U_1815)) )
& ( ( U_1814 != U_1815
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1813,tc_HOL_Obool)),U_1814),U_1815)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1813,tc_HOL_Obool)),U_1814),U_1815)) ) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
fof(f_352_3,plain,
( ! [U_1821,U_1819,U_1817] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1817,tc_HOL_Obool)),U_1819),U_1821))
| U_1819 = U_1821
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1817,tc_HOL_Obool)),U_1819),U_1821)) )
& ! [U_1820,U_1818,U_1816] :
( ( U_1818 != U_1820
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1816,tc_HOL_Obool)),U_1818),U_1820)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1816,tc_HOL_Obool)),U_1818),U_1820)) ) ),
inference(miniscope,[status(thm)],[f_352_2]) ).
fof(f_352_4,plain,
( ! [U_1818,U_1816,U_1820] :
( U_1818 != U_1820
| ~ sP86(U_1818,U_1816,U_1820) )
& ! [U_1818,U_1816,U_1820] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1816,tc_HOL_Obool)),U_1818),U_1820))
| ~ sP86(U_1818,U_1816,U_1820) )
& ! [U_1819,U_1817,U_1821] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1817,tc_HOL_Obool)),U_1819),U_1821))
| U_1819 = U_1821
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1817,tc_HOL_Obool)),U_1819),U_1821)) )
& ! [U_1818,U_1816,U_1820] :
( sP86(U_1818,U_1816,U_1820)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1816,tc_HOL_Obool)),U_1818),U_1820)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_352_3]) ).
cnf(f_352_5,plain,
( sP86(U_1818,U_1816,U_1820)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1816,tc_HOL_Obool)),U_1818),U_1820)) ),
inference(clausify,[status(thm)],[f_352_4]) ).
cnf(f_352_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1817,tc_HOL_Obool)),U_1819),U_1821))
| U_1819 = U_1821
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1817,tc_HOL_Obool)),U_1819),U_1821)) ),
inference(clausify,[status(thm)],[f_352_4]) ).
cnf(f_352_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1816,tc_HOL_Obool)),U_1818),U_1820))
| ~ sP86(U_1818,U_1816,U_1820) ),
inference(clausify,[status(thm)],[f_352_4]) ).
cnf(f_352_8,plain,
( U_1818 != U_1820
| ~ sP86(U_1818,U_1816,U_1820) ),
inference(clausify,[status(thm)],[f_352_4]) ).
fof(f_353_1,plain,
! [T_c] :
( c_Finite__Set_Ofun__left__comm(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c))
| ~ class_Groups_Oab__semigroup__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm]) ).
fof(f_353_2,plain,
! [U_1822] :
( c_Finite__Set_Ofun__left__comm(U_1822,U_1822,c_Groups_Otimes__class_Otimes(U_1822))
| ~ class_Groups_Oab__semigroup__mult(U_1822) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
fof(f_353_3,plain,
! [U_1822] :
( c_Finite__Set_Ofun__left__comm(U_1822,U_1822,c_Groups_Otimes__class_Otimes(U_1822))
| ~ class_Groups_Oab__semigroup__mult(U_1822) ),
inference(definitional_conversion,[status(esa)],[f_353_2]) ).
cnf(f_353_4,plain,
( c_Finite__Set_Ofun__left__comm(U_1822,U_1822,c_Groups_Otimes__class_Otimes(U_1822))
| ~ class_Groups_Oab__semigroup__mult(U_1822) ),
inference(clausify,[status(thm)],[f_353_3]) ).
fof(f_354_1,plain,
! [T_c] :
( c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem]) ).
fof(f_354_2,plain,
! [U_1823] :
( c_Finite__Set_Ofun__left__comm__idem(U_1823,U_1823,c_Groups_Otimes__class_Otimes(U_1823))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1823) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
fof(f_354_3,plain,
! [U_1823] :
( c_Finite__Set_Ofun__left__comm__idem(U_1823,U_1823,c_Groups_Otimes__class_Otimes(U_1823))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1823) ),
inference(definitional_conversion,[status(esa)],[f_354_2]) ).
cnf(f_354_4,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_1823,U_1823,c_Groups_Otimes__class_Otimes(U_1823))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1823) ),
inference(clausify,[status(thm)],[f_354_3]) ).
fof(f_355_1,plain,
! [V_A_2,V_f_2,T_d,V_r_2,T_c] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),hAPP(c_Groups_Otimes__class_Otimes(T_c),V_r_2)),V_f_2)),V_A_2)
| ~ class_Rings_Osemiring__0(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__right__distrib]) ).
fof(f_355_2,plain,
! [U_1828,U_1827,U_1826,U_1825,U_1824] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1824),U_1825),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1826,U_1824),U_1827),U_1828)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1826,U_1824),hAPP(hAPP(c_COMBB(U_1824,U_1824,U_1826),hAPP(c_Groups_Otimes__class_Otimes(U_1824),U_1825)),U_1827)),U_1828)
| ~ class_Rings_Osemiring__0(U_1824) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
fof(f_355_3,plain,
! [U_1824,U_1825,U_1826,U_1827,U_1828] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1824),U_1825),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1826,U_1824),U_1827),U_1828)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1826,U_1824),hAPP(hAPP(c_COMBB(U_1824,U_1824,U_1826),hAPP(c_Groups_Otimes__class_Otimes(U_1824),U_1825)),U_1827)),U_1828)
| ~ class_Rings_Osemiring__0(U_1824) ),
inference(definitional_conversion,[status(esa)],[f_355_2]) ).
cnf(f_355_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1824),U_1825),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1826,U_1824),U_1827),U_1828)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1826,U_1824),hAPP(hAPP(c_COMBB(U_1824,U_1824,U_1826),hAPP(c_Groups_Otimes__class_Otimes(U_1824),U_1825)),U_1827)),U_1828)
| ~ class_Rings_Osemiring__0(U_1824) ),
inference(clausify,[status(thm)],[f_355_3]) ).
fof(f_356_1,plain,
! [V_r_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Otimes__class_Otimes(T_c)),V_f_2)),V_r_2)),V_A_2)
| ~ class_Rings_Osemiring__0(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib]) ).
fof(f_356_2,plain,
! [U_1833,U_1832,U_1831,U_1830,U_1829] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1829),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1830,U_1829),U_1831),U_1832)),U_1833) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1830,U_1829),hAPP(hAPP(c_COMBC(U_1830,U_1829,U_1829),hAPP(hAPP(c_COMBB(U_1829,tc_fun(U_1829,U_1829),U_1830),c_Groups_Otimes__class_Otimes(U_1829)),U_1831)),U_1833)),U_1832)
| ~ class_Rings_Osemiring__0(U_1829) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
fof(f_356_3,plain,
! [U_1829,U_1830,U_1831,U_1832,U_1833] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1829),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1830,U_1829),U_1831),U_1832)),U_1833) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1830,U_1829),hAPP(hAPP(c_COMBC(U_1830,U_1829,U_1829),hAPP(hAPP(c_COMBB(U_1829,tc_fun(U_1829,U_1829),U_1830),c_Groups_Otimes__class_Otimes(U_1829)),U_1831)),U_1833)),U_1832)
| ~ class_Rings_Osemiring__0(U_1829) ),
inference(definitional_conversion,[status(esa)],[f_356_2]) ).
cnf(f_356_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1829),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1830,U_1829),U_1831),U_1832)),U_1833) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1830,U_1829),hAPP(hAPP(c_COMBC(U_1830,U_1829,U_1829),hAPP(hAPP(c_COMBB(U_1829,tc_fun(U_1829,U_1829),U_1830),c_Groups_Otimes__class_Otimes(U_1829)),U_1831)),U_1833)),U_1832)
| ~ class_Rings_Osemiring__0(U_1829) ),
inference(clausify,[status(thm)],[f_356_3]) ).
fof(f_357_1,plain,
! [V_B_2,V_g_2,T_e,V_A_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),tc_fun(tc_fun(T_e,tc_HOL_Obool),T_c),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_c),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,T_c)),T_d),c_COMBB(T_c,T_c,T_e)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Otimes__class_Otimes(T_c)),V_f_2))),V_g_2))),V_B_2)),V_A_2)
| ~ class_Rings_Osemiring__0(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__product]) ).
fof(f_357_2,plain,
! [U_1840,U_1839,U_1838,U_1837,U_1836,U_1835,U_1834] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1834),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1835,U_1834),U_1836),U_1837)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1838,U_1834),U_1839),U_1840)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1835,U_1834),hAPP(hAPP(c_COMBC(U_1835,tc_fun(U_1838,tc_HOL_Obool),U_1834),hAPP(hAPP(c_COMBB(tc_fun(U_1838,U_1834),tc_fun(tc_fun(U_1838,tc_HOL_Obool),U_1834),U_1835),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1838,U_1834)),hAPP(hAPP(c_COMBC(U_1835,tc_fun(U_1838,U_1834),tc_fun(U_1838,U_1834)),hAPP(hAPP(c_COMBB(tc_fun(U_1834,U_1834),tc_fun(tc_fun(U_1838,U_1834),tc_fun(U_1838,U_1834)),U_1835),c_COMBB(U_1834,U_1834,U_1838)),hAPP(hAPP(c_COMBB(U_1834,tc_fun(U_1834,U_1834),U_1835),c_Groups_Otimes__class_Otimes(U_1834)),U_1836))),U_1839))),U_1840)),U_1837)
| ~ class_Rings_Osemiring__0(U_1834) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
fof(f_357_3,plain,
! [U_1834,U_1835,U_1836,U_1837,U_1838,U_1839,U_1840] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1834),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1835,U_1834),U_1836),U_1837)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1838,U_1834),U_1839),U_1840)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1835,U_1834),hAPP(hAPP(c_COMBC(U_1835,tc_fun(U_1838,tc_HOL_Obool),U_1834),hAPP(hAPP(c_COMBB(tc_fun(U_1838,U_1834),tc_fun(tc_fun(U_1838,tc_HOL_Obool),U_1834),U_1835),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1838,U_1834)),hAPP(hAPP(c_COMBC(U_1835,tc_fun(U_1838,U_1834),tc_fun(U_1838,U_1834)),hAPP(hAPP(c_COMBB(tc_fun(U_1834,U_1834),tc_fun(tc_fun(U_1838,U_1834),tc_fun(U_1838,U_1834)),U_1835),c_COMBB(U_1834,U_1834,U_1838)),hAPP(hAPP(c_COMBB(U_1834,tc_fun(U_1834,U_1834),U_1835),c_Groups_Otimes__class_Otimes(U_1834)),U_1836))),U_1839))),U_1840)),U_1837)
| ~ class_Rings_Osemiring__0(U_1834) ),
inference(definitional_conversion,[status(esa)],[f_357_2]) ).
cnf(f_357_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1834),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1835,U_1834),U_1836),U_1837)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1838,U_1834),U_1839),U_1840)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1835,U_1834),hAPP(hAPP(c_COMBC(U_1835,tc_fun(U_1838,tc_HOL_Obool),U_1834),hAPP(hAPP(c_COMBB(tc_fun(U_1838,U_1834),tc_fun(tc_fun(U_1838,tc_HOL_Obool),U_1834),U_1835),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_1838,U_1834)),hAPP(hAPP(c_COMBC(U_1835,tc_fun(U_1838,U_1834),tc_fun(U_1838,U_1834)),hAPP(hAPP(c_COMBB(tc_fun(U_1834,U_1834),tc_fun(tc_fun(U_1838,U_1834),tc_fun(U_1838,U_1834)),U_1835),c_COMBB(U_1834,U_1834,U_1838)),hAPP(hAPP(c_COMBB(U_1834,tc_fun(U_1834,U_1834),U_1835),c_Groups_Otimes__class_Otimes(U_1834)),U_1836))),U_1839))),U_1840)),U_1837)
| ~ class_Rings_Osemiring__0(U_1834) ),
inference(clausify,[status(thm)],[f_357_3]) ).
fof(f_358_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_358_2,plain,
! [U_1845,U_1844,U_1843,U_1842,U_1841] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1841),U_1842),U_1844)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1841),U_1843),U_1845)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),U_1844),U_1845))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1841),U_1842),U_1843))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1841) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
fof(f_358_3,plain,
! [U_1841,U_1842,U_1843,U_1844,U_1845] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1841),U_1842),U_1844)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1841),U_1843),U_1845)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),U_1844),U_1845))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1841),U_1842),U_1843))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1841) ),
inference(definitional_conversion,[status(esa)],[f_358_2]) ).
cnf(f_358_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1841),U_1842),U_1844)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1841),U_1843),U_1845)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1841),U_1844),U_1845))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1841),U_1842),U_1843))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1841) ),
inference(clausify,[status(thm)],[f_358_3]) ).
fof(f_359_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_359_2,plain,
! [U_1850,U_1849,U_1848,U_1847,U_1846] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1846),U_1847),U_1849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1846),U_1848),U_1850)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1846),U_1849),U_1850))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1846),U_1847),U_1848))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1846) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
! [U_1846,U_1847,U_1848,U_1849,U_1850] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1846),U_1847),U_1849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1846),U_1848),U_1850)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1846),U_1849),U_1850))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1846),U_1847),U_1848))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1846) ),
inference(definitional_conversion,[status(esa)],[f_359_2]) ).
cnf(f_359_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1846),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1846),U_1847),U_1849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1846),U_1848),U_1850)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1846),U_1849),U_1850))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1846),U_1847),U_1848))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1846) ),
inference(clausify,[status(thm)],[f_359_3]) ).
fof(f_360_1,plain,
! [V_A_2,V_B_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset]) ).
fof(f_360_2,plain,
! [U_1855,U_1854,U_1853,U_1852,U_1851] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1852,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1851,U_1852,U_1853),U_1855)),hAPP(c_Set_Oimage(U_1851,U_1852,U_1853),U_1854)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1851,tc_HOL_Obool)),U_1855),U_1854))
| ~ c_Fun_Oinj__on(U_1851,U_1852,U_1853,U_1854) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
! [U_1852,U_1851,U_1853,U_1854,U_1855] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1852,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1851,U_1852,U_1853),U_1855)),hAPP(c_Set_Oimage(U_1851,U_1852,U_1853),U_1854)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1851,tc_HOL_Obool)),U_1855),U_1854))
| ~ c_Fun_Oinj__on(U_1851,U_1852,U_1853,U_1854) ),
inference(definitional_conversion,[status(esa)],[f_360_2]) ).
cnf(f_360_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1852,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1851,U_1852,U_1853),U_1855)),hAPP(c_Set_Oimage(U_1851,U_1852,U_1853),U_1854)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1851,tc_HOL_Obool)),U_1855),U_1854))
| ~ c_Fun_Oinj__on(U_1851,U_1852,U_1853,U_1854) ),
inference(clausify,[status(thm)],[f_360_3]) ).
fof(f_361_1,plain,
! [V_x_2,T_c] :
( c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_Osingleton]) ).
fof(f_361_2,plain,
! [U_1857,U_1856] :
( c_Big__Operators_Olinorder__class_OMin(U_1856,hAPP(hAPP(c_Set_Oinsert(U_1856),U_1857),c_Orderings_Obot__class_Obot(tc_fun(U_1856,tc_HOL_Obool)))) = U_1857
| ~ class_Orderings_Olinorder(U_1856) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
! [U_1856,U_1857] :
( c_Big__Operators_Olinorder__class_OMin(U_1856,hAPP(hAPP(c_Set_Oinsert(U_1856),U_1857),c_Orderings_Obot__class_Obot(tc_fun(U_1856,tc_HOL_Obool)))) = U_1857
| ~ class_Orderings_Olinorder(U_1856) ),
inference(definitional_conversion,[status(esa)],[f_361_2]) ).
cnf(f_361_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_1856,hAPP(hAPP(c_Set_Oinsert(U_1856),U_1857),c_Orderings_Obot__class_Obot(tc_fun(U_1856,tc_HOL_Obool)))) = U_1857
| ~ class_Orderings_Olinorder(U_1856) ),
inference(clausify,[status(thm)],[f_361_3]) ).
fof(f_362_1,plain,
! [V_x_2,T_c] :
( c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_Osingleton]) ).
fof(f_362_2,plain,
! [U_1859,U_1858] :
( c_Big__Operators_Olinorder__class_OMax(U_1858,hAPP(hAPP(c_Set_Oinsert(U_1858),U_1859),c_Orderings_Obot__class_Obot(tc_fun(U_1858,tc_HOL_Obool)))) = U_1859
| ~ class_Orderings_Olinorder(U_1858) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
fof(f_362_3,plain,
! [U_1858,U_1859] :
( c_Big__Operators_Olinorder__class_OMax(U_1858,hAPP(hAPP(c_Set_Oinsert(U_1858),U_1859),c_Orderings_Obot__class_Obot(tc_fun(U_1858,tc_HOL_Obool)))) = U_1859
| ~ class_Orderings_Olinorder(U_1858) ),
inference(definitional_conversion,[status(esa)],[f_362_2]) ).
cnf(f_362_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_1858,hAPP(hAPP(c_Set_Oinsert(U_1858),U_1859),c_Orderings_Obot__class_Obot(tc_fun(U_1858,tc_HOL_Obool)))) = U_1859
| ~ class_Orderings_Olinorder(U_1858) ),
inference(clausify,[status(thm)],[f_362_3]) ).
fof(f_363_1,plain,
! [V_z_2,V_y_2,V_A_2,V_b_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_z_2),V_y_2)))
| hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c),V_b_2,V_A_2),V_y_2))
| ~ class_Groups_Oab__semigroup__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph__insert__swap]) ).
fof(f_363_2,plain,
! [U_1864,U_1863,U_1862,U_1861,U_1860] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1860,U_1860,c_Groups_Otimes__class_Otimes(U_1860),U_1864,hAPP(hAPP(c_Set_Oinsert(U_1860),U_1861),U_1862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1860),U_1864),U_1863)))
| hBOOL(hAPP(hAPP(c_member(U_1860),U_1861),U_1862))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1860,U_1860,c_Groups_Otimes__class_Otimes(U_1860),U_1861,U_1862),U_1863))
| ~ class_Groups_Oab__semigroup__mult(U_1860) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
fof(f_363_3,plain,
! [U_1860,U_1861,U_1862,U_1863,U_1864] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1860,U_1860,c_Groups_Otimes__class_Otimes(U_1860),U_1864,hAPP(hAPP(c_Set_Oinsert(U_1860),U_1861),U_1862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1860),U_1864),U_1863)))
| hBOOL(hAPP(hAPP(c_member(U_1860),U_1861),U_1862))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1860,U_1860,c_Groups_Otimes__class_Otimes(U_1860),U_1861,U_1862),U_1863))
| ~ class_Groups_Oab__semigroup__mult(U_1860) ),
inference(definitional_conversion,[status(esa)],[f_363_2]) ).
cnf(f_363_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1860,U_1860,c_Groups_Otimes__class_Otimes(U_1860),U_1864,hAPP(hAPP(c_Set_Oinsert(U_1860),U_1861),U_1862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1860),U_1864),U_1863)))
| hBOOL(hAPP(hAPP(c_member(U_1860),U_1861),U_1862))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_1860,U_1860,c_Groups_Otimes__class_Otimes(U_1860),U_1861,U_1862),U_1863))
| ~ class_Groups_Oab__semigroup__mult(U_1860) ),
inference(clausify,[status(thm)],[f_363_3]) ).
fof(f_364_1,plain,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),V_x_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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min__le]) ).
fof(f_364_2,plain,
! [U_1867,U_1866,U_1865] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1865),c_Big__Operators_Olinorder__class_OMin(U_1865,U_1866)),U_1867))
| ~ hBOOL(hAPP(hAPP(c_member(U_1865),U_1867),U_1866))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1865),U_1866))
| ~ class_Orderings_Olinorder(U_1865) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
! [U_1866,U_1865,U_1867] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1865),c_Big__Operators_Olinorder__class_OMin(U_1865,U_1866)),U_1867))
| ~ hBOOL(hAPP(hAPP(c_member(U_1865),U_1867),U_1866))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1865),U_1866))
| ~ class_Orderings_Olinorder(U_1865) ),
inference(definitional_conversion,[status(esa)],[f_364_2]) ).
cnf(f_364_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1865),c_Big__Operators_Olinorder__class_OMin(U_1865,U_1866)),U_1867))
| ~ hBOOL(hAPP(hAPP(c_member(U_1865),U_1867),U_1866))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1865),U_1866))
| ~ class_Orderings_Olinorder(U_1865) ),
inference(clausify,[status(thm)],[f_364_3]) ).
fof(f_365_1,plain,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max__ge]) ).
fof(f_365_2,plain,
! [U_1870,U_1869,U_1868] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1868),U_1870),c_Big__Operators_Olinorder__class_OMax(U_1868,U_1869)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1868),U_1870),U_1869))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1868),U_1869))
| ~ class_Orderings_Olinorder(U_1868) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
fof(f_365_3,plain,
! [U_1869,U_1868,U_1870] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1868),U_1870),c_Big__Operators_Olinorder__class_OMax(U_1868,U_1869)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1868),U_1870),U_1869))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1868),U_1869))
| ~ class_Orderings_Olinorder(U_1868) ),
inference(definitional_conversion,[status(esa)],[f_365_2]) ).
cnf(f_365_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1868),U_1870),c_Big__Operators_Olinorder__class_OMax(U_1868,U_1869)))
| ~ hBOOL(hAPP(hAPP(c_member(U_1868),U_1870),U_1869))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1868),U_1869))
| ~ class_Orderings_Olinorder(U_1868) ),
inference(clausify,[status(thm)],[f_365_3]) ).
fof(f_366_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min__in]) ).
fof(f_366_2,plain,
! [U_1872,U_1871] :
( hBOOL(hAPP(hAPP(c_member(U_1871),c_Big__Operators_Olinorder__class_OMin(U_1871,U_1872)),U_1872))
| U_1872 = c_Orderings_Obot__class_Obot(tc_fun(U_1871,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1871),U_1872))
| ~ class_Orderings_Olinorder(U_1871) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
fof(f_366_3,plain,
! [U_1872,U_1871] :
( hBOOL(hAPP(hAPP(c_member(U_1871),c_Big__Operators_Olinorder__class_OMin(U_1871,U_1872)),U_1872))
| U_1872 = c_Orderings_Obot__class_Obot(tc_fun(U_1871,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1871),U_1872))
| ~ class_Orderings_Olinorder(U_1871) ),
inference(definitional_conversion,[status(esa)],[f_366_2]) ).
cnf(f_366_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1871),c_Big__Operators_Olinorder__class_OMin(U_1871,U_1872)),U_1872))
| U_1872 = c_Orderings_Obot__class_Obot(tc_fun(U_1871,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1871),U_1872))
| ~ class_Orderings_Olinorder(U_1871) ),
inference(clausify,[status(thm)],[f_366_3]) ).
fof(f_367_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max__in]) ).
fof(f_367_2,plain,
! [U_1874,U_1873] :
( hBOOL(hAPP(hAPP(c_member(U_1873),c_Big__Operators_Olinorder__class_OMax(U_1873,U_1874)),U_1874))
| U_1874 = c_Orderings_Obot__class_Obot(tc_fun(U_1873,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1873),U_1874))
| ~ class_Orderings_Olinorder(U_1873) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
fof(f_367_3,plain,
! [U_1873,U_1874] :
( hBOOL(hAPP(hAPP(c_member(U_1873),c_Big__Operators_Olinorder__class_OMax(U_1873,U_1874)),U_1874))
| U_1874 = c_Orderings_Obot__class_Obot(tc_fun(U_1873,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1873),U_1874))
| ~ class_Orderings_Olinorder(U_1873) ),
inference(definitional_conversion,[status(esa)],[f_367_2]) ).
cnf(f_367_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_1873),c_Big__Operators_Olinorder__class_OMax(U_1873,U_1874)),U_1874))
| U_1874 = c_Orderings_Obot__class_Obot(tc_fun(U_1873,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1873),U_1874))
| ~ class_Orderings_Olinorder(U_1873) ),
inference(clausify,[status(thm)],[f_367_3]) ).
fof(f_368_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_b_2),V_a_2)),V_e_2)),V_d_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_b_2),V_a_2)),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2))) ) )
| ~ class_Rings_Oordered__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff2]) ).
fof(f_368_2,plain,
! [U_1880,U_1879,U_1878,U_1877,U_1876,U_1875] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1876),U_1877)),U_1878)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1879),U_1877)),U_1880)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1875),U_1879),U_1876)),U_1877)),U_1880))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1875),U_1879),U_1876)),U_1877)),U_1880)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1876),U_1877)),U_1878)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1879),U_1877)),U_1880))) ) )
| ~ class_Rings_Oordered__ring(U_1875) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
fof(f_368_3,plain,
( ! [U_1875,U_1876,U_1877,U_1878,U_1879,U_1880] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1876),U_1877)),U_1878)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1879),U_1877)),U_1880)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1875),U_1879),U_1876)),U_1877)),U_1880)))
| ~ sP87(U_1875,U_1876,U_1877,U_1878,U_1879,U_1880) )
& ! [U_1875,U_1876,U_1877,U_1878,U_1879,U_1880] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1875),U_1879),U_1876)),U_1877)),U_1880)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1876),U_1877)),U_1878)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1879),U_1877)),U_1880)))
| ~ sP87(U_1875,U_1876,U_1877,U_1878,U_1879,U_1880) )
& ! [U_1875,U_1876,U_1877,U_1878,U_1879,U_1880] :
( sP87(U_1875,U_1876,U_1877,U_1878,U_1879,U_1880)
| ~ class_Rings_Oordered__ring(U_1875) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_368_2]) ).
cnf(f_368_4,plain,
( sP87(U_1875,U_1876,U_1877,U_1878,U_1879,U_1880)
| ~ class_Rings_Oordered__ring(U_1875) ),
inference(clausify,[status(thm)],[f_368_3]) ).
cnf(f_368_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1875),U_1879),U_1876)),U_1877)),U_1880)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1876),U_1877)),U_1878)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1879),U_1877)),U_1880)))
| ~ sP87(U_1875,U_1876,U_1877,U_1878,U_1879,U_1880) ),
inference(clausify,[status(thm)],[f_368_3]) ).
cnf(f_368_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1876),U_1877)),U_1878)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),U_1879),U_1877)),U_1880)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1875),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1875),U_1879),U_1876)),U_1877)),U_1880)))
| ~ sP87(U_1875,U_1876,U_1877,U_1878,U_1879,U_1880) ),
inference(clausify,[status(thm)],[f_368_3]) ).
fof(f_369_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2))) ) )
| ~ class_Rings_Oordered__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff1]) ).
fof(f_369_2,plain,
! [U_1886,U_1885,U_1884,U_1883,U_1882,U_1881] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1882),U_1883)),U_1884)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1885),U_1883)),U_1886)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1881),U_1882),U_1885)),U_1883)),U_1884)),U_1886)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1881),U_1882),U_1885)),U_1883)),U_1884)),U_1886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1882),U_1883)),U_1884)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1885),U_1883)),U_1886))) ) )
| ~ class_Rings_Oordered__ring(U_1881) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
fof(f_369_3,plain,
( ! [U_1881,U_1882,U_1883,U_1884,U_1885,U_1886] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1882),U_1883)),U_1884)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1885),U_1883)),U_1886)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1881),U_1882),U_1885)),U_1883)),U_1884)),U_1886))
| ~ sP88(U_1881,U_1882,U_1883,U_1884,U_1885,U_1886) )
& ! [U_1881,U_1882,U_1883,U_1884,U_1885,U_1886] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1881),U_1882),U_1885)),U_1883)),U_1884)),U_1886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1882),U_1883)),U_1884)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1885),U_1883)),U_1886)))
| ~ sP88(U_1881,U_1882,U_1883,U_1884,U_1885,U_1886) )
& ! [U_1881,U_1882,U_1883,U_1884,U_1885,U_1886] :
( sP88(U_1881,U_1882,U_1883,U_1884,U_1885,U_1886)
| ~ class_Rings_Oordered__ring(U_1881) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_369_2]) ).
cnf(f_369_4,plain,
( sP88(U_1881,U_1882,U_1883,U_1884,U_1885,U_1886)
| ~ class_Rings_Oordered__ring(U_1881) ),
inference(clausify,[status(thm)],[f_369_3]) ).
cnf(f_369_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1881),U_1882),U_1885)),U_1883)),U_1884)),U_1886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1882),U_1883)),U_1884)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1885),U_1883)),U_1886)))
| ~ sP88(U_1881,U_1882,U_1883,U_1884,U_1885,U_1886) ),
inference(clausify,[status(thm)],[f_369_3]) ).
cnf(f_369_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1882),U_1883)),U_1884)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1885),U_1883)),U_1886)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1881),U_1882),U_1885)),U_1883)),U_1884)),U_1886))
| ~ sP88(U_1881,U_1882,U_1883,U_1884,U_1885,U_1886) ),
inference(clausify,[status(thm)],[f_369_3]) ).
fof(f_370_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_b_2),V_a_2)),V_e_2)),V_d_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_b_2),V_a_2)),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2))) ) )
| ~ class_Rings_Oordered__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff2]) ).
fof(f_370_2,plain,
! [U_1892,U_1891,U_1890,U_1889,U_1888,U_1887] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1888),U_1889)),U_1890)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1891),U_1889)),U_1892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1887),U_1890),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1887),U_1891),U_1888)),U_1889)),U_1892))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1887),U_1890),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1887),U_1891),U_1888)),U_1889)),U_1892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1888),U_1889)),U_1890)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1891),U_1889)),U_1892))) ) )
| ~ class_Rings_Oordered__ring(U_1887) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
fof(f_370_3,plain,
( ! [U_1887,U_1888,U_1889,U_1890,U_1891,U_1892] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1888),U_1889)),U_1890)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1891),U_1889)),U_1892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1887),U_1890),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1887),U_1891),U_1888)),U_1889)),U_1892)))
| ~ sP89(U_1887,U_1888,U_1889,U_1890,U_1891,U_1892) )
& ! [U_1887,U_1888,U_1889,U_1890,U_1891,U_1892] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1887),U_1890),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1887),U_1891),U_1888)),U_1889)),U_1892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1888),U_1889)),U_1890)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1891),U_1889)),U_1892)))
| ~ sP89(U_1887,U_1888,U_1889,U_1890,U_1891,U_1892) )
& ! [U_1887,U_1888,U_1889,U_1890,U_1891,U_1892] :
( sP89(U_1887,U_1888,U_1889,U_1890,U_1891,U_1892)
| ~ class_Rings_Oordered__ring(U_1887) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_370_2]) ).
cnf(f_370_4,plain,
( sP89(U_1887,U_1888,U_1889,U_1890,U_1891,U_1892)
| ~ class_Rings_Oordered__ring(U_1887) ),
inference(clausify,[status(thm)],[f_370_3]) ).
cnf(f_370_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1887),U_1890),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1887),U_1891),U_1888)),U_1889)),U_1892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1888),U_1889)),U_1890)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1891),U_1889)),U_1892)))
| ~ sP89(U_1887,U_1888,U_1889,U_1890,U_1891,U_1892) ),
inference(clausify,[status(thm)],[f_370_3]) ).
cnf(f_370_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1888),U_1889)),U_1890)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1891),U_1889)),U_1892)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1887),U_1890),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1887),U_1891),U_1888)),U_1889)),U_1892)))
| ~ sP89(U_1887,U_1888,U_1889,U_1890,U_1891,U_1892) ),
inference(clausify,[status(thm)],[f_370_3]) ).
fof(f_371_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2))) ) )
| ~ class_Rings_Oordered__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff1]) ).
fof(f_371_2,plain,
! [U_1898,U_1897,U_1896,U_1895,U_1894,U_1893] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1894),U_1895)),U_1896)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1897),U_1895)),U_1898)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1893),U_1894),U_1897)),U_1895)),U_1896)),U_1898)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1893),U_1894),U_1897)),U_1895)),U_1896)),U_1898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1894),U_1895)),U_1896)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1897),U_1895)),U_1898))) ) )
| ~ class_Rings_Oordered__ring(U_1893) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
fof(f_371_3,plain,
( ! [U_1893,U_1894,U_1895,U_1896,U_1897,U_1898] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1894),U_1895)),U_1896)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1897),U_1895)),U_1898)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1893),U_1894),U_1897)),U_1895)),U_1896)),U_1898))
| ~ sP90(U_1893,U_1894,U_1895,U_1896,U_1897,U_1898) )
& ! [U_1893,U_1894,U_1895,U_1896,U_1897,U_1898] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1893),U_1894),U_1897)),U_1895)),U_1896)),U_1898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1894),U_1895)),U_1896)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1897),U_1895)),U_1898)))
| ~ sP90(U_1893,U_1894,U_1895,U_1896,U_1897,U_1898) )
& ! [U_1893,U_1894,U_1895,U_1896,U_1897,U_1898] :
( sP90(U_1893,U_1894,U_1895,U_1896,U_1897,U_1898)
| ~ class_Rings_Oordered__ring(U_1893) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_371_2]) ).
cnf(f_371_4,plain,
( sP90(U_1893,U_1894,U_1895,U_1896,U_1897,U_1898)
| ~ class_Rings_Oordered__ring(U_1893) ),
inference(clausify,[status(thm)],[f_371_3]) ).
cnf(f_371_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1893),U_1894),U_1897)),U_1895)),U_1896)),U_1898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1894),U_1895)),U_1896)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1897),U_1895)),U_1898)))
| ~ sP90(U_1893,U_1894,U_1895,U_1896,U_1897,U_1898) ),
inference(clausify,[status(thm)],[f_371_3]) ).
cnf(f_371_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1894),U_1895)),U_1896)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1897),U_1895)),U_1898)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1893),U_1894),U_1897)),U_1895)),U_1896)),U_1898))
| ~ sP90(U_1893,U_1894,U_1895,U_1896,U_1897,U_1898) ),
inference(clausify,[status(thm)],[f_371_3]) ).
fof(f_372_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2)
| V_c_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_b_2),V_a_2)),V_e_2)),V_d_2) )
& ( V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_b_2),V_a_2)),V_e_2)),V_d_2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2) ) )
| ~ class_Rings_Oring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff2]) ).
fof(f_372_2,plain,
! [U_1904,U_1903,U_1902,U_1901,U_1900,U_1899] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1900),U_1901)),U_1902) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1903),U_1901)),U_1904)
| U_1902 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1899),U_1903),U_1900)),U_1901)),U_1904) )
& ( U_1902 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1899),U_1903),U_1900)),U_1901)),U_1904)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1900),U_1901)),U_1902) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1903),U_1901)),U_1904) ) )
| ~ class_Rings_Oring(U_1899) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
fof(f_372_3,plain,
( ! [U_1900,U_1899,U_1901,U_1902,U_1903,U_1904] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1900),U_1901)),U_1902) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1903),U_1901)),U_1904)
| U_1902 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1899),U_1903),U_1900)),U_1901)),U_1904)
| ~ sP91(U_1900,U_1899,U_1901,U_1902,U_1903,U_1904) )
& ! [U_1900,U_1899,U_1901,U_1902,U_1903,U_1904] :
( U_1902 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1899),U_1903),U_1900)),U_1901)),U_1904)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1900),U_1901)),U_1902) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1903),U_1901)),U_1904)
| ~ sP91(U_1900,U_1899,U_1901,U_1902,U_1903,U_1904) )
& ! [U_1900,U_1899,U_1901,U_1902,U_1903,U_1904] :
( sP91(U_1900,U_1899,U_1901,U_1902,U_1903,U_1904)
| ~ class_Rings_Oring(U_1899) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_372_2]) ).
cnf(f_372_4,plain,
( sP91(U_1900,U_1899,U_1901,U_1902,U_1903,U_1904)
| ~ class_Rings_Oring(U_1899) ),
inference(clausify,[status(thm)],[f_372_3]) ).
cnf(f_372_5,plain,
( U_1902 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1899),U_1903),U_1900)),U_1901)),U_1904)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1900),U_1901)),U_1902) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1903),U_1901)),U_1904)
| ~ sP91(U_1900,U_1899,U_1901,U_1902,U_1903,U_1904) ),
inference(clausify,[status(thm)],[f_372_3]) ).
cnf(f_372_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1900),U_1901)),U_1902) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1903),U_1901)),U_1904)
| U_1902 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1899),U_1903),U_1900)),U_1901)),U_1904)
| ~ sP91(U_1900,U_1899,U_1901,U_1902,U_1903,U_1904) ),
inference(clausify,[status(thm)],[f_372_3]) ).
fof(f_373_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),V_e_2)),V_c_2) != V_d_2 )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_e_2)),V_d_2) ) )
| ~ class_Rings_Oring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff1]) ).
fof(f_373_2,plain,
! [U_1910,U_1909,U_1908,U_1907,U_1906,U_1905] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1906),U_1907)),U_1908) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1909),U_1907)),U_1910)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1905),U_1906),U_1909)),U_1907)),U_1908) != U_1910 )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1905),U_1906),U_1909)),U_1907)),U_1908) = U_1910
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1906),U_1907)),U_1908) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1909),U_1907)),U_1910) ) )
| ~ class_Rings_Oring(U_1905) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
fof(f_373_3,plain,
( ! [U_1906,U_1905,U_1907,U_1908,U_1909,U_1910] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1906),U_1907)),U_1908) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1909),U_1907)),U_1910)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1905),U_1906),U_1909)),U_1907)),U_1908) != U_1910
| ~ sP92(U_1906,U_1905,U_1907,U_1908,U_1909,U_1910) )
& ! [U_1906,U_1905,U_1907,U_1908,U_1909,U_1910] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1905),U_1906),U_1909)),U_1907)),U_1908) = U_1910
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1906),U_1907)),U_1908) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1909),U_1907)),U_1910)
| ~ sP92(U_1906,U_1905,U_1907,U_1908,U_1909,U_1910) )
& ! [U_1906,U_1905,U_1907,U_1908,U_1909,U_1910] :
( sP92(U_1906,U_1905,U_1907,U_1908,U_1909,U_1910)
| ~ class_Rings_Oring(U_1905) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92])],[f_373_2]) ).
cnf(f_373_4,plain,
( sP92(U_1906,U_1905,U_1907,U_1908,U_1909,U_1910)
| ~ class_Rings_Oring(U_1905) ),
inference(clausify,[status(thm)],[f_373_3]) ).
cnf(f_373_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1905),U_1906),U_1909)),U_1907)),U_1908) = U_1910
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1906),U_1907)),U_1908) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1909),U_1907)),U_1910)
| ~ sP92(U_1906,U_1905,U_1907,U_1908,U_1909,U_1910) ),
inference(clausify,[status(thm)],[f_373_3]) ).
cnf(f_373_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1906),U_1907)),U_1908) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1909),U_1907)),U_1910)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1905),U_1906),U_1909)),U_1907)),U_1908) != U_1910
| ~ sP92(U_1906,U_1905,U_1907,U_1908,U_1909,U_1910) ),
inference(clausify,[status(thm)],[f_373_3]) ).
fof(f_374_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_374_2,plain,
! [U_1914,U_1913,U_1912,U_1911] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1911),U_1912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1911),U_1913),U_1914)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1911),U_1912),U_1913)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1911),U_1912),U_1914))
| ~ class_Rings_Ocomm__semiring__1(U_1911) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
fof(f_374_3,plain,
! [U_1911,U_1912,U_1913,U_1914] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1911),U_1912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1911),U_1913),U_1914)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1911),U_1912),U_1913)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1911),U_1912),U_1914))
| ~ class_Rings_Ocomm__semiring__1(U_1911) ),
inference(definitional_conversion,[status(esa)],[f_374_2]) ).
cnf(f_374_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1911),U_1912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1911),U_1913),U_1914)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1911),U_1912),U_1913)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1911),U_1912),U_1914))
| ~ class_Rings_Ocomm__semiring__1(U_1911) ),
inference(clausify,[status(thm)],[f_374_3]) ).
fof(f_375_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( ( ( ( V_c_2 != V_d_2
& V_a_2 != V_b_2 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_d_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_c_2)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_c_2))
| V_c_2 = V_d_2
| V_a_2 = V_b_2 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_c) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq]) ).
fof(f_375_2,plain,
! [U_1919,U_1918,U_1917,U_1916,U_1915] :
( ( ( ( U_1918 != U_1919
& U_1916 != U_1917 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1916),U_1918)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1917),U_1919)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1916),U_1919)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1917),U_1918)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1916),U_1918)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1917),U_1919)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1916),U_1919)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1917),U_1918))
| U_1918 = U_1919
| U_1916 = U_1917 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1915) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
fof(f_375_3,plain,
( ! [U_1916,U_1917,U_1918,U_1919] :
( U_1918 != U_1919
| ~ sP93(U_1916,U_1917,U_1918,U_1919) )
& ! [U_1916,U_1917,U_1918,U_1919] :
( U_1916 != U_1917
| ~ sP93(U_1916,U_1917,U_1918,U_1919) )
& ! [U_1915,U_1916,U_1917,U_1918,U_1919] :
( sP93(U_1916,U_1917,U_1918,U_1919)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1916),U_1918)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1917),U_1919)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1916),U_1919)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1917),U_1918))
| ~ sP94(U_1915,U_1916,U_1917,U_1918,U_1919) )
& ! [U_1915,U_1916,U_1917,U_1918,U_1919] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1916),U_1918)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1917),U_1919)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1916),U_1919)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1917),U_1918))
| U_1918 = U_1919
| U_1916 = U_1917
| ~ sP94(U_1915,U_1916,U_1917,U_1918,U_1919) )
& ! [U_1915,U_1916,U_1917,U_1918,U_1919] :
( sP94(U_1915,U_1916,U_1917,U_1918,U_1919)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1915) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP93,sP94])],[f_375_2]) ).
cnf(f_375_4,plain,
( sP94(U_1915,U_1916,U_1917,U_1918,U_1919)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1915) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1916),U_1918)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1917),U_1919)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1916),U_1919)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1917),U_1918))
| U_1918 = U_1919
| U_1916 = U_1917
| ~ sP94(U_1915,U_1916,U_1917,U_1918,U_1919) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_6,plain,
( sP93(U_1916,U_1917,U_1918,U_1919)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1916),U_1918)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1917),U_1919)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1916),U_1919)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1915),U_1917),U_1918))
| ~ sP94(U_1915,U_1916,U_1917,U_1918,U_1919) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_7,plain,
( U_1916 != U_1917
| ~ sP93(U_1916,U_1917,U_1918,U_1919) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_8,plain,
( U_1918 != U_1919
| ~ sP93(U_1916,U_1917,U_1918,U_1919) ),
inference(clausify,[status(thm)],[f_375_3]) ).
fof(f_376_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_376_2,plain,
! [U_1923,U_1922,U_1921,U_1920] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1920),U_1921),U_1922)),U_1923) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1920),U_1921),U_1923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1920),U_1922),U_1923))
| ~ class_Rings_Ocomm__semiring(U_1920) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
fof(f_376_3,plain,
! [U_1922,U_1923,U_1921,U_1920] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1920),U_1921),U_1922)),U_1923) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1920),U_1921),U_1923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1920),U_1922),U_1923))
| ~ class_Rings_Ocomm__semiring(U_1920) ),
inference(definitional_conversion,[status(esa)],[f_376_2]) ).
cnf(f_376_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1920),U_1921),U_1922)),U_1923) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1920),U_1921),U_1923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1920),U_1922),U_1923))
| ~ class_Rings_Ocomm__semiring(U_1920) ),
inference(clausify,[status(thm)],[f_376_3]) ).
fof(f_377_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_377_2,plain,
! [U_1927,U_1926,U_1925,U_1924] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1924),U_1925),U_1926)),U_1927) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),U_1925),U_1927)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),U_1926),U_1927))
| ~ class_Rings_Ocomm__semiring__1(U_1924) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
fof(f_377_3,plain,
! [U_1924,U_1925,U_1926,U_1927] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1924),U_1925),U_1926)),U_1927) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),U_1925),U_1927)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),U_1926),U_1927))
| ~ class_Rings_Ocomm__semiring__1(U_1924) ),
inference(definitional_conversion,[status(esa)],[f_377_2]) ).
cnf(f_377_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1924),U_1925),U_1926)),U_1927) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),U_1925),U_1927)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),U_1926),U_1927))
| ~ class_Rings_Ocomm__semiring__1(U_1924) ),
inference(clausify,[status(thm)],[f_377_3]) ).
fof(f_378_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_378_2,plain,
! [U_1930,U_1929,U_1928] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1928),U_1930),U_1929))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1928),U_1929),U_1930))
| U_1929 = U_1930
| ~ class_Rings_Olinordered__idom(U_1928) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
fof(f_378_3,plain,
! [U_1928,U_1929,U_1930] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1928),U_1930),U_1929))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1928),U_1929),U_1930))
| U_1929 = U_1930
| ~ class_Rings_Olinordered__idom(U_1928) ),
inference(definitional_conversion,[status(esa)],[f_378_2]) ).
cnf(f_378_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1928),U_1930),U_1929))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1928),U_1929),U_1930))
| U_1929 = U_1930
| ~ class_Rings_Olinordered__idom(U_1928) ),
inference(clausify,[status(thm)],[f_378_3]) ).
fof(f_379_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_379_2,plain,
! [U_1935,U_1934,U_1933,U_1932,U_1931] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),U_1932),U_1933)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),U_1934),U_1935)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),U_1932),U_1934)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),U_1933),U_1935))
| ~ class_Rings_Ocomm__semiring__1(U_1931) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
fof(f_379_3,plain,
! [U_1931,U_1932,U_1933,U_1934,U_1935] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),U_1932),U_1933)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),U_1934),U_1935)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),U_1932),U_1934)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),U_1933),U_1935))
| ~ class_Rings_Ocomm__semiring__1(U_1931) ),
inference(definitional_conversion,[status(esa)],[f_379_2]) ).
cnf(f_379_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),U_1932),U_1933)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),U_1934),U_1935)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),U_1932),U_1934)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1931),U_1933),U_1935))
| ~ class_Rings_Ocomm__semiring__1(U_1931) ),
inference(clausify,[status(thm)],[f_379_3]) ).
fof(f_380_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_380_2,plain,
! [U_1939,U_1938,U_1937,U_1936] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),U_1937),U_1938)),U_1939) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),U_1937),U_1939)),U_1938)
| ~ class_Rings_Ocomm__semiring__1(U_1936) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
fof(f_380_3,plain,
! [U_1936,U_1937,U_1938,U_1939] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),U_1937),U_1938)),U_1939) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),U_1937),U_1939)),U_1938)
| ~ class_Rings_Ocomm__semiring__1(U_1936) ),
inference(definitional_conversion,[status(esa)],[f_380_2]) ).
cnf(f_380_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),U_1937),U_1938)),U_1939) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),U_1937),U_1939)),U_1938)
| ~ class_Rings_Ocomm__semiring__1(U_1936) ),
inference(clausify,[status(thm)],[f_380_3]) ).
fof(f_381_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_381_2,plain,
! [U_1943,U_1942,U_1941,U_1940] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),U_1941),U_1942)),U_1943) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),U_1941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),U_1942),U_1943))
| ~ class_Rings_Ocomm__semiring__1(U_1940) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
fof(f_381_3,plain,
! [U_1940,U_1941,U_1942,U_1943] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),U_1941),U_1942)),U_1943) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),U_1941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),U_1942),U_1943))
| ~ class_Rings_Ocomm__semiring__1(U_1940) ),
inference(definitional_conversion,[status(esa)],[f_381_2]) ).
cnf(f_381_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),U_1941),U_1942)),U_1943) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),U_1941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1940),U_1942),U_1943))
| ~ class_Rings_Ocomm__semiring__1(U_1940) ),
inference(clausify,[status(thm)],[f_381_3]) ).
fof(f_382_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_382_2,plain,
! [U_1947,U_1946,U_1945,U_1944] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),U_1945),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),U_1946),U_1947)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),U_1945),U_1946)),U_1947)
| ~ class_Rings_Ocomm__semiring__1(U_1944) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
fof(f_382_3,plain,
! [U_1944,U_1945,U_1946,U_1947] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),U_1945),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),U_1946),U_1947)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),U_1945),U_1946)),U_1947)
| ~ class_Rings_Ocomm__semiring__1(U_1944) ),
inference(definitional_conversion,[status(esa)],[f_382_2]) ).
cnf(f_382_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),U_1945),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),U_1946),U_1947)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),U_1945),U_1946)),U_1947)
| ~ class_Rings_Ocomm__semiring__1(U_1944) ),
inference(clausify,[status(thm)],[f_382_3]) ).
fof(f_383_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_383_2,plain,
! [U_1951,U_1950,U_1949,U_1948] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1948),U_1949),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1948),U_1950),U_1951)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1948),U_1950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1948),U_1949),U_1951))
| ~ class_Rings_Ocomm__semiring__1(U_1948) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
! [U_1948,U_1949,U_1950,U_1951] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1948),U_1949),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1948),U_1950),U_1951)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1948),U_1950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1948),U_1949),U_1951))
| ~ class_Rings_Ocomm__semiring__1(U_1948) ),
inference(definitional_conversion,[status(esa)],[f_383_2]) ).
cnf(f_383_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1948),U_1949),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1948),U_1950),U_1951)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1948),U_1950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1948),U_1949),U_1951))
| ~ class_Rings_Ocomm__semiring__1(U_1948) ),
inference(clausify,[status(thm)],[f_383_3]) ).
fof(f_384_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_384_2,plain,
! [U_1954,U_1953,U_1952] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1952),U_1953),U_1954) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1952),U_1954),U_1953)
| ~ class_Rings_Ocomm__semiring__1(U_1952) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
fof(f_384_3,plain,
! [U_1952,U_1953,U_1954] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1952),U_1953),U_1954) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1952),U_1954),U_1953)
| ~ class_Rings_Ocomm__semiring__1(U_1952) ),
inference(definitional_conversion,[status(esa)],[f_384_2]) ).
cnf(f_384_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1952),U_1953),U_1954) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1952),U_1954),U_1953)
| ~ class_Rings_Ocomm__semiring__1(U_1952) ),
inference(clausify,[status(thm)],[f_384_3]) ).
fof(f_385_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_385_2,plain,
! [U_1959,U_1958,U_1957,U_1956,U_1955] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1956),U_1957)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1958),U_1959)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1956),U_1958)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1957),U_1959))
| ~ class_Rings_Ocomm__semiring__1(U_1955) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
fof(f_385_3,plain,
! [U_1955,U_1956,U_1957,U_1958,U_1959] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1956),U_1957)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1958),U_1959)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1956),U_1958)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1957),U_1959))
| ~ class_Rings_Ocomm__semiring__1(U_1955) ),
inference(definitional_conversion,[status(esa)],[f_385_2]) ).
cnf(f_385_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1956),U_1957)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1958),U_1959)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1956),U_1958)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1957),U_1959))
| ~ class_Rings_Ocomm__semiring__1(U_1955) ),
inference(clausify,[status(thm)],[f_385_3]) ).
fof(f_386_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_386_2,plain,
! [U_1964,U_1963,U_1962,U_1961,U_1960] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),U_1961),U_1962)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),U_1963),U_1964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),U_1963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),U_1961),U_1962)),U_1964))
| ~ class_Rings_Ocomm__semiring__1(U_1960) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
fof(f_386_3,plain,
! [U_1960,U_1961,U_1962,U_1963,U_1964] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),U_1961),U_1962)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),U_1963),U_1964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),U_1963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),U_1961),U_1962)),U_1964))
| ~ class_Rings_Ocomm__semiring__1(U_1960) ),
inference(definitional_conversion,[status(esa)],[f_386_2]) ).
cnf(f_386_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),U_1961),U_1962)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),U_1963),U_1964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),U_1963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1960),U_1961),U_1962)),U_1964))
| ~ class_Rings_Ocomm__semiring__1(U_1960) ),
inference(clausify,[status(thm)],[f_386_3]) ).
fof(f_387_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_387_2,plain,
! [U_1969,U_1968,U_1967,U_1966,U_1965] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1966),U_1967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1968),U_1969)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1968),U_1969)))
| ~ class_Rings_Ocomm__semiring__1(U_1965) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
fof(f_387_3,plain,
! [U_1965,U_1966,U_1967,U_1968,U_1969] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1966),U_1967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1968),U_1969)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1968),U_1969)))
| ~ class_Rings_Ocomm__semiring__1(U_1965) ),
inference(definitional_conversion,[status(esa)],[f_387_2]) ).
cnf(f_387_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1966),U_1967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1968),U_1969)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1968),U_1969)))
| ~ class_Rings_Ocomm__semiring__1(U_1965) ),
inference(clausify,[status(thm)],[f_387_3]) ).
fof(f_388_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_388_2,plain,
! [U_1973,U_1972,U_1971,U_1970] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),U_1971),U_1972)),U_1973) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),U_1971),U_1973)),U_1972)
| ~ class_Rings_Ocomm__semiring__1(U_1970) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
fof(f_388_3,plain,
! [U_1970,U_1971,U_1972,U_1973] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),U_1971),U_1972)),U_1973) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),U_1971),U_1973)),U_1972)
| ~ class_Rings_Ocomm__semiring__1(U_1970) ),
inference(definitional_conversion,[status(esa)],[f_388_2]) ).
cnf(f_388_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),U_1971),U_1972)),U_1973) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),U_1971),U_1973)),U_1972)
| ~ class_Rings_Ocomm__semiring__1(U_1970) ),
inference(clausify,[status(thm)],[f_388_3]) ).
fof(f_389_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_389_2,plain,
! [U_1977,U_1976,U_1975,U_1974] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1976)),U_1977) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1976),U_1977))
| ~ class_Rings_Ocomm__semiring__1(U_1974) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
fof(f_389_3,plain,
! [U_1974,U_1975,U_1976,U_1977] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1976)),U_1977) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1976),U_1977))
| ~ class_Rings_Ocomm__semiring__1(U_1974) ),
inference(definitional_conversion,[status(esa)],[f_389_2]) ).
cnf(f_389_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1976)),U_1977) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1976),U_1977))
| ~ class_Rings_Ocomm__semiring__1(U_1974) ),
inference(clausify,[status(thm)],[f_389_3]) ).
fof(f_390_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_390_2,plain,
! [U_1981,U_1980,U_1979,U_1978] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1978),U_1979),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1978),U_1980),U_1981)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1978),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1978),U_1979),U_1980)),U_1981)
| ~ class_Rings_Ocomm__semiring__1(U_1978) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
fof(f_390_3,plain,
! [U_1978,U_1979,U_1980,U_1981] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1978),U_1979),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1978),U_1980),U_1981)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1978),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1978),U_1979),U_1980)),U_1981)
| ~ class_Rings_Ocomm__semiring__1(U_1978) ),
inference(definitional_conversion,[status(esa)],[f_390_2]) ).
cnf(f_390_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1978),U_1979),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1978),U_1980),U_1981)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1978),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1978),U_1979),U_1980)),U_1981)
| ~ class_Rings_Ocomm__semiring__1(U_1978) ),
inference(clausify,[status(thm)],[f_390_3]) ).
fof(f_391_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_391_2,plain,
! [U_1985,U_1984,U_1983,U_1982] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1982),U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1982),U_1984),U_1985)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1982),U_1984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1982),U_1983),U_1985))
| ~ class_Rings_Ocomm__semiring__1(U_1982) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
fof(f_391_3,plain,
! [U_1982,U_1983,U_1984,U_1985] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1982),U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1982),U_1984),U_1985)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1982),U_1984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1982),U_1983),U_1985))
| ~ class_Rings_Ocomm__semiring__1(U_1982) ),
inference(definitional_conversion,[status(esa)],[f_391_2]) ).
cnf(f_391_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1982),U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1982),U_1984),U_1985)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1982),U_1984),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1982),U_1983),U_1985))
| ~ class_Rings_Ocomm__semiring__1(U_1982) ),
inference(clausify,[status(thm)],[f_391_3]) ).
fof(f_392_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_392_2,plain,
! [U_1988,U_1987,U_1986] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1986),U_1987),U_1988) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1986),U_1988),U_1987)
| ~ class_Rings_Ocomm__semiring__1(U_1986) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
fof(f_392_3,plain,
! [U_1986,U_1987,U_1988] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1986),U_1987),U_1988) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1986),U_1988),U_1987)
| ~ class_Rings_Ocomm__semiring__1(U_1986) ),
inference(definitional_conversion,[status(esa)],[f_392_2]) ).
cnf(f_392_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1986),U_1987),U_1988) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1986),U_1988),U_1987)
| ~ class_Rings_Ocomm__semiring__1(U_1986) ),
inference(clausify,[status(thm)],[f_392_3]) ).
fof(f_393_1,plain,
! [V_z_2,V_x_2,V_y_2,V_w_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),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_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_z_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_y_2)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_c) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__eq]) ).
fof(f_393_2,plain,
! [U_1993,U_1992,U_1991,U_1990,U_1989] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1990),U_1991)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1992),U_1993)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1990),U_1993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1992),U_1991))
| ( U_1991 != U_1993
& U_1990 != U_1992 ) )
& ( U_1991 = U_1993
| U_1990 = U_1992
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1990),U_1991)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1992),U_1993)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1990),U_1993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1992),U_1991)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1989) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
fof(f_393_3,plain,
( ! [U_1990,U_1991,U_1992,U_1993] :
( U_1991 != U_1993
| ~ sP95(U_1990,U_1991,U_1992,U_1993) )
& ! [U_1990,U_1991,U_1992,U_1993] :
( U_1990 != U_1992
| ~ sP95(U_1990,U_1991,U_1992,U_1993) )
& ! [U_1989,U_1990,U_1991,U_1992,U_1993] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1990),U_1991)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1992),U_1993)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1990),U_1993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1992),U_1991))
| sP95(U_1990,U_1991,U_1992,U_1993)
| ~ sP96(U_1989,U_1990,U_1991,U_1992,U_1993) )
& ! [U_1989,U_1990,U_1991,U_1992,U_1993] :
( U_1991 = U_1993
| U_1990 = U_1992
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1990),U_1991)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1992),U_1993)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1990),U_1993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1992),U_1991))
| ~ sP96(U_1989,U_1990,U_1991,U_1992,U_1993) )
& ! [U_1989,U_1990,U_1991,U_1992,U_1993] :
( sP96(U_1989,U_1990,U_1991,U_1992,U_1993)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1989) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95,sP96])],[f_393_2]) ).
cnf(f_393_4,plain,
( sP96(U_1989,U_1990,U_1991,U_1992,U_1993)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1989) ),
inference(clausify,[status(thm)],[f_393_3]) ).
cnf(f_393_5,plain,
( U_1991 = U_1993
| U_1990 = U_1992
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1990),U_1991)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1992),U_1993)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1990),U_1993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1992),U_1991))
| ~ sP96(U_1989,U_1990,U_1991,U_1992,U_1993) ),
inference(clausify,[status(thm)],[f_393_3]) ).
cnf(f_393_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1990),U_1991)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1992),U_1993)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1989),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1990),U_1993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1989),U_1992),U_1991))
| sP95(U_1990,U_1991,U_1992,U_1993)
| ~ sP96(U_1989,U_1990,U_1991,U_1992,U_1993) ),
inference(clausify,[status(thm)],[f_393_3]) ).
cnf(f_393_7,plain,
( U_1990 != U_1992
| ~ sP95(U_1990,U_1991,U_1992,U_1993) ),
inference(clausify,[status(thm)],[f_393_3]) ).
cnf(f_393_8,plain,
( U_1991 != U_1993
| ~ sP95(U_1990,U_1991,U_1992,U_1993) ),
inference(clausify,[status(thm)],[f_393_3]) ).
fof(f_394_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_394_2,plain,
! [U_1998,U_1997,U_1996,U_1995,U_1994] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1994),U_1995),U_1996)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1994),U_1997),U_1996)),U_1998)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1994),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1994),U_1995),U_1997)),U_1996)),U_1998)
| ~ class_Rings_Osemiring(U_1994) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
! [U_1995,U_1996,U_1997,U_1994,U_1998] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1994),U_1995),U_1996)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1994),U_1997),U_1996)),U_1998)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1994),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1994),U_1995),U_1997)),U_1996)),U_1998)
| ~ class_Rings_Osemiring(U_1994) ),
inference(definitional_conversion,[status(esa)],[f_394_2]) ).
cnf(f_394_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1994),U_1995),U_1996)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1994),U_1997),U_1996)),U_1998)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1994),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1994),U_1995),U_1997)),U_1996)),U_1998)
| ~ class_Rings_Osemiring(U_1994) ),
inference(clausify,[status(thm)],[f_394_3]) ).
fof(f_395_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_395_2,plain,
! [U_2002,U_2001,U_2000,U_1999] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1999),U_2000),U_2001)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1999),U_2002),U_2001)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1999),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1999),U_2000),U_2002)),U_2001)
| ~ class_Rings_Ocomm__semiring__1(U_1999) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
fof(f_395_3,plain,
! [U_1999,U_2000,U_2001,U_2002] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1999),U_2000),U_2001)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1999),U_2002),U_2001)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1999),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1999),U_2000),U_2002)),U_2001)
| ~ class_Rings_Ocomm__semiring__1(U_1999) ),
inference(definitional_conversion,[status(esa)],[f_395_2]) ).
cnf(f_395_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1999),U_2000),U_2001)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1999),U_2002),U_2001)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1999),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1999),U_2000),U_2002)),U_2001)
| ~ class_Rings_Ocomm__semiring__1(U_1999) ),
inference(clausify,[status(thm)],[f_395_3]) ).
fof(f_396_1,plain,
! [V_g_2,V_f_2,V_A_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_d),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_d)
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__strict__mono]) ).
fof(f_396_2,plain,
! [U_2008,U_2007,U_2006,U_2005,U_2004] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2004),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2005,U_2004),U_2007),U_2006)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2005,U_2004),U_2008),U_2006)))
| ? [U_2003] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2004),hAPP(U_2007,U_2003)),hAPP(U_2008,U_2003)))
& hBOOL(hAPP(hAPP(c_member(U_2005),U_2003),U_2006)) )
| U_2006 = c_Orderings_Obot__class_Obot(tc_fun(U_2005,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2005),U_2006))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2004)
| ~ class_Groups_Ocomm__monoid__add(U_2004) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
fof(f_396_3,plain,
! [U_2008,U_2007,U_2006,U_2005,U_2004] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2004),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2005,U_2004),U_2007),U_2006)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2005,U_2004),U_2008),U_2006)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2004),hAPP(U_2007,sK37(U_2008,U_2007,U_2006,U_2005,U_2004))),hAPP(U_2008,sK37(U_2008,U_2007,U_2006,U_2005,U_2004))))
& hBOOL(hAPP(hAPP(c_member(U_2005),sK37(U_2008,U_2007,U_2006,U_2005,U_2004)),U_2006)) )
| U_2006 = c_Orderings_Obot__class_Obot(tc_fun(U_2005,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2005),U_2006))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2004)
| ~ class_Groups_Ocomm__monoid__add(U_2004) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_2003,sK37(U_2008,U_2007,U_2006,U_2005,U_2004))],[f_396_2]) ).
fof(f_396_4,plain,
( ! [U_2004,U_2005,U_2006,U_2007,U_2008] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2004),hAPP(U_2007,sK37(U_2008,U_2007,U_2006,U_2005,U_2004))),hAPP(U_2008,sK37(U_2008,U_2007,U_2006,U_2005,U_2004))))
| ~ sP97(U_2004,U_2005,U_2006,U_2007,U_2008) )
& ! [U_2004,U_2005,U_2006,U_2007,U_2008] :
( hBOOL(hAPP(hAPP(c_member(U_2005),sK37(U_2008,U_2007,U_2006,U_2005,U_2004)),U_2006))
| ~ sP97(U_2004,U_2005,U_2006,U_2007,U_2008) )
& ! [U_2004,U_2005,U_2006,U_2007,U_2008] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2004),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2005,U_2004),U_2007),U_2006)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2005,U_2004),U_2008),U_2006)))
| sP97(U_2004,U_2005,U_2006,U_2007,U_2008)
| U_2006 = c_Orderings_Obot__class_Obot(tc_fun(U_2005,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2005),U_2006))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2004)
| ~ class_Groups_Ocomm__monoid__add(U_2004) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP97])],[f_396_3]) ).
cnf(f_396_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2004),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2005,U_2004),U_2007),U_2006)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2005,U_2004),U_2008),U_2006)))
| sP97(U_2004,U_2005,U_2006,U_2007,U_2008)
| U_2006 = c_Orderings_Obot__class_Obot(tc_fun(U_2005,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2005),U_2006))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2004)
| ~ class_Groups_Ocomm__monoid__add(U_2004) ),
inference(clausify,[status(thm)],[f_396_4]) ).
cnf(f_396_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2005),sK37(U_2008,U_2007,U_2006,U_2005,U_2004)),U_2006))
| ~ sP97(U_2004,U_2005,U_2006,U_2007,U_2008) ),
inference(clausify,[status(thm)],[f_396_4]) ).
cnf(f_396_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2004),hAPP(U_2007,sK37(U_2008,U_2007,U_2006,U_2005,U_2004))),hAPP(U_2008,sK37(U_2008,U_2007,U_2006,U_2005,U_2004))))
| ~ sP97(U_2004,U_2005,U_2006,U_2007,U_2008) ),
inference(clausify,[status(thm)],[f_396_4]) ).
fof(f_397_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) = V_x_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)))) != 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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oremove]) ).
fof(f_397_2,plain,
! [U_2011,U_2010,U_2009] :
( ( ( c_Big__Operators_Olinorder__class_OMin(U_2009,U_2010) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2009),U_2011),c_Big__Operators_Olinorder__class_OMin(U_2009,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2009,tc_HOL_Obool)),U_2010),hAPP(hAPP(c_Set_Oinsert(U_2009),U_2011),c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2009,tc_HOL_Obool)),U_2010),hAPP(hAPP(c_Set_Oinsert(U_2009),U_2011),c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMin(U_2009,U_2010) = U_2011
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2009,tc_HOL_Obool)),U_2010),hAPP(hAPP(c_Set_Oinsert(U_2009),U_2011),c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2009),U_2011),U_2010))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2009),U_2010))
| ~ class_Orderings_Olinorder(U_2009) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
fof(f_397_3,plain,
( ! [U_2010,U_2009,U_2011] :
( c_Big__Operators_Olinorder__class_OMin(U_2009,U_2010) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2009),U_2011),c_Big__Operators_Olinorder__class_OMin(U_2009,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2009,tc_HOL_Obool)),U_2010),hAPP(hAPP(c_Set_Oinsert(U_2009),U_2011),c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2009,tc_HOL_Obool)),U_2010),hAPP(hAPP(c_Set_Oinsert(U_2009),U_2011),c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool))
| ~ sP98(U_2010,U_2009,U_2011) )
& ! [U_2010,U_2009,U_2011] :
( c_Big__Operators_Olinorder__class_OMin(U_2009,U_2010) = U_2011
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2009,tc_HOL_Obool)),U_2010),hAPP(hAPP(c_Set_Oinsert(U_2009),U_2011),c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool))
| ~ sP98(U_2010,U_2009,U_2011) )
& ! [U_2010,U_2009,U_2011] :
( sP98(U_2010,U_2009,U_2011)
| ~ hBOOL(hAPP(hAPP(c_member(U_2009),U_2011),U_2010))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2009),U_2010))
| ~ class_Orderings_Olinorder(U_2009) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98])],[f_397_2]) ).
cnf(f_397_4,plain,
( sP98(U_2010,U_2009,U_2011)
| ~ hBOOL(hAPP(hAPP(c_member(U_2009),U_2011),U_2010))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2009),U_2010))
| ~ class_Orderings_Olinorder(U_2009) ),
inference(clausify,[status(thm)],[f_397_3]) ).
cnf(f_397_5,plain,
( c_Big__Operators_Olinorder__class_OMin(U_2009,U_2010) = U_2011
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2009,tc_HOL_Obool)),U_2010),hAPP(hAPP(c_Set_Oinsert(U_2009),U_2011),c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool))
| ~ sP98(U_2010,U_2009,U_2011) ),
inference(clausify,[status(thm)],[f_397_3]) ).
cnf(f_397_6,plain,
( c_Big__Operators_Olinorder__class_OMin(U_2009,U_2010) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2009),U_2011),c_Big__Operators_Olinorder__class_OMin(U_2009,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2009,tc_HOL_Obool)),U_2010),hAPP(hAPP(c_Set_Oinsert(U_2009),U_2011),c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2009,tc_HOL_Obool)),U_2010),hAPP(hAPP(c_Set_Oinsert(U_2009),U_2011),c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2009,tc_HOL_Obool))
| ~ sP98(U_2010,U_2009,U_2011) ),
inference(clausify,[status(thm)],[f_397_3]) ).
fof(f_398_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) = V_x_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)))) != 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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oremove]) ).
fof(f_398_2,plain,
! [U_2014,U_2013,U_2012] :
( ( ( c_Big__Operators_Olinorder__class_OMax(U_2012,U_2013) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2012),U_2014),c_Big__Operators_Olinorder__class_OMax(U_2012,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2012,tc_HOL_Obool)),U_2013),hAPP(hAPP(c_Set_Oinsert(U_2012),U_2014),c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2012,tc_HOL_Obool)),U_2013),hAPP(hAPP(c_Set_Oinsert(U_2012),U_2014),c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMax(U_2012,U_2013) = U_2014
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2012,tc_HOL_Obool)),U_2013),hAPP(hAPP(c_Set_Oinsert(U_2012),U_2014),c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2012),U_2014),U_2013))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2012),U_2013))
| ~ class_Orderings_Olinorder(U_2012) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
fof(f_398_3,plain,
( ! [U_2013,U_2014,U_2012] :
( c_Big__Operators_Olinorder__class_OMax(U_2012,U_2013) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2012),U_2014),c_Big__Operators_Olinorder__class_OMax(U_2012,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2012,tc_HOL_Obool)),U_2013),hAPP(hAPP(c_Set_Oinsert(U_2012),U_2014),c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2012,tc_HOL_Obool)),U_2013),hAPP(hAPP(c_Set_Oinsert(U_2012),U_2014),c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool))
| ~ sP99(U_2013,U_2014,U_2012) )
& ! [U_2013,U_2014,U_2012] :
( c_Big__Operators_Olinorder__class_OMax(U_2012,U_2013) = U_2014
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2012,tc_HOL_Obool)),U_2013),hAPP(hAPP(c_Set_Oinsert(U_2012),U_2014),c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool))
| ~ sP99(U_2013,U_2014,U_2012) )
& ! [U_2013,U_2014,U_2012] :
( sP99(U_2013,U_2014,U_2012)
| ~ hBOOL(hAPP(hAPP(c_member(U_2012),U_2014),U_2013))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2012),U_2013))
| ~ class_Orderings_Olinorder(U_2012) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99])],[f_398_2]) ).
cnf(f_398_4,plain,
( sP99(U_2013,U_2014,U_2012)
| ~ hBOOL(hAPP(hAPP(c_member(U_2012),U_2014),U_2013))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2012),U_2013))
| ~ class_Orderings_Olinorder(U_2012) ),
inference(clausify,[status(thm)],[f_398_3]) ).
cnf(f_398_5,plain,
( c_Big__Operators_Olinorder__class_OMax(U_2012,U_2013) = U_2014
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2012,tc_HOL_Obool)),U_2013),hAPP(hAPP(c_Set_Oinsert(U_2012),U_2014),c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool))
| ~ sP99(U_2013,U_2014,U_2012) ),
inference(clausify,[status(thm)],[f_398_3]) ).
cnf(f_398_6,plain,
( c_Big__Operators_Olinorder__class_OMax(U_2012,U_2013) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2012),U_2014),c_Big__Operators_Olinorder__class_OMax(U_2012,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2012,tc_HOL_Obool)),U_2013),hAPP(hAPP(c_Set_Oinsert(U_2012),U_2014),c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2012,tc_HOL_Obool)),U_2013),hAPP(hAPP(c_Set_Oinsert(U_2012),U_2014),c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2012,tc_HOL_Obool))
| ~ sP99(U_2013,U_2014,U_2012) ),
inference(clausify,[status(thm)],[f_398_3]) ).
fof(f_399_1,plain,
! [V_a_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c)),V_a_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold]) ).
fof(f_399_2,plain,
! [U_2017,U_2016,U_2015] :
( hAPP(c_Finite__Set_Ofold1(U_2015,c_Groups_Otimes__class_Otimes(U_2015)),hAPP(hAPP(c_Set_Oinsert(U_2015),U_2017),U_2016)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2015,U_2015,c_Groups_Otimes__class_Otimes(U_2015)),U_2017),U_2016)
| hBOOL(hAPP(hAPP(c_member(U_2015),U_2017),U_2016))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2015),U_2016))
| ~ class_Groups_Oab__semigroup__mult(U_2015) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
fof(f_399_3,plain,
! [U_2016,U_2017,U_2015] :
( hAPP(c_Finite__Set_Ofold1(U_2015,c_Groups_Otimes__class_Otimes(U_2015)),hAPP(hAPP(c_Set_Oinsert(U_2015),U_2017),U_2016)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2015,U_2015,c_Groups_Otimes__class_Otimes(U_2015)),U_2017),U_2016)
| hBOOL(hAPP(hAPP(c_member(U_2015),U_2017),U_2016))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2015),U_2016))
| ~ class_Groups_Oab__semigroup__mult(U_2015) ),
inference(definitional_conversion,[status(esa)],[f_399_2]) ).
cnf(f_399_4,plain,
( hAPP(c_Finite__Set_Ofold1(U_2015,c_Groups_Otimes__class_Otimes(U_2015)),hAPP(hAPP(c_Set_Oinsert(U_2015),U_2017),U_2016)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2015,U_2015,c_Groups_Otimes__class_Otimes(U_2015)),U_2017),U_2016)
| hBOOL(hAPP(hAPP(c_member(U_2015),U_2017),U_2016))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2015),U_2016))
| ~ class_Groups_Oab__semigroup__mult(U_2015) ),
inference(clausify,[status(thm)],[f_399_3]) ).
fof(f_400_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold1__insert]) ).
fof(f_400_2,plain,
! [U_2020,U_2019,U_2018] :
( hAPP(c_Finite__Set_Ofold1(U_2018,c_Groups_Otimes__class_Otimes(U_2018)),hAPP(hAPP(c_Set_Oinsert(U_2018),U_2020),U_2019)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2018),U_2020),hAPP(c_Finite__Set_Ofold1(U_2018,c_Groups_Otimes__class_Otimes(U_2018)),U_2019))
| hBOOL(hAPP(hAPP(c_member(U_2018),U_2020),U_2019))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2018),U_2019))
| U_2019 = c_Orderings_Obot__class_Obot(tc_fun(U_2018,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(U_2018) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
fof(f_400_3,plain,
! [U_2018,U_2019,U_2020] :
( hAPP(c_Finite__Set_Ofold1(U_2018,c_Groups_Otimes__class_Otimes(U_2018)),hAPP(hAPP(c_Set_Oinsert(U_2018),U_2020),U_2019)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2018),U_2020),hAPP(c_Finite__Set_Ofold1(U_2018,c_Groups_Otimes__class_Otimes(U_2018)),U_2019))
| hBOOL(hAPP(hAPP(c_member(U_2018),U_2020),U_2019))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2018),U_2019))
| U_2019 = c_Orderings_Obot__class_Obot(tc_fun(U_2018,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(U_2018) ),
inference(definitional_conversion,[status(esa)],[f_400_2]) ).
cnf(f_400_4,plain,
( hAPP(c_Finite__Set_Ofold1(U_2018,c_Groups_Otimes__class_Otimes(U_2018)),hAPP(hAPP(c_Set_Oinsert(U_2018),U_2020),U_2019)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2018),U_2020),hAPP(c_Finite__Set_Ofold1(U_2018,c_Groups_Otimes__class_Otimes(U_2018)),U_2019))
| hBOOL(hAPP(hAPP(c_member(U_2018),U_2020),U_2019))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2018),U_2019))
| U_2019 = c_Orderings_Obot__class_Obot(tc_fun(U_2018,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(U_2018) ),
inference(clausify,[status(thm)],[f_400_3]) ).
fof(f_401_1,plain,
! [V_g_2,V_x_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oremove]) ).
fof(f_401_2,plain,
! [U_2025,U_2024,U_2023,U_2022,U_2021] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2022,U_2021),U_2025),U_2023) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2021),hAPP(U_2025,U_2024)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2022,U_2021),U_2025),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2022,tc_HOL_Obool)),U_2023),hAPP(hAPP(c_Set_Oinsert(U_2022),U_2024),c_Orderings_Obot__class_Obot(tc_fun(U_2022,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2022),U_2024),U_2023))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2022),U_2023))
| ~ class_Groups_Ocomm__monoid__mult(U_2021) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
fof(f_401_3,plain,
! [U_2021,U_2022,U_2023,U_2024,U_2025] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2022,U_2021),U_2025),U_2023) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2021),hAPP(U_2025,U_2024)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2022,U_2021),U_2025),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2022,tc_HOL_Obool)),U_2023),hAPP(hAPP(c_Set_Oinsert(U_2022),U_2024),c_Orderings_Obot__class_Obot(tc_fun(U_2022,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2022),U_2024),U_2023))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2022),U_2023))
| ~ class_Groups_Ocomm__monoid__mult(U_2021) ),
inference(definitional_conversion,[status(esa)],[f_401_2]) ).
cnf(f_401_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2022,U_2021),U_2025),U_2023) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2021),hAPP(U_2025,U_2024)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2022,U_2021),U_2025),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2022,tc_HOL_Obool)),U_2023),hAPP(hAPP(c_Set_Oinsert(U_2022),U_2024),c_Orderings_Obot__class_Obot(tc_fun(U_2022,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_2022),U_2024),U_2023))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2022),U_2023))
| ~ class_Groups_Ocomm__monoid__mult(U_2021) ),
inference(clausify,[status(thm)],[f_401_3]) ).
fof(f_402_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ? [B_y] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),B_y))
& hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min__eqI]) ).
fof(f_402_2,plain,
! [U_2029,U_2028,U_2027] :
( c_Big__Operators_Olinorder__class_OMin(U_2027,U_2028) = U_2029
| ~ hBOOL(hAPP(hAPP(c_member(U_2027),U_2029),U_2028))
| ? [U_2026] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2027),U_2029),U_2026))
& hBOOL(hAPP(hAPP(c_member(U_2027),U_2026),U_2028)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2027),U_2028))
| ~ class_Orderings_Olinorder(U_2027) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
fof(f_402_3,plain,
! [U_2029,U_2028,U_2027] :
( c_Big__Operators_Olinorder__class_OMin(U_2027,U_2028) = U_2029
| ~ hBOOL(hAPP(hAPP(c_member(U_2027),U_2029),U_2028))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2027),U_2029),sK38(U_2029,U_2028,U_2027)))
& hBOOL(hAPP(hAPP(c_member(U_2027),sK38(U_2029,U_2028,U_2027)),U_2028)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2027),U_2028))
| ~ class_Orderings_Olinorder(U_2027) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_2026,sK38(U_2029,U_2028,U_2027))],[f_402_2]) ).
fof(f_402_4,plain,
( ! [U_2027,U_2028,U_2029] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2027),U_2029),sK38(U_2029,U_2028,U_2027)))
| ~ sP100(U_2027,U_2028,U_2029) )
& ! [U_2027,U_2028,U_2029] :
( hBOOL(hAPP(hAPP(c_member(U_2027),sK38(U_2029,U_2028,U_2027)),U_2028))
| ~ sP100(U_2027,U_2028,U_2029) )
& ! [U_2027,U_2028,U_2029] :
( c_Big__Operators_Olinorder__class_OMin(U_2027,U_2028) = U_2029
| ~ hBOOL(hAPP(hAPP(c_member(U_2027),U_2029),U_2028))
| sP100(U_2027,U_2028,U_2029)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2027),U_2028))
| ~ class_Orderings_Olinorder(U_2027) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100])],[f_402_3]) ).
cnf(f_402_5,plain,
( c_Big__Operators_Olinorder__class_OMin(U_2027,U_2028) = U_2029
| ~ hBOOL(hAPP(hAPP(c_member(U_2027),U_2029),U_2028))
| sP100(U_2027,U_2028,U_2029)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2027),U_2028))
| ~ class_Orderings_Olinorder(U_2027) ),
inference(clausify,[status(thm)],[f_402_4]) ).
cnf(f_402_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2027),sK38(U_2029,U_2028,U_2027)),U_2028))
| ~ sP100(U_2027,U_2028,U_2029) ),
inference(clausify,[status(thm)],[f_402_4]) ).
cnf(f_402_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2027),U_2029),sK38(U_2029,U_2028,U_2027)))
| ~ sP100(U_2027,U_2028,U_2029) ),
inference(clausify,[status(thm)],[f_402_4]) ).
fof(f_403_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ? [B_y] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_y),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max__eqI]) ).
fof(f_403_2,plain,
! [U_2033,U_2032,U_2031] :
( c_Big__Operators_Olinorder__class_OMax(U_2031,U_2032) = U_2033
| ~ hBOOL(hAPP(hAPP(c_member(U_2031),U_2033),U_2032))
| ? [U_2030] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2031),U_2030),U_2033))
& hBOOL(hAPP(hAPP(c_member(U_2031),U_2030),U_2032)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2031),U_2032))
| ~ class_Orderings_Olinorder(U_2031) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
fof(f_403_3,plain,
! [U_2033,U_2032,U_2031] :
( c_Big__Operators_Olinorder__class_OMax(U_2031,U_2032) = U_2033
| ~ hBOOL(hAPP(hAPP(c_member(U_2031),U_2033),U_2032))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2031),sK39(U_2033,U_2032,U_2031)),U_2033))
& hBOOL(hAPP(hAPP(c_member(U_2031),sK39(U_2033,U_2032,U_2031)),U_2032)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2031),U_2032))
| ~ class_Orderings_Olinorder(U_2031) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_2030,sK39(U_2033,U_2032,U_2031))],[f_403_2]) ).
fof(f_403_4,plain,
( ! [U_2033,U_2032,U_2031] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2031),sK39(U_2033,U_2032,U_2031)),U_2033))
| ~ sP101(U_2033,U_2032,U_2031) )
& ! [U_2033,U_2032,U_2031] :
( hBOOL(hAPP(hAPP(c_member(U_2031),sK39(U_2033,U_2032,U_2031)),U_2032))
| ~ sP101(U_2033,U_2032,U_2031) )
& ! [U_2033,U_2032,U_2031] :
( c_Big__Operators_Olinorder__class_OMax(U_2031,U_2032) = U_2033
| ~ hBOOL(hAPP(hAPP(c_member(U_2031),U_2033),U_2032))
| sP101(U_2033,U_2032,U_2031)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2031),U_2032))
| ~ class_Orderings_Olinorder(U_2031) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_403_3]) ).
cnf(f_403_5,plain,
( c_Big__Operators_Olinorder__class_OMax(U_2031,U_2032) = U_2033
| ~ hBOOL(hAPP(hAPP(c_member(U_2031),U_2033),U_2032))
| sP101(U_2033,U_2032,U_2031)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2031),U_2032))
| ~ class_Orderings_Olinorder(U_2031) ),
inference(clausify,[status(thm)],[f_403_4]) ).
cnf(f_403_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2031),sK39(U_2033,U_2032,U_2031)),U_2032))
| ~ sP101(U_2033,U_2032,U_2031) ),
inference(clausify,[status(thm)],[f_403_4]) ).
cnf(f_403_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2031),sK39(U_2033,U_2032,U_2031)),U_2033))
| ~ sP101(U_2033,U_2032,U_2031) ),
inference(clausify,[status(thm)],[f_403_4]) ).
fof(f_404_1,plain,
! [V_S_2,T_c] :
( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),V_S_2))
| V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_minus__Max__eq__Min]) ).
fof(f_404_2,plain,
! [U_2035,U_2034] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2034),c_Big__Operators_Olinorder__class_OMax(U_2034,U_2035)) = c_Big__Operators_Olinorder__class_OMin(U_2034,hAPP(c_Set_Oimage(U_2034,U_2034,c_Groups_Ouminus__class_Ouminus(U_2034)),U_2035))
| U_2035 = c_Orderings_Obot__class_Obot(tc_fun(U_2034,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2034),U_2035))
| ~ class_Groups_Olinordered__ab__group__add(U_2034) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
fof(f_404_3,plain,
! [U_2035,U_2034] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2034),c_Big__Operators_Olinorder__class_OMax(U_2034,U_2035)) = c_Big__Operators_Olinorder__class_OMin(U_2034,hAPP(c_Set_Oimage(U_2034,U_2034,c_Groups_Ouminus__class_Ouminus(U_2034)),U_2035))
| U_2035 = c_Orderings_Obot__class_Obot(tc_fun(U_2034,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2034),U_2035))
| ~ class_Groups_Olinordered__ab__group__add(U_2034) ),
inference(definitional_conversion,[status(esa)],[f_404_2]) ).
cnf(f_404_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2034),c_Big__Operators_Olinorder__class_OMax(U_2034,U_2035)) = c_Big__Operators_Olinorder__class_OMin(U_2034,hAPP(c_Set_Oimage(U_2034,U_2034,c_Groups_Ouminus__class_Ouminus(U_2034)),U_2035))
| U_2035 = c_Orderings_Obot__class_Obot(tc_fun(U_2034,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2034),U_2035))
| ~ class_Groups_Olinordered__ab__group__add(U_2034) ),
inference(clausify,[status(thm)],[f_404_3]) ).
fof(f_405_1,plain,
! [V_S_2,T_c] :
( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),V_S_2))
| V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_minus__Min__eq__Max]) ).
fof(f_405_2,plain,
! [U_2037,U_2036] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2036),c_Big__Operators_Olinorder__class_OMin(U_2036,U_2037)) = c_Big__Operators_Olinorder__class_OMax(U_2036,hAPP(c_Set_Oimage(U_2036,U_2036,c_Groups_Ouminus__class_Ouminus(U_2036)),U_2037))
| U_2037 = c_Orderings_Obot__class_Obot(tc_fun(U_2036,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2036),U_2037))
| ~ class_Groups_Olinordered__ab__group__add(U_2036) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
fof(f_405_3,plain,
! [U_2036,U_2037] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2036),c_Big__Operators_Olinorder__class_OMin(U_2036,U_2037)) = c_Big__Operators_Olinorder__class_OMax(U_2036,hAPP(c_Set_Oimage(U_2036,U_2036,c_Groups_Ouminus__class_Ouminus(U_2036)),U_2037))
| U_2037 = c_Orderings_Obot__class_Obot(tc_fun(U_2036,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2036),U_2037))
| ~ class_Groups_Olinordered__ab__group__add(U_2036) ),
inference(definitional_conversion,[status(esa)],[f_405_2]) ).
cnf(f_405_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2036),c_Big__Operators_Olinorder__class_OMin(U_2036,U_2037)) = c_Big__Operators_Olinorder__class_OMax(U_2036,hAPP(c_Set_Oimage(U_2036,U_2036,c_Groups_Ouminus__class_Ouminus(U_2036)),U_2037))
| U_2037 = c_Orderings_Obot__class_Obot(tc_fun(U_2036,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2036),U_2037))
| ~ class_Groups_Olinordered__ab__group__add(U_2036) ),
inference(clausify,[status(thm)],[f_405_3]) ).
fof(f_406_1,plain,
! [V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))
| hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_ComplI]) ).
fof(f_406_2,plain,
! [U_2040,U_2039,U_2038] :
( hBOOL(hAPP(hAPP(c_member(U_2038),U_2039),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2038,tc_HOL_Obool)),U_2040)))
| hBOOL(hAPP(hAPP(c_member(U_2038),U_2039),U_2040)) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
fof(f_406_3,plain,
! [U_2038,U_2039,U_2040] :
( hBOOL(hAPP(hAPP(c_member(U_2038),U_2039),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2038,tc_HOL_Obool)),U_2040)))
| hBOOL(hAPP(hAPP(c_member(U_2038),U_2039),U_2040)) ),
inference(definitional_conversion,[status(esa)],[f_406_2]) ).
cnf(f_406_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2038),U_2039),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2038,tc_HOL_Obool)),U_2040)))
| hBOOL(hAPP(hAPP(c_member(U_2038),U_2039),U_2040)) ),
inference(clausify,[status(thm)],[f_406_3]) ).
fof(f_407_1,plain,
! [V_A_2,T_c] :
( c_Fun_Oinj__on(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c),V_A_2)
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inj__uminus]) ).
fof(f_407_2,plain,
! [U_2042,U_2041] :
( c_Fun_Oinj__on(U_2041,U_2041,c_Groups_Ouminus__class_Ouminus(U_2041),U_2042)
| ~ class_Groups_Oordered__ab__group__add(U_2041) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
fof(f_407_3,plain,
! [U_2041,U_2042] :
( c_Fun_Oinj__on(U_2041,U_2041,c_Groups_Ouminus__class_Ouminus(U_2041),U_2042)
| ~ class_Groups_Oordered__ab__group__add(U_2041) ),
inference(definitional_conversion,[status(esa)],[f_407_2]) ).
cnf(f_407_4,plain,
( c_Fun_Oinj__on(U_2041,U_2041,c_Groups_Ouminus__class_Ouminus(U_2041),U_2042)
| ~ class_Groups_Oordered__ab__group__add(U_2041) ),
inference(clausify,[status(thm)],[f_407_3]) ).
fof(f_408_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal]) ).
fof(f_408_2,plain,
! [U_2045,U_2044,U_2043] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2043),U_2044) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2043),U_2045)
| U_2044 != U_2045 )
& ( U_2044 = U_2045
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2043),U_2044) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2043),U_2045) ) )
| ~ class_Groups_Ogroup__add(U_2043) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
fof(f_408_3,plain,
( ! [U_2043,U_2044,U_2045] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2043),U_2044) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2043),U_2045)
| U_2044 != U_2045
| ~ sP102(U_2043,U_2044,U_2045) )
& ! [U_2043,U_2044,U_2045] :
( U_2044 = U_2045
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2043),U_2044) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2043),U_2045)
| ~ sP102(U_2043,U_2044,U_2045) )
& ! [U_2043,U_2044,U_2045] :
( sP102(U_2043,U_2044,U_2045)
| ~ class_Groups_Ogroup__add(U_2043) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_408_2]) ).
cnf(f_408_4,plain,
( sP102(U_2043,U_2044,U_2045)
| ~ class_Groups_Ogroup__add(U_2043) ),
inference(clausify,[status(thm)],[f_408_3]) ).
cnf(f_408_5,plain,
( U_2044 = U_2045
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2043),U_2044) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2043),U_2045)
| ~ sP102(U_2043,U_2044,U_2045) ),
inference(clausify,[status(thm)],[f_408_3]) ).
cnf(f_408_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2043),U_2044) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2043),U_2045)
| U_2044 != U_2045
| ~ sP102(U_2043,U_2044,U_2045) ),
inference(clausify,[status(thm)],[f_408_3]) ).
fof(f_409_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) = V_b_2
| hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2) != V_a_2 )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2) = V_a_2
| hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) != V_b_2 ) )
| ~ class_Groups_Ogroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_minus__equation__iff]) ).
fof(f_409_2,plain,
! [U_2048,U_2047,U_2046] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2046),U_2047) = U_2048
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2046),U_2048) != U_2047 )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2046),U_2048) = U_2047
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2046),U_2047) != U_2048 ) )
| ~ class_Groups_Ogroup__add(U_2046) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
fof(f_409_3,plain,
( ! [U_2048,U_2047,U_2046] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2046),U_2047) = U_2048
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2046),U_2048) != U_2047
| ~ sP103(U_2048,U_2047,U_2046) )
& ! [U_2048,U_2047,U_2046] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2046),U_2048) = U_2047
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2046),U_2047) != U_2048
| ~ sP103(U_2048,U_2047,U_2046) )
& ! [U_2048,U_2047,U_2046] :
( sP103(U_2048,U_2047,U_2046)
| ~ class_Groups_Ogroup__add(U_2046) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103])],[f_409_2]) ).
cnf(f_409_4,plain,
( sP103(U_2048,U_2047,U_2046)
| ~ class_Groups_Ogroup__add(U_2046) ),
inference(clausify,[status(thm)],[f_409_3]) ).
cnf(f_409_5,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2046),U_2048) = U_2047
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2046),U_2047) != U_2048
| ~ sP103(U_2048,U_2047,U_2046) ),
inference(clausify,[status(thm)],[f_409_3]) ).
cnf(f_409_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2046),U_2047) = U_2048
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2046),U_2048) != U_2047
| ~ sP103(U_2048,U_2047,U_2046) ),
inference(clausify,[status(thm)],[f_409_3]) ).
fof(f_410_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)
| V_b_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) )
& ( V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)
| V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_equation__minus__iff]) ).
fof(f_410_2,plain,
! [U_2051,U_2050,U_2049] :
( ( ( U_2050 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2049),U_2051)
| U_2051 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2049),U_2050) )
& ( U_2051 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2049),U_2050)
| U_2050 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2049),U_2051) ) )
| ~ class_Groups_Ogroup__add(U_2049) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
fof(f_410_3,plain,
( ! [U_2050,U_2051,U_2049] :
( U_2050 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2049),U_2051)
| U_2051 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2049),U_2050)
| ~ sP104(U_2050,U_2051,U_2049) )
& ! [U_2050,U_2051,U_2049] :
( U_2051 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2049),U_2050)
| U_2050 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2049),U_2051)
| ~ sP104(U_2050,U_2051,U_2049) )
& ! [U_2050,U_2051,U_2049] :
( sP104(U_2050,U_2051,U_2049)
| ~ class_Groups_Ogroup__add(U_2049) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104])],[f_410_2]) ).
cnf(f_410_4,plain,
( sP104(U_2050,U_2051,U_2049)
| ~ class_Groups_Ogroup__add(U_2049) ),
inference(clausify,[status(thm)],[f_410_3]) ).
cnf(f_410_5,plain,
( U_2051 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2049),U_2050)
| U_2050 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2049),U_2051)
| ~ sP104(U_2050,U_2051,U_2049) ),
inference(clausify,[status(thm)],[f_410_3]) ).
cnf(f_410_6,plain,
( U_2050 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2049),U_2051)
| U_2051 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2049),U_2050)
| ~ sP104(U_2050,U_2051,U_2049) ),
inference(clausify,[status(thm)],[f_410_3]) ).
fof(f_411_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_411_2,plain,
! [U_2054,U_2053,U_2052] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2052),U_2053),U_2054)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2052),hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),U_2053)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),U_2054))
| ~ class_Groups_Olinordered__ab__group__add(U_2052) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
fof(f_411_3,plain,
! [U_2054,U_2053,U_2052] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2052),U_2053),U_2054)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2052),hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),U_2053)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),U_2054))
| ~ class_Groups_Olinordered__ab__group__add(U_2052) ),
inference(definitional_conversion,[status(esa)],[f_411_2]) ).
cnf(f_411_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2052),U_2053),U_2054)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2052),hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),U_2053)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2052),U_2054))
| ~ class_Groups_Olinordered__ab__group__add(U_2052) ),
inference(clausify,[status(thm)],[f_411_3]) ).
fof(f_412_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_412_2,plain,
! [U_2057,U_2056,U_2055] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2055),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2055),U_2056),U_2057)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2055),hAPP(c_Groups_Ouminus__class_Ouminus(U_2055),U_2056)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2055),U_2057))
| ~ class_Groups_Olinordered__ab__group__add(U_2055) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
fof(f_412_3,plain,
! [U_2055,U_2056,U_2057] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2055),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2055),U_2056),U_2057)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2055),hAPP(c_Groups_Ouminus__class_Ouminus(U_2055),U_2056)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2055),U_2057))
| ~ class_Groups_Olinordered__ab__group__add(U_2055) ),
inference(definitional_conversion,[status(esa)],[f_412_2]) ).
cnf(f_412_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2055),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2055),U_2056),U_2057)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2055),hAPP(c_Groups_Ouminus__class_Ouminus(U_2055),U_2056)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2055),U_2057))
| ~ class_Groups_Olinordered__ab__group__add(U_2055) ),
inference(clausify,[status(thm)],[f_412_3]) ).
fof(f_413_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_413_2,plain,
! [U_2059,U_2058] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2058),hAPP(c_Groups_Ouminus__class_Ouminus(U_2058),U_2059)) = U_2059
| ~ class_Groups_Ogroup__add(U_2058) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
fof(f_413_3,plain,
! [U_2058,U_2059] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2058),hAPP(c_Groups_Ouminus__class_Ouminus(U_2058),U_2059)) = U_2059
| ~ class_Groups_Ogroup__add(U_2058) ),
inference(definitional_conversion,[status(esa)],[f_413_2]) ).
cnf(f_413_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2058),hAPP(c_Groups_Ouminus__class_Ouminus(U_2058),U_2059)) = U_2059
| ~ class_Groups_Ogroup__add(U_2058) ),
inference(clausify,[status(thm)],[f_413_3]) ).
fof(f_414_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_414_2,plain,
! [U_2063,U_2062,U_2061,U_2060] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2060),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2060),U_2061),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2060),U_2062),U_2063))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2060),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2060),U_2061),U_2062)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2060),U_2061),U_2063))))
| ~ class_Orderings_Olinorder(U_2060) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
fof(f_414_3,plain,
! [U_2060,U_2061,U_2062,U_2063] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2060),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2060),U_2061),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2060),U_2062),U_2063))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2060),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2060),U_2061),U_2062)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2060),U_2061),U_2063))))
| ~ class_Orderings_Olinorder(U_2060) ),
inference(definitional_conversion,[status(esa)],[f_414_2]) ).
cnf(f_414_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2060),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2060),U_2061),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2060),U_2062),U_2063))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2060),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2060),U_2061),U_2062)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2060),U_2061),U_2063))))
| ~ class_Orderings_Olinorder(U_2060) ),
inference(clausify,[status(thm)],[f_414_3]) ).
fof(f_415_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_415_2,plain,
! [U_2067,U_2066,U_2065,U_2064] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2064),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2064),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2064),U_2065),U_2066)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2064),U_2065),U_2067))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2064),U_2065),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2064),U_2066),U_2067))))
| ~ class_Orderings_Olinorder(U_2064) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
fof(f_415_3,plain,
! [U_2064,U_2065,U_2066,U_2067] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2064),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2064),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2064),U_2065),U_2066)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2064),U_2065),U_2067))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2064),U_2065),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2064),U_2066),U_2067))))
| ~ class_Orderings_Olinorder(U_2064) ),
inference(definitional_conversion,[status(esa)],[f_415_2]) ).
cnf(f_415_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2064),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2064),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2064),U_2065),U_2066)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2064),U_2065),U_2067))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2064),U_2065),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2064),U_2066),U_2067))))
| ~ class_Orderings_Olinorder(U_2064) ),
inference(clausify,[status(thm)],[f_415_3]) ).
fof(f_416_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_416_2,plain,
! [U_2071,U_2070,U_2069,U_2068] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2068),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2068),U_2069),U_2070)),U_2071) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2068),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2068),U_2069),U_2071)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2068),U_2070),U_2071))
| ~ class_Orderings_Olinorder(U_2068) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
fof(f_416_3,plain,
! [U_2068,U_2069,U_2070,U_2071] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2068),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2068),U_2069),U_2070)),U_2071) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2068),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2068),U_2069),U_2071)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2068),U_2070),U_2071))
| ~ class_Orderings_Olinorder(U_2068) ),
inference(definitional_conversion,[status(esa)],[f_416_2]) ).
cnf(f_416_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2068),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2068),U_2069),U_2070)),U_2071) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2068),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2068),U_2069),U_2071)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2068),U_2070),U_2071))
| ~ class_Orderings_Olinorder(U_2068) ),
inference(clausify,[status(thm)],[f_416_3]) ).
fof(f_417_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_417_2,plain,
! [U_2075,U_2074,U_2073,U_2072] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2072),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2072),U_2073),U_2074)),U_2075) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2072),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2072),U_2073),U_2075)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2072),U_2074),U_2075))
| ~ class_Orderings_Olinorder(U_2072) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
fof(f_417_3,plain,
! [U_2072,U_2073,U_2074,U_2075] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2072),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2072),U_2073),U_2074)),U_2075) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2072),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2072),U_2073),U_2075)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2072),U_2074),U_2075))
| ~ class_Orderings_Olinorder(U_2072) ),
inference(definitional_conversion,[status(esa)],[f_417_2]) ).
cnf(f_417_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2072),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2072),U_2073),U_2074)),U_2075) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2072),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2072),U_2073),U_2075)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2072),U_2074),U_2075))
| ~ class_Orderings_Olinorder(U_2072) ),
inference(clausify,[status(thm)],[f_417_3]) ).
fof(f_418_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_418_2,plain,
! [U_2079,U_2078,U_2077,U_2076] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2076),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2076),U_2077),U_2078)),U_2079) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2076),U_2077),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2076),U_2078),U_2079))
| ~ class_Orderings_Olinorder(U_2076) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
fof(f_418_3,plain,
! [U_2076,U_2077,U_2078,U_2079] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2076),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2076),U_2077),U_2078)),U_2079) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2076),U_2077),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2076),U_2078),U_2079))
| ~ class_Orderings_Olinorder(U_2076) ),
inference(definitional_conversion,[status(esa)],[f_418_2]) ).
cnf(f_418_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2076),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2076),U_2077),U_2078)),U_2079) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2076),U_2077),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2076),U_2078),U_2079))
| ~ class_Orderings_Olinorder(U_2076) ),
inference(clausify,[status(thm)],[f_418_3]) ).
fof(f_419_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_419_2,plain,
! [U_2083,U_2082,U_2081,U_2080] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2080),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2080),U_2081),U_2082)),U_2083) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2080),U_2081),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2080),U_2082),U_2083))
| ~ class_Orderings_Olinorder(U_2080) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
fof(f_419_3,plain,
! [U_2080,U_2081,U_2082,U_2083] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2080),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2080),U_2081),U_2082)),U_2083) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2080),U_2081),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2080),U_2082),U_2083))
| ~ class_Orderings_Olinorder(U_2080) ),
inference(definitional_conversion,[status(esa)],[f_419_2]) ).
cnf(f_419_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2080),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2080),U_2081),U_2082)),U_2083) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2080),U_2081),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2080),U_2082),U_2083))
| ~ class_Orderings_Olinorder(U_2080) ),
inference(clausify,[status(thm)],[f_419_3]) ).
fof(f_420_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_420_2,plain,
! [U_2087,U_2086,U_2085,U_2084] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2084),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2084),U_2085),U_2086)),U_2087) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2084),U_2085),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2084),U_2086),U_2087))
| ~ class_Orderings_Olinorder(U_2084) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
fof(f_420_3,plain,
! [U_2084,U_2085,U_2086,U_2087] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2084),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2084),U_2085),U_2086)),U_2087) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2084),U_2085),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2084),U_2086),U_2087))
| ~ class_Orderings_Olinorder(U_2084) ),
inference(definitional_conversion,[status(esa)],[f_420_2]) ).
cnf(f_420_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2084),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2084),U_2085),U_2086)),U_2087) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2084),U_2085),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2084),U_2086),U_2087))
| ~ class_Orderings_Olinorder(U_2084) ),
inference(clausify,[status(thm)],[f_420_3]) ).
fof(f_421_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_421_2,plain,
! [U_2091,U_2090,U_2089,U_2088] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2088),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2088),U_2089),U_2090)),U_2091) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2088),U_2089),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2088),U_2090),U_2091))
| ~ class_Orderings_Olinorder(U_2088) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
fof(f_421_3,plain,
! [U_2088,U_2089,U_2090,U_2091] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2088),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2088),U_2089),U_2090)),U_2091) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2088),U_2089),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2088),U_2090),U_2091))
| ~ class_Orderings_Olinorder(U_2088) ),
inference(definitional_conversion,[status(esa)],[f_421_2]) ).
cnf(f_421_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2088),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2088),U_2089),U_2090)),U_2091) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2088),U_2089),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2088),U_2090),U_2091))
| ~ class_Orderings_Olinorder(U_2088) ),
inference(clausify,[status(thm)],[f_421_3]) ).
fof(f_422_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2) ) )
| ~ class_Lattices_Oboolean__algebra(T_c) ),
inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff]) ).
fof(f_422_2,plain,
! [U_2094,U_2093,U_2092] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2092),U_2093) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2092),U_2094)
| U_2093 != U_2094 )
& ( U_2093 = U_2094
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2092),U_2093) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2092),U_2094) ) )
| ~ class_Lattices_Oboolean__algebra(U_2092) ),
inference(variable_rename,[status(thm)],[f_422_1]) ).
fof(f_422_3,plain,
( ! [U_2092,U_2093,U_2094] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2092),U_2093) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2092),U_2094)
| U_2093 != U_2094
| ~ sP105(U_2092,U_2093,U_2094) )
& ! [U_2092,U_2093,U_2094] :
( U_2093 = U_2094
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2092),U_2093) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2092),U_2094)
| ~ sP105(U_2092,U_2093,U_2094) )
& ! [U_2092,U_2093,U_2094] :
( sP105(U_2092,U_2093,U_2094)
| ~ class_Lattices_Oboolean__algebra(U_2092) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105])],[f_422_2]) ).
cnf(f_422_4,plain,
( sP105(U_2092,U_2093,U_2094)
| ~ class_Lattices_Oboolean__algebra(U_2092) ),
inference(clausify,[status(thm)],[f_422_3]) ).
cnf(f_422_5,plain,
( U_2093 = U_2094
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2092),U_2093) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2092),U_2094)
| ~ sP105(U_2092,U_2093,U_2094) ),
inference(clausify,[status(thm)],[f_422_3]) ).
cnf(f_422_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2092),U_2093) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2092),U_2094)
| U_2093 != U_2094
| ~ sP105(U_2092,U_2093,U_2094) ),
inference(clausify,[status(thm)],[f_422_3]) ).
fof(f_423_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_423_2,plain,
! [U_2098,U_2097,U_2096,U_2095] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2095),U_2096),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2095),U_2097),U_2098)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2095),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2095),U_2096),U_2097)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2095),U_2096),U_2098))
| ~ class_Orderings_Olinorder(U_2095) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
fof(f_423_3,plain,
! [U_2096,U_2095,U_2097,U_2098] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2095),U_2096),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2095),U_2097),U_2098)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2095),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2095),U_2096),U_2097)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2095),U_2096),U_2098))
| ~ class_Orderings_Olinorder(U_2095) ),
inference(definitional_conversion,[status(esa)],[f_423_2]) ).
cnf(f_423_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2095),U_2096),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2095),U_2097),U_2098)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2095),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2095),U_2096),U_2097)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2095),U_2096),U_2098))
| ~ class_Orderings_Olinorder(U_2095) ),
inference(clausify,[status(thm)],[f_423_3]) ).
fof(f_424_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_424_2,plain,
! [U_2102,U_2101,U_2100,U_2099] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2099),U_2100),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2099),U_2101),U_2102)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2099),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2099),U_2100),U_2101)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2099),U_2100),U_2102))
| ~ class_Orderings_Olinorder(U_2099) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
fof(f_424_3,plain,
! [U_2099,U_2100,U_2101,U_2102] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2099),U_2100),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2099),U_2101),U_2102)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2099),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2099),U_2100),U_2101)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2099),U_2100),U_2102))
| ~ class_Orderings_Olinorder(U_2099) ),
inference(definitional_conversion,[status(esa)],[f_424_2]) ).
cnf(f_424_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2099),U_2100),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2099),U_2101),U_2102)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2099),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2099),U_2100),U_2101)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2099),U_2100),U_2102))
| ~ class_Orderings_Olinorder(U_2099) ),
inference(clausify,[status(thm)],[f_424_3]) ).
fof(f_425_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_425_2,plain,
! [U_2106,U_2105,U_2104,U_2103] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2103),U_2104),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2103),U_2105),U_2106)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2103),U_2105),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2103),U_2104),U_2106))
| ~ class_Orderings_Olinorder(U_2103) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
fof(f_425_3,plain,
! [U_2103,U_2104,U_2105,U_2106] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2103),U_2104),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2103),U_2105),U_2106)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2103),U_2105),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2103),U_2104),U_2106))
| ~ class_Orderings_Olinorder(U_2103) ),
inference(definitional_conversion,[status(esa)],[f_425_2]) ).
cnf(f_425_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2103),U_2104),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2103),U_2105),U_2106)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2103),U_2105),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2103),U_2104),U_2106))
| ~ class_Orderings_Olinorder(U_2103) ),
inference(clausify,[status(thm)],[f_425_3]) ).
fof(f_426_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_426_2,plain,
! [U_2110,U_2109,U_2108,U_2107] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2107),U_2108),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2107),U_2109),U_2110)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2107),U_2109),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2107),U_2108),U_2110))
| ~ class_Orderings_Olinorder(U_2107) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
fof(f_426_3,plain,
! [U_2107,U_2108,U_2109,U_2110] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2107),U_2108),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2107),U_2109),U_2110)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2107),U_2109),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2107),U_2108),U_2110))
| ~ class_Orderings_Olinorder(U_2107) ),
inference(definitional_conversion,[status(esa)],[f_426_2]) ).
cnf(f_426_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2107),U_2108),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2107),U_2109),U_2110)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2107),U_2109),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2107),U_2108),U_2110))
| ~ class_Orderings_Olinorder(U_2107) ),
inference(clausify,[status(thm)],[f_426_3]) ).
fof(f_427_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_427_2,plain,
! [U_2114,U_2113,U_2112,U_2111] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2111),U_2112),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2111),U_2113),U_2114)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2111),U_2113),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2111),U_2112),U_2114))
| ~ class_Orderings_Olinorder(U_2111) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
fof(f_427_3,plain,
! [U_2111,U_2112,U_2113,U_2114] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2111),U_2112),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2111),U_2113),U_2114)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2111),U_2113),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2111),U_2112),U_2114))
| ~ class_Orderings_Olinorder(U_2111) ),
inference(definitional_conversion,[status(esa)],[f_427_2]) ).
cnf(f_427_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2111),U_2112),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2111),U_2113),U_2114)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2111),U_2113),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2111),U_2112),U_2114))
| ~ class_Orderings_Olinorder(U_2111) ),
inference(clausify,[status(thm)],[f_427_3]) ).
fof(f_428_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_428_2,plain,
! [U_2118,U_2117,U_2116,U_2115] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2115),U_2116),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2115),U_2117),U_2118)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2115),U_2117),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2115),U_2116),U_2118))
| ~ class_Orderings_Olinorder(U_2115) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
fof(f_428_3,plain,
! [U_2115,U_2116,U_2117,U_2118] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2115),U_2116),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2115),U_2117),U_2118)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2115),U_2117),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2115),U_2116),U_2118))
| ~ class_Orderings_Olinorder(U_2115) ),
inference(definitional_conversion,[status(esa)],[f_428_2]) ).
cnf(f_428_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2115),U_2116),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2115),U_2117),U_2118)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2115),U_2117),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2115),U_2116),U_2118))
| ~ class_Orderings_Olinorder(U_2115) ),
inference(clausify,[status(thm)],[f_428_3]) ).
fof(f_429_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_429_2,plain,
! [U_2121,U_2120,U_2119] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2119),U_2120),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2119),U_2120),U_2121)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2119),U_2120),U_2121)
| ~ class_Orderings_Olinorder(U_2119) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
fof(f_429_3,plain,
! [U_2119,U_2120,U_2121] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2119),U_2120),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2119),U_2120),U_2121)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2119),U_2120),U_2121)
| ~ class_Orderings_Olinorder(U_2119) ),
inference(definitional_conversion,[status(esa)],[f_429_2]) ).
cnf(f_429_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2119),U_2120),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2119),U_2120),U_2121)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2119),U_2120),U_2121)
| ~ class_Orderings_Olinorder(U_2119) ),
inference(clausify,[status(thm)],[f_429_3]) ).
fof(f_430_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_430_2,plain,
! [U_2124,U_2123,U_2122] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2122),U_2123),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2122),U_2123),U_2124)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2122),U_2123),U_2124)
| ~ class_Orderings_Olinorder(U_2122) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
fof(f_430_3,plain,
! [U_2122,U_2123,U_2124] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2122),U_2123),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2122),U_2123),U_2124)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2122),U_2123),U_2124)
| ~ class_Orderings_Olinorder(U_2122) ),
inference(definitional_conversion,[status(esa)],[f_430_2]) ).
cnf(f_430_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2122),U_2123),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2122),U_2123),U_2124)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2122),U_2123),U_2124)
| ~ class_Orderings_Olinorder(U_2122) ),
inference(clausify,[status(thm)],[f_430_3]) ).
fof(f_431_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_431_2,plain,
! [U_2127,U_2126,U_2125] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2125),U_2126),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2125),U_2126),U_2127)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2125),U_2126),U_2127)
| ~ class_Orderings_Olinorder(U_2125) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
fof(f_431_3,plain,
! [U_2125,U_2126,U_2127] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2125),U_2126),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2125),U_2126),U_2127)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2125),U_2126),U_2127)
| ~ class_Orderings_Olinorder(U_2125) ),
inference(definitional_conversion,[status(esa)],[f_431_2]) ).
cnf(f_431_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2125),U_2126),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2125),U_2126),U_2127)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2125),U_2126),U_2127)
| ~ class_Orderings_Olinorder(U_2125) ),
inference(clausify,[status(thm)],[f_431_3]) ).
fof(f_432_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_432_2,plain,
! [U_2130,U_2129,U_2128] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2128),U_2129),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2128),U_2129),U_2130)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2128),U_2129),U_2130)
| ~ class_Orderings_Olinorder(U_2128) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
fof(f_432_3,plain,
! [U_2128,U_2129,U_2130] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2128),U_2129),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2128),U_2129),U_2130)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2128),U_2129),U_2130)
| ~ class_Orderings_Olinorder(U_2128) ),
inference(definitional_conversion,[status(esa)],[f_432_2]) ).
cnf(f_432_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2128),U_2129),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2128),U_2129),U_2130)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2128),U_2129),U_2130)
| ~ class_Orderings_Olinorder(U_2128) ),
inference(clausify,[status(thm)],[f_432_3]) ).
fof(f_433_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_433_2,plain,
! [U_2133,U_2132,U_2131] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2131),U_2132),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2131),U_2132),U_2133)) = U_2132
| ~ class_Orderings_Olinorder(U_2131) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
fof(f_433_3,plain,
! [U_2131,U_2132,U_2133] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2131),U_2132),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2131),U_2132),U_2133)) = U_2132
| ~ class_Orderings_Olinorder(U_2131) ),
inference(definitional_conversion,[status(esa)],[f_433_2]) ).
cnf(f_433_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2131),U_2132),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2131),U_2132),U_2133)) = U_2132
| ~ class_Orderings_Olinorder(U_2131) ),
inference(clausify,[status(thm)],[f_433_3]) ).
fof(f_434_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_434_2,plain,
! [U_2136,U_2135,U_2134] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2134),U_2135),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2134),U_2135),U_2136)) = U_2135
| ~ class_Orderings_Olinorder(U_2134) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
fof(f_434_3,plain,
! [U_2134,U_2135,U_2136] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2134),U_2135),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2134),U_2135),U_2136)) = U_2135
| ~ class_Orderings_Olinorder(U_2134) ),
inference(definitional_conversion,[status(esa)],[f_434_2]) ).
cnf(f_434_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2134),U_2135),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2134),U_2135),U_2136)) = U_2135
| ~ class_Orderings_Olinorder(U_2134) ),
inference(clausify,[status(thm)],[f_434_3]) ).
fof(f_435_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_435_2,plain,
! [U_2139,U_2138,U_2137] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2137),U_2138),U_2139) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2137),U_2139),U_2138)
| ~ class_Orderings_Olinorder(U_2137) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
fof(f_435_3,plain,
! [U_2137,U_2138,U_2139] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2137),U_2138),U_2139) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2137),U_2139),U_2138)
| ~ class_Orderings_Olinorder(U_2137) ),
inference(definitional_conversion,[status(esa)],[f_435_2]) ).
cnf(f_435_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2137),U_2138),U_2139) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2137),U_2139),U_2138)
| ~ class_Orderings_Olinorder(U_2137) ),
inference(clausify,[status(thm)],[f_435_3]) ).
fof(f_436_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_436_2,plain,
! [U_2142,U_2141,U_2140] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2140),U_2141),U_2142) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2140),U_2142),U_2141)
| ~ class_Orderings_Olinorder(U_2140) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
fof(f_436_3,plain,
! [U_2140,U_2141,U_2142] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2140),U_2141),U_2142) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2140),U_2142),U_2141)
| ~ class_Orderings_Olinorder(U_2140) ),
inference(definitional_conversion,[status(esa)],[f_436_2]) ).
cnf(f_436_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2140),U_2141),U_2142) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2140),U_2142),U_2141)
| ~ class_Orderings_Olinorder(U_2140) ),
inference(clausify,[status(thm)],[f_436_3]) ).
fof(f_437_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_437_2,plain,
! [U_2145,U_2144,U_2143] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2143),U_2144),U_2145) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2143),U_2145),U_2144)
| ~ class_Orderings_Olinorder(U_2143) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
fof(f_437_3,plain,
! [U_2143,U_2144,U_2145] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2143),U_2144),U_2145) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2143),U_2145),U_2144)
| ~ class_Orderings_Olinorder(U_2143) ),
inference(definitional_conversion,[status(esa)],[f_437_2]) ).
cnf(f_437_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2143),U_2144),U_2145) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2143),U_2145),U_2144)
| ~ class_Orderings_Olinorder(U_2143) ),
inference(clausify,[status(thm)],[f_437_3]) ).
fof(f_438_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_438_2,plain,
! [U_2148,U_2147,U_2146] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2146),U_2147),U_2148) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2146),U_2148),U_2147)
| ~ class_Orderings_Olinorder(U_2146) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
fof(f_438_3,plain,
! [U_2146,U_2147,U_2148] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2146),U_2147),U_2148) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2146),U_2148),U_2147)
| ~ class_Orderings_Olinorder(U_2146) ),
inference(definitional_conversion,[status(esa)],[f_438_2]) ).
cnf(f_438_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2146),U_2147),U_2148) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2146),U_2148),U_2147)
| ~ class_Orderings_Olinorder(U_2146) ),
inference(clausify,[status(thm)],[f_438_3]) ).
fof(f_439_1,plain,
! [V_x_2,V_A_2,T_d,T_c] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,T_c)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(V_A_2,V_x_2))
| ~ class_Groups_Ouminus(T_c) ),
inference(fof_nnf,[status(thm)],[fact_uminus__apply]) ).
fof(f_439_2,plain,
! [U_2152,U_2151,U_2150,U_2149] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2150,U_2149)),U_2151),U_2152) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2149),hAPP(U_2151,U_2152))
| ~ class_Groups_Ouminus(U_2149) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
fof(f_439_3,plain,
! [U_2149,U_2150,U_2151,U_2152] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2150,U_2149)),U_2151),U_2152) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2149),hAPP(U_2151,U_2152))
| ~ class_Groups_Ouminus(U_2149) ),
inference(definitional_conversion,[status(esa)],[f_439_2]) ).
cnf(f_439_4,plain,
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2150,U_2149)),U_2151),U_2152) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2149),hAPP(U_2151,U_2152))
| ~ class_Groups_Ouminus(U_2149) ),
inference(clausify,[status(thm)],[f_439_3]) ).
fof(f_440_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_440_2,plain,
! [U_2154,U_2153] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2153),U_2154),U_2154) = U_2154
| ~ class_Orderings_Olinorder(U_2153) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
fof(f_440_3,plain,
! [U_2153,U_2154] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2153),U_2154),U_2154) = U_2154
| ~ class_Orderings_Olinorder(U_2153) ),
inference(definitional_conversion,[status(esa)],[f_440_2]) ).
cnf(f_440_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2153),U_2154),U_2154) = U_2154
| ~ class_Orderings_Olinorder(U_2153) ),
inference(clausify,[status(thm)],[f_440_3]) ).
fof(f_441_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_441_2,plain,
! [U_2156,U_2155] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2155),U_2156),U_2156) = U_2156
| ~ class_Orderings_Olinorder(U_2155) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
fof(f_441_3,plain,
! [U_2155,U_2156] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2155),U_2156),U_2156) = U_2156
| ~ class_Orderings_Olinorder(U_2155) ),
inference(definitional_conversion,[status(esa)],[f_441_2]) ).
cnf(f_441_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2155),U_2156),U_2156) = U_2156
| ~ class_Orderings_Olinorder(U_2155) ),
inference(clausify,[status(thm)],[f_441_3]) ).
fof(f_442_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_442_2,plain,
! [U_2158,U_2157] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2157),hAPP(c_Groups_Ouminus__class_Ouminus(U_2157),U_2158)) = U_2158
| ~ class_Lattices_Oboolean__algebra(U_2157) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
fof(f_442_3,plain,
! [U_2157,U_2158] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2157),hAPP(c_Groups_Ouminus__class_Ouminus(U_2157),U_2158)) = U_2158
| ~ class_Lattices_Oboolean__algebra(U_2157) ),
inference(definitional_conversion,[status(esa)],[f_442_2]) ).
cnf(f_442_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2157),hAPP(c_Groups_Ouminus__class_Ouminus(U_2157),U_2158)) = U_2158
| ~ class_Lattices_Oboolean__algebra(U_2157) ),
inference(clausify,[status(thm)],[f_442_3]) ).
fof(f_443_1,plain,
! [V_x_2,V_A_2,T_d,T_c] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,T_c)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(V_A_2,V_x_2))
| ~ class_Groups_Ouminus(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fun__Compl__def]) ).
fof(f_443_2,plain,
! [U_2162,U_2161,U_2160,U_2159] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2160,U_2159)),U_2161),U_2162) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2159),hAPP(U_2161,U_2162))
| ~ class_Groups_Ouminus(U_2159) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
fof(f_443_3,plain,
! [U_2159,U_2160,U_2161,U_2162] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2160,U_2159)),U_2161),U_2162) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2159),hAPP(U_2161,U_2162))
| ~ class_Groups_Ouminus(U_2159) ),
inference(definitional_conversion,[status(esa)],[f_443_2]) ).
cnf(f_443_4,plain,
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2160,U_2159)),U_2161),U_2162) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2159),hAPP(U_2161,U_2162))
| ~ class_Groups_Ouminus(U_2159) ),
inference(clausify,[status(thm)],[f_443_3]) ).
fof(f_444_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_444_2,plain,
! [U_2164,U_2163] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2163),U_2164),U_2164) = U_2164
| ~ class_Orderings_Olinorder(U_2163) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
fof(f_444_3,plain,
! [U_2163,U_2164] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2163),U_2164),U_2164) = U_2164
| ~ class_Orderings_Olinorder(U_2163) ),
inference(definitional_conversion,[status(esa)],[f_444_2]) ).
cnf(f_444_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2163),U_2164),U_2164) = U_2164
| ~ class_Orderings_Olinorder(U_2163) ),
inference(clausify,[status(thm)],[f_444_3]) ).
fof(f_445_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_445_2,plain,
! [U_2166,U_2165] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2165),U_2166),U_2166) = U_2166
| ~ class_Orderings_Olinorder(U_2165) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
fof(f_445_3,plain,
! [U_2165,U_2166] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2165),U_2166),U_2166) = U_2166
| ~ class_Orderings_Olinorder(U_2165) ),
inference(definitional_conversion,[status(esa)],[f_445_2]) ).
cnf(f_445_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2165),U_2166),U_2166) = U_2166
| ~ class_Orderings_Olinorder(U_2165) ),
inference(clausify,[status(thm)],[f_445_3]) ).
fof(f_446_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_446_2,plain,
! [U_2170,U_2169,U_2168,U_2167] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2167),U_2169),U_2170))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2167),U_2168),U_2170)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2167),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2167),U_2168),U_2169)),U_2170))
| ~ class_Orderings_Olinorder(U_2167) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
fof(f_446_3,plain,
( ! [U_2167,U_2168,U_2169,U_2170] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2167),U_2169),U_2170))
| ~ sP106(U_2167,U_2168,U_2169,U_2170) )
& ! [U_2167,U_2168,U_2169,U_2170] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2167),U_2168),U_2170))
| ~ sP106(U_2167,U_2168,U_2169,U_2170) )
& ! [U_2167,U_2168,U_2169,U_2170] :
( sP106(U_2167,U_2168,U_2169,U_2170)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2167),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2167),U_2168),U_2169)),U_2170))
| ~ class_Orderings_Olinorder(U_2167) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP106])],[f_446_2]) ).
cnf(f_446_4,plain,
( sP106(U_2167,U_2168,U_2169,U_2170)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2167),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2167),U_2168),U_2169)),U_2170))
| ~ class_Orderings_Olinorder(U_2167) ),
inference(clausify,[status(thm)],[f_446_3]) ).
cnf(f_446_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2167),U_2168),U_2170))
| ~ sP106(U_2167,U_2168,U_2169,U_2170) ),
inference(clausify,[status(thm)],[f_446_3]) ).
cnf(f_446_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2167),U_2169),U_2170))
| ~ sP106(U_2167,U_2168,U_2169,U_2170) ),
inference(clausify,[status(thm)],[f_446_3]) ).
fof(f_447_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_447_2,plain,
! [U_2175,U_2174,U_2173,U_2172,U_2171] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2171),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2171),U_2172),U_2174)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2171),U_2173),U_2175)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2171),U_2174),U_2175))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2171),U_2172),U_2173))
| ~ class_Orderings_Olinorder(U_2171) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
fof(f_447_3,plain,
! [U_2171,U_2172,U_2173,U_2174,U_2175] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2171),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2171),U_2172),U_2174)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2171),U_2173),U_2175)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2171),U_2174),U_2175))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2171),U_2172),U_2173))
| ~ class_Orderings_Olinorder(U_2171) ),
inference(definitional_conversion,[status(esa)],[f_447_2]) ).
cnf(f_447_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2171),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2171),U_2172),U_2174)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2171),U_2173),U_2175)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2171),U_2174),U_2175))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2171),U_2172),U_2173))
| ~ class_Orderings_Olinorder(U_2171) ),
inference(clausify,[status(thm)],[f_447_3]) ).
fof(f_448_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_448_2,plain,
! [U_2179,U_2178,U_2177,U_2176] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2176),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2176),U_2177),U_2179)),U_2178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2176),U_2179),U_2178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2176),U_2177),U_2178))
| ~ class_Orderings_Olinorder(U_2176) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
fof(f_448_3,plain,
! [U_2176,U_2177,U_2178,U_2179] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2176),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2176),U_2177),U_2179)),U_2178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2176),U_2179),U_2178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2176),U_2177),U_2178))
| ~ class_Orderings_Olinorder(U_2176) ),
inference(definitional_conversion,[status(esa)],[f_448_2]) ).
cnf(f_448_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2176),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2176),U_2177),U_2179)),U_2178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2176),U_2179),U_2178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2176),U_2177),U_2178))
| ~ class_Orderings_Olinorder(U_2176) ),
inference(clausify,[status(thm)],[f_448_3]) ).
fof(f_449_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_449_2,plain,
! [U_2183,U_2182,U_2181,U_2180] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2180),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2180),U_2181),U_2183)),U_2182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2180),U_2183),U_2182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2180),U_2181),U_2182))
| ~ class_Orderings_Olinorder(U_2180) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
fof(f_449_3,plain,
! [U_2180,U_2181,U_2182,U_2183] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2180),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2180),U_2181),U_2183)),U_2182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2180),U_2183),U_2182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2180),U_2181),U_2182))
| ~ class_Orderings_Olinorder(U_2180) ),
inference(definitional_conversion,[status(esa)],[f_449_2]) ).
cnf(f_449_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2180),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2180),U_2181),U_2183)),U_2182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2180),U_2183),U_2182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2180),U_2181),U_2182))
| ~ class_Orderings_Olinorder(U_2180) ),
inference(clausify,[status(thm)],[f_449_3]) ).
fof(f_450_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_450_2,plain,
! [U_2186,U_2185,U_2184] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2184),U_2186),U_2185) = U_2186
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2184),U_2185),U_2186))
| ~ class_Orderings_Olinorder(U_2184) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
fof(f_450_3,plain,
! [U_2184,U_2185,U_2186] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2184),U_2186),U_2185) = U_2186
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2184),U_2185),U_2186))
| ~ class_Orderings_Olinorder(U_2184) ),
inference(definitional_conversion,[status(esa)],[f_450_2]) ).
cnf(f_450_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2184),U_2186),U_2185) = U_2186
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2184),U_2185),U_2186))
| ~ class_Orderings_Olinorder(U_2184) ),
inference(clausify,[status(thm)],[f_450_3]) ).
fof(f_451_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_451_2,plain,
! [U_2189,U_2188,U_2187] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2187),U_2188),U_2189) = U_2189
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2187),U_2188),U_2189))
| ~ class_Orderings_Olinorder(U_2187) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
fof(f_451_3,plain,
! [U_2187,U_2188,U_2189] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2187),U_2188),U_2189) = U_2189
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2187),U_2188),U_2189))
| ~ class_Orderings_Olinorder(U_2187) ),
inference(definitional_conversion,[status(esa)],[f_451_2]) ).
cnf(f_451_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2187),U_2188),U_2189) = U_2189
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2187),U_2188),U_2189))
| ~ class_Orderings_Olinorder(U_2187) ),
inference(clausify,[status(thm)],[f_451_3]) ).
fof(f_452_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_452_2,plain,
! [U_2193,U_2192,U_2191,U_2190] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2190),U_2191),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2190),U_2193),U_2192)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2190),U_2191),U_2192))
| ~ class_Orderings_Olinorder(U_2190) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
fof(f_452_3,plain,
! [U_2190,U_2191,U_2192,U_2193] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2190),U_2191),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2190),U_2193),U_2192)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2190),U_2191),U_2192))
| ~ class_Orderings_Olinorder(U_2190) ),
inference(definitional_conversion,[status(esa)],[f_452_2]) ).
cnf(f_452_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2190),U_2191),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2190),U_2193),U_2192)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2190),U_2191),U_2192))
| ~ class_Orderings_Olinorder(U_2190) ),
inference(clausify,[status(thm)],[f_452_3]) ).
fof(f_453_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_453_2,plain,
! [U_2197,U_2196,U_2195,U_2194] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2195),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2194),U_2196),U_2197)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2195),U_2196))
| ~ class_Orderings_Olinorder(U_2194) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
fof(f_453_3,plain,
! [U_2194,U_2195,U_2196,U_2197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2195),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2194),U_2196),U_2197)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2195),U_2196))
| ~ class_Orderings_Olinorder(U_2194) ),
inference(definitional_conversion,[status(esa)],[f_453_2]) ).
cnf(f_453_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2195),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2194),U_2196),U_2197)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2194),U_2195),U_2196))
| ~ class_Orderings_Olinorder(U_2194) ),
inference(clausify,[status(thm)],[f_453_3]) ).
fof(f_454_1,plain,
! [V_z_2,V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2)),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2)),V_z_2)) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff]) ).
fof(f_454_2,plain,
! [U_2201,U_2200,U_2199,U_2198] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2198),U_2199),U_2200)),U_2201))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),U_2200),U_2201))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),U_2199),U_2201)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),U_2200),U_2201))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),U_2199),U_2201)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2198),U_2199),U_2200)),U_2201)) ) )
| ~ class_Orderings_Olinorder(U_2198) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
fof(f_454_3,plain,
( ! [U_2198,U_2199,U_2200,U_2201] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),U_2200),U_2201))
| ~ sP107(U_2198,U_2199,U_2200,U_2201) )
& ! [U_2198,U_2199,U_2200,U_2201] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),U_2199),U_2201))
| ~ sP107(U_2198,U_2199,U_2200,U_2201) )
& ! [U_2198,U_2199,U_2200,U_2201] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2198),U_2199),U_2200)),U_2201))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),U_2200),U_2201))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),U_2199),U_2201))
| ~ sP108(U_2198,U_2199,U_2200,U_2201) )
& ! [U_2198,U_2199,U_2200,U_2201] :
( sP107(U_2198,U_2199,U_2200,U_2201)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2198),U_2199),U_2200)),U_2201))
| ~ sP108(U_2198,U_2199,U_2200,U_2201) )
& ! [U_2198,U_2199,U_2200,U_2201] :
( sP108(U_2198,U_2199,U_2200,U_2201)
| ~ class_Orderings_Olinorder(U_2198) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107,sP108])],[f_454_2]) ).
cnf(f_454_4,plain,
( sP108(U_2198,U_2199,U_2200,U_2201)
| ~ class_Orderings_Olinorder(U_2198) ),
inference(clausify,[status(thm)],[f_454_3]) ).
cnf(f_454_5,plain,
( sP107(U_2198,U_2199,U_2200,U_2201)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2198),U_2199),U_2200)),U_2201))
| ~ sP108(U_2198,U_2199,U_2200,U_2201) ),
inference(clausify,[status(thm)],[f_454_3]) ).
cnf(f_454_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2198),U_2199),U_2200)),U_2201))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),U_2200),U_2201))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),U_2199),U_2201))
| ~ sP108(U_2198,U_2199,U_2200,U_2201) ),
inference(clausify,[status(thm)],[f_454_3]) ).
cnf(f_454_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),U_2199),U_2201))
| ~ sP107(U_2198,U_2199,U_2200,U_2201) ),
inference(clausify,[status(thm)],[f_454_3]) ).
cnf(f_454_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2198),U_2200),U_2201))
| ~ sP107(U_2198,U_2199,U_2200,U_2201) ),
inference(clausify,[status(thm)],[f_454_3]) ).
fof(f_455_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2) != V_y_2 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2) = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup]) ).
fof(f_455_2,plain,
! [U_2204,U_2203,U_2202] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2202),U_2203),U_2204))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2202),U_2203),U_2204) != U_2204 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2202),U_2203),U_2204) = U_2204
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2202),U_2203),U_2204)) ) )
| ~ class_Orderings_Olinorder(U_2202) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
fof(f_455_3,plain,
( ! [U_2203,U_2204,U_2202] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2202),U_2203),U_2204))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2202),U_2203),U_2204) != U_2204
| ~ sP109(U_2203,U_2204,U_2202) )
& ! [U_2203,U_2204,U_2202] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2202),U_2203),U_2204) = U_2204
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2202),U_2203),U_2204))
| ~ sP109(U_2203,U_2204,U_2202) )
& ! [U_2203,U_2204,U_2202] :
( sP109(U_2203,U_2204,U_2202)
| ~ class_Orderings_Olinorder(U_2202) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_455_2]) ).
cnf(f_455_4,plain,
( sP109(U_2203,U_2204,U_2202)
| ~ class_Orderings_Olinorder(U_2202) ),
inference(clausify,[status(thm)],[f_455_3]) ).
cnf(f_455_5,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2202),U_2203),U_2204) = U_2204
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2202),U_2203),U_2204))
| ~ sP109(U_2203,U_2204,U_2202) ),
inference(clausify,[status(thm)],[f_455_3]) ).
cnf(f_455_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2202),U_2203),U_2204))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2202),U_2203),U_2204) != U_2204
| ~ sP109(U_2203,U_2204,U_2202) ),
inference(clausify,[status(thm)],[f_455_3]) ).
fof(f_456_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_456_2,plain,
! [U_2207,U_2206,U_2205] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2205),U_2206),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2205),U_2207),U_2206)))
| ~ class_Orderings_Olinorder(U_2205) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
fof(f_456_3,plain,
! [U_2206,U_2207,U_2205] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2205),U_2206),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2205),U_2207),U_2206)))
| ~ class_Orderings_Olinorder(U_2205) ),
inference(definitional_conversion,[status(esa)],[f_456_2]) ).
cnf(f_456_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2205),U_2206),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2205),U_2207),U_2206)))
| ~ class_Orderings_Olinorder(U_2205) ),
inference(clausify,[status(thm)],[f_456_3]) ).
fof(f_457_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_457_2,plain,
! [U_2210,U_2209,U_2208] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2208),U_2209),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2208),U_2209),U_2210)))
| ~ class_Orderings_Olinorder(U_2208) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
fof(f_457_3,plain,
! [U_2208,U_2209,U_2210] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2208),U_2209),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2208),U_2209),U_2210)))
| ~ class_Orderings_Olinorder(U_2208) ),
inference(definitional_conversion,[status(esa)],[f_457_2]) ).
cnf(f_457_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2208),U_2209),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2208),U_2209),U_2210)))
| ~ class_Orderings_Olinorder(U_2208) ),
inference(clausify,[status(thm)],[f_457_3]) ).
fof(f_458_1,plain,
! [V_y_2,V_x_2,V_z_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_z_2),V_y_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_z_2),V_x_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_z_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_z_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2))) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__max__iff__disj]) ).
fof(f_458_2,plain,
! [U_2214,U_2213,U_2212,U_2211] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2211),U_2213),U_2214)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),U_2214))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),U_2213)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),U_2214))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),U_2213))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2211),U_2213),U_2214))) ) )
| ~ class_Orderings_Olinorder(U_2211) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
fof(f_458_3,plain,
( ! [U_2211,U_2212,U_2213,U_2214] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),U_2214))
| ~ sP110(U_2211,U_2212,U_2213,U_2214) )
& ! [U_2211,U_2212,U_2213,U_2214] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),U_2213))
| ~ sP110(U_2211,U_2212,U_2213,U_2214) )
& ! [U_2211,U_2212,U_2213,U_2214] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2211),U_2213),U_2214)))
| sP110(U_2211,U_2212,U_2213,U_2214)
| ~ sP111(U_2211,U_2212,U_2213,U_2214) )
& ! [U_2211,U_2212,U_2213,U_2214] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),U_2214))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),U_2213))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2211),U_2213),U_2214)))
| ~ sP111(U_2211,U_2212,U_2213,U_2214) )
& ! [U_2211,U_2212,U_2213,U_2214] :
( sP111(U_2211,U_2212,U_2213,U_2214)
| ~ class_Orderings_Olinorder(U_2211) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110,sP111])],[f_458_2]) ).
cnf(f_458_4,plain,
( sP111(U_2211,U_2212,U_2213,U_2214)
| ~ class_Orderings_Olinorder(U_2211) ),
inference(clausify,[status(thm)],[f_458_3]) ).
cnf(f_458_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),U_2214))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),U_2213))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2211),U_2213),U_2214)))
| ~ sP111(U_2211,U_2212,U_2213,U_2214) ),
inference(clausify,[status(thm)],[f_458_3]) ).
cnf(f_458_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2211),U_2213),U_2214)))
| sP110(U_2211,U_2212,U_2213,U_2214)
| ~ sP111(U_2211,U_2212,U_2213,U_2214) ),
inference(clausify,[status(thm)],[f_458_3]) ).
cnf(f_458_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),U_2213))
| ~ sP110(U_2211,U_2212,U_2213,U_2214) ),
inference(clausify,[status(thm)],[f_458_3]) ).
cnf(f_458_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2211),U_2212),U_2214))
| ~ sP110(U_2211,U_2212,U_2213,U_2214) ),
inference(clausify,[status(thm)],[f_458_3]) ).
fof(f_459_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_459_2,plain,
! [U_2217,U_2216,U_2215] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2215),hAPP(c_Groups_Ouminus__class_Ouminus(U_2215),U_2217)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2215),U_2216)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2215),U_2216),U_2217))
| ~ class_Lattices_Oboolean__algebra(U_2215) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
fof(f_459_3,plain,
! [U_2215,U_2217,U_2216] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2215),hAPP(c_Groups_Ouminus__class_Ouminus(U_2215),U_2217)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2215),U_2216)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2215),U_2216),U_2217))
| ~ class_Lattices_Oboolean__algebra(U_2215) ),
inference(definitional_conversion,[status(esa)],[f_459_2]) ).
cnf(f_459_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2215),hAPP(c_Groups_Ouminus__class_Ouminus(U_2215),U_2217)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2215),U_2216)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2215),U_2216),U_2217))
| ~ class_Lattices_Oboolean__algebra(U_2215) ),
inference(clausify,[status(thm)],[f_459_3]) ).
fof(f_460_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2))) ) )
| ~ class_Lattices_Oboolean__algebra(T_c) ),
inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff]) ).
fof(f_460_2,plain,
! [U_2220,U_2219,U_2218] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2218),hAPP(c_Groups_Ouminus__class_Ouminus(U_2218),U_2219)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2218),U_2220)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2218),U_2220),U_2219)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2218),U_2220),U_2219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2218),hAPP(c_Groups_Ouminus__class_Ouminus(U_2218),U_2219)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2218),U_2220))) ) )
| ~ class_Lattices_Oboolean__algebra(U_2218) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
fof(f_460_3,plain,
( ! [U_2218,U_2219,U_2220] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2218),hAPP(c_Groups_Ouminus__class_Ouminus(U_2218),U_2219)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2218),U_2220)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2218),U_2220),U_2219))
| ~ sP112(U_2218,U_2219,U_2220) )
& ! [U_2218,U_2219,U_2220] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2218),U_2220),U_2219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2218),hAPP(c_Groups_Ouminus__class_Ouminus(U_2218),U_2219)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2218),U_2220)))
| ~ sP112(U_2218,U_2219,U_2220) )
& ! [U_2218,U_2219,U_2220] :
( sP112(U_2218,U_2219,U_2220)
| ~ class_Lattices_Oboolean__algebra(U_2218) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112])],[f_460_2]) ).
cnf(f_460_4,plain,
( sP112(U_2218,U_2219,U_2220)
| ~ class_Lattices_Oboolean__algebra(U_2218) ),
inference(clausify,[status(thm)],[f_460_3]) ).
cnf(f_460_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2218),U_2220),U_2219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2218),hAPP(c_Groups_Ouminus__class_Ouminus(U_2218),U_2219)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2218),U_2220)))
| ~ sP112(U_2218,U_2219,U_2220) ),
inference(clausify,[status(thm)],[f_460_3]) ).
cnf(f_460_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2218),hAPP(c_Groups_Ouminus__class_Ouminus(U_2218),U_2219)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2218),U_2220)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2218),U_2220),U_2219))
| ~ sP112(U_2218,U_2219,U_2220) ),
inference(clausify,[status(thm)],[f_460_3]) ).
fof(f_461_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__iff]) ).
fof(f_461_2,plain,
! [U_2223,U_2222,U_2221] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2221),U_2222),hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),U_2223)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2221),U_2223),hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),U_2222))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2221),U_2223),hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),U_2222)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2221),U_2222),hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),U_2223))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2221) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
fof(f_461_3,plain,
( ! [U_2223,U_2222,U_2221] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2221),U_2222),hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),U_2223)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2221),U_2223),hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),U_2222)))
| ~ sP113(U_2223,U_2222,U_2221) )
& ! [U_2223,U_2222,U_2221] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2221),U_2223),hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),U_2222)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2221),U_2222),hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),U_2223)))
| ~ sP113(U_2223,U_2222,U_2221) )
& ! [U_2223,U_2222,U_2221] :
( sP113(U_2223,U_2222,U_2221)
| ~ class_Groups_Oordered__ab__group__add(U_2221) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113])],[f_461_2]) ).
cnf(f_461_4,plain,
( sP113(U_2223,U_2222,U_2221)
| ~ class_Groups_Oordered__ab__group__add(U_2221) ),
inference(clausify,[status(thm)],[f_461_3]) ).
cnf(f_461_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2221),U_2223),hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),U_2222)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2221),U_2222),hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),U_2223)))
| ~ sP113(U_2223,U_2222,U_2221) ),
inference(clausify,[status(thm)],[f_461_3]) ).
cnf(f_461_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2221),U_2222),hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),U_2223)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2221),U_2223),hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),U_2222)))
| ~ sP113(U_2223,U_2222,U_2221) ),
inference(clausify,[status(thm)],[f_461_3]) ).
fof(f_462_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__iff]) ).
fof(f_462_2,plain,
! [U_2226,U_2225,U_2224] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2224),hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),U_2225)),U_2226))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2224),hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),U_2226)),U_2225)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2224),hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),U_2226)),U_2225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2224),hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),U_2225)),U_2226)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2224) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
fof(f_462_3,plain,
( ! [U_2225,U_2226,U_2224] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2224),hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),U_2225)),U_2226))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2224),hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),U_2226)),U_2225))
| ~ sP114(U_2225,U_2226,U_2224) )
& ! [U_2225,U_2226,U_2224] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2224),hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),U_2226)),U_2225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2224),hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),U_2225)),U_2226))
| ~ sP114(U_2225,U_2226,U_2224) )
& ! [U_2225,U_2226,U_2224] :
( sP114(U_2225,U_2226,U_2224)
| ~ class_Groups_Oordered__ab__group__add(U_2224) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114])],[f_462_2]) ).
cnf(f_462_4,plain,
( sP114(U_2225,U_2226,U_2224)
| ~ class_Groups_Oordered__ab__group__add(U_2224) ),
inference(clausify,[status(thm)],[f_462_3]) ).
cnf(f_462_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2224),hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),U_2226)),U_2225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2224),hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),U_2225)),U_2226))
| ~ sP114(U_2225,U_2226,U_2224) ),
inference(clausify,[status(thm)],[f_462_3]) ).
cnf(f_462_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2224),hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),U_2225)),U_2226))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2224),hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),U_2226)),U_2225))
| ~ sP114(U_2225,U_2226,U_2224) ),
inference(clausify,[status(thm)],[f_462_3]) ).
fof(f_463_1,plain,
! [V_a_2,V_b_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le]) ).
fof(f_463_2,plain,
! [U_2229,U_2228,U_2227] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2227),hAPP(c_Groups_Ouminus__class_Ouminus(U_2227),U_2228)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2227),U_2229)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2227),U_2229),U_2228)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2227),U_2229),U_2228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2227),hAPP(c_Groups_Ouminus__class_Ouminus(U_2227),U_2228)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2227),U_2229))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2227) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
fof(f_463_3,plain,
( ! [U_2228,U_2229,U_2227] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2227),hAPP(c_Groups_Ouminus__class_Ouminus(U_2227),U_2228)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2227),U_2229)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2227),U_2229),U_2228))
| ~ sP115(U_2228,U_2229,U_2227) )
& ! [U_2228,U_2229,U_2227] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2227),U_2229),U_2228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2227),hAPP(c_Groups_Ouminus__class_Ouminus(U_2227),U_2228)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2227),U_2229)))
| ~ sP115(U_2228,U_2229,U_2227) )
& ! [U_2228,U_2229,U_2227] :
( sP115(U_2228,U_2229,U_2227)
| ~ class_Groups_Oordered__ab__group__add(U_2227) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115])],[f_463_2]) ).
cnf(f_463_4,plain,
( sP115(U_2228,U_2229,U_2227)
| ~ class_Groups_Oordered__ab__group__add(U_2227) ),
inference(clausify,[status(thm)],[f_463_3]) ).
cnf(f_463_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2227),U_2229),U_2228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2227),hAPP(c_Groups_Ouminus__class_Ouminus(U_2227),U_2228)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2227),U_2229)))
| ~ sP115(U_2228,U_2229,U_2227) ),
inference(clausify,[status(thm)],[f_463_3]) ).
cnf(f_463_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2227),hAPP(c_Groups_Ouminus__class_Ouminus(U_2227),U_2228)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2227),U_2229)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2227),U_2229),U_2228))
| ~ sP115(U_2228,U_2229,U_2227) ),
inference(clausify,[status(thm)],[f_463_3]) ).
fof(f_464_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_464_2,plain,
! [U_2232,U_2231,U_2230] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),hAPP(c_Groups_Ouminus__class_Ouminus(U_2230),U_2232)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2230),U_2231)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),U_2231),U_2232))
| ~ class_Groups_Oordered__ab__group__add(U_2230) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
fof(f_464_3,plain,
! [U_2231,U_2230,U_2232] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),hAPP(c_Groups_Ouminus__class_Ouminus(U_2230),U_2232)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2230),U_2231)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),U_2231),U_2232))
| ~ class_Groups_Oordered__ab__group__add(U_2230) ),
inference(definitional_conversion,[status(esa)],[f_464_2]) ).
cnf(f_464_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),hAPP(c_Groups_Ouminus__class_Ouminus(U_2230),U_2232)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2230),U_2231)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2230),U_2231),U_2232))
| ~ class_Groups_Oordered__ab__group__add(U_2230) ),
inference(clausify,[status(thm)],[f_464_3]) ).
fof(f_465_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_465_2,plain,
! [U_2236,U_2235,U_2234,U_2233] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2233),U_2234),U_2236))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2233),U_2234),U_2235)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2233),U_2234),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2233),U_2235),U_2236)))
| ~ class_Orderings_Olinorder(U_2233) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
fof(f_465_3,plain,
( ! [U_2233,U_2234,U_2235,U_2236] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2233),U_2234),U_2236))
| ~ sP116(U_2233,U_2234,U_2235,U_2236) )
& ! [U_2233,U_2234,U_2235,U_2236] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2233),U_2234),U_2235))
| ~ sP116(U_2233,U_2234,U_2235,U_2236) )
& ! [U_2233,U_2234,U_2235,U_2236] :
( sP116(U_2233,U_2234,U_2235,U_2236)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2233),U_2234),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2233),U_2235),U_2236)))
| ~ class_Orderings_Olinorder(U_2233) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116])],[f_465_2]) ).
cnf(f_465_4,plain,
( sP116(U_2233,U_2234,U_2235,U_2236)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2233),U_2234),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2233),U_2235),U_2236)))
| ~ class_Orderings_Olinorder(U_2233) ),
inference(clausify,[status(thm)],[f_465_3]) ).
cnf(f_465_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2233),U_2234),U_2235))
| ~ sP116(U_2233,U_2234,U_2235,U_2236) ),
inference(clausify,[status(thm)],[f_465_3]) ).
cnf(f_465_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2233),U_2234),U_2236))
| ~ sP116(U_2233,U_2234,U_2235,U_2236) ),
inference(clausify,[status(thm)],[f_465_3]) ).
fof(f_466_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_466_2,plain,
! [U_2241,U_2240,U_2239,U_2238,U_2237] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2237),U_2238),U_2240)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2237),U_2239),U_2241)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),U_2240),U_2241))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),U_2238),U_2239))
| ~ class_Orderings_Olinorder(U_2237) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
fof(f_466_3,plain,
! [U_2237,U_2238,U_2239,U_2240,U_2241] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2237),U_2238),U_2240)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2237),U_2239),U_2241)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),U_2240),U_2241))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),U_2238),U_2239))
| ~ class_Orderings_Olinorder(U_2237) ),
inference(definitional_conversion,[status(esa)],[f_466_2]) ).
cnf(f_466_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2237),U_2238),U_2240)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2237),U_2239),U_2241)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),U_2240),U_2241))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),U_2238),U_2239))
| ~ class_Orderings_Olinorder(U_2237) ),
inference(clausify,[status(thm)],[f_466_3]) ).
fof(f_467_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_467_2,plain,
! [U_2245,U_2244,U_2243,U_2242] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2242),U_2243),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2242),U_2244),U_2245)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2242),U_2243),U_2245))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2242),U_2243),U_2244))
| ~ class_Orderings_Olinorder(U_2242) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
fof(f_467_3,plain,
! [U_2242,U_2243,U_2244,U_2245] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2242),U_2243),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2242),U_2244),U_2245)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2242),U_2243),U_2245))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2242),U_2243),U_2244))
| ~ class_Orderings_Olinorder(U_2242) ),
inference(definitional_conversion,[status(esa)],[f_467_2]) ).
cnf(f_467_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2242),U_2243),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2242),U_2244),U_2245)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2242),U_2243),U_2245))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2242),U_2243),U_2244))
| ~ class_Orderings_Olinorder(U_2242) ),
inference(clausify,[status(thm)],[f_467_3]) ).
fof(f_468_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_468_2,plain,
! [U_2249,U_2248,U_2247,U_2246] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2246),U_2247),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2246),U_2248),U_2249)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2246),U_2247),U_2249))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2246),U_2247),U_2248))
| ~ class_Orderings_Olinorder(U_2246) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
fof(f_468_3,plain,
! [U_2246,U_2247,U_2248,U_2249] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2246),U_2247),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2246),U_2248),U_2249)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2246),U_2247),U_2249))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2246),U_2247),U_2248))
| ~ class_Orderings_Olinorder(U_2246) ),
inference(definitional_conversion,[status(esa)],[f_468_2]) ).
cnf(f_468_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2246),U_2247),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2246),U_2248),U_2249)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2246),U_2247),U_2249))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2246),U_2247),U_2248))
| ~ class_Orderings_Olinorder(U_2246) ),
inference(clausify,[status(thm)],[f_468_3]) ).
fof(f_469_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_469_2,plain,
! [U_2252,U_2251,U_2250] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2250),U_2252),U_2251) = U_2251
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2250),U_2251),U_2252))
| ~ class_Orderings_Olinorder(U_2250) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
fof(f_469_3,plain,
! [U_2250,U_2251,U_2252] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2250),U_2252),U_2251) = U_2251
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2250),U_2251),U_2252))
| ~ class_Orderings_Olinorder(U_2250) ),
inference(definitional_conversion,[status(esa)],[f_469_2]) ).
cnf(f_469_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2250),U_2252),U_2251) = U_2251
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2250),U_2251),U_2252))
| ~ class_Orderings_Olinorder(U_2250) ),
inference(clausify,[status(thm)],[f_469_3]) ).
fof(f_470_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_470_2,plain,
! [U_2255,U_2254,U_2253] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2253),U_2254),U_2255) = U_2254
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2253),U_2254),U_2255))
| ~ class_Orderings_Olinorder(U_2253) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
fof(f_470_3,plain,
! [U_2253,U_2254,U_2255] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2253),U_2254),U_2255) = U_2254
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2253),U_2254),U_2255))
| ~ class_Orderings_Olinorder(U_2253) ),
inference(definitional_conversion,[status(esa)],[f_470_2]) ).
cnf(f_470_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2253),U_2254),U_2255) = U_2254
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2253),U_2254),U_2255))
| ~ class_Orderings_Olinorder(U_2253) ),
inference(clausify,[status(thm)],[f_470_3]) ).
fof(f_471_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_471_2,plain,
! [U_2259,U_2258,U_2257,U_2256] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2256),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2256),U_2259),U_2257)),U_2258))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2256),U_2257),U_2258))
| ~ class_Orderings_Olinorder(U_2256) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
fof(f_471_3,plain,
! [U_2256,U_2257,U_2258,U_2259] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2256),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2256),U_2259),U_2257)),U_2258))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2256),U_2257),U_2258))
| ~ class_Orderings_Olinorder(U_2256) ),
inference(definitional_conversion,[status(esa)],[f_471_2]) ).
cnf(f_471_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2256),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2256),U_2259),U_2257)),U_2258))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2256),U_2257),U_2258))
| ~ class_Orderings_Olinorder(U_2256) ),
inference(clausify,[status(thm)],[f_471_3]) ).
fof(f_472_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_472_2,plain,
! [U_2263,U_2262,U_2261,U_2260] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2260),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2260),U_2261),U_2263)),U_2262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2260),U_2261),U_2262))
| ~ class_Orderings_Olinorder(U_2260) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
fof(f_472_3,plain,
! [U_2260,U_2261,U_2262,U_2263] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2260),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2260),U_2261),U_2263)),U_2262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2260),U_2261),U_2262))
| ~ class_Orderings_Olinorder(U_2260) ),
inference(definitional_conversion,[status(esa)],[f_472_2]) ).
cnf(f_472_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2260),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2260),U_2261),U_2263)),U_2262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2260),U_2261),U_2262))
| ~ class_Orderings_Olinorder(U_2260) ),
inference(clausify,[status(thm)],[f_472_3]) ).
fof(f_473_1,plain,
! [V_z_2,V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_y_2),V_z_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_y_2),V_z_2))) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff]) ).
fof(f_473_2,plain,
! [U_2267,U_2266,U_2265,U_2264] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2264),U_2266),U_2267)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),U_2267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),U_2266)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),U_2267))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),U_2266)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2264),U_2266),U_2267))) ) )
| ~ class_Orderings_Olinorder(U_2264) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
fof(f_473_3,plain,
( ! [U_2264,U_2265,U_2266,U_2267] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),U_2267))
| ~ sP117(U_2264,U_2265,U_2266,U_2267) )
& ! [U_2264,U_2265,U_2266,U_2267] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),U_2266))
| ~ sP117(U_2264,U_2265,U_2266,U_2267) )
& ! [U_2264,U_2265,U_2266,U_2267] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2264),U_2266),U_2267)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),U_2267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),U_2266))
| ~ sP118(U_2264,U_2265,U_2266,U_2267) )
& ! [U_2264,U_2265,U_2266,U_2267] :
( sP117(U_2264,U_2265,U_2266,U_2267)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2264),U_2266),U_2267)))
| ~ sP118(U_2264,U_2265,U_2266,U_2267) )
& ! [U_2264,U_2265,U_2266,U_2267] :
( sP118(U_2264,U_2265,U_2266,U_2267)
| ~ class_Orderings_Olinorder(U_2264) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117,sP118])],[f_473_2]) ).
cnf(f_473_4,plain,
( sP118(U_2264,U_2265,U_2266,U_2267)
| ~ class_Orderings_Olinorder(U_2264) ),
inference(clausify,[status(thm)],[f_473_3]) ).
cnf(f_473_5,plain,
( sP117(U_2264,U_2265,U_2266,U_2267)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2264),U_2266),U_2267)))
| ~ sP118(U_2264,U_2265,U_2266,U_2267) ),
inference(clausify,[status(thm)],[f_473_3]) ).
cnf(f_473_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2264),U_2266),U_2267)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),U_2267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),U_2266))
| ~ sP118(U_2264,U_2265,U_2266,U_2267) ),
inference(clausify,[status(thm)],[f_473_3]) ).
cnf(f_473_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),U_2266))
| ~ sP117(U_2264,U_2265,U_2266,U_2267) ),
inference(clausify,[status(thm)],[f_473_3]) ).
cnf(f_473_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2264),U_2265),U_2267))
| ~ sP117(U_2264,U_2265,U_2266,U_2267) ),
inference(clausify,[status(thm)],[f_473_3]) ).
fof(f_474_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2) != V_x_2 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf]) ).
fof(f_474_2,plain,
! [U_2270,U_2269,U_2268] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),U_2269),U_2270))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2268),U_2269),U_2270) != U_2269 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2268),U_2269),U_2270) = U_2269
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),U_2269),U_2270)) ) )
| ~ class_Orderings_Olinorder(U_2268) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
fof(f_474_3,plain,
( ! [U_2269,U_2270,U_2268] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),U_2269),U_2270))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2268),U_2269),U_2270) != U_2269
| ~ sP119(U_2269,U_2270,U_2268) )
& ! [U_2269,U_2270,U_2268] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2268),U_2269),U_2270) = U_2269
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),U_2269),U_2270))
| ~ sP119(U_2269,U_2270,U_2268) )
& ! [U_2269,U_2270,U_2268] :
( sP119(U_2269,U_2270,U_2268)
| ~ class_Orderings_Olinorder(U_2268) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119])],[f_474_2]) ).
cnf(f_474_4,plain,
( sP119(U_2269,U_2270,U_2268)
| ~ class_Orderings_Olinorder(U_2268) ),
inference(clausify,[status(thm)],[f_474_3]) ).
cnf(f_474_5,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2268),U_2269),U_2270) = U_2269
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),U_2269),U_2270))
| ~ sP119(U_2269,U_2270,U_2268) ),
inference(clausify,[status(thm)],[f_474_3]) ).
cnf(f_474_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),U_2269),U_2270))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2268),U_2269),U_2270) != U_2269
| ~ sP119(U_2269,U_2270,U_2268) ),
inference(clausify,[status(thm)],[f_474_3]) ).
fof(f_475_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_475_2,plain,
! [U_2273,U_2272,U_2271] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2271),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2271),U_2272),U_2273)),U_2273))
| ~ class_Orderings_Olinorder(U_2271) ),
inference(variable_rename,[status(thm)],[f_475_1]) ).
fof(f_475_3,plain,
! [U_2272,U_2273,U_2271] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2271),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2271),U_2272),U_2273)),U_2273))
| ~ class_Orderings_Olinorder(U_2271) ),
inference(definitional_conversion,[status(esa)],[f_475_2]) ).
cnf(f_475_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2271),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2271),U_2272),U_2273)),U_2273))
| ~ class_Orderings_Olinorder(U_2271) ),
inference(clausify,[status(thm)],[f_475_3]) ).
fof(f_476_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_476_2,plain,
! [U_2276,U_2275,U_2274] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2274),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2274),U_2275),U_2276)),U_2275))
| ~ class_Orderings_Olinorder(U_2274) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
fof(f_476_3,plain,
! [U_2274,U_2275,U_2276] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2274),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2274),U_2275),U_2276)),U_2275))
| ~ class_Orderings_Olinorder(U_2274) ),
inference(definitional_conversion,[status(esa)],[f_476_2]) ).
cnf(f_476_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2274),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2274),U_2275),U_2276)),U_2275))
| ~ class_Orderings_Olinorder(U_2274) ),
inference(clausify,[status(thm)],[f_476_3]) ).
fof(f_477_1,plain,
! [V_z_2,V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2)),V_z_2))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_z_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2)),V_z_2)) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj]) ).
fof(f_477_2,plain,
! [U_2280,U_2279,U_2278,U_2277] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2277),U_2278),U_2279)),U_2280))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2279),U_2280))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2278),U_2280)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2279),U_2280))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2278),U_2280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2277),U_2278),U_2279)),U_2280)) ) )
| ~ class_Orderings_Olinorder(U_2277) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
fof(f_477_3,plain,
( ! [U_2277,U_2278,U_2279,U_2280] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2279),U_2280))
| ~ sP120(U_2277,U_2278,U_2279,U_2280) )
& ! [U_2277,U_2278,U_2279,U_2280] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2278),U_2280))
| ~ sP120(U_2277,U_2278,U_2279,U_2280) )
& ! [U_2277,U_2278,U_2279,U_2280] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2277),U_2278),U_2279)),U_2280))
| sP120(U_2277,U_2278,U_2279,U_2280)
| ~ sP121(U_2277,U_2278,U_2279,U_2280) )
& ! [U_2277,U_2278,U_2279,U_2280] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2279),U_2280))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2278),U_2280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2277),U_2278),U_2279)),U_2280))
| ~ sP121(U_2277,U_2278,U_2279,U_2280) )
& ! [U_2277,U_2278,U_2279,U_2280] :
( sP121(U_2277,U_2278,U_2279,U_2280)
| ~ class_Orderings_Olinorder(U_2277) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP120,sP121])],[f_477_2]) ).
cnf(f_477_4,plain,
( sP121(U_2277,U_2278,U_2279,U_2280)
| ~ class_Orderings_Olinorder(U_2277) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2279),U_2280))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2278),U_2280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2277),U_2278),U_2279)),U_2280))
| ~ sP121(U_2277,U_2278,U_2279,U_2280) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2277),U_2278),U_2279)),U_2280))
| sP120(U_2277,U_2278,U_2279,U_2280)
| ~ sP121(U_2277,U_2278,U_2279,U_2280) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2278),U_2280))
| ~ sP120(U_2277,U_2278,U_2279,U_2280) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277),U_2279),U_2280))
| ~ sP120(U_2277,U_2278,U_2279,U_2280) ),
inference(clausify,[status(thm)],[f_477_3]) ).
fof(f_478_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_478_2,plain,
! [U_2284,U_2283,U_2282,U_2281] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2281),U_2282),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2281),U_2284),U_2283)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2281),U_2282),U_2283))
| ~ class_Orderings_Olinorder(U_2281) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
fof(f_478_3,plain,
! [U_2283,U_2281,U_2282,U_2284] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2281),U_2282),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2281),U_2284),U_2283)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2281),U_2282),U_2283))
| ~ class_Orderings_Olinorder(U_2281) ),
inference(definitional_conversion,[status(esa)],[f_478_2]) ).
cnf(f_478_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2281),U_2282),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2281),U_2284),U_2283)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2281),U_2282),U_2283))
| ~ class_Orderings_Olinorder(U_2281) ),
inference(clausify,[status(thm)],[f_478_3]) ).
fof(f_479_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_479_2,plain,
! [U_2288,U_2287,U_2286,U_2285] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2285),U_2286),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2285),U_2287),U_2288)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2285),U_2286),U_2287))
| ~ class_Orderings_Olinorder(U_2285) ),
inference(variable_rename,[status(thm)],[f_479_1]) ).
fof(f_479_3,plain,
! [U_2288,U_2285,U_2286,U_2287] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2285),U_2286),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2285),U_2287),U_2288)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2285),U_2286),U_2287))
| ~ class_Orderings_Olinorder(U_2285) ),
inference(definitional_conversion,[status(esa)],[f_479_2]) ).
cnf(f_479_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2285),U_2286),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2285),U_2287),U_2288)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2285),U_2286),U_2287))
| ~ class_Orderings_Olinorder(U_2285) ),
inference(clausify,[status(thm)],[f_479_3]) ).
fof(f_480_1,plain,
! [V_z_2,V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2)),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_z_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_z_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2)),V_z_2)) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj]) ).
fof(f_480_2,plain,
! [U_2292,U_2291,U_2290,U_2289] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2289),U_2290),U_2291)),U_2292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),U_2291),U_2292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),U_2290),U_2292)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),U_2291),U_2292))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),U_2290),U_2292)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2289),U_2290),U_2291)),U_2292)) ) )
| ~ class_Orderings_Olinorder(U_2289) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
fof(f_480_3,plain,
( ! [U_2289,U_2290,U_2291,U_2292] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),U_2291),U_2292))
| ~ sP122(U_2289,U_2290,U_2291,U_2292) )
& ! [U_2289,U_2290,U_2291,U_2292] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),U_2290),U_2292))
| ~ sP122(U_2289,U_2290,U_2291,U_2292) )
& ! [U_2289,U_2290,U_2291,U_2292] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2289),U_2290),U_2291)),U_2292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),U_2291),U_2292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),U_2290),U_2292))
| ~ sP123(U_2289,U_2290,U_2291,U_2292) )
& ! [U_2289,U_2290,U_2291,U_2292] :
( sP122(U_2289,U_2290,U_2291,U_2292)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2289),U_2290),U_2291)),U_2292))
| ~ sP123(U_2289,U_2290,U_2291,U_2292) )
& ! [U_2289,U_2290,U_2291,U_2292] :
( sP123(U_2289,U_2290,U_2291,U_2292)
| ~ class_Orderings_Olinorder(U_2289) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122,sP123])],[f_480_2]) ).
cnf(f_480_4,plain,
( sP123(U_2289,U_2290,U_2291,U_2292)
| ~ class_Orderings_Olinorder(U_2289) ),
inference(clausify,[status(thm)],[f_480_3]) ).
cnf(f_480_5,plain,
( sP122(U_2289,U_2290,U_2291,U_2292)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2289),U_2290),U_2291)),U_2292))
| ~ sP123(U_2289,U_2290,U_2291,U_2292) ),
inference(clausify,[status(thm)],[f_480_3]) ).
cnf(f_480_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2289),U_2290),U_2291)),U_2292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),U_2291),U_2292))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),U_2290),U_2292))
| ~ sP123(U_2289,U_2290,U_2291,U_2292) ),
inference(clausify,[status(thm)],[f_480_3]) ).
cnf(f_480_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),U_2290),U_2292))
| ~ sP122(U_2289,U_2290,U_2291,U_2292) ),
inference(clausify,[status(thm)],[f_480_3]) ).
cnf(f_480_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2289),U_2291),U_2292))
| ~ sP122(U_2289,U_2290,U_2291,U_2292) ),
inference(clausify,[status(thm)],[f_480_3]) ).
fof(f_481_1,plain,
! [V_y_2,V_x_2,V_z_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_y_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_x_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),V_y_2))) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj]) ).
fof(f_481_2,plain,
! [U_2296,U_2295,U_2294,U_2293] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2293),U_2295),U_2296)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),U_2296))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),U_2295)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),U_2296))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),U_2295))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2293),U_2295),U_2296))) ) )
| ~ class_Orderings_Olinorder(U_2293) ),
inference(variable_rename,[status(thm)],[f_481_1]) ).
fof(f_481_3,plain,
( ! [U_2294,U_2295,U_2296,U_2293] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),U_2296))
| ~ sP124(U_2294,U_2295,U_2296,U_2293) )
& ! [U_2294,U_2295,U_2296,U_2293] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),U_2295))
| ~ sP124(U_2294,U_2295,U_2296,U_2293) )
& ! [U_2294,U_2295,U_2296,U_2293] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2293),U_2295),U_2296)))
| sP124(U_2294,U_2295,U_2296,U_2293)
| ~ sP125(U_2294,U_2295,U_2296,U_2293) )
& ! [U_2294,U_2295,U_2296,U_2293] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),U_2296))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),U_2295))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2293),U_2295),U_2296)))
| ~ sP125(U_2294,U_2295,U_2296,U_2293) )
& ! [U_2294,U_2295,U_2296,U_2293] :
( sP125(U_2294,U_2295,U_2296,U_2293)
| ~ class_Orderings_Olinorder(U_2293) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124,sP125])],[f_481_2]) ).
cnf(f_481_4,plain,
( sP125(U_2294,U_2295,U_2296,U_2293)
| ~ class_Orderings_Olinorder(U_2293) ),
inference(clausify,[status(thm)],[f_481_3]) ).
cnf(f_481_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),U_2296))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),U_2295))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2293),U_2295),U_2296)))
| ~ sP125(U_2294,U_2295,U_2296,U_2293) ),
inference(clausify,[status(thm)],[f_481_3]) ).
cnf(f_481_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2293),U_2295),U_2296)))
| sP124(U_2294,U_2295,U_2296,U_2293)
| ~ sP125(U_2294,U_2295,U_2296,U_2293) ),
inference(clausify,[status(thm)],[f_481_3]) ).
cnf(f_481_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),U_2295))
| ~ sP124(U_2294,U_2295,U_2296,U_2293) ),
inference(clausify,[status(thm)],[f_481_3]) ).
cnf(f_481_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2293),U_2294),U_2296))
| ~ sP124(U_2294,U_2295,U_2296,U_2293) ),
inference(clausify,[status(thm)],[f_481_3]) ).
fof(f_482_1,plain,
! [V_a_2,V_b_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less]) ).
fof(f_482_2,plain,
! [U_2299,U_2298,U_2297] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),hAPP(c_Groups_Ouminus__class_Ouminus(U_2297),U_2298)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2297),U_2299)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),U_2299),U_2298)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),U_2299),U_2298))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),hAPP(c_Groups_Ouminus__class_Ouminus(U_2297),U_2298)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2297),U_2299))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2297) ),
inference(variable_rename,[status(thm)],[f_482_1]) ).
fof(f_482_3,plain,
( ! [U_2299,U_2298,U_2297] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),hAPP(c_Groups_Ouminus__class_Ouminus(U_2297),U_2298)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2297),U_2299)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),U_2299),U_2298))
| ~ sP126(U_2299,U_2298,U_2297) )
& ! [U_2299,U_2298,U_2297] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),U_2299),U_2298))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),hAPP(c_Groups_Ouminus__class_Ouminus(U_2297),U_2298)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2297),U_2299)))
| ~ sP126(U_2299,U_2298,U_2297) )
& ! [U_2299,U_2298,U_2297] :
( sP126(U_2299,U_2298,U_2297)
| ~ class_Groups_Oordered__ab__group__add(U_2297) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126])],[f_482_2]) ).
cnf(f_482_4,plain,
( sP126(U_2299,U_2298,U_2297)
| ~ class_Groups_Oordered__ab__group__add(U_2297) ),
inference(clausify,[status(thm)],[f_482_3]) ).
cnf(f_482_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),U_2299),U_2298))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),hAPP(c_Groups_Ouminus__class_Ouminus(U_2297),U_2298)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2297),U_2299)))
| ~ sP126(U_2299,U_2298,U_2297) ),
inference(clausify,[status(thm)],[f_482_3]) ).
cnf(f_482_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),hAPP(c_Groups_Ouminus__class_Ouminus(U_2297),U_2298)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2297),U_2299)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),U_2299),U_2298))
| ~ sP126(U_2299,U_2298,U_2297) ),
inference(clausify,[status(thm)],[f_482_3]) ).
fof(f_483_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_minus__less__iff]) ).
fof(f_483_2,plain,
! [U_2302,U_2301,U_2300] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2300),hAPP(c_Groups_Ouminus__class_Ouminus(U_2300),U_2301)),U_2302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2300),hAPP(c_Groups_Ouminus__class_Ouminus(U_2300),U_2302)),U_2301)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2300),hAPP(c_Groups_Ouminus__class_Ouminus(U_2300),U_2302)),U_2301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2300),hAPP(c_Groups_Ouminus__class_Ouminus(U_2300),U_2301)),U_2302)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2300) ),
inference(variable_rename,[status(thm)],[f_483_1]) ).
fof(f_483_3,plain,
( ! [U_2301,U_2300,U_2302] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2300),hAPP(c_Groups_Ouminus__class_Ouminus(U_2300),U_2301)),U_2302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2300),hAPP(c_Groups_Ouminus__class_Ouminus(U_2300),U_2302)),U_2301))
| ~ sP127(U_2301,U_2300,U_2302) )
& ! [U_2301,U_2300,U_2302] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2300),hAPP(c_Groups_Ouminus__class_Ouminus(U_2300),U_2302)),U_2301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2300),hAPP(c_Groups_Ouminus__class_Ouminus(U_2300),U_2301)),U_2302))
| ~ sP127(U_2301,U_2300,U_2302) )
& ! [U_2301,U_2300,U_2302] :
( sP127(U_2301,U_2300,U_2302)
| ~ class_Groups_Oordered__ab__group__add(U_2300) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP127])],[f_483_2]) ).
cnf(f_483_4,plain,
( sP127(U_2301,U_2300,U_2302)
| ~ class_Groups_Oordered__ab__group__add(U_2300) ),
inference(clausify,[status(thm)],[f_483_3]) ).
cnf(f_483_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2300),hAPP(c_Groups_Ouminus__class_Ouminus(U_2300),U_2302)),U_2301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2300),hAPP(c_Groups_Ouminus__class_Ouminus(U_2300),U_2301)),U_2302))
| ~ sP127(U_2301,U_2300,U_2302) ),
inference(clausify,[status(thm)],[f_483_3]) ).
cnf(f_483_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2300),hAPP(c_Groups_Ouminus__class_Ouminus(U_2300),U_2301)),U_2302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2300),hAPP(c_Groups_Ouminus__class_Ouminus(U_2300),U_2302)),U_2301))
| ~ sP127(U_2301,U_2300,U_2302) ),
inference(clausify,[status(thm)],[f_483_3]) ).
fof(f_484_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__iff]) ).
fof(f_484_2,plain,
! [U_2305,U_2304,U_2303] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2303),U_2304),hAPP(c_Groups_Ouminus__class_Ouminus(U_2303),U_2305)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2303),U_2305),hAPP(c_Groups_Ouminus__class_Ouminus(U_2303),U_2304))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2303),U_2305),hAPP(c_Groups_Ouminus__class_Ouminus(U_2303),U_2304)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2303),U_2304),hAPP(c_Groups_Ouminus__class_Ouminus(U_2303),U_2305))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2303) ),
inference(variable_rename,[status(thm)],[f_484_1]) ).
fof(f_484_3,plain,
( ! [U_2304,U_2305,U_2303] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2303),U_2304),hAPP(c_Groups_Ouminus__class_Ouminus(U_2303),U_2305)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2303),U_2305),hAPP(c_Groups_Ouminus__class_Ouminus(U_2303),U_2304)))
| ~ sP128(U_2304,U_2305,U_2303) )
& ! [U_2304,U_2305,U_2303] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2303),U_2305),hAPP(c_Groups_Ouminus__class_Ouminus(U_2303),U_2304)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2303),U_2304),hAPP(c_Groups_Ouminus__class_Ouminus(U_2303),U_2305)))
| ~ sP128(U_2304,U_2305,U_2303) )
& ! [U_2304,U_2305,U_2303] :
( sP128(U_2304,U_2305,U_2303)
| ~ class_Groups_Oordered__ab__group__add(U_2303) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128])],[f_484_2]) ).
cnf(f_484_4,plain,
( sP128(U_2304,U_2305,U_2303)
| ~ class_Groups_Oordered__ab__group__add(U_2303) ),
inference(clausify,[status(thm)],[f_484_3]) ).
cnf(f_484_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2303),U_2305),hAPP(c_Groups_Ouminus__class_Ouminus(U_2303),U_2304)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2303),U_2304),hAPP(c_Groups_Ouminus__class_Ouminus(U_2303),U_2305)))
| ~ sP128(U_2304,U_2305,U_2303) ),
inference(clausify,[status(thm)],[f_484_3]) ).
cnf(f_484_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2303),U_2304),hAPP(c_Groups_Ouminus__class_Ouminus(U_2303),U_2305)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2303),U_2305),hAPP(c_Groups_Ouminus__class_Ouminus(U_2303),U_2304)))
| ~ sP128(U_2304,U_2305,U_2303) ),
inference(clausify,[status(thm)],[f_484_3]) ).
fof(f_485_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_485_2,plain,
! [U_2309,U_2308,U_2307,U_2306] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2306),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2306),U_2309),U_2307)),U_2308))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2306),U_2307),U_2308))
| ~ class_Orderings_Olinorder(U_2306) ),
inference(variable_rename,[status(thm)],[f_485_1]) ).
fof(f_485_3,plain,
! [U_2306,U_2307,U_2308,U_2309] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2306),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2306),U_2309),U_2307)),U_2308))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2306),U_2307),U_2308))
| ~ class_Orderings_Olinorder(U_2306) ),
inference(definitional_conversion,[status(esa)],[f_485_2]) ).
cnf(f_485_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2306),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2306),U_2309),U_2307)),U_2308))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2306),U_2307),U_2308))
| ~ class_Orderings_Olinorder(U_2306) ),
inference(clausify,[status(thm)],[f_485_3]) ).
fof(f_486_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_486_2,plain,
! [U_2313,U_2312,U_2311,U_2310] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2310),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2310),U_2311),U_2313)),U_2312))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2310),U_2311),U_2312))
| ~ class_Orderings_Olinorder(U_2310) ),
inference(variable_rename,[status(thm)],[f_486_1]) ).
fof(f_486_3,plain,
! [U_2310,U_2311,U_2312,U_2313] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2310),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2310),U_2311),U_2313)),U_2312))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2310),U_2311),U_2312))
| ~ class_Orderings_Olinorder(U_2310) ),
inference(definitional_conversion,[status(esa)],[f_486_2]) ).
cnf(f_486_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2310),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2310),U_2311),U_2313)),U_2312))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2310),U_2311),U_2312))
| ~ class_Orderings_Olinorder(U_2310) ),
inference(clausify,[status(thm)],[f_486_3]) ).
fof(f_487_1,plain,
! [V_z_2,V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2)),V_z_2))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_z_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_z_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2)),V_z_2)) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj]) ).
fof(f_487_2,plain,
! [U_2317,U_2316,U_2315,U_2314] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2314),U_2315),U_2316)),U_2317))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),U_2316),U_2317))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),U_2315),U_2317)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),U_2316),U_2317))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),U_2315),U_2317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2314),U_2315),U_2316)),U_2317)) ) )
| ~ class_Orderings_Olinorder(U_2314) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
fof(f_487_3,plain,
( ! [U_2314,U_2315,U_2316,U_2317] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),U_2316),U_2317))
| ~ sP129(U_2314,U_2315,U_2316,U_2317) )
& ! [U_2314,U_2315,U_2316,U_2317] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),U_2315),U_2317))
| ~ sP129(U_2314,U_2315,U_2316,U_2317) )
& ! [U_2314,U_2315,U_2316,U_2317] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2314),U_2315),U_2316)),U_2317))
| sP129(U_2314,U_2315,U_2316,U_2317)
| ~ sP130(U_2314,U_2315,U_2316,U_2317) )
& ! [U_2314,U_2315,U_2316,U_2317] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),U_2316),U_2317))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),U_2315),U_2317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2314),U_2315),U_2316)),U_2317))
| ~ sP130(U_2314,U_2315,U_2316,U_2317) )
& ! [U_2314,U_2315,U_2316,U_2317] :
( sP130(U_2314,U_2315,U_2316,U_2317)
| ~ class_Orderings_Olinorder(U_2314) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129,sP130])],[f_487_2]) ).
cnf(f_487_4,plain,
( sP130(U_2314,U_2315,U_2316,U_2317)
| ~ class_Orderings_Olinorder(U_2314) ),
inference(clausify,[status(thm)],[f_487_3]) ).
cnf(f_487_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),U_2316),U_2317))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),U_2315),U_2317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2314),U_2315),U_2316)),U_2317))
| ~ sP130(U_2314,U_2315,U_2316,U_2317) ),
inference(clausify,[status(thm)],[f_487_3]) ).
cnf(f_487_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2314),U_2315),U_2316)),U_2317))
| sP129(U_2314,U_2315,U_2316,U_2317)
| ~ sP130(U_2314,U_2315,U_2316,U_2317) ),
inference(clausify,[status(thm)],[f_487_3]) ).
cnf(f_487_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),U_2315),U_2317))
| ~ sP129(U_2314,U_2315,U_2316,U_2317) ),
inference(clausify,[status(thm)],[f_487_3]) ).
cnf(f_487_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2314),U_2316),U_2317))
| ~ sP129(U_2314,U_2315,U_2316,U_2317) ),
inference(clausify,[status(thm)],[f_487_3]) ).
fof(f_488_1,plain,
! [V_y_2,V_x_2,V_z_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_x_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_y_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),V_x_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),V_y_2))) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj]) ).
fof(f_488_2,plain,
! [U_2321,U_2320,U_2319,U_2318] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2318),U_2320),U_2321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),U_2321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),U_2320)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),U_2321))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),U_2320)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2318),U_2320),U_2321))) ) )
| ~ class_Orderings_Olinorder(U_2318) ),
inference(variable_rename,[status(thm)],[f_488_1]) ).
fof(f_488_3,plain,
( ! [U_2319,U_2321,U_2318,U_2320] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),U_2321))
| ~ sP131(U_2319,U_2321,U_2318,U_2320) )
& ! [U_2319,U_2321,U_2318,U_2320] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),U_2320))
| ~ sP131(U_2319,U_2321,U_2318,U_2320) )
& ! [U_2319,U_2321,U_2318,U_2320] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2318),U_2320),U_2321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),U_2321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),U_2320))
| ~ sP132(U_2319,U_2321,U_2318,U_2320) )
& ! [U_2319,U_2321,U_2318,U_2320] :
( sP131(U_2319,U_2321,U_2318,U_2320)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2318),U_2320),U_2321)))
| ~ sP132(U_2319,U_2321,U_2318,U_2320) )
& ! [U_2319,U_2321,U_2318,U_2320] :
( sP132(U_2319,U_2321,U_2318,U_2320)
| ~ class_Orderings_Olinorder(U_2318) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131,sP132])],[f_488_2]) ).
cnf(f_488_4,plain,
( sP132(U_2319,U_2321,U_2318,U_2320)
| ~ class_Orderings_Olinorder(U_2318) ),
inference(clausify,[status(thm)],[f_488_3]) ).
cnf(f_488_5,plain,
( sP131(U_2319,U_2321,U_2318,U_2320)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2318),U_2320),U_2321)))
| ~ sP132(U_2319,U_2321,U_2318,U_2320) ),
inference(clausify,[status(thm)],[f_488_3]) ).
cnf(f_488_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2318),U_2320),U_2321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),U_2321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),U_2320))
| ~ sP132(U_2319,U_2321,U_2318,U_2320) ),
inference(clausify,[status(thm)],[f_488_3]) ).
cnf(f_488_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),U_2320))
| ~ sP131(U_2319,U_2321,U_2318,U_2320) ),
inference(clausify,[status(thm)],[f_488_3]) ).
cnf(f_488_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2318),U_2319),U_2321))
| ~ sP131(U_2319,U_2321,U_2318,U_2320) ),
inference(clausify,[status(thm)],[f_488_3]) ).
fof(f_489_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_489_2,plain,
! [U_2325,U_2324,U_2323,U_2322] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2322),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2322),U_2323),U_2324)),U_2325) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2322),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2322),U_2323),U_2325)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2322),U_2324),U_2325))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2322) ),
inference(variable_rename,[status(thm)],[f_489_1]) ).
fof(f_489_3,plain,
! [U_2323,U_2324,U_2325,U_2322] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2322),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2322),U_2323),U_2324)),U_2325) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2322),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2322),U_2323),U_2325)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2322),U_2324),U_2325))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2322) ),
inference(definitional_conversion,[status(esa)],[f_489_2]) ).
cnf(f_489_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2322),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2322),U_2323),U_2324)),U_2325) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2322),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2322),U_2323),U_2325)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2322),U_2324),U_2325))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2322) ),
inference(clausify,[status(thm)],[f_489_3]) ).
fof(f_490_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_490_2,plain,
! [U_2328,U_2327,U_2326] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2326),U_2327),U_2328)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2326),hAPP(c_Groups_Ouminus__class_Ouminus(U_2326),U_2327)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2326),U_2328))
| ~ class_Groups_Oab__group__add(U_2326) ),
inference(variable_rename,[status(thm)],[f_490_1]) ).
fof(f_490_3,plain,
! [U_2326,U_2327,U_2328] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2326),U_2327),U_2328)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2326),hAPP(c_Groups_Ouminus__class_Ouminus(U_2326),U_2327)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2326),U_2328))
| ~ class_Groups_Oab__group__add(U_2326) ),
inference(definitional_conversion,[status(esa)],[f_490_2]) ).
cnf(f_490_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2326),U_2327),U_2328)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2326),hAPP(c_Groups_Ouminus__class_Ouminus(U_2326),U_2327)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2326),U_2328))
| ~ class_Groups_Oab__group__add(U_2326) ),
inference(clausify,[status(thm)],[f_490_3]) ).
fof(f_491_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_491_2,plain,
! [U_2331,U_2330,U_2329] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2329),U_2330),U_2331)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2329),hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),U_2331)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),U_2330))
| ~ class_Groups_Ogroup__add(U_2329) ),
inference(variable_rename,[status(thm)],[f_491_1]) ).
fof(f_491_3,plain,
! [U_2329,U_2330,U_2331] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2329),U_2330),U_2331)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2329),hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),U_2331)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),U_2330))
| ~ class_Groups_Ogroup__add(U_2329) ),
inference(definitional_conversion,[status(esa)],[f_491_2]) ).
cnf(f_491_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2329),U_2330),U_2331)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2329),hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),U_2331)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2329),U_2330))
| ~ class_Groups_Ogroup__add(U_2329) ),
inference(clausify,[status(thm)],[f_491_3]) ).
fof(f_492_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_492_2,plain,
! [U_2334,U_2333,U_2332] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2332),U_2333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2332),hAPP(c_Groups_Ouminus__class_Ouminus(U_2332),U_2333)),U_2334)) = U_2334
| ~ class_Groups_Ogroup__add(U_2332) ),
inference(variable_rename,[status(thm)],[f_492_1]) ).
fof(f_492_3,plain,
! [U_2332,U_2333,U_2334] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2332),U_2333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2332),hAPP(c_Groups_Ouminus__class_Ouminus(U_2332),U_2333)),U_2334)) = U_2334
| ~ class_Groups_Ogroup__add(U_2332) ),
inference(definitional_conversion,[status(esa)],[f_492_2]) ).
cnf(f_492_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2332),U_2333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2332),hAPP(c_Groups_Ouminus__class_Ouminus(U_2332),U_2333)),U_2334)) = U_2334
| ~ class_Groups_Ogroup__add(U_2332) ),
inference(clausify,[status(thm)],[f_492_3]) ).
fof(f_493_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_493_2,plain,
! [U_2337,U_2336,U_2335] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2335),hAPP(c_Groups_Ouminus__class_Ouminus(U_2335),U_2336)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2335),U_2336),U_2337)) = U_2337
| ~ class_Groups_Ogroup__add(U_2335) ),
inference(variable_rename,[status(thm)],[f_493_1]) ).
fof(f_493_3,plain,
! [U_2335,U_2336,U_2337] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2335),hAPP(c_Groups_Ouminus__class_Ouminus(U_2335),U_2336)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2335),U_2336),U_2337)) = U_2337
| ~ class_Groups_Ogroup__add(U_2335) ),
inference(definitional_conversion,[status(esa)],[f_493_2]) ).
cnf(f_493_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2335),hAPP(c_Groups_Ouminus__class_Ouminus(U_2335),U_2336)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2335),U_2336),U_2337)) = U_2337
| ~ class_Groups_Ogroup__add(U_2335) ),
inference(clausify,[status(thm)],[f_493_3]) ).
fof(f_494_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_494_2,plain,
! [U_2340,U_2339,U_2338] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2340)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),hAPP(c_Groups_Ouminus__class_Ouminus(U_2338),U_2340))
| ~ class_Rings_Oring(U_2338) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
fof(f_494_3,plain,
! [U_2338,U_2339,U_2340] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2340)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),hAPP(c_Groups_Ouminus__class_Ouminus(U_2338),U_2340))
| ~ class_Rings_Oring(U_2338) ),
inference(definitional_conversion,[status(esa)],[f_494_2]) ).
cnf(f_494_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2340)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),hAPP(c_Groups_Ouminus__class_Ouminus(U_2338),U_2340))
| ~ class_Rings_Oring(U_2338) ),
inference(clausify,[status(thm)],[f_494_3]) ).
fof(f_495_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_495_2,plain,
! [U_2343,U_2342,U_2341] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2342),U_2343)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),hAPP(c_Groups_Ouminus__class_Ouminus(U_2341),U_2342)),U_2343)
| ~ class_Rings_Oring(U_2341) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
fof(f_495_3,plain,
! [U_2341,U_2342,U_2343] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2342),U_2343)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),hAPP(c_Groups_Ouminus__class_Ouminus(U_2341),U_2342)),U_2343)
| ~ class_Rings_Oring(U_2341) ),
inference(definitional_conversion,[status(esa)],[f_495_2]) ).
cnf(f_495_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2341),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2342),U_2343)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),hAPP(c_Groups_Ouminus__class_Ouminus(U_2341),U_2342)),U_2343)
| ~ class_Rings_Oring(U_2341) ),
inference(clausify,[status(thm)],[f_495_3]) ).
fof(f_496_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_496_2,plain,
! [U_2346,U_2345,U_2344] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2344),hAPP(c_Groups_Ouminus__class_Ouminus(U_2344),U_2345)),U_2346) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2344),U_2345),hAPP(c_Groups_Ouminus__class_Ouminus(U_2344),U_2346))
| ~ class_Rings_Oring(U_2344) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
fof(f_496_3,plain,
! [U_2344,U_2345,U_2346] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2344),hAPP(c_Groups_Ouminus__class_Ouminus(U_2344),U_2345)),U_2346) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2344),U_2345),hAPP(c_Groups_Ouminus__class_Ouminus(U_2344),U_2346))
| ~ class_Rings_Oring(U_2344) ),
inference(definitional_conversion,[status(esa)],[f_496_2]) ).
cnf(f_496_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2344),hAPP(c_Groups_Ouminus__class_Ouminus(U_2344),U_2345)),U_2346) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2344),U_2345),hAPP(c_Groups_Ouminus__class_Ouminus(U_2344),U_2346))
| ~ class_Rings_Oring(U_2344) ),
inference(clausify,[status(thm)],[f_496_3]) ).
fof(f_497_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_497_2,plain,
! [U_2349,U_2348,U_2347] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2347),hAPP(c_Groups_Ouminus__class_Ouminus(U_2347),U_2348)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2347),U_2349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2347),U_2348),U_2349)
| ~ class_Rings_Oring(U_2347) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
fof(f_497_3,plain,
! [U_2347,U_2348,U_2349] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2347),hAPP(c_Groups_Ouminus__class_Ouminus(U_2347),U_2348)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2347),U_2349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2347),U_2348),U_2349)
| ~ class_Rings_Oring(U_2347) ),
inference(definitional_conversion,[status(esa)],[f_497_2]) ).
cnf(f_497_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2347),hAPP(c_Groups_Ouminus__class_Ouminus(U_2347),U_2348)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2347),U_2349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2347),U_2348),U_2349)
| ~ class_Rings_Oring(U_2347) ),
inference(clausify,[status(thm)],[f_497_3]) ).
fof(f_498_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_b_2)
| ( V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)
& V_a_2 != V_b_2 ) )
& ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)
| V_a_2 = V_b_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_a_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_b_2) ) )
| ~ class_Rings_Oidom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__iff]) ).
fof(f_498_2,plain,
! [U_2352,U_2351,U_2350] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2350),U_2351),U_2351) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2350),U_2352),U_2352)
| ( U_2351 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2350),U_2352)
& U_2351 != U_2352 ) )
& ( U_2351 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2350),U_2352)
| U_2351 = U_2352
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2350),U_2351),U_2351) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2350),U_2352),U_2352) ) )
| ~ class_Rings_Oidom(U_2350) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
fof(f_498_3,plain,
( ! [U_2350,U_2351,U_2352] :
( U_2351 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2350),U_2352)
| ~ sP133(U_2350,U_2351,U_2352) )
& ! [U_2350,U_2351,U_2352] :
( U_2351 != U_2352
| ~ sP133(U_2350,U_2351,U_2352) )
& ! [U_2350,U_2351,U_2352] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2350),U_2351),U_2351) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2350),U_2352),U_2352)
| sP133(U_2350,U_2351,U_2352)
| ~ sP134(U_2350,U_2351,U_2352) )
& ! [U_2350,U_2351,U_2352] :
( U_2351 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2350),U_2352)
| U_2351 = U_2352
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2350),U_2351),U_2351) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2350),U_2352),U_2352)
| ~ sP134(U_2350,U_2351,U_2352) )
& ! [U_2350,U_2351,U_2352] :
( sP134(U_2350,U_2351,U_2352)
| ~ class_Rings_Oidom(U_2350) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133,sP134])],[f_498_2]) ).
cnf(f_498_4,plain,
( sP134(U_2350,U_2351,U_2352)
| ~ class_Rings_Oidom(U_2350) ),
inference(clausify,[status(thm)],[f_498_3]) ).
cnf(f_498_5,plain,
( U_2351 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2350),U_2352)
| U_2351 = U_2352
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2350),U_2351),U_2351) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2350),U_2352),U_2352)
| ~ sP134(U_2350,U_2351,U_2352) ),
inference(clausify,[status(thm)],[f_498_3]) ).
cnf(f_498_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2350),U_2351),U_2351) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2350),U_2352),U_2352)
| sP133(U_2350,U_2351,U_2352)
| ~ sP134(U_2350,U_2351,U_2352) ),
inference(clausify,[status(thm)],[f_498_3]) ).
cnf(f_498_7,plain,
( U_2351 != U_2352
| ~ sP133(U_2350,U_2351,U_2352) ),
inference(clausify,[status(thm)],[f_498_3]) ).
cnf(f_498_8,plain,
( U_2351 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2350),U_2352)
| ~ sP133(U_2350,U_2351,U_2352) ),
inference(clausify,[status(thm)],[f_498_3]) ).
fof(f_499_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_499_2,plain,
! [U_2356,U_2355,U_2354,U_2353] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2353),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2353),U_2354),U_2355)),U_2356) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2353),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2353),U_2354),U_2356)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2353),U_2355),U_2356))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2353) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
fof(f_499_3,plain,
! [U_2355,U_2354,U_2353,U_2356] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2353),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2353),U_2354),U_2355)),U_2356) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2353),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2353),U_2354),U_2356)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2353),U_2355),U_2356))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2353) ),
inference(definitional_conversion,[status(esa)],[f_499_2]) ).
cnf(f_499_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2353),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2353),U_2354),U_2355)),U_2356) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2353),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2353),U_2354),U_2356)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2353),U_2355),U_2356))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2353) ),
inference(clausify,[status(thm)],[f_499_3]) ).
fof(f_500_1,plain,
! [V_A_2,V_c_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_ComplE]) ).
fof(f_500_2,plain,
! [U_2359,U_2358,U_2357] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2357),U_2358),U_2359))
| ~ hBOOL(hAPP(hAPP(c_member(U_2357),U_2358),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2357,tc_HOL_Obool)),U_2359))) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
fof(f_500_3,plain,
! [U_2357,U_2358,U_2359] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2357),U_2358),U_2359))
| ~ hBOOL(hAPP(hAPP(c_member(U_2357),U_2358),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2357,tc_HOL_Obool)),U_2359))) ),
inference(definitional_conversion,[status(esa)],[f_500_2]) ).
cnf(f_500_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2357),U_2358),U_2359))
| ~ hBOOL(hAPP(hAPP(c_member(U_2357),U_2358),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2357,tc_HOL_Obool)),U_2359))) ),
inference(clausify,[status(thm)],[f_500_3]) ).
fof(f_501_1,plain,
! [V_A_2,V_c_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_ComplD]) ).
fof(f_501_2,plain,
! [U_2362,U_2361,U_2360] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2360),U_2361),U_2362))
| ~ hBOOL(hAPP(hAPP(c_member(U_2360),U_2361),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2360,tc_HOL_Obool)),U_2362))) ),
inference(variable_rename,[status(thm)],[f_501_1]) ).
fof(f_501_3,plain,
! [U_2360,U_2361,U_2362] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2360),U_2361),U_2362))
| ~ hBOOL(hAPP(hAPP(c_member(U_2360),U_2361),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2360,tc_HOL_Obool)),U_2362))) ),
inference(definitional_conversion,[status(esa)],[f_501_2]) ).
cnf(f_501_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2360),U_2361),U_2362))
| ~ hBOOL(hAPP(hAPP(c_member(U_2360),U_2361),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2360,tc_HOL_Obool)),U_2362))) ),
inference(clausify,[status(thm)],[f_501_3]) ).
fof(f_502_1,plain,
! [V_A_2,V_c_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))
| hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Compl__iff]) ).
fof(f_502_2,plain,
! [U_2365,U_2364,U_2363] :
( ( hBOOL(hAPP(hAPP(c_member(U_2363),U_2364),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2363,tc_HOL_Obool)),U_2365)))
| hBOOL(hAPP(hAPP(c_member(U_2363),U_2364),U_2365)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(U_2363),U_2364),U_2365))
| ~ hBOOL(hAPP(hAPP(c_member(U_2363),U_2364),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2363,tc_HOL_Obool)),U_2365))) ) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
fof(f_502_3,plain,
( ! [U_2371,U_2369,U_2367] :
( hBOOL(hAPP(hAPP(c_member(U_2367),U_2369),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2367,tc_HOL_Obool)),U_2371)))
| hBOOL(hAPP(hAPP(c_member(U_2367),U_2369),U_2371)) )
& ! [U_2370,U_2368,U_2366] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2368),U_2370))
| ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2368),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2366,tc_HOL_Obool)),U_2370))) ) ),
inference(miniscope,[status(thm)],[f_502_2]) ).
fof(f_502_4,plain,
( ! [U_2367,U_2369,U_2371] :
( hBOOL(hAPP(hAPP(c_member(U_2367),U_2369),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2367,tc_HOL_Obool)),U_2371)))
| hBOOL(hAPP(hAPP(c_member(U_2367),U_2369),U_2371)) )
& ! [U_2370,U_2368,U_2366] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2368),U_2370))
| ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2368),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2366,tc_HOL_Obool)),U_2370))) ) ),
inference(definitional_conversion,[status(esa)],[f_502_3]) ).
cnf(f_502_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2368),U_2370))
| ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2368),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2366,tc_HOL_Obool)),U_2370))) ),
inference(clausify,[status(thm)],[f_502_4]) ).
cnf(f_502_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2367),U_2369),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2367,tc_HOL_Obool)),U_2371)))
| hBOOL(hAPP(hAPP(c_member(U_2367),U_2369),U_2371)) ),
inference(clausify,[status(thm)],[f_502_4]) ).
fof(f_503_1,plain,
! [V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omax(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_OF__eq]) ).
fof(f_503_2,plain,
! [U_2373,U_2372] :
( c_Big__Operators_Olinorder__class_OMax(U_2372,U_2373) = hAPP(c_Finite__Set_Ofold1(U_2372,c_Orderings_Oord__class_Omax(U_2372)),U_2373)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2372),U_2373))
| ~ class_Orderings_Olinorder(U_2372) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
fof(f_503_3,plain,
! [U_2372,U_2373] :
( c_Big__Operators_Olinorder__class_OMax(U_2372,U_2373) = hAPP(c_Finite__Set_Ofold1(U_2372,c_Orderings_Oord__class_Omax(U_2372)),U_2373)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2372),U_2373))
| ~ class_Orderings_Olinorder(U_2372) ),
inference(definitional_conversion,[status(esa)],[f_503_2]) ).
cnf(f_503_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_2372,U_2373) = hAPP(c_Finite__Set_Ofold1(U_2372,c_Orderings_Oord__class_Omax(U_2372)),U_2373)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2372),U_2373))
| ~ class_Orderings_Olinorder(U_2372) ),
inference(clausify,[status(thm)],[f_503_3]) ).
fof(f_504_1,plain,
! [V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_OF__eq]) ).
fof(f_504_2,plain,
! [U_2375,U_2374] :
( c_Big__Operators_Olinorder__class_OMin(U_2374,U_2375) = hAPP(c_Finite__Set_Ofold1(U_2374,c_Orderings_Oord__class_Omin(U_2374)),U_2375)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2374),U_2375))
| ~ class_Orderings_Olinorder(U_2374) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
fof(f_504_3,plain,
! [U_2374,U_2375] :
( c_Big__Operators_Olinorder__class_OMin(U_2374,U_2375) = hAPP(c_Finite__Set_Ofold1(U_2374,c_Orderings_Oord__class_Omin(U_2374)),U_2375)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2374),U_2375))
| ~ class_Orderings_Olinorder(U_2374) ),
inference(definitional_conversion,[status(esa)],[f_504_2]) ).
cnf(f_504_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_2374,U_2375) = hAPP(c_Finite__Set_Ofold1(U_2374,c_Orderings_Oord__class_Omin(U_2374)),U_2375)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2374),U_2375))
| ~ class_Orderings_Olinorder(U_2374) ),
inference(clausify,[status(thm)],[f_504_3]) ).
fof(f_505_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_505_2,plain,
! [U_2379,U_2378,U_2377,U_2376] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2376),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2376),U_2377),U_2378)),U_2379) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2376),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2376),U_2377),U_2379)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2376),U_2378),U_2379))
| ~ class_Groups_Oordered__ab__group__add(U_2376) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
fof(f_505_3,plain,
! [U_2376,U_2377,U_2378,U_2379] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2376),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2376),U_2377),U_2378)),U_2379) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2376),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2376),U_2377),U_2379)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2376),U_2378),U_2379))
| ~ class_Groups_Oordered__ab__group__add(U_2376) ),
inference(definitional_conversion,[status(esa)],[f_505_2]) ).
cnf(f_505_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2376),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2376),U_2377),U_2378)),U_2379) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2376),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2376),U_2377),U_2379)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2376),U_2378),U_2379))
| ~ class_Groups_Oordered__ab__group__add(U_2376) ),
inference(clausify,[status(thm)],[f_505_3]) ).
fof(f_506_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_506_2,plain,
! [U_2382,U_2381,U_2380] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2380),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2380),U_2381),U_2382)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2380),U_2382),U_2381)
| ~ class_Groups_Oab__group__add(U_2380) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
fof(f_506_3,plain,
! [U_2380,U_2381,U_2382] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2380),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2380),U_2381),U_2382)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2380),U_2382),U_2381)
| ~ class_Groups_Oab__group__add(U_2380) ),
inference(definitional_conversion,[status(esa)],[f_506_2]) ).
cnf(f_506_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2380),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2380),U_2381),U_2382)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2380),U_2382),U_2381)
| ~ class_Groups_Oab__group__add(U_2380) ),
inference(clausify,[status(thm)],[f_506_3]) ).
fof(f_507_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_507_2,plain,
! [U_2386,U_2385,U_2384,U_2383] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2383),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2383),U_2384),U_2385)),U_2386) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2383),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2383),U_2384),U_2386)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2383),U_2385),U_2386))
| ~ class_Groups_Oordered__ab__group__add(U_2383) ),
inference(variable_rename,[status(thm)],[f_507_1]) ).
fof(f_507_3,plain,
! [U_2383,U_2384,U_2385,U_2386] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2383),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2383),U_2384),U_2385)),U_2386) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2383),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2383),U_2384),U_2386)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2383),U_2385),U_2386))
| ~ class_Groups_Oordered__ab__group__add(U_2383) ),
inference(definitional_conversion,[status(esa)],[f_507_2]) ).
cnf(f_507_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2383),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2383),U_2384),U_2385)),U_2386) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2383),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2383),U_2384),U_2386)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2383),U_2385),U_2386))
| ~ class_Groups_Oordered__ab__group__add(U_2383) ),
inference(clausify,[status(thm)],[f_507_3]) ).
fof(f_508_1,plain,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Compl__anti__mono]) ).
fof(f_508_2,plain,
! [U_2389,U_2388,U_2387] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2387,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2387,tc_HOL_Obool)),U_2389)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2387,tc_HOL_Obool)),U_2388)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2387,tc_HOL_Obool)),U_2388),U_2389)) ),
inference(variable_rename,[status(thm)],[f_508_1]) ).
fof(f_508_3,plain,
! [U_2387,U_2388,U_2389] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2387,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2387,tc_HOL_Obool)),U_2389)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2387,tc_HOL_Obool)),U_2388)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2387,tc_HOL_Obool)),U_2388),U_2389)) ),
inference(definitional_conversion,[status(esa)],[f_508_2]) ).
cnf(f_508_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2387,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2387,tc_HOL_Obool)),U_2389)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2387,tc_HOL_Obool)),U_2388)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2387,tc_HOL_Obool)),U_2388),U_2389)) ),
inference(clausify,[status(thm)],[f_508_3]) ).
fof(f_509_1,plain,
! [V_B_2,V_A_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_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(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff]) ).
fof(f_509_2,plain,
! [U_2392,U_2391,U_2390] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2390,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2390,tc_HOL_Obool)),U_2391)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2390,tc_HOL_Obool)),U_2392)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2390,tc_HOL_Obool)),U_2392),U_2391)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2390,tc_HOL_Obool)),U_2392),U_2391))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2390,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2390,tc_HOL_Obool)),U_2391)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2390,tc_HOL_Obool)),U_2392))) ) ),
inference(variable_rename,[status(thm)],[f_509_1]) ).
fof(f_509_3,plain,
( ! [U_2398,U_2396,U_2394] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2394,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2394,tc_HOL_Obool)),U_2396)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2394,tc_HOL_Obool)),U_2398)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2394,tc_HOL_Obool)),U_2398),U_2396)) )
& ! [U_2397,U_2395,U_2393] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2393,tc_HOL_Obool)),U_2397),U_2395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2393,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2393,tc_HOL_Obool)),U_2395)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2393,tc_HOL_Obool)),U_2397))) ) ),
inference(miniscope,[status(thm)],[f_509_2]) ).
fof(f_509_4,plain,
( ! [U_2394,U_2396,U_2398] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2394,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2394,tc_HOL_Obool)),U_2396)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2394,tc_HOL_Obool)),U_2398)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2394,tc_HOL_Obool)),U_2398),U_2396)) )
& ! [U_2395,U_2393,U_2397] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2393,tc_HOL_Obool)),U_2397),U_2395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2393,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2393,tc_HOL_Obool)),U_2395)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2393,tc_HOL_Obool)),U_2397))) ) ),
inference(definitional_conversion,[status(esa)],[f_509_3]) ).
cnf(f_509_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2393,tc_HOL_Obool)),U_2397),U_2395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2393,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2393,tc_HOL_Obool)),U_2395)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2393,tc_HOL_Obool)),U_2397))) ),
inference(clausify,[status(thm)],[f_509_4]) ).
cnf(f_509_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2394,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2394,tc_HOL_Obool)),U_2396)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2394,tc_HOL_Obool)),U_2398)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2394,tc_HOL_Obool)),U_2398),U_2396)) ),
inference(clausify,[status(thm)],[f_509_4]) ).
fof(f_510_1,plain,
! [V_A_2,V_g_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Groups_Otimes__class_Otimes(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_g_2),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__timesf]) ).
fof(f_510_2,plain,
! [U_2403,U_2402,U_2401,U_2400,U_2399] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2400,U_2399),hAPP(hAPP(c_COMBS(U_2400,U_2399,U_2399),hAPP(hAPP(c_COMBB(U_2399,tc_fun(U_2399,U_2399),U_2400),c_Groups_Otimes__class_Otimes(U_2399)),U_2401)),U_2402)),U_2403) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2399),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2400,U_2399),U_2401),U_2403)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2400,U_2399),U_2402),U_2403))
| ~ class_Groups_Ocomm__monoid__mult(U_2399) ),
inference(variable_rename,[status(thm)],[f_510_1]) ).
fof(f_510_3,plain,
! [U_2399,U_2400,U_2401,U_2402,U_2403] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2400,U_2399),hAPP(hAPP(c_COMBS(U_2400,U_2399,U_2399),hAPP(hAPP(c_COMBB(U_2399,tc_fun(U_2399,U_2399),U_2400),c_Groups_Otimes__class_Otimes(U_2399)),U_2401)),U_2402)),U_2403) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2399),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2400,U_2399),U_2401),U_2403)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2400,U_2399),U_2402),U_2403))
| ~ class_Groups_Ocomm__monoid__mult(U_2399) ),
inference(definitional_conversion,[status(esa)],[f_510_2]) ).
cnf(f_510_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2400,U_2399),hAPP(hAPP(c_COMBS(U_2400,U_2399,U_2399),hAPP(hAPP(c_COMBB(U_2399,tc_fun(U_2399,U_2399),U_2400),c_Groups_Otimes__class_Otimes(U_2399)),U_2401)),U_2402)),U_2403) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2399),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2400,U_2399),U_2401),U_2403)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2400,U_2399),U_2402),U_2403))
| ~ class_Groups_Ocomm__monoid__mult(U_2399) ),
inference(clausify,[status(thm)],[f_510_3]) ).
fof(f_511_1,plain,
! [T_c] :
( c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Orderings_Oord__class_Omax(T_c))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup]) ).
fof(f_511_2,plain,
! [U_2404] :
( c_Finite__Set_Ofun__left__comm__idem(U_2404,U_2404,c_Orderings_Oord__class_Omax(U_2404))
| ~ class_Orderings_Olinorder(U_2404) ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
fof(f_511_3,plain,
! [U_2404] :
( c_Finite__Set_Ofun__left__comm__idem(U_2404,U_2404,c_Orderings_Oord__class_Omax(U_2404))
| ~ class_Orderings_Olinorder(U_2404) ),
inference(definitional_conversion,[status(esa)],[f_511_2]) ).
cnf(f_511_4,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_2404,U_2404,c_Orderings_Oord__class_Omax(U_2404))
| ~ class_Orderings_Olinorder(U_2404) ),
inference(clausify,[status(thm)],[f_511_3]) ).
fof(f_512_1,plain,
! [T_c] :
( c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Orderings_Oord__class_Omin(T_c))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf]) ).
fof(f_512_2,plain,
! [U_2405] :
( c_Finite__Set_Ofun__left__comm__idem(U_2405,U_2405,c_Orderings_Oord__class_Omin(U_2405))
| ~ class_Orderings_Olinorder(U_2405) ),
inference(variable_rename,[status(thm)],[f_512_1]) ).
fof(f_512_3,plain,
! [U_2405] :
( c_Finite__Set_Ofun__left__comm__idem(U_2405,U_2405,c_Orderings_Oord__class_Omin(U_2405))
| ~ class_Orderings_Olinorder(U_2405) ),
inference(definitional_conversion,[status(esa)],[f_512_2]) ).
cnf(f_512_4,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_2405,U_2405,c_Orderings_Oord__class_Omin(U_2405))
| ~ class_Orderings_Olinorder(U_2405) ),
inference(clausify,[status(thm)],[f_512_3]) ).
fof(f_513_1,plain,
! [V_a_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold1__belowI]) ).
fof(f_513_2,plain,
! [U_2408,U_2407,U_2406] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2406),hAPP(c_Finite__Set_Ofold1(U_2406,c_Orderings_Oord__class_Omin(U_2406)),U_2407)),U_2408))
| ~ hBOOL(hAPP(hAPP(c_member(U_2406),U_2408),U_2407))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2406),U_2407))
| ~ class_Orderings_Olinorder(U_2406) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
fof(f_513_3,plain,
! [U_2406,U_2407,U_2408] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2406),hAPP(c_Finite__Set_Ofold1(U_2406,c_Orderings_Oord__class_Omin(U_2406)),U_2407)),U_2408))
| ~ hBOOL(hAPP(hAPP(c_member(U_2406),U_2408),U_2407))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2406),U_2407))
| ~ class_Orderings_Olinorder(U_2406) ),
inference(definitional_conversion,[status(esa)],[f_513_2]) ).
cnf(f_513_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2406),hAPP(c_Finite__Set_Ofold1(U_2406,c_Orderings_Oord__class_Omin(U_2406)),U_2407)),U_2408))
| ~ hBOOL(hAPP(hAPP(c_member(U_2406),U_2408),U_2407))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2406),U_2407))
| ~ class_Orderings_Olinorder(U_2406) ),
inference(clausify,[status(thm)],[f_513_3]) ).
fof(f_514_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)),V_x_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),V_x_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_c),B_x),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)),V_x_2)) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold1__below__iff]) ).
fof(f_514_2,plain,
! [U_2413,U_2412,U_2411] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Finite__Set_Ofold1(U_2411,c_Orderings_Oord__class_Omin(U_2411)),U_2412)),U_2413))
| ! [U_2410] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),U_2410),U_2413))
| ~ hBOOL(hAPP(hAPP(c_member(U_2411),U_2410),U_2412)) ) )
& ( ? [U_2409] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),U_2409),U_2413))
& hBOOL(hAPP(hAPP(c_member(U_2411),U_2409),U_2412)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Finite__Set_Ofold1(U_2411,c_Orderings_Oord__class_Omin(U_2411)),U_2412)),U_2413)) ) )
| U_2412 = c_Orderings_Obot__class_Obot(tc_fun(U_2411,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2411),U_2412))
| ~ class_Orderings_Olinorder(U_2411) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
fof(f_514_3,plain,
! [U_2413,U_2412,U_2411] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Finite__Set_Ofold1(U_2411,c_Orderings_Oord__class_Omin(U_2411)),U_2412)),U_2413))
| ! [U_2410] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),U_2410),U_2413))
| ~ hBOOL(hAPP(hAPP(c_member(U_2411),U_2410),U_2412)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),sK40(U_2413,U_2412,U_2411)),U_2413))
& hBOOL(hAPP(hAPP(c_member(U_2411),sK40(U_2413,U_2412,U_2411)),U_2412)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Finite__Set_Ofold1(U_2411,c_Orderings_Oord__class_Omin(U_2411)),U_2412)),U_2413)) ) )
| U_2412 = c_Orderings_Obot__class_Obot(tc_fun(U_2411,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2411),U_2412))
| ~ class_Orderings_Olinorder(U_2411) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_2409,sK40(U_2413,U_2412,U_2411))],[f_514_2]) ).
fof(f_514_4,plain,
( ! [U_2411,U_2412,U_2413] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),sK40(U_2413,U_2412,U_2411)),U_2413))
| ~ sP135(U_2411,U_2412,U_2413) )
& ! [U_2411,U_2412,U_2413] :
( hBOOL(hAPP(hAPP(c_member(U_2411),sK40(U_2413,U_2412,U_2411)),U_2412))
| ~ sP135(U_2411,U_2412,U_2413) )
& ! [U_2410,U_2411,U_2412,U_2413] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Finite__Set_Ofold1(U_2411,c_Orderings_Oord__class_Omin(U_2411)),U_2412)),U_2413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),U_2410),U_2413))
| ~ hBOOL(hAPP(hAPP(c_member(U_2411),U_2410),U_2412))
| ~ sP136(U_2410,U_2411,U_2412,U_2413) )
& ! [U_2410,U_2411,U_2412,U_2413] :
( sP135(U_2411,U_2412,U_2413)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Finite__Set_Ofold1(U_2411,c_Orderings_Oord__class_Omin(U_2411)),U_2412)),U_2413))
| ~ sP136(U_2410,U_2411,U_2412,U_2413) )
& ! [U_2410,U_2411,U_2412,U_2413] :
( sP136(U_2410,U_2411,U_2412,U_2413)
| U_2412 = c_Orderings_Obot__class_Obot(tc_fun(U_2411,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2411),U_2412))
| ~ class_Orderings_Olinorder(U_2411) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP135,sP136])],[f_514_3]) ).
cnf(f_514_5,plain,
( sP136(U_2410,U_2411,U_2412,U_2413)
| U_2412 = c_Orderings_Obot__class_Obot(tc_fun(U_2411,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2411),U_2412))
| ~ class_Orderings_Olinorder(U_2411) ),
inference(clausify,[status(thm)],[f_514_4]) ).
cnf(f_514_6,plain,
( sP135(U_2411,U_2412,U_2413)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Finite__Set_Ofold1(U_2411,c_Orderings_Oord__class_Omin(U_2411)),U_2412)),U_2413))
| ~ sP136(U_2410,U_2411,U_2412,U_2413) ),
inference(clausify,[status(thm)],[f_514_4]) ).
cnf(f_514_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),hAPP(c_Finite__Set_Ofold1(U_2411,c_Orderings_Oord__class_Omin(U_2411)),U_2412)),U_2413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),U_2410),U_2413))
| ~ hBOOL(hAPP(hAPP(c_member(U_2411),U_2410),U_2412))
| ~ sP136(U_2410,U_2411,U_2412,U_2413) ),
inference(clausify,[status(thm)],[f_514_4]) ).
cnf(f_514_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_2411),sK40(U_2413,U_2412,U_2411)),U_2412))
| ~ sP135(U_2411,U_2412,U_2413) ),
inference(clausify,[status(thm)],[f_514_4]) ).
cnf(f_514_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2411),sK40(U_2413,U_2412,U_2411)),U_2413))
| ~ sP135(U_2411,U_2412,U_2413) ),
inference(clausify,[status(thm)],[f_514_4]) ).
fof(f_515_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_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_c),V_x_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_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2))) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Obelow__fold1__iff]) ).
fof(f_515_2,plain,
! [U_2418,U_2417,U_2416] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),hAPP(c_Finite__Set_Ofold1(U_2416,c_Orderings_Oord__class_Omin(U_2416)),U_2417)))
| ? [U_2415] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),U_2415))
& hBOOL(hAPP(hAPP(c_member(U_2416),U_2415),U_2417)) ) )
& ( ! [U_2414] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),U_2414))
| ~ hBOOL(hAPP(hAPP(c_member(U_2416),U_2414),U_2417)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),hAPP(c_Finite__Set_Ofold1(U_2416,c_Orderings_Oord__class_Omin(U_2416)),U_2417))) ) )
| U_2417 = c_Orderings_Obot__class_Obot(tc_fun(U_2416,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2416),U_2417))
| ~ class_Orderings_Olinorder(U_2416) ),
inference(variable_rename,[status(thm)],[f_515_1]) ).
fof(f_515_3,plain,
! [U_2418,U_2417,U_2416] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),hAPP(c_Finite__Set_Ofold1(U_2416,c_Orderings_Oord__class_Omin(U_2416)),U_2417)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),sK41(U_2418,U_2417,U_2416)))
& hBOOL(hAPP(hAPP(c_member(U_2416),sK41(U_2418,U_2417,U_2416)),U_2417)) ) )
& ( ! [U_2414] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),U_2414))
| ~ hBOOL(hAPP(hAPP(c_member(U_2416),U_2414),U_2417)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),hAPP(c_Finite__Set_Ofold1(U_2416,c_Orderings_Oord__class_Omin(U_2416)),U_2417))) ) )
| U_2417 = c_Orderings_Obot__class_Obot(tc_fun(U_2416,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2416),U_2417))
| ~ class_Orderings_Olinorder(U_2416) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_2415,sK41(U_2418,U_2417,U_2416))],[f_515_2]) ).
fof(f_515_4,plain,
( ! [U_2417,U_2418,U_2416] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),sK41(U_2418,U_2417,U_2416)))
| ~ sP137(U_2417,U_2418,U_2416) )
& ! [U_2417,U_2418,U_2416] :
( hBOOL(hAPP(hAPP(c_member(U_2416),sK41(U_2418,U_2417,U_2416)),U_2417))
| ~ sP137(U_2417,U_2418,U_2416) )
& ! [U_2417,U_2418,U_2414,U_2416] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),hAPP(c_Finite__Set_Ofold1(U_2416,c_Orderings_Oord__class_Omin(U_2416)),U_2417)))
| sP137(U_2417,U_2418,U_2416)
| ~ sP138(U_2417,U_2418,U_2414,U_2416) )
& ! [U_2417,U_2418,U_2414,U_2416] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),U_2414))
| ~ hBOOL(hAPP(hAPP(c_member(U_2416),U_2414),U_2417))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),hAPP(c_Finite__Set_Ofold1(U_2416,c_Orderings_Oord__class_Omin(U_2416)),U_2417)))
| ~ sP138(U_2417,U_2418,U_2414,U_2416) )
& ! [U_2417,U_2418,U_2414,U_2416] :
( sP138(U_2417,U_2418,U_2414,U_2416)
| U_2417 = c_Orderings_Obot__class_Obot(tc_fun(U_2416,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2416),U_2417))
| ~ class_Orderings_Olinorder(U_2416) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137,sP138])],[f_515_3]) ).
cnf(f_515_5,plain,
( sP138(U_2417,U_2418,U_2414,U_2416)
| U_2417 = c_Orderings_Obot__class_Obot(tc_fun(U_2416,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2416),U_2417))
| ~ class_Orderings_Olinorder(U_2416) ),
inference(clausify,[status(thm)],[f_515_4]) ).
cnf(f_515_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),U_2414))
| ~ hBOOL(hAPP(hAPP(c_member(U_2416),U_2414),U_2417))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),hAPP(c_Finite__Set_Ofold1(U_2416,c_Orderings_Oord__class_Omin(U_2416)),U_2417)))
| ~ sP138(U_2417,U_2418,U_2414,U_2416) ),
inference(clausify,[status(thm)],[f_515_4]) ).
cnf(f_515_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),hAPP(c_Finite__Set_Ofold1(U_2416,c_Orderings_Oord__class_Omin(U_2416)),U_2417)))
| sP137(U_2417,U_2418,U_2416)
| ~ sP138(U_2417,U_2418,U_2414,U_2416) ),
inference(clausify,[status(thm)],[f_515_4]) ).
cnf(f_515_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_2416),sK41(U_2418,U_2417,U_2416)),U_2417))
| ~ sP137(U_2417,U_2418,U_2416) ),
inference(clausify,[status(thm)],[f_515_4]) ).
cnf(f_515_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2416),U_2418),sK41(U_2418,U_2417,U_2416)))
| ~ sP137(U_2417,U_2418,U_2416) ),
inference(clausify,[status(thm)],[f_515_4]) ).
fof(f_516_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Ouminus__class_Ouminus(T_c)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2))
| ~ class_Groups_Oab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__negf]) ).
fof(f_516_2,plain,
! [U_2422,U_2421,U_2420,U_2419] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2420,U_2419),hAPP(hAPP(c_COMBB(U_2419,U_2419,U_2420),c_Groups_Ouminus__class_Ouminus(U_2419)),U_2421)),U_2422) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2419),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2420,U_2419),U_2421),U_2422))
| ~ class_Groups_Oab__group__add(U_2419) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
fof(f_516_3,plain,
! [U_2421,U_2420,U_2422,U_2419] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2420,U_2419),hAPP(hAPP(c_COMBB(U_2419,U_2419,U_2420),c_Groups_Ouminus__class_Ouminus(U_2419)),U_2421)),U_2422) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2419),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2420,U_2419),U_2421),U_2422))
| ~ class_Groups_Oab__group__add(U_2419) ),
inference(definitional_conversion,[status(esa)],[f_516_2]) ).
cnf(f_516_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2420,U_2419),hAPP(hAPP(c_COMBB(U_2419,U_2419,U_2420),c_Groups_Ouminus__class_Ouminus(U_2419)),U_2421)),U_2422) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2419),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2420,U_2419),U_2421),U_2422))
| ~ class_Groups_Oab__group__add(U_2419) ),
inference(clausify,[status(thm)],[f_516_3]) ).
fof(f_517_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)),V_x_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),B_x),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),B_x),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)),V_x_2)) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold1__strict__below__iff]) ).
fof(f_517_2,plain,
! [U_2427,U_2426,U_2425] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),hAPP(c_Finite__Set_Ofold1(U_2425,c_Orderings_Oord__class_Omin(U_2425)),U_2426)),U_2427))
| ! [U_2424] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),U_2424),U_2427))
| ~ hBOOL(hAPP(hAPP(c_member(U_2425),U_2424),U_2426)) ) )
& ( ? [U_2423] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),U_2423),U_2427))
& hBOOL(hAPP(hAPP(c_member(U_2425),U_2423),U_2426)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),hAPP(c_Finite__Set_Ofold1(U_2425,c_Orderings_Oord__class_Omin(U_2425)),U_2426)),U_2427)) ) )
| U_2426 = c_Orderings_Obot__class_Obot(tc_fun(U_2425,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2425),U_2426))
| ~ class_Orderings_Olinorder(U_2425) ),
inference(variable_rename,[status(thm)],[f_517_1]) ).
fof(f_517_3,plain,
! [U_2427,U_2426,U_2425] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),hAPP(c_Finite__Set_Ofold1(U_2425,c_Orderings_Oord__class_Omin(U_2425)),U_2426)),U_2427))
| ! [U_2424] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),U_2424),U_2427))
| ~ hBOOL(hAPP(hAPP(c_member(U_2425),U_2424),U_2426)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),sK42(U_2427,U_2426,U_2425)),U_2427))
& hBOOL(hAPP(hAPP(c_member(U_2425),sK42(U_2427,U_2426,U_2425)),U_2426)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),hAPP(c_Finite__Set_Ofold1(U_2425,c_Orderings_Oord__class_Omin(U_2425)),U_2426)),U_2427)) ) )
| U_2426 = c_Orderings_Obot__class_Obot(tc_fun(U_2425,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2425),U_2426))
| ~ class_Orderings_Olinorder(U_2425) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_2423,sK42(U_2427,U_2426,U_2425))],[f_517_2]) ).
fof(f_517_4,plain,
( ! [U_2425,U_2426,U_2427] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),sK42(U_2427,U_2426,U_2425)),U_2427))
| ~ sP139(U_2425,U_2426,U_2427) )
& ! [U_2425,U_2426,U_2427] :
( hBOOL(hAPP(hAPP(c_member(U_2425),sK42(U_2427,U_2426,U_2425)),U_2426))
| ~ sP139(U_2425,U_2426,U_2427) )
& ! [U_2424,U_2425,U_2426,U_2427] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),hAPP(c_Finite__Set_Ofold1(U_2425,c_Orderings_Oord__class_Omin(U_2425)),U_2426)),U_2427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),U_2424),U_2427))
| ~ hBOOL(hAPP(hAPP(c_member(U_2425),U_2424),U_2426))
| ~ sP140(U_2424,U_2425,U_2426,U_2427) )
& ! [U_2424,U_2425,U_2426,U_2427] :
( sP139(U_2425,U_2426,U_2427)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),hAPP(c_Finite__Set_Ofold1(U_2425,c_Orderings_Oord__class_Omin(U_2425)),U_2426)),U_2427))
| ~ sP140(U_2424,U_2425,U_2426,U_2427) )
& ! [U_2424,U_2425,U_2426,U_2427] :
( sP140(U_2424,U_2425,U_2426,U_2427)
| U_2426 = c_Orderings_Obot__class_Obot(tc_fun(U_2425,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2425),U_2426))
| ~ class_Orderings_Olinorder(U_2425) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP139,sP140])],[f_517_3]) ).
cnf(f_517_5,plain,
( sP140(U_2424,U_2425,U_2426,U_2427)
| U_2426 = c_Orderings_Obot__class_Obot(tc_fun(U_2425,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2425),U_2426))
| ~ class_Orderings_Olinorder(U_2425) ),
inference(clausify,[status(thm)],[f_517_4]) ).
cnf(f_517_6,plain,
( sP139(U_2425,U_2426,U_2427)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),hAPP(c_Finite__Set_Ofold1(U_2425,c_Orderings_Oord__class_Omin(U_2425)),U_2426)),U_2427))
| ~ sP140(U_2424,U_2425,U_2426,U_2427) ),
inference(clausify,[status(thm)],[f_517_4]) ).
cnf(f_517_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),hAPP(c_Finite__Set_Ofold1(U_2425,c_Orderings_Oord__class_Omin(U_2425)),U_2426)),U_2427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),U_2424),U_2427))
| ~ hBOOL(hAPP(hAPP(c_member(U_2425),U_2424),U_2426))
| ~ sP140(U_2424,U_2425,U_2426,U_2427) ),
inference(clausify,[status(thm)],[f_517_4]) ).
cnf(f_517_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_2425),sK42(U_2427,U_2426,U_2425)),U_2426))
| ~ sP139(U_2425,U_2426,U_2427) ),
inference(clausify,[status(thm)],[f_517_4]) ).
cnf(f_517_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2425),sK42(U_2427,U_2426,U_2425)),U_2427))
| ~ sP139(U_2425,U_2426,U_2427) ),
inference(clausify,[status(thm)],[f_517_4]) ).
fof(f_518_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_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_c),V_x_2),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2))) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__below__fold1__iff]) ).
fof(f_518_2,plain,
! [U_2432,U_2431,U_2430] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),hAPP(c_Finite__Set_Ofold1(U_2430,c_Orderings_Oord__class_Omin(U_2430)),U_2431)))
| ? [U_2429] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),U_2429))
& hBOOL(hAPP(hAPP(c_member(U_2430),U_2429),U_2431)) ) )
& ( ! [U_2428] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),U_2428))
| ~ hBOOL(hAPP(hAPP(c_member(U_2430),U_2428),U_2431)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),hAPP(c_Finite__Set_Ofold1(U_2430,c_Orderings_Oord__class_Omin(U_2430)),U_2431))) ) )
| U_2431 = c_Orderings_Obot__class_Obot(tc_fun(U_2430,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2430),U_2431))
| ~ class_Orderings_Olinorder(U_2430) ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
fof(f_518_3,plain,
! [U_2432,U_2431,U_2430] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),hAPP(c_Finite__Set_Ofold1(U_2430,c_Orderings_Oord__class_Omin(U_2430)),U_2431)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),sK43(U_2432,U_2431,U_2430)))
& hBOOL(hAPP(hAPP(c_member(U_2430),sK43(U_2432,U_2431,U_2430)),U_2431)) ) )
& ( ! [U_2428] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),U_2428))
| ~ hBOOL(hAPP(hAPP(c_member(U_2430),U_2428),U_2431)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),hAPP(c_Finite__Set_Ofold1(U_2430,c_Orderings_Oord__class_Omin(U_2430)),U_2431))) ) )
| U_2431 = c_Orderings_Obot__class_Obot(tc_fun(U_2430,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2430),U_2431))
| ~ class_Orderings_Olinorder(U_2430) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_2429,sK43(U_2432,U_2431,U_2430))],[f_518_2]) ).
fof(f_518_4,plain,
( ! [U_2431,U_2432,U_2430] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),sK43(U_2432,U_2431,U_2430)))
| ~ sP141(U_2431,U_2432,U_2430) )
& ! [U_2431,U_2432,U_2430] :
( hBOOL(hAPP(hAPP(c_member(U_2430),sK43(U_2432,U_2431,U_2430)),U_2431))
| ~ sP141(U_2431,U_2432,U_2430) )
& ! [U_2431,U_2428,U_2432,U_2430] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),hAPP(c_Finite__Set_Ofold1(U_2430,c_Orderings_Oord__class_Omin(U_2430)),U_2431)))
| sP141(U_2431,U_2432,U_2430)
| ~ sP142(U_2431,U_2428,U_2432,U_2430) )
& ! [U_2431,U_2428,U_2432,U_2430] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),U_2428))
| ~ hBOOL(hAPP(hAPP(c_member(U_2430),U_2428),U_2431))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),hAPP(c_Finite__Set_Ofold1(U_2430,c_Orderings_Oord__class_Omin(U_2430)),U_2431)))
| ~ sP142(U_2431,U_2428,U_2432,U_2430) )
& ! [U_2431,U_2428,U_2432,U_2430] :
( sP142(U_2431,U_2428,U_2432,U_2430)
| U_2431 = c_Orderings_Obot__class_Obot(tc_fun(U_2430,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2430),U_2431))
| ~ class_Orderings_Olinorder(U_2430) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141,sP142])],[f_518_3]) ).
cnf(f_518_5,plain,
( sP142(U_2431,U_2428,U_2432,U_2430)
| U_2431 = c_Orderings_Obot__class_Obot(tc_fun(U_2430,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2430),U_2431))
| ~ class_Orderings_Olinorder(U_2430) ),
inference(clausify,[status(thm)],[f_518_4]) ).
cnf(f_518_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),U_2428))
| ~ hBOOL(hAPP(hAPP(c_member(U_2430),U_2428),U_2431))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),hAPP(c_Finite__Set_Ofold1(U_2430,c_Orderings_Oord__class_Omin(U_2430)),U_2431)))
| ~ sP142(U_2431,U_2428,U_2432,U_2430) ),
inference(clausify,[status(thm)],[f_518_4]) ).
cnf(f_518_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),hAPP(c_Finite__Set_Ofold1(U_2430,c_Orderings_Oord__class_Omin(U_2430)),U_2431)))
| sP141(U_2431,U_2432,U_2430)
| ~ sP142(U_2431,U_2428,U_2432,U_2430) ),
inference(clausify,[status(thm)],[f_518_4]) ).
cnf(f_518_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_2430),sK43(U_2432,U_2431,U_2430)),U_2431))
| ~ sP141(U_2431,U_2432,U_2430) ),
inference(clausify,[status(thm)],[f_518_4]) ).
cnf(f_518_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2430),U_2432),sK43(U_2432,U_2431,U_2430)))
| ~ sP141(U_2431,U_2432,U_2430) ),
inference(clausify,[status(thm)],[f_518_4]) ).
fof(f_519_1,plain,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)))
| ~ 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_A_2),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold1__antimono]) ).
fof(f_519_2,plain,
! [U_2435,U_2434,U_2433] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2433),hAPP(c_Finite__Set_Ofold1(U_2433,c_Orderings_Oord__class_Omin(U_2433)),U_2435)),hAPP(c_Finite__Set_Ofold1(U_2433,c_Orderings_Oord__class_Omin(U_2433)),U_2434)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2433),U_2435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2433,tc_HOL_Obool)),U_2434),U_2435))
| U_2434 = c_Orderings_Obot__class_Obot(tc_fun(U_2433,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(U_2433) ),
inference(variable_rename,[status(thm)],[f_519_1]) ).
fof(f_519_3,plain,
! [U_2434,U_2435,U_2433] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2433),hAPP(c_Finite__Set_Ofold1(U_2433,c_Orderings_Oord__class_Omin(U_2433)),U_2435)),hAPP(c_Finite__Set_Ofold1(U_2433,c_Orderings_Oord__class_Omin(U_2433)),U_2434)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2433),U_2435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2433,tc_HOL_Obool)),U_2434),U_2435))
| U_2434 = c_Orderings_Obot__class_Obot(tc_fun(U_2433,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(U_2433) ),
inference(definitional_conversion,[status(esa)],[f_519_2]) ).
cnf(f_519_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2433),hAPP(c_Finite__Set_Ofold1(U_2433,c_Orderings_Oord__class_Omin(U_2433)),U_2435)),hAPP(c_Finite__Set_Ofold1(U_2433,c_Orderings_Oord__class_Omin(U_2433)),U_2434)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2433),U_2435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2433,tc_HOL_Obool)),U_2434),U_2435))
| U_2434 = c_Orderings_Obot__class_Obot(tc_fun(U_2433,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(U_2433) ),
inference(clausify,[status(thm)],[f_519_3]) ).
fof(f_520_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_520_2,plain,
! [U_2438,U_2437,U_2436] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2436),U_2437),U_2438) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2436),U_2437),hAPP(c_Groups_Ouminus__class_Ouminus(U_2436),U_2438))
| ~ class_Groups_Ogroup__add(U_2436) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
fof(f_520_3,plain,
! [U_2438,U_2437,U_2436] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2436),U_2437),U_2438) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2436),U_2437),hAPP(c_Groups_Ouminus__class_Ouminus(U_2436),U_2438))
| ~ class_Groups_Ogroup__add(U_2436) ),
inference(definitional_conversion,[status(esa)],[f_520_2]) ).
cnf(f_520_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2436),U_2437),U_2438) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2436),U_2437),hAPP(c_Groups_Ouminus__class_Ouminus(U_2436),U_2438))
| ~ class_Groups_Ogroup__add(U_2436) ),
inference(clausify,[status(thm)],[f_520_3]) ).
fof(f_521_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_521_2,plain,
! [U_2441,U_2440,U_2439] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2439),U_2440),U_2441) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2439),U_2440),hAPP(c_Groups_Ouminus__class_Ouminus(U_2439),U_2441))
| ~ class_Groups_Oab__group__add(U_2439) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
fof(f_521_3,plain,
! [U_2439,U_2440,U_2441] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2439),U_2440),U_2441) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2439),U_2440),hAPP(c_Groups_Ouminus__class_Ouminus(U_2439),U_2441))
| ~ class_Groups_Oab__group__add(U_2439) ),
inference(definitional_conversion,[status(esa)],[f_521_2]) ).
cnf(f_521_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2439),U_2440),U_2441) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2439),U_2440),hAPP(c_Groups_Ouminus__class_Ouminus(U_2439),U_2441))
| ~ class_Groups_Oab__group__add(U_2439) ),
inference(clausify,[status(thm)],[f_521_3]) ).
fof(f_522_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_522_2,plain,
! [U_2444,U_2443,U_2442] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2442),U_2443),hAPP(c_Groups_Ouminus__class_Ouminus(U_2442),U_2444)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2442),U_2443),U_2444)
| ~ class_Groups_Ogroup__add(U_2442) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
fof(f_522_3,plain,
! [U_2442,U_2443,U_2444] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2442),U_2443),hAPP(c_Groups_Ouminus__class_Ouminus(U_2442),U_2444)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2442),U_2443),U_2444)
| ~ class_Groups_Ogroup__add(U_2442) ),
inference(definitional_conversion,[status(esa)],[f_522_2]) ).
cnf(f_522_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2442),U_2443),hAPP(c_Groups_Ouminus__class_Ouminus(U_2442),U_2444)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2442),U_2443),U_2444)
| ~ class_Groups_Ogroup__add(U_2442) ),
inference(clausify,[status(thm)],[f_522_3]) ).
fof(f_523_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_523_2,plain,
! [U_2447,U_2446,U_2445] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2445),U_2446),U_2447) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2445),U_2446),hAPP(c_Groups_Ouminus__class_Ouminus(U_2445),U_2447))
| ~ class_Rings_Ocomm__ring__1(U_2445) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
fof(f_523_3,plain,
! [U_2445,U_2446,U_2447] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2445),U_2446),U_2447) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2445),U_2446),hAPP(c_Groups_Ouminus__class_Ouminus(U_2445),U_2447))
| ~ class_Rings_Ocomm__ring__1(U_2445) ),
inference(definitional_conversion,[status(esa)],[f_523_2]) ).
cnf(f_523_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2445),U_2446),U_2447) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2445),U_2446),hAPP(c_Groups_Ouminus__class_Ouminus(U_2445),U_2447))
| ~ class_Rings_Ocomm__ring__1(U_2445) ),
inference(clausify,[status(thm)],[f_523_3]) ).
fof(f_524_1,plain,
! [V_A_2,T_c] :
( ( 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)),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))
| ~ 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)),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq]) ).
fof(f_524_2,plain,
! [U_2449,U_2448] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2448,tc_HOL_Obool)),U_2449),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2448,tc_HOL_Obool)),U_2449)))
| U_2449 != c_Orderings_Obot__class_Obot(tc_fun(U_2448,tc_HOL_Obool)) )
& ( U_2449 = c_Orderings_Obot__class_Obot(tc_fun(U_2448,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2448,tc_HOL_Obool)),U_2449),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2448,tc_HOL_Obool)),U_2449))) ) ),
inference(variable_rename,[status(thm)],[f_524_1]) ).
fof(f_524_3,plain,
( ! [U_2453,U_2451] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2451,tc_HOL_Obool)),U_2453),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2451,tc_HOL_Obool)),U_2453)))
| U_2453 != c_Orderings_Obot__class_Obot(tc_fun(U_2451,tc_HOL_Obool)) )
& ! [U_2452,U_2450] :
( U_2452 = c_Orderings_Obot__class_Obot(tc_fun(U_2450,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2450,tc_HOL_Obool)),U_2452),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2450,tc_HOL_Obool)),U_2452))) ) ),
inference(miniscope,[status(thm)],[f_524_2]) ).
fof(f_524_4,plain,
( ! [U_2451,U_2453] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2451,tc_HOL_Obool)),U_2453),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2451,tc_HOL_Obool)),U_2453)))
| U_2453 != c_Orderings_Obot__class_Obot(tc_fun(U_2451,tc_HOL_Obool)) )
& ! [U_2452,U_2450] :
( U_2452 = c_Orderings_Obot__class_Obot(tc_fun(U_2450,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2450,tc_HOL_Obool)),U_2452),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2450,tc_HOL_Obool)),U_2452))) ) ),
inference(definitional_conversion,[status(esa)],[f_524_3]) ).
cnf(f_524_5,plain,
( U_2452 = c_Orderings_Obot__class_Obot(tc_fun(U_2450,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2450,tc_HOL_Obool)),U_2452),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2450,tc_HOL_Obool)),U_2452))) ),
inference(clausify,[status(thm)],[f_524_4]) ).
cnf(f_524_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2451,tc_HOL_Obool)),U_2453),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2451,tc_HOL_Obool)),U_2453)))
| U_2453 != c_Orderings_Obot__class_Obot(tc_fun(U_2451,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_524_4]) ).
fof(f_525_1,plain,
! [V_h_2,V_g_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Groups_Otimes__class_Otimes(T_d)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Odistrib]) ).
fof(f_525_2,plain,
! [U_2458,U_2457,U_2456,U_2455,U_2454] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2455,U_2454),hAPP(hAPP(c_COMBS(U_2455,U_2454,U_2454),hAPP(hAPP(c_COMBB(U_2454,tc_fun(U_2454,U_2454),U_2455),c_Groups_Otimes__class_Otimes(U_2454)),U_2457)),U_2458)),U_2456) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2454),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2455,U_2454),U_2457),U_2456)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2455,U_2454),U_2458),U_2456))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2455),U_2456))
| ~ class_Groups_Ocomm__monoid__mult(U_2454) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
fof(f_525_3,plain,
! [U_2454,U_2455,U_2456,U_2457,U_2458] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2455,U_2454),hAPP(hAPP(c_COMBS(U_2455,U_2454,U_2454),hAPP(hAPP(c_COMBB(U_2454,tc_fun(U_2454,U_2454),U_2455),c_Groups_Otimes__class_Otimes(U_2454)),U_2457)),U_2458)),U_2456) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2454),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2455,U_2454),U_2457),U_2456)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2455,U_2454),U_2458),U_2456))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2455),U_2456))
| ~ class_Groups_Ocomm__monoid__mult(U_2454) ),
inference(definitional_conversion,[status(esa)],[f_525_2]) ).
cnf(f_525_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2455,U_2454),hAPP(hAPP(c_COMBS(U_2455,U_2454,U_2454),hAPP(hAPP(c_COMBB(U_2454,tc_fun(U_2454,U_2454),U_2455),c_Groups_Otimes__class_Otimes(U_2454)),U_2457)),U_2458)),U_2456) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2454),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2455,U_2454),U_2457),U_2456)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2455,U_2454),U_2458),U_2456))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2455),U_2456))
| ~ class_Groups_Ocomm__monoid__mult(U_2454) ),
inference(clausify,[status(thm)],[f_525_3]) ).
fof(f_526_1,plain,
! [V_a_2,V_f_2,T_c,V_g_2] :
( hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_a_2
| V_g_2 != c_Finite__Set_Ofold1(T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fold1__singleton__def]) ).
fof(f_526_2,plain,
! [U_2462,U_2461,U_2460,U_2459] :
( hAPP(U_2459,hAPP(hAPP(c_Set_Oinsert(U_2460),U_2462),c_Orderings_Obot__class_Obot(tc_fun(U_2460,tc_HOL_Obool)))) = U_2462
| U_2459 != c_Finite__Set_Ofold1(U_2460,U_2461) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
fof(f_526_3,plain,
! [U_2459,U_2460,U_2461,U_2462] :
( hAPP(U_2459,hAPP(hAPP(c_Set_Oinsert(U_2460),U_2462),c_Orderings_Obot__class_Obot(tc_fun(U_2460,tc_HOL_Obool)))) = U_2462
| U_2459 != c_Finite__Set_Ofold1(U_2460,U_2461) ),
inference(definitional_conversion,[status(esa)],[f_526_2]) ).
cnf(f_526_4,plain,
( hAPP(U_2459,hAPP(hAPP(c_Set_Oinsert(U_2460),U_2462),c_Orderings_Obot__class_Obot(tc_fun(U_2460,tc_HOL_Obool)))) = U_2462
| U_2459 != c_Finite__Set_Ofold1(U_2460,U_2461) ),
inference(clausify,[status(thm)],[f_526_3]) ).
fof(f_527_1,plain,
! [V_a_2,V_f_2,T_c] : hAPP(c_Finite__Set_Ofold1(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)))) = V_a_2,
inference(fof_nnf,[status(thm)],[fact_fold1__singleton]) ).
fof(f_527_2,plain,
! [U_2465,U_2464,U_2463] : hAPP(c_Finite__Set_Ofold1(U_2463,U_2464),hAPP(hAPP(c_Set_Oinsert(U_2463),U_2465),c_Orderings_Obot__class_Obot(tc_fun(U_2463,tc_HOL_Obool)))) = U_2465,
inference(variable_rename,[status(thm)],[f_527_1]) ).
fof(f_527_3,plain,
! [U_2463,U_2464,U_2465] : hAPP(c_Finite__Set_Ofold1(U_2463,U_2464),hAPP(hAPP(c_Set_Oinsert(U_2463),U_2465),c_Orderings_Obot__class_Obot(tc_fun(U_2463,tc_HOL_Obool)))) = U_2465,
inference(definitional_conversion,[status(esa)],[f_527_2]) ).
cnf(f_527_4,plain,
hAPP(c_Finite__Set_Ofold1(U_2463,U_2464),hAPP(hAPP(c_Set_Oinsert(U_2463),U_2465),c_Orderings_Obot__class_Obot(tc_fun(U_2463,tc_HOL_Obool)))) = U_2465,
inference(clausify,[status(thm)],[f_527_3]) ).
fof(f_528_1,plain,
! [V_A_2,V_F_2,V_f_2,T_c] :
( hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,V_f_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold]) ).
fof(f_528_2,plain,
! [U_2469,U_2468,U_2467,U_2466] :
( hAPP(U_2468,U_2469) = hAPP(c_Finite__Set_Ofold1(U_2466,U_2467),U_2469)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2466),U_2469))
| ~ c_Finite__Set_Ofolding__one(U_2466,U_2467,U_2468) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
fof(f_528_3,plain,
! [U_2466,U_2467,U_2468,U_2469] :
( hAPP(U_2468,U_2469) = hAPP(c_Finite__Set_Ofold1(U_2466,U_2467),U_2469)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2466),U_2469))
| ~ c_Finite__Set_Ofolding__one(U_2466,U_2467,U_2468) ),
inference(definitional_conversion,[status(esa)],[f_528_2]) ).
cnf(f_528_4,plain,
( hAPP(U_2468,U_2469) = hAPP(c_Finite__Set_Ofold1(U_2466,U_2467),U_2469)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2466),U_2469))
| ~ c_Finite__Set_Ofolding__one(U_2466,U_2467,U_2468) ),
inference(clausify,[status(thm)],[f_528_3]) ).
fof(f_529_1,plain,
! [V_a_2,V_b_2,V_A_2,T_c] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_b_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert]) ).
fof(f_529_2,plain,
! [U_2473,U_2472,U_2471,U_2470] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_2470,U_2470,c_Orderings_Oord__class_Omax(U_2470)),U_2472),hAPP(hAPP(c_Set_Oinsert(U_2470),U_2473),U_2471)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2470),U_2473),hAPP(hAPP(c_Finite__Set_Ofold(U_2470,U_2470,c_Orderings_Oord__class_Omax(U_2470)),U_2472),U_2471))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2470),U_2471))
| ~ class_Orderings_Olinorder(U_2470) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
fof(f_529_3,plain,
! [U_2470,U_2471,U_2472,U_2473] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_2470,U_2470,c_Orderings_Oord__class_Omax(U_2470)),U_2472),hAPP(hAPP(c_Set_Oinsert(U_2470),U_2473),U_2471)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2470),U_2473),hAPP(hAPP(c_Finite__Set_Ofold(U_2470,U_2470,c_Orderings_Oord__class_Omax(U_2470)),U_2472),U_2471))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2470),U_2471))
| ~ class_Orderings_Olinorder(U_2470) ),
inference(definitional_conversion,[status(esa)],[f_529_2]) ).
cnf(f_529_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_2470,U_2470,c_Orderings_Oord__class_Omax(U_2470)),U_2472),hAPP(hAPP(c_Set_Oinsert(U_2470),U_2473),U_2471)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2470),U_2473),hAPP(hAPP(c_Finite__Set_Ofold(U_2470,U_2470,c_Orderings_Oord__class_Omax(U_2470)),U_2472),U_2471))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2470),U_2471))
| ~ class_Orderings_Olinorder(U_2470) ),
inference(clausify,[status(thm)],[f_529_3]) ).
fof(f_530_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oin__idem]) ).
fof(f_530_2,plain,
! [U_2476,U_2475,U_2474] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2474),U_2476),c_Big__Operators_Olinorder__class_OMax(U_2474,U_2475)) = c_Big__Operators_Olinorder__class_OMax(U_2474,U_2475)
| ~ hBOOL(hAPP(hAPP(c_member(U_2474),U_2476),U_2475))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2474),U_2475))
| ~ class_Orderings_Olinorder(U_2474) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
fof(f_530_3,plain,
! [U_2474,U_2475,U_2476] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2474),U_2476),c_Big__Operators_Olinorder__class_OMax(U_2474,U_2475)) = c_Big__Operators_Olinorder__class_OMax(U_2474,U_2475)
| ~ hBOOL(hAPP(hAPP(c_member(U_2474),U_2476),U_2475))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2474),U_2475))
| ~ class_Orderings_Olinorder(U_2474) ),
inference(definitional_conversion,[status(esa)],[f_530_2]) ).
cnf(f_530_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2474),U_2476),c_Big__Operators_Olinorder__class_OMax(U_2474,U_2475)) = c_Big__Operators_Olinorder__class_OMax(U_2474,U_2475)
| ~ hBOOL(hAPP(hAPP(c_member(U_2474),U_2476),U_2475))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2474),U_2475))
| ~ class_Orderings_Olinorder(U_2474) ),
inference(clausify,[status(thm)],[f_530_3]) ).
fof(f_531_1,plain,
! [V_a_2,V_b_2,V_A_2,T_c] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_b_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__insert]) ).
fof(f_531_2,plain,
! [U_2480,U_2479,U_2478,U_2477] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_2477,U_2477,c_Orderings_Oord__class_Omin(U_2477)),U_2479),hAPP(hAPP(c_Set_Oinsert(U_2477),U_2480),U_2478)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2477),U_2480),hAPP(hAPP(c_Finite__Set_Ofold(U_2477,U_2477,c_Orderings_Oord__class_Omin(U_2477)),U_2479),U_2478))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2477),U_2478))
| ~ class_Orderings_Olinorder(U_2477) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
fof(f_531_3,plain,
! [U_2477,U_2478,U_2479,U_2480] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_2477,U_2477,c_Orderings_Oord__class_Omin(U_2477)),U_2479),hAPP(hAPP(c_Set_Oinsert(U_2477),U_2480),U_2478)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2477),U_2480),hAPP(hAPP(c_Finite__Set_Ofold(U_2477,U_2477,c_Orderings_Oord__class_Omin(U_2477)),U_2479),U_2478))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2477),U_2478))
| ~ class_Orderings_Olinorder(U_2477) ),
inference(definitional_conversion,[status(esa)],[f_531_2]) ).
cnf(f_531_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_2477,U_2477,c_Orderings_Oord__class_Omin(U_2477)),U_2479),hAPP(hAPP(c_Set_Oinsert(U_2477),U_2480),U_2478)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2477),U_2480),hAPP(hAPP(c_Finite__Set_Ofold(U_2477,U_2477,c_Orderings_Oord__class_Omin(U_2477)),U_2479),U_2478))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2477),U_2478))
| ~ class_Orderings_Olinorder(U_2477) ),
inference(clausify,[status(thm)],[f_531_3]) ).
fof(f_532_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oin__idem]) ).
fof(f_532_2,plain,
! [U_2483,U_2482,U_2481] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2481),U_2483),c_Big__Operators_Olinorder__class_OMin(U_2481,U_2482)) = c_Big__Operators_Olinorder__class_OMin(U_2481,U_2482)
| ~ hBOOL(hAPP(hAPP(c_member(U_2481),U_2483),U_2482))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2481),U_2482))
| ~ class_Orderings_Olinorder(U_2481) ),
inference(variable_rename,[status(thm)],[f_532_1]) ).
fof(f_532_3,plain,
! [U_2481,U_2482,U_2483] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2481),U_2483),c_Big__Operators_Olinorder__class_OMin(U_2481,U_2482)) = c_Big__Operators_Olinorder__class_OMin(U_2481,U_2482)
| ~ hBOOL(hAPP(hAPP(c_member(U_2481),U_2483),U_2482))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2481),U_2482))
| ~ class_Orderings_Olinorder(U_2481) ),
inference(definitional_conversion,[status(esa)],[f_532_2]) ).
cnf(f_532_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2481),U_2483),c_Big__Operators_Olinorder__class_OMin(U_2481,U_2482)) = c_Big__Operators_Olinorder__class_OMin(U_2481,U_2482)
| ~ hBOOL(hAPP(hAPP(c_member(U_2481),U_2483),U_2482))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2481),U_2482))
| ~ class_Orderings_Olinorder(U_2481) ),
inference(clausify,[status(thm)],[f_532_3]) ).
fof(f_533_1,plain,
! [V_A_2,V_f_2,T_c] : hAPP(c_Finite__Set_Ofold1(T_c,V_f_2),V_A_2) = c_HOL_OThe(T_c,c_Finite__Set_Ofold1Set(T_c,V_f_2,V_A_2)),
inference(fof_nnf,[status(thm)],[fact_fold1__def]) ).
fof(f_533_2,plain,
! [U_2486,U_2485,U_2484] : hAPP(c_Finite__Set_Ofold1(U_2484,U_2485),U_2486) = c_HOL_OThe(U_2484,c_Finite__Set_Ofold1Set(U_2484,U_2485,U_2486)),
inference(variable_rename,[status(thm)],[f_533_1]) ).
fof(f_533_3,plain,
! [U_2485,U_2484,U_2486] : hAPP(c_Finite__Set_Ofold1(U_2484,U_2485),U_2486) = c_HOL_OThe(U_2484,c_Finite__Set_Ofold1Set(U_2484,U_2485,U_2486)),
inference(definitional_conversion,[status(esa)],[f_533_2]) ).
cnf(f_533_4,plain,
hAPP(c_Finite__Set_Ofold1(U_2484,U_2485),U_2486) = c_HOL_OThe(U_2484,c_Finite__Set_Ofold1Set(U_2484,U_2485,U_2486)),
inference(clausify,[status(thm)],[f_533_3]) ).
fof(f_534_1,plain,
! [V_g_2,V_x_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert]) ).
fof(f_534_2,plain,
! [U_2491,U_2490,U_2489,U_2488,U_2487] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2488,U_2487),U_2491),hAPP(hAPP(c_Set_Oinsert(U_2488),U_2490),U_2489)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),hAPP(U_2491,U_2490)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2488,U_2487),U_2491),U_2489))
| hBOOL(hAPP(hAPP(c_member(U_2488),U_2490),U_2489))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2488),U_2489))
| ~ class_Groups_Ocomm__monoid__mult(U_2487) ),
inference(variable_rename,[status(thm)],[f_534_1]) ).
fof(f_534_3,plain,
! [U_2487,U_2488,U_2489,U_2490,U_2491] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2488,U_2487),U_2491),hAPP(hAPP(c_Set_Oinsert(U_2488),U_2490),U_2489)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),hAPP(U_2491,U_2490)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2488,U_2487),U_2491),U_2489))
| hBOOL(hAPP(hAPP(c_member(U_2488),U_2490),U_2489))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2488),U_2489))
| ~ class_Groups_Ocomm__monoid__mult(U_2487) ),
inference(definitional_conversion,[status(esa)],[f_534_2]) ).
cnf(f_534_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2488,U_2487),U_2491),hAPP(hAPP(c_Set_Oinsert(U_2488),U_2490),U_2489)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),hAPP(U_2491,U_2490)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2488,U_2487),U_2491),U_2489))
| hBOOL(hAPP(hAPP(c_member(U_2488),U_2490),U_2489))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2488),U_2489))
| ~ class_Groups_Ocomm__monoid__mult(U_2487) ),
inference(clausify,[status(thm)],[f_534_3]) ).
fof(f_535_1,plain,
! [V_f_2,V_a_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__insert]) ).
fof(f_535_2,plain,
! [U_2496,U_2495,U_2494,U_2493,U_2492] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2493,U_2492),U_2496),hAPP(hAPP(c_Set_Oinsert(U_2493),U_2495),U_2494)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2492),hAPP(U_2496,U_2495)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2493,U_2492),U_2496),U_2494))
| hBOOL(hAPP(hAPP(c_member(U_2493),U_2495),U_2494))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2493),U_2494))
| ~ class_Groups_Ocomm__monoid__mult(U_2492) ),
inference(variable_rename,[status(thm)],[f_535_1]) ).
fof(f_535_3,plain,
! [U_2493,U_2492,U_2494,U_2495,U_2496] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2493,U_2492),U_2496),hAPP(hAPP(c_Set_Oinsert(U_2493),U_2495),U_2494)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2492),hAPP(U_2496,U_2495)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2493,U_2492),U_2496),U_2494))
| hBOOL(hAPP(hAPP(c_member(U_2493),U_2495),U_2494))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2493),U_2494))
| ~ class_Groups_Ocomm__monoid__mult(U_2492) ),
inference(definitional_conversion,[status(esa)],[f_535_2]) ).
cnf(f_535_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2493,U_2492),U_2496),hAPP(hAPP(c_Set_Oinsert(U_2493),U_2495),U_2494)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2492),hAPP(U_2496,U_2495)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2493,U_2492),U_2496),U_2494))
| hBOOL(hAPP(hAPP(c_member(U_2493),U_2495),U_2494))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2493),U_2494))
| ~ class_Groups_Ocomm__monoid__mult(U_2492) ),
inference(clausify,[status(thm)],[f_535_3]) ).
fof(f_536_1,plain,
! [V_b_2,V_a_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_b_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__le__fold__sup]) ).
fof(f_536_2,plain,
! [U_2500,U_2499,U_2498,U_2497] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2497),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2497),U_2499),U_2500)),hAPP(hAPP(c_Finite__Set_Ofold(U_2497,U_2497,c_Orderings_Oord__class_Omax(U_2497)),U_2500),U_2498)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2497),U_2499),U_2498))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2497),U_2498))
| ~ class_Orderings_Olinorder(U_2497) ),
inference(variable_rename,[status(thm)],[f_536_1]) ).
fof(f_536_3,plain,
! [U_2497,U_2498,U_2499,U_2500] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2497),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2497),U_2499),U_2500)),hAPP(hAPP(c_Finite__Set_Ofold(U_2497,U_2497,c_Orderings_Oord__class_Omax(U_2497)),U_2500),U_2498)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2497),U_2499),U_2498))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2497),U_2498))
| ~ class_Orderings_Olinorder(U_2497) ),
inference(definitional_conversion,[status(esa)],[f_536_2]) ).
cnf(f_536_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2497),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2497),U_2499),U_2500)),hAPP(hAPP(c_Finite__Set_Ofold(U_2497,U_2497,c_Orderings_Oord__class_Omax(U_2497)),U_2500),U_2498)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2497),U_2499),U_2498))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2497),U_2498))
| ~ class_Orderings_Olinorder(U_2497) ),
inference(clausify,[status(thm)],[f_536_3]) ).
fof(f_537_1,plain,
! [V_b_2,V_a_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_a_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__le__inf]) ).
fof(f_537_2,plain,
! [U_2504,U_2503,U_2502,U_2501] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2501),hAPP(hAPP(c_Finite__Set_Ofold(U_2501,U_2501,c_Orderings_Oord__class_Omin(U_2501)),U_2504),U_2502)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2501),U_2503),U_2504)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2501),U_2503),U_2502))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2501),U_2502))
| ~ class_Orderings_Olinorder(U_2501) ),
inference(variable_rename,[status(thm)],[f_537_1]) ).
fof(f_537_3,plain,
! [U_2501,U_2502,U_2503,U_2504] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2501),hAPP(hAPP(c_Finite__Set_Ofold(U_2501,U_2501,c_Orderings_Oord__class_Omin(U_2501)),U_2504),U_2502)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2501),U_2503),U_2504)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2501),U_2503),U_2502))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2501),U_2502))
| ~ class_Orderings_Olinorder(U_2501) ),
inference(definitional_conversion,[status(esa)],[f_537_2]) ).
cnf(f_537_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2501),hAPP(hAPP(c_Finite__Set_Ofold(U_2501,U_2501,c_Orderings_Oord__class_Omin(U_2501)),U_2504),U_2502)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2501),U_2503),U_2504)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2501),U_2503),U_2502))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2501),U_2502))
| ~ class_Orderings_Olinorder(U_2501) ),
inference(clausify,[status(thm)],[f_537_3]) ).
fof(f_538_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max__insert]) ).
fof(f_538_2,plain,
! [U_2507,U_2506,U_2505] :
( c_Big__Operators_Olinorder__class_OMax(U_2505,hAPP(hAPP(c_Set_Oinsert(U_2505),U_2507),U_2506)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2505),U_2507),c_Big__Operators_Olinorder__class_OMax(U_2505,U_2506))
| U_2506 = c_Orderings_Obot__class_Obot(tc_fun(U_2505,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2505),U_2506))
| ~ class_Orderings_Olinorder(U_2505) ),
inference(variable_rename,[status(thm)],[f_538_1]) ).
fof(f_538_3,plain,
! [U_2505,U_2506,U_2507] :
( c_Big__Operators_Olinorder__class_OMax(U_2505,hAPP(hAPP(c_Set_Oinsert(U_2505),U_2507),U_2506)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2505),U_2507),c_Big__Operators_Olinorder__class_OMax(U_2505,U_2506))
| U_2506 = c_Orderings_Obot__class_Obot(tc_fun(U_2505,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2505),U_2506))
| ~ class_Orderings_Olinorder(U_2505) ),
inference(definitional_conversion,[status(esa)],[f_538_2]) ).
cnf(f_538_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_2505,hAPP(hAPP(c_Set_Oinsert(U_2505),U_2507),U_2506)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2505),U_2507),c_Big__Operators_Olinorder__class_OMax(U_2505,U_2506))
| U_2506 = c_Orderings_Obot__class_Obot(tc_fun(U_2505,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2505),U_2506))
| ~ class_Orderings_Olinorder(U_2505) ),
inference(clausify,[status(thm)],[f_538_3]) ).
fof(f_539_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min__insert]) ).
fof(f_539_2,plain,
! [U_2510,U_2509,U_2508] :
( c_Big__Operators_Olinorder__class_OMin(U_2508,hAPP(hAPP(c_Set_Oinsert(U_2508),U_2510),U_2509)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2508),U_2510),c_Big__Operators_Olinorder__class_OMin(U_2508,U_2509))
| U_2509 = c_Orderings_Obot__class_Obot(tc_fun(U_2508,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2508),U_2509))
| ~ class_Orderings_Olinorder(U_2508) ),
inference(variable_rename,[status(thm)],[f_539_1]) ).
fof(f_539_3,plain,
! [U_2508,U_2509,U_2510] :
( c_Big__Operators_Olinorder__class_OMin(U_2508,hAPP(hAPP(c_Set_Oinsert(U_2508),U_2510),U_2509)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2508),U_2510),c_Big__Operators_Olinorder__class_OMin(U_2508,U_2509))
| U_2509 = c_Orderings_Obot__class_Obot(tc_fun(U_2508,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2508),U_2509))
| ~ class_Orderings_Olinorder(U_2508) ),
inference(definitional_conversion,[status(esa)],[f_539_2]) ).
cnf(f_539_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_2508,hAPP(hAPP(c_Set_Oinsert(U_2508),U_2510),U_2509)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2508),U_2510),c_Big__Operators_Olinorder__class_OMin(U_2508,U_2509))
| U_2509 = c_Orderings_Obot__class_Obot(tc_fun(U_2508,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2508),U_2509))
| ~ class_Orderings_Olinorder(U_2508) ),
inference(clausify,[status(thm)],[f_539_3]) ).
fof(f_540_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_Osubset__idem]) ).
fof(f_540_2,plain,
! [U_2513,U_2512,U_2511] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2511),c_Big__Operators_Olinorder__class_OMax(U_2511,U_2513)),c_Big__Operators_Olinorder__class_OMax(U_2511,U_2512)) = c_Big__Operators_Olinorder__class_OMax(U_2511,U_2512)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2511,tc_HOL_Obool)),U_2513),U_2512))
| U_2513 = c_Orderings_Obot__class_Obot(tc_fun(U_2511,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2511),U_2512))
| ~ class_Orderings_Olinorder(U_2511) ),
inference(variable_rename,[status(thm)],[f_540_1]) ).
fof(f_540_3,plain,
! [U_2511,U_2512,U_2513] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2511),c_Big__Operators_Olinorder__class_OMax(U_2511,U_2513)),c_Big__Operators_Olinorder__class_OMax(U_2511,U_2512)) = c_Big__Operators_Olinorder__class_OMax(U_2511,U_2512)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2511,tc_HOL_Obool)),U_2513),U_2512))
| U_2513 = c_Orderings_Obot__class_Obot(tc_fun(U_2511,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2511),U_2512))
| ~ class_Orderings_Olinorder(U_2511) ),
inference(definitional_conversion,[status(esa)],[f_540_2]) ).
cnf(f_540_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2511),c_Big__Operators_Olinorder__class_OMax(U_2511,U_2513)),c_Big__Operators_Olinorder__class_OMax(U_2511,U_2512)) = c_Big__Operators_Olinorder__class_OMax(U_2511,U_2512)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2511,tc_HOL_Obool)),U_2513),U_2512))
| U_2513 = c_Orderings_Obot__class_Obot(tc_fun(U_2511,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2511),U_2512))
| ~ class_Orderings_Olinorder(U_2511) ),
inference(clausify,[status(thm)],[f_540_3]) ).
fof(f_541_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem]) ).
fof(f_541_2,plain,
! [U_2516,U_2515,U_2514] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2514),c_Big__Operators_Olinorder__class_OMin(U_2514,U_2516)),c_Big__Operators_Olinorder__class_OMin(U_2514,U_2515)) = c_Big__Operators_Olinorder__class_OMin(U_2514,U_2515)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2514,tc_HOL_Obool)),U_2516),U_2515))
| U_2516 = c_Orderings_Obot__class_Obot(tc_fun(U_2514,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2514),U_2515))
| ~ class_Orderings_Olinorder(U_2514) ),
inference(variable_rename,[status(thm)],[f_541_1]) ).
fof(f_541_3,plain,
! [U_2515,U_2516,U_2514] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2514),c_Big__Operators_Olinorder__class_OMin(U_2514,U_2516)),c_Big__Operators_Olinorder__class_OMin(U_2514,U_2515)) = c_Big__Operators_Olinorder__class_OMin(U_2514,U_2515)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2514,tc_HOL_Obool)),U_2516),U_2515))
| U_2516 = c_Orderings_Obot__class_Obot(tc_fun(U_2514,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2514),U_2515))
| ~ class_Orderings_Olinorder(U_2514) ),
inference(definitional_conversion,[status(esa)],[f_541_2]) ).
cnf(f_541_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2514),c_Big__Operators_Olinorder__class_OMin(U_2514,U_2516)),c_Big__Operators_Olinorder__class_OMin(U_2514,U_2515)) = c_Big__Operators_Olinorder__class_OMin(U_2514,U_2515)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2514,tc_HOL_Obool)),U_2516),U_2515))
| U_2516 = c_Orderings_Obot__class_Obot(tc_fun(U_2514,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2514),U_2515))
| ~ class_Orderings_Olinorder(U_2514) ),
inference(clausify,[status(thm)],[f_541_3]) ).
fof(f_542_1,plain,
! [V_a_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold__idem_H]) ).
fof(f_542_2,plain,
! [U_2519,U_2518,U_2517] :
( c_Big__Operators_Olinorder__class_OMax(U_2517,hAPP(hAPP(c_Set_Oinsert(U_2517),U_2519),U_2518)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2517,U_2517,c_Orderings_Oord__class_Omax(U_2517)),U_2519),U_2518)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2517),U_2518))
| ~ class_Orderings_Olinorder(U_2517) ),
inference(variable_rename,[status(thm)],[f_542_1]) ).
fof(f_542_3,plain,
! [U_2519,U_2517,U_2518] :
( c_Big__Operators_Olinorder__class_OMax(U_2517,hAPP(hAPP(c_Set_Oinsert(U_2517),U_2519),U_2518)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2517,U_2517,c_Orderings_Oord__class_Omax(U_2517)),U_2519),U_2518)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2517),U_2518))
| ~ class_Orderings_Olinorder(U_2517) ),
inference(definitional_conversion,[status(esa)],[f_542_2]) ).
cnf(f_542_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_2517,hAPP(hAPP(c_Set_Oinsert(U_2517),U_2519),U_2518)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2517,U_2517,c_Orderings_Oord__class_Omax(U_2517)),U_2519),U_2518)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2517),U_2518))
| ~ class_Orderings_Olinorder(U_2517) ),
inference(clausify,[status(thm)],[f_542_3]) ).
fof(f_543_1,plain,
! [V_a_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold__idem_H]) ).
fof(f_543_2,plain,
! [U_2522,U_2521,U_2520] :
( c_Big__Operators_Olinorder__class_OMin(U_2520,hAPP(hAPP(c_Set_Oinsert(U_2520),U_2522),U_2521)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2520,U_2520,c_Orderings_Oord__class_Omin(U_2520)),U_2522),U_2521)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2520),U_2521))
| ~ class_Orderings_Olinorder(U_2520) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
fof(f_543_3,plain,
! [U_2520,U_2521,U_2522] :
( c_Big__Operators_Olinorder__class_OMin(U_2520,hAPP(hAPP(c_Set_Oinsert(U_2520),U_2522),U_2521)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2520,U_2520,c_Orderings_Oord__class_Omin(U_2520)),U_2522),U_2521)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2520),U_2521))
| ~ class_Orderings_Olinorder(U_2520) ),
inference(definitional_conversion,[status(esa)],[f_543_2]) ).
cnf(f_543_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_2520,hAPP(hAPP(c_Set_Oinsert(U_2520),U_2522),U_2521)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2520,U_2520,c_Orderings_Oord__class_Omin(U_2520)),U_2522),U_2521)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2520),U_2521))
| ~ class_Orderings_Olinorder(U_2520) ),
inference(clausify,[status(thm)],[f_543_3]) ).
fof(f_544_1,plain,
! [V_x_2,V_g_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove]) ).
fof(f_544_2,plain,
! [U_2527,U_2526,U_2525,U_2524,U_2523] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2524,U_2523),U_2526),hAPP(hAPP(c_Set_Oinsert(U_2524),U_2527),U_2525)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2523),hAPP(U_2526,U_2527)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2524,U_2523),U_2526),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2524,tc_HOL_Obool)),U_2525),hAPP(hAPP(c_Set_Oinsert(U_2524),U_2527),c_Orderings_Obot__class_Obot(tc_fun(U_2524,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2524),U_2525))
| ~ class_Groups_Ocomm__monoid__mult(U_2523) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
fof(f_544_3,plain,
! [U_2523,U_2524,U_2525,U_2526,U_2527] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2524,U_2523),U_2526),hAPP(hAPP(c_Set_Oinsert(U_2524),U_2527),U_2525)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2523),hAPP(U_2526,U_2527)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2524,U_2523),U_2526),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2524,tc_HOL_Obool)),U_2525),hAPP(hAPP(c_Set_Oinsert(U_2524),U_2527),c_Orderings_Obot__class_Obot(tc_fun(U_2524,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2524),U_2525))
| ~ class_Groups_Ocomm__monoid__mult(U_2523) ),
inference(definitional_conversion,[status(esa)],[f_544_2]) ).
cnf(f_544_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2524,U_2523),U_2526),hAPP(hAPP(c_Set_Oinsert(U_2524),U_2527),U_2525)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2523),hAPP(U_2526,U_2527)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_2524,U_2523),U_2526),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2524,tc_HOL_Obool)),U_2525),hAPP(hAPP(c_Set_Oinsert(U_2524),U_2527),c_Orderings_Obot__class_Obot(tc_fun(U_2524,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2524),U_2525))
| ~ class_Groups_Ocomm__monoid__mult(U_2523) ),
inference(clausify,[status(thm)],[f_544_3]) ).
fof(f_545_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem]) ).
fof(f_545_2,plain,
! [U_2530,U_2529,U_2528] :
( hAPP(c_Finite__Set_Ofold1(U_2528,c_Groups_Otimes__class_Otimes(U_2528)),hAPP(hAPP(c_Set_Oinsert(U_2528),U_2530),U_2529)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2528),U_2530),hAPP(c_Finite__Set_Ofold1(U_2528,c_Groups_Otimes__class_Otimes(U_2528)),U_2529))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2528),U_2529))
| U_2529 = c_Orderings_Obot__class_Obot(tc_fun(U_2528,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2528) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
fof(f_545_3,plain,
! [U_2528,U_2529,U_2530] :
( hAPP(c_Finite__Set_Ofold1(U_2528,c_Groups_Otimes__class_Otimes(U_2528)),hAPP(hAPP(c_Set_Oinsert(U_2528),U_2530),U_2529)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2528),U_2530),hAPP(c_Finite__Set_Ofold1(U_2528,c_Groups_Otimes__class_Otimes(U_2528)),U_2529))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2528),U_2529))
| U_2529 = c_Orderings_Obot__class_Obot(tc_fun(U_2528,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2528) ),
inference(definitional_conversion,[status(esa)],[f_545_2]) ).
cnf(f_545_4,plain,
( hAPP(c_Finite__Set_Ofold1(U_2528,c_Groups_Otimes__class_Otimes(U_2528)),hAPP(hAPP(c_Set_Oinsert(U_2528),U_2530),U_2529)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2528),U_2530),hAPP(c_Finite__Set_Ofold1(U_2528,c_Groups_Otimes__class_Otimes(U_2528)),U_2529))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2528),U_2529))
| U_2529 = c_Orderings_Obot__class_Obot(tc_fun(U_2528,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2528) ),
inference(clausify,[status(thm)],[f_545_3]) ).
fof(f_546_1,plain,
! [V_a_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Groups_Otimes__class_Otimes(T_c)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem]) ).
fof(f_546_2,plain,
! [U_2533,U_2532,U_2531] :
( hAPP(c_Finite__Set_Ofold1(U_2531,c_Groups_Otimes__class_Otimes(U_2531)),hAPP(hAPP(c_Set_Oinsert(U_2531),U_2533),U_2532)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2531,U_2531,c_Groups_Otimes__class_Otimes(U_2531)),U_2533),U_2532)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2531),U_2532))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2531) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
fof(f_546_3,plain,
! [U_2531,U_2532,U_2533] :
( hAPP(c_Finite__Set_Ofold1(U_2531,c_Groups_Otimes__class_Otimes(U_2531)),hAPP(hAPP(c_Set_Oinsert(U_2531),U_2533),U_2532)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2531,U_2531,c_Groups_Otimes__class_Otimes(U_2531)),U_2533),U_2532)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2531),U_2532))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2531) ),
inference(definitional_conversion,[status(esa)],[f_546_2]) ).
cnf(f_546_4,plain,
( hAPP(c_Finite__Set_Ofold1(U_2531,c_Groups_Otimes__class_Otimes(U_2531)),hAPP(hAPP(c_Set_Oinsert(U_2531),U_2533),U_2532)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2531,U_2531,c_Groups_Otimes__class_Otimes(U_2531)),U_2533),U_2532)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2531),U_2532))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2531) ),
inference(clausify,[status(thm)],[f_546_3]) ).
fof(f_547_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2))
| V_A_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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oinsert]) ).
fof(f_547_2,plain,
! [U_2536,U_2535,U_2534] :
( c_Big__Operators_Olinorder__class_OMax(U_2534,hAPP(hAPP(c_Set_Oinsert(U_2534),U_2536),U_2535)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2534),U_2536),c_Big__Operators_Olinorder__class_OMax(U_2534,U_2535))
| U_2535 = c_Orderings_Obot__class_Obot(tc_fun(U_2534,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2534),U_2536),U_2535))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2534),U_2535))
| ~ class_Orderings_Olinorder(U_2534) ),
inference(variable_rename,[status(thm)],[f_547_1]) ).
fof(f_547_3,plain,
! [U_2534,U_2535,U_2536] :
( c_Big__Operators_Olinorder__class_OMax(U_2534,hAPP(hAPP(c_Set_Oinsert(U_2534),U_2536),U_2535)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2534),U_2536),c_Big__Operators_Olinorder__class_OMax(U_2534,U_2535))
| U_2535 = c_Orderings_Obot__class_Obot(tc_fun(U_2534,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2534),U_2536),U_2535))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2534),U_2535))
| ~ class_Orderings_Olinorder(U_2534) ),
inference(definitional_conversion,[status(esa)],[f_547_2]) ).
cnf(f_547_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_2534,hAPP(hAPP(c_Set_Oinsert(U_2534),U_2536),U_2535)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2534),U_2536),c_Big__Operators_Olinorder__class_OMax(U_2534,U_2535))
| U_2535 = c_Orderings_Obot__class_Obot(tc_fun(U_2534,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2534),U_2536),U_2535))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2534),U_2535))
| ~ class_Orderings_Olinorder(U_2534) ),
inference(clausify,[status(thm)],[f_547_3]) ).
fof(f_548_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2))
| V_A_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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oinsert]) ).
fof(f_548_2,plain,
! [U_2539,U_2538,U_2537] :
( c_Big__Operators_Olinorder__class_OMin(U_2537,hAPP(hAPP(c_Set_Oinsert(U_2537),U_2539),U_2538)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2537),U_2539),c_Big__Operators_Olinorder__class_OMin(U_2537,U_2538))
| U_2538 = c_Orderings_Obot__class_Obot(tc_fun(U_2537,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2537),U_2539),U_2538))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2537),U_2538))
| ~ class_Orderings_Olinorder(U_2537) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
fof(f_548_3,plain,
! [U_2537,U_2538,U_2539] :
( c_Big__Operators_Olinorder__class_OMin(U_2537,hAPP(hAPP(c_Set_Oinsert(U_2537),U_2539),U_2538)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2537),U_2539),c_Big__Operators_Olinorder__class_OMin(U_2537,U_2538))
| U_2538 = c_Orderings_Obot__class_Obot(tc_fun(U_2537,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2537),U_2539),U_2538))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2537),U_2538))
| ~ class_Orderings_Olinorder(U_2537) ),
inference(definitional_conversion,[status(esa)],[f_548_2]) ).
cnf(f_548_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_2537,hAPP(hAPP(c_Set_Oinsert(U_2537),U_2539),U_2538)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2537),U_2539),c_Big__Operators_Olinorder__class_OMin(U_2537,U_2538))
| U_2538 = c_Orderings_Obot__class_Obot(tc_fun(U_2537,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2537),U_2539),U_2538))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2537),U_2538))
| ~ class_Orderings_Olinorder(U_2537) ),
inference(clausify,[status(thm)],[f_548_3]) ).
fof(f_549_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_c,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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oinsert__remove]) ).
fof(f_549_2,plain,
! [U_2542,U_2541,U_2540] :
( ( ( c_Big__Operators_Olinorder__class_OMax(U_2540,hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),U_2541)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2540),U_2542),c_Big__Operators_Olinorder__class_OMax(U_2540,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2541),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2541),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMax(U_2540,hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),U_2541)) = U_2542
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2541),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2540),U_2541))
| ~ class_Orderings_Olinorder(U_2540) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
fof(f_549_3,plain,
( ! [U_2540,U_2541,U_2542] :
( c_Big__Operators_Olinorder__class_OMax(U_2540,hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),U_2541)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2540),U_2542),c_Big__Operators_Olinorder__class_OMax(U_2540,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2541),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2541),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool))
| ~ sP143(U_2540,U_2541,U_2542) )
& ! [U_2540,U_2541,U_2542] :
( c_Big__Operators_Olinorder__class_OMax(U_2540,hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),U_2541)) = U_2542
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2541),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool))
| ~ sP143(U_2540,U_2541,U_2542) )
& ! [U_2540,U_2541,U_2542] :
( sP143(U_2540,U_2541,U_2542)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2540),U_2541))
| ~ class_Orderings_Olinorder(U_2540) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP143])],[f_549_2]) ).
cnf(f_549_4,plain,
( sP143(U_2540,U_2541,U_2542)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2540),U_2541))
| ~ class_Orderings_Olinorder(U_2540) ),
inference(clausify,[status(thm)],[f_549_3]) ).
cnf(f_549_5,plain,
( c_Big__Operators_Olinorder__class_OMax(U_2540,hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),U_2541)) = U_2542
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2541),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool))
| ~ sP143(U_2540,U_2541,U_2542) ),
inference(clausify,[status(thm)],[f_549_3]) ).
cnf(f_549_6,plain,
( c_Big__Operators_Olinorder__class_OMax(U_2540,hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),U_2541)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2540),U_2542),c_Big__Operators_Olinorder__class_OMax(U_2540,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2541),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2541),hAPP(hAPP(c_Set_Oinsert(U_2540),U_2542),c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2540,tc_HOL_Obool))
| ~ sP143(U_2540,U_2541,U_2542) ),
inference(clausify,[status(thm)],[f_549_3]) ).
fof(f_550_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_c,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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oinsert__remove]) ).
fof(f_550_2,plain,
! [U_2545,U_2544,U_2543] :
( ( ( c_Big__Operators_Olinorder__class_OMin(U_2543,hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),U_2544)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2543),U_2545),c_Big__Operators_Olinorder__class_OMin(U_2543,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2543,tc_HOL_Obool)),U_2544),hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2543,tc_HOL_Obool)),U_2544),hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMin(U_2543,hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),U_2544)) = U_2545
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2543,tc_HOL_Obool)),U_2544),hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2543),U_2544))
| ~ class_Orderings_Olinorder(U_2543) ),
inference(variable_rename,[status(thm)],[f_550_1]) ).
fof(f_550_3,plain,
( ! [U_2544,U_2545,U_2543] :
( c_Big__Operators_Olinorder__class_OMin(U_2543,hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),U_2544)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2543),U_2545),c_Big__Operators_Olinorder__class_OMin(U_2543,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2543,tc_HOL_Obool)),U_2544),hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2543,tc_HOL_Obool)),U_2544),hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool))
| ~ sP144(U_2544,U_2545,U_2543) )
& ! [U_2544,U_2545,U_2543] :
( c_Big__Operators_Olinorder__class_OMin(U_2543,hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),U_2544)) = U_2545
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2543,tc_HOL_Obool)),U_2544),hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool))
| ~ sP144(U_2544,U_2545,U_2543) )
& ! [U_2544,U_2545,U_2543] :
( sP144(U_2544,U_2545,U_2543)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2543),U_2544))
| ~ class_Orderings_Olinorder(U_2543) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP144])],[f_550_2]) ).
cnf(f_550_4,plain,
( sP144(U_2544,U_2545,U_2543)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2543),U_2544))
| ~ class_Orderings_Olinorder(U_2543) ),
inference(clausify,[status(thm)],[f_550_3]) ).
cnf(f_550_5,plain,
( c_Big__Operators_Olinorder__class_OMin(U_2543,hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),U_2544)) = U_2545
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2543,tc_HOL_Obool)),U_2544),hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool))
| ~ sP144(U_2544,U_2545,U_2543) ),
inference(clausify,[status(thm)],[f_550_3]) ).
cnf(f_550_6,plain,
( c_Big__Operators_Olinorder__class_OMin(U_2543,hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),U_2544)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2543),U_2545),c_Big__Operators_Olinorder__class_OMin(U_2543,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2543,tc_HOL_Obool)),U_2544),hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2543,tc_HOL_Obool)),U_2544),hAPP(hAPP(c_Set_Oinsert(U_2543),U_2545),c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2543,tc_HOL_Obool))
| ~ sP144(U_2544,U_2545,U_2543) ),
inference(clausify,[status(thm)],[f_550_3]) ).
fof(f_551_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_x_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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold_H]) ).
fof(f_551_2,plain,
! [U_2548,U_2547,U_2546] :
( c_Big__Operators_Olinorder__class_OMax(U_2546,hAPP(hAPP(c_Set_Oinsert(U_2546),U_2548),U_2547)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2546,U_2546,c_Orderings_Oord__class_Omax(U_2546)),U_2548),U_2547)
| hBOOL(hAPP(hAPP(c_member(U_2546),U_2548),U_2547))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2547))
| ~ class_Orderings_Olinorder(U_2546) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
fof(f_551_3,plain,
! [U_2547,U_2548,U_2546] :
( c_Big__Operators_Olinorder__class_OMax(U_2546,hAPP(hAPP(c_Set_Oinsert(U_2546),U_2548),U_2547)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2546,U_2546,c_Orderings_Oord__class_Omax(U_2546)),U_2548),U_2547)
| hBOOL(hAPP(hAPP(c_member(U_2546),U_2548),U_2547))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2547))
| ~ class_Orderings_Olinorder(U_2546) ),
inference(definitional_conversion,[status(esa)],[f_551_2]) ).
cnf(f_551_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_2546,hAPP(hAPP(c_Set_Oinsert(U_2546),U_2548),U_2547)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2546,U_2546,c_Orderings_Oord__class_Omax(U_2546)),U_2548),U_2547)
| hBOOL(hAPP(hAPP(c_member(U_2546),U_2548),U_2547))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2546),U_2547))
| ~ class_Orderings_Olinorder(U_2546) ),
inference(clausify,[status(thm)],[f_551_3]) ).
fof(f_552_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_x_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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold_H]) ).
fof(f_552_2,plain,
! [U_2551,U_2550,U_2549] :
( c_Big__Operators_Olinorder__class_OMin(U_2549,hAPP(hAPP(c_Set_Oinsert(U_2549),U_2551),U_2550)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2549,U_2549,c_Orderings_Oord__class_Omin(U_2549)),U_2551),U_2550)
| hBOOL(hAPP(hAPP(c_member(U_2549),U_2551),U_2550))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2549),U_2550))
| ~ class_Orderings_Olinorder(U_2549) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
fof(f_552_3,plain,
! [U_2549,U_2550,U_2551] :
( c_Big__Operators_Olinorder__class_OMin(U_2549,hAPP(hAPP(c_Set_Oinsert(U_2549),U_2551),U_2550)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2549,U_2549,c_Orderings_Oord__class_Omin(U_2549)),U_2551),U_2550)
| hBOOL(hAPP(hAPP(c_member(U_2549),U_2551),U_2550))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2549),U_2550))
| ~ class_Orderings_Olinorder(U_2549) ),
inference(definitional_conversion,[status(esa)],[f_552_2]) ).
cnf(f_552_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_2549,hAPP(hAPP(c_Set_Oinsert(U_2549),U_2551),U_2550)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2549,U_2549,c_Orderings_Oord__class_Omin(U_2549)),U_2551),U_2550)
| hBOOL(hAPP(hAPP(c_member(U_2549),U_2551),U_2550))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2549),U_2550))
| ~ class_Orderings_Olinorder(U_2549) ),
inference(clausify,[status(thm)],[f_552_3]) ).
fof(f_553_1,plain,
! [V_A_2,V_F_2,V_f_2,T_c] :
( hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,V_f_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Big__Operators_Osemilattice__big(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_semilattice__big_OF__eq]) ).
fof(f_553_2,plain,
! [U_2555,U_2554,U_2553,U_2552] :
( hAPP(U_2554,U_2555) = hAPP(c_Finite__Set_Ofold1(U_2552,U_2553),U_2555)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2552),U_2555))
| ~ c_Big__Operators_Osemilattice__big(U_2552,U_2553,U_2554) ),
inference(variable_rename,[status(thm)],[f_553_1]) ).
fof(f_553_3,plain,
! [U_2555,U_2552,U_2554,U_2553] :
( hAPP(U_2554,U_2555) = hAPP(c_Finite__Set_Ofold1(U_2552,U_2553),U_2555)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2552),U_2555))
| ~ c_Big__Operators_Osemilattice__big(U_2552,U_2553,U_2554) ),
inference(definitional_conversion,[status(esa)],[f_553_2]) ).
cnf(f_553_4,plain,
( hAPP(U_2554,U_2555) = hAPP(c_Finite__Set_Ofold1(U_2552,U_2553),U_2555)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2552),U_2555))
| ~ c_Big__Operators_Osemilattice__big(U_2552,U_2553,U_2554) ),
inference(clausify,[status(thm)],[f_553_3]) ).
fof(f_554_1,plain,
! [T_c] :
( c_Orderings_Oord_Omin(T_c,hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_c))) = c_Orderings_Oord__class_Omax(T_c)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_dual__min]) ).
fof(f_554_2,plain,
! [U_2556] :
( c_Orderings_Oord_Omin(U_2556,hAPP(c_COMBC(U_2556,U_2556,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_2556))) = c_Orderings_Oord__class_Omax(U_2556)
| ~ class_Orderings_Olinorder(U_2556) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
fof(f_554_3,plain,
! [U_2556] :
( c_Orderings_Oord_Omin(U_2556,hAPP(c_COMBC(U_2556,U_2556,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_2556))) = c_Orderings_Oord__class_Omax(U_2556)
| ~ class_Orderings_Olinorder(U_2556) ),
inference(definitional_conversion,[status(esa)],[f_554_2]) ).
cnf(f_554_4,plain,
( c_Orderings_Oord_Omin(U_2556,hAPP(c_COMBC(U_2556,U_2556,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_2556))) = c_Orderings_Oord__class_Omax(U_2556)
| ~ class_Orderings_Olinorder(U_2556) ),
inference(clausify,[status(thm)],[f_554_3]) ).
fof(f_555_1,plain,
! [T_c] :
( c_Orderings_Oord_Omax(T_c,hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_c))) = c_Orderings_Oord__class_Omin(T_c)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_dual__max]) ).
fof(f_555_2,plain,
! [U_2557] :
( c_Orderings_Oord_Omax(U_2557,hAPP(c_COMBC(U_2557,U_2557,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_2557))) = c_Orderings_Oord__class_Omin(U_2557)
| ~ class_Orderings_Olinorder(U_2557) ),
inference(variable_rename,[status(thm)],[f_555_1]) ).
fof(f_555_3,plain,
! [U_2557] :
( c_Orderings_Oord_Omax(U_2557,hAPP(c_COMBC(U_2557,U_2557,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_2557))) = c_Orderings_Oord__class_Omin(U_2557)
| ~ class_Orderings_Olinorder(U_2557) ),
inference(definitional_conversion,[status(esa)],[f_555_2]) ).
cnf(f_555_4,plain,
( c_Orderings_Oord_Omax(U_2557,hAPP(c_COMBC(U_2557,U_2557,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_2557))) = c_Orderings_Oord__class_Omin(U_2557)
| ~ class_Orderings_Olinorder(U_2557) ),
inference(clausify,[status(thm)],[f_555_3]) ).
fof(f_556_1,plain,
! [T_c] :
( c_Orderings_Oord__class_Omax(T_c) = c_Orderings_Oord_Omax(T_c,c_Orderings_Oord__class_Oless__eq(T_c))
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_max__ord__max]) ).
fof(f_556_2,plain,
! [U_2558] :
( c_Orderings_Oord__class_Omax(U_2558) = c_Orderings_Oord_Omax(U_2558,c_Orderings_Oord__class_Oless__eq(U_2558))
| ~ class_Orderings_Oord(U_2558) ),
inference(variable_rename,[status(thm)],[f_556_1]) ).
fof(f_556_3,plain,
! [U_2558] :
( c_Orderings_Oord__class_Omax(U_2558) = c_Orderings_Oord_Omax(U_2558,c_Orderings_Oord__class_Oless__eq(U_2558))
| ~ class_Orderings_Oord(U_2558) ),
inference(definitional_conversion,[status(esa)],[f_556_2]) ).
cnf(f_556_4,plain,
( c_Orderings_Oord__class_Omax(U_2558) = c_Orderings_Oord_Omax(U_2558,c_Orderings_Oord__class_Oless__eq(U_2558))
| ~ class_Orderings_Oord(U_2558) ),
inference(clausify,[status(thm)],[f_556_3]) ).
fof(f_557_1,plain,
! [T_c] :
( c_Orderings_Oord__class_Omin(T_c) = c_Orderings_Oord_Omin(T_c,c_Orderings_Oord__class_Oless__eq(T_c))
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__ord__min]) ).
fof(f_557_2,plain,
! [U_2559] :
( c_Orderings_Oord__class_Omin(U_2559) = c_Orderings_Oord_Omin(U_2559,c_Orderings_Oord__class_Oless__eq(U_2559))
| ~ class_Orderings_Oord(U_2559) ),
inference(variable_rename,[status(thm)],[f_557_1]) ).
fof(f_557_3,plain,
! [U_2559] :
( c_Orderings_Oord__class_Omin(U_2559) = c_Orderings_Oord_Omin(U_2559,c_Orderings_Oord__class_Oless__eq(U_2559))
| ~ class_Orderings_Oord(U_2559) ),
inference(definitional_conversion,[status(esa)],[f_557_2]) ).
cnf(f_557_4,plain,
( c_Orderings_Oord__class_Omin(U_2559) = c_Orderings_Oord_Omin(U_2559,c_Orderings_Oord__class_Oless__eq(U_2559))
| ~ class_Orderings_Oord(U_2559) ),
inference(clausify,[status(thm)],[f_557_3]) ).
fof(f_558_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oclosed]) ).
fof(f_558_2,plain,
! [U_2563,U_2562] :
( hBOOL(hAPP(hAPP(c_member(U_2562),c_Big__Operators_Olinorder__class_OMax(U_2562,U_2563)),U_2563))
| ? [U_2561,U_2560] : ~ hBOOL(hAPP(hAPP(c_member(U_2562),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2562),U_2561),U_2560)),hAPP(hAPP(c_Set_Oinsert(U_2562),U_2561),hAPP(hAPP(c_Set_Oinsert(U_2562),U_2560),c_Orderings_Obot__class_Obot(tc_fun(U_2562,tc_HOL_Obool))))))
| U_2563 = c_Orderings_Obot__class_Obot(tc_fun(U_2562,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2562),U_2563))
| ~ class_Orderings_Olinorder(U_2562) ),
inference(variable_rename,[status(thm)],[f_558_1]) ).
fof(f_558_3,plain,
! [U_2563,U_2562] :
( hBOOL(hAPP(hAPP(c_member(U_2562),c_Big__Operators_Olinorder__class_OMax(U_2562,U_2563)),U_2563))
| ? [U_2560] : ~ hBOOL(hAPP(hAPP(c_member(U_2562),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2562),sK44(U_2563,U_2562)),U_2560)),hAPP(hAPP(c_Set_Oinsert(U_2562),sK44(U_2563,U_2562)),hAPP(hAPP(c_Set_Oinsert(U_2562),U_2560),c_Orderings_Obot__class_Obot(tc_fun(U_2562,tc_HOL_Obool))))))
| U_2563 = c_Orderings_Obot__class_Obot(tc_fun(U_2562,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2562),U_2563))
| ~ class_Orderings_Olinorder(U_2562) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_2561,sK44(U_2563,U_2562))],[f_558_2]) ).
fof(f_558_4,plain,
! [U_2563,U_2562] :
( hBOOL(hAPP(hAPP(c_member(U_2562),c_Big__Operators_Olinorder__class_OMax(U_2562,U_2563)),U_2563))
| ~ hBOOL(hAPP(hAPP(c_member(U_2562),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2562),sK44(U_2563,U_2562)),sK45(U_2563,U_2562))),hAPP(hAPP(c_Set_Oinsert(U_2562),sK44(U_2563,U_2562)),hAPP(hAPP(c_Set_Oinsert(U_2562),sK45(U_2563,U_2562)),c_Orderings_Obot__class_Obot(tc_fun(U_2562,tc_HOL_Obool))))))
| U_2563 = c_Orderings_Obot__class_Obot(tc_fun(U_2562,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2562),U_2563))
| ~ class_Orderings_Olinorder(U_2562) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_2560,sK45(U_2563,U_2562))],[f_558_3]) ).
fof(f_558_5,plain,
! [U_2562,U_2563] :
( hBOOL(hAPP(hAPP(c_member(U_2562),c_Big__Operators_Olinorder__class_OMax(U_2562,U_2563)),U_2563))
| ~ hBOOL(hAPP(hAPP(c_member(U_2562),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2562),sK44(U_2563,U_2562)),sK45(U_2563,U_2562))),hAPP(hAPP(c_Set_Oinsert(U_2562),sK44(U_2563,U_2562)),hAPP(hAPP(c_Set_Oinsert(U_2562),sK45(U_2563,U_2562)),c_Orderings_Obot__class_Obot(tc_fun(U_2562,tc_HOL_Obool))))))
| U_2563 = c_Orderings_Obot__class_Obot(tc_fun(U_2562,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2562),U_2563))
| ~ class_Orderings_Olinorder(U_2562) ),
inference(definitional_conversion,[status(esa)],[f_558_4]) ).
cnf(f_558_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2562),c_Big__Operators_Olinorder__class_OMax(U_2562,U_2563)),U_2563))
| ~ hBOOL(hAPP(hAPP(c_member(U_2562),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2562),sK44(U_2563,U_2562)),sK45(U_2563,U_2562))),hAPP(hAPP(c_Set_Oinsert(U_2562),sK44(U_2563,U_2562)),hAPP(hAPP(c_Set_Oinsert(U_2562),sK45(U_2563,U_2562)),c_Orderings_Obot__class_Obot(tc_fun(U_2562,tc_HOL_Obool))))))
| U_2563 = c_Orderings_Obot__class_Obot(tc_fun(U_2562,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2562),U_2563))
| ~ class_Orderings_Olinorder(U_2562) ),
inference(clausify,[status(thm)],[f_558_5]) ).
fof(f_559_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oclosed]) ).
fof(f_559_2,plain,
! [U_2567,U_2566] :
( hBOOL(hAPP(hAPP(c_member(U_2566),c_Big__Operators_Olinorder__class_OMin(U_2566,U_2567)),U_2567))
| ? [U_2565,U_2564] : ~ hBOOL(hAPP(hAPP(c_member(U_2566),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2566),U_2565),U_2564)),hAPP(hAPP(c_Set_Oinsert(U_2566),U_2565),hAPP(hAPP(c_Set_Oinsert(U_2566),U_2564),c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))))))
| U_2567 = c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2566),U_2567))
| ~ class_Orderings_Olinorder(U_2566) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
fof(f_559_3,plain,
! [U_2567,U_2566] :
( hBOOL(hAPP(hAPP(c_member(U_2566),c_Big__Operators_Olinorder__class_OMin(U_2566,U_2567)),U_2567))
| ? [U_2564] : ~ hBOOL(hAPP(hAPP(c_member(U_2566),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2566),sK46(U_2567,U_2566)),U_2564)),hAPP(hAPP(c_Set_Oinsert(U_2566),sK46(U_2567,U_2566)),hAPP(hAPP(c_Set_Oinsert(U_2566),U_2564),c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))))))
| U_2567 = c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2566),U_2567))
| ~ class_Orderings_Olinorder(U_2566) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_2565,sK46(U_2567,U_2566))],[f_559_2]) ).
fof(f_559_4,plain,
! [U_2567,U_2566] :
( hBOOL(hAPP(hAPP(c_member(U_2566),c_Big__Operators_Olinorder__class_OMin(U_2566,U_2567)),U_2567))
| ~ hBOOL(hAPP(hAPP(c_member(U_2566),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2566),sK46(U_2567,U_2566)),sK47(U_2567,U_2566))),hAPP(hAPP(c_Set_Oinsert(U_2566),sK46(U_2567,U_2566)),hAPP(hAPP(c_Set_Oinsert(U_2566),sK47(U_2567,U_2566)),c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))))))
| U_2567 = c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2566),U_2567))
| ~ class_Orderings_Olinorder(U_2566) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_2564,sK47(U_2567,U_2566))],[f_559_3]) ).
fof(f_559_5,plain,
! [U_2566,U_2567] :
( hBOOL(hAPP(hAPP(c_member(U_2566),c_Big__Operators_Olinorder__class_OMin(U_2566,U_2567)),U_2567))
| ~ hBOOL(hAPP(hAPP(c_member(U_2566),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2566),sK46(U_2567,U_2566)),sK47(U_2567,U_2566))),hAPP(hAPP(c_Set_Oinsert(U_2566),sK46(U_2567,U_2566)),hAPP(hAPP(c_Set_Oinsert(U_2566),sK47(U_2567,U_2566)),c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))))))
| U_2567 = c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2566),U_2567))
| ~ class_Orderings_Olinorder(U_2566) ),
inference(definitional_conversion,[status(esa)],[f_559_4]) ).
cnf(f_559_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2566),c_Big__Operators_Olinorder__class_OMin(U_2566,U_2567)),U_2567))
| ~ hBOOL(hAPP(hAPP(c_member(U_2566),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2566),sK46(U_2567,U_2566)),sK47(U_2567,U_2566))),hAPP(hAPP(c_Set_Oinsert(U_2566),sK46(U_2567,U_2566)),hAPP(hAPP(c_Set_Oinsert(U_2566),sK47(U_2567,U_2566)),c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))))))
| U_2567 = c_Orderings_Obot__class_Obot(tc_fun(U_2566,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2566),U_2567))
| ~ class_Orderings_Olinorder(U_2566) ),
inference(clausify,[status(thm)],[f_559_5]) ).
fof(f_560_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold1__in]) ).
fof(f_560_2,plain,
! [U_2571,U_2570] :
( hBOOL(hAPP(hAPP(c_member(U_2570),hAPP(c_Finite__Set_Ofold1(U_2570,c_Groups_Otimes__class_Otimes(U_2570)),U_2571)),U_2571))
| ? [U_2569,U_2568] : ~ hBOOL(hAPP(hAPP(c_member(U_2570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2570),U_2569),U_2568)),hAPP(hAPP(c_Set_Oinsert(U_2570),U_2569),hAPP(hAPP(c_Set_Oinsert(U_2570),U_2568),c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool))))))
| U_2571 = c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2570),U_2571))
| ~ class_Groups_Oab__semigroup__mult(U_2570) ),
inference(variable_rename,[status(thm)],[f_560_1]) ).
fof(f_560_3,plain,
! [U_2571,U_2570] :
( hBOOL(hAPP(hAPP(c_member(U_2570),hAPP(c_Finite__Set_Ofold1(U_2570,c_Groups_Otimes__class_Otimes(U_2570)),U_2571)),U_2571))
| ? [U_2568] : ~ hBOOL(hAPP(hAPP(c_member(U_2570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2570),sK48(U_2571,U_2570)),U_2568)),hAPP(hAPP(c_Set_Oinsert(U_2570),sK48(U_2571,U_2570)),hAPP(hAPP(c_Set_Oinsert(U_2570),U_2568),c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool))))))
| U_2571 = c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2570),U_2571))
| ~ class_Groups_Oab__semigroup__mult(U_2570) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_2569,sK48(U_2571,U_2570))],[f_560_2]) ).
fof(f_560_4,plain,
! [U_2571,U_2570] :
( hBOOL(hAPP(hAPP(c_member(U_2570),hAPP(c_Finite__Set_Ofold1(U_2570,c_Groups_Otimes__class_Otimes(U_2570)),U_2571)),U_2571))
| ~ hBOOL(hAPP(hAPP(c_member(U_2570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2570),sK48(U_2571,U_2570)),sK49(U_2571,U_2570))),hAPP(hAPP(c_Set_Oinsert(U_2570),sK48(U_2571,U_2570)),hAPP(hAPP(c_Set_Oinsert(U_2570),sK49(U_2571,U_2570)),c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool))))))
| U_2571 = c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2570),U_2571))
| ~ class_Groups_Oab__semigroup__mult(U_2570) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_2568,sK49(U_2571,U_2570))],[f_560_3]) ).
fof(f_560_5,plain,
! [U_2570,U_2571] :
( hBOOL(hAPP(hAPP(c_member(U_2570),hAPP(c_Finite__Set_Ofold1(U_2570,c_Groups_Otimes__class_Otimes(U_2570)),U_2571)),U_2571))
| ~ hBOOL(hAPP(hAPP(c_member(U_2570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2570),sK48(U_2571,U_2570)),sK49(U_2571,U_2570))),hAPP(hAPP(c_Set_Oinsert(U_2570),sK48(U_2571,U_2570)),hAPP(hAPP(c_Set_Oinsert(U_2570),sK49(U_2571,U_2570)),c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool))))))
| U_2571 = c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2570),U_2571))
| ~ class_Groups_Oab__semigroup__mult(U_2570) ),
inference(definitional_conversion,[status(esa)],[f_560_4]) ).
cnf(f_560_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2570),hAPP(c_Finite__Set_Ofold1(U_2570,c_Groups_Otimes__class_Otimes(U_2570)),U_2571)),U_2571))
| ~ hBOOL(hAPP(hAPP(c_member(U_2570),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2570),sK48(U_2571,U_2570)),sK49(U_2571,U_2570))),hAPP(hAPP(c_Set_Oinsert(U_2570),sK48(U_2571,U_2570)),hAPP(hAPP(c_Set_Oinsert(U_2570),sK49(U_2571,U_2570)),c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool))))))
| U_2571 = c_Orderings_Obot__class_Obot(tc_fun(U_2570,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2570),U_2571))
| ~ class_Groups_Oab__semigroup__mult(U_2570) ),
inference(clausify,[status(thm)],[f_560_5]) ).
fof(f_561_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2) = V_x_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)))) != 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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oremove]) ).
fof(f_561_2,plain,
! [U_2574,U_2573,U_2572] :
( ( ( c_Big__Operators_Olattice_OSup__fin(U_2572,c_Orderings_Oord__class_Omax(U_2572),U_2573) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2572),U_2574),c_Big__Operators_Olattice_OSup__fin(U_2572,c_Orderings_Oord__class_Omax(U_2572),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2572,tc_HOL_Obool)),U_2573),hAPP(hAPP(c_Set_Oinsert(U_2572),U_2574),c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2572,tc_HOL_Obool)),U_2573),hAPP(hAPP(c_Set_Oinsert(U_2572),U_2574),c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OSup__fin(U_2572,c_Orderings_Oord__class_Omax(U_2572),U_2573) = U_2574
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2572,tc_HOL_Obool)),U_2573),hAPP(hAPP(c_Set_Oinsert(U_2572),U_2574),c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2572),U_2574),U_2573))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2572),U_2573))
| ~ class_Orderings_Olinorder(U_2572) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
fof(f_561_3,plain,
( ! [U_2573,U_2572,U_2574] :
( c_Big__Operators_Olattice_OSup__fin(U_2572,c_Orderings_Oord__class_Omax(U_2572),U_2573) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2572),U_2574),c_Big__Operators_Olattice_OSup__fin(U_2572,c_Orderings_Oord__class_Omax(U_2572),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2572,tc_HOL_Obool)),U_2573),hAPP(hAPP(c_Set_Oinsert(U_2572),U_2574),c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2572,tc_HOL_Obool)),U_2573),hAPP(hAPP(c_Set_Oinsert(U_2572),U_2574),c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool))
| ~ sP145(U_2573,U_2572,U_2574) )
& ! [U_2573,U_2572,U_2574] :
( c_Big__Operators_Olattice_OSup__fin(U_2572,c_Orderings_Oord__class_Omax(U_2572),U_2573) = U_2574
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2572,tc_HOL_Obool)),U_2573),hAPP(hAPP(c_Set_Oinsert(U_2572),U_2574),c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool))
| ~ sP145(U_2573,U_2572,U_2574) )
& ! [U_2573,U_2572,U_2574] :
( sP145(U_2573,U_2572,U_2574)
| ~ hBOOL(hAPP(hAPP(c_member(U_2572),U_2574),U_2573))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2572),U_2573))
| ~ class_Orderings_Olinorder(U_2572) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145])],[f_561_2]) ).
cnf(f_561_4,plain,
( sP145(U_2573,U_2572,U_2574)
| ~ hBOOL(hAPP(hAPP(c_member(U_2572),U_2574),U_2573))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2572),U_2573))
| ~ class_Orderings_Olinorder(U_2572) ),
inference(clausify,[status(thm)],[f_561_3]) ).
cnf(f_561_5,plain,
( c_Big__Operators_Olattice_OSup__fin(U_2572,c_Orderings_Oord__class_Omax(U_2572),U_2573) = U_2574
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2572,tc_HOL_Obool)),U_2573),hAPP(hAPP(c_Set_Oinsert(U_2572),U_2574),c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool))
| ~ sP145(U_2573,U_2572,U_2574) ),
inference(clausify,[status(thm)],[f_561_3]) ).
cnf(f_561_6,plain,
( c_Big__Operators_Olattice_OSup__fin(U_2572,c_Orderings_Oord__class_Omax(U_2572),U_2573) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2572),U_2574),c_Big__Operators_Olattice_OSup__fin(U_2572,c_Orderings_Oord__class_Omax(U_2572),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2572,tc_HOL_Obool)),U_2573),hAPP(hAPP(c_Set_Oinsert(U_2572),U_2574),c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2572,tc_HOL_Obool)),U_2573),hAPP(hAPP(c_Set_Oinsert(U_2572),U_2574),c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2572,tc_HOL_Obool))
| ~ sP145(U_2573,U_2572,U_2574) ),
inference(clausify,[status(thm)],[f_561_3]) ).
fof(f_562_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) = V_x_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)))) != 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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oremove]) ).
fof(f_562_2,plain,
! [U_2577,U_2576,U_2575] :
( ( ( c_Big__Operators_Olattice_OInf__fin(U_2575,c_Orderings_Oord__class_Omin(U_2575),U_2576) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2575),U_2577),c_Big__Operators_Olattice_OInf__fin(U_2575,c_Orderings_Oord__class_Omin(U_2575),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2575,tc_HOL_Obool)),U_2576),hAPP(hAPP(c_Set_Oinsert(U_2575),U_2577),c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2575,tc_HOL_Obool)),U_2576),hAPP(hAPP(c_Set_Oinsert(U_2575),U_2577),c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OInf__fin(U_2575,c_Orderings_Oord__class_Omin(U_2575),U_2576) = U_2577
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2575,tc_HOL_Obool)),U_2576),hAPP(hAPP(c_Set_Oinsert(U_2575),U_2577),c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_2575),U_2577),U_2576))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2575),U_2576))
| ~ class_Orderings_Olinorder(U_2575) ),
inference(variable_rename,[status(thm)],[f_562_1]) ).
fof(f_562_3,plain,
( ! [U_2577,U_2576,U_2575] :
( c_Big__Operators_Olattice_OInf__fin(U_2575,c_Orderings_Oord__class_Omin(U_2575),U_2576) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2575),U_2577),c_Big__Operators_Olattice_OInf__fin(U_2575,c_Orderings_Oord__class_Omin(U_2575),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2575,tc_HOL_Obool)),U_2576),hAPP(hAPP(c_Set_Oinsert(U_2575),U_2577),c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2575,tc_HOL_Obool)),U_2576),hAPP(hAPP(c_Set_Oinsert(U_2575),U_2577),c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool))
| ~ sP146(U_2577,U_2576,U_2575) )
& ! [U_2577,U_2576,U_2575] :
( c_Big__Operators_Olattice_OInf__fin(U_2575,c_Orderings_Oord__class_Omin(U_2575),U_2576) = U_2577
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2575,tc_HOL_Obool)),U_2576),hAPP(hAPP(c_Set_Oinsert(U_2575),U_2577),c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool))
| ~ sP146(U_2577,U_2576,U_2575) )
& ! [U_2577,U_2576,U_2575] :
( sP146(U_2577,U_2576,U_2575)
| ~ hBOOL(hAPP(hAPP(c_member(U_2575),U_2577),U_2576))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2575),U_2576))
| ~ class_Orderings_Olinorder(U_2575) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP146])],[f_562_2]) ).
cnf(f_562_4,plain,
( sP146(U_2577,U_2576,U_2575)
| ~ hBOOL(hAPP(hAPP(c_member(U_2575),U_2577),U_2576))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2575),U_2576))
| ~ class_Orderings_Olinorder(U_2575) ),
inference(clausify,[status(thm)],[f_562_3]) ).
cnf(f_562_5,plain,
( c_Big__Operators_Olattice_OInf__fin(U_2575,c_Orderings_Oord__class_Omin(U_2575),U_2576) = U_2577
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2575,tc_HOL_Obool)),U_2576),hAPP(hAPP(c_Set_Oinsert(U_2575),U_2577),c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool))
| ~ sP146(U_2577,U_2576,U_2575) ),
inference(clausify,[status(thm)],[f_562_3]) ).
cnf(f_562_6,plain,
( c_Big__Operators_Olattice_OInf__fin(U_2575,c_Orderings_Oord__class_Omin(U_2575),U_2576) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2575),U_2577),c_Big__Operators_Olattice_OInf__fin(U_2575,c_Orderings_Oord__class_Omin(U_2575),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2575,tc_HOL_Obool)),U_2576),hAPP(hAPP(c_Set_Oinsert(U_2575),U_2577),c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2575,tc_HOL_Obool)),U_2576),hAPP(hAPP(c_Set_Oinsert(U_2575),U_2577),c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2575,tc_HOL_Obool))
| ~ sP146(U_2577,U_2576,U_2575) ),
inference(clausify,[status(thm)],[f_562_3]) ).
fof(f_563_1,plain,
! [V_B_2,V_A_2,T_c] :
( ( 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_c,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_c,tc_HOL_Obool)),V_A_2) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff]) ).
fof(f_563_2,plain,
! [U_2580,U_2579,U_2578] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2578,tc_HOL_Obool)),U_2579) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2578,tc_HOL_Obool)),U_2580)
| U_2579 != U_2580 )
& ( U_2579 = U_2580
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2578,tc_HOL_Obool)),U_2579) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2578,tc_HOL_Obool)),U_2580) ) ),
inference(variable_rename,[status(thm)],[f_563_1]) ).
fof(f_563_3,plain,
( ! [U_2586,U_2584] :
( ! [U_2582] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2582,tc_HOL_Obool)),U_2584) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2582,tc_HOL_Obool)),U_2586)
| U_2584 != U_2586 )
& ! [U_2585,U_2583] :
( ! [U_2581] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2581,tc_HOL_Obool)),U_2583) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2581,tc_HOL_Obool)),U_2585)
| U_2583 = U_2585 ) ),
inference(miniscope,[status(thm)],[f_563_2]) ).
fof(f_563_4,plain,
( ! [U_2584,U_2586,U_2582] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2582,tc_HOL_Obool)),U_2584) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2582,tc_HOL_Obool)),U_2586)
| U_2584 != U_2586 )
& ! [U_2581,U_2585,U_2583] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2581,tc_HOL_Obool)),U_2583) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2581,tc_HOL_Obool)),U_2585)
| U_2583 = U_2585 ) ),
inference(definitional_conversion,[status(esa)],[f_563_3]) ).
cnf(f_563_5,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2581,tc_HOL_Obool)),U_2583) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2581,tc_HOL_Obool)),U_2585)
| U_2583 = U_2585 ),
inference(clausify,[status(thm)],[f_563_4]) ).
cnf(f_563_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2582,tc_HOL_Obool)),U_2584) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2582,tc_HOL_Obool)),U_2586)
| U_2584 != U_2586 ),
inference(clausify,[status(thm)],[f_563_4]) ).
fof(f_564_1,plain,
! [V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_double__complement]) ).
fof(f_564_2,plain,
! [U_2588,U_2587] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2587,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2587,tc_HOL_Obool)),U_2588)) = U_2588,
inference(variable_rename,[status(thm)],[f_564_1]) ).
fof(f_564_3,plain,
! [U_2587,U_2588] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2587,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2587,tc_HOL_Obool)),U_2588)) = U_2588,
inference(definitional_conversion,[status(esa)],[f_564_2]) ).
cnf(f_564_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2587,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2587,tc_HOL_Obool)),U_2588)) = U_2588,
inference(clausify,[status(thm)],[f_564_3]) ).
fof(f_565_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup]) ).
fof(f_565_2,plain,
! [U_2590,U_2589] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2589),c_Big__Operators_Olattice_OInf__fin(U_2589,c_Orderings_Oord__class_Omin(U_2589),U_2590)),c_Big__Operators_Olattice_OSup__fin(U_2589,c_Orderings_Oord__class_Omax(U_2589),U_2590)))
| U_2590 = c_Orderings_Obot__class_Obot(tc_fun(U_2589,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2589),U_2590))
| ~ class_Orderings_Olinorder(U_2589) ),
inference(variable_rename,[status(thm)],[f_565_1]) ).
fof(f_565_3,plain,
! [U_2589,U_2590] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2589),c_Big__Operators_Olattice_OInf__fin(U_2589,c_Orderings_Oord__class_Omin(U_2589),U_2590)),c_Big__Operators_Olattice_OSup__fin(U_2589,c_Orderings_Oord__class_Omax(U_2589),U_2590)))
| U_2590 = c_Orderings_Obot__class_Obot(tc_fun(U_2589,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2589),U_2590))
| ~ class_Orderings_Olinorder(U_2589) ),
inference(definitional_conversion,[status(esa)],[f_565_2]) ).
cnf(f_565_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2589),c_Big__Operators_Olattice_OInf__fin(U_2589,c_Orderings_Oord__class_Omin(U_2589),U_2590)),c_Big__Operators_Olattice_OSup__fin(U_2589,c_Orderings_Oord__class_Omax(U_2589),U_2590)))
| U_2590 = c_Orderings_Obot__class_Obot(tc_fun(U_2589,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2589),U_2590))
| ~ class_Orderings_Olinorder(U_2589) ),
inference(clausify,[status(thm)],[f_565_3]) ).
fof(f_566_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oin__idem]) ).
fof(f_566_2,plain,
! [U_2593,U_2592,U_2591] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2591),U_2593),c_Big__Operators_Olattice_OInf__fin(U_2591,c_Orderings_Oord__class_Omin(U_2591),U_2592)) = c_Big__Operators_Olattice_OInf__fin(U_2591,c_Orderings_Oord__class_Omin(U_2591),U_2592)
| ~ hBOOL(hAPP(hAPP(c_member(U_2591),U_2593),U_2592))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),U_2592))
| ~ class_Orderings_Olinorder(U_2591) ),
inference(variable_rename,[status(thm)],[f_566_1]) ).
fof(f_566_3,plain,
! [U_2592,U_2591,U_2593] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2591),U_2593),c_Big__Operators_Olattice_OInf__fin(U_2591,c_Orderings_Oord__class_Omin(U_2591),U_2592)) = c_Big__Operators_Olattice_OInf__fin(U_2591,c_Orderings_Oord__class_Omin(U_2591),U_2592)
| ~ hBOOL(hAPP(hAPP(c_member(U_2591),U_2593),U_2592))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),U_2592))
| ~ class_Orderings_Olinorder(U_2591) ),
inference(definitional_conversion,[status(esa)],[f_566_2]) ).
cnf(f_566_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2591),U_2593),c_Big__Operators_Olattice_OInf__fin(U_2591,c_Orderings_Oord__class_Omin(U_2591),U_2592)) = c_Big__Operators_Olattice_OInf__fin(U_2591,c_Orderings_Oord__class_Omin(U_2591),U_2592)
| ~ hBOOL(hAPP(hAPP(c_member(U_2591),U_2593),U_2592))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2591),U_2592))
| ~ class_Orderings_Olinorder(U_2591) ),
inference(clausify,[status(thm)],[f_566_3]) ).
fof(f_567_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem]) ).
fof(f_567_2,plain,
! [U_2596,U_2595,U_2594] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2594),U_2596),c_Big__Operators_Olattice_OSup__fin(U_2594,c_Orderings_Oord__class_Omax(U_2594),U_2595)) = c_Big__Operators_Olattice_OSup__fin(U_2594,c_Orderings_Oord__class_Omax(U_2594),U_2595)
| ~ hBOOL(hAPP(hAPP(c_member(U_2594),U_2596),U_2595))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2594),U_2595))
| ~ class_Orderings_Olinorder(U_2594) ),
inference(variable_rename,[status(thm)],[f_567_1]) ).
fof(f_567_3,plain,
! [U_2594,U_2595,U_2596] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2594),U_2596),c_Big__Operators_Olattice_OSup__fin(U_2594,c_Orderings_Oord__class_Omax(U_2594),U_2595)) = c_Big__Operators_Olattice_OSup__fin(U_2594,c_Orderings_Oord__class_Omax(U_2594),U_2595)
| ~ hBOOL(hAPP(hAPP(c_member(U_2594),U_2596),U_2595))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2594),U_2595))
| ~ class_Orderings_Olinorder(U_2594) ),
inference(definitional_conversion,[status(esa)],[f_567_2]) ).
cnf(f_567_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2594),U_2596),c_Big__Operators_Olattice_OSup__fin(U_2594,c_Orderings_Oord__class_Omax(U_2594),U_2595)) = c_Big__Operators_Olattice_OSup__fin(U_2594,c_Orderings_Oord__class_Omax(U_2594),U_2595)
| ~ hBOOL(hAPP(hAPP(c_member(U_2594),U_2596),U_2595))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2594),U_2595))
| ~ class_Orderings_Olinorder(U_2594) ),
inference(clausify,[status(thm)],[f_567_3]) ).
fof(f_568_1,plain,
! [V_x_2,T_c] :
( c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osingleton]) ).
fof(f_568_2,plain,
! [U_2598,U_2597] :
( c_Big__Operators_Olattice_OInf__fin(U_2597,c_Orderings_Oord__class_Omin(U_2597),hAPP(hAPP(c_Set_Oinsert(U_2597),U_2598),c_Orderings_Obot__class_Obot(tc_fun(U_2597,tc_HOL_Obool)))) = U_2598
| ~ class_Orderings_Olinorder(U_2597) ),
inference(variable_rename,[status(thm)],[f_568_1]) ).
fof(f_568_3,plain,
! [U_2598,U_2597] :
( c_Big__Operators_Olattice_OInf__fin(U_2597,c_Orderings_Oord__class_Omin(U_2597),hAPP(hAPP(c_Set_Oinsert(U_2597),U_2598),c_Orderings_Obot__class_Obot(tc_fun(U_2597,tc_HOL_Obool)))) = U_2598
| ~ class_Orderings_Olinorder(U_2597) ),
inference(definitional_conversion,[status(esa)],[f_568_2]) ).
cnf(f_568_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_2597,c_Orderings_Oord__class_Omin(U_2597),hAPP(hAPP(c_Set_Oinsert(U_2597),U_2598),c_Orderings_Obot__class_Obot(tc_fun(U_2597,tc_HOL_Obool)))) = U_2598
| ~ class_Orderings_Olinorder(U_2597) ),
inference(clausify,[status(thm)],[f_568_3]) ).
fof(f_569_1,plain,
! [V_x_2,T_c] :
( c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton]) ).
fof(f_569_2,plain,
! [U_2600,U_2599] :
( c_Big__Operators_Olattice_OSup__fin(U_2599,c_Orderings_Oord__class_Omax(U_2599),hAPP(hAPP(c_Set_Oinsert(U_2599),U_2600),c_Orderings_Obot__class_Obot(tc_fun(U_2599,tc_HOL_Obool)))) = U_2600
| ~ class_Orderings_Olinorder(U_2599) ),
inference(variable_rename,[status(thm)],[f_569_1]) ).
fof(f_569_3,plain,
! [U_2599,U_2600] :
( c_Big__Operators_Olattice_OSup__fin(U_2599,c_Orderings_Oord__class_Omax(U_2599),hAPP(hAPP(c_Set_Oinsert(U_2599),U_2600),c_Orderings_Obot__class_Obot(tc_fun(U_2599,tc_HOL_Obool)))) = U_2600
| ~ class_Orderings_Olinorder(U_2599) ),
inference(definitional_conversion,[status(esa)],[f_569_2]) ).
cnf(f_569_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_2599,c_Orderings_Oord__class_Omax(U_2599),hAPP(hAPP(c_Set_Oinsert(U_2599),U_2600),c_Orderings_Obot__class_Obot(tc_fun(U_2599,tc_HOL_Obool)))) = U_2600
| ~ class_Orderings_Olinorder(U_2599) ),
inference(clausify,[status(thm)],[f_569_3]) ).
fof(f_570_1,plain,
! [V_A_2,T_c] :
( c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omin(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq]) ).
fof(f_570_2,plain,
! [U_2602,U_2601] :
( c_Big__Operators_Olattice_OInf__fin(U_2601,c_Orderings_Oord__class_Omin(U_2601),U_2602) = hAPP(c_Finite__Set_Ofold1(U_2601,c_Orderings_Oord__class_Omin(U_2601)),U_2602)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2601),U_2602))
| ~ class_Orderings_Olinorder(U_2601) ),
inference(variable_rename,[status(thm)],[f_570_1]) ).
fof(f_570_3,plain,
! [U_2601,U_2602] :
( c_Big__Operators_Olattice_OInf__fin(U_2601,c_Orderings_Oord__class_Omin(U_2601),U_2602) = hAPP(c_Finite__Set_Ofold1(U_2601,c_Orderings_Oord__class_Omin(U_2601)),U_2602)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2601),U_2602))
| ~ class_Orderings_Olinorder(U_2601) ),
inference(definitional_conversion,[status(esa)],[f_570_2]) ).
cnf(f_570_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_2601,c_Orderings_Oord__class_Omin(U_2601),U_2602) = hAPP(c_Finite__Set_Ofold1(U_2601,c_Orderings_Oord__class_Omin(U_2601)),U_2602)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2601),U_2602))
| ~ class_Orderings_Olinorder(U_2601) ),
inference(clausify,[status(thm)],[f_570_3]) ).
fof(f_571_1,plain,
! [V_A_2,T_c] :
( c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Orderings_Oord__class_Omax(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_OF__eq]) ).
fof(f_571_2,plain,
! [U_2604,U_2603] :
( c_Big__Operators_Olattice_OSup__fin(U_2603,c_Orderings_Oord__class_Omax(U_2603),U_2604) = hAPP(c_Finite__Set_Ofold1(U_2603,c_Orderings_Oord__class_Omax(U_2603)),U_2604)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2603),U_2604))
| ~ class_Orderings_Olinorder(U_2603) ),
inference(variable_rename,[status(thm)],[f_571_1]) ).
fof(f_571_3,plain,
! [U_2603,U_2604] :
( c_Big__Operators_Olattice_OSup__fin(U_2603,c_Orderings_Oord__class_Omax(U_2603),U_2604) = hAPP(c_Finite__Set_Ofold1(U_2603,c_Orderings_Oord__class_Omax(U_2603)),U_2604)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2603),U_2604))
| ~ class_Orderings_Olinorder(U_2603) ),
inference(definitional_conversion,[status(esa)],[f_571_2]) ).
cnf(f_571_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_2603,c_Orderings_Oord__class_Omax(U_2603),U_2604) = hAPP(c_Finite__Set_Ofold1(U_2603,c_Orderings_Oord__class_Omax(U_2603)),U_2604)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2603),U_2604))
| ~ class_Orderings_Olinorder(U_2603) ),
inference(clausify,[status(thm)],[f_571_3]) ).
fof(f_572_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem]) ).
fof(f_572_2,plain,
! [U_2607,U_2606,U_2605] :
( c_Big__Operators_Olattice_OInf__fin(U_2605,c_Orderings_Oord__class_Omin(U_2605),hAPP(hAPP(c_Set_Oinsert(U_2605),U_2607),U_2606)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2605),U_2607),c_Big__Operators_Olattice_OInf__fin(U_2605,c_Orderings_Oord__class_Omin(U_2605),U_2606))
| U_2606 = c_Orderings_Obot__class_Obot(tc_fun(U_2605,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2605),U_2606))
| ~ class_Orderings_Olinorder(U_2605) ),
inference(variable_rename,[status(thm)],[f_572_1]) ).
fof(f_572_3,plain,
! [U_2605,U_2606,U_2607] :
( c_Big__Operators_Olattice_OInf__fin(U_2605,c_Orderings_Oord__class_Omin(U_2605),hAPP(hAPP(c_Set_Oinsert(U_2605),U_2607),U_2606)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2605),U_2607),c_Big__Operators_Olattice_OInf__fin(U_2605,c_Orderings_Oord__class_Omin(U_2605),U_2606))
| U_2606 = c_Orderings_Obot__class_Obot(tc_fun(U_2605,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2605),U_2606))
| ~ class_Orderings_Olinorder(U_2605) ),
inference(definitional_conversion,[status(esa)],[f_572_2]) ).
cnf(f_572_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_2605,c_Orderings_Oord__class_Omin(U_2605),hAPP(hAPP(c_Set_Oinsert(U_2605),U_2607),U_2606)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2605),U_2607),c_Big__Operators_Olattice_OInf__fin(U_2605,c_Orderings_Oord__class_Omin(U_2605),U_2606))
| U_2606 = c_Orderings_Obot__class_Obot(tc_fun(U_2605,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2605),U_2606))
| ~ class_Orderings_Olinorder(U_2605) ),
inference(clausify,[status(thm)],[f_572_3]) ).
fof(f_573_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem]) ).
fof(f_573_2,plain,
! [U_2610,U_2609,U_2608] :
( c_Big__Operators_Olattice_OSup__fin(U_2608,c_Orderings_Oord__class_Omax(U_2608),hAPP(hAPP(c_Set_Oinsert(U_2608),U_2610),U_2609)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2608),U_2610),c_Big__Operators_Olattice_OSup__fin(U_2608,c_Orderings_Oord__class_Omax(U_2608),U_2609))
| U_2609 = c_Orderings_Obot__class_Obot(tc_fun(U_2608,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2608),U_2609))
| ~ class_Orderings_Olinorder(U_2608) ),
inference(variable_rename,[status(thm)],[f_573_1]) ).
fof(f_573_3,plain,
! [U_2608,U_2609,U_2610] :
( c_Big__Operators_Olattice_OSup__fin(U_2608,c_Orderings_Oord__class_Omax(U_2608),hAPP(hAPP(c_Set_Oinsert(U_2608),U_2610),U_2609)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2608),U_2610),c_Big__Operators_Olattice_OSup__fin(U_2608,c_Orderings_Oord__class_Omax(U_2608),U_2609))
| U_2609 = c_Orderings_Obot__class_Obot(tc_fun(U_2608,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2608),U_2609))
| ~ class_Orderings_Olinorder(U_2608) ),
inference(definitional_conversion,[status(esa)],[f_573_2]) ).
cnf(f_573_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_2608,c_Orderings_Oord__class_Omax(U_2608),hAPP(hAPP(c_Set_Oinsert(U_2608),U_2610),U_2609)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2608),U_2610),c_Big__Operators_Olattice_OSup__fin(U_2608,c_Orderings_Oord__class_Omax(U_2608),U_2609))
| U_2609 = c_Orderings_Obot__class_Obot(tc_fun(U_2608,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2608),U_2609))
| ~ class_Orderings_Olinorder(U_2608) ),
inference(clausify,[status(thm)],[f_573_3]) ).
fof(f_574_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem]) ).
fof(f_574_2,plain,
! [U_2613,U_2612,U_2611] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2611),c_Big__Operators_Olattice_OInf__fin(U_2611,c_Orderings_Oord__class_Omin(U_2611),U_2613)),c_Big__Operators_Olattice_OInf__fin(U_2611,c_Orderings_Oord__class_Omin(U_2611),U_2612)) = c_Big__Operators_Olattice_OInf__fin(U_2611,c_Orderings_Oord__class_Omin(U_2611),U_2612)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2611,tc_HOL_Obool)),U_2613),U_2612))
| U_2613 = c_Orderings_Obot__class_Obot(tc_fun(U_2611,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2611),U_2612))
| ~ class_Orderings_Olinorder(U_2611) ),
inference(variable_rename,[status(thm)],[f_574_1]) ).
fof(f_574_3,plain,
! [U_2612,U_2611,U_2613] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2611),c_Big__Operators_Olattice_OInf__fin(U_2611,c_Orderings_Oord__class_Omin(U_2611),U_2613)),c_Big__Operators_Olattice_OInf__fin(U_2611,c_Orderings_Oord__class_Omin(U_2611),U_2612)) = c_Big__Operators_Olattice_OInf__fin(U_2611,c_Orderings_Oord__class_Omin(U_2611),U_2612)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2611,tc_HOL_Obool)),U_2613),U_2612))
| U_2613 = c_Orderings_Obot__class_Obot(tc_fun(U_2611,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2611),U_2612))
| ~ class_Orderings_Olinorder(U_2611) ),
inference(definitional_conversion,[status(esa)],[f_574_2]) ).
cnf(f_574_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2611),c_Big__Operators_Olattice_OInf__fin(U_2611,c_Orderings_Oord__class_Omin(U_2611),U_2613)),c_Big__Operators_Olattice_OInf__fin(U_2611,c_Orderings_Oord__class_Omin(U_2611),U_2612)) = c_Big__Operators_Olattice_OInf__fin(U_2611,c_Orderings_Oord__class_Omin(U_2611),U_2612)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2611,tc_HOL_Obool)),U_2613),U_2612))
| U_2613 = c_Orderings_Obot__class_Obot(tc_fun(U_2611,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2611),U_2612))
| ~ class_Orderings_Olinorder(U_2611) ),
inference(clausify,[status(thm)],[f_574_3]) ).
fof(f_575_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem]) ).
fof(f_575_2,plain,
! [U_2616,U_2615,U_2614] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2614),c_Big__Operators_Olattice_OSup__fin(U_2614,c_Orderings_Oord__class_Omax(U_2614),U_2616)),c_Big__Operators_Olattice_OSup__fin(U_2614,c_Orderings_Oord__class_Omax(U_2614),U_2615)) = c_Big__Operators_Olattice_OSup__fin(U_2614,c_Orderings_Oord__class_Omax(U_2614),U_2615)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2614,tc_HOL_Obool)),U_2616),U_2615))
| U_2616 = c_Orderings_Obot__class_Obot(tc_fun(U_2614,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2614),U_2615))
| ~ class_Orderings_Olinorder(U_2614) ),
inference(variable_rename,[status(thm)],[f_575_1]) ).
fof(f_575_3,plain,
! [U_2616,U_2614,U_2615] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2614),c_Big__Operators_Olattice_OSup__fin(U_2614,c_Orderings_Oord__class_Omax(U_2614),U_2616)),c_Big__Operators_Olattice_OSup__fin(U_2614,c_Orderings_Oord__class_Omax(U_2614),U_2615)) = c_Big__Operators_Olattice_OSup__fin(U_2614,c_Orderings_Oord__class_Omax(U_2614),U_2615)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2614,tc_HOL_Obool)),U_2616),U_2615))
| U_2616 = c_Orderings_Obot__class_Obot(tc_fun(U_2614,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2614),U_2615))
| ~ class_Orderings_Olinorder(U_2614) ),
inference(definitional_conversion,[status(esa)],[f_575_2]) ).
cnf(f_575_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2614),c_Big__Operators_Olattice_OSup__fin(U_2614,c_Orderings_Oord__class_Omax(U_2614),U_2616)),c_Big__Operators_Olattice_OSup__fin(U_2614,c_Orderings_Oord__class_Omax(U_2614),U_2615)) = c_Big__Operators_Olattice_OSup__fin(U_2614,c_Orderings_Oord__class_Omax(U_2614),U_2615)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2614,tc_HOL_Obool)),U_2616),U_2615))
| U_2616 = c_Orderings_Obot__class_Obot(tc_fun(U_2614,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2614),U_2615))
| ~ class_Orderings_Olinorder(U_2614) ),
inference(clausify,[status(thm)],[f_575_3]) ).
fof(f_576_1,plain,
! [V_a_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) = V_a_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup__absorb]) ).
fof(f_576_2,plain,
! [U_2619,U_2618,U_2617] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2617),U_2619),c_Big__Operators_Olattice_OSup__fin(U_2617,c_Orderings_Oord__class_Omax(U_2617),U_2618)) = U_2619
| ~ hBOOL(hAPP(hAPP(c_member(U_2617),U_2619),U_2618))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2617),U_2618))
| ~ class_Orderings_Olinorder(U_2617) ),
inference(variable_rename,[status(thm)],[f_576_1]) ).
fof(f_576_3,plain,
! [U_2618,U_2617,U_2619] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2617),U_2619),c_Big__Operators_Olattice_OSup__fin(U_2617,c_Orderings_Oord__class_Omax(U_2617),U_2618)) = U_2619
| ~ hBOOL(hAPP(hAPP(c_member(U_2617),U_2619),U_2618))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2617),U_2618))
| ~ class_Orderings_Olinorder(U_2617) ),
inference(definitional_conversion,[status(esa)],[f_576_2]) ).
cnf(f_576_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2617),U_2619),c_Big__Operators_Olattice_OSup__fin(U_2617,c_Orderings_Oord__class_Omax(U_2617),U_2618)) = U_2619
| ~ hBOOL(hAPP(hAPP(c_member(U_2617),U_2619),U_2618))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2617),U_2618))
| ~ class_Orderings_Olinorder(U_2617) ),
inference(clausify,[status(thm)],[f_576_3]) ).
fof(f_577_1,plain,
! [V_a_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) = V_a_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf__absorb]) ).
fof(f_577_2,plain,
! [U_2622,U_2621,U_2620] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2620),U_2622),c_Big__Operators_Olattice_OInf__fin(U_2620,c_Orderings_Oord__class_Omin(U_2620),U_2621)) = U_2622
| ~ hBOOL(hAPP(hAPP(c_member(U_2620),U_2622),U_2621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2620),U_2621))
| ~ class_Orderings_Olinorder(U_2620) ),
inference(variable_rename,[status(thm)],[f_577_1]) ).
fof(f_577_3,plain,
! [U_2620,U_2621,U_2622] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2620),U_2622),c_Big__Operators_Olattice_OInf__fin(U_2620,c_Orderings_Oord__class_Omin(U_2620),U_2621)) = U_2622
| ~ hBOOL(hAPP(hAPP(c_member(U_2620),U_2622),U_2621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2620),U_2621))
| ~ class_Orderings_Olinorder(U_2620) ),
inference(definitional_conversion,[status(esa)],[f_577_2]) ).
cnf(f_577_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2620),U_2622),c_Big__Operators_Olattice_OInf__fin(U_2620,c_Orderings_Oord__class_Omin(U_2620),U_2621)) = U_2622
| ~ hBOOL(hAPP(hAPP(c_member(U_2620),U_2622),U_2621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2620),U_2621))
| ~ class_Orderings_Olinorder(U_2620) ),
inference(clausify,[status(thm)],[f_577_3]) ).
fof(f_578_1,plain,
! [V_a_2,V_A_2,T_c] :
( c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H]) ).
fof(f_578_2,plain,
! [U_2625,U_2624,U_2623] :
( c_Big__Operators_Olattice_OInf__fin(U_2623,c_Orderings_Oord__class_Omin(U_2623),hAPP(hAPP(c_Set_Oinsert(U_2623),U_2625),U_2624)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2623,U_2623,c_Orderings_Oord__class_Omin(U_2623)),U_2625),U_2624)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2623),U_2624))
| ~ class_Orderings_Olinorder(U_2623) ),
inference(variable_rename,[status(thm)],[f_578_1]) ).
fof(f_578_3,plain,
! [U_2624,U_2623,U_2625] :
( c_Big__Operators_Olattice_OInf__fin(U_2623,c_Orderings_Oord__class_Omin(U_2623),hAPP(hAPP(c_Set_Oinsert(U_2623),U_2625),U_2624)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2623,U_2623,c_Orderings_Oord__class_Omin(U_2623)),U_2625),U_2624)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2623),U_2624))
| ~ class_Orderings_Olinorder(U_2623) ),
inference(definitional_conversion,[status(esa)],[f_578_2]) ).
cnf(f_578_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_2623,c_Orderings_Oord__class_Omin(U_2623),hAPP(hAPP(c_Set_Oinsert(U_2623),U_2625),U_2624)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2623,U_2623,c_Orderings_Oord__class_Omin(U_2623)),U_2625),U_2624)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2623),U_2624))
| ~ class_Orderings_Olinorder(U_2623) ),
inference(clausify,[status(thm)],[f_578_3]) ).
fof(f_579_1,plain,
! [V_a_2,V_A_2,T_c] :
( c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H]) ).
fof(f_579_2,plain,
! [U_2628,U_2627,U_2626] :
( c_Big__Operators_Olattice_OSup__fin(U_2626,c_Orderings_Oord__class_Omax(U_2626),hAPP(hAPP(c_Set_Oinsert(U_2626),U_2628),U_2627)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2626,U_2626,c_Orderings_Oord__class_Omax(U_2626)),U_2628),U_2627)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2626),U_2627))
| ~ class_Orderings_Olinorder(U_2626) ),
inference(variable_rename,[status(thm)],[f_579_1]) ).
fof(f_579_3,plain,
! [U_2626,U_2627,U_2628] :
( c_Big__Operators_Olattice_OSup__fin(U_2626,c_Orderings_Oord__class_Omax(U_2626),hAPP(hAPP(c_Set_Oinsert(U_2626),U_2628),U_2627)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2626,U_2626,c_Orderings_Oord__class_Omax(U_2626)),U_2628),U_2627)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2626),U_2627))
| ~ class_Orderings_Olinorder(U_2626) ),
inference(definitional_conversion,[status(esa)],[f_579_2]) ).
cnf(f_579_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_2626,c_Orderings_Oord__class_Omax(U_2626),hAPP(hAPP(c_Set_Oinsert(U_2626),U_2628),U_2627)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2626,U_2626,c_Orderings_Oord__class_Omax(U_2626)),U_2628),U_2627)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2626),U_2627))
| ~ class_Orderings_Olinorder(U_2626) ),
inference(clausify,[status(thm)],[f_579_3]) ).
fof(f_580_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2))
| V_A_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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert]) ).
fof(f_580_2,plain,
! [U_2631,U_2630,U_2629] :
( c_Big__Operators_Olattice_OInf__fin(U_2629,c_Orderings_Oord__class_Omin(U_2629),hAPP(hAPP(c_Set_Oinsert(U_2629),U_2631),U_2630)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2629),U_2631),c_Big__Operators_Olattice_OInf__fin(U_2629,c_Orderings_Oord__class_Omin(U_2629),U_2630))
| U_2630 = c_Orderings_Obot__class_Obot(tc_fun(U_2629,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2629),U_2631),U_2630))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2629),U_2630))
| ~ class_Orderings_Olinorder(U_2629) ),
inference(variable_rename,[status(thm)],[f_580_1]) ).
fof(f_580_3,plain,
! [U_2629,U_2630,U_2631] :
( c_Big__Operators_Olattice_OInf__fin(U_2629,c_Orderings_Oord__class_Omin(U_2629),hAPP(hAPP(c_Set_Oinsert(U_2629),U_2631),U_2630)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2629),U_2631),c_Big__Operators_Olattice_OInf__fin(U_2629,c_Orderings_Oord__class_Omin(U_2629),U_2630))
| U_2630 = c_Orderings_Obot__class_Obot(tc_fun(U_2629,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2629),U_2631),U_2630))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2629),U_2630))
| ~ class_Orderings_Olinorder(U_2629) ),
inference(definitional_conversion,[status(esa)],[f_580_2]) ).
cnf(f_580_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_2629,c_Orderings_Oord__class_Omin(U_2629),hAPP(hAPP(c_Set_Oinsert(U_2629),U_2631),U_2630)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2629),U_2631),c_Big__Operators_Olattice_OInf__fin(U_2629,c_Orderings_Oord__class_Omin(U_2629),U_2630))
| U_2630 = c_Orderings_Obot__class_Obot(tc_fun(U_2629,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2629),U_2631),U_2630))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2629),U_2630))
| ~ class_Orderings_Olinorder(U_2629) ),
inference(clausify,[status(thm)],[f_580_3]) ).
fof(f_581_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2))
| V_A_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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert]) ).
fof(f_581_2,plain,
! [U_2634,U_2633,U_2632] :
( c_Big__Operators_Olattice_OSup__fin(U_2632,c_Orderings_Oord__class_Omax(U_2632),hAPP(hAPP(c_Set_Oinsert(U_2632),U_2634),U_2633)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2632),U_2634),c_Big__Operators_Olattice_OSup__fin(U_2632,c_Orderings_Oord__class_Omax(U_2632),U_2633))
| U_2633 = c_Orderings_Obot__class_Obot(tc_fun(U_2632,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2632),U_2634),U_2633))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2632),U_2633))
| ~ class_Orderings_Olinorder(U_2632) ),
inference(variable_rename,[status(thm)],[f_581_1]) ).
fof(f_581_3,plain,
! [U_2632,U_2633,U_2634] :
( c_Big__Operators_Olattice_OSup__fin(U_2632,c_Orderings_Oord__class_Omax(U_2632),hAPP(hAPP(c_Set_Oinsert(U_2632),U_2634),U_2633)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2632),U_2634),c_Big__Operators_Olattice_OSup__fin(U_2632,c_Orderings_Oord__class_Omax(U_2632),U_2633))
| U_2633 = c_Orderings_Obot__class_Obot(tc_fun(U_2632,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2632),U_2634),U_2633))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2632),U_2633))
| ~ class_Orderings_Olinorder(U_2632) ),
inference(definitional_conversion,[status(esa)],[f_581_2]) ).
cnf(f_581_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_2632,c_Orderings_Oord__class_Omax(U_2632),hAPP(hAPP(c_Set_Oinsert(U_2632),U_2634),U_2633)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2632),U_2634),c_Big__Operators_Olattice_OSup__fin(U_2632,c_Orderings_Oord__class_Omax(U_2632),U_2633))
| U_2633 = c_Orderings_Obot__class_Obot(tc_fun(U_2632,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_2632),U_2634),U_2633))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2632),U_2633))
| ~ class_Orderings_Olinorder(U_2632) ),
inference(clausify,[status(thm)],[f_581_3]) ).
fof(f_582_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove]) ).
fof(f_582_2,plain,
! [U_2637,U_2636,U_2635] :
( ( ( c_Big__Operators_Olattice_OInf__fin(U_2635,c_Orderings_Oord__class_Omin(U_2635),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),U_2636)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2635),U_2637),c_Big__Operators_Olattice_OInf__fin(U_2635,c_Orderings_Oord__class_Omin(U_2635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2635,tc_HOL_Obool)),U_2636),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2635,tc_HOL_Obool)),U_2636),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OInf__fin(U_2635,c_Orderings_Oord__class_Omin(U_2635),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),U_2636)) = U_2637
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2635,tc_HOL_Obool)),U_2636),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2635),U_2636))
| ~ class_Orderings_Olinorder(U_2635) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
fof(f_582_3,plain,
( ! [U_2636,U_2635,U_2637] :
( c_Big__Operators_Olattice_OInf__fin(U_2635,c_Orderings_Oord__class_Omin(U_2635),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),U_2636)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2635),U_2637),c_Big__Operators_Olattice_OInf__fin(U_2635,c_Orderings_Oord__class_Omin(U_2635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2635,tc_HOL_Obool)),U_2636),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2635,tc_HOL_Obool)),U_2636),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool))
| ~ sP147(U_2636,U_2635,U_2637) )
& ! [U_2636,U_2635,U_2637] :
( c_Big__Operators_Olattice_OInf__fin(U_2635,c_Orderings_Oord__class_Omin(U_2635),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),U_2636)) = U_2637
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2635,tc_HOL_Obool)),U_2636),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool))
| ~ sP147(U_2636,U_2635,U_2637) )
& ! [U_2636,U_2635,U_2637] :
( sP147(U_2636,U_2635,U_2637)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2635),U_2636))
| ~ class_Orderings_Olinorder(U_2635) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147])],[f_582_2]) ).
cnf(f_582_4,plain,
( sP147(U_2636,U_2635,U_2637)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2635),U_2636))
| ~ class_Orderings_Olinorder(U_2635) ),
inference(clausify,[status(thm)],[f_582_3]) ).
cnf(f_582_5,plain,
( c_Big__Operators_Olattice_OInf__fin(U_2635,c_Orderings_Oord__class_Omin(U_2635),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),U_2636)) = U_2637
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2635,tc_HOL_Obool)),U_2636),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool))
| ~ sP147(U_2636,U_2635,U_2637) ),
inference(clausify,[status(thm)],[f_582_3]) ).
cnf(f_582_6,plain,
( c_Big__Operators_Olattice_OInf__fin(U_2635,c_Orderings_Oord__class_Omin(U_2635),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),U_2636)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2635),U_2637),c_Big__Operators_Olattice_OInf__fin(U_2635,c_Orderings_Oord__class_Omin(U_2635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2635,tc_HOL_Obool)),U_2636),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2635,tc_HOL_Obool)),U_2636),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2635,tc_HOL_Obool))
| ~ sP147(U_2636,U_2635,U_2637) ),
inference(clausify,[status(thm)],[f_582_3]) ).
fof(f_583_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove]) ).
fof(f_583_2,plain,
! [U_2640,U_2639,U_2638] :
( ( ( c_Big__Operators_Olattice_OSup__fin(U_2638,c_Orderings_Oord__class_Omax(U_2638),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),U_2639)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2638),U_2640),c_Big__Operators_Olattice_OSup__fin(U_2638,c_Orderings_Oord__class_Omax(U_2638),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2638,tc_HOL_Obool)),U_2639),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2638,tc_HOL_Obool)),U_2639),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OSup__fin(U_2638,c_Orderings_Oord__class_Omax(U_2638),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),U_2639)) = U_2640
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2638,tc_HOL_Obool)),U_2639),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2638),U_2639))
| ~ class_Orderings_Olinorder(U_2638) ),
inference(variable_rename,[status(thm)],[f_583_1]) ).
fof(f_583_3,plain,
( ! [U_2639,U_2638,U_2640] :
( c_Big__Operators_Olattice_OSup__fin(U_2638,c_Orderings_Oord__class_Omax(U_2638),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),U_2639)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2638),U_2640),c_Big__Operators_Olattice_OSup__fin(U_2638,c_Orderings_Oord__class_Omax(U_2638),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2638,tc_HOL_Obool)),U_2639),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2638,tc_HOL_Obool)),U_2639),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool))
| ~ sP148(U_2639,U_2638,U_2640) )
& ! [U_2639,U_2638,U_2640] :
( c_Big__Operators_Olattice_OSup__fin(U_2638,c_Orderings_Oord__class_Omax(U_2638),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),U_2639)) = U_2640
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2638,tc_HOL_Obool)),U_2639),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool))
| ~ sP148(U_2639,U_2638,U_2640) )
& ! [U_2639,U_2638,U_2640] :
( sP148(U_2639,U_2638,U_2640)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2638),U_2639))
| ~ class_Orderings_Olinorder(U_2638) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP148])],[f_583_2]) ).
cnf(f_583_4,plain,
( sP148(U_2639,U_2638,U_2640)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2638),U_2639))
| ~ class_Orderings_Olinorder(U_2638) ),
inference(clausify,[status(thm)],[f_583_3]) ).
cnf(f_583_5,plain,
( c_Big__Operators_Olattice_OSup__fin(U_2638,c_Orderings_Oord__class_Omax(U_2638),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),U_2639)) = U_2640
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2638,tc_HOL_Obool)),U_2639),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool))
| ~ sP148(U_2639,U_2638,U_2640) ),
inference(clausify,[status(thm)],[f_583_3]) ).
cnf(f_583_6,plain,
( c_Big__Operators_Olattice_OSup__fin(U_2638,c_Orderings_Oord__class_Omax(U_2638),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),U_2639)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2638),U_2640),c_Big__Operators_Olattice_OSup__fin(U_2638,c_Orderings_Oord__class_Omax(U_2638),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2638,tc_HOL_Obool)),U_2639),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2638,tc_HOL_Obool)),U_2639),hAPP(hAPP(c_Set_Oinsert(U_2638),U_2640),c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2638,tc_HOL_Obool))
| ~ sP148(U_2639,U_2638,U_2640) ),
inference(clausify,[status(thm)],[f_583_3]) ).
fof(f_584_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_x_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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold_H]) ).
fof(f_584_2,plain,
! [U_2643,U_2642,U_2641] :
( c_Big__Operators_Olattice_OInf__fin(U_2641,c_Orderings_Oord__class_Omin(U_2641),hAPP(hAPP(c_Set_Oinsert(U_2641),U_2643),U_2642)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2641,U_2641,c_Orderings_Oord__class_Omin(U_2641)),U_2643),U_2642)
| hBOOL(hAPP(hAPP(c_member(U_2641),U_2643),U_2642))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2641),U_2642))
| ~ class_Orderings_Olinorder(U_2641) ),
inference(variable_rename,[status(thm)],[f_584_1]) ).
fof(f_584_3,plain,
! [U_2642,U_2641,U_2643] :
( c_Big__Operators_Olattice_OInf__fin(U_2641,c_Orderings_Oord__class_Omin(U_2641),hAPP(hAPP(c_Set_Oinsert(U_2641),U_2643),U_2642)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2641,U_2641,c_Orderings_Oord__class_Omin(U_2641)),U_2643),U_2642)
| hBOOL(hAPP(hAPP(c_member(U_2641),U_2643),U_2642))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2641),U_2642))
| ~ class_Orderings_Olinorder(U_2641) ),
inference(definitional_conversion,[status(esa)],[f_584_2]) ).
cnf(f_584_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_2641,c_Orderings_Oord__class_Omin(U_2641),hAPP(hAPP(c_Set_Oinsert(U_2641),U_2643),U_2642)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2641,U_2641,c_Orderings_Oord__class_Omin(U_2641)),U_2643),U_2642)
| hBOOL(hAPP(hAPP(c_member(U_2641),U_2643),U_2642))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2641),U_2642))
| ~ class_Orderings_Olinorder(U_2641) ),
inference(clausify,[status(thm)],[f_584_3]) ).
fof(f_585_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_x_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))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold_H]) ).
fof(f_585_2,plain,
! [U_2646,U_2645,U_2644] :
( c_Big__Operators_Olattice_OSup__fin(U_2644,c_Orderings_Oord__class_Omax(U_2644),hAPP(hAPP(c_Set_Oinsert(U_2644),U_2646),U_2645)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2644,U_2644,c_Orderings_Oord__class_Omax(U_2644)),U_2646),U_2645)
| hBOOL(hAPP(hAPP(c_member(U_2644),U_2646),U_2645))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2644),U_2645))
| ~ class_Orderings_Olinorder(U_2644) ),
inference(variable_rename,[status(thm)],[f_585_1]) ).
fof(f_585_3,plain,
! [U_2646,U_2644,U_2645] :
( c_Big__Operators_Olattice_OSup__fin(U_2644,c_Orderings_Oord__class_Omax(U_2644),hAPP(hAPP(c_Set_Oinsert(U_2644),U_2646),U_2645)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2644,U_2644,c_Orderings_Oord__class_Omax(U_2644)),U_2646),U_2645)
| hBOOL(hAPP(hAPP(c_member(U_2644),U_2646),U_2645))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2644),U_2645))
| ~ class_Orderings_Olinorder(U_2644) ),
inference(definitional_conversion,[status(esa)],[f_585_2]) ).
cnf(f_585_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_2644,c_Orderings_Oord__class_Omax(U_2644),hAPP(hAPP(c_Set_Oinsert(U_2644),U_2646),U_2645)) = hAPP(hAPP(c_Finite__Set_Ofold(U_2644,U_2644,c_Orderings_Oord__class_Omax(U_2644)),U_2646),U_2645)
| hBOOL(hAPP(hAPP(c_member(U_2644),U_2646),U_2645))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2644),U_2645))
| ~ class_Orderings_Olinorder(U_2644) ),
inference(clausify,[status(thm)],[f_585_3]) ).
fof(f_586_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oclosed]) ).
fof(f_586_2,plain,
! [U_2650,U_2649] :
( hBOOL(hAPP(hAPP(c_member(U_2649),c_Big__Operators_Olattice_OSup__fin(U_2649,c_Orderings_Oord__class_Omax(U_2649),U_2650)),U_2650))
| ? [U_2648,U_2647] : ~ hBOOL(hAPP(hAPP(c_member(U_2649),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2649),U_2648),U_2647)),hAPP(hAPP(c_Set_Oinsert(U_2649),U_2648),hAPP(hAPP(c_Set_Oinsert(U_2649),U_2647),c_Orderings_Obot__class_Obot(tc_fun(U_2649,tc_HOL_Obool))))))
| U_2650 = c_Orderings_Obot__class_Obot(tc_fun(U_2649,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2649),U_2650))
| ~ class_Orderings_Olinorder(U_2649) ),
inference(variable_rename,[status(thm)],[f_586_1]) ).
fof(f_586_3,plain,
! [U_2650,U_2649] :
( hBOOL(hAPP(hAPP(c_member(U_2649),c_Big__Operators_Olattice_OSup__fin(U_2649,c_Orderings_Oord__class_Omax(U_2649),U_2650)),U_2650))
| ? [U_2647] : ~ hBOOL(hAPP(hAPP(c_member(U_2649),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2649),sK50(U_2650,U_2649)),U_2647)),hAPP(hAPP(c_Set_Oinsert(U_2649),sK50(U_2650,U_2649)),hAPP(hAPP(c_Set_Oinsert(U_2649),U_2647),c_Orderings_Obot__class_Obot(tc_fun(U_2649,tc_HOL_Obool))))))
| U_2650 = c_Orderings_Obot__class_Obot(tc_fun(U_2649,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2649),U_2650))
| ~ class_Orderings_Olinorder(U_2649) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_2648,sK50(U_2650,U_2649))],[f_586_2]) ).
fof(f_586_4,plain,
! [U_2650,U_2649] :
( hBOOL(hAPP(hAPP(c_member(U_2649),c_Big__Operators_Olattice_OSup__fin(U_2649,c_Orderings_Oord__class_Omax(U_2649),U_2650)),U_2650))
| ~ hBOOL(hAPP(hAPP(c_member(U_2649),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2649),sK50(U_2650,U_2649)),sK51(U_2650,U_2649))),hAPP(hAPP(c_Set_Oinsert(U_2649),sK50(U_2650,U_2649)),hAPP(hAPP(c_Set_Oinsert(U_2649),sK51(U_2650,U_2649)),c_Orderings_Obot__class_Obot(tc_fun(U_2649,tc_HOL_Obool))))))
| U_2650 = c_Orderings_Obot__class_Obot(tc_fun(U_2649,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2649),U_2650))
| ~ class_Orderings_Olinorder(U_2649) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_2647,sK51(U_2650,U_2649))],[f_586_3]) ).
fof(f_586_5,plain,
! [U_2649,U_2650] :
( hBOOL(hAPP(hAPP(c_member(U_2649),c_Big__Operators_Olattice_OSup__fin(U_2649,c_Orderings_Oord__class_Omax(U_2649),U_2650)),U_2650))
| ~ hBOOL(hAPP(hAPP(c_member(U_2649),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2649),sK50(U_2650,U_2649)),sK51(U_2650,U_2649))),hAPP(hAPP(c_Set_Oinsert(U_2649),sK50(U_2650,U_2649)),hAPP(hAPP(c_Set_Oinsert(U_2649),sK51(U_2650,U_2649)),c_Orderings_Obot__class_Obot(tc_fun(U_2649,tc_HOL_Obool))))))
| U_2650 = c_Orderings_Obot__class_Obot(tc_fun(U_2649,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2649),U_2650))
| ~ class_Orderings_Olinorder(U_2649) ),
inference(definitional_conversion,[status(esa)],[f_586_4]) ).
cnf(f_586_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2649),c_Big__Operators_Olattice_OSup__fin(U_2649,c_Orderings_Oord__class_Omax(U_2649),U_2650)),U_2650))
| ~ hBOOL(hAPP(hAPP(c_member(U_2649),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2649),sK50(U_2650,U_2649)),sK51(U_2650,U_2649))),hAPP(hAPP(c_Set_Oinsert(U_2649),sK50(U_2650,U_2649)),hAPP(hAPP(c_Set_Oinsert(U_2649),sK51(U_2650,U_2649)),c_Orderings_Obot__class_Obot(tc_fun(U_2649,tc_HOL_Obool))))))
| U_2650 = c_Orderings_Obot__class_Obot(tc_fun(U_2649,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2649),U_2650))
| ~ class_Orderings_Olinorder(U_2649) ),
inference(clausify,[status(thm)],[f_586_5]) ).
fof(f_587_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oclosed]) ).
fof(f_587_2,plain,
! [U_2654,U_2653] :
( hBOOL(hAPP(hAPP(c_member(U_2653),c_Big__Operators_Olattice_OInf__fin(U_2653,c_Orderings_Oord__class_Omin(U_2653),U_2654)),U_2654))
| ? [U_2652,U_2651] : ~ hBOOL(hAPP(hAPP(c_member(U_2653),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2653),U_2652),U_2651)),hAPP(hAPP(c_Set_Oinsert(U_2653),U_2652),hAPP(hAPP(c_Set_Oinsert(U_2653),U_2651),c_Orderings_Obot__class_Obot(tc_fun(U_2653,tc_HOL_Obool))))))
| U_2654 = c_Orderings_Obot__class_Obot(tc_fun(U_2653,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2653),U_2654))
| ~ class_Orderings_Olinorder(U_2653) ),
inference(variable_rename,[status(thm)],[f_587_1]) ).
fof(f_587_3,plain,
! [U_2654,U_2653] :
( hBOOL(hAPP(hAPP(c_member(U_2653),c_Big__Operators_Olattice_OInf__fin(U_2653,c_Orderings_Oord__class_Omin(U_2653),U_2654)),U_2654))
| ? [U_2651] : ~ hBOOL(hAPP(hAPP(c_member(U_2653),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2653),sK52(U_2654,U_2653)),U_2651)),hAPP(hAPP(c_Set_Oinsert(U_2653),sK52(U_2654,U_2653)),hAPP(hAPP(c_Set_Oinsert(U_2653),U_2651),c_Orderings_Obot__class_Obot(tc_fun(U_2653,tc_HOL_Obool))))))
| U_2654 = c_Orderings_Obot__class_Obot(tc_fun(U_2653,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2653),U_2654))
| ~ class_Orderings_Olinorder(U_2653) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_2652,sK52(U_2654,U_2653))],[f_587_2]) ).
fof(f_587_4,plain,
! [U_2654,U_2653] :
( hBOOL(hAPP(hAPP(c_member(U_2653),c_Big__Operators_Olattice_OInf__fin(U_2653,c_Orderings_Oord__class_Omin(U_2653),U_2654)),U_2654))
| ~ hBOOL(hAPP(hAPP(c_member(U_2653),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2653),sK52(U_2654,U_2653)),sK53(U_2654,U_2653))),hAPP(hAPP(c_Set_Oinsert(U_2653),sK52(U_2654,U_2653)),hAPP(hAPP(c_Set_Oinsert(U_2653),sK53(U_2654,U_2653)),c_Orderings_Obot__class_Obot(tc_fun(U_2653,tc_HOL_Obool))))))
| U_2654 = c_Orderings_Obot__class_Obot(tc_fun(U_2653,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2653),U_2654))
| ~ class_Orderings_Olinorder(U_2653) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_2651,sK53(U_2654,U_2653))],[f_587_3]) ).
fof(f_587_5,plain,
! [U_2654,U_2653] :
( hBOOL(hAPP(hAPP(c_member(U_2653),c_Big__Operators_Olattice_OInf__fin(U_2653,c_Orderings_Oord__class_Omin(U_2653),U_2654)),U_2654))
| ~ hBOOL(hAPP(hAPP(c_member(U_2653),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2653),sK52(U_2654,U_2653)),sK53(U_2654,U_2653))),hAPP(hAPP(c_Set_Oinsert(U_2653),sK52(U_2654,U_2653)),hAPP(hAPP(c_Set_Oinsert(U_2653),sK53(U_2654,U_2653)),c_Orderings_Obot__class_Obot(tc_fun(U_2653,tc_HOL_Obool))))))
| U_2654 = c_Orderings_Obot__class_Obot(tc_fun(U_2653,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2653),U_2654))
| ~ class_Orderings_Olinorder(U_2653) ),
inference(definitional_conversion,[status(esa)],[f_587_4]) ).
cnf(f_587_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2653),c_Big__Operators_Olattice_OInf__fin(U_2653,c_Orderings_Oord__class_Omin(U_2653),U_2654)),U_2654))
| ~ hBOOL(hAPP(hAPP(c_member(U_2653),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2653),sK52(U_2654,U_2653)),sK53(U_2654,U_2653))),hAPP(hAPP(c_Set_Oinsert(U_2653),sK52(U_2654,U_2653)),hAPP(hAPP(c_Set_Oinsert(U_2653),sK53(U_2654,U_2653)),c_Orderings_Obot__class_Obot(tc_fun(U_2653,tc_HOL_Obool))))))
| U_2654 = c_Orderings_Obot__class_Obot(tc_fun(U_2653,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2653),U_2654))
| ~ class_Orderings_Olinorder(U_2653) ),
inference(clausify,[status(thm)],[f_587_5]) ).
fof(f_588_1,plain,
! [V_N_2,V_h_2,T_c] :
( hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute]) ).
fof(f_588_2,plain,
! [U_2659,U_2658,U_2657] :
( hAPP(U_2658,c_Big__Operators_Olattice_OSup__fin(U_2657,c_Orderings_Oord__class_Omax(U_2657),U_2659)) = c_Big__Operators_Olattice_OSup__fin(U_2657,c_Orderings_Oord__class_Omax(U_2657),hAPP(c_Set_Oimage(U_2657,U_2657,U_2658),U_2659))
| U_2659 = c_Orderings_Obot__class_Obot(tc_fun(U_2657,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2657),U_2659))
| ? [U_2656,U_2655] : hAPP(U_2658,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2657),U_2656),U_2655)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2657),hAPP(U_2658,U_2656)),hAPP(U_2658,U_2655))
| ~ class_Orderings_Olinorder(U_2657) ),
inference(variable_rename,[status(thm)],[f_588_1]) ).
fof(f_588_3,plain,
! [U_2659,U_2658,U_2657] :
( hAPP(U_2658,c_Big__Operators_Olattice_OSup__fin(U_2657,c_Orderings_Oord__class_Omax(U_2657),U_2659)) = c_Big__Operators_Olattice_OSup__fin(U_2657,c_Orderings_Oord__class_Omax(U_2657),hAPP(c_Set_Oimage(U_2657,U_2657,U_2658),U_2659))
| U_2659 = c_Orderings_Obot__class_Obot(tc_fun(U_2657,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2657),U_2659))
| ? [U_2655] : hAPP(U_2658,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2657),sK54(U_2659,U_2658,U_2657)),U_2655)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2657),hAPP(U_2658,sK54(U_2659,U_2658,U_2657))),hAPP(U_2658,U_2655))
| ~ class_Orderings_Olinorder(U_2657) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_2656,sK54(U_2659,U_2658,U_2657))],[f_588_2]) ).
fof(f_588_4,plain,
! [U_2659,U_2658,U_2657] :
( hAPP(U_2658,c_Big__Operators_Olattice_OSup__fin(U_2657,c_Orderings_Oord__class_Omax(U_2657),U_2659)) = c_Big__Operators_Olattice_OSup__fin(U_2657,c_Orderings_Oord__class_Omax(U_2657),hAPP(c_Set_Oimage(U_2657,U_2657,U_2658),U_2659))
| U_2659 = c_Orderings_Obot__class_Obot(tc_fun(U_2657,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2657),U_2659))
| hAPP(U_2658,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2657),sK54(U_2659,U_2658,U_2657)),sK55(U_2659,U_2658,U_2657))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2657),hAPP(U_2658,sK54(U_2659,U_2658,U_2657))),hAPP(U_2658,sK55(U_2659,U_2658,U_2657)))
| ~ class_Orderings_Olinorder(U_2657) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_2655,sK55(U_2659,U_2658,U_2657))],[f_588_3]) ).
fof(f_588_5,plain,
! [U_2657,U_2658,U_2659] :
( hAPP(U_2658,c_Big__Operators_Olattice_OSup__fin(U_2657,c_Orderings_Oord__class_Omax(U_2657),U_2659)) = c_Big__Operators_Olattice_OSup__fin(U_2657,c_Orderings_Oord__class_Omax(U_2657),hAPP(c_Set_Oimage(U_2657,U_2657,U_2658),U_2659))
| U_2659 = c_Orderings_Obot__class_Obot(tc_fun(U_2657,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2657),U_2659))
| hAPP(U_2658,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2657),sK54(U_2659,U_2658,U_2657)),sK55(U_2659,U_2658,U_2657))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2657),hAPP(U_2658,sK54(U_2659,U_2658,U_2657))),hAPP(U_2658,sK55(U_2659,U_2658,U_2657)))
| ~ class_Orderings_Olinorder(U_2657) ),
inference(definitional_conversion,[status(esa)],[f_588_4]) ).
cnf(f_588_6,plain,
( hAPP(U_2658,c_Big__Operators_Olattice_OSup__fin(U_2657,c_Orderings_Oord__class_Omax(U_2657),U_2659)) = c_Big__Operators_Olattice_OSup__fin(U_2657,c_Orderings_Oord__class_Omax(U_2657),hAPP(c_Set_Oimage(U_2657,U_2657,U_2658),U_2659))
| U_2659 = c_Orderings_Obot__class_Obot(tc_fun(U_2657,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2657),U_2659))
| hAPP(U_2658,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2657),sK54(U_2659,U_2658,U_2657)),sK55(U_2659,U_2658,U_2657))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2657),hAPP(U_2658,sK54(U_2659,U_2658,U_2657))),hAPP(U_2658,sK55(U_2659,U_2658,U_2657)))
| ~ class_Orderings_Olinorder(U_2657) ),
inference(clausify,[status(thm)],[f_588_5]) ).
fof(f_589_1,plain,
! [V_N_2,V_h_2,T_c] :
( hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute]) ).
fof(f_589_2,plain,
! [U_2664,U_2663,U_2662] :
( hAPP(U_2663,c_Big__Operators_Olattice_OInf__fin(U_2662,c_Orderings_Oord__class_Omin(U_2662),U_2664)) = c_Big__Operators_Olattice_OInf__fin(U_2662,c_Orderings_Oord__class_Omin(U_2662),hAPP(c_Set_Oimage(U_2662,U_2662,U_2663),U_2664))
| U_2664 = c_Orderings_Obot__class_Obot(tc_fun(U_2662,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2662),U_2664))
| ? [U_2661,U_2660] : hAPP(U_2663,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2662),U_2661),U_2660)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2662),hAPP(U_2663,U_2661)),hAPP(U_2663,U_2660))
| ~ class_Orderings_Olinorder(U_2662) ),
inference(variable_rename,[status(thm)],[f_589_1]) ).
fof(f_589_3,plain,
! [U_2664,U_2663,U_2662] :
( hAPP(U_2663,c_Big__Operators_Olattice_OInf__fin(U_2662,c_Orderings_Oord__class_Omin(U_2662),U_2664)) = c_Big__Operators_Olattice_OInf__fin(U_2662,c_Orderings_Oord__class_Omin(U_2662),hAPP(c_Set_Oimage(U_2662,U_2662,U_2663),U_2664))
| U_2664 = c_Orderings_Obot__class_Obot(tc_fun(U_2662,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2662),U_2664))
| ? [U_2660] : hAPP(U_2663,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2662),sK56(U_2664,U_2663,U_2662)),U_2660)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2662),hAPP(U_2663,sK56(U_2664,U_2663,U_2662))),hAPP(U_2663,U_2660))
| ~ class_Orderings_Olinorder(U_2662) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_2661,sK56(U_2664,U_2663,U_2662))],[f_589_2]) ).
fof(f_589_4,plain,
! [U_2664,U_2663,U_2662] :
( hAPP(U_2663,c_Big__Operators_Olattice_OInf__fin(U_2662,c_Orderings_Oord__class_Omin(U_2662),U_2664)) = c_Big__Operators_Olattice_OInf__fin(U_2662,c_Orderings_Oord__class_Omin(U_2662),hAPP(c_Set_Oimage(U_2662,U_2662,U_2663),U_2664))
| U_2664 = c_Orderings_Obot__class_Obot(tc_fun(U_2662,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2662),U_2664))
| hAPP(U_2663,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2662),sK56(U_2664,U_2663,U_2662)),sK57(U_2664,U_2663,U_2662))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2662),hAPP(U_2663,sK56(U_2664,U_2663,U_2662))),hAPP(U_2663,sK57(U_2664,U_2663,U_2662)))
| ~ class_Orderings_Olinorder(U_2662) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_2660,sK57(U_2664,U_2663,U_2662))],[f_589_3]) ).
fof(f_589_5,plain,
! [U_2662,U_2663,U_2664] :
( hAPP(U_2663,c_Big__Operators_Olattice_OInf__fin(U_2662,c_Orderings_Oord__class_Omin(U_2662),U_2664)) = c_Big__Operators_Olattice_OInf__fin(U_2662,c_Orderings_Oord__class_Omin(U_2662),hAPP(c_Set_Oimage(U_2662,U_2662,U_2663),U_2664))
| U_2664 = c_Orderings_Obot__class_Obot(tc_fun(U_2662,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2662),U_2664))
| hAPP(U_2663,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2662),sK56(U_2664,U_2663,U_2662)),sK57(U_2664,U_2663,U_2662))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2662),hAPP(U_2663,sK56(U_2664,U_2663,U_2662))),hAPP(U_2663,sK57(U_2664,U_2663,U_2662)))
| ~ class_Orderings_Olinorder(U_2662) ),
inference(definitional_conversion,[status(esa)],[f_589_4]) ).
cnf(f_589_6,plain,
( hAPP(U_2663,c_Big__Operators_Olattice_OInf__fin(U_2662,c_Orderings_Oord__class_Omin(U_2662),U_2664)) = c_Big__Operators_Olattice_OInf__fin(U_2662,c_Orderings_Oord__class_Omin(U_2662),hAPP(c_Set_Oimage(U_2662,U_2662,U_2663),U_2664))
| U_2664 = c_Orderings_Obot__class_Obot(tc_fun(U_2662,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2662),U_2664))
| hAPP(U_2663,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2662),sK56(U_2664,U_2663,U_2662)),sK57(U_2664,U_2663,U_2662))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2662),hAPP(U_2663,sK56(U_2664,U_2663,U_2662))),hAPP(U_2663,sK57(U_2664,U_2663,U_2662)))
| ~ class_Orderings_Olinorder(U_2662) ),
inference(clausify,[status(thm)],[f_589_5]) ).
fof(f_590_1,plain,
! [V_N_2,V_h_2,T_c] :
( hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_c,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_Ohom__commute]) ).
fof(f_590_2,plain,
! [U_2669,U_2668,U_2667] :
( hAPP(U_2668,c_Big__Operators_Olinorder__class_OMax(U_2667,U_2669)) = c_Big__Operators_Olinorder__class_OMax(U_2667,hAPP(c_Set_Oimage(U_2667,U_2667,U_2668),U_2669))
| U_2669 = c_Orderings_Obot__class_Obot(tc_fun(U_2667,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2667),U_2669))
| ? [U_2666,U_2665] : hAPP(U_2668,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2667),U_2666),U_2665)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2667),hAPP(U_2668,U_2666)),hAPP(U_2668,U_2665))
| ~ class_Orderings_Olinorder(U_2667) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
fof(f_590_3,plain,
! [U_2669,U_2668,U_2667] :
( hAPP(U_2668,c_Big__Operators_Olinorder__class_OMax(U_2667,U_2669)) = c_Big__Operators_Olinorder__class_OMax(U_2667,hAPP(c_Set_Oimage(U_2667,U_2667,U_2668),U_2669))
| U_2669 = c_Orderings_Obot__class_Obot(tc_fun(U_2667,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2667),U_2669))
| ? [U_2665] : hAPP(U_2668,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2667),sK58(U_2669,U_2668,U_2667)),U_2665)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2667),hAPP(U_2668,sK58(U_2669,U_2668,U_2667))),hAPP(U_2668,U_2665))
| ~ class_Orderings_Olinorder(U_2667) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_2666,sK58(U_2669,U_2668,U_2667))],[f_590_2]) ).
fof(f_590_4,plain,
! [U_2669,U_2668,U_2667] :
( hAPP(U_2668,c_Big__Operators_Olinorder__class_OMax(U_2667,U_2669)) = c_Big__Operators_Olinorder__class_OMax(U_2667,hAPP(c_Set_Oimage(U_2667,U_2667,U_2668),U_2669))
| U_2669 = c_Orderings_Obot__class_Obot(tc_fun(U_2667,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2667),U_2669))
| hAPP(U_2668,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2667),sK58(U_2669,U_2668,U_2667)),sK59(U_2669,U_2668,U_2667))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2667),hAPP(U_2668,sK58(U_2669,U_2668,U_2667))),hAPP(U_2668,sK59(U_2669,U_2668,U_2667)))
| ~ class_Orderings_Olinorder(U_2667) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_2665,sK59(U_2669,U_2668,U_2667))],[f_590_3]) ).
fof(f_590_5,plain,
! [U_2667,U_2668,U_2669] :
( hAPP(U_2668,c_Big__Operators_Olinorder__class_OMax(U_2667,U_2669)) = c_Big__Operators_Olinorder__class_OMax(U_2667,hAPP(c_Set_Oimage(U_2667,U_2667,U_2668),U_2669))
| U_2669 = c_Orderings_Obot__class_Obot(tc_fun(U_2667,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2667),U_2669))
| hAPP(U_2668,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2667),sK58(U_2669,U_2668,U_2667)),sK59(U_2669,U_2668,U_2667))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2667),hAPP(U_2668,sK58(U_2669,U_2668,U_2667))),hAPP(U_2668,sK59(U_2669,U_2668,U_2667)))
| ~ class_Orderings_Olinorder(U_2667) ),
inference(definitional_conversion,[status(esa)],[f_590_4]) ).
cnf(f_590_6,plain,
( hAPP(U_2668,c_Big__Operators_Olinorder__class_OMax(U_2667,U_2669)) = c_Big__Operators_Olinorder__class_OMax(U_2667,hAPP(c_Set_Oimage(U_2667,U_2667,U_2668),U_2669))
| U_2669 = c_Orderings_Obot__class_Obot(tc_fun(U_2667,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2667),U_2669))
| hAPP(U_2668,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2667),sK58(U_2669,U_2668,U_2667)),sK59(U_2669,U_2668,U_2667))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2667),hAPP(U_2668,sK58(U_2669,U_2668,U_2667))),hAPP(U_2668,sK59(U_2669,U_2668,U_2667)))
| ~ class_Orderings_Olinorder(U_2667) ),
inference(clausify,[status(thm)],[f_590_5]) ).
fof(f_591_1,plain,
! [V_N_2,V_h_2,T_c] :
( hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_c,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_Ohom__commute]) ).
fof(f_591_2,plain,
! [U_2674,U_2673,U_2672] :
( hAPP(U_2673,c_Big__Operators_Olinorder__class_OMin(U_2672,U_2674)) = c_Big__Operators_Olinorder__class_OMin(U_2672,hAPP(c_Set_Oimage(U_2672,U_2672,U_2673),U_2674))
| U_2674 = c_Orderings_Obot__class_Obot(tc_fun(U_2672,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2672),U_2674))
| ? [U_2671,U_2670] : hAPP(U_2673,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2672),U_2671),U_2670)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2672),hAPP(U_2673,U_2671)),hAPP(U_2673,U_2670))
| ~ class_Orderings_Olinorder(U_2672) ),
inference(variable_rename,[status(thm)],[f_591_1]) ).
fof(f_591_3,plain,
! [U_2674,U_2673,U_2672] :
( hAPP(U_2673,c_Big__Operators_Olinorder__class_OMin(U_2672,U_2674)) = c_Big__Operators_Olinorder__class_OMin(U_2672,hAPP(c_Set_Oimage(U_2672,U_2672,U_2673),U_2674))
| U_2674 = c_Orderings_Obot__class_Obot(tc_fun(U_2672,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2672),U_2674))
| ? [U_2670] : hAPP(U_2673,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2672),sK60(U_2674,U_2673,U_2672)),U_2670)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2672),hAPP(U_2673,sK60(U_2674,U_2673,U_2672))),hAPP(U_2673,U_2670))
| ~ class_Orderings_Olinorder(U_2672) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_2671,sK60(U_2674,U_2673,U_2672))],[f_591_2]) ).
fof(f_591_4,plain,
! [U_2674,U_2673,U_2672] :
( hAPP(U_2673,c_Big__Operators_Olinorder__class_OMin(U_2672,U_2674)) = c_Big__Operators_Olinorder__class_OMin(U_2672,hAPP(c_Set_Oimage(U_2672,U_2672,U_2673),U_2674))
| U_2674 = c_Orderings_Obot__class_Obot(tc_fun(U_2672,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2672),U_2674))
| hAPP(U_2673,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2672),sK60(U_2674,U_2673,U_2672)),sK61(U_2674,U_2673,U_2672))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2672),hAPP(U_2673,sK60(U_2674,U_2673,U_2672))),hAPP(U_2673,sK61(U_2674,U_2673,U_2672)))
| ~ class_Orderings_Olinorder(U_2672) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_2670,sK61(U_2674,U_2673,U_2672))],[f_591_3]) ).
fof(f_591_5,plain,
! [U_2672,U_2673,U_2674] :
( hAPP(U_2673,c_Big__Operators_Olinorder__class_OMin(U_2672,U_2674)) = c_Big__Operators_Olinorder__class_OMin(U_2672,hAPP(c_Set_Oimage(U_2672,U_2672,U_2673),U_2674))
| U_2674 = c_Orderings_Obot__class_Obot(tc_fun(U_2672,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2672),U_2674))
| hAPP(U_2673,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2672),sK60(U_2674,U_2673,U_2672)),sK61(U_2674,U_2673,U_2672))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2672),hAPP(U_2673,sK60(U_2674,U_2673,U_2672))),hAPP(U_2673,sK61(U_2674,U_2673,U_2672)))
| ~ class_Orderings_Olinorder(U_2672) ),
inference(definitional_conversion,[status(esa)],[f_591_4]) ).
cnf(f_591_6,plain,
( hAPP(U_2673,c_Big__Operators_Olinorder__class_OMin(U_2672,U_2674)) = c_Big__Operators_Olinorder__class_OMin(U_2672,hAPP(c_Set_Oimage(U_2672,U_2672,U_2673),U_2674))
| U_2674 = c_Orderings_Obot__class_Obot(tc_fun(U_2672,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2672),U_2674))
| hAPP(U_2673,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2672),sK60(U_2674,U_2673,U_2672)),sK61(U_2674,U_2673,U_2672))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2672),hAPP(U_2673,sK60(U_2674,U_2673,U_2672))),hAPP(U_2673,sK61(U_2674,U_2673,U_2672)))
| ~ class_Orderings_Olinorder(U_2672) ),
inference(clausify,[status(thm)],[f_591_5]) ).
fof(f_592_1,plain,
! [V_N_2,V_h_2,T_c] :
( hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),B_x),B_y)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute]) ).
fof(f_592_2,plain,
! [U_2679,U_2678,U_2677] :
( hAPP(U_2678,hAPP(c_Finite__Set_Ofold1(U_2677,c_Groups_Otimes__class_Otimes(U_2677)),U_2679)) = hAPP(c_Finite__Set_Ofold1(U_2677,c_Groups_Otimes__class_Otimes(U_2677)),hAPP(c_Set_Oimage(U_2677,U_2677,U_2678),U_2679))
| U_2679 = c_Orderings_Obot__class_Obot(tc_fun(U_2677,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2677),U_2679))
| ? [U_2676,U_2675] : hAPP(U_2678,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2676),U_2675)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),hAPP(U_2678,U_2676)),hAPP(U_2678,U_2675))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2677) ),
inference(variable_rename,[status(thm)],[f_592_1]) ).
fof(f_592_3,plain,
! [U_2679,U_2678,U_2677] :
( hAPP(U_2678,hAPP(c_Finite__Set_Ofold1(U_2677,c_Groups_Otimes__class_Otimes(U_2677)),U_2679)) = hAPP(c_Finite__Set_Ofold1(U_2677,c_Groups_Otimes__class_Otimes(U_2677)),hAPP(c_Set_Oimage(U_2677,U_2677,U_2678),U_2679))
| U_2679 = c_Orderings_Obot__class_Obot(tc_fun(U_2677,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2677),U_2679))
| ? [U_2675] : hAPP(U_2678,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),sK62(U_2679,U_2678,U_2677)),U_2675)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),hAPP(U_2678,sK62(U_2679,U_2678,U_2677))),hAPP(U_2678,U_2675))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_2676,sK62(U_2679,U_2678,U_2677))],[f_592_2]) ).
fof(f_592_4,plain,
! [U_2679,U_2678,U_2677] :
( hAPP(U_2678,hAPP(c_Finite__Set_Ofold1(U_2677,c_Groups_Otimes__class_Otimes(U_2677)),U_2679)) = hAPP(c_Finite__Set_Ofold1(U_2677,c_Groups_Otimes__class_Otimes(U_2677)),hAPP(c_Set_Oimage(U_2677,U_2677,U_2678),U_2679))
| U_2679 = c_Orderings_Obot__class_Obot(tc_fun(U_2677,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2677),U_2679))
| hAPP(U_2678,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),sK62(U_2679,U_2678,U_2677)),sK63(U_2679,U_2678,U_2677))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),hAPP(U_2678,sK62(U_2679,U_2678,U_2677))),hAPP(U_2678,sK63(U_2679,U_2678,U_2677)))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2677) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_2675,sK63(U_2679,U_2678,U_2677))],[f_592_3]) ).
fof(f_592_5,plain,
! [U_2677,U_2678,U_2679] :
( hAPP(U_2678,hAPP(c_Finite__Set_Ofold1(U_2677,c_Groups_Otimes__class_Otimes(U_2677)),U_2679)) = hAPP(c_Finite__Set_Ofold1(U_2677,c_Groups_Otimes__class_Otimes(U_2677)),hAPP(c_Set_Oimage(U_2677,U_2677,U_2678),U_2679))
| U_2679 = c_Orderings_Obot__class_Obot(tc_fun(U_2677,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2677),U_2679))
| hAPP(U_2678,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),sK62(U_2679,U_2678,U_2677)),sK63(U_2679,U_2678,U_2677))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),hAPP(U_2678,sK62(U_2679,U_2678,U_2677))),hAPP(U_2678,sK63(U_2679,U_2678,U_2677)))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2677) ),
inference(definitional_conversion,[status(esa)],[f_592_4]) ).
cnf(f_592_6,plain,
( hAPP(U_2678,hAPP(c_Finite__Set_Ofold1(U_2677,c_Groups_Otimes__class_Otimes(U_2677)),U_2679)) = hAPP(c_Finite__Set_Ofold1(U_2677,c_Groups_Otimes__class_Otimes(U_2677)),hAPP(c_Set_Oimage(U_2677,U_2677,U_2678),U_2679))
| U_2679 = c_Orderings_Obot__class_Obot(tc_fun(U_2677,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2677),U_2679))
| hAPP(U_2678,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),sK62(U_2679,U_2678,U_2677)),sK63(U_2679,U_2678,U_2677))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),hAPP(U_2678,sK62(U_2679,U_2678,U_2677))),hAPP(U_2678,sK63(U_2679,U_2678,U_2677)))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2677) ),
inference(clausify,[status(thm)],[f_592_5]) ).
fof(f_593_1,plain,
! [V_c_2,V_b_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omax(T_c)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_b_2),V_c_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__le__sup]) ).
fof(f_593_2,plain,
! [U_2684,U_2683,U_2682,U_2681] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2681),hAPP(hAPP(c_Finite__Set_Ofold(U_2681,U_2681,c_Orderings_Oord__class_Omax(U_2681)),U_2684),U_2682)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2681),U_2683),U_2684)))
| ? [U_2680] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2681),U_2680),U_2683))
& hBOOL(hAPP(hAPP(c_member(U_2681),U_2680),U_2682)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2681),U_2682))
| ~ class_Orderings_Olinorder(U_2681) ),
inference(variable_rename,[status(thm)],[f_593_1]) ).
fof(f_593_3,plain,
! [U_2684,U_2683,U_2682,U_2681] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2681),hAPP(hAPP(c_Finite__Set_Ofold(U_2681,U_2681,c_Orderings_Oord__class_Omax(U_2681)),U_2684),U_2682)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2681),U_2683),U_2684)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2681),sK64(U_2684,U_2683,U_2682,U_2681)),U_2683))
& hBOOL(hAPP(hAPP(c_member(U_2681),sK64(U_2684,U_2683,U_2682,U_2681)),U_2682)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2681),U_2682))
| ~ class_Orderings_Olinorder(U_2681) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_2680,sK64(U_2684,U_2683,U_2682,U_2681))],[f_593_2]) ).
fof(f_593_4,plain,
( ! [U_2682,U_2681,U_2683,U_2684] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2681),sK64(U_2684,U_2683,U_2682,U_2681)),U_2683))
| ~ sP149(U_2682,U_2681,U_2683,U_2684) )
& ! [U_2682,U_2681,U_2683,U_2684] :
( hBOOL(hAPP(hAPP(c_member(U_2681),sK64(U_2684,U_2683,U_2682,U_2681)),U_2682))
| ~ sP149(U_2682,U_2681,U_2683,U_2684) )
& ! [U_2682,U_2681,U_2683,U_2684] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2681),hAPP(hAPP(c_Finite__Set_Ofold(U_2681,U_2681,c_Orderings_Oord__class_Omax(U_2681)),U_2684),U_2682)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2681),U_2683),U_2684)))
| sP149(U_2682,U_2681,U_2683,U_2684)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2681),U_2682))
| ~ class_Orderings_Olinorder(U_2681) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP149])],[f_593_3]) ).
cnf(f_593_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2681),hAPP(hAPP(c_Finite__Set_Ofold(U_2681,U_2681,c_Orderings_Oord__class_Omax(U_2681)),U_2684),U_2682)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2681),U_2683),U_2684)))
| sP149(U_2682,U_2681,U_2683,U_2684)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2681),U_2682))
| ~ class_Orderings_Olinorder(U_2681) ),
inference(clausify,[status(thm)],[f_593_4]) ).
cnf(f_593_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2681),sK64(U_2684,U_2683,U_2682,U_2681)),U_2682))
| ~ sP149(U_2682,U_2681,U_2683,U_2684) ),
inference(clausify,[status(thm)],[f_593_4]) ).
cnf(f_593_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2681),sK64(U_2684,U_2683,U_2682,U_2681)),U_2683))
| ~ sP149(U_2682,U_2681,U_2683,U_2684) ),
inference(clausify,[status(thm)],[f_593_4]) ).
fof(f_594_1,plain,
! [V_c_2,V_b_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Orderings_Oord__class_Omin(T_c)),V_c_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le__fold__inf]) ).
fof(f_594_2,plain,
! [U_2689,U_2688,U_2687,U_2686] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2686),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2686),U_2688),U_2689)),hAPP(hAPP(c_Finite__Set_Ofold(U_2686,U_2686,c_Orderings_Oord__class_Omin(U_2686)),U_2689),U_2687)))
| ? [U_2685] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2686),U_2688),U_2685))
& hBOOL(hAPP(hAPP(c_member(U_2686),U_2685),U_2687)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2686),U_2687))
| ~ class_Orderings_Olinorder(U_2686) ),
inference(variable_rename,[status(thm)],[f_594_1]) ).
fof(f_594_3,plain,
! [U_2689,U_2688,U_2687,U_2686] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2686),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2686),U_2688),U_2689)),hAPP(hAPP(c_Finite__Set_Ofold(U_2686,U_2686,c_Orderings_Oord__class_Omin(U_2686)),U_2689),U_2687)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2686),U_2688),sK65(U_2689,U_2688,U_2687,U_2686)))
& hBOOL(hAPP(hAPP(c_member(U_2686),sK65(U_2689,U_2688,U_2687,U_2686)),U_2687)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2686),U_2687))
| ~ class_Orderings_Olinorder(U_2686) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_2685,sK65(U_2689,U_2688,U_2687,U_2686))],[f_594_2]) ).
fof(f_594_4,plain,
( ! [U_2686,U_2687,U_2688,U_2689] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2686),U_2688),sK65(U_2689,U_2688,U_2687,U_2686)))
| ~ sP150(U_2686,U_2687,U_2688,U_2689) )
& ! [U_2686,U_2687,U_2688,U_2689] :
( hBOOL(hAPP(hAPP(c_member(U_2686),sK65(U_2689,U_2688,U_2687,U_2686)),U_2687))
| ~ sP150(U_2686,U_2687,U_2688,U_2689) )
& ! [U_2686,U_2687,U_2688,U_2689] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2686),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2686),U_2688),U_2689)),hAPP(hAPP(c_Finite__Set_Ofold(U_2686,U_2686,c_Orderings_Oord__class_Omin(U_2686)),U_2689),U_2687)))
| sP150(U_2686,U_2687,U_2688,U_2689)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2686),U_2687))
| ~ class_Orderings_Olinorder(U_2686) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150])],[f_594_3]) ).
cnf(f_594_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2686),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2686),U_2688),U_2689)),hAPP(hAPP(c_Finite__Set_Ofold(U_2686,U_2686,c_Orderings_Oord__class_Omin(U_2686)),U_2689),U_2687)))
| sP150(U_2686,U_2687,U_2688,U_2689)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2686),U_2687))
| ~ class_Orderings_Olinorder(U_2686) ),
inference(clausify,[status(thm)],[f_594_4]) ).
cnf(f_594_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2686),sK65(U_2689,U_2688,U_2687,U_2686)),U_2687))
| ~ sP150(U_2686,U_2687,U_2688,U_2689) ),
inference(clausify,[status(thm)],[f_594_4]) ).
cnf(f_594_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2686),U_2688),sK65(U_2689,U_2688,U_2687,U_2686)))
| ~ sP150(U_2686,U_2687,U_2688,U_2689) ),
inference(clausify,[status(thm)],[f_594_4]) ).
fof(f_595_1,plain,
! [V_y_2,V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),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))))),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_c),V_A_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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff2__less]) ).
fof(f_595_2,plain,
! [U_2693,U_2692,U_2691,U_2690] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2690,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2690,tc_HOL_Obool)),U_2691),hAPP(hAPP(c_Set_Oinsert(U_2690),U_2692),c_Orderings_Obot__class_Obot(tc_fun(U_2690,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_2690),U_2693),c_Orderings_Obot__class_Obot(tc_fun(U_2690,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_2690),U_2691)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2690),U_2693),U_2691))
| ~ hBOOL(hAPP(hAPP(c_member(U_2690),U_2692),U_2691))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2690),U_2691)) ),
inference(variable_rename,[status(thm)],[f_595_1]) ).
fof(f_595_3,plain,
! [U_2690,U_2691,U_2692,U_2693] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2690,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2690,tc_HOL_Obool)),U_2691),hAPP(hAPP(c_Set_Oinsert(U_2690),U_2692),c_Orderings_Obot__class_Obot(tc_fun(U_2690,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_2690),U_2693),c_Orderings_Obot__class_Obot(tc_fun(U_2690,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_2690),U_2691)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2690),U_2693),U_2691))
| ~ hBOOL(hAPP(hAPP(c_member(U_2690),U_2692),U_2691))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2690),U_2691)) ),
inference(definitional_conversion,[status(esa)],[f_595_2]) ).
cnf(f_595_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2690,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2690,tc_HOL_Obool)),U_2691),hAPP(hAPP(c_Set_Oinsert(U_2690),U_2692),c_Orderings_Obot__class_Obot(tc_fun(U_2690,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_2690),U_2693),c_Orderings_Obot__class_Obot(tc_fun(U_2690,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_2690),U_2691)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2690),U_2693),U_2691))
| ~ hBOOL(hAPP(hAPP(c_member(U_2690),U_2692),U_2691))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2690),U_2691)) ),
inference(clausify,[status(thm)],[f_595_3]) ).
fof(f_596_1,plain,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),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)))))),hAPP(c_Finite__Set_Ocard(T_c),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)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff1__less]) ).
fof(f_596_2,plain,
! [U_2696,U_2695,U_2694] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2694),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2694,tc_HOL_Obool)),U_2695),hAPP(hAPP(c_Set_Oinsert(U_2694),U_2696),c_Orderings_Obot__class_Obot(tc_fun(U_2694,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_2694),U_2695)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2694),U_2696),U_2695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2694),U_2695)) ),
inference(variable_rename,[status(thm)],[f_596_1]) ).
fof(f_596_3,plain,
! [U_2695,U_2694,U_2696] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2694),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2694,tc_HOL_Obool)),U_2695),hAPP(hAPP(c_Set_Oinsert(U_2694),U_2696),c_Orderings_Obot__class_Obot(tc_fun(U_2694,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_2694),U_2695)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2694),U_2696),U_2695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2694),U_2695)) ),
inference(definitional_conversion,[status(esa)],[f_596_2]) ).
cnf(f_596_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_2694),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2694,tc_HOL_Obool)),U_2695),hAPP(hAPP(c_Set_Oinsert(U_2694),U_2696),c_Orderings_Obot__class_Obot(tc_fun(U_2694,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_2694),U_2695)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2694),U_2696),U_2695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2694),U_2695)) ),
inference(clausify,[status(thm)],[f_596_3]) ).
fof(f_597_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset]) ).
fof(f_597_2,plain,
! [U_2700,U_2699,U_2698,U_2697] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2698,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2697,U_2698,U_2699),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2697,tc_HOL_Obool)),U_2700))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2698,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2697,U_2698,U_2699),U_2700))))
| ~ c_Fun_Oinj__on(U_2697,U_2698,U_2699,c_Orderings_Otop__class_Otop(tc_fun(U_2697,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
fof(f_597_3,plain,
! [U_2697,U_2698,U_2699,U_2700] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2698,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2697,U_2698,U_2699),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2697,tc_HOL_Obool)),U_2700))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2698,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2697,U_2698,U_2699),U_2700))))
| ~ c_Fun_Oinj__on(U_2697,U_2698,U_2699,c_Orderings_Otop__class_Otop(tc_fun(U_2697,tc_HOL_Obool))) ),
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_2698,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2697,U_2698,U_2699),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2697,tc_HOL_Obool)),U_2700))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2698,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2697,U_2698,U_2699),U_2700))))
| ~ c_Fun_Oinj__on(U_2697,U_2698,U_2699,c_Orderings_Otop__class_Otop(tc_fun(U_2697,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_597_3]) ).
fof(f_598_1,plain,
! [V_z_2,V_g_2,V_a_2,V_A_2,T_c,T_d] :
( 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(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_g_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),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__insert]) ).
fof(f_598_2,plain,
! [U_2706,U_2705,U_2704,U_2703,U_2702,U_2701] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_2701,U_2702,c_Groups_Otimes__class_Otimes(U_2701)),U_2705),U_2706),hAPP(hAPP(c_Set_Oinsert(U_2702),U_2704),U_2703)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),hAPP(U_2705,U_2704)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_2701,U_2702,c_Groups_Otimes__class_Otimes(U_2701)),U_2705),U_2706),U_2703))
| hBOOL(hAPP(hAPP(c_member(U_2702),U_2704),U_2703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2702),U_2703))
| ~ class_Groups_Oab__semigroup__mult(U_2701) ),
inference(variable_rename,[status(thm)],[f_598_1]) ).
fof(f_598_3,plain,
! [U_2701,U_2702,U_2703,U_2704,U_2705,U_2706] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_2701,U_2702,c_Groups_Otimes__class_Otimes(U_2701)),U_2705),U_2706),hAPP(hAPP(c_Set_Oinsert(U_2702),U_2704),U_2703)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),hAPP(U_2705,U_2704)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_2701,U_2702,c_Groups_Otimes__class_Otimes(U_2701)),U_2705),U_2706),U_2703))
| hBOOL(hAPP(hAPP(c_member(U_2702),U_2704),U_2703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2702),U_2703))
| ~ class_Groups_Oab__semigroup__mult(U_2701) ),
inference(definitional_conversion,[status(esa)],[f_598_2]) ).
cnf(f_598_4,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_2701,U_2702,c_Groups_Otimes__class_Otimes(U_2701)),U_2705),U_2706),hAPP(hAPP(c_Set_Oinsert(U_2702),U_2704),U_2703)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),hAPP(U_2705,U_2704)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_2701,U_2702,c_Groups_Otimes__class_Otimes(U_2701)),U_2705),U_2706),U_2703))
| hBOOL(hAPP(hAPP(c_member(U_2702),U_2704),U_2703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2702),U_2703))
| ~ class_Groups_Oab__semigroup__mult(U_2701) ),
inference(clausify,[status(thm)],[f_598_3]) ).
fof(f_599_1,plain,
! [V_g_2,V_f_2,V_K_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_K_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_K_2)))
| ? [B_i] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,B_i)),hAPP(V_g_2,B_i)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_K_2)) )
| ~ class_Groups_Oordered__ab__semigroup__add(T_d)
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono]) ).
fof(f_599_2,plain,
! [U_2712,U_2711,U_2710,U_2709,U_2708] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2708),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2709,U_2708),U_2711),U_2710)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2709,U_2708),U_2712),U_2710)))
| ? [U_2707] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2708),hAPP(U_2711,U_2707)),hAPP(U_2712,U_2707)))
& hBOOL(hAPP(hAPP(c_member(U_2709),U_2707),U_2710)) )
| ~ class_Groups_Oordered__ab__semigroup__add(U_2708)
| ~ class_Groups_Ocomm__monoid__add(U_2708) ),
inference(variable_rename,[status(thm)],[f_599_1]) ).
fof(f_599_3,plain,
! [U_2712,U_2711,U_2710,U_2709,U_2708] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2708),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2709,U_2708),U_2711),U_2710)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2709,U_2708),U_2712),U_2710)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2708),hAPP(U_2711,sK66(U_2712,U_2711,U_2710,U_2709,U_2708))),hAPP(U_2712,sK66(U_2712,U_2711,U_2710,U_2709,U_2708))))
& hBOOL(hAPP(hAPP(c_member(U_2709),sK66(U_2712,U_2711,U_2710,U_2709,U_2708)),U_2710)) )
| ~ class_Groups_Oordered__ab__semigroup__add(U_2708)
| ~ class_Groups_Ocomm__monoid__add(U_2708) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_2707,sK66(U_2712,U_2711,U_2710,U_2709,U_2708))],[f_599_2]) ).
fof(f_599_4,plain,
( ! [U_2708,U_2709,U_2710,U_2711,U_2712] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2708),hAPP(U_2711,sK66(U_2712,U_2711,U_2710,U_2709,U_2708))),hAPP(U_2712,sK66(U_2712,U_2711,U_2710,U_2709,U_2708))))
| ~ sP151(U_2708,U_2709,U_2710,U_2711,U_2712) )
& ! [U_2708,U_2709,U_2710,U_2711,U_2712] :
( hBOOL(hAPP(hAPP(c_member(U_2709),sK66(U_2712,U_2711,U_2710,U_2709,U_2708)),U_2710))
| ~ sP151(U_2708,U_2709,U_2710,U_2711,U_2712) )
& ! [U_2708,U_2709,U_2710,U_2711,U_2712] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2708),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2709,U_2708),U_2711),U_2710)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2709,U_2708),U_2712),U_2710)))
| sP151(U_2708,U_2709,U_2710,U_2711,U_2712)
| ~ class_Groups_Oordered__ab__semigroup__add(U_2708)
| ~ class_Groups_Ocomm__monoid__add(U_2708) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP151])],[f_599_3]) ).
cnf(f_599_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2708),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2709,U_2708),U_2711),U_2710)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_2709,U_2708),U_2712),U_2710)))
| sP151(U_2708,U_2709,U_2710,U_2711,U_2712)
| ~ class_Groups_Oordered__ab__semigroup__add(U_2708)
| ~ class_Groups_Ocomm__monoid__add(U_2708) ),
inference(clausify,[status(thm)],[f_599_4]) ).
cnf(f_599_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2709),sK66(U_2712,U_2711,U_2710,U_2709,U_2708)),U_2710))
| ~ sP151(U_2708,U_2709,U_2710,U_2711,U_2712) ),
inference(clausify,[status(thm)],[f_599_4]) ).
cnf(f_599_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2708),hAPP(U_2711,sK66(U_2712,U_2711,U_2710,U_2709,U_2708))),hAPP(U_2712,sK66(U_2712,U_2711,U_2710,U_2709,U_2708))))
| ~ sP151(U_2708,U_2709,U_2710,U_2711,U_2712) ),
inference(clausify,[status(thm)],[f_599_4]) ).
fof(f_600_1,plain,
! [V_B_2,V_A_2,T_c] :
( c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),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_c),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem]) ).
fof(f_600_2,plain,
! [U_2715,U_2714,U_2713] :
( c_Big__Operators_Olattice_OSup__fin(U_2713,c_Orderings_Oord__class_Omax(U_2713),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2713,tc_HOL_Obool)),U_2714),U_2715)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2713),c_Big__Operators_Olattice_OSup__fin(U_2713,c_Orderings_Oord__class_Omax(U_2713),U_2714)),c_Big__Operators_Olattice_OSup__fin(U_2713,c_Orderings_Oord__class_Omax(U_2713),U_2715))
| U_2715 = c_Orderings_Obot__class_Obot(tc_fun(U_2713,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2713),U_2715))
| U_2714 = c_Orderings_Obot__class_Obot(tc_fun(U_2713,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2713),U_2714))
| ~ class_Orderings_Olinorder(U_2713) ),
inference(variable_rename,[status(thm)],[f_600_1]) ).
fof(f_600_3,plain,
! [U_2713,U_2714,U_2715] :
( c_Big__Operators_Olattice_OSup__fin(U_2713,c_Orderings_Oord__class_Omax(U_2713),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2713,tc_HOL_Obool)),U_2714),U_2715)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2713),c_Big__Operators_Olattice_OSup__fin(U_2713,c_Orderings_Oord__class_Omax(U_2713),U_2714)),c_Big__Operators_Olattice_OSup__fin(U_2713,c_Orderings_Oord__class_Omax(U_2713),U_2715))
| U_2715 = c_Orderings_Obot__class_Obot(tc_fun(U_2713,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2713),U_2715))
| U_2714 = c_Orderings_Obot__class_Obot(tc_fun(U_2713,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2713),U_2714))
| ~ class_Orderings_Olinorder(U_2713) ),
inference(definitional_conversion,[status(esa)],[f_600_2]) ).
cnf(f_600_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_2713,c_Orderings_Oord__class_Omax(U_2713),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2713,tc_HOL_Obool)),U_2714),U_2715)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2713),c_Big__Operators_Olattice_OSup__fin(U_2713,c_Orderings_Oord__class_Omax(U_2713),U_2714)),c_Big__Operators_Olattice_OSup__fin(U_2713,c_Orderings_Oord__class_Omax(U_2713),U_2715))
| U_2715 = c_Orderings_Obot__class_Obot(tc_fun(U_2713,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2713),U_2715))
| U_2714 = c_Orderings_Obot__class_Obot(tc_fun(U_2713,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2713),U_2714))
| ~ class_Orderings_Olinorder(U_2713) ),
inference(clausify,[status(thm)],[f_600_3]) ).
fof(f_601_1,plain,
! [V_B_2,V_A_2,T_c] :
( c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),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_c),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem]) ).
fof(f_601_2,plain,
! [U_2718,U_2717,U_2716] :
( c_Big__Operators_Olattice_OInf__fin(U_2716,c_Orderings_Oord__class_Omin(U_2716),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2716,tc_HOL_Obool)),U_2717),U_2718)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2716),c_Big__Operators_Olattice_OInf__fin(U_2716,c_Orderings_Oord__class_Omin(U_2716),U_2717)),c_Big__Operators_Olattice_OInf__fin(U_2716,c_Orderings_Oord__class_Omin(U_2716),U_2718))
| U_2718 = c_Orderings_Obot__class_Obot(tc_fun(U_2716,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2716),U_2718))
| U_2717 = c_Orderings_Obot__class_Obot(tc_fun(U_2716,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2716),U_2717))
| ~ class_Orderings_Olinorder(U_2716) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
fof(f_601_3,plain,
! [U_2718,U_2717,U_2716] :
( c_Big__Operators_Olattice_OInf__fin(U_2716,c_Orderings_Oord__class_Omin(U_2716),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2716,tc_HOL_Obool)),U_2717),U_2718)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2716),c_Big__Operators_Olattice_OInf__fin(U_2716,c_Orderings_Oord__class_Omin(U_2716),U_2717)),c_Big__Operators_Olattice_OInf__fin(U_2716,c_Orderings_Oord__class_Omin(U_2716),U_2718))
| U_2718 = c_Orderings_Obot__class_Obot(tc_fun(U_2716,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2716),U_2718))
| U_2717 = c_Orderings_Obot__class_Obot(tc_fun(U_2716,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2716),U_2717))
| ~ class_Orderings_Olinorder(U_2716) ),
inference(definitional_conversion,[status(esa)],[f_601_2]) ).
cnf(f_601_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_2716,c_Orderings_Oord__class_Omin(U_2716),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2716,tc_HOL_Obool)),U_2717),U_2718)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2716),c_Big__Operators_Olattice_OInf__fin(U_2716,c_Orderings_Oord__class_Omin(U_2716),U_2717)),c_Big__Operators_Olattice_OInf__fin(U_2716,c_Orderings_Oord__class_Omin(U_2716),U_2718))
| U_2718 = c_Orderings_Obot__class_Obot(tc_fun(U_2716,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2716),U_2718))
| U_2717 = c_Orderings_Obot__class_Obot(tc_fun(U_2716,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2716),U_2717))
| ~ class_Orderings_Olinorder(U_2716) ),
inference(clausify,[status(thm)],[f_601_3]) ).
fof(f_602_1,plain,
! [V_B_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_c,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_c),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max__Un]) ).
fof(f_602_2,plain,
! [U_2721,U_2720,U_2719] :
( c_Big__Operators_Olinorder__class_OMax(U_2719,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2719,tc_HOL_Obool)),U_2720),U_2721)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2719),c_Big__Operators_Olinorder__class_OMax(U_2719,U_2720)),c_Big__Operators_Olinorder__class_OMax(U_2719,U_2721))
| U_2721 = c_Orderings_Obot__class_Obot(tc_fun(U_2719,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2719),U_2721))
| U_2720 = c_Orderings_Obot__class_Obot(tc_fun(U_2719,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2719),U_2720))
| ~ class_Orderings_Olinorder(U_2719) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
fof(f_602_3,plain,
! [U_2720,U_2721,U_2719] :
( c_Big__Operators_Olinorder__class_OMax(U_2719,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2719,tc_HOL_Obool)),U_2720),U_2721)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2719),c_Big__Operators_Olinorder__class_OMax(U_2719,U_2720)),c_Big__Operators_Olinorder__class_OMax(U_2719,U_2721))
| U_2721 = c_Orderings_Obot__class_Obot(tc_fun(U_2719,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2719),U_2721))
| U_2720 = c_Orderings_Obot__class_Obot(tc_fun(U_2719,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2719),U_2720))
| ~ class_Orderings_Olinorder(U_2719) ),
inference(definitional_conversion,[status(esa)],[f_602_2]) ).
cnf(f_602_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_2719,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2719,tc_HOL_Obool)),U_2720),U_2721)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2719),c_Big__Operators_Olinorder__class_OMax(U_2719,U_2720)),c_Big__Operators_Olinorder__class_OMax(U_2719,U_2721))
| U_2721 = c_Orderings_Obot__class_Obot(tc_fun(U_2719,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2719),U_2721))
| U_2720 = c_Orderings_Obot__class_Obot(tc_fun(U_2719,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2719),U_2720))
| ~ class_Orderings_Olinorder(U_2719) ),
inference(clausify,[status(thm)],[f_602_3]) ).
fof(f_603_1,plain,
! [V_B_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_c,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_c),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min__Un]) ).
fof(f_603_2,plain,
! [U_2724,U_2723,U_2722] :
( c_Big__Operators_Olinorder__class_OMin(U_2722,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2722,tc_HOL_Obool)),U_2723),U_2724)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2722),c_Big__Operators_Olinorder__class_OMin(U_2722,U_2723)),c_Big__Operators_Olinorder__class_OMin(U_2722,U_2724))
| U_2724 = c_Orderings_Obot__class_Obot(tc_fun(U_2722,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2722),U_2724))
| U_2723 = c_Orderings_Obot__class_Obot(tc_fun(U_2722,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2722),U_2723))
| ~ class_Orderings_Olinorder(U_2722) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
fof(f_603_3,plain,
! [U_2723,U_2724,U_2722] :
( c_Big__Operators_Olinorder__class_OMin(U_2722,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2722,tc_HOL_Obool)),U_2723),U_2724)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2722),c_Big__Operators_Olinorder__class_OMin(U_2722,U_2723)),c_Big__Operators_Olinorder__class_OMin(U_2722,U_2724))
| U_2724 = c_Orderings_Obot__class_Obot(tc_fun(U_2722,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2722),U_2724))
| U_2723 = c_Orderings_Obot__class_Obot(tc_fun(U_2722,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2722),U_2723))
| ~ class_Orderings_Olinorder(U_2722) ),
inference(definitional_conversion,[status(esa)],[f_603_2]) ).
cnf(f_603_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_2722,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2722,tc_HOL_Obool)),U_2723),U_2724)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2722),c_Big__Operators_Olinorder__class_OMin(U_2722,U_2723)),c_Big__Operators_Olinorder__class_OMin(U_2722,U_2724))
| U_2724 = c_Orderings_Obot__class_Obot(tc_fun(U_2722,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2722),U_2724))
| U_2723 = c_Orderings_Obot__class_Obot(tc_fun(U_2722,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2722),U_2723))
| ~ class_Orderings_Olinorder(U_2722) ),
inference(clausify,[status(thm)],[f_603_3]) ).
fof(f_604_1,plain,
! [V_x_2,T_c] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_top1I]) ).
fof(f_604_2,plain,
! [U_2726,U_2725] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_2725,tc_HOL_Obool)),U_2726)),
inference(variable_rename,[status(thm)],[f_604_1]) ).
fof(f_604_3,plain,
! [U_2726,U_2725] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_2725,tc_HOL_Obool)),U_2726)),
inference(definitional_conversion,[status(esa)],[f_604_2]) ).
cnf(f_604_4,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_2725,tc_HOL_Obool)),U_2726)),
inference(clausify,[status(thm)],[f_604_3]) ).
fof(f_605_1,plain,
! [V_x_2,V_B_2,V_A_2,T_c] :
( 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_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup1E]) ).
fof(f_605_2,plain,
! [U_2730,U_2729,U_2728,U_2727] :
( hBOOL(hAPP(U_2729,U_2730))
| hBOOL(hAPP(U_2728,U_2730))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2727,tc_HOL_Obool)),U_2728),U_2729),U_2730)) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
fof(f_605_3,plain,
! [U_2730,U_2729,U_2728] :
( ! [U_2727] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2727,tc_HOL_Obool)),U_2728),U_2729),U_2730))
| hBOOL(hAPP(U_2729,U_2730))
| hBOOL(hAPP(U_2728,U_2730)) ),
inference(miniscope,[status(thm)],[f_605_2]) ).
fof(f_605_4,plain,
! [U_2728,U_2727,U_2729,U_2730] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2727,tc_HOL_Obool)),U_2728),U_2729),U_2730))
| hBOOL(hAPP(U_2729,U_2730))
| hBOOL(hAPP(U_2728,U_2730)) ),
inference(definitional_conversion,[status(esa)],[f_605_3]) ).
cnf(f_605_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2727,tc_HOL_Obool)),U_2728),U_2729),U_2730))
| hBOOL(hAPP(U_2729,U_2730))
| hBOOL(hAPP(U_2728,U_2730)) ),
inference(clausify,[status(thm)],[f_605_4]) ).
fof(f_606_1,plain,
! [T_c,V_A_2,V_x_2,V_B_2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_606_2,plain,
! [U_2734,U_2733,U_2732,U_2731] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2734,tc_HOL_Obool)),U_2733),U_2731),U_2732))
| ( ~ hBOOL(hAPP(U_2733,U_2732))
& ~ hBOOL(hAPP(U_2731,U_2732)) ) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
fof(f_606_3,plain,
( ! [U_2731,U_2732,U_2733] :
( ~ hBOOL(hAPP(U_2733,U_2732))
| ~ sP152(U_2731,U_2732,U_2733) )
& ! [U_2731,U_2732,U_2733] :
( ~ hBOOL(hAPP(U_2731,U_2732))
| ~ sP152(U_2731,U_2732,U_2733) )
& ! [U_2731,U_2732,U_2733,U_2734] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2734,tc_HOL_Obool)),U_2733),U_2731),U_2732))
| sP152(U_2731,U_2732,U_2733) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152])],[f_606_2]) ).
cnf(f_606_4,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2734,tc_HOL_Obool)),U_2733),U_2731),U_2732))
| sP152(U_2731,U_2732,U_2733) ),
inference(clausify,[status(thm)],[f_606_3]) ).
cnf(f_606_5,plain,
( ~ hBOOL(hAPP(U_2731,U_2732))
| ~ sP152(U_2731,U_2732,U_2733) ),
inference(clausify,[status(thm)],[f_606_3]) ).
cnf(f_606_6,plain,
( ~ hBOOL(hAPP(U_2733,U_2732))
| ~ sP152(U_2731,U_2732,U_2733) ),
inference(clausify,[status(thm)],[f_606_3]) ).
fof(f_607_1,plain,
! [V_x_2,T_c] : hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_UNIV__I]) ).
fof(f_607_2,plain,
! [U_2736,U_2735] : hBOOL(hAPP(hAPP(c_member(U_2735),U_2736),c_Orderings_Otop__class_Otop(tc_fun(U_2735,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_607_1]) ).
fof(f_607_3,plain,
! [U_2736,U_2735] : hBOOL(hAPP(hAPP(c_member(U_2735),U_2736),c_Orderings_Otop__class_Otop(tc_fun(U_2735,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_607_2]) ).
cnf(f_607_4,plain,
hBOOL(hAPP(hAPP(c_member(U_2735),U_2736),c_Orderings_Otop__class_Otop(tc_fun(U_2735,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_607_3]) ).
fof(f_608_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_UnE]) ).
fof(f_608_2,plain,
! [U_2740,U_2739,U_2738,U_2737] :
( hBOOL(hAPP(hAPP(c_member(U_2737),U_2738),U_2740))
| hBOOL(hAPP(hAPP(c_member(U_2737),U_2738),U_2739))
| ~ hBOOL(hAPP(hAPP(c_member(U_2737),U_2738),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2737,tc_HOL_Obool)),U_2739),U_2740))) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
fof(f_608_3,plain,
! [U_2737,U_2738,U_2739,U_2740] :
( hBOOL(hAPP(hAPP(c_member(U_2737),U_2738),U_2740))
| hBOOL(hAPP(hAPP(c_member(U_2737),U_2738),U_2739))
| ~ hBOOL(hAPP(hAPP(c_member(U_2737),U_2738),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2737,tc_HOL_Obool)),U_2739),U_2740))) ),
inference(definitional_conversion,[status(esa)],[f_608_2]) ).
cnf(f_608_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2737),U_2738),U_2740))
| hBOOL(hAPP(hAPP(c_member(U_2737),U_2738),U_2739))
| ~ hBOOL(hAPP(hAPP(c_member(U_2737),U_2738),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2737,tc_HOL_Obool)),U_2739),U_2740))) ),
inference(clausify,[status(thm)],[f_608_3]) ).
fof(f_609_1,plain,
! [V_A_2,V_B_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_UnCI]) ).
fof(f_609_2,plain,
! [U_2744,U_2743,U_2742,U_2741] :
( hBOOL(hAPP(hAPP(c_member(U_2741),U_2742),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2741,tc_HOL_Obool)),U_2744),U_2743)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_2741),U_2742),U_2744))
& ~ hBOOL(hAPP(hAPP(c_member(U_2741),U_2742),U_2743)) ) ),
inference(variable_rename,[status(thm)],[f_609_1]) ).
fof(f_609_3,plain,
( ! [U_2741,U_2742,U_2743,U_2744] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2741),U_2742),U_2744))
| ~ sP153(U_2741,U_2742,U_2743,U_2744) )
& ! [U_2741,U_2742,U_2743,U_2744] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2741),U_2742),U_2743))
| ~ sP153(U_2741,U_2742,U_2743,U_2744) )
& ! [U_2741,U_2742,U_2743,U_2744] :
( hBOOL(hAPP(hAPP(c_member(U_2741),U_2742),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2741,tc_HOL_Obool)),U_2744),U_2743)))
| sP153(U_2741,U_2742,U_2743,U_2744) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153])],[f_609_2]) ).
cnf(f_609_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2741),U_2742),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2741,tc_HOL_Obool)),U_2744),U_2743)))
| sP153(U_2741,U_2742,U_2743,U_2744) ),
inference(clausify,[status(thm)],[f_609_3]) ).
cnf(f_609_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2741),U_2742),U_2743))
| ~ sP153(U_2741,U_2742,U_2743,U_2744) ),
inference(clausify,[status(thm)],[f_609_3]) ).
cnf(f_609_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2741),U_2742),U_2744))
| ~ sP153(U_2741,U_2742,U_2743,U_2744) ),
inference(clausify,[status(thm)],[f_609_3]) ).
fof(f_610_1,plain,
! [T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(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_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_c),tc_HOL_Obool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV]) ).
fof(f_610_2,plain,
! [U_2745] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2745)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2745),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2745),c_Orderings_Otop__class_Otop(tc_fun(U_2745,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2745),c_Orderings_Otop__class_Otop(tc_fun(U_2745,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2745)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2745),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
fof(f_610_3,plain,
( ! [U_2747] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2747)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2747),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2747),c_Orderings_Otop__class_Otop(tc_fun(U_2747,tc_HOL_Obool)))) )
& ! [U_2746] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2746),c_Orderings_Otop__class_Otop(tc_fun(U_2746,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2746)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2746),tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_610_2]) ).
fof(f_610_4,plain,
( ! [U_2747] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2747)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2747),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2747),c_Orderings_Otop__class_Otop(tc_fun(U_2747,tc_HOL_Obool)))) )
& ! [U_2746] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2746),c_Orderings_Otop__class_Otop(tc_fun(U_2746,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2746)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2746),tc_HOL_Obool)))) ) ),
inference(definitional_conversion,[status(esa)],[f_610_3]) ).
cnf(f_610_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2746),c_Orderings_Otop__class_Otop(tc_fun(U_2746,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2746)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2746),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_610_4]) ).
cnf(f_610_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2747)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2747),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2747),c_Orderings_Otop__class_Otop(tc_fun(U_2747,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_610_4]) ).
fof(f_611_1,plain,
! [T_d,T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_c,T_d),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,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_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,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_sum(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_c,T_d),tc_HOL_Obool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Plus__UNIV__iff]) ).
fof(f_611_2,plain,
! [U_2749,U_2748] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2748,U_2749)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2748,U_2749),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2749),c_Orderings_Otop__class_Otop(tc_fun(U_2749,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2748),c_Orderings_Otop__class_Otop(tc_fun(U_2748,tc_HOL_Obool)))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2749),c_Orderings_Otop__class_Otop(tc_fun(U_2749,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2748),c_Orderings_Otop__class_Otop(tc_fun(U_2748,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2748,U_2749)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2748,U_2749),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
fof(f_611_3,plain,
( ! [U_2753,U_2751] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2751,U_2753)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2751,U_2753),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2753),c_Orderings_Otop__class_Otop(tc_fun(U_2753,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2751),c_Orderings_Otop__class_Otop(tc_fun(U_2751,tc_HOL_Obool)))) )
& ! [U_2752,U_2750] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2752),c_Orderings_Otop__class_Otop(tc_fun(U_2752,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2750),c_Orderings_Otop__class_Otop(tc_fun(U_2750,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2750,U_2752)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2750,U_2752),tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_611_2]) ).
fof(f_611_4,plain,
( ! [U_2752,U_2750] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2752),c_Orderings_Otop__class_Otop(tc_fun(U_2752,tc_HOL_Obool))))
| ~ sP154(U_2752,U_2750) )
& ! [U_2752,U_2750] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2750),c_Orderings_Otop__class_Otop(tc_fun(U_2750,tc_HOL_Obool))))
| ~ sP154(U_2752,U_2750) )
& ! [U_2751,U_2753] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2751,U_2753)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2751,U_2753),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2753),c_Orderings_Otop__class_Otop(tc_fun(U_2753,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2751),c_Orderings_Otop__class_Otop(tc_fun(U_2751,tc_HOL_Obool)))) )
& ! [U_2752,U_2750] :
( sP154(U_2752,U_2750)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2750,U_2752)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2750,U_2752),tc_HOL_Obool)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP154])],[f_611_3]) ).
cnf(f_611_5,plain,
( sP154(U_2752,U_2750)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2750,U_2752)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2750,U_2752),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_611_4]) ).
cnf(f_611_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2751,U_2753)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2751,U_2753),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2753),c_Orderings_Otop__class_Otop(tc_fun(U_2753,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2751),c_Orderings_Otop__class_Otop(tc_fun(U_2751,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_611_4]) ).
cnf(f_611_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2750),c_Orderings_Otop__class_Otop(tc_fun(U_2750,tc_HOL_Obool))))
| ~ sP154(U_2752,U_2750) ),
inference(clausify,[status(thm)],[f_611_4]) ).
cnf(f_611_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2752),c_Orderings_Otop__class_Otop(tc_fun(U_2752,tc_HOL_Obool))))
| ~ sP154(U_2752,U_2750) ),
inference(clausify,[status(thm)],[f_611_4]) ).
fof(f_612_1,plain,
! [T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV]) ).
fof(f_612_2,plain,
! [U_2755,U_2754] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_2754,U_2755)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_2754,U_2755),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2755),c_Orderings_Otop__class_Otop(tc_fun(U_2755,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2754),c_Orderings_Otop__class_Otop(tc_fun(U_2754,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
fof(f_612_3,plain,
! [U_2754,U_2755] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_2754,U_2755)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_2754,U_2755),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2755),c_Orderings_Otop__class_Otop(tc_fun(U_2755,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2754),c_Orderings_Otop__class_Otop(tc_fun(U_2754,tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_612_2]) ).
cnf(f_612_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_2754,U_2755)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_2754,U_2755),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2755),c_Orderings_Otop__class_Otop(tc_fun(U_2755,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2754),c_Orderings_Otop__class_Otop(tc_fun(U_2754,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_612_3]) ).
fof(f_613_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_613_2,plain,
! [U_2757,U_2756] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2756),U_2757),U_2757) = U_2757
| ~ class_Lattices_Olattice(U_2756) ),
inference(variable_rename,[status(thm)],[f_613_1]) ).
fof(f_613_3,plain,
! [U_2757,U_2756] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2756),U_2757),U_2757) = U_2757
| ~ class_Lattices_Olattice(U_2756) ),
inference(definitional_conversion,[status(esa)],[f_613_2]) ).
cnf(f_613_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2756),U_2757),U_2757) = U_2757
| ~ class_Lattices_Olattice(U_2756) ),
inference(clausify,[status(thm)],[f_613_3]) ).
fof(f_614_1,plain,
! [V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Un__UNIV__left]) ).
fof(f_614_2,plain,
! [U_2759,U_2758] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2758,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_2758,tc_HOL_Obool))),U_2759) = c_Orderings_Otop__class_Otop(tc_fun(U_2758,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_614_1]) ).
fof(f_614_3,plain,
! [U_2758,U_2759] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2758,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_2758,tc_HOL_Obool))),U_2759) = c_Orderings_Otop__class_Otop(tc_fun(U_2758,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_614_2]) ).
cnf(f_614_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2758,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_2758,tc_HOL_Obool))),U_2759) = c_Orderings_Otop__class_Otop(tc_fun(U_2758,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_614_3]) ).
fof(f_615_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Un__UNIV__right]) ).
fof(f_615_2,plain,
! [U_2761,U_2760] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2760,tc_HOL_Obool)),U_2761),c_Orderings_Otop__class_Otop(tc_fun(U_2760,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_2760,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_615_1]) ).
fof(f_615_3,plain,
! [U_2760,U_2761] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2760,tc_HOL_Obool)),U_2761),c_Orderings_Otop__class_Otop(tc_fun(U_2760,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_2760,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_615_2]) ).
cnf(f_615_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2760,tc_HOL_Obool)),U_2761),c_Orderings_Otop__class_Otop(tc_fun(U_2760,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_2760,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_615_3]) ).
fof(f_616_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Un__absorb]) ).
fof(f_616_2,plain,
! [U_2763,U_2762] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2762,tc_HOL_Obool)),U_2763),U_2763) = U_2763,
inference(variable_rename,[status(thm)],[f_616_1]) ).
fof(f_616_3,plain,
! [U_2763,U_2762] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2762,tc_HOL_Obool)),U_2763),U_2763) = U_2763,
inference(definitional_conversion,[status(esa)],[f_616_2]) ).
cnf(f_616_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2762,tc_HOL_Obool)),U_2763),U_2763) = U_2763,
inference(clausify,[status(thm)],[f_616_3]) ).
fof(f_617_1,plain,
! [V_B_2,V_A_2,T_c] : 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_c,tc_HOL_Obool)),V_B_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_Un__commute]) ).
fof(f_617_2,plain,
! [U_2766,U_2765,U_2764] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2764,tc_HOL_Obool)),U_2765),U_2766) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2764,tc_HOL_Obool)),U_2766),U_2765),
inference(variable_rename,[status(thm)],[f_617_1]) ).
fof(f_617_3,plain,
! [U_2764,U_2765,U_2766] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2764,tc_HOL_Obool)),U_2765),U_2766) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2764,tc_HOL_Obool)),U_2766),U_2765),
inference(definitional_conversion,[status(esa)],[f_617_2]) ).
cnf(f_617_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2764,tc_HOL_Obool)),U_2765),U_2766) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2764,tc_HOL_Obool)),U_2766),U_2765),
inference(clausify,[status(thm)],[f_617_3]) ).
fof(f_618_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_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_c,tc_HOL_Obool)),V_A_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Un__left__absorb]) ).
fof(f_618_2,plain,
! [U_2769,U_2768,U_2767] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2767,tc_HOL_Obool)),U_2768),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2767,tc_HOL_Obool)),U_2768),U_2769)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2767,tc_HOL_Obool)),U_2768),U_2769),
inference(variable_rename,[status(thm)],[f_618_1]) ).
fof(f_618_3,plain,
! [U_2767,U_2768,U_2769] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2767,tc_HOL_Obool)),U_2768),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2767,tc_HOL_Obool)),U_2768),U_2769)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2767,tc_HOL_Obool)),U_2768),U_2769),
inference(definitional_conversion,[status(esa)],[f_618_2]) ).
cnf(f_618_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2767,tc_HOL_Obool)),U_2768),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2767,tc_HOL_Obool)),U_2768),U_2769)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2767,tc_HOL_Obool)),U_2768),U_2769),
inference(clausify,[status(thm)],[f_618_3]) ).
fof(f_619_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Un__left__commute]) ).
fof(f_619_2,plain,
! [U_2773,U_2772,U_2771,U_2770] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2770,tc_HOL_Obool)),U_2771),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2770,tc_HOL_Obool)),U_2772),U_2773)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2770,tc_HOL_Obool)),U_2772),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2770,tc_HOL_Obool)),U_2771),U_2773)),
inference(variable_rename,[status(thm)],[f_619_1]) ).
fof(f_619_3,plain,
! [U_2770,U_2771,U_2772,U_2773] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2770,tc_HOL_Obool)),U_2771),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2770,tc_HOL_Obool)),U_2772),U_2773)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2770,tc_HOL_Obool)),U_2772),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2770,tc_HOL_Obool)),U_2771),U_2773)),
inference(definitional_conversion,[status(esa)],[f_619_2]) ).
cnf(f_619_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2770,tc_HOL_Obool)),U_2771),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2770,tc_HOL_Obool)),U_2772),U_2773)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2770,tc_HOL_Obool)),U_2772),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2770,tc_HOL_Obool)),U_2771),U_2773)),
inference(clausify,[status(thm)],[f_619_3]) ).
fof(f_620_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Un__assoc]) ).
fof(f_620_2,plain,
! [U_2777,U_2776,U_2775,U_2774] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2774,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2774,tc_HOL_Obool)),U_2775),U_2776)),U_2777) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2774,tc_HOL_Obool)),U_2775),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2774,tc_HOL_Obool)),U_2776),U_2777)),
inference(variable_rename,[status(thm)],[f_620_1]) ).
fof(f_620_3,plain,
! [U_2774,U_2775,U_2776,U_2777] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2774,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2774,tc_HOL_Obool)),U_2775),U_2776)),U_2777) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2774,tc_HOL_Obool)),U_2775),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2774,tc_HOL_Obool)),U_2776),U_2777)),
inference(definitional_conversion,[status(esa)],[f_620_2]) ).
cnf(f_620_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2774,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2774,tc_HOL_Obool)),U_2775),U_2776)),U_2777) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2774,tc_HOL_Obool)),U_2775),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2774,tc_HOL_Obool)),U_2776),U_2777)),
inference(clausify,[status(thm)],[f_620_3]) ).
fof(f_621_1,plain,
! [V_Pa_2,V_B_2,V_A_2,T_c] :
( ( ? [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ( ! [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_B_2)) )
& ! [B_x] :
( ~ hBOOL(hAPP(V_Pa_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_c),B_x),V_B_2)) )
| ? [B_x] :
( hBOOL(hAPP(V_Pa_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_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_bex__Un]) ).
fof(f_621_2,plain,
! [U_2787,U_2786,U_2785,U_2784] :
( ( ? [U_2783] :
( hBOOL(hAPP(U_2787,U_2783))
& hBOOL(hAPP(hAPP(c_member(U_2784),U_2783),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2784,tc_HOL_Obool)),U_2785),U_2786))) )
| ( ! [U_2782] :
( ~ hBOOL(hAPP(U_2787,U_2782))
| ~ hBOOL(hAPP(hAPP(c_member(U_2784),U_2782),U_2786)) )
& ! [U_2781] :
( ~ hBOOL(hAPP(U_2787,U_2781))
| ~ hBOOL(hAPP(hAPP(c_member(U_2784),U_2781),U_2785)) ) ) )
& ( ? [U_2780] :
( hBOOL(hAPP(U_2787,U_2780))
& hBOOL(hAPP(hAPP(c_member(U_2784),U_2780),U_2786)) )
| ? [U_2779] :
( hBOOL(hAPP(U_2787,U_2779))
& hBOOL(hAPP(hAPP(c_member(U_2784),U_2779),U_2785)) )
| ! [U_2778] :
( ~ hBOOL(hAPP(U_2787,U_2778))
| ~ hBOOL(hAPP(hAPP(c_member(U_2784),U_2778),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2784,tc_HOL_Obool)),U_2785),U_2786))) ) ) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
fof(f_621_3,plain,
( ! [U_2795,U_2793,U_2791,U_2789] :
( ? [U_2783] :
( hBOOL(hAPP(U_2795,U_2783))
& hBOOL(hAPP(hAPP(c_member(U_2789),U_2783),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2789,tc_HOL_Obool)),U_2791),U_2793))) )
| ( ! [U_2782] :
( ~ hBOOL(hAPP(U_2795,U_2782))
| ~ hBOOL(hAPP(hAPP(c_member(U_2789),U_2782),U_2793)) )
& ! [U_2781] :
( ~ hBOOL(hAPP(U_2795,U_2781))
| ~ hBOOL(hAPP(hAPP(c_member(U_2789),U_2781),U_2791)) ) ) )
& ! [U_2794,U_2792,U_2790,U_2788] :
( ? [U_2780] :
( hBOOL(hAPP(U_2794,U_2780))
& hBOOL(hAPP(hAPP(c_member(U_2788),U_2780),U_2792)) )
| ? [U_2779] :
( hBOOL(hAPP(U_2794,U_2779))
& hBOOL(hAPP(hAPP(c_member(U_2788),U_2779),U_2790)) )
| ! [U_2778] :
( ~ hBOOL(hAPP(U_2794,U_2778))
| ~ hBOOL(hAPP(hAPP(c_member(U_2788),U_2778),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2788,tc_HOL_Obool)),U_2790),U_2792))) ) ) ),
inference(miniscope,[status(thm)],[f_621_2]) ).
fof(f_621_4,plain,
( ! [U_2795,U_2793,U_2791,U_2789] :
( ? [U_2783] :
( hBOOL(hAPP(U_2795,U_2783))
& hBOOL(hAPP(hAPP(c_member(U_2789),U_2783),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2789,tc_HOL_Obool)),U_2791),U_2793))) )
| ( ! [U_2782] :
( ~ hBOOL(hAPP(U_2795,U_2782))
| ~ hBOOL(hAPP(hAPP(c_member(U_2789),U_2782),U_2793)) )
& ! [U_2781] :
( ~ hBOOL(hAPP(U_2795,U_2781))
| ~ hBOOL(hAPP(hAPP(c_member(U_2789),U_2781),U_2791)) ) ) )
& ! [U_2794,U_2792,U_2790,U_2788] :
( ? [U_2780] :
( hBOOL(hAPP(U_2794,U_2780))
& hBOOL(hAPP(hAPP(c_member(U_2788),U_2780),U_2792)) )
| ( hBOOL(hAPP(U_2794,sK67(U_2794,U_2792,U_2790,U_2788)))
& hBOOL(hAPP(hAPP(c_member(U_2788),sK67(U_2794,U_2792,U_2790,U_2788)),U_2790)) )
| ! [U_2778] :
( ~ hBOOL(hAPP(U_2794,U_2778))
| ~ hBOOL(hAPP(hAPP(c_member(U_2788),U_2778),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2788,tc_HOL_Obool)),U_2790),U_2792))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_2779,sK67(U_2794,U_2792,U_2790,U_2788))],[f_621_3]) ).
fof(f_621_5,plain,
( ! [U_2795,U_2793,U_2791,U_2789] :
( ? [U_2783] :
( hBOOL(hAPP(U_2795,U_2783))
& hBOOL(hAPP(hAPP(c_member(U_2789),U_2783),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2789,tc_HOL_Obool)),U_2791),U_2793))) )
| ( ! [U_2782] :
( ~ hBOOL(hAPP(U_2795,U_2782))
| ~ hBOOL(hAPP(hAPP(c_member(U_2789),U_2782),U_2793)) )
& ! [U_2781] :
( ~ hBOOL(hAPP(U_2795,U_2781))
| ~ hBOOL(hAPP(hAPP(c_member(U_2789),U_2781),U_2791)) ) ) )
& ! [U_2794,U_2792,U_2790,U_2788] :
( ( hBOOL(hAPP(U_2794,sK68(U_2794,U_2792,U_2790,U_2788)))
& hBOOL(hAPP(hAPP(c_member(U_2788),sK68(U_2794,U_2792,U_2790,U_2788)),U_2792)) )
| ( hBOOL(hAPP(U_2794,sK67(U_2794,U_2792,U_2790,U_2788)))
& hBOOL(hAPP(hAPP(c_member(U_2788),sK67(U_2794,U_2792,U_2790,U_2788)),U_2790)) )
| ! [U_2778] :
( ~ hBOOL(hAPP(U_2794,U_2778))
| ~ hBOOL(hAPP(hAPP(c_member(U_2788),U_2778),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2788,tc_HOL_Obool)),U_2790),U_2792))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_2780,sK68(U_2794,U_2792,U_2790,U_2788))],[f_621_4]) ).
fof(f_621_6,plain,
( ! [U_2795,U_2793,U_2791,U_2789] :
( ( hBOOL(hAPP(U_2795,sK69(U_2795,U_2793,U_2791,U_2789)))
& hBOOL(hAPP(hAPP(c_member(U_2789),sK69(U_2795,U_2793,U_2791,U_2789)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2789,tc_HOL_Obool)),U_2791),U_2793))) )
| ( ! [U_2782] :
( ~ hBOOL(hAPP(U_2795,U_2782))
| ~ hBOOL(hAPP(hAPP(c_member(U_2789),U_2782),U_2793)) )
& ! [U_2781] :
( ~ hBOOL(hAPP(U_2795,U_2781))
| ~ hBOOL(hAPP(hAPP(c_member(U_2789),U_2781),U_2791)) ) ) )
& ! [U_2794,U_2792,U_2790,U_2788] :
( ( hBOOL(hAPP(U_2794,sK68(U_2794,U_2792,U_2790,U_2788)))
& hBOOL(hAPP(hAPP(c_member(U_2788),sK68(U_2794,U_2792,U_2790,U_2788)),U_2792)) )
| ( hBOOL(hAPP(U_2794,sK67(U_2794,U_2792,U_2790,U_2788)))
& hBOOL(hAPP(hAPP(c_member(U_2788),sK67(U_2794,U_2792,U_2790,U_2788)),U_2790)) )
| ! [U_2778] :
( ~ hBOOL(hAPP(U_2794,U_2778))
| ~ hBOOL(hAPP(hAPP(c_member(U_2788),U_2778),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2788,tc_HOL_Obool)),U_2790),U_2792))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_2783,sK69(U_2795,U_2793,U_2791,U_2789))],[f_621_5]) ).
fof(f_621_7,plain,
( ! [U_2789,U_2793,U_2791,U_2795] :
( hBOOL(hAPP(U_2795,sK69(U_2795,U_2793,U_2791,U_2789)))
| ~ sP158(U_2789,U_2793,U_2791,U_2795) )
& ! [U_2789,U_2793,U_2791,U_2795] :
( hBOOL(hAPP(hAPP(c_member(U_2789),sK69(U_2795,U_2793,U_2791,U_2789)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2789,tc_HOL_Obool)),U_2791),U_2793)))
| ~ sP158(U_2789,U_2793,U_2791,U_2795) )
& ! [U_2789,U_2781,U_2782,U_2793,U_2791,U_2795] :
( ~ hBOOL(hAPP(U_2795,U_2782))
| ~ hBOOL(hAPP(hAPP(c_member(U_2789),U_2782),U_2793))
| ~ sP157(U_2789,U_2781,U_2782,U_2793,U_2791,U_2795) )
& ! [U_2789,U_2781,U_2782,U_2793,U_2791,U_2795] :
( ~ hBOOL(hAPP(U_2795,U_2781))
| ~ hBOOL(hAPP(hAPP(c_member(U_2789),U_2781),U_2791))
| ~ sP157(U_2789,U_2781,U_2782,U_2793,U_2791,U_2795) )
& ! [U_2788,U_2792,U_2794,U_2790] :
( hBOOL(hAPP(U_2794,sK68(U_2794,U_2792,U_2790,U_2788)))
| ~ sP156(U_2788,U_2792,U_2794,U_2790) )
& ! [U_2788,U_2792,U_2794,U_2790] :
( hBOOL(hAPP(hAPP(c_member(U_2788),sK68(U_2794,U_2792,U_2790,U_2788)),U_2792))
| ~ sP156(U_2788,U_2792,U_2794,U_2790) )
& ! [U_2788,U_2792,U_2794,U_2790] :
( hBOOL(hAPP(U_2794,sK67(U_2794,U_2792,U_2790,U_2788)))
| ~ sP155(U_2788,U_2792,U_2794,U_2790) )
& ! [U_2788,U_2792,U_2794,U_2790] :
( hBOOL(hAPP(hAPP(c_member(U_2788),sK67(U_2794,U_2792,U_2790,U_2788)),U_2790))
| ~ sP155(U_2788,U_2792,U_2794,U_2790) )
& ! [U_2789,U_2781,U_2782,U_2793,U_2791,U_2795] :
( sP158(U_2789,U_2793,U_2791,U_2795)
| sP157(U_2789,U_2781,U_2782,U_2793,U_2791,U_2795) )
& ! [U_2778,U_2788,U_2792,U_2794,U_2790] :
( sP156(U_2788,U_2792,U_2794,U_2790)
| sP155(U_2788,U_2792,U_2794,U_2790)
| ~ hBOOL(hAPP(U_2794,U_2778))
| ~ hBOOL(hAPP(hAPP(c_member(U_2788),U_2778),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2788,tc_HOL_Obool)),U_2790),U_2792))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155,sP156,sP157,sP158])],[f_621_6]) ).
cnf(f_621_8,plain,
( sP156(U_2788,U_2792,U_2794,U_2790)
| sP155(U_2788,U_2792,U_2794,U_2790)
| ~ hBOOL(hAPP(U_2794,U_2778))
| ~ hBOOL(hAPP(hAPP(c_member(U_2788),U_2778),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2788,tc_HOL_Obool)),U_2790),U_2792))) ),
inference(clausify,[status(thm)],[f_621_7]) ).
cnf(f_621_9,plain,
( sP158(U_2789,U_2793,U_2791,U_2795)
| sP157(U_2789,U_2781,U_2782,U_2793,U_2791,U_2795) ),
inference(clausify,[status(thm)],[f_621_7]) ).
cnf(f_621_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_2788),sK67(U_2794,U_2792,U_2790,U_2788)),U_2790))
| ~ sP155(U_2788,U_2792,U_2794,U_2790) ),
inference(clausify,[status(thm)],[f_621_7]) ).
cnf(f_621_11,plain,
( hBOOL(hAPP(U_2794,sK67(U_2794,U_2792,U_2790,U_2788)))
| ~ sP155(U_2788,U_2792,U_2794,U_2790) ),
inference(clausify,[status(thm)],[f_621_7]) ).
cnf(f_621_12,plain,
( hBOOL(hAPP(hAPP(c_member(U_2788),sK68(U_2794,U_2792,U_2790,U_2788)),U_2792))
| ~ sP156(U_2788,U_2792,U_2794,U_2790) ),
inference(clausify,[status(thm)],[f_621_7]) ).
cnf(f_621_13,plain,
( hBOOL(hAPP(U_2794,sK68(U_2794,U_2792,U_2790,U_2788)))
| ~ sP156(U_2788,U_2792,U_2794,U_2790) ),
inference(clausify,[status(thm)],[f_621_7]) ).
cnf(f_621_14,plain,
( ~ hBOOL(hAPP(U_2795,U_2781))
| ~ hBOOL(hAPP(hAPP(c_member(U_2789),U_2781),U_2791))
| ~ sP157(U_2789,U_2781,U_2782,U_2793,U_2791,U_2795) ),
inference(clausify,[status(thm)],[f_621_7]) ).
cnf(f_621_15,plain,
( ~ hBOOL(hAPP(U_2795,U_2782))
| ~ hBOOL(hAPP(hAPP(c_member(U_2789),U_2782),U_2793))
| ~ sP157(U_2789,U_2781,U_2782,U_2793,U_2791,U_2795) ),
inference(clausify,[status(thm)],[f_621_7]) ).
cnf(f_621_16,plain,
( hBOOL(hAPP(hAPP(c_member(U_2789),sK69(U_2795,U_2793,U_2791,U_2789)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2789,tc_HOL_Obool)),U_2791),U_2793)))
| ~ sP158(U_2789,U_2793,U_2791,U_2795) ),
inference(clausify,[status(thm)],[f_621_7]) ).
cnf(f_621_17,plain,
( hBOOL(hAPP(U_2795,sK69(U_2795,U_2793,U_2791,U_2789)))
| ~ sP158(U_2789,U_2793,U_2791,U_2795) ),
inference(clausify,[status(thm)],[f_621_7]) ).
fof(f_622_1,plain,
! [V_Pa_2,V_B_2,V_A_2,T_c] :
( ( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_B_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_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_c),B_x),V_B_2)) )
& ! [B_x] :
( hBOOL(hAPP(V_Pa_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_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ball__Un]) ).
fof(f_622_2,plain,
! [U_2805,U_2804,U_2803,U_2802] :
( ( ! [U_2801] :
( hBOOL(hAPP(U_2805,U_2801))
| ~ hBOOL(hAPP(hAPP(c_member(U_2802),U_2801),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2802,tc_HOL_Obool)),U_2803),U_2804))) )
| ? [U_2800] :
( ~ hBOOL(hAPP(U_2805,U_2800))
& hBOOL(hAPP(hAPP(c_member(U_2802),U_2800),U_2804)) )
| ? [U_2799] :
( ~ hBOOL(hAPP(U_2805,U_2799))
& hBOOL(hAPP(hAPP(c_member(U_2802),U_2799),U_2803)) ) )
& ( ( ! [U_2798] :
( hBOOL(hAPP(U_2805,U_2798))
| ~ hBOOL(hAPP(hAPP(c_member(U_2802),U_2798),U_2804)) )
& ! [U_2797] :
( hBOOL(hAPP(U_2805,U_2797))
| ~ hBOOL(hAPP(hAPP(c_member(U_2802),U_2797),U_2803)) ) )
| ? [U_2796] :
( ~ hBOOL(hAPP(U_2805,U_2796))
& hBOOL(hAPP(hAPP(c_member(U_2802),U_2796),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2802,tc_HOL_Obool)),U_2803),U_2804))) ) ) ),
inference(variable_rename,[status(thm)],[f_622_1]) ).
fof(f_622_3,plain,
( ! [U_2813,U_2811,U_2809,U_2807] :
( ! [U_2801] :
( hBOOL(hAPP(U_2813,U_2801))
| ~ hBOOL(hAPP(hAPP(c_member(U_2807),U_2801),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2807,tc_HOL_Obool)),U_2809),U_2811))) )
| ? [U_2800] :
( ~ hBOOL(hAPP(U_2813,U_2800))
& hBOOL(hAPP(hAPP(c_member(U_2807),U_2800),U_2811)) )
| ? [U_2799] :
( ~ hBOOL(hAPP(U_2813,U_2799))
& hBOOL(hAPP(hAPP(c_member(U_2807),U_2799),U_2809)) ) )
& ! [U_2812,U_2810,U_2808,U_2806] :
( ( ! [U_2798] :
( hBOOL(hAPP(U_2812,U_2798))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2798),U_2810)) )
& ! [U_2797] :
( hBOOL(hAPP(U_2812,U_2797))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2797),U_2808)) ) )
| ? [U_2796] :
( ~ hBOOL(hAPP(U_2812,U_2796))
& hBOOL(hAPP(hAPP(c_member(U_2806),U_2796),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2806,tc_HOL_Obool)),U_2808),U_2810))) ) ) ),
inference(miniscope,[status(thm)],[f_622_2]) ).
fof(f_622_4,plain,
( ! [U_2813,U_2811,U_2809,U_2807] :
( ! [U_2801] :
( hBOOL(hAPP(U_2813,U_2801))
| ~ hBOOL(hAPP(hAPP(c_member(U_2807),U_2801),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2807,tc_HOL_Obool)),U_2809),U_2811))) )
| ? [U_2800] :
( ~ hBOOL(hAPP(U_2813,U_2800))
& hBOOL(hAPP(hAPP(c_member(U_2807),U_2800),U_2811)) )
| ? [U_2799] :
( ~ hBOOL(hAPP(U_2813,U_2799))
& hBOOL(hAPP(hAPP(c_member(U_2807),U_2799),U_2809)) ) )
& ! [U_2812,U_2810,U_2808,U_2806] :
( ( ! [U_2798] :
( hBOOL(hAPP(U_2812,U_2798))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2798),U_2810)) )
& ! [U_2797] :
( hBOOL(hAPP(U_2812,U_2797))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2797),U_2808)) ) )
| ( ~ hBOOL(hAPP(U_2812,sK70(U_2812,U_2810,U_2808,U_2806)))
& hBOOL(hAPP(hAPP(c_member(U_2806),sK70(U_2812,U_2810,U_2808,U_2806)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2806,tc_HOL_Obool)),U_2808),U_2810))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_2796,sK70(U_2812,U_2810,U_2808,U_2806))],[f_622_3]) ).
fof(f_622_5,plain,
( ! [U_2813,U_2811,U_2809,U_2807] :
( ! [U_2801] :
( hBOOL(hAPP(U_2813,U_2801))
| ~ hBOOL(hAPP(hAPP(c_member(U_2807),U_2801),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2807,tc_HOL_Obool)),U_2809),U_2811))) )
| ? [U_2800] :
( ~ hBOOL(hAPP(U_2813,U_2800))
& hBOOL(hAPP(hAPP(c_member(U_2807),U_2800),U_2811)) )
| ( ~ hBOOL(hAPP(U_2813,sK71(U_2813,U_2811,U_2809,U_2807)))
& hBOOL(hAPP(hAPP(c_member(U_2807),sK71(U_2813,U_2811,U_2809,U_2807)),U_2809)) ) )
& ! [U_2812,U_2810,U_2808,U_2806] :
( ( ! [U_2798] :
( hBOOL(hAPP(U_2812,U_2798))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2798),U_2810)) )
& ! [U_2797] :
( hBOOL(hAPP(U_2812,U_2797))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2797),U_2808)) ) )
| ( ~ hBOOL(hAPP(U_2812,sK70(U_2812,U_2810,U_2808,U_2806)))
& hBOOL(hAPP(hAPP(c_member(U_2806),sK70(U_2812,U_2810,U_2808,U_2806)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2806,tc_HOL_Obool)),U_2808),U_2810))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_2799,sK71(U_2813,U_2811,U_2809,U_2807))],[f_622_4]) ).
fof(f_622_6,plain,
( ! [U_2813,U_2811,U_2809,U_2807] :
( ! [U_2801] :
( hBOOL(hAPP(U_2813,U_2801))
| ~ hBOOL(hAPP(hAPP(c_member(U_2807),U_2801),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2807,tc_HOL_Obool)),U_2809),U_2811))) )
| ( ~ hBOOL(hAPP(U_2813,sK72(U_2813,U_2811,U_2809,U_2807)))
& hBOOL(hAPP(hAPP(c_member(U_2807),sK72(U_2813,U_2811,U_2809,U_2807)),U_2811)) )
| ( ~ hBOOL(hAPP(U_2813,sK71(U_2813,U_2811,U_2809,U_2807)))
& hBOOL(hAPP(hAPP(c_member(U_2807),sK71(U_2813,U_2811,U_2809,U_2807)),U_2809)) ) )
& ! [U_2812,U_2810,U_2808,U_2806] :
( ( ! [U_2798] :
( hBOOL(hAPP(U_2812,U_2798))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2798),U_2810)) )
& ! [U_2797] :
( hBOOL(hAPP(U_2812,U_2797))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2797),U_2808)) ) )
| ( ~ hBOOL(hAPP(U_2812,sK70(U_2812,U_2810,U_2808,U_2806)))
& hBOOL(hAPP(hAPP(c_member(U_2806),sK70(U_2812,U_2810,U_2808,U_2806)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2806,tc_HOL_Obool)),U_2808),U_2810))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_2800,sK72(U_2813,U_2811,U_2809,U_2807))],[f_622_5]) ).
fof(f_622_7,plain,
( ! [U_2811,U_2807,U_2809,U_2813] :
( ~ hBOOL(hAPP(U_2813,sK72(U_2813,U_2811,U_2809,U_2807)))
| ~ sP162(U_2811,U_2807,U_2809,U_2813) )
& ! [U_2811,U_2807,U_2809,U_2813] :
( hBOOL(hAPP(hAPP(c_member(U_2807),sK72(U_2813,U_2811,U_2809,U_2807)),U_2811))
| ~ sP162(U_2811,U_2807,U_2809,U_2813) )
& ! [U_2811,U_2807,U_2809,U_2813] :
( ~ hBOOL(hAPP(U_2813,sK71(U_2813,U_2811,U_2809,U_2807)))
| ~ sP161(U_2811,U_2807,U_2809,U_2813) )
& ! [U_2811,U_2807,U_2809,U_2813] :
( hBOOL(hAPP(hAPP(c_member(U_2807),sK71(U_2813,U_2811,U_2809,U_2807)),U_2809))
| ~ sP161(U_2811,U_2807,U_2809,U_2813) )
& ! [U_2797,U_2798,U_2806,U_2810,U_2808,U_2812] :
( hBOOL(hAPP(U_2812,U_2798))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2798),U_2810))
| ~ sP160(U_2797,U_2798,U_2806,U_2810,U_2808,U_2812) )
& ! [U_2797,U_2798,U_2806,U_2810,U_2808,U_2812] :
( hBOOL(hAPP(U_2812,U_2797))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2797),U_2808))
| ~ sP160(U_2797,U_2798,U_2806,U_2810,U_2808,U_2812) )
& ! [U_2806,U_2810,U_2808,U_2812] :
( ~ hBOOL(hAPP(U_2812,sK70(U_2812,U_2810,U_2808,U_2806)))
| ~ sP159(U_2806,U_2810,U_2808,U_2812) )
& ! [U_2806,U_2810,U_2808,U_2812] :
( hBOOL(hAPP(hAPP(c_member(U_2806),sK70(U_2812,U_2810,U_2808,U_2806)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2806,tc_HOL_Obool)),U_2808),U_2810)))
| ~ sP159(U_2806,U_2810,U_2808,U_2812) )
& ! [U_2811,U_2801,U_2807,U_2809,U_2813] :
( hBOOL(hAPP(U_2813,U_2801))
| ~ hBOOL(hAPP(hAPP(c_member(U_2807),U_2801),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2807,tc_HOL_Obool)),U_2809),U_2811)))
| sP162(U_2811,U_2807,U_2809,U_2813)
| sP161(U_2811,U_2807,U_2809,U_2813) )
& ! [U_2797,U_2798,U_2806,U_2810,U_2808,U_2812] :
( sP160(U_2797,U_2798,U_2806,U_2810,U_2808,U_2812)
| sP159(U_2806,U_2810,U_2808,U_2812) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP159,sP160,sP161,sP162])],[f_622_6]) ).
cnf(f_622_8,plain,
( sP160(U_2797,U_2798,U_2806,U_2810,U_2808,U_2812)
| sP159(U_2806,U_2810,U_2808,U_2812) ),
inference(clausify,[status(thm)],[f_622_7]) ).
cnf(f_622_9,plain,
( hBOOL(hAPP(U_2813,U_2801))
| ~ hBOOL(hAPP(hAPP(c_member(U_2807),U_2801),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2807,tc_HOL_Obool)),U_2809),U_2811)))
| sP162(U_2811,U_2807,U_2809,U_2813)
| sP161(U_2811,U_2807,U_2809,U_2813) ),
inference(clausify,[status(thm)],[f_622_7]) ).
cnf(f_622_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_2806),sK70(U_2812,U_2810,U_2808,U_2806)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2806,tc_HOL_Obool)),U_2808),U_2810)))
| ~ sP159(U_2806,U_2810,U_2808,U_2812) ),
inference(clausify,[status(thm)],[f_622_7]) ).
cnf(f_622_11,plain,
( ~ hBOOL(hAPP(U_2812,sK70(U_2812,U_2810,U_2808,U_2806)))
| ~ sP159(U_2806,U_2810,U_2808,U_2812) ),
inference(clausify,[status(thm)],[f_622_7]) ).
cnf(f_622_12,plain,
( hBOOL(hAPP(U_2812,U_2797))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2797),U_2808))
| ~ sP160(U_2797,U_2798,U_2806,U_2810,U_2808,U_2812) ),
inference(clausify,[status(thm)],[f_622_7]) ).
cnf(f_622_13,plain,
( hBOOL(hAPP(U_2812,U_2798))
| ~ hBOOL(hAPP(hAPP(c_member(U_2806),U_2798),U_2810))
| ~ sP160(U_2797,U_2798,U_2806,U_2810,U_2808,U_2812) ),
inference(clausify,[status(thm)],[f_622_7]) ).
cnf(f_622_14,plain,
( hBOOL(hAPP(hAPP(c_member(U_2807),sK71(U_2813,U_2811,U_2809,U_2807)),U_2809))
| ~ sP161(U_2811,U_2807,U_2809,U_2813) ),
inference(clausify,[status(thm)],[f_622_7]) ).
cnf(f_622_15,plain,
( ~ hBOOL(hAPP(U_2813,sK71(U_2813,U_2811,U_2809,U_2807)))
| ~ sP161(U_2811,U_2807,U_2809,U_2813) ),
inference(clausify,[status(thm)],[f_622_7]) ).
cnf(f_622_16,plain,
( hBOOL(hAPP(hAPP(c_member(U_2807),sK72(U_2813,U_2811,U_2809,U_2807)),U_2811))
| ~ sP162(U_2811,U_2807,U_2809,U_2813) ),
inference(clausify,[status(thm)],[f_622_7]) ).
cnf(f_622_17,plain,
( ~ hBOOL(hAPP(U_2813,sK72(U_2813,U_2811,U_2809,U_2807)))
| ~ sP162(U_2811,U_2807,U_2809,U_2813) ),
inference(clausify,[status(thm)],[f_622_7]) ).
fof(f_623_1,plain,
! [V_x_2,T_d,T_c] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_d,T_c)),V_x_2) = c_Orderings_Otop__class_Otop(T_c)
| ~ class_Orderings_Otop(T_c) ),
inference(fof_nnf,[status(thm)],[fact_top__apply]) ).
fof(f_623_2,plain,
! [U_2816,U_2815,U_2814] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_2815,U_2814)),U_2816) = c_Orderings_Otop__class_Otop(U_2814)
| ~ class_Orderings_Otop(U_2814) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
fof(f_623_3,plain,
! [U_2814,U_2816,U_2815] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_2815,U_2814)),U_2816) = c_Orderings_Otop__class_Otop(U_2814)
| ~ class_Orderings_Otop(U_2814) ),
inference(definitional_conversion,[status(esa)],[f_623_2]) ).
cnf(f_623_4,plain,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_2815,U_2814)),U_2816) = c_Orderings_Otop__class_Otop(U_2814)
| ~ class_Orderings_Otop(U_2814) ),
inference(clausify,[status(thm)],[f_623_3]) ).
fof(f_624_1,plain,
! [V_B_2,T_c,V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_624_2,plain,
! [U_2820,U_2819,U_2818,U_2817] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2819,tc_HOL_Obool)),U_2817),U_2820),U_2818))
| ~ hBOOL(hAPP(U_2817,U_2818)) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
fof(f_624_3,plain,
! [U_2817,U_2820,U_2818,U_2819] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2819,tc_HOL_Obool)),U_2817),U_2820),U_2818))
| ~ hBOOL(hAPP(U_2817,U_2818)) ),
inference(definitional_conversion,[status(esa)],[f_624_2]) ).
cnf(f_624_4,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2819,tc_HOL_Obool)),U_2817),U_2820),U_2818))
| ~ hBOOL(hAPP(U_2817,U_2818)) ),
inference(clausify,[status(thm)],[f_624_3]) ).
fof(f_625_1,plain,
! [V_A_2,T_c,V_x_2,V_B_2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_625_2,plain,
! [U_2824,U_2823,U_2822,U_2821] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2823,tc_HOL_Obool)),U_2824),U_2821),U_2822))
| ~ hBOOL(hAPP(U_2821,U_2822)) ),
inference(variable_rename,[status(thm)],[f_625_1]) ).
fof(f_625_3,plain,
! [U_2823,U_2822,U_2821,U_2824] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2823,tc_HOL_Obool)),U_2824),U_2821),U_2822))
| ~ hBOOL(hAPP(U_2821,U_2822)) ),
inference(definitional_conversion,[status(esa)],[f_625_2]) ).
cnf(f_625_4,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2823,tc_HOL_Obool)),U_2824),U_2821),U_2822))
| ~ hBOOL(hAPP(U_2821,U_2822)) ),
inference(clausify,[status(thm)],[f_625_3]) ).
fof(f_626_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_626_2,plain,
! [U_2826,U_2825] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2825),c_Orderings_Otop__class_Otop(U_2825)),U_2826) = c_Orderings_Otop__class_Otop(U_2825)
| ~ class_Lattices_Obounded__lattice__top(U_2825) ),
inference(variable_rename,[status(thm)],[f_626_1]) ).
fof(f_626_3,plain,
! [U_2825,U_2826] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2825),c_Orderings_Otop__class_Otop(U_2825)),U_2826) = c_Orderings_Otop__class_Otop(U_2825)
| ~ class_Lattices_Obounded__lattice__top(U_2825) ),
inference(definitional_conversion,[status(esa)],[f_626_2]) ).
cnf(f_626_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2825),c_Orderings_Otop__class_Otop(U_2825)),U_2826) = c_Orderings_Otop__class_Otop(U_2825)
| ~ class_Lattices_Obounded__lattice__top(U_2825) ),
inference(clausify,[status(thm)],[f_626_3]) ).
fof(f_627_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_627_2,plain,
! [U_2828,U_2827] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2827),U_2828),c_Orderings_Otop__class_Otop(U_2827)) = c_Orderings_Otop__class_Otop(U_2827)
| ~ class_Lattices_Obounded__lattice__top(U_2827) ),
inference(variable_rename,[status(thm)],[f_627_1]) ).
fof(f_627_3,plain,
! [U_2827,U_2828] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2827),U_2828),c_Orderings_Otop__class_Otop(U_2827)) = c_Orderings_Otop__class_Otop(U_2827)
| ~ class_Lattices_Obounded__lattice__top(U_2827) ),
inference(definitional_conversion,[status(esa)],[f_627_2]) ).
cnf(f_627_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2827),U_2828),c_Orderings_Otop__class_Otop(U_2827)) = c_Orderings_Otop__class_Otop(U_2827)
| ~ class_Lattices_Obounded__lattice__top(U_2827) ),
inference(clausify,[status(thm)],[f_627_3]) ).
fof(f_628_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_628_2,plain,
! [U_2830,U_2829] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2829),U_2830),U_2830) = U_2830
| ~ class_Lattices_Osemilattice__sup(U_2829) ),
inference(variable_rename,[status(thm)],[f_628_1]) ).
fof(f_628_3,plain,
! [U_2829,U_2830] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2829),U_2830),U_2830) = U_2830
| ~ class_Lattices_Osemilattice__sup(U_2829) ),
inference(definitional_conversion,[status(esa)],[f_628_2]) ).
cnf(f_628_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2829),U_2830),U_2830) = U_2830
| ~ class_Lattices_Osemilattice__sup(U_2829) ),
inference(clausify,[status(thm)],[f_628_3]) ).
fof(f_629_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_629_2,plain,
! [U_2832,U_2831] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2831),U_2832),U_2832) = U_2832
| ~ class_Lattices_Osemilattice__sup(U_2831) ),
inference(variable_rename,[status(thm)],[f_629_1]) ).
fof(f_629_3,plain,
! [U_2831,U_2832] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2831),U_2832),U_2832) = U_2832
| ~ class_Lattices_Osemilattice__sup(U_2831) ),
inference(definitional_conversion,[status(esa)],[f_629_2]) ).
cnf(f_629_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2831),U_2832),U_2832) = U_2832
| ~ class_Lattices_Osemilattice__sup(U_2831) ),
inference(clausify,[status(thm)],[f_629_3]) ).
fof(f_630_1,plain,
! [V_x_2,V_g_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,T_c)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sup__fun__def]) ).
fof(f_630_2,plain,
! [U_2837,U_2836,U_2835,U_2834,U_2833] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2834,U_2833)),U_2835),U_2836),U_2837) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2833),hAPP(U_2835,U_2837)),hAPP(U_2836,U_2837))
| ~ class_Lattices_Olattice(U_2833) ),
inference(variable_rename,[status(thm)],[f_630_1]) ).
fof(f_630_3,plain,
! [U_2833,U_2834,U_2835,U_2836,U_2837] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2834,U_2833)),U_2835),U_2836),U_2837) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2833),hAPP(U_2835,U_2837)),hAPP(U_2836,U_2837))
| ~ class_Lattices_Olattice(U_2833) ),
inference(definitional_conversion,[status(esa)],[f_630_2]) ).
cnf(f_630_4,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2834,U_2833)),U_2835),U_2836),U_2837) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2833),hAPP(U_2835,U_2837)),hAPP(U_2836,U_2837))
| ~ class_Lattices_Olattice(U_2833) ),
inference(clausify,[status(thm)],[f_630_3]) ).
fof(f_631_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_631_2,plain,
! [U_2840,U_2839,U_2838] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2838),U_2839),U_2840) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2838),U_2840),U_2839)
| ~ class_Lattices_Osemilattice__sup(U_2838) ),
inference(variable_rename,[status(thm)],[f_631_1]) ).
fof(f_631_3,plain,
! [U_2838,U_2839,U_2840] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2838),U_2839),U_2840) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2838),U_2840),U_2839)
| ~ class_Lattices_Osemilattice__sup(U_2838) ),
inference(definitional_conversion,[status(esa)],[f_631_2]) ).
cnf(f_631_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2838),U_2839),U_2840) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2838),U_2840),U_2839)
| ~ class_Lattices_Osemilattice__sup(U_2838) ),
inference(clausify,[status(thm)],[f_631_3]) ).
fof(f_632_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_632_2,plain,
! [U_2843,U_2842,U_2841] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2841),U_2842),U_2843) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2841),U_2843),U_2842)
| ~ class_Lattices_Olattice(U_2841) ),
inference(variable_rename,[status(thm)],[f_632_1]) ).
fof(f_632_3,plain,
! [U_2841,U_2842,U_2843] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2841),U_2842),U_2843) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2841),U_2843),U_2842)
| ~ class_Lattices_Olattice(U_2841) ),
inference(definitional_conversion,[status(esa)],[f_632_2]) ).
cnf(f_632_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2841),U_2842),U_2843) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2841),U_2843),U_2842)
| ~ class_Lattices_Olattice(U_2841) ),
inference(clausify,[status(thm)],[f_632_3]) ).
fof(f_633_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_633_2,plain,
! [U_2846,U_2845,U_2844] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2844),U_2845),U_2846) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2844),U_2846),U_2845)
| ~ class_Lattices_Osemilattice__sup(U_2844) ),
inference(variable_rename,[status(thm)],[f_633_1]) ).
fof(f_633_3,plain,
! [U_2844,U_2845,U_2846] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2844),U_2845),U_2846) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2844),U_2846),U_2845)
| ~ class_Lattices_Osemilattice__sup(U_2844) ),
inference(definitional_conversion,[status(esa)],[f_633_2]) ).
cnf(f_633_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2844),U_2845),U_2846) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2844),U_2846),U_2845)
| ~ class_Lattices_Osemilattice__sup(U_2844) ),
inference(clausify,[status(thm)],[f_633_3]) ).
fof(f_634_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_634_2,plain,
! [U_2849,U_2848,U_2847] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2847),U_2848),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2847),U_2848),U_2849)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2847),U_2848),U_2849)
| ~ class_Lattices_Osemilattice__sup(U_2847) ),
inference(variable_rename,[status(thm)],[f_634_1]) ).
fof(f_634_3,plain,
! [U_2847,U_2848,U_2849] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2847),U_2848),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2847),U_2848),U_2849)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2847),U_2848),U_2849)
| ~ class_Lattices_Osemilattice__sup(U_2847) ),
inference(definitional_conversion,[status(esa)],[f_634_2]) ).
cnf(f_634_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2847),U_2848),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2847),U_2848),U_2849)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2847),U_2848),U_2849)
| ~ class_Lattices_Osemilattice__sup(U_2847) ),
inference(clausify,[status(thm)],[f_634_3]) ).
fof(f_635_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_635_2,plain,
! [U_2852,U_2851,U_2850] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2850),U_2851),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2850),U_2851),U_2852)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2850),U_2851),U_2852)
| ~ class_Lattices_Olattice(U_2850) ),
inference(variable_rename,[status(thm)],[f_635_1]) ).
fof(f_635_3,plain,
! [U_2850,U_2851,U_2852] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2850),U_2851),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2850),U_2851),U_2852)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2850),U_2851),U_2852)
| ~ class_Lattices_Olattice(U_2850) ),
inference(definitional_conversion,[status(esa)],[f_635_2]) ).
cnf(f_635_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2850),U_2851),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2850),U_2851),U_2852)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2850),U_2851),U_2852)
| ~ class_Lattices_Olattice(U_2850) ),
inference(clausify,[status(thm)],[f_635_3]) ).
fof(f_636_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_636_2,plain,
! [U_2855,U_2854,U_2853] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2853),U_2854),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2853),U_2854),U_2855)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2853),U_2854),U_2855)
| ~ class_Lattices_Osemilattice__sup(U_2853) ),
inference(variable_rename,[status(thm)],[f_636_1]) ).
fof(f_636_3,plain,
! [U_2853,U_2854,U_2855] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2853),U_2854),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2853),U_2854),U_2855)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2853),U_2854),U_2855)
| ~ class_Lattices_Osemilattice__sup(U_2853) ),
inference(definitional_conversion,[status(esa)],[f_636_2]) ).
cnf(f_636_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2853),U_2854),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2853),U_2854),U_2855)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2853),U_2854),U_2855)
| ~ class_Lattices_Osemilattice__sup(U_2853) ),
inference(clausify,[status(thm)],[f_636_3]) ).
fof(f_637_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_637_2,plain,
! [U_2859,U_2858,U_2857,U_2856] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2856),U_2857),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2856),U_2858),U_2859)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2856),U_2858),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2856),U_2857),U_2859))
| ~ class_Lattices_Osemilattice__sup(U_2856) ),
inference(variable_rename,[status(thm)],[f_637_1]) ).
fof(f_637_3,plain,
! [U_2856,U_2857,U_2858,U_2859] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2856),U_2857),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2856),U_2858),U_2859)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2856),U_2858),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2856),U_2857),U_2859))
| ~ class_Lattices_Osemilattice__sup(U_2856) ),
inference(definitional_conversion,[status(esa)],[f_637_2]) ).
cnf(f_637_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2856),U_2857),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2856),U_2858),U_2859)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2856),U_2858),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2856),U_2857),U_2859))
| ~ class_Lattices_Osemilattice__sup(U_2856) ),
inference(clausify,[status(thm)],[f_637_3]) ).
fof(f_638_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_638_2,plain,
! [U_2863,U_2862,U_2861,U_2860] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2860),U_2861),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2860),U_2862),U_2863)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2860),U_2862),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2860),U_2861),U_2863))
| ~ class_Lattices_Olattice(U_2860) ),
inference(variable_rename,[status(thm)],[f_638_1]) ).
fof(f_638_3,plain,
! [U_2860,U_2861,U_2862,U_2863] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2860),U_2861),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2860),U_2862),U_2863)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2860),U_2862),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2860),U_2861),U_2863))
| ~ class_Lattices_Olattice(U_2860) ),
inference(definitional_conversion,[status(esa)],[f_638_2]) ).
cnf(f_638_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2860),U_2861),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2860),U_2862),U_2863)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2860),U_2862),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2860),U_2861),U_2863))
| ~ class_Lattices_Olattice(U_2860) ),
inference(clausify,[status(thm)],[f_638_3]) ).
fof(f_639_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_639_2,plain,
! [U_2867,U_2866,U_2865,U_2864] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2864),U_2865),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2864),U_2866),U_2867)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2864),U_2866),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2864),U_2865),U_2867))
| ~ class_Lattices_Osemilattice__sup(U_2864) ),
inference(variable_rename,[status(thm)],[f_639_1]) ).
fof(f_639_3,plain,
! [U_2864,U_2865,U_2866,U_2867] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2864),U_2865),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2864),U_2866),U_2867)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2864),U_2866),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2864),U_2865),U_2867))
| ~ class_Lattices_Osemilattice__sup(U_2864) ),
inference(definitional_conversion,[status(esa)],[f_639_2]) ).
cnf(f_639_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2864),U_2865),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2864),U_2866),U_2867)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2864),U_2866),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2864),U_2865),U_2867))
| ~ class_Lattices_Osemilattice__sup(U_2864) ),
inference(clausify,[status(thm)],[f_639_3]) ).
fof(f_640_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_640_2,plain,
! [U_2871,U_2870,U_2869,U_2868] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),U_2869),U_2870)),U_2871) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),U_2869),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),U_2870),U_2871))
| ~ class_Lattices_Osemilattice__sup(U_2868) ),
inference(variable_rename,[status(thm)],[f_640_1]) ).
fof(f_640_3,plain,
! [U_2868,U_2869,U_2870,U_2871] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),U_2869),U_2870)),U_2871) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),U_2869),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),U_2870),U_2871))
| ~ class_Lattices_Osemilattice__sup(U_2868) ),
inference(definitional_conversion,[status(esa)],[f_640_2]) ).
cnf(f_640_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),U_2869),U_2870)),U_2871) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),U_2869),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2868),U_2870),U_2871))
| ~ class_Lattices_Osemilattice__sup(U_2868) ),
inference(clausify,[status(thm)],[f_640_3]) ).
fof(f_641_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_641_2,plain,
! [U_2875,U_2874,U_2873,U_2872] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2872),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2872),U_2873),U_2874)),U_2875) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2872),U_2873),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2872),U_2874),U_2875))
| ~ class_Lattices_Olattice(U_2872) ),
inference(variable_rename,[status(thm)],[f_641_1]) ).
fof(f_641_3,plain,
! [U_2872,U_2873,U_2874,U_2875] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2872),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2872),U_2873),U_2874)),U_2875) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2872),U_2873),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2872),U_2874),U_2875))
| ~ class_Lattices_Olattice(U_2872) ),
inference(definitional_conversion,[status(esa)],[f_641_2]) ).
cnf(f_641_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2872),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2872),U_2873),U_2874)),U_2875) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2872),U_2873),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2872),U_2874),U_2875))
| ~ class_Lattices_Olattice(U_2872) ),
inference(clausify,[status(thm)],[f_641_3]) ).
fof(f_642_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_642_2,plain,
! [U_2879,U_2878,U_2877,U_2876] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2876),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2876),U_2877),U_2878)),U_2879) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2876),U_2877),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2876),U_2878),U_2879))
| ~ class_Lattices_Osemilattice__sup(U_2876) ),
inference(variable_rename,[status(thm)],[f_642_1]) ).
fof(f_642_3,plain,
! [U_2876,U_2877,U_2878,U_2879] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2876),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2876),U_2877),U_2878)),U_2879) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2876),U_2877),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2876),U_2878),U_2879))
| ~ class_Lattices_Osemilattice__sup(U_2876) ),
inference(definitional_conversion,[status(esa)],[f_642_2]) ).
cnf(f_642_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2876),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2876),U_2877),U_2878)),U_2879) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2876),U_2877),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2876),U_2878),U_2879))
| ~ class_Lattices_Osemilattice__sup(U_2876) ),
inference(clausify,[status(thm)],[f_642_3]) ).
fof(f_643_1,plain,
! [V_x_2,V_g_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,T_c)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sup__apply]) ).
fof(f_643_2,plain,
! [U_2884,U_2883,U_2882,U_2881,U_2880] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2881,U_2880)),U_2882),U_2883),U_2884) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2880),hAPP(U_2882,U_2884)),hAPP(U_2883,U_2884))
| ~ class_Lattices_Olattice(U_2880) ),
inference(variable_rename,[status(thm)],[f_643_1]) ).
fof(f_643_3,plain,
! [U_2880,U_2881,U_2882,U_2883,U_2884] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2881,U_2880)),U_2882),U_2883),U_2884) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2880),hAPP(U_2882,U_2884)),hAPP(U_2883,U_2884))
| ~ class_Lattices_Olattice(U_2880) ),
inference(definitional_conversion,[status(esa)],[f_643_2]) ).
cnf(f_643_4,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2881,U_2880)),U_2882),U_2883),U_2884) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2880),hAPP(U_2882,U_2884)),hAPP(U_2883,U_2884))
| ~ class_Lattices_Olattice(U_2880) ),
inference(clausify,[status(thm)],[f_643_3]) ).
fof(f_644_1,plain,
! [T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,T_d),tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2]) ).
fof(f_644_2,plain,
! [U_2886,U_2885] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2886),c_Orderings_Otop__class_Otop(tc_fun(U_2886,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2885,U_2886)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_2885,U_2886),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
fof(f_644_3,plain,
! [U_2886] :
( ! [U_2885] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2885,U_2886)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_2885,U_2886),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_2886),c_Orderings_Otop__class_Otop(tc_fun(U_2886,tc_HOL_Obool)))) ),
inference(miniscope,[status(thm)],[f_644_2]) ).
fof(f_644_4,plain,
! [U_2885,U_2886] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2885,U_2886)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_2885,U_2886),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_2886),c_Orderings_Otop__class_Otop(tc_fun(U_2886,tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_644_3]) ).
cnf(f_644_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2885,U_2886)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_2885,U_2886),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_2886),c_Orderings_Otop__class_Otop(tc_fun(U_2886,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_644_4]) ).
fof(f_645_1,plain,
! [V_A_2,T_c] :
( V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(T_c),V_A_2) != hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(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)))) ),
inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV]) ).
fof(f_645_2,plain,
! [U_2888,U_2887] :
( U_2888 = c_Orderings_Otop__class_Otop(tc_fun(U_2887,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_2887),U_2888) != hAPP(c_Finite__Set_Ocard(U_2887),c_Orderings_Otop__class_Otop(tc_fun(U_2887,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2887),c_Orderings_Otop__class_Otop(tc_fun(U_2887,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_645_1]) ).
fof(f_645_3,plain,
! [U_2887,U_2888] :
( U_2888 = c_Orderings_Otop__class_Otop(tc_fun(U_2887,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_2887),U_2888) != hAPP(c_Finite__Set_Ocard(U_2887),c_Orderings_Otop__class_Otop(tc_fun(U_2887,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2887),c_Orderings_Otop__class_Otop(tc_fun(U_2887,tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_645_2]) ).
cnf(f_645_4,plain,
( U_2888 = c_Orderings_Otop__class_Otop(tc_fun(U_2887,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_2887),U_2888) != hAPP(c_Finite__Set_Ocard(U_2887),c_Orderings_Otop__class_Otop(tc_fun(U_2887,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2887),c_Orderings_Otop__class_Otop(tc_fun(U_2887,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_645_3]) ).
fof(f_646_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Compl__partition]) ).
fof(f_646_2,plain,
! [U_2890,U_2889] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2889,tc_HOL_Obool)),U_2890),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2889,tc_HOL_Obool)),U_2890)) = c_Orderings_Otop__class_Otop(tc_fun(U_2889,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_646_1]) ).
fof(f_646_3,plain,
! [U_2889,U_2890] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2889,tc_HOL_Obool)),U_2890),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2889,tc_HOL_Obool)),U_2890)) = c_Orderings_Otop__class_Otop(tc_fun(U_2889,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_646_2]) ).
cnf(f_646_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2889,tc_HOL_Obool)),U_2890),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2889,tc_HOL_Obool)),U_2890)) = c_Orderings_Otop__class_Otop(tc_fun(U_2889,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_646_3]) ).
fof(f_647_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Compl__partition2]) ).
fof(f_647_2,plain,
! [U_2892,U_2891] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2891,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2891,tc_HOL_Obool)),U_2892)),U_2892) = c_Orderings_Otop__class_Otop(tc_fun(U_2891,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_647_1]) ).
fof(f_647_3,plain,
! [U_2891,U_2892] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2891,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2891,tc_HOL_Obool)),U_2892)),U_2892) = c_Orderings_Otop__class_Otop(tc_fun(U_2891,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_647_2]) ).
cnf(f_647_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2891,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2891,tc_HOL_Obool)),U_2892)),U_2892) = c_Orderings_Otop__class_Otop(tc_fun(U_2891,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_647_3]) ).
fof(f_648_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_648_2,plain,
! [U_2894,U_2893] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2893),U_2894),hAPP(c_Groups_Ouminus__class_Ouminus(U_2893),U_2894)) = c_Orderings_Otop__class_Otop(U_2893)
| ~ class_Lattices_Oboolean__algebra(U_2893) ),
inference(variable_rename,[status(thm)],[f_648_1]) ).
fof(f_648_3,plain,
! [U_2893,U_2894] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2893),U_2894),hAPP(c_Groups_Ouminus__class_Ouminus(U_2893),U_2894)) = c_Orderings_Otop__class_Otop(U_2893)
| ~ class_Lattices_Oboolean__algebra(U_2893) ),
inference(definitional_conversion,[status(esa)],[f_648_2]) ).
cnf(f_648_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2893),U_2894),hAPP(c_Groups_Ouminus__class_Ouminus(U_2893),U_2894)) = c_Orderings_Otop__class_Otop(U_2893)
| ~ class_Lattices_Oboolean__algebra(U_2893) ),
inference(clausify,[status(thm)],[f_648_3]) ).
fof(f_649_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_649_2,plain,
! [U_2896,U_2895] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2895),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2896)),U_2896) = c_Orderings_Otop__class_Otop(U_2895)
| ~ class_Lattices_Oboolean__algebra(U_2895) ),
inference(variable_rename,[status(thm)],[f_649_1]) ).
fof(f_649_3,plain,
! [U_2895,U_2896] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2895),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2896)),U_2896) = c_Orderings_Otop__class_Otop(U_2895)
| ~ class_Lattices_Oboolean__algebra(U_2895) ),
inference(definitional_conversion,[status(esa)],[f_649_2]) ).
cnf(f_649_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2895),hAPP(c_Groups_Ouminus__class_Ouminus(U_2895),U_2896)),U_2896) = c_Orderings_Otop__class_Otop(U_2895)
| ~ class_Lattices_Oboolean__algebra(U_2895) ),
inference(clausify,[status(thm)],[f_649_3]) ).
fof(f_650_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_650_2,plain,
! [U_2899,U_2898,U_2897] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2897),U_2898),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2897),U_2898),U_2899)))
| ~ class_Lattices_Olattice(U_2897) ),
inference(variable_rename,[status(thm)],[f_650_1]) ).
fof(f_650_3,plain,
! [U_2897,U_2898,U_2899] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2897),U_2898),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2897),U_2898),U_2899)))
| ~ class_Lattices_Olattice(U_2897) ),
inference(definitional_conversion,[status(esa)],[f_650_2]) ).
cnf(f_650_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2897),U_2898),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2897),U_2898),U_2899)))
| ~ class_Lattices_Olattice(U_2897) ),
inference(clausify,[status(thm)],[f_650_3]) ).
fof(f_651_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_651_2,plain,
! [U_2902,U_2901,U_2900] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2900),U_2901),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2900),U_2901),U_2902)))
| ~ class_Lattices_Osemilattice__sup(U_2900) ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
fof(f_651_3,plain,
! [U_2900,U_2901,U_2902] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2900),U_2901),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2900),U_2901),U_2902)))
| ~ class_Lattices_Osemilattice__sup(U_2900) ),
inference(definitional_conversion,[status(esa)],[f_651_2]) ).
cnf(f_651_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2900),U_2901),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2900),U_2901),U_2902)))
| ~ class_Lattices_Osemilattice__sup(U_2900) ),
inference(clausify,[status(thm)],[f_651_3]) ).
fof(f_652_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_652_2,plain,
! [U_2905,U_2904,U_2903] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2903),U_2904),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2903),U_2905),U_2904)))
| ~ class_Lattices_Olattice(U_2903) ),
inference(variable_rename,[status(thm)],[f_652_1]) ).
fof(f_652_3,plain,
! [U_2903,U_2904,U_2905] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2903),U_2904),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2903),U_2905),U_2904)))
| ~ class_Lattices_Olattice(U_2903) ),
inference(definitional_conversion,[status(esa)],[f_652_2]) ).
cnf(f_652_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2903),U_2904),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2903),U_2905),U_2904)))
| ~ class_Lattices_Olattice(U_2903) ),
inference(clausify,[status(thm)],[f_652_3]) ).
fof(f_653_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_653_2,plain,
! [U_2908,U_2907,U_2906] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2906),U_2907),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2906),U_2908),U_2907)))
| ~ class_Lattices_Osemilattice__sup(U_2906) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
fof(f_653_3,plain,
! [U_2906,U_2907,U_2908] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2906),U_2907),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2906),U_2908),U_2907)))
| ~ class_Lattices_Osemilattice__sup(U_2906) ),
inference(definitional_conversion,[status(esa)],[f_653_2]) ).
cnf(f_653_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2906),U_2907),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2906),U_2908),U_2907)))
| ~ class_Lattices_Osemilattice__sup(U_2906) ),
inference(clausify,[status(thm)],[f_653_3]) ).
fof(f_654_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_y_2) != V_y_2 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_y_2) = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) )
| ~ class_Lattices_Osemilattice__sup(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__sup]) ).
fof(f_654_2,plain,
! [U_2911,U_2910,U_2909] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2909),U_2910),U_2911))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2909),U_2910),U_2911) != U_2911 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2909),U_2910),U_2911) = U_2911
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2909),U_2910),U_2911)) ) )
| ~ class_Lattices_Osemilattice__sup(U_2909) ),
inference(variable_rename,[status(thm)],[f_654_1]) ).
fof(f_654_3,plain,
( ! [U_2909,U_2910,U_2911] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2909),U_2910),U_2911))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2909),U_2910),U_2911) != U_2911
| ~ sP163(U_2909,U_2910,U_2911) )
& ! [U_2909,U_2910,U_2911] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2909),U_2910),U_2911) = U_2911
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2909),U_2910),U_2911))
| ~ sP163(U_2909,U_2910,U_2911) )
& ! [U_2909,U_2910,U_2911] :
( sP163(U_2909,U_2910,U_2911)
| ~ class_Lattices_Osemilattice__sup(U_2909) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP163])],[f_654_2]) ).
cnf(f_654_4,plain,
( sP163(U_2909,U_2910,U_2911)
| ~ class_Lattices_Osemilattice__sup(U_2909) ),
inference(clausify,[status(thm)],[f_654_3]) ).
cnf(f_654_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2909),U_2910),U_2911) = U_2911
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2909),U_2910),U_2911))
| ~ sP163(U_2909,U_2910,U_2911) ),
inference(clausify,[status(thm)],[f_654_3]) ).
cnf(f_654_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2909),U_2910),U_2911))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2909),U_2910),U_2911) != U_2911
| ~ sP163(U_2909,U_2910,U_2911) ),
inference(clausify,[status(thm)],[f_654_3]) ).
fof(f_655_1,plain,
! [V_z_2,V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_y_2)),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_y_2)),V_z_2)) ) )
| ~ class_Lattices_Osemilattice__sup(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__sup__iff]) ).
fof(f_655_2,plain,
! [U_2915,U_2914,U_2913,U_2912] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2912),U_2913),U_2914)),U_2915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),U_2914),U_2915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),U_2913),U_2915)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),U_2914),U_2915))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),U_2913),U_2915)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2912),U_2913),U_2914)),U_2915)) ) )
| ~ class_Lattices_Osemilattice__sup(U_2912) ),
inference(variable_rename,[status(thm)],[f_655_1]) ).
fof(f_655_3,plain,
( ! [U_2912,U_2913,U_2914,U_2915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),U_2914),U_2915))
| ~ sP164(U_2912,U_2913,U_2914,U_2915) )
& ! [U_2912,U_2913,U_2914,U_2915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),U_2913),U_2915))
| ~ sP164(U_2912,U_2913,U_2914,U_2915) )
& ! [U_2912,U_2913,U_2914,U_2915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2912),U_2913),U_2914)),U_2915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),U_2914),U_2915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),U_2913),U_2915))
| ~ sP165(U_2912,U_2913,U_2914,U_2915) )
& ! [U_2912,U_2913,U_2914,U_2915] :
( sP164(U_2912,U_2913,U_2914,U_2915)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2912),U_2913),U_2914)),U_2915))
| ~ sP165(U_2912,U_2913,U_2914,U_2915) )
& ! [U_2912,U_2913,U_2914,U_2915] :
( sP165(U_2912,U_2913,U_2914,U_2915)
| ~ class_Lattices_Osemilattice__sup(U_2912) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164,sP165])],[f_655_2]) ).
cnf(f_655_4,plain,
( sP165(U_2912,U_2913,U_2914,U_2915)
| ~ class_Lattices_Osemilattice__sup(U_2912) ),
inference(clausify,[status(thm)],[f_655_3]) ).
cnf(f_655_5,plain,
( sP164(U_2912,U_2913,U_2914,U_2915)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2912),U_2913),U_2914)),U_2915))
| ~ sP165(U_2912,U_2913,U_2914,U_2915) ),
inference(clausify,[status(thm)],[f_655_3]) ).
cnf(f_655_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2912),U_2913),U_2914)),U_2915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),U_2914),U_2915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),U_2913),U_2915))
| ~ sP165(U_2912,U_2913,U_2914,U_2915) ),
inference(clausify,[status(thm)],[f_655_3]) ).
cnf(f_655_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),U_2913),U_2915))
| ~ sP164(U_2912,U_2913,U_2914,U_2915) ),
inference(clausify,[status(thm)],[f_655_3]) ).
cnf(f_655_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2912),U_2914),U_2915))
| ~ sP164(U_2912,U_2913,U_2914,U_2915) ),
inference(clausify,[status(thm)],[f_655_3]) ).
fof(f_656_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_656_2,plain,
! [U_2919,U_2918,U_2917,U_2916] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2916),U_2917),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2916),U_2918),U_2919)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2916),U_2917),U_2918))
| ~ class_Lattices_Osemilattice__sup(U_2916) ),
inference(variable_rename,[status(thm)],[f_656_1]) ).
fof(f_656_3,plain,
! [U_2919,U_2918,U_2916,U_2917] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2916),U_2917),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2916),U_2918),U_2919)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2916),U_2917),U_2918))
| ~ class_Lattices_Osemilattice__sup(U_2916) ),
inference(definitional_conversion,[status(esa)],[f_656_2]) ).
cnf(f_656_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2916),U_2917),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2916),U_2918),U_2919)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2916),U_2917),U_2918))
| ~ class_Lattices_Osemilattice__sup(U_2916) ),
inference(clausify,[status(thm)],[f_656_3]) ).
fof(f_657_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_657_2,plain,
! [U_2923,U_2922,U_2921,U_2920] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2920),U_2921),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2920),U_2923),U_2922)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2920),U_2921),U_2922))
| ~ class_Lattices_Osemilattice__sup(U_2920) ),
inference(variable_rename,[status(thm)],[f_657_1]) ).
fof(f_657_3,plain,
! [U_2920,U_2921,U_2922,U_2923] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2920),U_2921),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2920),U_2923),U_2922)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2920),U_2921),U_2922))
| ~ class_Lattices_Osemilattice__sup(U_2920) ),
inference(definitional_conversion,[status(esa)],[f_657_2]) ).
cnf(f_657_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2920),U_2921),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2920),U_2923),U_2922)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2920),U_2921),U_2922))
| ~ class_Lattices_Osemilattice__sup(U_2920) ),
inference(clausify,[status(thm)],[f_657_3]) ).
fof(f_658_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_658_2,plain,
! [U_2926,U_2925,U_2924] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2924),U_2925),U_2926) = U_2926
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2924),U_2925),U_2926))
| ~ class_Lattices_Osemilattice__sup(U_2924) ),
inference(variable_rename,[status(thm)],[f_658_1]) ).
fof(f_658_3,plain,
! [U_2924,U_2925,U_2926] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2924),U_2925),U_2926) = U_2926
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2924),U_2925),U_2926))
| ~ class_Lattices_Osemilattice__sup(U_2924) ),
inference(definitional_conversion,[status(esa)],[f_658_2]) ).
cnf(f_658_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2924),U_2925),U_2926) = U_2926
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2924),U_2925),U_2926))
| ~ class_Lattices_Osemilattice__sup(U_2924) ),
inference(clausify,[status(thm)],[f_658_3]) ).
fof(f_659_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_659_2,plain,
! [U_2929,U_2928,U_2927] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2927),U_2929),U_2928) = U_2929
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2927),U_2928),U_2929))
| ~ class_Lattices_Osemilattice__sup(U_2927) ),
inference(variable_rename,[status(thm)],[f_659_1]) ).
fof(f_659_3,plain,
! [U_2927,U_2928,U_2929] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2927),U_2929),U_2928) = U_2929
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2927),U_2928),U_2929))
| ~ class_Lattices_Osemilattice__sup(U_2927) ),
inference(definitional_conversion,[status(esa)],[f_659_2]) ).
cnf(f_659_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2927),U_2929),U_2928) = U_2929
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2927),U_2928),U_2929))
| ~ class_Lattices_Osemilattice__sup(U_2927) ),
inference(clausify,[status(thm)],[f_659_3]) ).
fof(f_660_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_660_2,plain,
! [U_2933,U_2932,U_2931,U_2930] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2930),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2930),U_2931),U_2933)),U_2932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2930),U_2933),U_2932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2930),U_2931),U_2932))
| ~ class_Lattices_Osemilattice__sup(U_2930) ),
inference(variable_rename,[status(thm)],[f_660_1]) ).
fof(f_660_3,plain,
! [U_2930,U_2931,U_2932,U_2933] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2930),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2930),U_2931),U_2933)),U_2932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2930),U_2933),U_2932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2930),U_2931),U_2932))
| ~ class_Lattices_Osemilattice__sup(U_2930) ),
inference(definitional_conversion,[status(esa)],[f_660_2]) ).
cnf(f_660_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2930),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2930),U_2931),U_2933)),U_2932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2930),U_2933),U_2932))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2930),U_2931),U_2932))
| ~ class_Lattices_Osemilattice__sup(U_2930) ),
inference(clausify,[status(thm)],[f_660_3]) ).
fof(f_661_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_661_2,plain,
! [U_2937,U_2936,U_2935,U_2934] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2934),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2934),U_2935),U_2937)),U_2936))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2934),U_2937),U_2936))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2934),U_2935),U_2936))
| ~ class_Lattices_Osemilattice__sup(U_2934) ),
inference(variable_rename,[status(thm)],[f_661_1]) ).
fof(f_661_3,plain,
! [U_2934,U_2935,U_2936,U_2937] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2934),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2934),U_2935),U_2937)),U_2936))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2934),U_2937),U_2936))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2934),U_2935),U_2936))
| ~ class_Lattices_Osemilattice__sup(U_2934) ),
inference(definitional_conversion,[status(esa)],[f_661_2]) ).
cnf(f_661_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2934),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2934),U_2935),U_2937)),U_2936))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2934),U_2937),U_2936))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2934),U_2935),U_2936))
| ~ class_Lattices_Osemilattice__sup(U_2934) ),
inference(clausify,[status(thm)],[f_661_3]) ).
fof(f_662_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_662_2,plain,
! [U_2942,U_2941,U_2940,U_2939,U_2938] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2938),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2938),U_2939),U_2941)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2938),U_2940),U_2942)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2938),U_2941),U_2942))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2938),U_2939),U_2940))
| ~ class_Lattices_Osemilattice__sup(U_2938) ),
inference(variable_rename,[status(thm)],[f_662_1]) ).
fof(f_662_3,plain,
! [U_2938,U_2939,U_2940,U_2941,U_2942] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2938),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2938),U_2939),U_2941)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2938),U_2940),U_2942)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2938),U_2941),U_2942))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2938),U_2939),U_2940))
| ~ class_Lattices_Osemilattice__sup(U_2938) ),
inference(definitional_conversion,[status(esa)],[f_662_2]) ).
cnf(f_662_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2938),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2938),U_2939),U_2941)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2938),U_2940),U_2942)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2938),U_2941),U_2942))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2938),U_2939),U_2940))
| ~ class_Lattices_Osemilattice__sup(U_2938) ),
inference(clausify,[status(thm)],[f_662_3]) ).
fof(f_663_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_663_2,plain,
! [U_2946,U_2945,U_2944,U_2943] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2943),U_2945),U_2946))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2943),U_2944),U_2946)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2943),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2943),U_2944),U_2945)),U_2946))
| ~ class_Lattices_Osemilattice__sup(U_2943) ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
fof(f_663_3,plain,
( ! [U_2943,U_2944,U_2945,U_2946] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2943),U_2945),U_2946))
| ~ sP166(U_2943,U_2944,U_2945,U_2946) )
& ! [U_2943,U_2944,U_2945,U_2946] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2943),U_2944),U_2946))
| ~ sP166(U_2943,U_2944,U_2945,U_2946) )
& ! [U_2943,U_2944,U_2945,U_2946] :
( sP166(U_2943,U_2944,U_2945,U_2946)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2943),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2943),U_2944),U_2945)),U_2946))
| ~ class_Lattices_Osemilattice__sup(U_2943) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166])],[f_663_2]) ).
cnf(f_663_4,plain,
( sP166(U_2943,U_2944,U_2945,U_2946)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2943),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2943),U_2944),U_2945)),U_2946))
| ~ class_Lattices_Osemilattice__sup(U_2943) ),
inference(clausify,[status(thm)],[f_663_3]) ).
cnf(f_663_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2943),U_2944),U_2946))
| ~ sP166(U_2943,U_2944,U_2945,U_2946) ),
inference(clausify,[status(thm)],[f_663_3]) ).
cnf(f_663_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2943),U_2945),U_2946))
| ~ sP166(U_2943,U_2944,U_2945,U_2946) ),
inference(clausify,[status(thm)],[f_663_3]) ).
fof(f_664_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_664_2,plain,
! [U_2950,U_2949,U_2948,U_2947] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2947),U_2948),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2947),U_2949),U_2950)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2947),U_2948),U_2949))
| ~ class_Lattices_Osemilattice__sup(U_2947) ),
inference(variable_rename,[status(thm)],[f_664_1]) ).
fof(f_664_3,plain,
! [U_2948,U_2947,U_2949,U_2950] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2947),U_2948),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2947),U_2949),U_2950)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2947),U_2948),U_2949))
| ~ class_Lattices_Osemilattice__sup(U_2947) ),
inference(definitional_conversion,[status(esa)],[f_664_2]) ).
cnf(f_664_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2947),U_2948),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2947),U_2949),U_2950)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2947),U_2948),U_2949))
| ~ class_Lattices_Osemilattice__sup(U_2947) ),
inference(clausify,[status(thm)],[f_664_3]) ).
fof(f_665_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_665_2,plain,
! [U_2954,U_2953,U_2952,U_2951] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2951),U_2952),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2951),U_2954),U_2953)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2951),U_2952),U_2953))
| ~ class_Lattices_Osemilattice__sup(U_2951) ),
inference(variable_rename,[status(thm)],[f_665_1]) ).
fof(f_665_3,plain,
! [U_2951,U_2952,U_2953,U_2954] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2951),U_2952),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2951),U_2954),U_2953)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2951),U_2952),U_2953))
| ~ class_Lattices_Osemilattice__sup(U_2951) ),
inference(definitional_conversion,[status(esa)],[f_665_2]) ).
cnf(f_665_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2951),U_2952),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2951),U_2954),U_2953)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2951),U_2952),U_2953))
| ~ class_Lattices_Osemilattice__sup(U_2951) ),
inference(clausify,[status(thm)],[f_665_3]) ).
fof(f_666_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_666_2,plain,
! [U_2956,U_2955] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2955),c_Orderings_Obot__class_Obot(U_2955)),U_2956) = U_2956
| ~ class_Lattices_Obounded__lattice__bot(U_2955) ),
inference(variable_rename,[status(thm)],[f_666_1]) ).
fof(f_666_3,plain,
! [U_2956,U_2955] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2955),c_Orderings_Obot__class_Obot(U_2955)),U_2956) = U_2956
| ~ class_Lattices_Obounded__lattice__bot(U_2955) ),
inference(definitional_conversion,[status(esa)],[f_666_2]) ).
cnf(f_666_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2955),c_Orderings_Obot__class_Obot(U_2955)),U_2956) = U_2956
| ~ class_Lattices_Obounded__lattice__bot(U_2955) ),
inference(clausify,[status(thm)],[f_666_3]) ).
fof(f_667_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_667_2,plain,
! [U_2958,U_2957] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2957),U_2958),c_Orderings_Obot__class_Obot(U_2957)) = U_2958
| ~ class_Lattices_Obounded__lattice__bot(U_2957) ),
inference(variable_rename,[status(thm)],[f_667_1]) ).
fof(f_667_3,plain,
! [U_2957,U_2958] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2957),U_2958),c_Orderings_Obot__class_Obot(U_2957)) = U_2958
| ~ class_Lattices_Obounded__lattice__bot(U_2957) ),
inference(definitional_conversion,[status(esa)],[f_667_2]) ).
cnf(f_667_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2957),U_2958),c_Orderings_Obot__class_Obot(U_2957)) = U_2958
| ~ class_Lattices_Obounded__lattice__bot(U_2957) ),
inference(clausify,[status(thm)],[f_667_3]) ).
fof(f_668_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_c)
| V_y_2 != c_Orderings_Obot__class_Obot(T_c)
| V_x_2 != c_Orderings_Obot__class_Obot(T_c) )
& ( ( V_y_2 = c_Orderings_Obot__class_Obot(T_c)
& V_x_2 = c_Orderings_Obot__class_Obot(T_c) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),V_y_2) != c_Orderings_Obot__class_Obot(T_c) ) )
| ~ class_Lattices_Obounded__lattice__bot(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff]) ).
fof(f_668_2,plain,
! [U_2961,U_2960,U_2959] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2959),U_2960),U_2961) = c_Orderings_Obot__class_Obot(U_2959)
| U_2961 != c_Orderings_Obot__class_Obot(U_2959)
| U_2960 != c_Orderings_Obot__class_Obot(U_2959) )
& ( ( U_2961 = c_Orderings_Obot__class_Obot(U_2959)
& U_2960 = c_Orderings_Obot__class_Obot(U_2959) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2959),U_2960),U_2961) != c_Orderings_Obot__class_Obot(U_2959) ) )
| ~ class_Lattices_Obounded__lattice__bot(U_2959) ),
inference(variable_rename,[status(thm)],[f_668_1]) ).
fof(f_668_3,plain,
( ! [U_2959,U_2960,U_2961] :
( U_2961 = c_Orderings_Obot__class_Obot(U_2959)
| ~ sP167(U_2959,U_2960,U_2961) )
& ! [U_2959,U_2960,U_2961] :
( U_2960 = c_Orderings_Obot__class_Obot(U_2959)
| ~ sP167(U_2959,U_2960,U_2961) )
& ! [U_2959,U_2960,U_2961] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2959),U_2960),U_2961) = c_Orderings_Obot__class_Obot(U_2959)
| U_2961 != c_Orderings_Obot__class_Obot(U_2959)
| U_2960 != c_Orderings_Obot__class_Obot(U_2959)
| ~ sP168(U_2959,U_2960,U_2961) )
& ! [U_2959,U_2960,U_2961] :
( sP167(U_2959,U_2960,U_2961)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2959),U_2960),U_2961) != c_Orderings_Obot__class_Obot(U_2959)
| ~ sP168(U_2959,U_2960,U_2961) )
& ! [U_2959,U_2960,U_2961] :
( sP168(U_2959,U_2960,U_2961)
| ~ class_Lattices_Obounded__lattice__bot(U_2959) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP167,sP168])],[f_668_2]) ).
cnf(f_668_4,plain,
( sP168(U_2959,U_2960,U_2961)
| ~ class_Lattices_Obounded__lattice__bot(U_2959) ),
inference(clausify,[status(thm)],[f_668_3]) ).
cnf(f_668_5,plain,
( sP167(U_2959,U_2960,U_2961)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2959),U_2960),U_2961) != c_Orderings_Obot__class_Obot(U_2959)
| ~ sP168(U_2959,U_2960,U_2961) ),
inference(clausify,[status(thm)],[f_668_3]) ).
cnf(f_668_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2959),U_2960),U_2961) = c_Orderings_Obot__class_Obot(U_2959)
| U_2961 != c_Orderings_Obot__class_Obot(U_2959)
| U_2960 != c_Orderings_Obot__class_Obot(U_2959)
| ~ sP168(U_2959,U_2960,U_2961) ),
inference(clausify,[status(thm)],[f_668_3]) ).
cnf(f_668_7,plain,
( U_2960 = c_Orderings_Obot__class_Obot(U_2959)
| ~ sP167(U_2959,U_2960,U_2961) ),
inference(clausify,[status(thm)],[f_668_3]) ).
cnf(f_668_8,plain,
( U_2961 = c_Orderings_Obot__class_Obot(U_2959)
| ~ sP167(U_2959,U_2960,U_2961) ),
inference(clausify,[status(thm)],[f_668_3]) ).
fof(f_669_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Un__iff]) ).
fof(f_669_2,plain,
! [U_2965,U_2964,U_2963,U_2962] :
( ( hBOOL(hAPP(hAPP(c_member(U_2962),U_2963),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2962,tc_HOL_Obool)),U_2964),U_2965)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_2962),U_2963),U_2965))
& ~ hBOOL(hAPP(hAPP(c_member(U_2962),U_2963),U_2964)) ) )
& ( hBOOL(hAPP(hAPP(c_member(U_2962),U_2963),U_2965))
| hBOOL(hAPP(hAPP(c_member(U_2962),U_2963),U_2964))
| ~ hBOOL(hAPP(hAPP(c_member(U_2962),U_2963),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2962,tc_HOL_Obool)),U_2964),U_2965))) ) ),
inference(variable_rename,[status(thm)],[f_669_1]) ).
fof(f_669_3,plain,
( ! [U_2973,U_2971,U_2969,U_2967] :
( hBOOL(hAPP(hAPP(c_member(U_2967),U_2969),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2967,tc_HOL_Obool)),U_2971),U_2973)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_2967),U_2969),U_2973))
& ~ hBOOL(hAPP(hAPP(c_member(U_2967),U_2969),U_2971)) ) )
& ! [U_2972,U_2970,U_2968,U_2966] :
( hBOOL(hAPP(hAPP(c_member(U_2966),U_2968),U_2972))
| hBOOL(hAPP(hAPP(c_member(U_2966),U_2968),U_2970))
| ~ hBOOL(hAPP(hAPP(c_member(U_2966),U_2968),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2966,tc_HOL_Obool)),U_2970),U_2972))) ) ),
inference(miniscope,[status(thm)],[f_669_2]) ).
fof(f_669_4,plain,
( ! [U_2969,U_2971,U_2973,U_2967] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2967),U_2969),U_2973))
| ~ sP169(U_2969,U_2971,U_2973,U_2967) )
& ! [U_2969,U_2971,U_2973,U_2967] :
( ~ hBOOL(hAPP(hAPP(c_member(U_2967),U_2969),U_2971))
| ~ sP169(U_2969,U_2971,U_2973,U_2967) )
& ! [U_2969,U_2971,U_2973,U_2967] :
( hBOOL(hAPP(hAPP(c_member(U_2967),U_2969),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2967,tc_HOL_Obool)),U_2971),U_2973)))
| sP169(U_2969,U_2971,U_2973,U_2967) )
& ! [U_2966,U_2972,U_2968,U_2970] :
( hBOOL(hAPP(hAPP(c_member(U_2966),U_2968),U_2972))
| hBOOL(hAPP(hAPP(c_member(U_2966),U_2968),U_2970))
| ~ hBOOL(hAPP(hAPP(c_member(U_2966),U_2968),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2966,tc_HOL_Obool)),U_2970),U_2972))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP169])],[f_669_3]) ).
cnf(f_669_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_2966),U_2968),U_2972))
| hBOOL(hAPP(hAPP(c_member(U_2966),U_2968),U_2970))
| ~ hBOOL(hAPP(hAPP(c_member(U_2966),U_2968),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2966,tc_HOL_Obool)),U_2970),U_2972))) ),
inference(clausify,[status(thm)],[f_669_4]) ).
cnf(f_669_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_2967),U_2969),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2967,tc_HOL_Obool)),U_2971),U_2973)))
| sP169(U_2969,U_2971,U_2973,U_2967) ),
inference(clausify,[status(thm)],[f_669_4]) ).
cnf(f_669_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2967),U_2969),U_2971))
| ~ sP169(U_2969,U_2971,U_2973,U_2967) ),
inference(clausify,[status(thm)],[f_669_4]) ).
cnf(f_669_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_2967),U_2969),U_2973))
| ~ sP169(U_2969,U_2971,U_2973,U_2967) ),
inference(clausify,[status(thm)],[f_669_4]) ).
fof(f_670_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UnI1]) ).
fof(f_670_2,plain,
! [U_2977,U_2976,U_2975,U_2974] :
( hBOOL(hAPP(hAPP(c_member(U_2974),U_2975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2974,tc_HOL_Obool)),U_2976),U_2977)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2974),U_2975),U_2976)) ),
inference(variable_rename,[status(thm)],[f_670_1]) ).
fof(f_670_3,plain,
! [U_2974,U_2975,U_2976,U_2977] :
( hBOOL(hAPP(hAPP(c_member(U_2974),U_2975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2974,tc_HOL_Obool)),U_2976),U_2977)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2974),U_2975),U_2976)) ),
inference(definitional_conversion,[status(esa)],[f_670_2]) ).
cnf(f_670_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2974),U_2975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2974,tc_HOL_Obool)),U_2976),U_2977)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2974),U_2975),U_2976)) ),
inference(clausify,[status(thm)],[f_670_3]) ).
fof(f_671_1,plain,
! [V_A_2,V_B_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_UnI2]) ).
fof(f_671_2,plain,
! [U_2981,U_2980,U_2979,U_2978] :
( hBOOL(hAPP(hAPP(c_member(U_2978),U_2979),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2978,tc_HOL_Obool)),U_2981),U_2980)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2978),U_2979),U_2980)) ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
fof(f_671_3,plain,
! [U_2978,U_2979,U_2980,U_2981] :
( hBOOL(hAPP(hAPP(c_member(U_2978),U_2979),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2978,tc_HOL_Obool)),U_2981),U_2980)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2978),U_2979),U_2980)) ),
inference(definitional_conversion,[status(esa)],[f_671_2]) ).
cnf(f_671_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_2978),U_2979),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2978,tc_HOL_Obool)),U_2981),U_2980)))
| ~ hBOOL(hAPP(hAPP(c_member(U_2978),U_2979),U_2980)) ),
inference(clausify,[status(thm)],[f_671_3]) ).
fof(f_672_1,plain,
! [T_c] :
( c_Lattices_Osemilattice__sup__class_Osup(T_c) = c_Orderings_Oord__class_Omax(T_c)
| ~ class_Orderings_Olinorder(T_c)
| ~ class_Lattices_Osemilattice__sup(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sup__max]) ).
fof(f_672_2,plain,
! [U_2982] :
( c_Lattices_Osemilattice__sup__class_Osup(U_2982) = c_Orderings_Oord__class_Omax(U_2982)
| ~ class_Orderings_Olinorder(U_2982)
| ~ class_Lattices_Osemilattice__sup(U_2982) ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
fof(f_672_3,plain,
! [U_2982] :
( c_Lattices_Osemilattice__sup__class_Osup(U_2982) = c_Orderings_Oord__class_Omax(U_2982)
| ~ class_Orderings_Olinorder(U_2982)
| ~ class_Lattices_Osemilattice__sup(U_2982) ),
inference(definitional_conversion,[status(esa)],[f_672_2]) ).
cnf(f_672_4,plain,
( c_Lattices_Osemilattice__sup__class_Osup(U_2982) = c_Orderings_Oord__class_Omax(U_2982)
| ~ class_Orderings_Olinorder(U_2982)
| ~ class_Lattices_Osemilattice__sup(U_2982) ),
inference(clausify,[status(thm)],[f_672_3]) ).
fof(f_673_1,plain,
! [V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = V_B_2,
inference(fof_nnf,[status(thm)],[fact_Un__empty__left]) ).
fof(f_673_2,plain,
! [U_2984,U_2983] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2983,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool))),U_2984) = U_2984,
inference(variable_rename,[status(thm)],[f_673_1]) ).
fof(f_673_3,plain,
! [U_2983,U_2984] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2983,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool))),U_2984) = U_2984,
inference(definitional_conversion,[status(esa)],[f_673_2]) ).
cnf(f_673_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2983,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool))),U_2984) = U_2984,
inference(clausify,[status(thm)],[f_673_3]) ).
fof(f_674_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Un__empty__right]) ).
fof(f_674_2,plain,
! [U_2986,U_2985] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2985,tc_HOL_Obool)),U_2986),c_Orderings_Obot__class_Obot(tc_fun(U_2985,tc_HOL_Obool))) = U_2986,
inference(variable_rename,[status(thm)],[f_674_1]) ).
fof(f_674_3,plain,
! [U_2985,U_2986] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2985,tc_HOL_Obool)),U_2986),c_Orderings_Obot__class_Obot(tc_fun(U_2985,tc_HOL_Obool))) = U_2986,
inference(definitional_conversion,[status(esa)],[f_674_2]) ).
cnf(f_674_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2985,tc_HOL_Obool)),U_2986),c_Orderings_Obot__class_Obot(tc_fun(U_2985,tc_HOL_Obool))) = U_2986,
inference(clausify,[status(thm)],[f_674_3]) ).
fof(f_675_1,plain,
! [V_B_2,V_A_2,T_c] :
( ( hAPP(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_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_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_c,tc_HOL_Obool)) )
| hAPP(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)) ) ),
inference(fof_nnf,[status(thm)],[fact_Un__empty]) ).
fof(f_675_2,plain,
! [U_2989,U_2988,U_2987] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2987,tc_HOL_Obool)),U_2988),U_2989) = c_Orderings_Obot__class_Obot(tc_fun(U_2987,tc_HOL_Obool))
| U_2989 != c_Orderings_Obot__class_Obot(tc_fun(U_2987,tc_HOL_Obool))
| U_2988 != c_Orderings_Obot__class_Obot(tc_fun(U_2987,tc_HOL_Obool)) )
& ( ( U_2989 = c_Orderings_Obot__class_Obot(tc_fun(U_2987,tc_HOL_Obool))
& U_2988 = c_Orderings_Obot__class_Obot(tc_fun(U_2987,tc_HOL_Obool)) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2987,tc_HOL_Obool)),U_2988),U_2989) != c_Orderings_Obot__class_Obot(tc_fun(U_2987,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_675_1]) ).
fof(f_675_3,plain,
( ! [U_2995,U_2993,U_2991] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2991,tc_HOL_Obool)),U_2993),U_2995) = c_Orderings_Obot__class_Obot(tc_fun(U_2991,tc_HOL_Obool))
| U_2995 != c_Orderings_Obot__class_Obot(tc_fun(U_2991,tc_HOL_Obool))
| U_2993 != c_Orderings_Obot__class_Obot(tc_fun(U_2991,tc_HOL_Obool)) )
& ! [U_2994,U_2992,U_2990] :
( ( U_2994 = c_Orderings_Obot__class_Obot(tc_fun(U_2990,tc_HOL_Obool))
& U_2992 = c_Orderings_Obot__class_Obot(tc_fun(U_2990,tc_HOL_Obool)) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2990,tc_HOL_Obool)),U_2992),U_2994) != c_Orderings_Obot__class_Obot(tc_fun(U_2990,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_675_2]) ).
fof(f_675_4,plain,
( ! [U_2992,U_2990,U_2994] :
( U_2994 = c_Orderings_Obot__class_Obot(tc_fun(U_2990,tc_HOL_Obool))
| ~ sP170(U_2992,U_2990,U_2994) )
& ! [U_2992,U_2990,U_2994] :
( U_2992 = c_Orderings_Obot__class_Obot(tc_fun(U_2990,tc_HOL_Obool))
| ~ sP170(U_2992,U_2990,U_2994) )
& ! [U_2995,U_2991,U_2993] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2991,tc_HOL_Obool)),U_2993),U_2995) = c_Orderings_Obot__class_Obot(tc_fun(U_2991,tc_HOL_Obool))
| U_2995 != c_Orderings_Obot__class_Obot(tc_fun(U_2991,tc_HOL_Obool))
| U_2993 != c_Orderings_Obot__class_Obot(tc_fun(U_2991,tc_HOL_Obool)) )
& ! [U_2992,U_2990,U_2994] :
( sP170(U_2992,U_2990,U_2994)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2990,tc_HOL_Obool)),U_2992),U_2994) != c_Orderings_Obot__class_Obot(tc_fun(U_2990,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170])],[f_675_3]) ).
cnf(f_675_5,plain,
( sP170(U_2992,U_2990,U_2994)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2990,tc_HOL_Obool)),U_2992),U_2994) != c_Orderings_Obot__class_Obot(tc_fun(U_2990,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_675_4]) ).
cnf(f_675_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2991,tc_HOL_Obool)),U_2993),U_2995) = c_Orderings_Obot__class_Obot(tc_fun(U_2991,tc_HOL_Obool))
| U_2995 != c_Orderings_Obot__class_Obot(tc_fun(U_2991,tc_HOL_Obool))
| U_2993 != c_Orderings_Obot__class_Obot(tc_fun(U_2991,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_675_4]) ).
cnf(f_675_7,plain,
( U_2992 = c_Orderings_Obot__class_Obot(tc_fun(U_2990,tc_HOL_Obool))
| ~ sP170(U_2992,U_2990,U_2994) ),
inference(clausify,[status(thm)],[f_675_4]) ).
cnf(f_675_8,plain,
( U_2994 = c_Orderings_Obot__class_Obot(tc_fun(U_2990,tc_HOL_Obool))
| ~ sP170(U_2992,U_2990,U_2994) ),
inference(clausify,[status(thm)],[f_675_4]) ).
fof(f_676_1,plain,
! [V_Ga_2,V_F_2,T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_Ga_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Ga_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Ga_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Un]) ).
fof(f_676_2,plain,
! [U_2998,U_2997,U_2996] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2996),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2996,tc_HOL_Obool)),U_2997),U_2998)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2996),U_2998))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2996),U_2997)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2996),U_2998))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2996),U_2997)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2996),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2996,tc_HOL_Obool)),U_2997),U_2998))) ) ),
inference(variable_rename,[status(thm)],[f_676_1]) ).
fof(f_676_3,plain,
( ! [U_3004,U_3002,U_3000] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3000),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3000,tc_HOL_Obool)),U_3002),U_3004)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3000),U_3004))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3000),U_3002)) )
& ! [U_3003,U_3001,U_2999] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2999),U_3003))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_2999),U_3001)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2999),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2999,tc_HOL_Obool)),U_3001),U_3003))) ) ),
inference(miniscope,[status(thm)],[f_676_2]) ).
fof(f_676_4,plain,
( ! [U_3001,U_2999,U_3003] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2999),U_3003))
| ~ sP171(U_3001,U_2999,U_3003) )
& ! [U_3001,U_2999,U_3003] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2999),U_3001))
| ~ sP171(U_3001,U_2999,U_3003) )
& ! [U_3004,U_3002,U_3000] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3000),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3000,tc_HOL_Obool)),U_3002),U_3004)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3000),U_3004))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3000),U_3002)) )
& ! [U_3001,U_2999,U_3003] :
( sP171(U_3001,U_2999,U_3003)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2999),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2999,tc_HOL_Obool)),U_3001),U_3003))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP171])],[f_676_3]) ).
cnf(f_676_5,plain,
( sP171(U_3001,U_2999,U_3003)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2999),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2999,tc_HOL_Obool)),U_3001),U_3003))) ),
inference(clausify,[status(thm)],[f_676_4]) ).
cnf(f_676_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3000),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3000,tc_HOL_Obool)),U_3002),U_3004)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3000),U_3004))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3000),U_3002)) ),
inference(clausify,[status(thm)],[f_676_4]) ).
cnf(f_676_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2999),U_3001))
| ~ sP171(U_3001,U_2999,U_3003) ),
inference(clausify,[status(thm)],[f_676_4]) ).
cnf(f_676_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2999),U_3003))
| ~ sP171(U_3001,U_2999,U_3003) ),
inference(clausify,[status(thm)],[f_676_4]) ).
fof(f_677_1,plain,
! [V_Ga_2,V_F_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_Ga_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Ga_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__UnI]) ).
fof(f_677_2,plain,
! [U_3007,U_3006,U_3005] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3005),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3005,tc_HOL_Obool)),U_3006),U_3007)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3005),U_3007))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3005),U_3006)) ),
inference(variable_rename,[status(thm)],[f_677_1]) ).
fof(f_677_3,plain,
! [U_3005,U_3007,U_3006] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3005),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3005,tc_HOL_Obool)),U_3006),U_3007)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3005),U_3007))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3005),U_3006)) ),
inference(definitional_conversion,[status(esa)],[f_677_2]) ).
cnf(f_677_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3005),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3005,tc_HOL_Obool)),U_3006),U_3007)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3005),U_3007))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3005),U_3006)) ),
inference(clausify,[status(thm)],[f_677_3]) ).
fof(f_678_1,plain,
! [V_B_2,V_a_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Un__insert__right]) ).
fof(f_678_2,plain,
! [U_3011,U_3010,U_3009,U_3008] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3008,tc_HOL_Obool)),U_3009),hAPP(hAPP(c_Set_Oinsert(U_3008),U_3010),U_3011)) = hAPP(hAPP(c_Set_Oinsert(U_3008),U_3010),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3008,tc_HOL_Obool)),U_3009),U_3011)),
inference(variable_rename,[status(thm)],[f_678_1]) ).
fof(f_678_3,plain,
! [U_3008,U_3009,U_3010,U_3011] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3008,tc_HOL_Obool)),U_3009),hAPP(hAPP(c_Set_Oinsert(U_3008),U_3010),U_3011)) = hAPP(hAPP(c_Set_Oinsert(U_3008),U_3010),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3008,tc_HOL_Obool)),U_3009),U_3011)),
inference(definitional_conversion,[status(esa)],[f_678_2]) ).
cnf(f_678_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3008,tc_HOL_Obool)),U_3009),hAPP(hAPP(c_Set_Oinsert(U_3008),U_3010),U_3011)) = hAPP(hAPP(c_Set_Oinsert(U_3008),U_3010),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3008,tc_HOL_Obool)),U_3009),U_3011)),
inference(clausify,[status(thm)],[f_678_3]) ).
fof(f_679_1,plain,
! [V_C_2,V_B_2,V_a_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Un__insert__left]) ).
fof(f_679_2,plain,
! [U_3015,U_3014,U_3013,U_3012] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3012,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_3012),U_3013),U_3014)),U_3015) = hAPP(hAPP(c_Set_Oinsert(U_3012),U_3013),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3012,tc_HOL_Obool)),U_3014),U_3015)),
inference(variable_rename,[status(thm)],[f_679_1]) ).
fof(f_679_3,plain,
! [U_3012,U_3013,U_3014,U_3015] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3012,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_3012),U_3013),U_3014)),U_3015) = hAPP(hAPP(c_Set_Oinsert(U_3012),U_3013),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3012,tc_HOL_Obool)),U_3014),U_3015)),
inference(definitional_conversion,[status(esa)],[f_679_2]) ).
cnf(f_679_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3012,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_3012),U_3013),U_3014)),U_3015) = hAPP(hAPP(c_Set_Oinsert(U_3012),U_3013),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3012,tc_HOL_Obool)),U_3014),U_3015)),
inference(clausify,[status(thm)],[f_679_3]) ).
fof(f_680_1,plain,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Un__upper1]) ).
fof(f_680_2,plain,
! [U_3018,U_3017,U_3016] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3016,tc_HOL_Obool)),U_3017),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3016,tc_HOL_Obool)),U_3017),U_3018))),
inference(variable_rename,[status(thm)],[f_680_1]) ).
fof(f_680_3,plain,
! [U_3016,U_3017,U_3018] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3016,tc_HOL_Obool)),U_3017),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3016,tc_HOL_Obool)),U_3017),U_3018))),
inference(definitional_conversion,[status(esa)],[f_680_2]) ).
cnf(f_680_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3016,tc_HOL_Obool)),U_3017),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3016,tc_HOL_Obool)),U_3017),U_3018))),
inference(clausify,[status(thm)],[f_680_3]) ).
fof(f_681_1,plain,
! [V_A_2,V_B_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Un__upper2]) ).
fof(f_681_2,plain,
! [U_3021,U_3020,U_3019] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3019,tc_HOL_Obool)),U_3020),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3019,tc_HOL_Obool)),U_3021),U_3020))),
inference(variable_rename,[status(thm)],[f_681_1]) ).
fof(f_681_3,plain,
! [U_3019,U_3020,U_3021] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3019,tc_HOL_Obool)),U_3020),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3019,tc_HOL_Obool)),U_3021),U_3020))),
inference(definitional_conversion,[status(esa)],[f_681_2]) ).
cnf(f_681_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3019,tc_HOL_Obool)),U_3020),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3019,tc_HOL_Obool)),U_3021),U_3020))),
inference(clausify,[status(thm)],[f_681_3]) ).
fof(f_682_1,plain,
! [V_B_2,V_A_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),V_B_2) != V_B_2 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__Un__eq]) ).
fof(f_682_2,plain,
! [U_3024,U_3023,U_3022] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3022,tc_HOL_Obool)),U_3023),U_3024))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3022,tc_HOL_Obool)),U_3023),U_3024) != U_3024 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3022,tc_HOL_Obool)),U_3023),U_3024) = U_3024
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3022,tc_HOL_Obool)),U_3023),U_3024)) ) ),
inference(variable_rename,[status(thm)],[f_682_1]) ).
fof(f_682_3,plain,
( ! [U_3030,U_3028,U_3026] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3026,tc_HOL_Obool)),U_3028),U_3030))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3026,tc_HOL_Obool)),U_3028),U_3030) != U_3030 )
& ! [U_3029,U_3027,U_3025] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3025,tc_HOL_Obool)),U_3027),U_3029) = U_3029
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3025,tc_HOL_Obool)),U_3027),U_3029)) ) ),
inference(miniscope,[status(thm)],[f_682_2]) ).
fof(f_682_4,plain,
( ! [U_3026,U_3028,U_3030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3026,tc_HOL_Obool)),U_3028),U_3030))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3026,tc_HOL_Obool)),U_3028),U_3030) != U_3030 )
& ! [U_3027,U_3029,U_3025] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3025,tc_HOL_Obool)),U_3027),U_3029) = U_3029
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3025,tc_HOL_Obool)),U_3027),U_3029)) ) ),
inference(definitional_conversion,[status(esa)],[f_682_3]) ).
cnf(f_682_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3025,tc_HOL_Obool)),U_3027),U_3029) = U_3029
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3025,tc_HOL_Obool)),U_3027),U_3029)) ),
inference(clausify,[status(thm)],[f_682_4]) ).
cnf(f_682_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3026,tc_HOL_Obool)),U_3028),U_3030))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3026,tc_HOL_Obool)),U_3028),U_3030) != U_3030 ),
inference(clausify,[status(thm)],[f_682_4]) ).
fof(f_683_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Un__absorb1]) ).
fof(f_683_2,plain,
! [U_3033,U_3032,U_3031] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3031,tc_HOL_Obool)),U_3032),U_3033) = U_3033
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3031,tc_HOL_Obool)),U_3032),U_3033)) ),
inference(variable_rename,[status(thm)],[f_683_1]) ).
fof(f_683_3,plain,
! [U_3031,U_3032,U_3033] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3031,tc_HOL_Obool)),U_3032),U_3033) = U_3033
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3031,tc_HOL_Obool)),U_3032),U_3033)) ),
inference(definitional_conversion,[status(esa)],[f_683_2]) ).
cnf(f_683_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3031,tc_HOL_Obool)),U_3032),U_3033) = U_3033
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3031,tc_HOL_Obool)),U_3032),U_3033)) ),
inference(clausify,[status(thm)],[f_683_3]) ).
fof(f_684_1,plain,
! [V_A_2,V_B_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_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),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Un__absorb2]) ).
fof(f_684_2,plain,
! [U_3036,U_3035,U_3034] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3034,tc_HOL_Obool)),U_3036),U_3035) = U_3036
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3034,tc_HOL_Obool)),U_3035),U_3036)) ),
inference(variable_rename,[status(thm)],[f_684_1]) ).
fof(f_684_3,plain,
! [U_3034,U_3035,U_3036] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3034,tc_HOL_Obool)),U_3036),U_3035) = U_3036
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3034,tc_HOL_Obool)),U_3035),U_3036)) ),
inference(definitional_conversion,[status(esa)],[f_684_2]) ).
cnf(f_684_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3034,tc_HOL_Obool)),U_3036),U_3035) = U_3036
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3034,tc_HOL_Obool)),U_3035),U_3036)) ),
inference(clausify,[status(thm)],[f_684_3]) ).
fof(f_685_1,plain,
! [V_B_2,V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Un__least]) ).
fof(f_685_2,plain,
! [U_3040,U_3039,U_3038,U_3037] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3037,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3037,tc_HOL_Obool)),U_3038),U_3040)),U_3039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3037,tc_HOL_Obool)),U_3040),U_3039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3037,tc_HOL_Obool)),U_3038),U_3039)) ),
inference(variable_rename,[status(thm)],[f_685_1]) ).
fof(f_685_3,plain,
! [U_3037,U_3038,U_3039,U_3040] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3037,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3037,tc_HOL_Obool)),U_3038),U_3040)),U_3039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3037,tc_HOL_Obool)),U_3040),U_3039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3037,tc_HOL_Obool)),U_3038),U_3039)) ),
inference(definitional_conversion,[status(esa)],[f_685_2]) ).
cnf(f_685_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3037,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3037,tc_HOL_Obool)),U_3038),U_3040)),U_3039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3037,tc_HOL_Obool)),U_3040),U_3039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3037,tc_HOL_Obool)),U_3038),U_3039)) ),
inference(clausify,[status(thm)],[f_685_3]) ).
fof(f_686_1,plain,
! [V_D_2,V_B_2,V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_C_2),V_D_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Un__mono]) ).
fof(f_686_2,plain,
! [U_3045,U_3044,U_3043,U_3042,U_3041] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3041,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3041,tc_HOL_Obool)),U_3042),U_3044)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3041,tc_HOL_Obool)),U_3043),U_3045)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3041,tc_HOL_Obool)),U_3044),U_3045))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3041,tc_HOL_Obool)),U_3042),U_3043)) ),
inference(variable_rename,[status(thm)],[f_686_1]) ).
fof(f_686_3,plain,
! [U_3041,U_3042,U_3043,U_3044,U_3045] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3041,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3041,tc_HOL_Obool)),U_3042),U_3044)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3041,tc_HOL_Obool)),U_3043),U_3045)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3041,tc_HOL_Obool)),U_3044),U_3045))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3041,tc_HOL_Obool)),U_3042),U_3043)) ),
inference(definitional_conversion,[status(esa)],[f_686_2]) ).
cnf(f_686_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3041,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3041,tc_HOL_Obool)),U_3042),U_3044)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3041,tc_HOL_Obool)),U_3043),U_3045)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3041,tc_HOL_Obool)),U_3044),U_3045))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3041,tc_HOL_Obool)),U_3042),U_3043)) ),
inference(clausify,[status(thm)],[f_686_3]) ).
fof(f_687_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_image__Un]) ).
fof(f_687_2,plain,
! [U_3050,U_3049,U_3048,U_3047,U_3046] : hAPP(c_Set_Oimage(U_3046,U_3047,U_3048),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3046,tc_HOL_Obool)),U_3049),U_3050)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3047,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3046,U_3047,U_3048),U_3049)),hAPP(c_Set_Oimage(U_3046,U_3047,U_3048),U_3050)),
inference(variable_rename,[status(thm)],[f_687_1]) ).
fof(f_687_3,plain,
! [U_3046,U_3047,U_3048,U_3049,U_3050] : hAPP(c_Set_Oimage(U_3046,U_3047,U_3048),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3046,tc_HOL_Obool)),U_3049),U_3050)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3047,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3046,U_3047,U_3048),U_3049)),hAPP(c_Set_Oimage(U_3046,U_3047,U_3048),U_3050)),
inference(definitional_conversion,[status(esa)],[f_687_2]) ).
cnf(f_687_4,plain,
hAPP(c_Set_Oimage(U_3046,U_3047,U_3048),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3046,tc_HOL_Obool)),U_3049),U_3050)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3047,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3046,U_3047,U_3048),U_3049)),hAPP(c_Set_Oimage(U_3046,U_3047,U_3048),U_3050)),
inference(clausify,[status(thm)],[f_687_3]) ).
fof(f_688_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Un__Diff__cancel]) ).
fof(f_688_2,plain,
! [U_3053,U_3052,U_3051] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3051,tc_HOL_Obool)),U_3052),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3051,tc_HOL_Obool)),U_3053),U_3052)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3051,tc_HOL_Obool)),U_3052),U_3053),
inference(variable_rename,[status(thm)],[f_688_1]) ).
fof(f_688_3,plain,
! [U_3051,U_3052,U_3053] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3051,tc_HOL_Obool)),U_3052),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3051,tc_HOL_Obool)),U_3053),U_3052)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3051,tc_HOL_Obool)),U_3052),U_3053),
inference(definitional_conversion,[status(esa)],[f_688_2]) ).
cnf(f_688_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3051,tc_HOL_Obool)),U_3052),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3051,tc_HOL_Obool)),U_3053),U_3052)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3051,tc_HOL_Obool)),U_3052),U_3053),
inference(clausify,[status(thm)],[f_688_3]) ).
fof(f_689_1,plain,
! [V_A_2,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_Un__Diff__cancel2]) ).
fof(f_689_2,plain,
! [U_3056,U_3055,U_3054] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3054,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3054,tc_HOL_Obool)),U_3055),U_3056)),U_3056) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3054,tc_HOL_Obool)),U_3055),U_3056),
inference(variable_rename,[status(thm)],[f_689_1]) ).
fof(f_689_3,plain,
! [U_3054,U_3055,U_3056] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3054,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3054,tc_HOL_Obool)),U_3055),U_3056)),U_3056) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3054,tc_HOL_Obool)),U_3055),U_3056),
inference(definitional_conversion,[status(esa)],[f_689_2]) ).
cnf(f_689_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3054,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3054,tc_HOL_Obool)),U_3055),U_3056)),U_3056) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3054,tc_HOL_Obool)),U_3055),U_3056),
inference(clausify,[status(thm)],[f_689_3]) ).
fof(f_690_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,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_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Un__Diff]) ).
fof(f_690_2,plain,
! [U_3060,U_3059,U_3058,U_3057] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3057,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3057,tc_HOL_Obool)),U_3058),U_3059)),U_3060) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3057,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3057,tc_HOL_Obool)),U_3058),U_3060)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3057,tc_HOL_Obool)),U_3059),U_3060)),
inference(variable_rename,[status(thm)],[f_690_1]) ).
fof(f_690_3,plain,
! [U_3057,U_3058,U_3059,U_3060] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3057,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3057,tc_HOL_Obool)),U_3058),U_3059)),U_3060) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3057,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3057,tc_HOL_Obool)),U_3058),U_3060)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3057,tc_HOL_Obool)),U_3059),U_3060)),
inference(definitional_conversion,[status(esa)],[f_690_2]) ).
cnf(f_690_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3057,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3057,tc_HOL_Obool)),U_3058),U_3059)),U_3060) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3057,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3057,tc_HOL_Obool)),U_3058),U_3060)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3057,tc_HOL_Obool)),U_3059),U_3060)),
inference(clausify,[status(thm)],[f_690_3]) ).
fof(f_691_1,plain,
! [T_c] : c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_UNIV__not__empty]) ).
fof(f_691_2,plain,
! [U_3061] : c_Orderings_Otop__class_Otop(tc_fun(U_3061,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_3061,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_691_1]) ).
fof(f_691_3,plain,
! [U_3061] : c_Orderings_Otop__class_Otop(tc_fun(U_3061,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_3061,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_691_2]) ).
cnf(f_691_4,plain,
c_Orderings_Otop__class_Otop(tc_fun(U_3061,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_3061,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_691_3]) ).
fof(f_692_1,plain,
! [T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(T_c) ),
inference(fof_nnf,[status(thm)],[fact_finite__UNIV]) ).
fof(f_692_2,plain,
! [U_3062] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3062),c_Orderings_Otop__class_Otop(tc_fun(U_3062,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(U_3062) ),
inference(variable_rename,[status(thm)],[f_692_1]) ).
fof(f_692_3,plain,
! [U_3062] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3062),c_Orderings_Otop__class_Otop(tc_fun(U_3062,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(U_3062) ),
inference(definitional_conversion,[status(esa)],[f_692_2]) ).
cnf(f_692_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3062),c_Orderings_Otop__class_Otop(tc_fun(U_3062,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(U_3062) ),
inference(clausify,[status(thm)],[f_692_3]) ).
fof(f_693_1,plain,
! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_subset__UNIV]) ).
fof(f_693_2,plain,
! [U_3064,U_3063] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3063,tc_HOL_Obool)),U_3064),c_Orderings_Otop__class_Otop(tc_fun(U_3063,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_693_1]) ).
fof(f_693_3,plain,
! [U_3063,U_3064] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3063,tc_HOL_Obool)),U_3064),c_Orderings_Otop__class_Otop(tc_fun(U_3063,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_693_2]) ).
cnf(f_693_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3063,tc_HOL_Obool)),U_3064),c_Orderings_Otop__class_Otop(tc_fun(U_3063,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_693_3]) ).
fof(f_694_1,plain,
! [V_y_2,V_x_2,V_f_2,T_d,T_c] :
( ( ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) )
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__eq]) ).
fof(f_694_2,plain,
! [U_3069,U_3068,U_3067,U_3066,U_3065] :
( ( ( hAPP(U_3067,U_3068) = hAPP(U_3067,U_3069)
| U_3068 != U_3069 )
& ( U_3068 = U_3069
| hAPP(U_3067,U_3068) != hAPP(U_3067,U_3069) ) )
| ~ c_Fun_Oinj__on(U_3065,U_3066,U_3067,c_Orderings_Otop__class_Otop(tc_fun(U_3065,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_694_1]) ).
fof(f_694_3,plain,
! [U_3069,U_3068,U_3067] :
( ! [U_3066,U_3065] : ~ c_Fun_Oinj__on(U_3065,U_3066,U_3067,c_Orderings_Otop__class_Otop(tc_fun(U_3065,tc_HOL_Obool)))
| ( ( hAPP(U_3067,U_3068) = hAPP(U_3067,U_3069)
| U_3068 != U_3069 )
& ( U_3068 = U_3069
| hAPP(U_3067,U_3068) != hAPP(U_3067,U_3069) ) ) ),
inference(miniscope,[status(thm)],[f_694_2]) ).
fof(f_694_4,plain,
( ! [U_3067,U_3068,U_3069] :
( hAPP(U_3067,U_3068) = hAPP(U_3067,U_3069)
| U_3068 != U_3069
| ~ sP172(U_3067,U_3068,U_3069) )
& ! [U_3067,U_3068,U_3069] :
( U_3068 = U_3069
| hAPP(U_3067,U_3068) != hAPP(U_3067,U_3069)
| ~ sP172(U_3067,U_3068,U_3069) )
& ! [U_3065,U_3066,U_3067,U_3068,U_3069] :
( ~ c_Fun_Oinj__on(U_3065,U_3066,U_3067,c_Orderings_Otop__class_Otop(tc_fun(U_3065,tc_HOL_Obool)))
| sP172(U_3067,U_3068,U_3069) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172])],[f_694_3]) ).
cnf(f_694_5,plain,
( ~ c_Fun_Oinj__on(U_3065,U_3066,U_3067,c_Orderings_Otop__class_Otop(tc_fun(U_3065,tc_HOL_Obool)))
| sP172(U_3067,U_3068,U_3069) ),
inference(clausify,[status(thm)],[f_694_4]) ).
cnf(f_694_6,plain,
( U_3068 = U_3069
| hAPP(U_3067,U_3068) != hAPP(U_3067,U_3069)
| ~ sP172(U_3067,U_3068,U_3069) ),
inference(clausify,[status(thm)],[f_694_4]) ).
cnf(f_694_7,plain,
( hAPP(U_3067,U_3068) = hAPP(U_3067,U_3069)
| U_3068 != U_3069
| ~ sP172(U_3067,U_3068,U_3069) ),
inference(clausify,[status(thm)],[f_694_4]) ).
fof(f_695_1,plain,
! [V_y_2,V_x_2,V_f_2,T_d,T_c] :
( V_x_2 = V_y_2
| hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_injD]) ).
fof(f_695_2,plain,
! [U_3074,U_3073,U_3072,U_3071,U_3070] :
( U_3073 = U_3074
| hAPP(U_3072,U_3073) != hAPP(U_3072,U_3074)
| ~ c_Fun_Oinj__on(U_3070,U_3071,U_3072,c_Orderings_Otop__class_Otop(tc_fun(U_3070,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_695_1]) ).
fof(f_695_3,plain,
! [U_3074,U_3073,U_3072] :
( ! [U_3071,U_3070] : ~ c_Fun_Oinj__on(U_3070,U_3071,U_3072,c_Orderings_Otop__class_Otop(tc_fun(U_3070,tc_HOL_Obool)))
| U_3073 = U_3074
| hAPP(U_3072,U_3073) != hAPP(U_3072,U_3074) ),
inference(miniscope,[status(thm)],[f_695_2]) ).
fof(f_695_4,plain,
! [U_3072,U_3070,U_3074,U_3073,U_3071] :
( ~ c_Fun_Oinj__on(U_3070,U_3071,U_3072,c_Orderings_Otop__class_Otop(tc_fun(U_3070,tc_HOL_Obool)))
| U_3073 = U_3074
| hAPP(U_3072,U_3073) != hAPP(U_3072,U_3074) ),
inference(definitional_conversion,[status(esa)],[f_695_3]) ).
cnf(f_695_5,plain,
( ~ c_Fun_Oinj__on(U_3070,U_3071,U_3072,c_Orderings_Otop__class_Otop(tc_fun(U_3070,tc_HOL_Obool)))
| U_3073 = U_3074
| hAPP(U_3072,U_3073) != hAPP(U_3072,U_3074) ),
inference(clausify,[status(thm)],[f_695_4]) ).
fof(f_696_1,plain,
! [V_z_2,V_g_2,V_f_2,T_d,T_c] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = V_z_2,
inference(fof_nnf,[status(thm)],[fact_fold__image__empty]) ).
fof(f_696_2,plain,
! [U_3079,U_3078,U_3077,U_3076,U_3075] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3075,U_3076,U_3077),U_3078),U_3079),c_Orderings_Obot__class_Obot(tc_fun(U_3076,tc_HOL_Obool))) = U_3079,
inference(variable_rename,[status(thm)],[f_696_1]) ).
fof(f_696_3,plain,
! [U_3075,U_3076,U_3077,U_3078,U_3079] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3075,U_3076,U_3077),U_3078),U_3079),c_Orderings_Obot__class_Obot(tc_fun(U_3076,tc_HOL_Obool))) = U_3079,
inference(definitional_conversion,[status(esa)],[f_696_2]) ).
cnf(f_696_4,plain,
hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3075,U_3076,U_3077),U_3078),U_3079),c_Orderings_Obot__class_Obot(tc_fun(U_3076,tc_HOL_Obool))) = U_3079,
inference(clausify,[status(thm)],[f_696_3]) ).
fof(f_697_1,plain,
! [T_c] :
( c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c))
| ~ class_Lattices_Osemilattice__sup(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__sup]) ).
fof(f_697_2,plain,
! [U_3080] :
( c_Finite__Set_Ofun__left__comm__idem(U_3080,U_3080,c_Lattices_Osemilattice__sup__class_Osup(U_3080))
| ~ class_Lattices_Osemilattice__sup(U_3080) ),
inference(variable_rename,[status(thm)],[f_697_1]) ).
fof(f_697_3,plain,
! [U_3080] :
( c_Finite__Set_Ofun__left__comm__idem(U_3080,U_3080,c_Lattices_Osemilattice__sup__class_Osup(U_3080))
| ~ class_Lattices_Osemilattice__sup(U_3080) ),
inference(definitional_conversion,[status(esa)],[f_697_2]) ).
cnf(f_697_4,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_3080,U_3080,c_Lattices_Osemilattice__sup__class_Osup(U_3080))
| ~ class_Lattices_Osemilattice__sup(U_3080) ),
inference(clausify,[status(thm)],[f_697_3]) ).
fof(f_698_1,plain,
! [V_x_2,V_S_2,V_R_2,T_c] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_R_2),V_S_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_R_2),V_S_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_sup__Un__eq]) ).
fof(f_698_2,plain,
! [U_3084,U_3083,U_3082,U_3081] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3081,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_3081,tc_fun(U_3081,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3081)),U_3082)),hAPP(hAPP(c_COMBC(U_3081,tc_fun(U_3081,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3081)),U_3083)),U_3084))
| ~ hBOOL(hAPP(hAPP(c_member(U_3081),U_3084),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3081,tc_HOL_Obool)),U_3082),U_3083))) )
& ( hBOOL(hAPP(hAPP(c_member(U_3081),U_3084),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3081,tc_HOL_Obool)),U_3082),U_3083)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3081,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_3081,tc_fun(U_3081,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3081)),U_3082)),hAPP(hAPP(c_COMBC(U_3081,tc_fun(U_3081,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3081)),U_3083)),U_3084)) ) ),
inference(variable_rename,[status(thm)],[f_698_1]) ).
fof(f_698_3,plain,
( ! [U_3092,U_3090,U_3088,U_3086] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3086,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_3086,tc_fun(U_3086,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3086)),U_3088)),hAPP(hAPP(c_COMBC(U_3086,tc_fun(U_3086,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3086)),U_3090)),U_3092))
| ~ hBOOL(hAPP(hAPP(c_member(U_3086),U_3092),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3086,tc_HOL_Obool)),U_3088),U_3090))) )
& ! [U_3091,U_3089,U_3087,U_3085] :
( hBOOL(hAPP(hAPP(c_member(U_3085),U_3091),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3085,tc_HOL_Obool)),U_3087),U_3089)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3085,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_3085,tc_fun(U_3085,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3085)),U_3087)),hAPP(hAPP(c_COMBC(U_3085,tc_fun(U_3085,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3085)),U_3089)),U_3091)) ) ),
inference(miniscope,[status(thm)],[f_698_2]) ).
fof(f_698_4,plain,
( ! [U_3086,U_3088,U_3090,U_3092] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3086,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_3086,tc_fun(U_3086,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3086)),U_3088)),hAPP(hAPP(c_COMBC(U_3086,tc_fun(U_3086,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3086)),U_3090)),U_3092))
| ~ hBOOL(hAPP(hAPP(c_member(U_3086),U_3092),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3086,tc_HOL_Obool)),U_3088),U_3090))) )
& ! [U_3087,U_3089,U_3091,U_3085] :
( hBOOL(hAPP(hAPP(c_member(U_3085),U_3091),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3085,tc_HOL_Obool)),U_3087),U_3089)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3085,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_3085,tc_fun(U_3085,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3085)),U_3087)),hAPP(hAPP(c_COMBC(U_3085,tc_fun(U_3085,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3085)),U_3089)),U_3091)) ) ),
inference(definitional_conversion,[status(esa)],[f_698_3]) ).
cnf(f_698_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_3085),U_3091),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3085,tc_HOL_Obool)),U_3087),U_3089)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3085,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_3085,tc_fun(U_3085,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3085)),U_3087)),hAPP(hAPP(c_COMBC(U_3085,tc_fun(U_3085,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3085)),U_3089)),U_3091)) ),
inference(clausify,[status(thm)],[f_698_4]) ).
cnf(f_698_6,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3086,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_3086,tc_fun(U_3086,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3086)),U_3088)),hAPP(hAPP(c_COMBC(U_3086,tc_fun(U_3086,tc_HOL_Obool),tc_HOL_Obool),c_member(U_3086)),U_3090)),U_3092))
| ~ hBOOL(hAPP(hAPP(c_member(U_3086),U_3092),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3086,tc_HOL_Obool)),U_3088),U_3090))) ),
inference(clausify,[status(thm)],[f_698_4]) ).
fof(f_699_1,plain,
! [V_g_2,V_f_2,T_e,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,hAPP(hAPP(c_COMBB(T_e,T_c,T_d),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_e,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_e,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_range__composition]) ).
fof(f_699_2,plain,
! [U_3097,U_3096,U_3095,U_3094,U_3093] : hAPP(c_Set_Oimage(U_3093,U_3094,hAPP(hAPP(c_COMBB(U_3095,U_3094,U_3093),U_3096),U_3097)),c_Orderings_Otop__class_Otop(tc_fun(U_3093,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_3095,U_3094,U_3096),hAPP(c_Set_Oimage(U_3093,U_3095,U_3097),c_Orderings_Otop__class_Otop(tc_fun(U_3093,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_699_1]) ).
fof(f_699_3,plain,
! [U_3094,U_3095,U_3093,U_3096,U_3097] : hAPP(c_Set_Oimage(U_3093,U_3094,hAPP(hAPP(c_COMBB(U_3095,U_3094,U_3093),U_3096),U_3097)),c_Orderings_Otop__class_Otop(tc_fun(U_3093,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_3095,U_3094,U_3096),hAPP(c_Set_Oimage(U_3093,U_3095,U_3097),c_Orderings_Otop__class_Otop(tc_fun(U_3093,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_699_2]) ).
cnf(f_699_4,plain,
hAPP(c_Set_Oimage(U_3093,U_3094,hAPP(hAPP(c_COMBB(U_3095,U_3094,U_3093),U_3096),U_3097)),c_Orderings_Otop__class_Otop(tc_fun(U_3093,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_3095,U_3094,U_3096),hAPP(c_Set_Oimage(U_3093,U_3095,U_3097),c_Orderings_Otop__class_Otop(tc_fun(U_3093,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_699_3]) ).
fof(f_700_1,plain,
! [T_e,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,tc_fun(T_e,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,T_d),T_c),c_COMBK(T_d,T_e)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__fun]) ).
fof(f_700_2,plain,
! [U_3101,U_3100,U_3099,U_3098] :
( c_Fun_Oinj__on(U_3098,tc_fun(U_3101,U_3099),hAPP(hAPP(c_COMBB(U_3099,tc_fun(U_3101,U_3099),U_3098),c_COMBK(U_3099,U_3101)),U_3100),c_Orderings_Otop__class_Otop(tc_fun(U_3098,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_3098,U_3099,U_3100,c_Orderings_Otop__class_Otop(tc_fun(U_3098,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_700_1]) ).
fof(f_700_3,plain,
! [U_3098,U_3099,U_3100,U_3101] :
( c_Fun_Oinj__on(U_3098,tc_fun(U_3101,U_3099),hAPP(hAPP(c_COMBB(U_3099,tc_fun(U_3101,U_3099),U_3098),c_COMBK(U_3099,U_3101)),U_3100),c_Orderings_Otop__class_Otop(tc_fun(U_3098,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_3098,U_3099,U_3100,c_Orderings_Otop__class_Otop(tc_fun(U_3098,tc_HOL_Obool))) ),
inference(definitional_conversion,[status(esa)],[f_700_2]) ).
cnf(f_700_4,plain,
( c_Fun_Oinj__on(U_3098,tc_fun(U_3101,U_3099),hAPP(hAPP(c_COMBB(U_3099,tc_fun(U_3101,U_3099),U_3098),c_COMBK(U_3099,U_3101)),U_3100),c_Orderings_Otop__class_Otop(tc_fun(U_3098,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_3098,U_3099,U_3100,c_Orderings_Otop__class_Otop(tc_fun(U_3098,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_700_3]) ).
fof(f_701_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_701_2,plain,
! [U_3103,U_3102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3102),U_3103),c_Orderings_Otop__class_Otop(U_3102)))
| ~ class_Orderings_Otop(U_3102) ),
inference(variable_rename,[status(thm)],[f_701_1]) ).
fof(f_701_3,plain,
! [U_3102,U_3103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3102),U_3103),c_Orderings_Otop__class_Otop(U_3102)))
| ~ class_Orderings_Otop(U_3102) ),
inference(definitional_conversion,[status(esa)],[f_701_2]) ).
cnf(f_701_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3102),U_3103),c_Orderings_Otop__class_Otop(U_3102)))
| ~ class_Orderings_Otop(U_3102) ),
inference(clausify,[status(thm)],[f_701_3]) ).
fof(f_702_1,plain,
! [V_g_2,V_f_2,T_d,T_c] : hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_d,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)),
inference(fof_nnf,[status(thm)],[fact_fold__image__def]) ).
fof(f_702_2,plain,
! [U_3107,U_3106,U_3105,U_3104] : hAPP(c_Finite__Set_Ofold__image(U_3104,U_3105,U_3106),U_3107) = c_Finite__Set_Ofold(U_3105,U_3104,hAPP(hAPP(c_COMBB(U_3104,tc_fun(U_3104,U_3104),U_3105),U_3106),U_3107)),
inference(variable_rename,[status(thm)],[f_702_1]) ).
fof(f_702_3,plain,
! [U_3104,U_3105,U_3106,U_3107] : hAPP(c_Finite__Set_Ofold__image(U_3104,U_3105,U_3106),U_3107) = c_Finite__Set_Ofold(U_3105,U_3104,hAPP(hAPP(c_COMBB(U_3104,tc_fun(U_3104,U_3104),U_3105),U_3106),U_3107)),
inference(definitional_conversion,[status(esa)],[f_702_2]) ).
cnf(f_702_4,plain,
hAPP(c_Finite__Set_Ofold__image(U_3104,U_3105,U_3106),U_3107) = c_Finite__Set_Ofold(U_3105,U_3104,hAPP(hAPP(c_COMBB(U_3104,tc_fun(U_3104,U_3104),U_3105),U_3106),U_3107)),
inference(clausify,[status(thm)],[f_702_3]) ).
fof(f_703_1,plain,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__insert__le]) ).
fof(f_703_2,plain,
! [U_3110,U_3109,U_3108] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3108),U_3109)),hAPP(c_Finite__Set_Ocard(U_3108),hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),U_3109))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3108),U_3109)) ),
inference(variable_rename,[status(thm)],[f_703_1]) ).
fof(f_703_3,plain,
! [U_3108,U_3109,U_3110] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3108),U_3109)),hAPP(c_Finite__Set_Ocard(U_3108),hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),U_3109))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3108),U_3109)) ),
inference(definitional_conversion,[status(esa)],[f_703_2]) ).
cnf(f_703_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3108),U_3109)),hAPP(c_Finite__Set_Ocard(U_3108),hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),U_3109))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3108),U_3109)) ),
inference(clausify,[status(thm)],[f_703_3]) ).
fof(f_704_1,plain,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__mono]) ).
fof(f_704_2,plain,
! [U_3113,U_3112,U_3111] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3111),U_3113)),hAPP(c_Finite__Set_Ocard(U_3111),U_3112)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3111,tc_HOL_Obool)),U_3113),U_3112))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3111),U_3112)) ),
inference(variable_rename,[status(thm)],[f_704_1]) ).
fof(f_704_3,plain,
! [U_3111,U_3112,U_3113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3111),U_3113)),hAPP(c_Finite__Set_Ocard(U_3111),U_3112)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3111,tc_HOL_Obool)),U_3113),U_3112))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3111),U_3112)) ),
inference(definitional_conversion,[status(esa)],[f_704_2]) ).
cnf(f_704_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3111),U_3113)),hAPP(c_Finite__Set_Ocard(U_3111),U_3112)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3111,tc_HOL_Obool)),U_3113),U_3112))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3111),U_3112)) ),
inference(clausify,[status(thm)],[f_704_3]) ).
fof(f_705_1,plain,
! [V_A_2,V_B_2,T_c] :
( V_A_2 = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__seteq]) ).
fof(f_705_2,plain,
! [U_3116,U_3115,U_3114] :
( U_3116 = U_3115
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3114),U_3115)),hAPP(c_Finite__Set_Ocard(U_3114),U_3116)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3114,tc_HOL_Obool)),U_3116),U_3115))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3114),U_3115)) ),
inference(variable_rename,[status(thm)],[f_705_1]) ).
fof(f_705_3,plain,
! [U_3114,U_3115,U_3116] :
( U_3116 = U_3115
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3114),U_3115)),hAPP(c_Finite__Set_Ocard(U_3114),U_3116)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3114,tc_HOL_Obool)),U_3116),U_3115))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3114),U_3115)) ),
inference(definitional_conversion,[status(esa)],[f_705_2]) ).
cnf(f_705_4,plain,
( U_3116 = U_3115
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3114),U_3115)),hAPP(c_Finite__Set_Ocard(U_3114),U_3116)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3114,tc_HOL_Obool)),U_3116),U_3115))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3114),U_3115)) ),
inference(clausify,[status(thm)],[f_705_3]) ).
fof(f_706_1,plain,
! [V_f_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__image__le]) ).
fof(f_706_2,plain,
! [U_3120,U_3119,U_3118,U_3117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3119),hAPP(c_Set_Oimage(U_3117,U_3119,U_3120),U_3118))),hAPP(c_Finite__Set_Ocard(U_3117),U_3118)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3117),U_3118)) ),
inference(variable_rename,[status(thm)],[f_706_1]) ).
fof(f_706_3,plain,
! [U_3118,U_3117,U_3119,U_3120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3119),hAPP(c_Set_Oimage(U_3117,U_3119,U_3120),U_3118))),hAPP(c_Finite__Set_Ocard(U_3117),U_3118)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3117),U_3118)) ),
inference(definitional_conversion,[status(esa)],[f_706_2]) ).
cnf(f_706_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3119),hAPP(c_Set_Oimage(U_3117,U_3119,U_3120),U_3118))),hAPP(c_Finite__Set_Ocard(U_3117),U_3118)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3117),U_3118)) ),
inference(clausify,[status(thm)],[f_706_3]) ).
fof(f_707_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( ~ c_Fun_Oinj__on(T_d,T_c,V_f_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_d),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_pigeonhole]) ).
fof(f_707_2,plain,
! [U_3124,U_3123,U_3122,U_3121] :
( ~ c_Fun_Oinj__on(U_3122,U_3121,U_3123,U_3124)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3121),hAPP(c_Set_Oimage(U_3122,U_3121,U_3123),U_3124))),hAPP(c_Finite__Set_Ocard(U_3122),U_3124))) ),
inference(variable_rename,[status(thm)],[f_707_1]) ).
fof(f_707_3,plain,
! [U_3121,U_3122,U_3123,U_3124] :
( ~ c_Fun_Oinj__on(U_3122,U_3121,U_3123,U_3124)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3121),hAPP(c_Set_Oimage(U_3122,U_3121,U_3123),U_3124))),hAPP(c_Finite__Set_Ocard(U_3122),U_3124))) ),
inference(definitional_conversion,[status(esa)],[f_707_2]) ).
cnf(f_707_4,plain,
( ~ c_Fun_Oinj__on(U_3122,U_3121,U_3123,U_3124)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3121),hAPP(c_Set_Oimage(U_3122,U_3121,U_3123),U_3124))),hAPP(c_Finite__Set_Ocard(U_3122),U_3124))) ),
inference(clausify,[status(thm)],[f_707_3]) ).
fof(f_708_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2)
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_card__image]) ).
fof(f_708_2,plain,
! [U_3128,U_3127,U_3126,U_3125] :
( hAPP(c_Finite__Set_Ocard(U_3126),hAPP(c_Set_Oimage(U_3125,U_3126,U_3127),U_3128)) = hAPP(c_Finite__Set_Ocard(U_3125),U_3128)
| ~ c_Fun_Oinj__on(U_3125,U_3126,U_3127,U_3128) ),
inference(variable_rename,[status(thm)],[f_708_1]) ).
fof(f_708_3,plain,
! [U_3125,U_3126,U_3127,U_3128] :
( hAPP(c_Finite__Set_Ocard(U_3126),hAPP(c_Set_Oimage(U_3125,U_3126,U_3127),U_3128)) = hAPP(c_Finite__Set_Ocard(U_3125),U_3128)
| ~ c_Fun_Oinj__on(U_3125,U_3126,U_3127,U_3128) ),
inference(definitional_conversion,[status(esa)],[f_708_2]) ).
cnf(f_708_4,plain,
( hAPP(c_Finite__Set_Ocard(U_3126),hAPP(c_Set_Oimage(U_3125,U_3126,U_3127),U_3128)) = hAPP(c_Finite__Set_Ocard(U_3125),U_3128)
| ~ c_Fun_Oinj__on(U_3125,U_3126,U_3127,U_3128) ),
inference(clausify,[status(thm)],[f_708_3]) ).
fof(f_709_1,plain,
! [V_A_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_A_2),
inference(fof_nnf,[status(thm)],[fact_insert__is__Un]) ).
fof(f_709_2,plain,
! [U_3131,U_3130,U_3129] : hAPP(hAPP(c_Set_Oinsert(U_3129),U_3130),U_3131) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3129,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_3129),U_3130),c_Orderings_Obot__class_Obot(tc_fun(U_3129,tc_HOL_Obool)))),U_3131),
inference(variable_rename,[status(thm)],[f_709_1]) ).
fof(f_709_3,plain,
! [U_3129,U_3130,U_3131] : hAPP(hAPP(c_Set_Oinsert(U_3129),U_3130),U_3131) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3129,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_3129),U_3130),c_Orderings_Obot__class_Obot(tc_fun(U_3129,tc_HOL_Obool)))),U_3131),
inference(definitional_conversion,[status(esa)],[f_709_2]) ).
cnf(f_709_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_3129),U_3130),U_3131) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3129,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_3129),U_3130),c_Orderings_Obot__class_Obot(tc_fun(U_3129,tc_HOL_Obool)))),U_3131),
inference(clausify,[status(thm)],[f_709_3]) ).
fof(f_710_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv]) ).
fof(f_710_2,plain,
! [U_3135,U_3134,U_3133,U_3132] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3132,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3132,tc_HOL_Obool)),U_3133),U_3134)),U_3135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3132,tc_HOL_Obool)),U_3133),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3132,tc_HOL_Obool)),U_3134),U_3135))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3132,tc_HOL_Obool)),U_3133),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3132,tc_HOL_Obool)),U_3134),U_3135)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3132,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3132,tc_HOL_Obool)),U_3133),U_3134)),U_3135)) ) ),
inference(variable_rename,[status(thm)],[f_710_1]) ).
fof(f_710_3,plain,
( ! [U_3143,U_3141,U_3139,U_3137] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3137,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3137,tc_HOL_Obool)),U_3139),U_3141)),U_3143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3137,tc_HOL_Obool)),U_3139),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3137,tc_HOL_Obool)),U_3141),U_3143))) )
& ! [U_3142,U_3140,U_3138,U_3136] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3136,tc_HOL_Obool)),U_3138),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3136,tc_HOL_Obool)),U_3140),U_3142)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3136,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3136,tc_HOL_Obool)),U_3138),U_3140)),U_3142)) ) ),
inference(miniscope,[status(thm)],[f_710_2]) ).
fof(f_710_4,plain,
( ! [U_3137,U_3139,U_3141,U_3143] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3137,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3137,tc_HOL_Obool)),U_3139),U_3141)),U_3143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3137,tc_HOL_Obool)),U_3139),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3137,tc_HOL_Obool)),U_3141),U_3143))) )
& ! [U_3142,U_3138,U_3140,U_3136] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3136,tc_HOL_Obool)),U_3138),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3136,tc_HOL_Obool)),U_3140),U_3142)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3136,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3136,tc_HOL_Obool)),U_3138),U_3140)),U_3142)) ) ),
inference(definitional_conversion,[status(esa)],[f_710_3]) ).
cnf(f_710_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3136,tc_HOL_Obool)),U_3138),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3136,tc_HOL_Obool)),U_3140),U_3142)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3136,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3136,tc_HOL_Obool)),U_3138),U_3140)),U_3142)) ),
inference(clausify,[status(thm)],[f_710_4]) ).
cnf(f_710_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3137,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3137,tc_HOL_Obool)),U_3139),U_3141)),U_3143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3137,tc_HOL_Obool)),U_3139),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3137,tc_HOL_Obool)),U_3141),U_3143))) ),
inference(clausify,[status(thm)],[f_710_4]) ).
fof(f_711_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_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),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Diff__partition]) ).
fof(f_711_2,plain,
! [U_3146,U_3145,U_3144] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3144,tc_HOL_Obool)),U_3145),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3144,tc_HOL_Obool)),U_3146),U_3145)) = U_3146
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3144,tc_HOL_Obool)),U_3145),U_3146)) ),
inference(variable_rename,[status(thm)],[f_711_1]) ).
fof(f_711_3,plain,
! [U_3144,U_3145,U_3146] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3144,tc_HOL_Obool)),U_3145),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3144,tc_HOL_Obool)),U_3146),U_3145)) = U_3146
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3144,tc_HOL_Obool)),U_3145),U_3146)) ),
inference(definitional_conversion,[status(esa)],[f_711_2]) ).
cnf(f_711_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3144,tc_HOL_Obool)),U_3145),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3144,tc_HOL_Obool)),U_3146),U_3145)) = U_3146
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3144,tc_HOL_Obool)),U_3145),U_3146)) ),
inference(clausify,[status(thm)],[f_711_3]) ).
fof(f_712_1,plain,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__card__mono]) ).
fof(f_712_2,plain,
! [U_3149,U_3148,U_3147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3147),U_3149)),hAPP(c_Finite__Set_Ocard(U_3147),U_3148)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_3147,tc_HOL_Obool)),U_3149),U_3148))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3147),U_3148)) ),
inference(variable_rename,[status(thm)],[f_712_1]) ).
fof(f_712_3,plain,
! [U_3147,U_3148,U_3149] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3147),U_3149)),hAPP(c_Finite__Set_Ocard(U_3147),U_3148)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_3147,tc_HOL_Obool)),U_3149),U_3148))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3147),U_3148)) ),
inference(definitional_conversion,[status(esa)],[f_712_2]) ).
cnf(f_712_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3147),U_3149)),hAPP(c_Finite__Set_Ocard(U_3147),U_3148)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_3147,tc_HOL_Obool)),U_3149),U_3148))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3147),U_3148)) ),
inference(clausify,[status(thm)],[f_712_3]) ).
fof(f_713_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( ( ( hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)
| V_A_2 != V_B_2 )
& ( V_A_2 = V_B_2
| hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) != hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2) ) )
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__Un__image__eq__iff]) ).
fof(f_713_2,plain,
! [U_3154,U_3153,U_3152,U_3151,U_3150] :
( ( ( hAPP(c_Set_Oimage(U_3150,U_3151,U_3152),U_3153) = hAPP(c_Set_Oimage(U_3150,U_3151,U_3152),U_3154)
| U_3153 != U_3154 )
& ( U_3153 = U_3154
| hAPP(c_Set_Oimage(U_3150,U_3151,U_3152),U_3153) != hAPP(c_Set_Oimage(U_3150,U_3151,U_3152),U_3154) ) )
| ~ c_Fun_Oinj__on(U_3150,U_3151,U_3152,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3150,tc_HOL_Obool)),U_3153),U_3154)) ),
inference(variable_rename,[status(thm)],[f_713_1]) ).
fof(f_713_3,plain,
( ! [U_3150,U_3151,U_3152,U_3153,U_3154] :
( hAPP(c_Set_Oimage(U_3150,U_3151,U_3152),U_3153) = hAPP(c_Set_Oimage(U_3150,U_3151,U_3152),U_3154)
| U_3153 != U_3154
| ~ sP173(U_3150,U_3151,U_3152,U_3153,U_3154) )
& ! [U_3150,U_3151,U_3152,U_3153,U_3154] :
( U_3153 = U_3154
| hAPP(c_Set_Oimage(U_3150,U_3151,U_3152),U_3153) != hAPP(c_Set_Oimage(U_3150,U_3151,U_3152),U_3154)
| ~ sP173(U_3150,U_3151,U_3152,U_3153,U_3154) )
& ! [U_3150,U_3151,U_3152,U_3153,U_3154] :
( sP173(U_3150,U_3151,U_3152,U_3153,U_3154)
| ~ c_Fun_Oinj__on(U_3150,U_3151,U_3152,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3150,tc_HOL_Obool)),U_3153),U_3154)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173])],[f_713_2]) ).
cnf(f_713_4,plain,
( sP173(U_3150,U_3151,U_3152,U_3153,U_3154)
| ~ c_Fun_Oinj__on(U_3150,U_3151,U_3152,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3150,tc_HOL_Obool)),U_3153),U_3154)) ),
inference(clausify,[status(thm)],[f_713_3]) ).
cnf(f_713_5,plain,
( U_3153 = U_3154
| hAPP(c_Set_Oimage(U_3150,U_3151,U_3152),U_3153) != hAPP(c_Set_Oimage(U_3150,U_3151,U_3152),U_3154)
| ~ sP173(U_3150,U_3151,U_3152,U_3153,U_3154) ),
inference(clausify,[status(thm)],[f_713_3]) ).
cnf(f_713_6,plain,
( hAPP(c_Set_Oimage(U_3150,U_3151,U_3152),U_3153) = hAPP(c_Set_Oimage(U_3150,U_3151,U_3152),U_3154)
| U_3153 != U_3154
| ~ sP173(U_3150,U_3151,U_3152,U_3153,U_3154) ),
inference(clausify,[status(thm)],[f_713_3]) ).
fof(f_714_1,plain,
! [T_d,V_x_2,V_f_2,T_c] : hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_rangeI]) ).
fof(f_714_2,plain,
! [U_3158,U_3157,U_3156,U_3155] : hBOOL(hAPP(hAPP(c_member(U_3155),hAPP(U_3156,U_3157)),hAPP(c_Set_Oimage(U_3158,U_3155,U_3156),c_Orderings_Otop__class_Otop(tc_fun(U_3158,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_714_1]) ).
fof(f_714_3,plain,
! [U_3158,U_3156,U_3155,U_3157] : hBOOL(hAPP(hAPP(c_member(U_3155),hAPP(U_3156,U_3157)),hAPP(c_Set_Oimage(U_3158,U_3155,U_3156),c_Orderings_Otop__class_Otop(tc_fun(U_3158,tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_714_2]) ).
cnf(f_714_4,plain,
hBOOL(hAPP(hAPP(c_member(U_3155),hAPP(U_3156,U_3157)),hAPP(c_Set_Oimage(U_3158,U_3155,U_3156),c_Orderings_Otop__class_Otop(tc_fun(U_3158,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_714_3]) ).
fof(f_715_1,plain,
! [T_d,T_c,V_x_2,V_f_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))))
| V_b_2 != hAPP(V_f_2,V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_range__eqI]) ).
fof(f_715_2,plain,
! [U_3163,U_3162,U_3161,U_3160,U_3159] :
( hBOOL(hAPP(hAPP(c_member(U_3162),U_3159),hAPP(c_Set_Oimage(U_3163,U_3162,U_3160),c_Orderings_Otop__class_Otop(tc_fun(U_3163,tc_HOL_Obool)))))
| U_3159 != hAPP(U_3160,U_3161) ),
inference(variable_rename,[status(thm)],[f_715_1]) ).
fof(f_715_3,plain,
! [U_3159,U_3160,U_3161,U_3162,U_3163] :
( hBOOL(hAPP(hAPP(c_member(U_3162),U_3159),hAPP(c_Set_Oimage(U_3163,U_3162,U_3160),c_Orderings_Otop__class_Otop(tc_fun(U_3163,tc_HOL_Obool)))))
| U_3159 != hAPP(U_3160,U_3161) ),
inference(definitional_conversion,[status(esa)],[f_715_2]) ).
cnf(f_715_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_3162),U_3159),hAPP(c_Set_Oimage(U_3163,U_3162,U_3160),c_Orderings_Otop__class_Otop(tc_fun(U_3163,tc_HOL_Obool)))))
| U_3159 != hAPP(U_3160,U_3161) ),
inference(clausify,[status(thm)],[f_715_3]) ).
fof(f_716_1,plain,
! [V_f_2,T_d,V_A_2,T_c] :
( hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_d,tc_HOL_Obool),T_c,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_d,tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_d)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__eq__fold__image]) ).
fof(f_716_2,plain,
! [U_3167,U_3166,U_3165,U_3164] :
( hAPP(c_Set_Oimage(U_3164,U_3166,U_3167),U_3165) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_3166,tc_HOL_Obool),U_3164,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3166,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_3164,tc_fun(U_3166,tc_HOL_Obool),tc_fun(U_3166,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_3166,tc_fun(tc_fun(U_3166,tc_HOL_Obool),tc_fun(U_3166,tc_HOL_Obool)),U_3164),c_Set_Oinsert(U_3166)),U_3167)),c_Orderings_Obot__class_Obot(tc_fun(U_3166,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_3166,tc_HOL_Obool))),U_3165)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3164),U_3165)) ),
inference(variable_rename,[status(thm)],[f_716_1]) ).
fof(f_716_3,plain,
! [U_3164,U_3165,U_3166,U_3167] :
( hAPP(c_Set_Oimage(U_3164,U_3166,U_3167),U_3165) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_3166,tc_HOL_Obool),U_3164,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3166,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_3164,tc_fun(U_3166,tc_HOL_Obool),tc_fun(U_3166,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_3166,tc_fun(tc_fun(U_3166,tc_HOL_Obool),tc_fun(U_3166,tc_HOL_Obool)),U_3164),c_Set_Oinsert(U_3166)),U_3167)),c_Orderings_Obot__class_Obot(tc_fun(U_3166,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_3166,tc_HOL_Obool))),U_3165)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3164),U_3165)) ),
inference(definitional_conversion,[status(esa)],[f_716_2]) ).
cnf(f_716_4,plain,
( hAPP(c_Set_Oimage(U_3164,U_3166,U_3167),U_3165) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_3166,tc_HOL_Obool),U_3164,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3166,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_3164,tc_fun(U_3166,tc_HOL_Obool),tc_fun(U_3166,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_3166,tc_fun(tc_fun(U_3166,tc_HOL_Obool),tc_fun(U_3166,tc_HOL_Obool)),U_3164),c_Set_Oinsert(U_3166)),U_3167)),c_Orderings_Obot__class_Obot(tc_fun(U_3166,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_3166,tc_HOL_Obool))),U_3165)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3164),U_3165)) ),
inference(clausify,[status(thm)],[f_716_3]) ).
fof(f_717_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Diff__UNIV]) ).
fof(f_717_2,plain,
! [U_3169,U_3168] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3168,tc_HOL_Obool)),U_3169),c_Orderings_Otop__class_Otop(tc_fun(U_3168,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_3168,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_717_1]) ).
fof(f_717_3,plain,
! [U_3168,U_3169] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3168,tc_HOL_Obool)),U_3169),c_Orderings_Otop__class_Otop(tc_fun(U_3168,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_3168,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_717_2]) ).
cnf(f_717_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3168,tc_HOL_Obool)),U_3169),c_Orderings_Otop__class_Otop(tc_fun(U_3168,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_3168,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_717_3]) ).
fof(f_718_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Compl__Diff__eq]) ).
fof(f_718_2,plain,
! [U_3172,U_3171,U_3170] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3170,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3170,tc_HOL_Obool)),U_3171),U_3172)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3170,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3170,tc_HOL_Obool)),U_3171)),U_3172),
inference(variable_rename,[status(thm)],[f_718_1]) ).
fof(f_718_3,plain,
! [U_3170,U_3171,U_3172] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3170,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3170,tc_HOL_Obool)),U_3171),U_3172)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3170,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3170,tc_HOL_Obool)),U_3171)),U_3172),
inference(definitional_conversion,[status(esa)],[f_718_2]) ).
cnf(f_718_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3170,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3170,tc_HOL_Obool)),U_3171),U_3172)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3170,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3170,tc_HOL_Obool)),U_3171)),U_3172),
inference(clausify,[status(thm)],[f_718_3]) ).
fof(f_719_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( ( ( hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)
| V_A_2 != V_B_2 )
& ( V_A_2 = V_B_2
| hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2) != hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2) ) )
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__image__eq__iff]) ).
fof(f_719_2,plain,
! [U_3177,U_3176,U_3175,U_3174,U_3173] :
( ( ( hAPP(c_Set_Oimage(U_3173,U_3174,U_3175),U_3176) = hAPP(c_Set_Oimage(U_3173,U_3174,U_3175),U_3177)
| U_3176 != U_3177 )
& ( U_3176 = U_3177
| hAPP(c_Set_Oimage(U_3173,U_3174,U_3175),U_3176) != hAPP(c_Set_Oimage(U_3173,U_3174,U_3175),U_3177) ) )
| ~ c_Fun_Oinj__on(U_3173,U_3174,U_3175,c_Orderings_Otop__class_Otop(tc_fun(U_3173,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_719_1]) ).
fof(f_719_3,plain,
( ! [U_3173,U_3174,U_3175,U_3176,U_3177] :
( hAPP(c_Set_Oimage(U_3173,U_3174,U_3175),U_3176) = hAPP(c_Set_Oimage(U_3173,U_3174,U_3175),U_3177)
| U_3176 != U_3177
| ~ sP174(U_3173,U_3174,U_3175,U_3176,U_3177) )
& ! [U_3173,U_3174,U_3175,U_3176,U_3177] :
( U_3176 = U_3177
| hAPP(c_Set_Oimage(U_3173,U_3174,U_3175),U_3176) != hAPP(c_Set_Oimage(U_3173,U_3174,U_3175),U_3177)
| ~ sP174(U_3173,U_3174,U_3175,U_3176,U_3177) )
& ! [U_3173,U_3174,U_3175,U_3176,U_3177] :
( sP174(U_3173,U_3174,U_3175,U_3176,U_3177)
| ~ c_Fun_Oinj__on(U_3173,U_3174,U_3175,c_Orderings_Otop__class_Otop(tc_fun(U_3173,tc_HOL_Obool))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174])],[f_719_2]) ).
cnf(f_719_4,plain,
( sP174(U_3173,U_3174,U_3175,U_3176,U_3177)
| ~ c_Fun_Oinj__on(U_3173,U_3174,U_3175,c_Orderings_Otop__class_Otop(tc_fun(U_3173,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_719_3]) ).
cnf(f_719_5,plain,
( U_3176 = U_3177
| hAPP(c_Set_Oimage(U_3173,U_3174,U_3175),U_3176) != hAPP(c_Set_Oimage(U_3173,U_3174,U_3175),U_3177)
| ~ sP174(U_3173,U_3174,U_3175,U_3176,U_3177) ),
inference(clausify,[status(thm)],[f_719_3]) ).
cnf(f_719_6,plain,
( hAPP(c_Set_Oimage(U_3173,U_3174,U_3175),U_3176) = hAPP(c_Set_Oimage(U_3173,U_3174,U_3175),U_3177)
| U_3176 != U_3177
| ~ sP174(U_3173,U_3174,U_3175,U_3176,U_3177) ),
inference(clausify,[status(thm)],[f_719_3]) ).
fof(f_720_1,plain,
! [T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Compl__empty__eq]) ).
fof(f_720_2,plain,
! [U_3178] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3178,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_3178,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3178,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_720_1]) ).
fof(f_720_3,plain,
! [U_3178] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3178,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_3178,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3178,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_720_2]) ).
cnf(f_720_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3178,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_3178,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3178,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_720_3]) ).
fof(f_721_1,plain,
! [T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Compl__UNIV__eq]) ).
fof(f_721_2,plain,
! [U_3179] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3179,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3179,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_3179,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_721_1]) ).
fof(f_721_3,plain,
! [U_3179] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3179,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3179,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_3179,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_721_2]) ).
cnf(f_721_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3179,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3179,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_3179,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_721_3]) ).
fof(f_722_1,plain,
! [V_A_2,T_c] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))
| ~ 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_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__compl]) ).
fof(f_722_2,plain,
! [U_3181,U_3180] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3180,tc_HOL_Obool)),U_3181)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),c_Orderings_Otop__class_Otop(tc_fun(U_3180,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),c_Orderings_Otop__class_Otop(tc_fun(U_3180,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3180,tc_HOL_Obool)),U_3181))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),U_3181)) ),
inference(variable_rename,[status(thm)],[f_722_1]) ).
fof(f_722_3,plain,
( ! [U_3180,U_3181] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3180,tc_HOL_Obool)),U_3181)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),c_Orderings_Otop__class_Otop(tc_fun(U_3180,tc_HOL_Obool))))
| ~ sP175(U_3180,U_3181) )
& ! [U_3180,U_3181] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),c_Orderings_Otop__class_Otop(tc_fun(U_3180,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3180,tc_HOL_Obool)),U_3181)))
| ~ sP175(U_3180,U_3181) )
& ! [U_3180,U_3181] :
( sP175(U_3180,U_3181)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),U_3181)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP175])],[f_722_2]) ).
cnf(f_722_4,plain,
( sP175(U_3180,U_3181)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),U_3181)) ),
inference(clausify,[status(thm)],[f_722_3]) ).
cnf(f_722_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),c_Orderings_Otop__class_Otop(tc_fun(U_3180,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3180,tc_HOL_Obool)),U_3181)))
| ~ sP175(U_3180,U_3181) ),
inference(clausify,[status(thm)],[f_722_3]) ).
cnf(f_722_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3180,tc_HOL_Obool)),U_3181)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3180),c_Orderings_Otop__class_Otop(tc_fun(U_3180,tc_HOL_Obool))))
| ~ sP175(U_3180,U_3181) ),
inference(clausify,[status(thm)],[f_722_3]) ).
fof(f_723_1,plain,
! [V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_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_A_2),
inference(fof_nnf,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).
fof(f_723_2,plain,
! [U_3183,U_3182] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3182,tc_HOL_Obool)),U_3183) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3182,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3182,tc_HOL_Obool))),U_3183),
inference(variable_rename,[status(thm)],[f_723_1]) ).
fof(f_723_3,plain,
! [U_3183,U_3182] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3182,tc_HOL_Obool)),U_3183) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3182,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3182,tc_HOL_Obool))),U_3183),
inference(definitional_conversion,[status(esa)],[f_723_2]) ).
cnf(f_723_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3182,tc_HOL_Obool)),U_3183) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3182,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_3182,tc_HOL_Obool))),U_3183),
inference(clausify,[status(thm)],[f_723_3]) ).
fof(f_724_1,plain,
! [T_c] : c_Fun_Oinj__on(T_c,tc_fun(T_c,tc_HOL_Obool),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))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_inj__singleton]) ).
fof(f_724_2,plain,
! [U_3184] : c_Fun_Oinj__on(U_3184,tc_fun(U_3184,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_3184,tc_fun(U_3184,tc_HOL_Obool),tc_fun(U_3184,tc_HOL_Obool)),c_Set_Oinsert(U_3184)),c_Orderings_Obot__class_Obot(tc_fun(U_3184,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_3184,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_724_1]) ).
fof(f_724_3,plain,
! [U_3184] : c_Fun_Oinj__on(U_3184,tc_fun(U_3184,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_3184,tc_fun(U_3184,tc_HOL_Obool),tc_fun(U_3184,tc_HOL_Obool)),c_Set_Oinsert(U_3184)),c_Orderings_Obot__class_Obot(tc_fun(U_3184,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_3184,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_724_2]) ).
cnf(f_724_4,plain,
c_Fun_Oinj__on(U_3184,tc_fun(U_3184,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_3184,tc_fun(U_3184,tc_HOL_Obool),tc_fun(U_3184,tc_HOL_Obool)),c_Set_Oinsert(U_3184)),c_Orderings_Obot__class_Obot(tc_fun(U_3184,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_3184,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_724_3]) ).
fof(f_725_1,plain,
! [V_f_2,T_e,V_g_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_e),hAPP(c_Set_Oimage(T_d,T_e,hAPP(hAPP(c_COMBB(T_c,T_e,T_d),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))))) ),
inference(fof_nnf,[status(thm)],[fact_finite__range__imageI]) ).
fof(f_725_2,plain,
! [U_3189,U_3188,U_3187,U_3186,U_3185] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3188),hAPP(c_Set_Oimage(U_3186,U_3188,hAPP(hAPP(c_COMBB(U_3185,U_3188,U_3186),U_3189),U_3187)),c_Orderings_Otop__class_Otop(tc_fun(U_3186,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3185),hAPP(c_Set_Oimage(U_3186,U_3185,U_3187),c_Orderings_Otop__class_Otop(tc_fun(U_3186,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[f_725_1]) ).
fof(f_725_3,plain,
! [U_3185,U_3186,U_3187,U_3188,U_3189] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3188),hAPP(c_Set_Oimage(U_3186,U_3188,hAPP(hAPP(c_COMBB(U_3185,U_3188,U_3186),U_3189),U_3187)),c_Orderings_Otop__class_Otop(tc_fun(U_3186,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3185),hAPP(c_Set_Oimage(U_3186,U_3185,U_3187),c_Orderings_Otop__class_Otop(tc_fun(U_3186,tc_HOL_Obool))))) ),
inference(definitional_conversion,[status(esa)],[f_725_2]) ).
cnf(f_725_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3188),hAPP(c_Set_Oimage(U_3186,U_3188,hAPP(hAPP(c_COMBB(U_3185,U_3188,U_3186),U_3189),U_3187)),c_Orderings_Otop__class_Otop(tc_fun(U_3186,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3185),hAPP(c_Set_Oimage(U_3186,U_3185,U_3187),c_Orderings_Otop__class_Otop(tc_fun(U_3186,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_725_3]) ).
fof(f_726_1,plain,
! [V_x_2,V_f_2,T_d,T_c] :
( hAPP(c_Fun_Othe__inv__into(T_c,T_d,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_the__inv__f__f]) ).
fof(f_726_2,plain,
! [U_3193,U_3192,U_3191,U_3190] :
( hAPP(c_Fun_Othe__inv__into(U_3190,U_3191,c_Orderings_Otop__class_Otop(tc_fun(U_3190,tc_HOL_Obool)),U_3192),hAPP(U_3192,U_3193)) = U_3193
| ~ c_Fun_Oinj__on(U_3190,U_3191,U_3192,c_Orderings_Otop__class_Otop(tc_fun(U_3190,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_726_1]) ).
fof(f_726_3,plain,
! [U_3190,U_3191,U_3192,U_3193] :
( hAPP(c_Fun_Othe__inv__into(U_3190,U_3191,c_Orderings_Otop__class_Otop(tc_fun(U_3190,tc_HOL_Obool)),U_3192),hAPP(U_3192,U_3193)) = U_3193
| ~ c_Fun_Oinj__on(U_3190,U_3191,U_3192,c_Orderings_Otop__class_Otop(tc_fun(U_3190,tc_HOL_Obool))) ),
inference(definitional_conversion,[status(esa)],[f_726_2]) ).
cnf(f_726_4,plain,
( hAPP(c_Fun_Othe__inv__into(U_3190,U_3191,c_Orderings_Otop__class_Otop(tc_fun(U_3190,tc_HOL_Obool)),U_3192),hAPP(U_3192,U_3193)) = U_3193
| ~ c_Fun_Oinj__on(U_3190,U_3191,U_3192,c_Orderings_Otop__class_Otop(tc_fun(U_3190,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_726_3]) ).
fof(f_727_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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_d),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_c,T_d,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_727_2,plain,
! [U_3201,U_3200,U_3199,U_3198,U_3197,U_3196,U_3195,U_3194] :
( hAPP(U_3199,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3195,tc_HOL_Obool)),U_3200),U_3201)) = hAPP(hAPP(U_3196,hAPP(U_3199,U_3200)),hAPP(U_3199,U_3201))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3195),U_3201))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3195),U_3200))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_3194,U_3195,U_3196,U_3197,U_3198,U_3199) ),
inference(variable_rename,[status(thm)],[f_727_1]) ).
fof(f_727_3,plain,
! [U_3201,U_3200,U_3199,U_3198,U_3197,U_3196,U_3195] :
( ! [U_3194] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_3194,U_3195,U_3196,U_3197,U_3198,U_3199)
| hAPP(U_3199,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3195,tc_HOL_Obool)),U_3200),U_3201)) = hAPP(hAPP(U_3196,hAPP(U_3199,U_3200)),hAPP(U_3199,U_3201))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3195),U_3201))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3195),U_3200)) ),
inference(miniscope,[status(thm)],[f_727_2]) ).
fof(f_727_4,plain,
! [U_3194,U_3195,U_3196,U_3197,U_3198,U_3199,U_3200,U_3201] :
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_3194,U_3195,U_3196,U_3197,U_3198,U_3199)
| hAPP(U_3199,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3195,tc_HOL_Obool)),U_3200),U_3201)) = hAPP(hAPP(U_3196,hAPP(U_3199,U_3200)),hAPP(U_3199,U_3201))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3195),U_3201))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3195),U_3200)) ),
inference(definitional_conversion,[status(esa)],[f_727_3]) ).
cnf(f_727_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_3194,U_3195,U_3196,U_3197,U_3198,U_3199)
| hAPP(U_3199,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3195,tc_HOL_Obool)),U_3200),U_3201)) = hAPP(hAPP(U_3196,hAPP(U_3199,U_3200)),hAPP(U_3199,U_3201))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3195),U_3201))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3195),U_3200)) ),
inference(clausify,[status(thm)],[f_727_4]) ).
fof(f_728_1,plain,
! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2),V_z_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_c,T_d,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_728_2,plain,
! [U_3208,U_3207,U_3206,U_3205,U_3204,U_3203,U_3202] :
( hAPP(U_3207,U_3208) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3202,U_3203,U_3204),U_3206),U_3205),U_3208)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3203),U_3208))
| ~ c_Finite__Set_Ofolding__image__simple(U_3202,U_3203,U_3204,U_3205,U_3206,U_3207) ),
inference(variable_rename,[status(thm)],[f_728_1]) ).
fof(f_728_3,plain,
! [U_3202,U_3203,U_3204,U_3205,U_3206,U_3207,U_3208] :
( hAPP(U_3207,U_3208) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3202,U_3203,U_3204),U_3206),U_3205),U_3208)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3203),U_3208))
| ~ c_Finite__Set_Ofolding__image__simple(U_3202,U_3203,U_3204,U_3205,U_3206,U_3207) ),
inference(definitional_conversion,[status(esa)],[f_728_2]) ).
cnf(f_728_4,plain,
( hAPP(U_3207,U_3208) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3202,U_3203,U_3204),U_3206),U_3205),U_3208)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3203),U_3208))
| ~ c_Finite__Set_Ofolding__image__simple(U_3202,U_3203,U_3204,U_3205,U_3206,U_3207) ),
inference(clausify,[status(thm)],[f_728_3]) ).
fof(f_729_1,plain,
! [V_f_2,T_d,V_A_2,T_c] :
( ( ( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
| hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) != hAPP(c_Finite__Set_Ocard(T_c),V_A_2) )
& ( hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2)
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card]) ).
fof(f_729_2,plain,
! [U_3212,U_3211,U_3210,U_3209] :
( ( ( c_Fun_Oinj__on(U_3209,U_3211,U_3212,U_3210)
| hAPP(c_Finite__Set_Ocard(U_3211),hAPP(c_Set_Oimage(U_3209,U_3211,U_3212),U_3210)) != hAPP(c_Finite__Set_Ocard(U_3209),U_3210) )
& ( hAPP(c_Finite__Set_Ocard(U_3211),hAPP(c_Set_Oimage(U_3209,U_3211,U_3212),U_3210)) = hAPP(c_Finite__Set_Ocard(U_3209),U_3210)
| ~ c_Fun_Oinj__on(U_3209,U_3211,U_3212,U_3210) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3209),U_3210)) ),
inference(variable_rename,[status(thm)],[f_729_1]) ).
fof(f_729_3,plain,
( ! [U_3209,U_3210,U_3211,U_3212] :
( c_Fun_Oinj__on(U_3209,U_3211,U_3212,U_3210)
| hAPP(c_Finite__Set_Ocard(U_3211),hAPP(c_Set_Oimage(U_3209,U_3211,U_3212),U_3210)) != hAPP(c_Finite__Set_Ocard(U_3209),U_3210)
| ~ sP176(U_3209,U_3210,U_3211,U_3212) )
& ! [U_3209,U_3210,U_3211,U_3212] :
( hAPP(c_Finite__Set_Ocard(U_3211),hAPP(c_Set_Oimage(U_3209,U_3211,U_3212),U_3210)) = hAPP(c_Finite__Set_Ocard(U_3209),U_3210)
| ~ c_Fun_Oinj__on(U_3209,U_3211,U_3212,U_3210)
| ~ sP176(U_3209,U_3210,U_3211,U_3212) )
& ! [U_3209,U_3210,U_3211,U_3212] :
( sP176(U_3209,U_3210,U_3211,U_3212)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3209),U_3210)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176])],[f_729_2]) ).
cnf(f_729_4,plain,
( sP176(U_3209,U_3210,U_3211,U_3212)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3209),U_3210)) ),
inference(clausify,[status(thm)],[f_729_3]) ).
cnf(f_729_5,plain,
( hAPP(c_Finite__Set_Ocard(U_3211),hAPP(c_Set_Oimage(U_3209,U_3211,U_3212),U_3210)) = hAPP(c_Finite__Set_Ocard(U_3209),U_3210)
| ~ c_Fun_Oinj__on(U_3209,U_3211,U_3212,U_3210)
| ~ sP176(U_3209,U_3210,U_3211,U_3212) ),
inference(clausify,[status(thm)],[f_729_3]) ).
cnf(f_729_6,plain,
( c_Fun_Oinj__on(U_3209,U_3211,U_3212,U_3210)
| hAPP(c_Finite__Set_Ocard(U_3211),hAPP(c_Set_Oimage(U_3209,U_3211,U_3212),U_3210)) != hAPP(c_Finite__Set_Ocard(U_3209),U_3210)
| ~ sP176(U_3209,U_3210,U_3211,U_3212) ),
inference(clausify,[status(thm)],[f_729_3]) ).
fof(f_730_1,plain,
! [V_f_2,T_d,V_A_2,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2)
| hAPP(c_Finite__Set_Ocard(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) != hAPP(c_Finite__Set_Ocard(T_c),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on]) ).
fof(f_730_2,plain,
! [U_3216,U_3215,U_3214,U_3213] :
( c_Fun_Oinj__on(U_3213,U_3215,U_3216,U_3214)
| hAPP(c_Finite__Set_Ocard(U_3215),hAPP(c_Set_Oimage(U_3213,U_3215,U_3216),U_3214)) != hAPP(c_Finite__Set_Ocard(U_3213),U_3214)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3213),U_3214)) ),
inference(variable_rename,[status(thm)],[f_730_1]) ).
fof(f_730_3,plain,
! [U_3216,U_3214,U_3215,U_3213] :
( c_Fun_Oinj__on(U_3213,U_3215,U_3216,U_3214)
| hAPP(c_Finite__Set_Ocard(U_3215),hAPP(c_Set_Oimage(U_3213,U_3215,U_3216),U_3214)) != hAPP(c_Finite__Set_Ocard(U_3213),U_3214)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3213),U_3214)) ),
inference(definitional_conversion,[status(esa)],[f_730_2]) ).
cnf(f_730_4,plain,
( c_Fun_Oinj__on(U_3213,U_3215,U_3216,U_3214)
| hAPP(c_Finite__Set_Ocard(U_3215),hAPP(c_Set_Oimage(U_3213,U_3215,U_3216),U_3214)) != hAPP(c_Finite__Set_Ocard(U_3213),U_3214)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3213),U_3214)) ),
inference(clausify,[status(thm)],[f_730_3]) ).
fof(f_731_1,plain,
! [V_A_2,V_B_2,T_c] :
( 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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff]) ).
fof(f_731_2,plain,
! [U_3219,U_3218,U_3217] :
( 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_3217),U_3219)),hAPP(c_Finite__Set_Ocard(U_3217),U_3218))),hAPP(c_Finite__Set_Ocard(U_3217),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3217,tc_HOL_Obool)),U_3219),U_3218))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3217),U_3218)) ),
inference(variable_rename,[status(thm)],[f_731_1]) ).
fof(f_731_3,plain,
! [U_3217,U_3218,U_3219] :
( 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_3217),U_3219)),hAPP(c_Finite__Set_Ocard(U_3217),U_3218))),hAPP(c_Finite__Set_Ocard(U_3217),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3217,tc_HOL_Obool)),U_3219),U_3218))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3217),U_3218)) ),
inference(definitional_conversion,[status(esa)],[f_731_2]) ).
cnf(f_731_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_3217),U_3219)),hAPP(c_Finite__Set_Ocard(U_3217),U_3218))),hAPP(c_Finite__Set_Ocard(U_3217),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3217,tc_HOL_Obool)),U_3219),U_3218))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3217),U_3218)) ),
inference(clausify,[status(thm)],[f_731_3]) ).
fof(f_732_1,plain,
! [V_a_2,V_b_2,V_A_2,T_c] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_b_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Osemilattice__sup(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__sup__insert]) ).
fof(f_732_2,plain,
! [U_3223,U_3222,U_3221,U_3220] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3220,U_3220,c_Lattices_Osemilattice__sup__class_Osup(U_3220)),U_3222),hAPP(hAPP(c_Set_Oinsert(U_3220),U_3223),U_3221)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3220),U_3223),hAPP(hAPP(c_Finite__Set_Ofold(U_3220,U_3220,c_Lattices_Osemilattice__sup__class_Osup(U_3220)),U_3222),U_3221))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3220),U_3221))
| ~ class_Lattices_Osemilattice__sup(U_3220) ),
inference(variable_rename,[status(thm)],[f_732_1]) ).
fof(f_732_3,plain,
! [U_3220,U_3221,U_3222,U_3223] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_3220,U_3220,c_Lattices_Osemilattice__sup__class_Osup(U_3220)),U_3222),hAPP(hAPP(c_Set_Oinsert(U_3220),U_3223),U_3221)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3220),U_3223),hAPP(hAPP(c_Finite__Set_Ofold(U_3220,U_3220,c_Lattices_Osemilattice__sup__class_Osup(U_3220)),U_3222),U_3221))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3220),U_3221))
| ~ class_Lattices_Osemilattice__sup(U_3220) ),
inference(definitional_conversion,[status(esa)],[f_732_2]) ).
cnf(f_732_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_3220,U_3220,c_Lattices_Osemilattice__sup__class_Osup(U_3220)),U_3222),hAPP(hAPP(c_Set_Oinsert(U_3220),U_3223),U_3221)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3220),U_3223),hAPP(hAPP(c_Finite__Set_Ofold(U_3220,U_3220,c_Lattices_Osemilattice__sup__class_Osup(U_3220)),U_3222),U_3221))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3220),U_3221))
| ~ class_Lattices_Osemilattice__sup(U_3220) ),
inference(clausify,[status(thm)],[f_732_3]) ).
fof(f_733_1,plain,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__psubset]) ).
fof(f_733_2,plain,
! [U_3226,U_3225,U_3224] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_3224,tc_HOL_Obool)),U_3226),U_3225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3224),U_3226)),hAPP(c_Finite__Set_Ocard(U_3224),U_3225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3224,tc_HOL_Obool)),U_3226),U_3225))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3224),U_3225)) ),
inference(variable_rename,[status(thm)],[f_733_1]) ).
fof(f_733_3,plain,
! [U_3224,U_3225,U_3226] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_3224,tc_HOL_Obool)),U_3226),U_3225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3224),U_3226)),hAPP(c_Finite__Set_Ocard(U_3224),U_3225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3224,tc_HOL_Obool)),U_3226),U_3225))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3224),U_3225)) ),
inference(definitional_conversion,[status(esa)],[f_733_2]) ).
cnf(f_733_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_3224,tc_HOL_Obool)),U_3226),U_3225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3224),U_3226)),hAPP(c_Finite__Set_Ocard(U_3224),U_3225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3224,tc_HOL_Obool)),U_3226),U_3225))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3224),U_3225)) ),
inference(clausify,[status(thm)],[f_733_3]) ).
fof(f_734_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_734_2,plain,
! [U_3227] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3227),c_Orderings_Otop__class_Otop(U_3227)) = c_Orderings_Obot__class_Obot(U_3227)
| ~ class_Lattices_Oboolean__algebra(U_3227) ),
inference(variable_rename,[status(thm)],[f_734_1]) ).
fof(f_734_3,plain,
! [U_3227] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3227),c_Orderings_Otop__class_Otop(U_3227)) = c_Orderings_Obot__class_Obot(U_3227)
| ~ class_Lattices_Oboolean__algebra(U_3227) ),
inference(definitional_conversion,[status(esa)],[f_734_2]) ).
cnf(f_734_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3227),c_Orderings_Otop__class_Otop(U_3227)) = c_Orderings_Obot__class_Obot(U_3227)
| ~ class_Lattices_Oboolean__algebra(U_3227) ),
inference(clausify,[status(thm)],[f_734_3]) ).
fof(f_735_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_735_2,plain,
! [U_3228] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3228),c_Orderings_Obot__class_Obot(U_3228)) = c_Orderings_Otop__class_Otop(U_3228)
| ~ class_Lattices_Oboolean__algebra(U_3228) ),
inference(variable_rename,[status(thm)],[f_735_1]) ).
fof(f_735_3,plain,
! [U_3228] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3228),c_Orderings_Obot__class_Obot(U_3228)) = c_Orderings_Otop__class_Otop(U_3228)
| ~ class_Lattices_Oboolean__algebra(U_3228) ),
inference(definitional_conversion,[status(esa)],[f_735_2]) ).
cnf(f_735_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3228),c_Orderings_Obot__class_Obot(U_3228)) = c_Orderings_Otop__class_Otop(U_3228)
| ~ class_Lattices_Oboolean__algebra(U_3228) ),
inference(clausify,[status(thm)],[f_735_3]) ).
fof(f_736_1,plain,
! [V_b_2,V_f_2,T_d,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
| ! [B_x] :
( ? [B_y] :
( B_y != B_x
& V_b_2 = hAPP(V_f_2,B_y) )
| V_b_2 != hAPP(V_f_2,B_x) ) )
& ( ? [B_x] :
( ! [B_y] :
( B_y = B_x
| V_b_2 != hAPP(V_f_2,B_y) )
& V_b_2 = hAPP(V_f_2,B_x) )
| ~ hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) )
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_range__ex1__eq]) ).
fof(f_736_2,plain,
! [U_3236,U_3235,U_3234,U_3233] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_3234),U_3236),hAPP(c_Set_Oimage(U_3233,U_3234,U_3235),c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool)))))
| ! [U_3232] :
( ? [U_3231] :
( U_3231 != U_3232
& U_3236 = hAPP(U_3235,U_3231) )
| U_3236 != hAPP(U_3235,U_3232) ) )
& ( ? [U_3230] :
( ! [U_3229] :
( U_3229 = U_3230
| U_3236 != hAPP(U_3235,U_3229) )
& U_3236 = hAPP(U_3235,U_3230) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3234),U_3236),hAPP(c_Set_Oimage(U_3233,U_3234,U_3235),c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool))))) ) )
| ~ c_Fun_Oinj__on(U_3233,U_3234,U_3235,c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_736_1]) ).
fof(f_736_3,plain,
! [U_3236,U_3235,U_3234,U_3233] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_3234),U_3236),hAPP(c_Set_Oimage(U_3233,U_3234,U_3235),c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool)))))
| ! [U_3232] :
( ? [U_3231] :
( U_3231 != U_3232
& U_3236 = hAPP(U_3235,U_3231) )
| U_3236 != hAPP(U_3235,U_3232) ) )
& ( ( ! [U_3229] :
( U_3229 = sK73(U_3236,U_3235,U_3234,U_3233)
| U_3236 != hAPP(U_3235,U_3229) )
& U_3236 = hAPP(U_3235,sK73(U_3236,U_3235,U_3234,U_3233)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3234),U_3236),hAPP(c_Set_Oimage(U_3233,U_3234,U_3235),c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool))))) ) )
| ~ c_Fun_Oinj__on(U_3233,U_3234,U_3235,c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_3230,sK73(U_3236,U_3235,U_3234,U_3233))],[f_736_2]) ).
fof(f_736_4,plain,
! [U_3236,U_3235,U_3234,U_3233] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_3234),U_3236),hAPP(c_Set_Oimage(U_3233,U_3234,U_3235),c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool)))))
| ! [U_3232] :
( ( sK74(U_3236,U_3235,U_3234,U_3233,U_3232) != U_3232
& U_3236 = hAPP(U_3235,sK74(U_3236,U_3235,U_3234,U_3233,U_3232)) )
| U_3236 != hAPP(U_3235,U_3232) ) )
& ( ( ! [U_3229] :
( U_3229 = sK73(U_3236,U_3235,U_3234,U_3233)
| U_3236 != hAPP(U_3235,U_3229) )
& U_3236 = hAPP(U_3235,sK73(U_3236,U_3235,U_3234,U_3233)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3234),U_3236),hAPP(c_Set_Oimage(U_3233,U_3234,U_3235),c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool))))) ) )
| ~ c_Fun_Oinj__on(U_3233,U_3234,U_3235,c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_3231,sK74(U_3236,U_3235,U_3234,U_3233,U_3232))],[f_736_3]) ).
fof(f_736_5,plain,
( ! [U_3232,U_3233,U_3234,U_3235,U_3236] :
( sK74(U_3236,U_3235,U_3234,U_3233,U_3232) != U_3232
| ~ sP178(U_3232,U_3233,U_3234,U_3235,U_3236) )
& ! [U_3232,U_3233,U_3234,U_3235,U_3236] :
( U_3236 = hAPP(U_3235,sK74(U_3236,U_3235,U_3234,U_3233,U_3232))
| ~ sP178(U_3232,U_3233,U_3234,U_3235,U_3236) )
& ! [U_3229,U_3233,U_3234,U_3235,U_3236] :
( U_3229 = sK73(U_3236,U_3235,U_3234,U_3233)
| U_3236 != hAPP(U_3235,U_3229)
| ~ sP177(U_3229,U_3233,U_3234,U_3235,U_3236) )
& ! [U_3229,U_3233,U_3234,U_3235,U_3236] :
( U_3236 = hAPP(U_3235,sK73(U_3236,U_3235,U_3234,U_3233))
| ~ sP177(U_3229,U_3233,U_3234,U_3235,U_3236) )
& ! [U_3229,U_3232,U_3233,U_3234,U_3235,U_3236] :
( hBOOL(hAPP(hAPP(c_member(U_3234),U_3236),hAPP(c_Set_Oimage(U_3233,U_3234,U_3235),c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool)))))
| sP178(U_3232,U_3233,U_3234,U_3235,U_3236)
| U_3236 != hAPP(U_3235,U_3232)
| ~ sP179(U_3229,U_3232,U_3233,U_3234,U_3235,U_3236) )
& ! [U_3229,U_3232,U_3233,U_3234,U_3235,U_3236] :
( sP177(U_3229,U_3233,U_3234,U_3235,U_3236)
| ~ hBOOL(hAPP(hAPP(c_member(U_3234),U_3236),hAPP(c_Set_Oimage(U_3233,U_3234,U_3235),c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool)))))
| ~ sP179(U_3229,U_3232,U_3233,U_3234,U_3235,U_3236) )
& ! [U_3229,U_3232,U_3233,U_3234,U_3235,U_3236] :
( sP179(U_3229,U_3232,U_3233,U_3234,U_3235,U_3236)
| ~ c_Fun_Oinj__on(U_3233,U_3234,U_3235,c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177,sP178,sP179])],[f_736_4]) ).
cnf(f_736_6,plain,
( sP179(U_3229,U_3232,U_3233,U_3234,U_3235,U_3236)
| ~ c_Fun_Oinj__on(U_3233,U_3234,U_3235,c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_736_5]) ).
cnf(f_736_7,plain,
( sP177(U_3229,U_3233,U_3234,U_3235,U_3236)
| ~ hBOOL(hAPP(hAPP(c_member(U_3234),U_3236),hAPP(c_Set_Oimage(U_3233,U_3234,U_3235),c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool)))))
| ~ sP179(U_3229,U_3232,U_3233,U_3234,U_3235,U_3236) ),
inference(clausify,[status(thm)],[f_736_5]) ).
cnf(f_736_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_3234),U_3236),hAPP(c_Set_Oimage(U_3233,U_3234,U_3235),c_Orderings_Otop__class_Otop(tc_fun(U_3233,tc_HOL_Obool)))))
| sP178(U_3232,U_3233,U_3234,U_3235,U_3236)
| U_3236 != hAPP(U_3235,U_3232)
| ~ sP179(U_3229,U_3232,U_3233,U_3234,U_3235,U_3236) ),
inference(clausify,[status(thm)],[f_736_5]) ).
cnf(f_736_9,plain,
( U_3236 = hAPP(U_3235,sK73(U_3236,U_3235,U_3234,U_3233))
| ~ sP177(U_3229,U_3233,U_3234,U_3235,U_3236) ),
inference(clausify,[status(thm)],[f_736_5]) ).
cnf(f_736_10,plain,
( U_3229 = sK73(U_3236,U_3235,U_3234,U_3233)
| U_3236 != hAPP(U_3235,U_3229)
| ~ sP177(U_3229,U_3233,U_3234,U_3235,U_3236) ),
inference(clausify,[status(thm)],[f_736_5]) ).
cnf(f_736_11,plain,
( U_3236 = hAPP(U_3235,sK74(U_3236,U_3235,U_3234,U_3233,U_3232))
| ~ sP178(U_3232,U_3233,U_3234,U_3235,U_3236) ),
inference(clausify,[status(thm)],[f_736_5]) ).
cnf(f_736_12,plain,
( sK74(U_3236,U_3235,U_3234,U_3233,U_3232) != U_3232
| ~ sP178(U_3232,U_3233,U_3234,U_3235,U_3236) ),
inference(clausify,[status(thm)],[f_736_5]) ).
fof(f_737_1,plain,
! [V_A_2,V_a_2,V_f_2,T_d,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2))) ) )
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__image__mem__iff]) ).
fof(f_737_2,plain,
! [U_3241,U_3240,U_3239,U_3238,U_3237] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_3238),hAPP(U_3239,U_3240)),hAPP(c_Set_Oimage(U_3237,U_3238,U_3239),U_3241)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3237),U_3240),U_3241)) )
& ( hBOOL(hAPP(hAPP(c_member(U_3237),U_3240),U_3241))
| ~ hBOOL(hAPP(hAPP(c_member(U_3238),hAPP(U_3239,U_3240)),hAPP(c_Set_Oimage(U_3237,U_3238,U_3239),U_3241))) ) )
| ~ c_Fun_Oinj__on(U_3237,U_3238,U_3239,c_Orderings_Otop__class_Otop(tc_fun(U_3237,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_737_1]) ).
fof(f_737_3,plain,
( ! [U_3238,U_3240,U_3237,U_3241,U_3239] :
( hBOOL(hAPP(hAPP(c_member(U_3238),hAPP(U_3239,U_3240)),hAPP(c_Set_Oimage(U_3237,U_3238,U_3239),U_3241)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3237),U_3240),U_3241))
| ~ sP180(U_3238,U_3240,U_3237,U_3241,U_3239) )
& ! [U_3238,U_3240,U_3237,U_3241,U_3239] :
( hBOOL(hAPP(hAPP(c_member(U_3237),U_3240),U_3241))
| ~ hBOOL(hAPP(hAPP(c_member(U_3238),hAPP(U_3239,U_3240)),hAPP(c_Set_Oimage(U_3237,U_3238,U_3239),U_3241)))
| ~ sP180(U_3238,U_3240,U_3237,U_3241,U_3239) )
& ! [U_3238,U_3240,U_3237,U_3241,U_3239] :
( sP180(U_3238,U_3240,U_3237,U_3241,U_3239)
| ~ c_Fun_Oinj__on(U_3237,U_3238,U_3239,c_Orderings_Otop__class_Otop(tc_fun(U_3237,tc_HOL_Obool))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180])],[f_737_2]) ).
cnf(f_737_4,plain,
( sP180(U_3238,U_3240,U_3237,U_3241,U_3239)
| ~ c_Fun_Oinj__on(U_3237,U_3238,U_3239,c_Orderings_Otop__class_Otop(tc_fun(U_3237,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_737_3]) ).
cnf(f_737_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_3237),U_3240),U_3241))
| ~ hBOOL(hAPP(hAPP(c_member(U_3238),hAPP(U_3239,U_3240)),hAPP(c_Set_Oimage(U_3237,U_3238,U_3239),U_3241)))
| ~ sP180(U_3238,U_3240,U_3237,U_3241,U_3239) ),
inference(clausify,[status(thm)],[f_737_3]) ).
cnf(f_737_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3238),hAPP(U_3239,U_3240)),hAPP(c_Set_Oimage(U_3237,U_3238,U_3239),U_3241)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3237),U_3240),U_3241))
| ~ sP180(U_3238,U_3240,U_3237,U_3241,U_3239) ),
inference(clausify,[status(thm)],[f_737_3]) ).
fof(f_738_1,plain,
! [V_f_2,T_c] :
( hAPP(c_Set_Oimage(T_c,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_c,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(T_c,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(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)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj]) ).
fof(f_738_2,plain,
! [U_3243,U_3242] :
( hAPP(c_Set_Oimage(U_3242,U_3242,U_3243),c_Orderings_Otop__class_Otop(tc_fun(U_3242,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3242,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_3242,U_3242,U_3243,c_Orderings_Otop__class_Otop(tc_fun(U_3242,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3242),c_Orderings_Otop__class_Otop(tc_fun(U_3242,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_738_1]) ).
fof(f_738_3,plain,
! [U_3243,U_3242] :
( hAPP(c_Set_Oimage(U_3242,U_3242,U_3243),c_Orderings_Otop__class_Otop(tc_fun(U_3242,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3242,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_3242,U_3242,U_3243,c_Orderings_Otop__class_Otop(tc_fun(U_3242,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3242),c_Orderings_Otop__class_Otop(tc_fun(U_3242,tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_738_2]) ).
cnf(f_738_4,plain,
( hAPP(c_Set_Oimage(U_3242,U_3242,U_3243),c_Orderings_Otop__class_Otop(tc_fun(U_3242,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_3242,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_3242,U_3242,U_3243,c_Orderings_Otop__class_Otop(tc_fun(U_3242,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3242),c_Orderings_Otop__class_Otop(tc_fun(U_3242,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_738_3]) ).
fof(f_739_1,plain,
! [V_f_2,T_c] :
( c_Fun_Oinj__on(T_c,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(T_c,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_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj]) ).
fof(f_739_2,plain,
! [U_3245,U_3244] :
( c_Fun_Oinj__on(U_3244,U_3244,U_3245,c_Orderings_Otop__class_Otop(tc_fun(U_3244,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(U_3244,U_3244,U_3245),c_Orderings_Otop__class_Otop(tc_fun(U_3244,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3244,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3244),c_Orderings_Otop__class_Otop(tc_fun(U_3244,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_739_1]) ).
fof(f_739_3,plain,
! [U_3244,U_3245] :
( c_Fun_Oinj__on(U_3244,U_3244,U_3245,c_Orderings_Otop__class_Otop(tc_fun(U_3244,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(U_3244,U_3244,U_3245),c_Orderings_Otop__class_Otop(tc_fun(U_3244,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3244,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3244),c_Orderings_Otop__class_Otop(tc_fun(U_3244,tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_739_2]) ).
cnf(f_739_4,plain,
( c_Fun_Oinj__on(U_3244,U_3244,U_3245,c_Orderings_Otop__class_Otop(tc_fun(U_3244,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(U_3244,U_3244,U_3245),c_Orderings_Otop__class_Otop(tc_fun(U_3244,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3244,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3244),c_Orderings_Otop__class_Otop(tc_fun(U_3244,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_739_3]) ).
fof(f_740_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2))) ) )
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff]) ).
fof(f_740_2,plain,
! [U_3250,U_3249,U_3248,U_3247,U_3246] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3247,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3246,U_3247,U_3248),U_3249)),hAPP(c_Set_Oimage(U_3246,U_3247,U_3248),U_3250)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3246,tc_HOL_Obool)),U_3249),U_3250)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3246,tc_HOL_Obool)),U_3249),U_3250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3247,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3246,U_3247,U_3248),U_3249)),hAPP(c_Set_Oimage(U_3246,U_3247,U_3248),U_3250))) ) )
| ~ c_Fun_Oinj__on(U_3246,U_3247,U_3248,c_Orderings_Otop__class_Otop(tc_fun(U_3246,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_740_1]) ).
fof(f_740_3,plain,
( ! [U_3246,U_3247,U_3248,U_3249,U_3250] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3247,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3246,U_3247,U_3248),U_3249)),hAPP(c_Set_Oimage(U_3246,U_3247,U_3248),U_3250)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3246,tc_HOL_Obool)),U_3249),U_3250))
| ~ sP181(U_3246,U_3247,U_3248,U_3249,U_3250) )
& ! [U_3246,U_3247,U_3248,U_3249,U_3250] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3246,tc_HOL_Obool)),U_3249),U_3250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3247,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3246,U_3247,U_3248),U_3249)),hAPP(c_Set_Oimage(U_3246,U_3247,U_3248),U_3250)))
| ~ sP181(U_3246,U_3247,U_3248,U_3249,U_3250) )
& ! [U_3246,U_3247,U_3248,U_3249,U_3250] :
( sP181(U_3246,U_3247,U_3248,U_3249,U_3250)
| ~ c_Fun_Oinj__on(U_3246,U_3247,U_3248,c_Orderings_Otop__class_Otop(tc_fun(U_3246,tc_HOL_Obool))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181])],[f_740_2]) ).
cnf(f_740_4,plain,
( sP181(U_3246,U_3247,U_3248,U_3249,U_3250)
| ~ c_Fun_Oinj__on(U_3246,U_3247,U_3248,c_Orderings_Otop__class_Otop(tc_fun(U_3246,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_740_3]) ).
cnf(f_740_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3246,tc_HOL_Obool)),U_3249),U_3250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3247,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3246,U_3247,U_3248),U_3249)),hAPP(c_Set_Oimage(U_3246,U_3247,U_3248),U_3250)))
| ~ sP181(U_3246,U_3247,U_3248,U_3249,U_3250) ),
inference(clausify,[status(thm)],[f_740_3]) ).
cnf(f_740_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3247,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3246,U_3247,U_3248),U_3249)),hAPP(c_Set_Oimage(U_3246,U_3247,U_3248),U_3250)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3246,tc_HOL_Obool)),U_3249),U_3250))
| ~ sP181(U_3246,U_3247,U_3248,U_3249,U_3250) ),
inference(clausify,[status(thm)],[f_740_3]) ).
fof(f_741_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_image__set__diff]) ).
fof(f_741_2,plain,
! [U_3255,U_3254,U_3253,U_3252,U_3251] :
( hAPP(c_Set_Oimage(U_3251,U_3252,U_3253),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3251,tc_HOL_Obool)),U_3254),U_3255)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3252,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3251,U_3252,U_3253),U_3254)),hAPP(c_Set_Oimage(U_3251,U_3252,U_3253),U_3255))
| ~ c_Fun_Oinj__on(U_3251,U_3252,U_3253,c_Orderings_Otop__class_Otop(tc_fun(U_3251,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_741_1]) ).
fof(f_741_3,plain,
! [U_3254,U_3251,U_3252,U_3253,U_3255] :
( hAPP(c_Set_Oimage(U_3251,U_3252,U_3253),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3251,tc_HOL_Obool)),U_3254),U_3255)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3252,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3251,U_3252,U_3253),U_3254)),hAPP(c_Set_Oimage(U_3251,U_3252,U_3253),U_3255))
| ~ c_Fun_Oinj__on(U_3251,U_3252,U_3253,c_Orderings_Otop__class_Otop(tc_fun(U_3251,tc_HOL_Obool))) ),
inference(definitional_conversion,[status(esa)],[f_741_2]) ).
cnf(f_741_4,plain,
( hAPP(c_Set_Oimage(U_3251,U_3252,U_3253),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3251,tc_HOL_Obool)),U_3254),U_3255)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3252,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3251,U_3252,U_3253),U_3254)),hAPP(c_Set_Oimage(U_3251,U_3252,U_3253),U_3255))
| ~ c_Fun_Oinj__on(U_3251,U_3252,U_3253,c_Orderings_Otop__class_Otop(tc_fun(U_3251,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_741_3]) ).
fof(f_742_1,plain,
! [V_A_2,V_f_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,tc_HOL_Obool)),V_A_2))))
| hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset]) ).
fof(f_742_2,plain,
! [U_3259,U_3258,U_3257,U_3256] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3257,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3257,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3256,U_3257,U_3258),U_3259))),hAPP(c_Set_Oimage(U_3256,U_3257,U_3258),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3256,tc_HOL_Obool)),U_3259))))
| hAPP(c_Set_Oimage(U_3256,U_3257,U_3258),c_Orderings_Otop__class_Otop(tc_fun(U_3256,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3257,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_742_1]) ).
fof(f_742_3,plain,
! [U_3256,U_3257,U_3258,U_3259] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3257,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3257,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3256,U_3257,U_3258),U_3259))),hAPP(c_Set_Oimage(U_3256,U_3257,U_3258),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3256,tc_HOL_Obool)),U_3259))))
| hAPP(c_Set_Oimage(U_3256,U_3257,U_3258),c_Orderings_Otop__class_Otop(tc_fun(U_3256,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3257,tc_HOL_Obool)) ),
inference(definitional_conversion,[status(esa)],[f_742_2]) ).
cnf(f_742_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3257,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3257,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3256,U_3257,U_3258),U_3259))),hAPP(c_Set_Oimage(U_3256,U_3257,U_3258),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3256,tc_HOL_Obool)),U_3259))))
| hAPP(c_Set_Oimage(U_3256,U_3257,U_3258),c_Orderings_Otop__class_Otop(tc_fun(U_3256,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_3257,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_742_3]) ).
fof(f_743_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c] :
( 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))
| 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))
| V_A_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__one__idem(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ounion__idem]) ).
fof(f_743_2,plain,
! [U_3264,U_3263,U_3262,U_3261,U_3260] :
( hAPP(U_3262,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3260,tc_HOL_Obool)),U_3263),U_3264)) = hAPP(hAPP(U_3261,hAPP(U_3262,U_3263)),hAPP(U_3262,U_3264))
| U_3264 = c_Orderings_Obot__class_Obot(tc_fun(U_3260,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3260),U_3264))
| U_3263 = c_Orderings_Obot__class_Obot(tc_fun(U_3260,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3260),U_3263))
| ~ c_Finite__Set_Ofolding__one__idem(U_3260,U_3261,U_3262) ),
inference(variable_rename,[status(thm)],[f_743_1]) ).
fof(f_743_3,plain,
! [U_3260,U_3261,U_3262,U_3263,U_3264] :
( hAPP(U_3262,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3260,tc_HOL_Obool)),U_3263),U_3264)) = hAPP(hAPP(U_3261,hAPP(U_3262,U_3263)),hAPP(U_3262,U_3264))
| U_3264 = c_Orderings_Obot__class_Obot(tc_fun(U_3260,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3260),U_3264))
| U_3263 = c_Orderings_Obot__class_Obot(tc_fun(U_3260,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3260),U_3263))
| ~ c_Finite__Set_Ofolding__one__idem(U_3260,U_3261,U_3262) ),
inference(definitional_conversion,[status(esa)],[f_743_2]) ).
cnf(f_743_4,plain,
( hAPP(U_3262,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3260,tc_HOL_Obool)),U_3263),U_3264)) = hAPP(hAPP(U_3261,hAPP(U_3262,U_3263)),hAPP(U_3262,U_3264))
| U_3264 = c_Orderings_Obot__class_Obot(tc_fun(U_3260,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3260),U_3264))
| U_3263 = c_Orderings_Obot__class_Obot(tc_fun(U_3260,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3260),U_3263))
| ~ c_Finite__Set_Ofolding__one__idem(U_3260,U_3261,U_3262) ),
inference(clausify,[status(thm)],[f_743_3]) ).
fof(f_744_1,plain,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_d,T_c] :
( ( ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) )
& ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_d,V_f_2),V_g_2),V_z_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2)) ) )
| ~ c_Big__Operators_Ocomm__monoid__big(T_c,T_d,V_f_2,V_z_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_comm__monoid__big_OF__eq]) ).
fof(f_744_2,plain,
! [U_3271,U_3270,U_3269,U_3268,U_3267,U_3266,U_3265] :
( ( ( hAPP(hAPP(U_3269,U_3271),U_3270) = U_3268
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3266),U_3270)) )
& ( hAPP(hAPP(U_3269,U_3271),U_3270) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3265,U_3266,U_3267),U_3271),U_3268),U_3270)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3266),U_3270)) ) )
| ~ c_Big__Operators_Ocomm__monoid__big(U_3265,U_3266,U_3267,U_3268,U_3269) ),
inference(variable_rename,[status(thm)],[f_744_1]) ).
fof(f_744_3,plain,
( ! [U_3265,U_3268,U_3267,U_3266,U_3270,U_3269,U_3271] :
( hAPP(hAPP(U_3269,U_3271),U_3270) = U_3268
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3266),U_3270))
| ~ sP182(U_3265,U_3268,U_3267,U_3266,U_3270,U_3269,U_3271) )
& ! [U_3265,U_3268,U_3267,U_3266,U_3270,U_3269,U_3271] :
( hAPP(hAPP(U_3269,U_3271),U_3270) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3265,U_3266,U_3267),U_3271),U_3268),U_3270)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3266),U_3270))
| ~ sP182(U_3265,U_3268,U_3267,U_3266,U_3270,U_3269,U_3271) )
& ! [U_3265,U_3268,U_3267,U_3266,U_3270,U_3269,U_3271] :
( sP182(U_3265,U_3268,U_3267,U_3266,U_3270,U_3269,U_3271)
| ~ c_Big__Operators_Ocomm__monoid__big(U_3265,U_3266,U_3267,U_3268,U_3269) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182])],[f_744_2]) ).
cnf(f_744_4,plain,
( sP182(U_3265,U_3268,U_3267,U_3266,U_3270,U_3269,U_3271)
| ~ c_Big__Operators_Ocomm__monoid__big(U_3265,U_3266,U_3267,U_3268,U_3269) ),
inference(clausify,[status(thm)],[f_744_3]) ).
cnf(f_744_5,plain,
( hAPP(hAPP(U_3269,U_3271),U_3270) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3265,U_3266,U_3267),U_3271),U_3268),U_3270)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3266),U_3270))
| ~ sP182(U_3265,U_3268,U_3267,U_3266,U_3270,U_3269,U_3271) ),
inference(clausify,[status(thm)],[f_744_3]) ).
cnf(f_744_6,plain,
( hAPP(hAPP(U_3269,U_3271),U_3270) = U_3268
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3266),U_3270))
| ~ sP182(U_3265,U_3268,U_3267,U_3266,U_3270,U_3269,U_3271) ),
inference(clausify,[status(thm)],[f_744_3]) ).
fof(f_745_1,plain,
! [V_x_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),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)))))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff1__le]) ).
fof(f_745_2,plain,
! [U_3274,U_3273,U_3272] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3272),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3272,tc_HOL_Obool)),U_3273),hAPP(hAPP(c_Set_Oinsert(U_3272),U_3274),c_Orderings_Obot__class_Obot(tc_fun(U_3272,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3272),U_3273)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3272),U_3273)) ),
inference(variable_rename,[status(thm)],[f_745_1]) ).
fof(f_745_3,plain,
! [U_3272,U_3273,U_3274] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3272),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3272,tc_HOL_Obool)),U_3273),hAPP(hAPP(c_Set_Oinsert(U_3272),U_3274),c_Orderings_Obot__class_Obot(tc_fun(U_3272,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3272),U_3273)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3272),U_3273)) ),
inference(definitional_conversion,[status(esa)],[f_745_2]) ).
cnf(f_745_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3272),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3272,tc_HOL_Obool)),U_3273),hAPP(hAPP(c_Set_Oinsert(U_3272),U_3274),c_Orderings_Obot__class_Obot(tc_fun(U_3272,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_3272),U_3273)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3272),U_3273)) ),
inference(clausify,[status(thm)],[f_745_3]) ).
fof(f_746_1,plain,
! [V_b_2,V_a_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_b_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Osemilattice__sup(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sup__le__fold__sup]) ).
fof(f_746_2,plain,
! [U_3278,U_3277,U_3276,U_3275] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3275),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3275),U_3277),U_3278)),hAPP(hAPP(c_Finite__Set_Ofold(U_3275,U_3275,c_Lattices_Osemilattice__sup__class_Osup(U_3275)),U_3278),U_3276)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3275),U_3277),U_3276))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3275),U_3276))
| ~ class_Lattices_Osemilattice__sup(U_3275) ),
inference(variable_rename,[status(thm)],[f_746_1]) ).
fof(f_746_3,plain,
! [U_3275,U_3276,U_3277,U_3278] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3275),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3275),U_3277),U_3278)),hAPP(hAPP(c_Finite__Set_Ofold(U_3275,U_3275,c_Lattices_Osemilattice__sup__class_Osup(U_3275)),U_3278),U_3276)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3275),U_3277),U_3276))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3275),U_3276))
| ~ class_Lattices_Osemilattice__sup(U_3275) ),
inference(definitional_conversion,[status(esa)],[f_746_2]) ).
cnf(f_746_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3275),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3275),U_3277),U_3278)),hAPP(hAPP(c_Finite__Set_Ofold(U_3275,U_3275,c_Lattices_Osemilattice__sup__class_Osup(U_3275)),U_3278),U_3276)))
| ~ hBOOL(hAPP(hAPP(c_member(U_3275),U_3277),U_3276))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3275),U_3276))
| ~ class_Lattices_Osemilattice__sup(U_3275) ),
inference(clausify,[status(thm)],[f_746_3]) ).
fof(f_747_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_card__inj__on__le]) ).
fof(f_747_2,plain,
! [U_3283,U_3282,U_3281,U_3280,U_3279] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3279),U_3282)),hAPP(c_Finite__Set_Ocard(U_3280),U_3283)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3280),U_3283))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3280,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3279,U_3280,U_3281),U_3282)),U_3283))
| ~ c_Fun_Oinj__on(U_3279,U_3280,U_3281,U_3282) ),
inference(variable_rename,[status(thm)],[f_747_1]) ).
fof(f_747_3,plain,
! [U_3279,U_3280,U_3281,U_3282,U_3283] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3279),U_3282)),hAPP(c_Finite__Set_Ocard(U_3280),U_3283)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3280),U_3283))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3280,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3279,U_3280,U_3281),U_3282)),U_3283))
| ~ c_Fun_Oinj__on(U_3279,U_3280,U_3281,U_3282) ),
inference(definitional_conversion,[status(esa)],[f_747_2]) ).
cnf(f_747_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3279),U_3282)),hAPP(c_Finite__Set_Ocard(U_3280),U_3283)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3280),U_3283))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3280,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3279,U_3280,U_3281),U_3282)),U_3283))
| ~ c_Fun_Oinj__on(U_3279,U_3280,U_3281,U_3282) ),
inference(clausify,[status(thm)],[f_747_3]) ).
fof(f_748_1,plain,
! [V_g_2,V_B_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(c_Finite__Set_Ocard(T_d),V_B_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_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)),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2)),V_A_2))
| ~ c_Fun_Oinj__on(T_d,T_c,V_g_2,V_B_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_card__bij__eq]) ).
fof(f_748_2,plain,
! [U_3289,U_3288,U_3287,U_3286,U_3285,U_3284] :
( hAPP(c_Finite__Set_Ocard(U_3284),U_3287) = hAPP(c_Finite__Set_Ocard(U_3285),U_3288)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3285),U_3288))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3284),U_3287))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3284,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3285,U_3284,U_3289),U_3288)),U_3287))
| ~ c_Fun_Oinj__on(U_3285,U_3284,U_3289,U_3288)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3284,U_3285,U_3286),U_3287)),U_3288))
| ~ c_Fun_Oinj__on(U_3284,U_3285,U_3286,U_3287) ),
inference(variable_rename,[status(thm)],[f_748_1]) ).
fof(f_748_3,plain,
! [U_3284,U_3285,U_3286,U_3287,U_3288,U_3289] :
( hAPP(c_Finite__Set_Ocard(U_3284),U_3287) = hAPP(c_Finite__Set_Ocard(U_3285),U_3288)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3285),U_3288))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3284),U_3287))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3284,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3285,U_3284,U_3289),U_3288)),U_3287))
| ~ c_Fun_Oinj__on(U_3285,U_3284,U_3289,U_3288)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3284,U_3285,U_3286),U_3287)),U_3288))
| ~ c_Fun_Oinj__on(U_3284,U_3285,U_3286,U_3287) ),
inference(definitional_conversion,[status(esa)],[f_748_2]) ).
cnf(f_748_4,plain,
( hAPP(c_Finite__Set_Ocard(U_3284),U_3287) = hAPP(c_Finite__Set_Ocard(U_3285),U_3288)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3285),U_3288))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3284),U_3287))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3284,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3285,U_3284,U_3289),U_3288)),U_3287))
| ~ c_Fun_Oinj__on(U_3285,U_3284,U_3289,U_3288)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3285,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3284,U_3285,U_3286),U_3287)),U_3288))
| ~ c_Fun_Oinj__on(U_3284,U_3285,U_3286,U_3287) ),
inference(clausify,[status(thm)],[f_748_3]) ).
fof(f_749_1,plain,
! [V_A_2,V_B_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),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_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_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_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__subset]) ).
fof(f_749_2,plain,
! [U_3292,U_3291,U_3290] :
( hAPP(c_Finite__Set_Ocard(U_3290),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3290,tc_HOL_Obool)),U_3292),U_3291)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3290),U_3292)),hAPP(c_Finite__Set_Ocard(U_3290),U_3291))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3290,tc_HOL_Obool)),U_3291),U_3292))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3290),U_3291)) ),
inference(variable_rename,[status(thm)],[f_749_1]) ).
fof(f_749_3,plain,
! [U_3290,U_3291,U_3292] :
( hAPP(c_Finite__Set_Ocard(U_3290),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3290,tc_HOL_Obool)),U_3292),U_3291)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3290),U_3292)),hAPP(c_Finite__Set_Ocard(U_3290),U_3291))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3290,tc_HOL_Obool)),U_3291),U_3292))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3290),U_3291)) ),
inference(definitional_conversion,[status(esa)],[f_749_2]) ).
cnf(f_749_4,plain,
( hAPP(c_Finite__Set_Ocard(U_3290),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3290,tc_HOL_Obool)),U_3292),U_3291)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3290),U_3292)),hAPP(c_Finite__Set_Ocard(U_3290),U_3291))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3290,tc_HOL_Obool)),U_3291),U_3292))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3290),U_3291)) ),
inference(clausify,[status(thm)],[f_749_3]) ).
fof(f_750_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,tc_fun(T_c,tc_HOL_Obool),c_Set_Oinsert(T_c)),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_union__fold__insert]) ).
fof(f_750_2,plain,
! [U_3295,U_3294,U_3293] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3293,tc_HOL_Obool)),U_3294),U_3295) = hAPP(hAPP(c_Finite__Set_Ofold(U_3293,tc_fun(U_3293,tc_HOL_Obool),c_Set_Oinsert(U_3293)),U_3295),U_3294)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3293),U_3294)) ),
inference(variable_rename,[status(thm)],[f_750_1]) ).
fof(f_750_3,plain,
! [U_3295,U_3293,U_3294] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3293,tc_HOL_Obool)),U_3294),U_3295) = hAPP(hAPP(c_Finite__Set_Ofold(U_3293,tc_fun(U_3293,tc_HOL_Obool),c_Set_Oinsert(U_3293)),U_3295),U_3294)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3293),U_3294)) ),
inference(definitional_conversion,[status(esa)],[f_750_2]) ).
cnf(f_750_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3293,tc_HOL_Obool)),U_3294),U_3295) = hAPP(hAPP(c_Finite__Set_Ofold(U_3293,tc_fun(U_3293,tc_HOL_Obool),c_Set_Oinsert(U_3293)),U_3295),U_3294)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3293),U_3294)) ),
inference(clausify,[status(thm)],[f_750_3]) ).
fof(f_751_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),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_c),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold1__Un2]) ).
fof(f_751_2,plain,
! [U_3298,U_3297,U_3296] :
( hAPP(c_Finite__Set_Ofold1(U_3296,c_Groups_Otimes__class_Otimes(U_3296)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3296,tc_HOL_Obool)),U_3297),U_3298)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3296),hAPP(c_Finite__Set_Ofold1(U_3296,c_Groups_Otimes__class_Otimes(U_3296)),U_3297)),hAPP(c_Finite__Set_Ofold1(U_3296,c_Groups_Otimes__class_Otimes(U_3296)),U_3298))
| U_3298 = c_Orderings_Obot__class_Obot(tc_fun(U_3296,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3296),U_3298))
| U_3297 = c_Orderings_Obot__class_Obot(tc_fun(U_3296,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3296),U_3297))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3296) ),
inference(variable_rename,[status(thm)],[f_751_1]) ).
fof(f_751_3,plain,
! [U_3296,U_3297,U_3298] :
( hAPP(c_Finite__Set_Ofold1(U_3296,c_Groups_Otimes__class_Otimes(U_3296)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3296,tc_HOL_Obool)),U_3297),U_3298)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3296),hAPP(c_Finite__Set_Ofold1(U_3296,c_Groups_Otimes__class_Otimes(U_3296)),U_3297)),hAPP(c_Finite__Set_Ofold1(U_3296,c_Groups_Otimes__class_Otimes(U_3296)),U_3298))
| U_3298 = c_Orderings_Obot__class_Obot(tc_fun(U_3296,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3296),U_3298))
| U_3297 = c_Orderings_Obot__class_Obot(tc_fun(U_3296,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3296),U_3297))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3296) ),
inference(definitional_conversion,[status(esa)],[f_751_2]) ).
cnf(f_751_4,plain,
( hAPP(c_Finite__Set_Ofold1(U_3296,c_Groups_Otimes__class_Otimes(U_3296)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3296,tc_HOL_Obool)),U_3297),U_3298)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3296),hAPP(c_Finite__Set_Ofold1(U_3296,c_Groups_Otimes__class_Otimes(U_3296)),U_3297)),hAPP(c_Finite__Set_Ofold1(U_3296,c_Groups_Otimes__class_Otimes(U_3296)),U_3298))
| U_3298 = c_Orderings_Obot__class_Obot(tc_fun(U_3296,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3296),U_3298))
| U_3297 = c_Orderings_Obot__class_Obot(tc_fun(U_3296,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3296),U_3297))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_3296) ),
inference(clausify,[status(thm)],[f_751_3]) ).
fof(f_752_1,plain,
! [V_B_2,T_d,V_A_2,T_c] :
( ( ( ? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,B_f),V_A_2)),V_B_2))
& c_Fun_Oinj__on(T_c,T_d,B_f,V_A_2) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2)))
| ! [B_f] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,B_f),V_A_2)),V_B_2))
| ~ c_Fun_Oinj__on(T_c,T_d,B_f,V_A_2) ) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__iff__card__le]) ).
fof(f_752_2,plain,
! [U_3304,U_3303,U_3302,U_3301] :
( ( ( ? [U_3300] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3303,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3301,U_3303,U_3300),U_3302)),U_3304))
& c_Fun_Oinj__on(U_3301,U_3303,U_3300,U_3302) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3301),U_3302)),hAPP(c_Finite__Set_Ocard(U_3303),U_3304))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3301),U_3302)),hAPP(c_Finite__Set_Ocard(U_3303),U_3304)))
| ! [U_3299] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3303,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3301,U_3303,U_3299),U_3302)),U_3304))
| ~ c_Fun_Oinj__on(U_3301,U_3303,U_3299,U_3302) ) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3303),U_3304))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3301),U_3302)) ),
inference(variable_rename,[status(thm)],[f_752_1]) ).
fof(f_752_3,plain,
! [U_3304,U_3303,U_3302,U_3301] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3303,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3301,U_3303,sK75(U_3304,U_3303,U_3302,U_3301)),U_3302)),U_3304))
& c_Fun_Oinj__on(U_3301,U_3303,sK75(U_3304,U_3303,U_3302,U_3301),U_3302) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3301),U_3302)),hAPP(c_Finite__Set_Ocard(U_3303),U_3304))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3301),U_3302)),hAPP(c_Finite__Set_Ocard(U_3303),U_3304)))
| ! [U_3299] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3303,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3301,U_3303,U_3299),U_3302)),U_3304))
| ~ c_Fun_Oinj__on(U_3301,U_3303,U_3299,U_3302) ) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3303),U_3304))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3301),U_3302)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_3300,sK75(U_3304,U_3303,U_3302,U_3301))],[f_752_2]) ).
fof(f_752_4,plain,
( ! [U_3301,U_3302,U_3303,U_3304] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3303,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3301,U_3303,sK75(U_3304,U_3303,U_3302,U_3301)),U_3302)),U_3304))
| ~ sP183(U_3301,U_3302,U_3303,U_3304) )
& ! [U_3301,U_3302,U_3303,U_3304] :
( c_Fun_Oinj__on(U_3301,U_3303,sK75(U_3304,U_3303,U_3302,U_3301),U_3302)
| ~ sP183(U_3301,U_3302,U_3303,U_3304) )
& ! [U_3299,U_3301,U_3302,U_3303,U_3304] :
( sP183(U_3301,U_3302,U_3303,U_3304)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3301),U_3302)),hAPP(c_Finite__Set_Ocard(U_3303),U_3304)))
| ~ sP184(U_3299,U_3301,U_3302,U_3303,U_3304) )
& ! [U_3299,U_3301,U_3302,U_3303,U_3304] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3301),U_3302)),hAPP(c_Finite__Set_Ocard(U_3303),U_3304)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3303,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3301,U_3303,U_3299),U_3302)),U_3304))
| ~ c_Fun_Oinj__on(U_3301,U_3303,U_3299,U_3302)
| ~ sP184(U_3299,U_3301,U_3302,U_3303,U_3304) )
& ! [U_3299,U_3301,U_3302,U_3303,U_3304] :
( sP184(U_3299,U_3301,U_3302,U_3303,U_3304)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3303),U_3304))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3301),U_3302)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP183,sP184])],[f_752_3]) ).
cnf(f_752_5,plain,
( sP184(U_3299,U_3301,U_3302,U_3303,U_3304)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3303),U_3304))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3301),U_3302)) ),
inference(clausify,[status(thm)],[f_752_4]) ).
cnf(f_752_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3301),U_3302)),hAPP(c_Finite__Set_Ocard(U_3303),U_3304)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3303,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3301,U_3303,U_3299),U_3302)),U_3304))
| ~ c_Fun_Oinj__on(U_3301,U_3303,U_3299,U_3302)
| ~ sP184(U_3299,U_3301,U_3302,U_3303,U_3304) ),
inference(clausify,[status(thm)],[f_752_4]) ).
cnf(f_752_7,plain,
( sP183(U_3301,U_3302,U_3303,U_3304)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3301),U_3302)),hAPP(c_Finite__Set_Ocard(U_3303),U_3304)))
| ~ sP184(U_3299,U_3301,U_3302,U_3303,U_3304) ),
inference(clausify,[status(thm)],[f_752_4]) ).
cnf(f_752_8,plain,
( c_Fun_Oinj__on(U_3301,U_3303,sK75(U_3304,U_3303,U_3302,U_3301),U_3302)
| ~ sP183(U_3301,U_3302,U_3303,U_3304) ),
inference(clausify,[status(thm)],[f_752_4]) ).
cnf(f_752_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3303,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_3301,U_3303,sK75(U_3304,U_3303,U_3302,U_3301)),U_3302)),U_3304))
| ~ sP183(U_3301,U_3302,U_3303,U_3304) ),
inference(clausify,[status(thm)],[f_752_4]) ).
fof(f_753_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( hAPP(c_Finite__Set_Ocard(T_c),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))))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) )
& ( hAPP(c_Finite__Set_Ocard(T_c),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))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton__if]) ).
fof(f_753_2,plain,
! [U_3307,U_3306,U_3305] :
( ( ( hAPP(c_Finite__Set_Ocard(U_3305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3305,tc_HOL_Obool)),U_3306),hAPP(hAPP(c_Set_Oinsert(U_3305),U_3307),c_Orderings_Obot__class_Obot(tc_fun(U_3305,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_3305),U_3306)
| hBOOL(hAPP(hAPP(c_member(U_3305),U_3307),U_3306)) )
& ( hAPP(c_Finite__Set_Ocard(U_3305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3305,tc_HOL_Obool)),U_3306),hAPP(hAPP(c_Set_Oinsert(U_3305),U_3307),c_Orderings_Obot__class_Obot(tc_fun(U_3305,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3305),U_3306)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_3305),U_3307),U_3306)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3305),U_3306)) ),
inference(variable_rename,[status(thm)],[f_753_1]) ).
fof(f_753_3,plain,
( ! [U_3307,U_3306,U_3305] :
( hAPP(c_Finite__Set_Ocard(U_3305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3305,tc_HOL_Obool)),U_3306),hAPP(hAPP(c_Set_Oinsert(U_3305),U_3307),c_Orderings_Obot__class_Obot(tc_fun(U_3305,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_3305),U_3306)
| hBOOL(hAPP(hAPP(c_member(U_3305),U_3307),U_3306))
| ~ sP185(U_3307,U_3306,U_3305) )
& ! [U_3307,U_3306,U_3305] :
( hAPP(c_Finite__Set_Ocard(U_3305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3305,tc_HOL_Obool)),U_3306),hAPP(hAPP(c_Set_Oinsert(U_3305),U_3307),c_Orderings_Obot__class_Obot(tc_fun(U_3305,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3305),U_3306)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_3305),U_3307),U_3306))
| ~ sP185(U_3307,U_3306,U_3305) )
& ! [U_3307,U_3306,U_3305] :
( sP185(U_3307,U_3306,U_3305)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3305),U_3306)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_753_2]) ).
cnf(f_753_4,plain,
( sP185(U_3307,U_3306,U_3305)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3305),U_3306)) ),
inference(clausify,[status(thm)],[f_753_3]) ).
cnf(f_753_5,plain,
( hAPP(c_Finite__Set_Ocard(U_3305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3305,tc_HOL_Obool)),U_3306),hAPP(hAPP(c_Set_Oinsert(U_3305),U_3307),c_Orderings_Obot__class_Obot(tc_fun(U_3305,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3305),U_3306)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_3305),U_3307),U_3306))
| ~ sP185(U_3307,U_3306,U_3305) ),
inference(clausify,[status(thm)],[f_753_3]) ).
cnf(f_753_6,plain,
( hAPP(c_Finite__Set_Ocard(U_3305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3305,tc_HOL_Obool)),U_3306),hAPP(hAPP(c_Set_Oinsert(U_3305),U_3307),c_Orderings_Obot__class_Obot(tc_fun(U_3305,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_3305),U_3306)
| hBOOL(hAPP(hAPP(c_member(U_3305),U_3307),U_3306))
| ~ sP185(U_3307,U_3306,U_3305) ),
inference(clausify,[status(thm)],[f_753_3]) ).
fof(f_754_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),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))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton]) ).
fof(f_754_2,plain,
! [U_3310,U_3309,U_3308] :
( hAPP(c_Finite__Set_Ocard(U_3308),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3308,tc_HOL_Obool)),U_3309),hAPP(hAPP(c_Set_Oinsert(U_3308),U_3310),c_Orderings_Obot__class_Obot(tc_fun(U_3308,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3308),U_3309)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_3308),U_3310),U_3309))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3308),U_3309)) ),
inference(variable_rename,[status(thm)],[f_754_1]) ).
fof(f_754_3,plain,
! [U_3309,U_3308,U_3310] :
( hAPP(c_Finite__Set_Ocard(U_3308),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3308,tc_HOL_Obool)),U_3309),hAPP(hAPP(c_Set_Oinsert(U_3308),U_3310),c_Orderings_Obot__class_Obot(tc_fun(U_3308,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3308),U_3309)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_3308),U_3310),U_3309))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3308),U_3309)) ),
inference(definitional_conversion,[status(esa)],[f_754_2]) ).
cnf(f_754_4,plain,
( hAPP(c_Finite__Set_Ocard(U_3308),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3308,tc_HOL_Obool)),U_3309),hAPP(hAPP(c_Set_Oinsert(U_3308),U_3310),c_Orderings_Obot__class_Obot(tc_fun(U_3308,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3308),U_3309)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_3308),U_3310),U_3309))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3308),U_3309)) ),
inference(clausify,[status(thm)],[f_754_3]) ).
fof(f_755_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_755_2,plain,
! [U_3313,U_3312,U_3311] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3311),U_3313)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3312),U_3313)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3313),U_3311))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3311),U_3312)) ),
inference(variable_rename,[status(thm)],[f_755_1]) ).
fof(f_755_3,plain,
! [U_3311,U_3312,U_3313] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3311),U_3313)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3312),U_3313)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3313),U_3311))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3311),U_3312)) ),
inference(definitional_conversion,[status(esa)],[f_755_2]) ).
cnf(f_755_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3311),U_3313)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3312),U_3313)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3313),U_3311))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3311),U_3312)) ),
inference(clausify,[status(thm)],[f_755_3]) ).
fof(f_756_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_756_2,plain,
! [U_3316,U_3315,U_3314] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3315),U_3314)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3316),U_3314)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3315),U_3316)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3315),U_3316))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3315),U_3314)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3316),U_3314))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3314),U_3316))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3314),U_3315)) ),
inference(variable_rename,[status(thm)],[f_756_1]) ).
fof(f_756_3,plain,
( ! [U_3314,U_3315,U_3316] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3315),U_3314)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3316),U_3314)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3315),U_3316))
| ~ sP186(U_3314,U_3315,U_3316) )
& ! [U_3314,U_3315,U_3316] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3315),U_3316))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3315),U_3314)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3316),U_3314)))
| ~ sP186(U_3314,U_3315,U_3316) )
& ! [U_3314,U_3315,U_3316] :
( sP186(U_3314,U_3315,U_3316)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3314),U_3316))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3314),U_3315)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_756_2]) ).
cnf(f_756_4,plain,
( sP186(U_3314,U_3315,U_3316)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3314),U_3316))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3314),U_3315)) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3315),U_3316))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3315),U_3314)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3316),U_3314)))
| ~ sP186(U_3314,U_3315,U_3316) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3315),U_3314)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3316),U_3314)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3315),U_3316))
| ~ sP186(U_3314,U_3315,U_3316) ),
inference(clausify,[status(thm)],[f_756_3]) ).
fof(f_757_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_757_2,plain,
! [U_3319,U_3318,U_3317] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3319),U_3318)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3319),U_3317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3317),U_3319))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3317),U_3318)) ),
inference(variable_rename,[status(thm)],[f_757_1]) ).
fof(f_757_3,plain,
! [U_3318,U_3319,U_3317] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3319),U_3318)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3319),U_3317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3317),U_3319))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3317),U_3318)) ),
inference(definitional_conversion,[status(esa)],[f_757_2]) ).
cnf(f_757_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3319),U_3318)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3319),U_3317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3317),U_3319))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3317),U_3318)) ),
inference(clausify,[status(thm)],[f_757_3]) ).
fof(f_758_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_758_2,plain,
! [U_3322,U_3321,U_3320] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3320),U_3322)),U_3321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3320),U_3321)) ),
inference(variable_rename,[status(thm)],[f_758_1]) ).
fof(f_758_3,plain,
! [U_3320,U_3321,U_3322] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3320),U_3322)),U_3321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3320),U_3321)) ),
inference(definitional_conversion,[status(esa)],[f_758_2]) ).
cnf(f_758_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3320),U_3322)),U_3321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3320),U_3321)) ),
inference(clausify,[status(thm)],[f_758_3]) ).
fof(f_759_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_759_2,plain,
! [U_3324,U_3323] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3324),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3323),U_3324)) = U_3323
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3323),U_3324)) ),
inference(variable_rename,[status(thm)],[f_759_1]) ).
fof(f_759_3,plain,
! [U_3323,U_3324] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3324),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3323),U_3324)) = U_3323
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3323),U_3324)) ),
inference(definitional_conversion,[status(esa)],[f_759_2]) ).
cnf(f_759_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3324),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3323),U_3324)) = U_3323
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3323),U_3324)) ),
inference(clausify,[status(thm)],[f_759_3]) ).
fof(f_760_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_760_2,plain,
! [U_3327,U_3326,U_3325] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3325),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3326),U_3327)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3325),U_3327)),U_3326)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3325),U_3327)),U_3326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3325),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3326),U_3327))) ) ),
inference(variable_rename,[status(thm)],[f_760_1]) ).
fof(f_760_3,plain,
( ! [U_3333,U_3331,U_3329] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3329),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3331),U_3333)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3329),U_3333)),U_3331)) )
& ! [U_3332,U_3330,U_3328] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3328),U_3332)),U_3330))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3328),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3330),U_3332))) ) ),
inference(miniscope,[status(thm)],[f_760_2]) ).
fof(f_760_4,plain,
( ! [U_3331,U_3329,U_3333] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3329),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3331),U_3333)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3329),U_3333)),U_3331)) )
& ! [U_3330,U_3332,U_3328] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3328),U_3332)),U_3330))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3328),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3330),U_3332))) ) ),
inference(definitional_conversion,[status(esa)],[f_760_3]) ).
cnf(f_760_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3328),U_3332)),U_3330))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3328),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3330),U_3332))) ),
inference(clausify,[status(thm)],[f_760_4]) ).
cnf(f_760_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3329),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3331),U_3333)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3329),U_3333)),U_3331)) ),
inference(clausify,[status(thm)],[f_760_4]) ).
fof(f_761_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_761_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_761_1]) ).
cnf(f_761_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_761_2]) ).
fof(f_762_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_762_2,plain,
! [U_3334] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3334),U_3334)),
inference(variable_rename,[status(thm)],[f_762_1]) ).
fof(f_762_3,plain,
! [U_3334] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3334),U_3334)),
inference(definitional_conversion,[status(esa)],[f_762_2]) ).
cnf(f_762_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3334),U_3334)),
inference(clausify,[status(thm)],[f_762_3]) ).
fof(f_763_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_763_2,plain,
! [U_3336,U_3335] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3335),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3336),U_3335))),
inference(variable_rename,[status(thm)],[f_763_1]) ).
fof(f_763_3,plain,
! [U_3335,U_3336] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3335),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3336),U_3335))),
inference(definitional_conversion,[status(esa)],[f_763_2]) ).
cnf(f_763_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3335),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3336),U_3335))),
inference(clausify,[status(thm)],[f_763_3]) ).
fof(f_764_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_764_2,plain,
! [U_3338,U_3337] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3337),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3337),U_3338))),
inference(variable_rename,[status(thm)],[f_764_1]) ).
fof(f_764_3,plain,
! [U_3337,U_3338] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3337),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3337),U_3338))),
inference(definitional_conversion,[status(esa)],[f_764_2]) ).
cnf(f_764_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3337),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3337),U_3338))),
inference(clausify,[status(thm)],[f_764_3]) ).
fof(f_765_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_inj__on__add__nat]) ).
fof(f_765_2,plain,
! [U_3340,U_3339] : 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)),U_3339),U_3340),
inference(variable_rename,[status(thm)],[f_765_1]) ).
fof(f_765_3,plain,
! [U_3339,U_3340] : 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)),U_3339),U_3340),
inference(definitional_conversion,[status(esa)],[f_765_2]) ).
cnf(f_765_4,plain,
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)),U_3339),U_3340),
inference(clausify,[status(thm)],[f_765_3]) ).
fof(f_766_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_766_2,plain,
! [U_3344,U_3343] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3343),U_3344))
| ! [U_3342] : U_3344 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3343),U_3342) )
& ( ? [U_3341] : U_3344 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3343),U_3341)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3343),U_3344)) ) ),
inference(variable_rename,[status(thm)],[f_766_1]) ).
fof(f_766_3,plain,
( ! [U_3348,U_3346] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3346),U_3348))
| ! [U_3342] : U_3348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3346),U_3342) )
& ! [U_3347,U_3345] :
( ? [U_3341] : U_3347 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3345),U_3341)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3345),U_3347)) ) ),
inference(miniscope,[status(thm)],[f_766_2]) ).
fof(f_766_4,plain,
( ! [U_3348,U_3346] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3346),U_3348))
| ! [U_3342] : U_3348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3346),U_3342) )
& ! [U_3347,U_3345] :
( U_3347 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3345),sK76(U_3347,U_3345))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3345),U_3347)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_3341,sK76(U_3347,U_3345))],[f_766_3]) ).
fof(f_766_5,plain,
( ! [U_3342,U_3346,U_3348] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3346),U_3348))
| U_3348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3346),U_3342) )
& ! [U_3347,U_3345] :
( U_3347 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3345),sK76(U_3347,U_3345))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3345),U_3347)) ) ),
inference(definitional_conversion,[status(esa)],[f_766_4]) ).
cnf(f_766_6,plain,
( U_3347 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3345),sK76(U_3347,U_3345))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3345),U_3347)) ),
inference(clausify,[status(thm)],[f_766_5]) ).
cnf(f_766_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3346),U_3348))
| U_3348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3346),U_3342) ),
inference(clausify,[status(thm)],[f_766_5]) ).
fof(f_767_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_767_2,plain,
! [U_3350,U_3349] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3350),U_3349))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3349),U_3350)) ),
inference(variable_rename,[status(thm)],[f_767_1]) ).
fof(f_767_3,plain,
! [U_3350,U_3349] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3350),U_3349))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3349),U_3350)) ),
inference(definitional_conversion,[status(esa)],[f_767_2]) ).
cnf(f_767_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3350),U_3349))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3349),U_3350)) ),
inference(clausify,[status(thm)],[f_767_3]) ).
fof(f_768_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_768_2,plain,
! [U_3353,U_3352,U_3351] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3351),U_3352)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3351),U_3353)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3352),U_3353)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3352),U_3353))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3351),U_3352)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3351),U_3353))) ) ),
inference(variable_rename,[status(thm)],[f_768_1]) ).
fof(f_768_3,plain,
( ! [U_3359,U_3357] :
( ! [U_3355] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3355),U_3357)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3355),U_3359)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3357),U_3359)) )
& ! [U_3358,U_3356] :
( ! [U_3354] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3354),U_3356)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3354),U_3358)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3356),U_3358)) ) ),
inference(miniscope,[status(thm)],[f_768_2]) ).
fof(f_768_4,plain,
( ! [U_3357,U_3355,U_3359] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3355),U_3357)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3355),U_3359)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3357),U_3359)) )
& ! [U_3358,U_3356,U_3354] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3354),U_3356)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3354),U_3358)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3356),U_3358)) ) ),
inference(definitional_conversion,[status(esa)],[f_768_3]) ).
cnf(f_768_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_3354),U_3356)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3354),U_3358)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3356),U_3358)) ),
inference(clausify,[status(thm)],[f_768_4]) ).
cnf(f_768_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_3355),U_3357)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3355),U_3359)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3357),U_3359)) ),
inference(clausify,[status(thm)],[f_768_4]) ).
fof(f_769_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_769_2,plain,
! [U_3361,U_3360] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3360),U_3361))
| U_3360 != U_3361 ),
inference(variable_rename,[status(thm)],[f_769_1]) ).
fof(f_769_3,plain,
! [U_3360,U_3361] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3360),U_3361))
| U_3360 != U_3361 ),
inference(definitional_conversion,[status(esa)],[f_769_2]) ).
cnf(f_769_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3360),U_3361))
| U_3360 != U_3361 ),
inference(clausify,[status(thm)],[f_769_3]) ).
fof(f_770_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_770_2,plain,
! [U_3364,U_3363,U_3362] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3363),U_3364)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3362),U_3363)) ),
inference(variable_rename,[status(thm)],[f_770_1]) ).
fof(f_770_3,plain,
! [U_3362,U_3363,U_3364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3363),U_3364)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3362),U_3363)) ),
inference(definitional_conversion,[status(esa)],[f_770_2]) ).
cnf(f_770_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3363),U_3364)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3362),U_3363)) ),
inference(clausify,[status(thm)],[f_770_3]) ).
fof(f_771_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_771_2,plain,
! [U_3367,U_3366,U_3365] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3365),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3367),U_3366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3365),U_3366)) ),
inference(variable_rename,[status(thm)],[f_771_1]) ).
fof(f_771_3,plain,
! [U_3365,U_3366,U_3367] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3365),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3367),U_3366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3365),U_3366)) ),
inference(definitional_conversion,[status(esa)],[f_771_2]) ).
cnf(f_771_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3365),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3367),U_3366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3365),U_3366)) ),
inference(clausify,[status(thm)],[f_771_3]) ).
fof(f_772_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_772_2,plain,
! [U_3370,U_3369,U_3368] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3368),U_3370)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3369),U_3370)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3368),U_3369)) ),
inference(variable_rename,[status(thm)],[f_772_1]) ).
fof(f_772_3,plain,
! [U_3368,U_3369,U_3370] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3368),U_3370)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3369),U_3370)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3368),U_3369)) ),
inference(definitional_conversion,[status(esa)],[f_772_2]) ).
cnf(f_772_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_3368),U_3370)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3369),U_3370)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3368),U_3369)) ),
inference(clausify,[status(thm)],[f_772_3]) ).
fof(f_773_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_773_2,plain,
! [U_3373,U_3372,U_3371] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3371),U_3373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3372),U_3373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3371),U_3372)) ),
inference(variable_rename,[status(thm)],[f_773_1]) ).
fof(f_773_3,plain,
! [U_3371,U_3372,U_3373] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3371),U_3373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3372),U_3373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3371),U_3372)) ),
inference(definitional_conversion,[status(esa)],[f_773_2]) ).
cnf(f_773_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3371),U_3373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3372),U_3373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3371),U_3372)) ),
inference(clausify,[status(thm)],[f_773_3]) ).
fof(f_774_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_774_2,plain,
! [U_3375,U_3374] :
( U_3374 = U_3375
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3375),U_3374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3374),U_3375)) ),
inference(variable_rename,[status(thm)],[f_774_1]) ).
fof(f_774_3,plain,
! [U_3374,U_3375] :
( U_3374 = U_3375
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3375),U_3374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3374),U_3375)) ),
inference(definitional_conversion,[status(esa)],[f_774_2]) ).
cnf(f_774_4,plain,
( U_3374 = U_3375
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3375),U_3374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3374),U_3375)) ),
inference(clausify,[status(thm)],[f_774_3]) ).
fof(f_775_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_775_2,plain,
! [U_3379,U_3378,U_3377,U_3376] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3376),U_3378)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3377),U_3379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3378),U_3379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3376),U_3377)) ),
inference(variable_rename,[status(thm)],[f_775_1]) ).
fof(f_775_3,plain,
! [U_3376,U_3377,U_3378,U_3379] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3376),U_3378)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3377),U_3379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3378),U_3379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3376),U_3377)) ),
inference(definitional_conversion,[status(esa)],[f_775_2]) ).
cnf(f_775_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_3376),U_3378)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3377),U_3379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3378),U_3379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3376),U_3377)) ),
inference(clausify,[status(thm)],[f_775_3]) ).
fof(f_776_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_776_2,plain,
! [U_3382,U_3381,U_3380] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3381),U_3382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3380),U_3381)),U_3382)) ),
inference(variable_rename,[status(thm)],[f_776_1]) ).
fof(f_776_3,plain,
! [U_3382,U_3381] :
( ! [U_3380] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3380),U_3381)),U_3382))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3381),U_3382)) ),
inference(miniscope,[status(thm)],[f_776_2]) ).
fof(f_776_4,plain,
! [U_3381,U_3380,U_3382] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3380),U_3381)),U_3382))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3381),U_3382)) ),
inference(definitional_conversion,[status(esa)],[f_776_3]) ).
cnf(f_776_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_3380),U_3381)),U_3382))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3381),U_3382)) ),
inference(clausify,[status(thm)],[f_776_4]) ).
fof(f_777_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_777_2,plain,
! [U_3385,U_3384,U_3383] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3383),U_3385))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3383),U_3384)),U_3385)) ),
inference(variable_rename,[status(thm)],[f_777_1]) ).
fof(f_777_3,plain,
! [U_3383,U_3384,U_3385] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3383),U_3385))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3383),U_3384)),U_3385)) ),
inference(definitional_conversion,[status(esa)],[f_777_2]) ).
cnf(f_777_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3383),U_3385))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3383),U_3384)),U_3385)) ),
inference(clausify,[status(thm)],[f_777_3]) ).
fof(f_778_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_778_2,plain,
! [U_3388,U_3387,U_3386] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3387),U_3388))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3386),U_3388)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3386),U_3387)),U_3388)) ),
inference(variable_rename,[status(thm)],[f_778_1]) ).
fof(f_778_3,plain,
( ! [U_3386,U_3387,U_3388] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3387),U_3388))
| ~ sP187(U_3386,U_3387,U_3388) )
& ! [U_3386,U_3387,U_3388] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3386),U_3388))
| ~ sP187(U_3386,U_3387,U_3388) )
& ! [U_3386,U_3387,U_3388] :
( sP187(U_3386,U_3387,U_3388)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3386),U_3387)),U_3388)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187])],[f_778_2]) ).
cnf(f_778_4,plain,
( sP187(U_3386,U_3387,U_3388)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3386),U_3387)),U_3388)) ),
inference(clausify,[status(thm)],[f_778_3]) ).
cnf(f_778_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3386),U_3388))
| ~ sP187(U_3386,U_3387,U_3388) ),
inference(clausify,[status(thm)],[f_778_3]) ).
cnf(f_778_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3387),U_3388))
| ~ sP187(U_3386,U_3387,U_3388) ),
inference(clausify,[status(thm)],[f_778_3]) ).
fof(f_779_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_779_2,plain,
! [U_3393] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3393))
| ! [U_3392] :
? [U_3391] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3391),U_3392))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3391),U_3393)) ) )
& ( ? [U_3390] :
! [U_3389] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3389),U_3390))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3389),U_3393)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3393)) ) ),
inference(variable_rename,[status(thm)],[f_779_1]) ).
fof(f_779_3,plain,
( ! [U_3395] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3395))
| ! [U_3392] :
? [U_3391] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3391),U_3392))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3391),U_3395)) ) )
& ! [U_3394] :
( ? [U_3390] :
! [U_3389] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3389),U_3390))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3389),U_3394)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3394)) ) ),
inference(miniscope,[status(thm)],[f_779_2]) ).
fof(f_779_4,plain,
( ! [U_3395] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3395))
| ! [U_3392] :
? [U_3391] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3391),U_3392))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3391),U_3395)) ) )
& ! [U_3394] :
( ! [U_3389] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3389),sK77(U_3394)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3389),U_3394)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3394)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_3390,sK77(U_3394))],[f_779_3]) ).
fof(f_779_5,plain,
( ! [U_3395] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3395))
| ! [U_3392] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK78(U_3395,U_3392)),U_3392))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK78(U_3395,U_3392)),U_3395)) ) )
& ! [U_3394] :
( ! [U_3389] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3389),sK77(U_3394)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3389),U_3394)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3394)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_3391,sK78(U_3395,U_3392))],[f_779_4]) ).
fof(f_779_6,plain,
( ! [U_3392,U_3395] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK78(U_3395,U_3392)),U_3392))
| ~ sP188(U_3392,U_3395) )
& ! [U_3392,U_3395] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK78(U_3395,U_3392)),U_3395))
| ~ sP188(U_3392,U_3395) )
& ! [U_3392,U_3395] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3395))
| sP188(U_3392,U_3395) )
& ! [U_3389,U_3394] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3389),sK77(U_3394)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3389),U_3394))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3394)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188])],[f_779_5]) ).
cnf(f_779_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3389),sK77(U_3394)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3389),U_3394))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3394)) ),
inference(clausify,[status(thm)],[f_779_6]) ).
cnf(f_779_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3395))
| sP188(U_3392,U_3395) ),
inference(clausify,[status(thm)],[f_779_6]) ).
cnf(f_779_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK78(U_3395,U_3392)),U_3395))
| ~ sP188(U_3392,U_3395) ),
inference(clausify,[status(thm)],[f_779_6]) ).
cnf(f_779_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK78(U_3395,U_3392)),U_3392))
| ~ sP188(U_3392,U_3395) ),
inference(clausify,[status(thm)],[f_779_6]) ).
fof(f_780_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_780_2,plain,
! [U_3398,U_3397,U_3396] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3396),U_3397) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3398),U_3397)
| U_3396 != U_3398 )
& ( U_3396 = U_3398
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3396),U_3397) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3398),U_3397) ) ),
inference(variable_rename,[status(thm)],[f_780_1]) ).
fof(f_780_3,plain,
( ! [U_3404,U_3402,U_3400] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3400),U_3402) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3404),U_3402)
| U_3400 != U_3404 )
& ! [U_3403,U_3401,U_3399] :
( U_3399 = U_3403
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3399),U_3401) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3403),U_3401) ) ),
inference(miniscope,[status(thm)],[f_780_2]) ).
fof(f_780_4,plain,
( ! [U_3402,U_3400,U_3404] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3400),U_3402) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3404),U_3402)
| U_3400 != U_3404 )
& ! [U_3403,U_3399,U_3401] :
( U_3399 = U_3403
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3399),U_3401) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3403),U_3401) ) ),
inference(definitional_conversion,[status(esa)],[f_780_3]) ).
cnf(f_780_5,plain,
( U_3399 = U_3403
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3399),U_3401) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3403),U_3401) ),
inference(clausify,[status(thm)],[f_780_4]) ).
cnf(f_780_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3400),U_3402) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3404),U_3402)
| U_3400 != U_3404 ),
inference(clausify,[status(thm)],[f_780_4]) ).
fof(f_781_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_781_2,plain,
! [U_3407,U_3406,U_3405] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3405),U_3406) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3405),U_3407)
| U_3406 != U_3407 )
& ( U_3406 = U_3407
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3405),U_3406) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3405),U_3407) ) ),
inference(variable_rename,[status(thm)],[f_781_1]) ).
fof(f_781_3,plain,
( ! [U_3413,U_3411] :
( ! [U_3409] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3409),U_3411) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3409),U_3413)
| U_3411 != U_3413 )
& ! [U_3412,U_3410] :
( ! [U_3408] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3408),U_3410) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3408),U_3412)
| U_3410 = U_3412 ) ),
inference(miniscope,[status(thm)],[f_781_2]) ).
fof(f_781_4,plain,
( ! [U_3413,U_3409,U_3411] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3409),U_3411) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3409),U_3413)
| U_3411 != U_3413 )
& ! [U_3410,U_3412,U_3408] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3408),U_3410) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3408),U_3412)
| U_3410 = U_3412 ) ),
inference(definitional_conversion,[status(esa)],[f_781_3]) ).
cnf(f_781_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3408),U_3410) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3408),U_3412)
| U_3410 = U_3412 ),
inference(clausify,[status(thm)],[f_781_4]) ).
cnf(f_781_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3409),U_3411) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3409),U_3413)
| U_3411 != U_3413 ),
inference(clausify,[status(thm)],[f_781_4]) ).
fof(f_782_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_782_2,plain,
! [U_3416,U_3415,U_3414] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3414),U_3415)),U_3416) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3414),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3415),U_3416)),
inference(variable_rename,[status(thm)],[f_782_1]) ).
fof(f_782_3,plain,
! [U_3414,U_3415,U_3416] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3414),U_3415)),U_3416) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3414),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3415),U_3416)),
inference(definitional_conversion,[status(esa)],[f_782_2]) ).
cnf(f_782_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3414),U_3415)),U_3416) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3414),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3415),U_3416)),
inference(clausify,[status(thm)],[f_782_3]) ).
fof(f_783_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_783_2,plain,
! [U_3419,U_3418,U_3417] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3418),U_3419)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3418),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3417),U_3419)),
inference(variable_rename,[status(thm)],[f_783_1]) ).
fof(f_783_3,plain,
! [U_3417,U_3418,U_3419] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3418),U_3419)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3418),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3417),U_3419)),
inference(definitional_conversion,[status(esa)],[f_783_2]) ).
cnf(f_783_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3418),U_3419)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3418),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3417),U_3419)),
inference(clausify,[status(thm)],[f_783_3]) ).
fof(f_784_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_784_2,plain,
! [U_3421,U_3420] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3420),U_3421) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3421),U_3420),
inference(variable_rename,[status(thm)],[f_784_1]) ).
fof(f_784_3,plain,
! [U_3420,U_3421] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3420),U_3421) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3421),U_3420),
inference(definitional_conversion,[status(esa)],[f_784_2]) ).
cnf(f_784_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3420),U_3421) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3421),U_3420),
inference(clausify,[status(thm)],[f_784_3]) ).
fof(f_785_1,plain,
! [V_x_2,T_c] :
( ( ( c_Groups_Oone__class_Oone(T_c) = V_x_2
| V_x_2 != c_Groups_Oone__class_Oone(T_c) )
& ( V_x_2 = c_Groups_Oone__class_Oone(T_c)
| c_Groups_Oone__class_Oone(T_c) != V_x_2 ) )
| ~ class_Groups_Oone(T_c) ),
inference(fof_nnf,[status(thm)],[fact_one__reorient]) ).
fof(f_785_2,plain,
! [U_3423,U_3422] :
( ( ( c_Groups_Oone__class_Oone(U_3422) = U_3423
| U_3423 != c_Groups_Oone__class_Oone(U_3422) )
& ( U_3423 = c_Groups_Oone__class_Oone(U_3422)
| c_Groups_Oone__class_Oone(U_3422) != U_3423 ) )
| ~ class_Groups_Oone(U_3422) ),
inference(variable_rename,[status(thm)],[f_785_1]) ).
fof(f_785_3,plain,
( ! [U_3422,U_3423] :
( c_Groups_Oone__class_Oone(U_3422) = U_3423
| U_3423 != c_Groups_Oone__class_Oone(U_3422)
| ~ sP189(U_3422,U_3423) )
& ! [U_3422,U_3423] :
( U_3423 = c_Groups_Oone__class_Oone(U_3422)
| c_Groups_Oone__class_Oone(U_3422) != U_3423
| ~ sP189(U_3422,U_3423) )
& ! [U_3422,U_3423] :
( sP189(U_3422,U_3423)
| ~ class_Groups_Oone(U_3422) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189])],[f_785_2]) ).
cnf(f_785_4,plain,
( sP189(U_3422,U_3423)
| ~ class_Groups_Oone(U_3422) ),
inference(clausify,[status(thm)],[f_785_3]) ).
cnf(f_785_5,plain,
( U_3423 = c_Groups_Oone__class_Oone(U_3422)
| c_Groups_Oone__class_Oone(U_3422) != U_3423
| ~ sP189(U_3422,U_3423) ),
inference(clausify,[status(thm)],[f_785_3]) ).
cnf(f_785_6,plain,
( c_Groups_Oone__class_Oone(U_3422) = U_3423
| U_3423 != c_Groups_Oone__class_Oone(U_3422)
| ~ sP189(U_3422,U_3423) ),
inference(clausify,[status(thm)],[f_785_3]) ).
fof(f_786_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_786_2,plain,
! [U_3425,U_3424] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3424),U_3425) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3425 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3424 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_3425 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_3424 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3424),U_3425) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_786_1]) ).
fof(f_786_3,plain,
( ! [U_3429,U_3427] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3427),U_3429) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3429 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3427 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_3428,U_3426] :
( ( U_3428 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_3426 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3426),U_3428) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_786_2]) ).
fof(f_786_4,plain,
( ! [U_3426,U_3428] :
( U_3428 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP190(U_3426,U_3428) )
& ! [U_3426,U_3428] :
( U_3426 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP190(U_3426,U_3428) )
& ! [U_3429,U_3427] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3427),U_3429) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3429 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3427 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_3426,U_3428] :
( sP190(U_3426,U_3428)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3426),U_3428) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP190])],[f_786_3]) ).
cnf(f_786_5,plain,
( sP190(U_3426,U_3428)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3426),U_3428) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_786_4]) ).
cnf(f_786_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3427),U_3429) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3429 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3427 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_786_4]) ).
cnf(f_786_7,plain,
( U_3426 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP190(U_3426,U_3428) ),
inference(clausify,[status(thm)],[f_786_4]) ).
cnf(f_786_8,plain,
( U_3428 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP190(U_3426,U_3428) ),
inference(clausify,[status(thm)],[f_786_4]) ).
fof(f_787_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_787_2,plain,
! [U_3430] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3430),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3430,
inference(variable_rename,[status(thm)],[f_787_1]) ).
fof(f_787_3,plain,
! [U_3430] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3430),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3430,
inference(definitional_conversion,[status(esa)],[f_787_2]) ).
cnf(f_787_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3430),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3430,
inference(clausify,[status(thm)],[f_787_3]) ).
fof(f_788_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_788_2,plain,
! [U_3432,U_3431] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3431),U_3432)
| U_3432 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3431 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_3432 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_3431 = 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_3431),U_3432) ) ),
inference(variable_rename,[status(thm)],[f_788_1]) ).
fof(f_788_3,plain,
( ! [U_3436,U_3434] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3434),U_3436)
| U_3436 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3434 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_3435,U_3433] :
( ( U_3435 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_3433 = 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_3433),U_3435) ) ),
inference(miniscope,[status(thm)],[f_788_2]) ).
fof(f_788_4,plain,
( ! [U_3435,U_3433] :
( U_3435 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP191(U_3435,U_3433) )
& ! [U_3435,U_3433] :
( U_3433 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP191(U_3435,U_3433) )
& ! [U_3436,U_3434] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3434),U_3436)
| U_3436 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3434 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_3435,U_3433] :
( sP191(U_3435,U_3433)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3433),U_3435) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP191])],[f_788_3]) ).
cnf(f_788_5,plain,
( sP191(U_3435,U_3433)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3433),U_3435) ),
inference(clausify,[status(thm)],[f_788_4]) ).
cnf(f_788_6,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3434),U_3436)
| U_3436 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_3434 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_788_4]) ).
cnf(f_788_7,plain,
( U_3433 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP191(U_3435,U_3433) ),
inference(clausify,[status(thm)],[f_788_4]) ).
cnf(f_788_8,plain,
( U_3435 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP191(U_3435,U_3433) ),
inference(clausify,[status(thm)],[f_788_4]) ).
fof(f_789_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_789_2,plain,
! [U_3437] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3437) = U_3437,
inference(variable_rename,[status(thm)],[f_789_1]) ).
fof(f_789_3,plain,
! [U_3437] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3437) = U_3437,
inference(definitional_conversion,[status(esa)],[f_789_2]) ).
cnf(f_789_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3437) = U_3437,
inference(clausify,[status(thm)],[f_789_3]) ).
fof(f_790_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_790_2,plain,
! [U_3440,U_3439,U_3438] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3438),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3439),U_3440)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3438),U_3439)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3438),U_3440)),
inference(variable_rename,[status(thm)],[f_790_1]) ).
fof(f_790_3,plain,
! [U_3438,U_3439,U_3440] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3438),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3439),U_3440)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3438),U_3439)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3438),U_3440)),
inference(definitional_conversion,[status(esa)],[f_790_2]) ).
cnf(f_790_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3438),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3439),U_3440)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3438),U_3439)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3438),U_3440)),
inference(clausify,[status(thm)],[f_790_3]) ).
fof(f_791_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_791_2,plain,
! [U_3443,U_3442,U_3441] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3441),U_3442)),U_3443) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3441),U_3443)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3442),U_3443)),
inference(variable_rename,[status(thm)],[f_791_1]) ).
fof(f_791_3,plain,
! [U_3441,U_3442,U_3443] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3441),U_3442)),U_3443) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3441),U_3443)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3442),U_3443)),
inference(definitional_conversion,[status(esa)],[f_791_2]) ).
cnf(f_791_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3441),U_3442)),U_3443) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3441),U_3443)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3442),U_3443)),
inference(clausify,[status(thm)],[f_791_3]) ).
fof(f_792_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_792_2,plain,
! [U_3447,U_3446,U_3445,U_3444] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3444),U_3446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3445),U_3447)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3446),U_3447))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3444),U_3445)) ),
inference(variable_rename,[status(thm)],[f_792_1]) ).
fof(f_792_3,plain,
! [U_3444,U_3445,U_3446,U_3447] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3444),U_3446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3445),U_3447)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3446),U_3447))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3444),U_3445)) ),
inference(definitional_conversion,[status(esa)],[f_792_2]) ).
cnf(f_792_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_3444),U_3446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3445),U_3447)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3446),U_3447))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3444),U_3445)) ),
inference(clausify,[status(thm)],[f_792_3]) ).
fof(f_793_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_793_2,plain,
! [U_3450,U_3449,U_3448] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3450),U_3448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3450),U_3449)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3448),U_3449)) ),
inference(variable_rename,[status(thm)],[f_793_1]) ).
fof(f_793_3,plain,
! [U_3448,U_3449,U_3450] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3450),U_3448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3450),U_3449)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3448),U_3449)) ),
inference(definitional_conversion,[status(esa)],[f_793_2]) ).
cnf(f_793_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_3450),U_3448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3450),U_3449)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3448),U_3449)) ),
inference(clausify,[status(thm)],[f_793_3]) ).
fof(f_794_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_794_2,plain,
! [U_3453,U_3452,U_3451] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3451),U_3453)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3452),U_3453)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3451),U_3452)) ),
inference(variable_rename,[status(thm)],[f_794_1]) ).
fof(f_794_3,plain,
! [U_3451,U_3452,U_3453] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3451),U_3453)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3452),U_3453)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3451),U_3452)) ),
inference(definitional_conversion,[status(esa)],[f_794_2]) ).
cnf(f_794_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_3451),U_3453)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3452),U_3453)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3451),U_3452)) ),
inference(clausify,[status(thm)],[f_794_3]) ).
fof(f_795_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_795_2,plain,
! [U_3454] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3454),U_3454)))),
inference(variable_rename,[status(thm)],[f_795_1]) ).
fof(f_795_3,plain,
! [U_3454] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3454),U_3454)))),
inference(definitional_conversion,[status(esa)],[f_795_2]) ).
cnf(f_795_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3454),U_3454)))),
inference(clausify,[status(thm)],[f_795_3]) ).
fof(f_796_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_796_2,plain,
! [U_3455] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3455),U_3455))),
inference(variable_rename,[status(thm)],[f_796_1]) ).
fof(f_796_3,plain,
! [U_3455] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3455),U_3455))),
inference(definitional_conversion,[status(esa)],[f_796_2]) ).
cnf(f_796_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3455),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3455),U_3455))),
inference(clausify,[status(thm)],[f_796_3]) ).
fof(f_797_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_797_2,plain,
! [U_3457,U_3456] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3456),U_3457),c_Groups_Oone__class_Oone(U_3456)) = U_3457
| ~ class_Groups_Ocomm__monoid__mult(U_3456) ),
inference(variable_rename,[status(thm)],[f_797_1]) ).
fof(f_797_3,plain,
! [U_3456,U_3457] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3456),U_3457),c_Groups_Oone__class_Oone(U_3456)) = U_3457
| ~ class_Groups_Ocomm__monoid__mult(U_3456) ),
inference(definitional_conversion,[status(esa)],[f_797_2]) ).
cnf(f_797_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3456),U_3457),c_Groups_Oone__class_Oone(U_3456)) = U_3457
| ~ class_Groups_Ocomm__monoid__mult(U_3456) ),
inference(clausify,[status(thm)],[f_797_3]) ).
fof(f_798_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_798_2,plain,
! [U_3459,U_3458] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3458),U_3459),c_Groups_Oone__class_Oone(U_3458)) = U_3459
| ~ class_Groups_Omonoid__mult(U_3458) ),
inference(variable_rename,[status(thm)],[f_798_1]) ).
fof(f_798_3,plain,
! [U_3458,U_3459] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3458),U_3459),c_Groups_Oone__class_Oone(U_3458)) = U_3459
| ~ class_Groups_Omonoid__mult(U_3458) ),
inference(definitional_conversion,[status(esa)],[f_798_2]) ).
cnf(f_798_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3458),U_3459),c_Groups_Oone__class_Oone(U_3458)) = U_3459
| ~ class_Groups_Omonoid__mult(U_3458) ),
inference(clausify,[status(thm)],[f_798_3]) ).
fof(f_799_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_799_2,plain,
! [U_3461,U_3460] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3460),c_Groups_Oone__class_Oone(U_3460)),U_3461) = U_3461
| ~ class_Groups_Ocomm__monoid__mult(U_3460) ),
inference(variable_rename,[status(thm)],[f_799_1]) ).
fof(f_799_3,plain,
! [U_3460,U_3461] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3460),c_Groups_Oone__class_Oone(U_3460)),U_3461) = U_3461
| ~ class_Groups_Ocomm__monoid__mult(U_3460) ),
inference(definitional_conversion,[status(esa)],[f_799_2]) ).
cnf(f_799_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3460),c_Groups_Oone__class_Oone(U_3460)),U_3461) = U_3461
| ~ class_Groups_Ocomm__monoid__mult(U_3460) ),
inference(clausify,[status(thm)],[f_799_3]) ).
fof(f_800_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_800_2,plain,
! [U_3463,U_3462] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3462),c_Groups_Oone__class_Oone(U_3462)),U_3463) = U_3463
| ~ class_Groups_Omonoid__mult(U_3462) ),
inference(variable_rename,[status(thm)],[f_800_1]) ).
fof(f_800_3,plain,
! [U_3462,U_3463] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3462),c_Groups_Oone__class_Oone(U_3462)),U_3463) = U_3463
| ~ class_Groups_Omonoid__mult(U_3462) ),
inference(definitional_conversion,[status(esa)],[f_800_2]) ).
cnf(f_800_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3462),c_Groups_Oone__class_Oone(U_3462)),U_3463) = U_3463
| ~ class_Groups_Omonoid__mult(U_3462) ),
inference(clausify,[status(thm)],[f_800_3]) ).
fof(f_801_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_801_2,plain,
! [U_3465,U_3464] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3464),c_Groups_Oone__class_Oone(U_3464)),U_3465) = U_3465
| ~ class_Rings_Ocomm__semiring__1(U_3464) ),
inference(variable_rename,[status(thm)],[f_801_1]) ).
fof(f_801_3,plain,
! [U_3464,U_3465] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3464),c_Groups_Oone__class_Oone(U_3464)),U_3465) = U_3465
| ~ class_Rings_Ocomm__semiring__1(U_3464) ),
inference(definitional_conversion,[status(esa)],[f_801_2]) ).
cnf(f_801_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3464),c_Groups_Oone__class_Oone(U_3464)),U_3465) = U_3465
| ~ class_Rings_Ocomm__semiring__1(U_3464) ),
inference(clausify,[status(thm)],[f_801_3]) ).
fof(f_802_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_802_2,plain,
! [U_3467,U_3466] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3466),U_3467),c_Groups_Oone__class_Oone(U_3466)) = U_3467
| ~ class_Rings_Ocomm__semiring__1(U_3466) ),
inference(variable_rename,[status(thm)],[f_802_1]) ).
fof(f_802_3,plain,
! [U_3466,U_3467] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3466),U_3467),c_Groups_Oone__class_Oone(U_3466)) = U_3467
| ~ class_Rings_Ocomm__semiring__1(U_3466) ),
inference(definitional_conversion,[status(esa)],[f_802_2]) ).
cnf(f_802_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3466),U_3467),c_Groups_Oone__class_Oone(U_3466)) = U_3467
| ~ class_Rings_Ocomm__semiring__1(U_3466) ),
inference(clausify,[status(thm)],[f_802_3]) ).
fof(f_803_1,plain,
! [V_f_2,V_F_2,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,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_c),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_c),B_x),V_F_2)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_F_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_setprod__eq__1__iff]) ).
fof(f_803_2,plain,
! [U_3472,U_3471,U_3470] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3470,tc_Nat_Onat),U_3472),U_3471) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ? [U_3469] :
( hAPP(U_3472,U_3469) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_3470),U_3469),U_3471)) ) )
& ( ! [U_3468] :
( hAPP(U_3472,U_3468) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_3470),U_3468),U_3471)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3470,tc_Nat_Onat),U_3472),U_3471) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3470),U_3471)) ),
inference(variable_rename,[status(thm)],[f_803_1]) ).
fof(f_803_3,plain,
! [U_3472,U_3471,U_3470] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3470,tc_Nat_Onat),U_3472),U_3471) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ( hAPP(U_3472,sK79(U_3472,U_3471,U_3470)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_3470),sK79(U_3472,U_3471,U_3470)),U_3471)) ) )
& ( ! [U_3468] :
( hAPP(U_3472,U_3468) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_3470),U_3468),U_3471)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3470,tc_Nat_Onat),U_3472),U_3471) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3470),U_3471)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_3469,sK79(U_3472,U_3471,U_3470))],[f_803_2]) ).
fof(f_803_4,plain,
( ! [U_3470,U_3471,U_3472] :
( hAPP(U_3472,sK79(U_3472,U_3471,U_3470)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP192(U_3470,U_3471,U_3472) )
& ! [U_3470,U_3471,U_3472] :
( hBOOL(hAPP(hAPP(c_member(U_3470),sK79(U_3472,U_3471,U_3470)),U_3471))
| ~ sP192(U_3470,U_3471,U_3472) )
& ! [U_3468,U_3470,U_3471,U_3472] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3470,tc_Nat_Onat),U_3472),U_3471) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| sP192(U_3470,U_3471,U_3472)
| ~ sP193(U_3468,U_3470,U_3471,U_3472) )
& ! [U_3468,U_3470,U_3471,U_3472] :
( hAPP(U_3472,U_3468) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_3470),U_3468),U_3471))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3470,tc_Nat_Onat),U_3472),U_3471) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP193(U_3468,U_3470,U_3471,U_3472) )
& ! [U_3468,U_3470,U_3471,U_3472] :
( sP193(U_3468,U_3470,U_3471,U_3472)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3470),U_3471)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192,sP193])],[f_803_3]) ).
cnf(f_803_5,plain,
( sP193(U_3468,U_3470,U_3471,U_3472)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3470),U_3471)) ),
inference(clausify,[status(thm)],[f_803_4]) ).
cnf(f_803_6,plain,
( hAPP(U_3472,U_3468) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_3470),U_3468),U_3471))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3470,tc_Nat_Onat),U_3472),U_3471) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP193(U_3468,U_3470,U_3471,U_3472) ),
inference(clausify,[status(thm)],[f_803_4]) ).
cnf(f_803_7,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3470,tc_Nat_Onat),U_3472),U_3471) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| sP192(U_3470,U_3471,U_3472)
| ~ sP193(U_3468,U_3470,U_3471,U_3472) ),
inference(clausify,[status(thm)],[f_803_4]) ).
cnf(f_803_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_3470),sK79(U_3472,U_3471,U_3470)),U_3471))
| ~ sP192(U_3470,U_3471,U_3472) ),
inference(clausify,[status(thm)],[f_803_4]) ).
cnf(f_803_9,plain,
( hAPP(U_3472,sK79(U_3472,U_3471,U_3470)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP192(U_3470,U_3471,U_3472) ),
inference(clausify,[status(thm)],[f_803_4]) ).
fof(f_804_1,plain,
! [V_A_2,T_d,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(c_COMBK(T_c,T_d),c_Groups_Oone__class_Oone(T_c))),V_A_2) = c_Groups_Oone__class_Oone(T_c)
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__1]) ).
fof(f_804_2,plain,
! [U_3475,U_3474,U_3473] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3474,U_3473),hAPP(c_COMBK(U_3473,U_3474),c_Groups_Oone__class_Oone(U_3473))),U_3475) = c_Groups_Oone__class_Oone(U_3473)
| ~ class_Groups_Ocomm__monoid__mult(U_3473) ),
inference(variable_rename,[status(thm)],[f_804_1]) ).
fof(f_804_3,plain,
! [U_3475,U_3473,U_3474] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3474,U_3473),hAPP(c_COMBK(U_3473,U_3474),c_Groups_Oone__class_Oone(U_3473))),U_3475) = c_Groups_Oone__class_Oone(U_3473)
| ~ class_Groups_Ocomm__monoid__mult(U_3473) ),
inference(definitional_conversion,[status(esa)],[f_804_2]) ).
cnf(f_804_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3474,U_3473),hAPP(c_COMBK(U_3473,U_3474),c_Groups_Oone__class_Oone(U_3473))),U_3475) = c_Groups_Oone__class_Oone(U_3473)
| ~ class_Groups_Ocomm__monoid__mult(U_3473) ),
inference(clausify,[status(thm)],[f_804_3]) ).
fof(f_805_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_805_2,plain,
! [U_3477,U_3476] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3476),U_3477),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3476),U_3477),c_Groups_Oone__class_Oone(U_3476))))
| ~ class_Rings_Olinordered__semidom(U_3476) ),
inference(variable_rename,[status(thm)],[f_805_1]) ).
fof(f_805_3,plain,
! [U_3476,U_3477] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3476),U_3477),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3476),U_3477),c_Groups_Oone__class_Oone(U_3476))))
| ~ class_Rings_Olinordered__semidom(U_3476) ),
inference(definitional_conversion,[status(esa)],[f_805_2]) ).
cnf(f_805_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3476),U_3477),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3476),U_3477),c_Groups_Oone__class_Oone(U_3476))))
| ~ class_Rings_Olinordered__semidom(U_3476) ),
inference(clausify,[status(thm)],[f_805_3]) ).
fof(f_806_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_806_2,plain,
! [U_3480,U_3479,U_3478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3478),c_Groups_Oone__class_Oone(U_3478)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3478),U_3479),U_3480)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3478),c_Groups_Oone__class_Oone(U_3478)),U_3480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3478),c_Groups_Oone__class_Oone(U_3478)),U_3479))
| ~ class_Rings_Olinordered__semidom(U_3478) ),
inference(variable_rename,[status(thm)],[f_806_1]) ).
fof(f_806_3,plain,
! [U_3478,U_3479,U_3480] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3478),c_Groups_Oone__class_Oone(U_3478)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3478),U_3479),U_3480)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3478),c_Groups_Oone__class_Oone(U_3478)),U_3480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3478),c_Groups_Oone__class_Oone(U_3478)),U_3479))
| ~ class_Rings_Olinordered__semidom(U_3478) ),
inference(definitional_conversion,[status(esa)],[f_806_2]) ).
cnf(f_806_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3478),c_Groups_Oone__class_Oone(U_3478)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3478),U_3479),U_3480)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3478),c_Groups_Oone__class_Oone(U_3478)),U_3480))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3478),c_Groups_Oone__class_Oone(U_3478)),U_3479))
| ~ class_Rings_Olinordered__semidom(U_3478) ),
inference(clausify,[status(thm)],[f_806_3]) ).
fof(f_807_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_807_2,plain,
! [U_3483,U_3482,U_3481] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3481),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3481),U_3482),U_3483)),U_3483) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3481),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3481),U_3482),c_Groups_Oone__class_Oone(U_3481))),U_3483)
| ~ class_Rings_Ocomm__semiring__1(U_3481) ),
inference(variable_rename,[status(thm)],[f_807_1]) ).
fof(f_807_3,plain,
! [U_3481,U_3482,U_3483] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3481),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3481),U_3482),U_3483)),U_3483) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3481),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3481),U_3482),c_Groups_Oone__class_Oone(U_3481))),U_3483)
| ~ class_Rings_Ocomm__semiring__1(U_3481) ),
inference(definitional_conversion,[status(esa)],[f_807_2]) ).
cnf(f_807_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3481),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3481),U_3482),U_3483)),U_3483) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3481),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3481),U_3482),c_Groups_Oone__class_Oone(U_3481))),U_3483)
| ~ class_Rings_Ocomm__semiring__1(U_3481) ),
inference(clausify,[status(thm)],[f_807_3]) ).
fof(f_808_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_808_2,plain,
! [U_3486,U_3485,U_3484] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3484),U_3485),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3484),U_3486),U_3485)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3484),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3484),U_3486),c_Groups_Oone__class_Oone(U_3484))),U_3485)
| ~ class_Rings_Ocomm__semiring__1(U_3484) ),
inference(variable_rename,[status(thm)],[f_808_1]) ).
fof(f_808_3,plain,
! [U_3484,U_3485,U_3486] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3484),U_3485),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3484),U_3486),U_3485)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3484),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3484),U_3486),c_Groups_Oone__class_Oone(U_3484))),U_3485)
| ~ class_Rings_Ocomm__semiring__1(U_3484) ),
inference(definitional_conversion,[status(esa)],[f_808_2]) ).
cnf(f_808_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3484),U_3485),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3484),U_3486),U_3485)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3484),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3484),U_3486),c_Groups_Oone__class_Oone(U_3484))),U_3485)
| ~ class_Rings_Ocomm__semiring__1(U_3484) ),
inference(clausify,[status(thm)],[f_808_3]) ).
fof(f_809_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_809_2,plain,
! [U_3488,U_3487] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3487),U_3488),U_3488) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3487),c_Groups_Oone__class_Oone(U_3487)),c_Groups_Oone__class_Oone(U_3487))),U_3488)
| ~ class_Rings_Ocomm__semiring__1(U_3487) ),
inference(variable_rename,[status(thm)],[f_809_1]) ).
fof(f_809_3,plain,
! [U_3487,U_3488] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3487),U_3488),U_3488) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3487),c_Groups_Oone__class_Oone(U_3487)),c_Groups_Oone__class_Oone(U_3487))),U_3488)
| ~ class_Rings_Ocomm__semiring__1(U_3487) ),
inference(definitional_conversion,[status(esa)],[f_809_2]) ).
cnf(f_809_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3487),U_3488),U_3488) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3487),c_Groups_Oone__class_Oone(U_3487)),c_Groups_Oone__class_Oone(U_3487))),U_3488)
| ~ class_Rings_Ocomm__semiring__1(U_3487) ),
inference(clausify,[status(thm)],[f_809_3]) ).
fof(f_810_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_810_2,plain,
! [U_3490,U_3489] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3489),U_3490) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3489),hAPP(c_Groups_Ouminus__class_Ouminus(U_3489),c_Groups_Oone__class_Oone(U_3489))),U_3490)
| ~ class_Rings_Ocomm__ring__1(U_3489) ),
inference(variable_rename,[status(thm)],[f_810_1]) ).
fof(f_810_3,plain,
! [U_3489,U_3490] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3489),U_3490) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3489),hAPP(c_Groups_Ouminus__class_Ouminus(U_3489),c_Groups_Oone__class_Oone(U_3489))),U_3490)
| ~ class_Rings_Ocomm__ring__1(U_3489) ),
inference(definitional_conversion,[status(esa)],[f_810_2]) ).
cnf(f_810_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3489),U_3490) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3489),hAPP(c_Groups_Ouminus__class_Ouminus(U_3489),c_Groups_Oone__class_Oone(U_3489))),U_3490)
| ~ class_Rings_Ocomm__ring__1(U_3489) ),
inference(clausify,[status(thm)],[f_810_3]) ).
fof(f_811_1,plain,
! [V_x_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_c)
| ( V_x_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Groups_Oone__class_Oone(T_c))
& V_x_2 != c_Groups_Oone__class_Oone(T_c) ) )
& ( V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Groups_Oone__class_Oone(T_c))
| V_x_2 = c_Groups_Oone__class_Oone(T_c)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2) != c_Groups_Oone__class_Oone(T_c) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_c) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff]) ).
fof(f_811_2,plain,
! [U_3492,U_3491] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3491),U_3492),U_3492) = c_Groups_Oone__class_Oone(U_3491)
| ( U_3492 != hAPP(c_Groups_Ouminus__class_Ouminus(U_3491),c_Groups_Oone__class_Oone(U_3491))
& U_3492 != c_Groups_Oone__class_Oone(U_3491) ) )
& ( U_3492 = hAPP(c_Groups_Ouminus__class_Ouminus(U_3491),c_Groups_Oone__class_Oone(U_3491))
| U_3492 = c_Groups_Oone__class_Oone(U_3491)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3491),U_3492),U_3492) != c_Groups_Oone__class_Oone(U_3491) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_3491) ),
inference(variable_rename,[status(thm)],[f_811_1]) ).
fof(f_811_3,plain,
( ! [U_3491,U_3492] :
( U_3492 != hAPP(c_Groups_Ouminus__class_Ouminus(U_3491),c_Groups_Oone__class_Oone(U_3491))
| ~ sP194(U_3491,U_3492) )
& ! [U_3491,U_3492] :
( U_3492 != c_Groups_Oone__class_Oone(U_3491)
| ~ sP194(U_3491,U_3492) )
& ! [U_3491,U_3492] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3491),U_3492),U_3492) = c_Groups_Oone__class_Oone(U_3491)
| sP194(U_3491,U_3492)
| ~ sP195(U_3491,U_3492) )
& ! [U_3491,U_3492] :
( U_3492 = hAPP(c_Groups_Ouminus__class_Ouminus(U_3491),c_Groups_Oone__class_Oone(U_3491))
| U_3492 = c_Groups_Oone__class_Oone(U_3491)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3491),U_3492),U_3492) != c_Groups_Oone__class_Oone(U_3491)
| ~ sP195(U_3491,U_3492) )
& ! [U_3491,U_3492] :
( sP195(U_3491,U_3492)
| ~ class_Rings_Oring__1__no__zero__divisors(U_3491) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP194,sP195])],[f_811_2]) ).
cnf(f_811_4,plain,
( sP195(U_3491,U_3492)
| ~ class_Rings_Oring__1__no__zero__divisors(U_3491) ),
inference(clausify,[status(thm)],[f_811_3]) ).
cnf(f_811_5,plain,
( U_3492 = hAPP(c_Groups_Ouminus__class_Ouminus(U_3491),c_Groups_Oone__class_Oone(U_3491))
| U_3492 = c_Groups_Oone__class_Oone(U_3491)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3491),U_3492),U_3492) != c_Groups_Oone__class_Oone(U_3491)
| ~ sP195(U_3491,U_3492) ),
inference(clausify,[status(thm)],[f_811_3]) ).
cnf(f_811_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3491),U_3492),U_3492) = c_Groups_Oone__class_Oone(U_3491)
| sP194(U_3491,U_3492)
| ~ sP195(U_3491,U_3492) ),
inference(clausify,[status(thm)],[f_811_3]) ).
cnf(f_811_7,plain,
( U_3492 != c_Groups_Oone__class_Oone(U_3491)
| ~ sP194(U_3491,U_3492) ),
inference(clausify,[status(thm)],[f_811_3]) ).
cnf(f_811_8,plain,
( U_3492 != hAPP(c_Groups_Ouminus__class_Ouminus(U_3491),c_Groups_Oone__class_Oone(U_3491))
| ~ sP194(U_3491,U_3492) ),
inference(clausify,[status(thm)],[f_811_3]) ).
fof(f_812_1,plain,
! [V_g_2,T_d,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_c)
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oempty]) ).
fof(f_812_2,plain,
! [U_3495,U_3494,U_3493] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3494,U_3493),U_3495),c_Orderings_Obot__class_Obot(tc_fun(U_3494,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_3493)
| ~ class_Groups_Ocomm__monoid__mult(U_3493) ),
inference(variable_rename,[status(thm)],[f_812_1]) ).
fof(f_812_3,plain,
! [U_3495,U_3493,U_3494] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3494,U_3493),U_3495),c_Orderings_Obot__class_Obot(tc_fun(U_3494,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_3493)
| ~ class_Groups_Ocomm__monoid__mult(U_3493) ),
inference(definitional_conversion,[status(esa)],[f_812_2]) ).
cnf(f_812_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3494,U_3493),U_3495),c_Orderings_Obot__class_Obot(tc_fun(U_3494,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_3493)
| ~ class_Groups_Ocomm__monoid__mult(U_3493) ),
inference(clausify,[status(thm)],[f_812_3]) ).
fof(f_813_1,plain,
! [V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_c)
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__empty]) ).
fof(f_813_2,plain,
! [U_3498,U_3497,U_3496] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3497,U_3496),U_3498),c_Orderings_Obot__class_Obot(tc_fun(U_3497,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_3496)
| ~ class_Groups_Ocomm__monoid__mult(U_3496) ),
inference(variable_rename,[status(thm)],[f_813_1]) ).
fof(f_813_3,plain,
! [U_3496,U_3497,U_3498] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3497,U_3496),U_3498),c_Orderings_Obot__class_Obot(tc_fun(U_3497,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_3496)
| ~ class_Groups_Ocomm__monoid__mult(U_3496) ),
inference(definitional_conversion,[status(esa)],[f_813_2]) ).
cnf(f_813_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3497,U_3496),U_3498),c_Orderings_Obot__class_Obot(tc_fun(U_3497,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_3496)
| ~ class_Groups_Ocomm__monoid__mult(U_3496) ),
inference(clausify,[status(thm)],[f_813_3]) ).
fof(f_814_1,plain,
! [V_f_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_d)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__infinite]) ).
fof(f_814_2,plain,
! [U_3502,U_3501,U_3500,U_3499] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3500,U_3499),U_3502),U_3501) = c_Groups_Oone__class_Oone(U_3499)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3500),U_3501))
| ~ class_Groups_Ocomm__monoid__mult(U_3499) ),
inference(variable_rename,[status(thm)],[f_814_1]) ).
fof(f_814_3,plain,
! [U_3499,U_3500,U_3501,U_3502] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3500,U_3499),U_3502),U_3501) = c_Groups_Oone__class_Oone(U_3499)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3500),U_3501))
| ~ class_Groups_Ocomm__monoid__mult(U_3499) ),
inference(definitional_conversion,[status(esa)],[f_814_2]) ).
cnf(f_814_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3500,U_3499),U_3502),U_3501) = c_Groups_Oone__class_Oone(U_3499)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3500),U_3501))
| ~ class_Groups_Ocomm__monoid__mult(U_3499) ),
inference(clausify,[status(thm)],[f_814_3]) ).
fof(f_815_1,plain,
! [V_g_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_d)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oinfinite]) ).
fof(f_815_2,plain,
! [U_3506,U_3505,U_3504,U_3503] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3504,U_3503),U_3506),U_3505) = c_Groups_Oone__class_Oone(U_3503)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3504),U_3505))
| ~ class_Groups_Ocomm__monoid__mult(U_3503) ),
inference(variable_rename,[status(thm)],[f_815_1]) ).
fof(f_815_3,plain,
! [U_3503,U_3504,U_3505,U_3506] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3504,U_3503),U_3506),U_3505) = c_Groups_Oone__class_Oone(U_3503)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3504),U_3505))
| ~ class_Groups_Ocomm__monoid__mult(U_3503) ),
inference(definitional_conversion,[status(esa)],[f_815_2]) ).
cnf(f_815_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3504,U_3503),U_3506),U_3505) = c_Groups_Oone__class_Oone(U_3503)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3504),U_3505))
| ~ class_Groups_Ocomm__monoid__mult(U_3503) ),
inference(clausify,[status(thm)],[f_815_3]) ).
fof(f_816_1,plain,
! [V_A_2,T_c] : hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_c),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2),
inference(fof_nnf,[status(thm)],[fact_card__eq__setsum]) ).
fof(f_816_2,plain,
! [U_3508,U_3507] : hAPP(c_Finite__Set_Ocard(U_3507),U_3508) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3507,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_3507),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3508),
inference(variable_rename,[status(thm)],[f_816_1]) ).
fof(f_816_3,plain,
! [U_3507,U_3508] : hAPP(c_Finite__Set_Ocard(U_3507),U_3508) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3507,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_3507),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3508),
inference(definitional_conversion,[status(esa)],[f_816_2]) ).
cnf(f_816_4,plain,
hAPP(c_Finite__Set_Ocard(U_3507),U_3508) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3507,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_3507),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3508),
inference(clausify,[status(thm)],[f_816_3]) ).
fof(f_817_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_817_2,plain,
! [U_3510,U_3509] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3509),U_3510))
| U_3509 = U_3510
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3509),U_3510)) )
& ( ( U_3509 != U_3510
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3509),U_3510)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3509),U_3510)) ) ),
inference(variable_rename,[status(thm)],[f_817_1]) ).
fof(f_817_3,plain,
( ! [U_3514,U_3512] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3512),U_3514))
| U_3512 = U_3514
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3512),U_3514)) )
& ! [U_3513,U_3511] :
( ( U_3511 != U_3513
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3511),U_3513)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3511),U_3513)) ) ),
inference(miniscope,[status(thm)],[f_817_2]) ).
fof(f_817_4,plain,
( ! [U_3511,U_3513] :
( U_3511 != U_3513
| ~ sP196(U_3511,U_3513) )
& ! [U_3511,U_3513] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3511),U_3513))
| ~ sP196(U_3511,U_3513) )
& ! [U_3514,U_3512] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3512),U_3514))
| U_3512 = U_3514
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3512),U_3514)) )
& ! [U_3511,U_3513] :
( sP196(U_3511,U_3513)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3511),U_3513)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP196])],[f_817_3]) ).
cnf(f_817_5,plain,
( sP196(U_3511,U_3513)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3511),U_3513)) ),
inference(clausify,[status(thm)],[f_817_4]) ).
cnf(f_817_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3512),U_3514))
| U_3512 = U_3514
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3512),U_3514)) ),
inference(clausify,[status(thm)],[f_817_4]) ).
cnf(f_817_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3511),U_3513))
| ~ sP196(U_3511,U_3513) ),
inference(clausify,[status(thm)],[f_817_4]) ).
cnf(f_817_8,plain,
( U_3511 != U_3513
| ~ sP196(U_3511,U_3513) ),
inference(clausify,[status(thm)],[f_817_4]) ).
fof(f_818_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_818_2,plain,
! [U_3516,U_3515] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3515),U_3516))
| ( U_3515 != U_3516
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3515),U_3516)) ) )
& ( U_3515 = U_3516
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3515),U_3516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3515),U_3516)) ) ),
inference(variable_rename,[status(thm)],[f_818_1]) ).
fof(f_818_3,plain,
( ! [U_3520,U_3518] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3518),U_3520))
| ( U_3518 != U_3520
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3518),U_3520)) ) )
& ! [U_3519,U_3517] :
( U_3517 = U_3519
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3517),U_3519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3517),U_3519)) ) ),
inference(miniscope,[status(thm)],[f_818_2]) ).
fof(f_818_4,plain,
( ! [U_3518,U_3520] :
( U_3518 != U_3520
| ~ sP197(U_3518,U_3520) )
& ! [U_3518,U_3520] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3518),U_3520))
| ~ sP197(U_3518,U_3520) )
& ! [U_3518,U_3520] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3518),U_3520))
| sP197(U_3518,U_3520) )
& ! [U_3517,U_3519] :
( U_3517 = U_3519
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3517),U_3519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3517),U_3519)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP197])],[f_818_3]) ).
cnf(f_818_5,plain,
( U_3517 = U_3519
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3517),U_3519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3517),U_3519)) ),
inference(clausify,[status(thm)],[f_818_4]) ).
cnf(f_818_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3518),U_3520))
| sP197(U_3518,U_3520) ),
inference(clausify,[status(thm)],[f_818_4]) ).
cnf(f_818_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3518),U_3520))
| ~ sP197(U_3518,U_3520) ),
inference(clausify,[status(thm)],[f_818_4]) ).
cnf(f_818_8,plain,
( U_3518 != U_3520
| ~ sP197(U_3518,U_3520) ),
inference(clausify,[status(thm)],[f_818_4]) ).
fof(f_819_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_819_2,plain,
! [U_3522,U_3521] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3521),U_3522))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3521),U_3522)) ),
inference(variable_rename,[status(thm)],[f_819_1]) ).
fof(f_819_3,plain,
! [U_3521,U_3522] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3521),U_3522))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3521),U_3522)) ),
inference(definitional_conversion,[status(esa)],[f_819_2]) ).
cnf(f_819_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3521),U_3522))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3521),U_3522)) ),
inference(clausify,[status(thm)],[f_819_3]) ).
fof(f_820_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_820_2,plain,
! [U_3524,U_3523] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3523),U_3524))
| U_3523 = U_3524
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3523),U_3524)) ),
inference(variable_rename,[status(thm)],[f_820_1]) ).
fof(f_820_3,plain,
! [U_3523,U_3524] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3523),U_3524))
| U_3523 = U_3524
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3523),U_3524)) ),
inference(definitional_conversion,[status(esa)],[f_820_2]) ).
cnf(f_820_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3523),U_3524))
| U_3523 = U_3524
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3523),U_3524)) ),
inference(clausify,[status(thm)],[f_820_3]) ).
fof(f_821_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_821_2,plain,
! [U_3526,U_3525] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3525),U_3526))
| ( U_3525 != U_3526
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3525),U_3526)) ) ),
inference(variable_rename,[status(thm)],[f_821_1]) ).
fof(f_821_3,plain,
( ! [U_3525,U_3526] :
( U_3525 != U_3526
| ~ sP198(U_3525,U_3526) )
& ! [U_3525,U_3526] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3525),U_3526))
| ~ sP198(U_3525,U_3526) )
& ! [U_3525,U_3526] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3525),U_3526))
| sP198(U_3525,U_3526) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP198])],[f_821_2]) ).
cnf(f_821_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3525),U_3526))
| sP198(U_3525,U_3526) ),
inference(clausify,[status(thm)],[f_821_3]) ).
cnf(f_821_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3525),U_3526))
| ~ sP198(U_3525,U_3526) ),
inference(clausify,[status(thm)],[f_821_3]) ).
cnf(f_821_6,plain,
( U_3525 != U_3526
| ~ sP198(U_3525,U_3526) ),
inference(clausify,[status(thm)],[f_821_3]) ).
fof(f_822_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_822_2,plain,
! [U_3529,U_3528,U_3527] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3527),U_3529))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3527),U_3528)),U_3529)) ),
inference(variable_rename,[status(thm)],[f_822_1]) ).
fof(f_822_3,plain,
! [U_3527,U_3528,U_3529] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3527),U_3529))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3527),U_3528)),U_3529)) ),
inference(definitional_conversion,[status(esa)],[f_822_2]) ).
cnf(f_822_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3527),U_3529))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3527),U_3528)),U_3529)) ),
inference(clausify,[status(thm)],[f_822_3]) ).
fof(f_823_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_823_2,plain,
! [U_3533,U_3532,U_3531,U_3530] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3532),U_3533))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3532),U_3531) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3530),U_3533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3530),U_3531)) ),
inference(variable_rename,[status(thm)],[f_823_1]) ).
fof(f_823_3,plain,
! [U_3530,U_3531,U_3532,U_3533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3532),U_3533))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3532),U_3531) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3530),U_3533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3530),U_3531)) ),
inference(definitional_conversion,[status(esa)],[f_823_2]) ).
cnf(f_823_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3532),U_3533))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3532),U_3531) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3530),U_3533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3530),U_3531)) ),
inference(clausify,[status(thm)],[f_823_3]) ).
fof(f_824_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_824_2,plain,
! [U_3537,U_3536,U_3535,U_3534] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3534),U_3536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3535),U_3537)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3536),U_3537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3534),U_3535)) ),
inference(variable_rename,[status(thm)],[f_824_1]) ).
fof(f_824_3,plain,
! [U_3534,U_3535,U_3536,U_3537] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3534),U_3536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3535),U_3537)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3536),U_3537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3534),U_3535)) ),
inference(definitional_conversion,[status(esa)],[f_824_2]) ).
cnf(f_824_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3534),U_3536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3535),U_3537)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3536),U_3537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3534),U_3535)) ),
inference(clausify,[status(thm)],[f_824_3]) ).
fof(f_825_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_825_2,plain,
! [U_3540,U_3539,U_3538] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3538),U_3540)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3539),U_3540)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3538),U_3539)) ),
inference(variable_rename,[status(thm)],[f_825_1]) ).
fof(f_825_3,plain,
! [U_3538,U_3539,U_3540] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3538),U_3540)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3539),U_3540)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3538),U_3539)) ),
inference(definitional_conversion,[status(esa)],[f_825_2]) ).
cnf(f_825_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3538),U_3540)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3539),U_3540)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3538),U_3539)) ),
inference(clausify,[status(thm)],[f_825_3]) ).
fof(f_826_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_826_2,plain,
! [U_3543,U_3542,U_3541] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3541),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3543),U_3542)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3541),U_3542)) ),
inference(variable_rename,[status(thm)],[f_826_1]) ).
fof(f_826_3,plain,
! [U_3541,U_3542,U_3543] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3541),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3543),U_3542)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3541),U_3542)) ),
inference(definitional_conversion,[status(esa)],[f_826_2]) ).
cnf(f_826_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3541),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3543),U_3542)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3541),U_3542)) ),
inference(clausify,[status(thm)],[f_826_3]) ).
fof(f_827_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_827_2,plain,
! [U_3546,U_3545,U_3544] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3544),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3545),U_3546)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3544),U_3545)) ),
inference(variable_rename,[status(thm)],[f_827_1]) ).
fof(f_827_3,plain,
! [U_3544,U_3545,U_3546] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3544),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3545),U_3546)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3544),U_3545)) ),
inference(definitional_conversion,[status(esa)],[f_827_2]) ).
cnf(f_827_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3544),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3545),U_3546)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3544),U_3545)) ),
inference(clausify,[status(thm)],[f_827_3]) ).
fof(f_828_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_828_2,plain,
! [U_3549,U_3548,U_3547] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3547),U_3548)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3547),U_3549)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3548),U_3549)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3548),U_3549))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3547),U_3548)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3547),U_3549))) ) ),
inference(variable_rename,[status(thm)],[f_828_1]) ).
fof(f_828_3,plain,
( ! [U_3555,U_3553] :
( ! [U_3551] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3551),U_3553)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3551),U_3555)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3553),U_3555)) )
& ! [U_3554,U_3552] :
( ! [U_3550] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3550),U_3552)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3550),U_3554)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3552),U_3554)) ) ),
inference(miniscope,[status(thm)],[f_828_2]) ).
fof(f_828_4,plain,
( ! [U_3555,U_3551,U_3553] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3551),U_3553)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3551),U_3555)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3553),U_3555)) )
& ! [U_3552,U_3554,U_3550] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3550),U_3552)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3550),U_3554)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3552),U_3554)) ) ),
inference(definitional_conversion,[status(esa)],[f_828_3]) ).
cnf(f_828_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3550),U_3552)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3550),U_3554)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3552),U_3554)) ),
inference(clausify,[status(thm)],[f_828_4]) ).
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),U_3551),U_3553)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3551),U_3555)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3553),U_3555)) ),
inference(clausify,[status(thm)],[f_828_4]) ).
fof(f_829_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_829_2,plain,
! [U_3557,U_3556] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3556),U_3557)),U_3557)),
inference(variable_rename,[status(thm)],[f_829_1]) ).
fof(f_829_3,plain,
! [U_3557,U_3556] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3556),U_3557)),U_3557)),
inference(definitional_conversion,[status(esa)],[f_829_2]) ).
cnf(f_829_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3556),U_3557)),U_3557)),
inference(clausify,[status(thm)],[f_829_3]) ).
fof(f_830_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_830_2,plain,
! [U_3559,U_3558] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3558),U_3559)),U_3558)),
inference(variable_rename,[status(thm)],[f_830_1]) ).
fof(f_830_3,plain,
! [U_3558,U_3559] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3558),U_3559)),U_3558)),
inference(definitional_conversion,[status(esa)],[f_830_2]) ).
cnf(f_830_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3558),U_3559)),U_3558)),
inference(clausify,[status(thm)],[f_830_3]) ).
fof(f_831_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_831_2,plain,
! [U_3560] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3560),U_3560)),
inference(variable_rename,[status(thm)],[f_831_1]) ).
fof(f_831_3,plain,
! [U_3560] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3560),U_3560)),
inference(definitional_conversion,[status(esa)],[f_831_2]) ).
cnf(f_831_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3560),U_3560)),
inference(clausify,[status(thm)],[f_831_3]) ).
fof(f_832_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_832_2,plain,
! [U_3562,U_3561] :
( ( U_3561 != U_3562
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3562),U_3561))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3561),U_3562)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3562),U_3561))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3561),U_3562))
| U_3561 = U_3562 ) ),
inference(variable_rename,[status(thm)],[f_832_1]) ).
fof(f_832_3,plain,
( ! [U_3566,U_3564] :
( U_3564 != U_3566
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3566),U_3564))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3564),U_3566)) ) )
& ! [U_3565,U_3563] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3565),U_3563))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3563),U_3565))
| U_3563 = U_3565 ) ),
inference(miniscope,[status(thm)],[f_832_2]) ).
fof(f_832_4,plain,
( ! [U_3566,U_3564] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3566),U_3564))
| ~ sP199(U_3566,U_3564) )
& ! [U_3566,U_3564] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3564),U_3566))
| ~ sP199(U_3566,U_3564) )
& ! [U_3566,U_3564] :
( U_3564 != U_3566
| sP199(U_3566,U_3564) )
& ! [U_3565,U_3563] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3565),U_3563))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3563),U_3565))
| U_3563 = U_3565 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199])],[f_832_3]) ).
cnf(f_832_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3565),U_3563))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3563),U_3565))
| U_3563 = U_3565 ),
inference(clausify,[status(thm)],[f_832_4]) ).
cnf(f_832_6,plain,
( U_3564 != U_3566
| sP199(U_3566,U_3564) ),
inference(clausify,[status(thm)],[f_832_4]) ).
cnf(f_832_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3564),U_3566))
| ~ sP199(U_3566,U_3564) ),
inference(clausify,[status(thm)],[f_832_4]) ).
cnf(f_832_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3566),U_3564))
| ~ sP199(U_3566,U_3564) ),
inference(clausify,[status(thm)],[f_832_4]) ).
fof(f_833_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_833_2,plain,
! [U_3568,U_3567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3568),U_3567))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3567),U_3568))
| U_3567 = U_3568 ),
inference(variable_rename,[status(thm)],[f_833_1]) ).
fof(f_833_3,plain,
! [U_3568,U_3567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3568),U_3567))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3567),U_3568))
| U_3567 = U_3568 ),
inference(definitional_conversion,[status(esa)],[f_833_2]) ).
cnf(f_833_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3568),U_3567))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3567),U_3568))
| U_3567 = U_3568 ),
inference(clausify,[status(thm)],[f_833_3]) ).
fof(f_834_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_834_2,plain,
! [U_3569] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3569),U_3569)),
inference(variable_rename,[status(thm)],[f_834_1]) ).
fof(f_834_3,plain,
! [U_3569] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3569),U_3569)),
inference(definitional_conversion,[status(esa)],[f_834_2]) ).
cnf(f_834_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3569),U_3569)),
inference(clausify,[status(thm)],[f_834_3]) ).
fof(f_835_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_835_2,plain,
! [U_3571,U_3570] :
( U_3571 != U_3570
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3570),U_3571)) ),
inference(variable_rename,[status(thm)],[f_835_1]) ).
fof(f_835_3,plain,
! [U_3570,U_3571] :
( U_3571 != U_3570
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3570),U_3571)) ),
inference(definitional_conversion,[status(esa)],[f_835_2]) ).
cnf(f_835_4,plain,
( U_3571 != U_3570
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3570),U_3571)) ),
inference(clausify,[status(thm)],[f_835_3]) ).
fof(f_836_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_836_2,plain,
! [U_3573,U_3572] :
( U_3572 != U_3573
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3572),U_3573)) ),
inference(variable_rename,[status(thm)],[f_836_1]) ).
fof(f_836_3,plain,
! [U_3572,U_3573] :
( U_3572 != U_3573
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3572),U_3573)) ),
inference(definitional_conversion,[status(esa)],[f_836_2]) ).
cnf(f_836_4,plain,
( U_3572 != U_3573
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3572),U_3573)) ),
inference(clausify,[status(thm)],[f_836_3]) ).
fof(f_837_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_837_2,plain,
! [U_3576,U_3575,U_3574] :
( hBOOL(hAPP(hAPP(U_3576,U_3575),U_3574))
| ( ~ hBOOL(hAPP(hAPP(U_3576,U_3575),U_3574))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3575),U_3574)) )
| ( ~ hBOOL(hAPP(hAPP(U_3576,U_3575),U_3574))
& U_3574 = U_3575 )
| ( ~ hBOOL(hAPP(hAPP(U_3576,U_3575),U_3574))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3574),U_3575)) ) ),
inference(variable_rename,[status(thm)],[f_837_1]) ).
fof(f_837_3,plain,
( ! [U_3574,U_3575,U_3576] :
( ~ hBOOL(hAPP(hAPP(U_3576,U_3575),U_3574))
| ~ sP202(U_3574,U_3575,U_3576) )
& ! [U_3574,U_3575,U_3576] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3575),U_3574))
| ~ sP202(U_3574,U_3575,U_3576) )
& ! [U_3574,U_3575,U_3576] :
( ~ hBOOL(hAPP(hAPP(U_3576,U_3575),U_3574))
| ~ sP201(U_3574,U_3575,U_3576) )
& ! [U_3574,U_3575,U_3576] :
( U_3574 = U_3575
| ~ sP201(U_3574,U_3575,U_3576) )
& ! [U_3574,U_3575,U_3576] :
( ~ hBOOL(hAPP(hAPP(U_3576,U_3575),U_3574))
| ~ sP200(U_3574,U_3575,U_3576) )
& ! [U_3574,U_3575,U_3576] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3574),U_3575))
| ~ sP200(U_3574,U_3575,U_3576) )
& ! [U_3574,U_3575,U_3576] :
( hBOOL(hAPP(hAPP(U_3576,U_3575),U_3574))
| sP202(U_3574,U_3575,U_3576)
| sP201(U_3574,U_3575,U_3576)
| sP200(U_3574,U_3575,U_3576) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP200,sP201,sP202])],[f_837_2]) ).
cnf(f_837_4,plain,
( hBOOL(hAPP(hAPP(U_3576,U_3575),U_3574))
| sP202(U_3574,U_3575,U_3576)
| sP201(U_3574,U_3575,U_3576)
| sP200(U_3574,U_3575,U_3576) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3574),U_3575))
| ~ sP200(U_3574,U_3575,U_3576) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_6,plain,
( ~ hBOOL(hAPP(hAPP(U_3576,U_3575),U_3574))
| ~ sP200(U_3574,U_3575,U_3576) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_7,plain,
( U_3574 = U_3575
| ~ sP201(U_3574,U_3575,U_3576) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_8,plain,
( ~ hBOOL(hAPP(hAPP(U_3576,U_3575),U_3574))
| ~ sP201(U_3574,U_3575,U_3576) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3575),U_3574))
| ~ sP202(U_3574,U_3575,U_3576) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_10,plain,
( ~ hBOOL(hAPP(hAPP(U_3576,U_3575),U_3574))
| ~ sP202(U_3574,U_3575,U_3576) ),
inference(clausify,[status(thm)],[f_837_3]) ).
fof(f_838_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_838_2,plain,
! [U_3581] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3581))
| ! [U_3580] :
? [U_3579] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3579),U_3580))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3579),U_3581)) ) )
& ( ? [U_3578] :
! [U_3577] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3577),U_3578))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3577),U_3581)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3581)) ) ),
inference(variable_rename,[status(thm)],[f_838_1]) ).
fof(f_838_3,plain,
( ! [U_3583] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3583))
| ! [U_3580] :
? [U_3579] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3579),U_3580))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3579),U_3583)) ) )
& ! [U_3582] :
( ? [U_3578] :
! [U_3577] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3577),U_3578))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3577),U_3582)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3582)) ) ),
inference(miniscope,[status(thm)],[f_838_2]) ).
fof(f_838_4,plain,
( ! [U_3583] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3583))
| ! [U_3580] :
? [U_3579] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3579),U_3580))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3579),U_3583)) ) )
& ! [U_3582] :
( ! [U_3577] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3577),sK80(U_3582)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3577),U_3582)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3582)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_3578,sK80(U_3582))],[f_838_3]) ).
fof(f_838_5,plain,
( ! [U_3583] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3583))
| ! [U_3580] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK81(U_3583,U_3580)),U_3580))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK81(U_3583,U_3580)),U_3583)) ) )
& ! [U_3582] :
( ! [U_3577] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3577),sK80(U_3582)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3577),U_3582)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3582)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_3579,sK81(U_3583,U_3580))],[f_838_4]) ).
fof(f_838_6,plain,
( ! [U_3580,U_3583] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK81(U_3583,U_3580)),U_3580))
| ~ sP203(U_3580,U_3583) )
& ! [U_3580,U_3583] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK81(U_3583,U_3580)),U_3583))
| ~ sP203(U_3580,U_3583) )
& ! [U_3580,U_3583] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3583))
| sP203(U_3580,U_3583) )
& ! [U_3582,U_3577] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3577),sK80(U_3582)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3577),U_3582))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3582)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP203])],[f_838_5]) ).
cnf(f_838_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3577),sK80(U_3582)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3577),U_3582))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3582)) ),
inference(clausify,[status(thm)],[f_838_6]) ).
cnf(f_838_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3583))
| sP203(U_3580,U_3583) ),
inference(clausify,[status(thm)],[f_838_6]) ).
cnf(f_838_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK81(U_3583,U_3580)),U_3583))
| ~ sP203(U_3580,U_3583) ),
inference(clausify,[status(thm)],[f_838_6]) ).
cnf(f_838_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK81(U_3583,U_3580)),U_3580))
| ~ sP203(U_3580,U_3583) ),
inference(clausify,[status(thm)],[f_838_6]) ).
fof(f_839_1,plain,
! [V_b_2,V_a_2,V_S_2,T_c,T_d] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_d))),V_S_2) = c_Groups_Oone__class_Oone(T_d)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_d))),V_S_2) = hAPP(V_b_2,V_a_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__delta]) ).
fof(f_839_2,plain,
! [U_3588,U_3587,U_3586,U_3585,U_3584] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3585,U_3584),hAPP(hAPP(c_COMBC(U_3585,U_3584,U_3584),hAPP(hAPP(c_COMBS(U_3585,U_3584,tc_fun(U_3584,U_3584)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3584,tc_fun(U_3584,U_3584)),U_3585),c_If(U_3584)),hAPP(hAPP(c_COMBC(U_3585,U_3585,tc_HOL_Obool),c_fequal),U_3587))),U_3588)),c_Groups_Oone__class_Oone(U_3584))),U_3586) = c_Groups_Oone__class_Oone(U_3584)
| hBOOL(hAPP(hAPP(c_member(U_3585),U_3587),U_3586)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3585,U_3584),hAPP(hAPP(c_COMBC(U_3585,U_3584,U_3584),hAPP(hAPP(c_COMBS(U_3585,U_3584,tc_fun(U_3584,U_3584)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3584,tc_fun(U_3584,U_3584)),U_3585),c_If(U_3584)),hAPP(hAPP(c_COMBC(U_3585,U_3585,tc_HOL_Obool),c_fequal),U_3587))),U_3588)),c_Groups_Oone__class_Oone(U_3584))),U_3586) = hAPP(U_3588,U_3587)
| ~ hBOOL(hAPP(hAPP(c_member(U_3585),U_3587),U_3586)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3585),U_3586))
| ~ class_Groups_Ocomm__monoid__mult(U_3584) ),
inference(variable_rename,[status(thm)],[f_839_1]) ).
fof(f_839_3,plain,
( ! [U_3584,U_3585,U_3586,U_3587,U_3588] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3585,U_3584),hAPP(hAPP(c_COMBC(U_3585,U_3584,U_3584),hAPP(hAPP(c_COMBS(U_3585,U_3584,tc_fun(U_3584,U_3584)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3584,tc_fun(U_3584,U_3584)),U_3585),c_If(U_3584)),hAPP(hAPP(c_COMBC(U_3585,U_3585,tc_HOL_Obool),c_fequal),U_3587))),U_3588)),c_Groups_Oone__class_Oone(U_3584))),U_3586) = c_Groups_Oone__class_Oone(U_3584)
| hBOOL(hAPP(hAPP(c_member(U_3585),U_3587),U_3586))
| ~ sP204(U_3584,U_3585,U_3586,U_3587,U_3588) )
& ! [U_3584,U_3585,U_3586,U_3587,U_3588] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3585,U_3584),hAPP(hAPP(c_COMBC(U_3585,U_3584,U_3584),hAPP(hAPP(c_COMBS(U_3585,U_3584,tc_fun(U_3584,U_3584)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3584,tc_fun(U_3584,U_3584)),U_3585),c_If(U_3584)),hAPP(hAPP(c_COMBC(U_3585,U_3585,tc_HOL_Obool),c_fequal),U_3587))),U_3588)),c_Groups_Oone__class_Oone(U_3584))),U_3586) = hAPP(U_3588,U_3587)
| ~ hBOOL(hAPP(hAPP(c_member(U_3585),U_3587),U_3586))
| ~ sP204(U_3584,U_3585,U_3586,U_3587,U_3588) )
& ! [U_3584,U_3585,U_3586,U_3587,U_3588] :
( sP204(U_3584,U_3585,U_3586,U_3587,U_3588)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3585),U_3586))
| ~ class_Groups_Ocomm__monoid__mult(U_3584) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_839_2]) ).
cnf(f_839_4,plain,
( sP204(U_3584,U_3585,U_3586,U_3587,U_3588)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3585),U_3586))
| ~ class_Groups_Ocomm__monoid__mult(U_3584) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3585,U_3584),hAPP(hAPP(c_COMBC(U_3585,U_3584,U_3584),hAPP(hAPP(c_COMBS(U_3585,U_3584,tc_fun(U_3584,U_3584)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3584,tc_fun(U_3584,U_3584)),U_3585),c_If(U_3584)),hAPP(hAPP(c_COMBC(U_3585,U_3585,tc_HOL_Obool),c_fequal),U_3587))),U_3588)),c_Groups_Oone__class_Oone(U_3584))),U_3586) = hAPP(U_3588,U_3587)
| ~ hBOOL(hAPP(hAPP(c_member(U_3585),U_3587),U_3586))
| ~ sP204(U_3584,U_3585,U_3586,U_3587,U_3588) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3585,U_3584),hAPP(hAPP(c_COMBC(U_3585,U_3584,U_3584),hAPP(hAPP(c_COMBS(U_3585,U_3584,tc_fun(U_3584,U_3584)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3584,tc_fun(U_3584,U_3584)),U_3585),c_If(U_3584)),hAPP(hAPP(c_COMBC(U_3585,U_3585,tc_HOL_Obool),c_fequal),U_3587))),U_3588)),c_Groups_Oone__class_Oone(U_3584))),U_3586) = c_Groups_Oone__class_Oone(U_3584)
| hBOOL(hAPP(hAPP(c_member(U_3585),U_3587),U_3586))
| ~ sP204(U_3584,U_3585,U_3586,U_3587,U_3588) ),
inference(clausify,[status(thm)],[f_839_3]) ).
fof(f_840_1,plain,
! [V_b_2,V_a_2,V_S_2,T_c,T_d] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_d))),V_S_2) = c_Groups_Oone__class_Oone(T_d)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_d))),V_S_2) = hAPP(V_b_2,V_a_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__delta_H]) ).
fof(f_840_2,plain,
! [U_3593,U_3592,U_3591,U_3590,U_3589] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3590,U_3589),hAPP(hAPP(c_COMBC(U_3590,U_3589,U_3589),hAPP(hAPP(c_COMBS(U_3590,U_3589,tc_fun(U_3589,U_3589)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3589,tc_fun(U_3589,U_3589)),U_3590),c_If(U_3589)),hAPP(c_fequal,U_3592))),U_3593)),c_Groups_Oone__class_Oone(U_3589))),U_3591) = c_Groups_Oone__class_Oone(U_3589)
| hBOOL(hAPP(hAPP(c_member(U_3590),U_3592),U_3591)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3590,U_3589),hAPP(hAPP(c_COMBC(U_3590,U_3589,U_3589),hAPP(hAPP(c_COMBS(U_3590,U_3589,tc_fun(U_3589,U_3589)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3589,tc_fun(U_3589,U_3589)),U_3590),c_If(U_3589)),hAPP(c_fequal,U_3592))),U_3593)),c_Groups_Oone__class_Oone(U_3589))),U_3591) = hAPP(U_3593,U_3592)
| ~ hBOOL(hAPP(hAPP(c_member(U_3590),U_3592),U_3591)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3590),U_3591))
| ~ class_Groups_Ocomm__monoid__mult(U_3589) ),
inference(variable_rename,[status(thm)],[f_840_1]) ).
fof(f_840_3,plain,
( ! [U_3590,U_3591,U_3589,U_3592,U_3593] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3590,U_3589),hAPP(hAPP(c_COMBC(U_3590,U_3589,U_3589),hAPP(hAPP(c_COMBS(U_3590,U_3589,tc_fun(U_3589,U_3589)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3589,tc_fun(U_3589,U_3589)),U_3590),c_If(U_3589)),hAPP(c_fequal,U_3592))),U_3593)),c_Groups_Oone__class_Oone(U_3589))),U_3591) = c_Groups_Oone__class_Oone(U_3589)
| hBOOL(hAPP(hAPP(c_member(U_3590),U_3592),U_3591))
| ~ sP205(U_3590,U_3591,U_3589,U_3592,U_3593) )
& ! [U_3590,U_3591,U_3589,U_3592,U_3593] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3590,U_3589),hAPP(hAPP(c_COMBC(U_3590,U_3589,U_3589),hAPP(hAPP(c_COMBS(U_3590,U_3589,tc_fun(U_3589,U_3589)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3589,tc_fun(U_3589,U_3589)),U_3590),c_If(U_3589)),hAPP(c_fequal,U_3592))),U_3593)),c_Groups_Oone__class_Oone(U_3589))),U_3591) = hAPP(U_3593,U_3592)
| ~ hBOOL(hAPP(hAPP(c_member(U_3590),U_3592),U_3591))
| ~ sP205(U_3590,U_3591,U_3589,U_3592,U_3593) )
& ! [U_3590,U_3591,U_3589,U_3592,U_3593] :
( sP205(U_3590,U_3591,U_3589,U_3592,U_3593)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3590),U_3591))
| ~ class_Groups_Ocomm__monoid__mult(U_3589) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_840_2]) ).
cnf(f_840_4,plain,
( sP205(U_3590,U_3591,U_3589,U_3592,U_3593)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3590),U_3591))
| ~ class_Groups_Ocomm__monoid__mult(U_3589) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3590,U_3589),hAPP(hAPP(c_COMBC(U_3590,U_3589,U_3589),hAPP(hAPP(c_COMBS(U_3590,U_3589,tc_fun(U_3589,U_3589)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3589,tc_fun(U_3589,U_3589)),U_3590),c_If(U_3589)),hAPP(c_fequal,U_3592))),U_3593)),c_Groups_Oone__class_Oone(U_3589))),U_3591) = hAPP(U_3593,U_3592)
| ~ hBOOL(hAPP(hAPP(c_member(U_3590),U_3592),U_3591))
| ~ sP205(U_3590,U_3591,U_3589,U_3592,U_3593) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3590,U_3589),hAPP(hAPP(c_COMBC(U_3590,U_3589,U_3589),hAPP(hAPP(c_COMBS(U_3590,U_3589,tc_fun(U_3589,U_3589)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3589,tc_fun(U_3589,U_3589)),U_3590),c_If(U_3589)),hAPP(c_fequal,U_3592))),U_3593)),c_Groups_Oone__class_Oone(U_3589))),U_3591) = c_Groups_Oone__class_Oone(U_3589)
| hBOOL(hAPP(hAPP(c_member(U_3590),U_3592),U_3591))
| ~ sP205(U_3590,U_3591,U_3589,U_3592,U_3593) ),
inference(clausify,[status(thm)],[f_840_3]) ).
fof(f_841_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_841_2,plain,
! [U_3595,U_3594] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3594),U_3595)),U_3595) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_3594),U_3595),
inference(variable_rename,[status(thm)],[f_841_1]) ).
fof(f_841_3,plain,
! [U_3595,U_3594] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3594),U_3595)),U_3595) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_3594),U_3595),
inference(definitional_conversion,[status(esa)],[f_841_2]) ).
cnf(f_841_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3594),U_3595)),U_3595) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_3594),U_3595),
inference(clausify,[status(thm)],[f_841_3]) ).
fof(f_842_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_842_2,plain,
! [U_3598,U_3597,U_3596] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3596),U_3597)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3598),U_3597)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_3596),U_3598)),U_3597),
inference(variable_rename,[status(thm)],[f_842_1]) ).
fof(f_842_3,plain,
! [U_3596,U_3598,U_3597] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3596),U_3597)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3598),U_3597)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_3596),U_3598)),U_3597),
inference(definitional_conversion,[status(esa)],[f_842_2]) ).
cnf(f_842_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3596),U_3597)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3598),U_3597)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_3596),U_3598)),U_3597),
inference(clausify,[status(thm)],[f_842_3]) ).
fof(f_843_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_843_2,plain,
! [U_3601,U_3600,U_3599] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3600),U_3601)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3599),U_3600)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3599),U_3601)),
inference(variable_rename,[status(thm)],[f_843_1]) ).
fof(f_843_3,plain,
! [U_3599,U_3600,U_3601] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3600),U_3601)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3599),U_3600)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3599),U_3601)),
inference(definitional_conversion,[status(esa)],[f_843_2]) ).
cnf(f_843_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3600),U_3601)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3599),U_3600)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3599),U_3601)),
inference(clausify,[status(thm)],[f_843_3]) ).
fof(f_844_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_844_2,plain,
! [U_3604,U_3603,U_3602] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3602),U_3603)),U_3604) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3602),U_3604)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3603),U_3604)),
inference(variable_rename,[status(thm)],[f_844_1]) ).
fof(f_844_3,plain,
! [U_3602,U_3603,U_3604] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3602),U_3603)),U_3604) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3602),U_3604)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3603),U_3604)),
inference(definitional_conversion,[status(esa)],[f_844_2]) ).
cnf(f_844_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3602),U_3603)),U_3604) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3602),U_3604)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3603),U_3604)),
inference(clausify,[status(thm)],[f_844_3]) ).
fof(f_845_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_845_2,plain,
! [U_3606,U_3605] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3605),U_3606)),U_3606) = U_3605,
inference(variable_rename,[status(thm)],[f_845_1]) ).
fof(f_845_3,plain,
! [U_3605,U_3606] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3605),U_3606)),U_3606) = U_3605,
inference(definitional_conversion,[status(esa)],[f_845_2]) ).
cnf(f_845_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3605),U_3606)),U_3606) = U_3605,
inference(clausify,[status(thm)],[f_845_3]) ).
fof(f_846_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_846_2,plain,
! [U_3608,U_3607] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3607),U_3608)),U_3607) = U_3608,
inference(variable_rename,[status(thm)],[f_846_1]) ).
fof(f_846_3,plain,
! [U_3607,U_3608] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3607),U_3608)),U_3607) = U_3608,
inference(definitional_conversion,[status(esa)],[f_846_2]) ).
cnf(f_846_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3607),U_3608)),U_3607) = U_3608,
inference(clausify,[status(thm)],[f_846_3]) ).
fof(f_847_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_847_2,plain,
! [U_3611,U_3610,U_3609] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3609),U_3610)),U_3611) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3610),U_3611)),
inference(variable_rename,[status(thm)],[f_847_1]) ).
fof(f_847_3,plain,
! [U_3609,U_3610,U_3611] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3609),U_3610)),U_3611) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3610),U_3611)),
inference(definitional_conversion,[status(esa)],[f_847_2]) ).
cnf(f_847_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3609),U_3610)),U_3611) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3610),U_3611)),
inference(clausify,[status(thm)],[f_847_3]) ).
fof(f_848_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_848_2,plain,
! [U_3614,U_3613,U_3612] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3612),U_3613)),U_3614) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3612),U_3614)),U_3613),
inference(variable_rename,[status(thm)],[f_848_1]) ).
fof(f_848_3,plain,
! [U_3612,U_3613,U_3614] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3612),U_3613)),U_3614) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3612),U_3614)),U_3613),
inference(definitional_conversion,[status(esa)],[f_848_2]) ).
cnf(f_848_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3612),U_3613)),U_3614) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3612),U_3614)),U_3613),
inference(clausify,[status(thm)],[f_848_3]) ).
fof(f_849_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_849_2,plain,
! [U_3617,U_3616,U_3615] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3615),U_3616)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3615),U_3617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3616),U_3617),
inference(variable_rename,[status(thm)],[f_849_1]) ).
fof(f_849_3,plain,
! [U_3615,U_3616,U_3617] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3615),U_3616)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3615),U_3617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3616),U_3617),
inference(definitional_conversion,[status(esa)],[f_849_2]) ).
cnf(f_849_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3615),U_3616)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3615),U_3617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3616),U_3617),
inference(clausify,[status(thm)],[f_849_3]) ).
fof(f_850_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_850_2,plain,
! [U_3620,U_3619,U_3618] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3618),U_3619)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3620),U_3619)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3618),U_3620),
inference(variable_rename,[status(thm)],[f_850_1]) ).
fof(f_850_3,plain,
! [U_3618,U_3619,U_3620] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3618),U_3619)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3620),U_3619)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3618),U_3620),
inference(definitional_conversion,[status(esa)],[f_850_2]) ).
cnf(f_850_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3618),U_3619)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3620),U_3619)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3618),U_3620),
inference(clausify,[status(thm)],[f_850_3]) ).
fof(f_851_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_851_2,plain,
! [U_3623,U_3622,U_3621] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3622),U_3621)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3623),U_3621)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3622),U_3623)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3622),U_3623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3622),U_3621)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3623),U_3621))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3621),U_3623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3621),U_3622)) ),
inference(variable_rename,[status(thm)],[f_851_1]) ).
fof(f_851_3,plain,
( ! [U_3621,U_3622,U_3623] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3622),U_3621)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3623),U_3621)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3622),U_3623))
| ~ sP206(U_3621,U_3622,U_3623) )
& ! [U_3621,U_3622,U_3623] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3622),U_3623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3622),U_3621)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3623),U_3621)))
| ~ sP206(U_3621,U_3622,U_3623) )
& ! [U_3621,U_3622,U_3623] :
( sP206(U_3621,U_3622,U_3623)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3621),U_3623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3621),U_3622)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206])],[f_851_2]) ).
cnf(f_851_4,plain,
( sP206(U_3621,U_3622,U_3623)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3621),U_3623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3621),U_3622)) ),
inference(clausify,[status(thm)],[f_851_3]) ).
cnf(f_851_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3622),U_3623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3622),U_3621)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3623),U_3621)))
| ~ sP206(U_3621,U_3622,U_3623) ),
inference(clausify,[status(thm)],[f_851_3]) ).
cnf(f_851_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_3622),U_3621)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3623),U_3621)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3622),U_3623))
| ~ sP206(U_3621,U_3622,U_3623) ),
inference(clausify,[status(thm)],[f_851_3]) ).
fof(f_852_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_852_2,plain,
! [U_3626,U_3625,U_3624] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3625),U_3624)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3626),U_3624)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3625),U_3626)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3624),U_3626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3624),U_3625)) ),
inference(variable_rename,[status(thm)],[f_852_1]) ).
fof(f_852_3,plain,
! [U_3624,U_3625,U_3626] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3625),U_3624)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3626),U_3624)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3625),U_3626)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3624),U_3626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3624),U_3625)) ),
inference(definitional_conversion,[status(esa)],[f_852_2]) ).
cnf(f_852_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3625),U_3624)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3626),U_3624)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3625),U_3626)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3624),U_3626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3624),U_3625)) ),
inference(clausify,[status(thm)],[f_852_3]) ).
fof(f_853_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_853_2,plain,
! [U_3629,U_3628,U_3627] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3628),U_3627) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3629),U_3627)
| U_3628 != U_3629 )
& ( U_3628 = U_3629
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3628),U_3627) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3629),U_3627) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3627),U_3629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3627),U_3628)) ),
inference(variable_rename,[status(thm)],[f_853_1]) ).
fof(f_853_3,plain,
( ! [U_3627,U_3628,U_3629] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3628),U_3627) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3629),U_3627)
| U_3628 != U_3629
| ~ sP207(U_3627,U_3628,U_3629) )
& ! [U_3627,U_3628,U_3629] :
( U_3628 = U_3629
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3628),U_3627) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3629),U_3627)
| ~ sP207(U_3627,U_3628,U_3629) )
& ! [U_3627,U_3628,U_3629] :
( sP207(U_3627,U_3628,U_3629)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3627),U_3629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3627),U_3628)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207])],[f_853_2]) ).
cnf(f_853_4,plain,
( sP207(U_3627,U_3628,U_3629)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3627),U_3629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3627),U_3628)) ),
inference(clausify,[status(thm)],[f_853_3]) ).
cnf(f_853_5,plain,
( U_3628 = U_3629
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3628),U_3627) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3629),U_3627)
| ~ sP207(U_3627,U_3628,U_3629) ),
inference(clausify,[status(thm)],[f_853_3]) ).
cnf(f_853_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3628),U_3627) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3629),U_3627)
| U_3628 != U_3629
| ~ sP207(U_3627,U_3628,U_3629) ),
inference(clausify,[status(thm)],[f_853_3]) ).
fof(f_854_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_854_2,plain,
! [U_3632,U_3631,U_3630] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3631),U_3632)),U_3630) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3631),U_3630)),U_3632)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3630),U_3631)) ),
inference(variable_rename,[status(thm)],[f_854_1]) ).
fof(f_854_3,plain,
! [U_3630,U_3631,U_3632] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3631),U_3632)),U_3630) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3631),U_3630)),U_3632)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3630),U_3631)) ),
inference(definitional_conversion,[status(esa)],[f_854_2]) ).
cnf(f_854_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3631),U_3632)),U_3630) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3631),U_3630)),U_3632)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3630),U_3631)) ),
inference(clausify,[status(thm)],[f_854_3]) ).
fof(f_855_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_855_2,plain,
! [U_3635,U_3634,U_3633] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3634),U_3633)),U_3635) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3634),U_3635)),U_3633)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3633),U_3634)) ),
inference(variable_rename,[status(thm)],[f_855_1]) ).
fof(f_855_3,plain,
! [U_3633,U_3634,U_3635] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3634),U_3633)),U_3635) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3634),U_3635)),U_3633)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3633),U_3634)) ),
inference(definitional_conversion,[status(esa)],[f_855_2]) ).
cnf(f_855_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3634),U_3633)),U_3635) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3634),U_3635)),U_3633)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3633),U_3634)) ),
inference(clausify,[status(thm)],[f_855_3]) ).
fof(f_856_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_856_2,plain,
! [U_3638,U_3637,U_3636] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3638),U_3637)),U_3636) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3638),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3637),U_3636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3636),U_3637)) ),
inference(variable_rename,[status(thm)],[f_856_1]) ).
fof(f_856_3,plain,
! [U_3636,U_3637,U_3638] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3638),U_3637)),U_3636) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3638),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3637),U_3636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3636),U_3637)) ),
inference(definitional_conversion,[status(esa)],[f_856_2]) ).
cnf(f_856_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3638),U_3637)),U_3636) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3638),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3637),U_3636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3636),U_3637)) ),
inference(clausify,[status(thm)],[f_856_3]) ).
fof(f_857_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_857_2,plain,
! [U_3641,U_3640,U_3639] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3640),U_3639) = U_3641
| U_3640 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3641),U_3639) )
& ( U_3640 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3641),U_3639)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3640),U_3639) != U_3641 ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3639),U_3640)) ),
inference(variable_rename,[status(thm)],[f_857_1]) ).
fof(f_857_3,plain,
( ! [U_3639,U_3640,U_3641] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3640),U_3639) = U_3641
| U_3640 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3641),U_3639)
| ~ sP208(U_3639,U_3640,U_3641) )
& ! [U_3639,U_3640,U_3641] :
( U_3640 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3641),U_3639)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3640),U_3639) != U_3641
| ~ sP208(U_3639,U_3640,U_3641) )
& ! [U_3639,U_3640,U_3641] :
( sP208(U_3639,U_3640,U_3641)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3639),U_3640)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208])],[f_857_2]) ).
cnf(f_857_4,plain,
( sP208(U_3639,U_3640,U_3641)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3639),U_3640)) ),
inference(clausify,[status(thm)],[f_857_3]) ).
cnf(f_857_5,plain,
( U_3640 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3641),U_3639)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3640),U_3639) != U_3641
| ~ sP208(U_3639,U_3640,U_3641) ),
inference(clausify,[status(thm)],[f_857_3]) ).
cnf(f_857_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3640),U_3639) = U_3641
| U_3640 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3641),U_3639)
| ~ sP208(U_3639,U_3640,U_3641) ),
inference(clausify,[status(thm)],[f_857_3]) ).
fof(f_858_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_858_2,plain,
! [U_3643,U_3642] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3643),U_3642)),U_3642) = U_3643
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3642),U_3643)) ),
inference(variable_rename,[status(thm)],[f_858_1]) ).
fof(f_858_3,plain,
! [U_3643,U_3642] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3643),U_3642)),U_3642) = U_3643
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3642),U_3643)) ),
inference(definitional_conversion,[status(esa)],[f_858_2]) ).
cnf(f_858_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3643),U_3642)),U_3642) = U_3643
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3642),U_3643)) ),
inference(clausify,[status(thm)],[f_858_3]) ).
fof(f_859_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_859_2,plain,
! [U_3646,U_3645,U_3644] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3645),U_3644)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3646),U_3644)),U_3645)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3646),U_3644)),U_3645))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3645),U_3644))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3644),U_3645)) ),
inference(variable_rename,[status(thm)],[f_859_1]) ).
fof(f_859_3,plain,
( ! [U_3644,U_3645,U_3646] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3645),U_3644)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3646),U_3644)),U_3645))
| ~ sP209(U_3644,U_3645,U_3646) )
& ! [U_3644,U_3645,U_3646] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3646),U_3644)),U_3645))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3645),U_3644)))
| ~ sP209(U_3644,U_3645,U_3646) )
& ! [U_3644,U_3645,U_3646] :
( sP209(U_3644,U_3645,U_3646)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3644),U_3645)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209])],[f_859_2]) ).
cnf(f_859_4,plain,
( sP209(U_3644,U_3645,U_3646)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3644),U_3645)) ),
inference(clausify,[status(thm)],[f_859_3]) ).
cnf(f_859_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_3646),U_3644)),U_3645))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3645),U_3644)))
| ~ sP209(U_3644,U_3645,U_3646) ),
inference(clausify,[status(thm)],[f_859_3]) ).
cnf(f_859_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3645),U_3644)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3646),U_3644)),U_3645))
| ~ sP209(U_3644,U_3645,U_3646) ),
inference(clausify,[status(thm)],[f_859_3]) ).
fof(f_860_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_860_2,plain,
! [U_3649,U_3648,U_3647] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3649),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3648),U_3647)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3649),U_3648)),U_3647)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3647),U_3648)) ),
inference(variable_rename,[status(thm)],[f_860_1]) ).
fof(f_860_3,plain,
! [U_3647,U_3648,U_3649] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3649),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3648),U_3647)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3649),U_3648)),U_3647)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3647),U_3648)) ),
inference(definitional_conversion,[status(esa)],[f_860_2]) ).
cnf(f_860_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3649),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3648),U_3647)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3649),U_3648)),U_3647)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3647),U_3648)) ),
inference(clausify,[status(thm)],[f_860_3]) ).
fof(f_861_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_861_2,plain,
! [U_3651,U_3650] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3650),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3651),U_3650)) = U_3651
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3650),U_3651)) ),
inference(variable_rename,[status(thm)],[f_861_1]) ).
fof(f_861_3,plain,
! [U_3650,U_3651] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3650),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3651),U_3650)) = U_3651
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3650),U_3651)) ),
inference(definitional_conversion,[status(esa)],[f_861_2]) ).
cnf(f_861_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3650),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3651),U_3650)) = U_3651
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3650),U_3651)) ),
inference(clausify,[status(thm)],[f_861_3]) ).
fof(f_862_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_862_2,plain,
! [U_3653,U_3652] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3653),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3653),U_3652)) = U_3652
| ~ 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] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3653),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3653),U_3652)) = U_3652
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3652),U_3653)) ),
inference(definitional_conversion,[status(esa)],[f_862_2]) ).
cnf(f_862_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3653),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3653),U_3652)) = U_3652
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3652),U_3653)) ),
inference(clausify,[status(thm)],[f_862_3]) ).
fof(f_863_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_863_2,plain,
! [U_3656,U_3655,U_3654] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3654),U_3656)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3655),U_3656)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3654),U_3655)) ),
inference(variable_rename,[status(thm)],[f_863_1]) ).
fof(f_863_3,plain,
! [U_3654,U_3655,U_3656] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3654),U_3656)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3655),U_3656)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3654),U_3655)) ),
inference(definitional_conversion,[status(esa)],[f_863_2]) ).
cnf(f_863_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_3654),U_3656)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3655),U_3656)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3654),U_3655)) ),
inference(clausify,[status(thm)],[f_863_3]) ).
fof(f_864_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_864_2,plain,
! [U_3659,U_3658,U_3657] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3659),U_3658)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3659),U_3657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3657),U_3658)) ),
inference(variable_rename,[status(thm)],[f_864_1]) ).
fof(f_864_3,plain,
! [U_3657,U_3658,U_3659] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3659),U_3658)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3659),U_3657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3657),U_3658)) ),
inference(definitional_conversion,[status(esa)],[f_864_2]) ).
cnf(f_864_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_3659),U_3658)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3659),U_3657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3657),U_3658)) ),
inference(clausify,[status(thm)],[f_864_3]) ).
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_3662,U_3661,U_3660] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3662),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3661),U_3662)),U_3660)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3660),U_3661)) ),
inference(variable_rename,[status(thm)],[f_865_1]) ).
fof(f_865_3,plain,
! [U_3660,U_3661,U_3662] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3662),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3661),U_3662)),U_3660)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3660),U_3661)) ),
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_3662),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3661),U_3662)),U_3660)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3660),U_3661)) ),
inference(clausify,[status(thm)],[f_865_3]) ).
fof(f_866_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_866_2,plain,
! [U_3665,U_3664,U_3663] :
( ( 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_3664)),U_3665))
| ~ 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_3665),U_3664))) )
& ( 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_3665),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_3663),U_3664)),U_3665)) ) ),
inference(variable_rename,[status(thm)],[f_866_1]) ).
fof(f_866_3,plain,
( ! [U_3671,U_3669,U_3667] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3667),U_3669)),U_3671))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3671),U_3669))) )
& ! [U_3670,U_3668,U_3666] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3666),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3670),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_3666),U_3668)),U_3670)) ) ),
inference(miniscope,[status(thm)],[f_866_2]) ).
fof(f_866_4,plain,
( ! [U_3667,U_3669,U_3671] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3667),U_3669)),U_3671))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3671),U_3669))) )
& ! [U_3668,U_3670,U_3666] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3666),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3670),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_3666),U_3668)),U_3670)) ) ),
inference(definitional_conversion,[status(esa)],[f_866_3]) ).
cnf(f_866_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3666),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3670),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_3666),U_3668)),U_3670)) ),
inference(clausify,[status(thm)],[f_866_4]) ).
cnf(f_866_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_3667),U_3669)),U_3671))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3671),U_3669))) ),
inference(clausify,[status(thm)],[f_866_4]) ).
fof(f_867_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_867_2,plain,
! [U_3674,U_3673,U_3672] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3674),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3673),U_3672)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3674),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_867_1]) ).
fof(f_867_3,plain,
! [U_3672,U_3673,U_3674] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3674),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3673),U_3672)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3674),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_867_2]) ).
cnf(f_867_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3674),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3673),U_3672)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3674),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_867_3]) ).
fof(f_868_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_868_2,plain,
! [U_3676,U_3675] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3675),U_3676)),U_3675)),
inference(variable_rename,[status(thm)],[f_868_1]) ).
fof(f_868_3,plain,
! [U_3675,U_3676] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3675),U_3676)),U_3675)),
inference(definitional_conversion,[status(esa)],[f_868_2]) ).
cnf(f_868_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_3675),U_3676)),U_3675)),
inference(clausify,[status(thm)],[f_868_3]) ).
fof(f_869_1,plain,
! [V_h_2,V_g_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Groups_Otimes__class_Otimes(T_d)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),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)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_h_2),c_Groups_Oone__class_Oone(T_d)),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__distrib]) ).
fof(f_869_2,plain,
! [U_3681,U_3680,U_3679,U_3678,U_3677] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3677,U_3678,c_Groups_Otimes__class_Otimes(U_3677)),hAPP(hAPP(c_COMBS(U_3678,U_3677,U_3677),hAPP(hAPP(c_COMBB(U_3677,tc_fun(U_3677,U_3677),U_3678),c_Groups_Otimes__class_Otimes(U_3677)),U_3680)),U_3681)),c_Groups_Oone__class_Oone(U_3677)),U_3679) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3677,U_3678,c_Groups_Otimes__class_Otimes(U_3677)),U_3680),c_Groups_Oone__class_Oone(U_3677)),U_3679)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3677,U_3678,c_Groups_Otimes__class_Otimes(U_3677)),U_3681),c_Groups_Oone__class_Oone(U_3677)),U_3679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3678),U_3679))
| ~ class_Groups_Ocomm__monoid__mult(U_3677) ),
inference(variable_rename,[status(thm)],[f_869_1]) ).
fof(f_869_3,plain,
! [U_3677,U_3678,U_3679,U_3680,U_3681] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3677,U_3678,c_Groups_Otimes__class_Otimes(U_3677)),hAPP(hAPP(c_COMBS(U_3678,U_3677,U_3677),hAPP(hAPP(c_COMBB(U_3677,tc_fun(U_3677,U_3677),U_3678),c_Groups_Otimes__class_Otimes(U_3677)),U_3680)),U_3681)),c_Groups_Oone__class_Oone(U_3677)),U_3679) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3677,U_3678,c_Groups_Otimes__class_Otimes(U_3677)),U_3680),c_Groups_Oone__class_Oone(U_3677)),U_3679)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3677,U_3678,c_Groups_Otimes__class_Otimes(U_3677)),U_3681),c_Groups_Oone__class_Oone(U_3677)),U_3679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3678),U_3679))
| ~ class_Groups_Ocomm__monoid__mult(U_3677) ),
inference(definitional_conversion,[status(esa)],[f_869_2]) ).
cnf(f_869_4,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3677,U_3678,c_Groups_Otimes__class_Otimes(U_3677)),hAPP(hAPP(c_COMBS(U_3678,U_3677,U_3677),hAPP(hAPP(c_COMBB(U_3677,tc_fun(U_3677,U_3677),U_3678),c_Groups_Otimes__class_Otimes(U_3677)),U_3680)),U_3681)),c_Groups_Oone__class_Oone(U_3677)),U_3679) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3677,U_3678,c_Groups_Otimes__class_Otimes(U_3677)),U_3680),c_Groups_Oone__class_Oone(U_3677)),U_3679)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3677,U_3678,c_Groups_Otimes__class_Otimes(U_3677)),U_3681),c_Groups_Oone__class_Oone(U_3677)),U_3679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3678),U_3679))
| ~ class_Groups_Ocomm__monoid__mult(U_3677) ),
inference(clausify,[status(thm)],[f_869_3]) ).
fof(f_870_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),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_c),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)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oinsert]) ).
fof(f_870_2,plain,
! [U_3684,U_3683,U_3682] :
( hAPP(c_Finite__Set_Ocard(U_3682),hAPP(hAPP(c_Set_Oinsert(U_3682),U_3684),U_3683)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3682),U_3683))
| hBOOL(hAPP(hAPP(c_member(U_3682),U_3684),U_3683))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3682),U_3683)) ),
inference(variable_rename,[status(thm)],[f_870_1]) ).
fof(f_870_3,plain,
! [U_3682,U_3683,U_3684] :
( hAPP(c_Finite__Set_Ocard(U_3682),hAPP(hAPP(c_Set_Oinsert(U_3682),U_3684),U_3683)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3682),U_3683))
| hBOOL(hAPP(hAPP(c_member(U_3682),U_3684),U_3683))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3682),U_3683)) ),
inference(definitional_conversion,[status(esa)],[f_870_2]) ).
cnf(f_870_4,plain,
( hAPP(c_Finite__Set_Ocard(U_3682),hAPP(hAPP(c_Set_Oinsert(U_3682),U_3684),U_3683)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3682),U_3683))
| hBOOL(hAPP(hAPP(c_member(U_3682),U_3684),U_3683))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3682),U_3683)) ),
inference(clausify,[status(thm)],[f_870_3]) ).
fof(f_871_1,plain,
! [V_g_2,V_A_2,T_c,T_d] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_d)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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),c_Groups_Oone__class_Oone(T_d)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) )
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod_OF__eq]) ).
fof(f_871_2,plain,
! [U_3688,U_3687,U_3686,U_3685] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3686,U_3685),U_3688),U_3687) = c_Groups_Oone__class_Oone(U_3685)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3686),U_3687)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3686,U_3685),U_3688),U_3687) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3685,U_3686,c_Groups_Otimes__class_Otimes(U_3685)),U_3688),c_Groups_Oone__class_Oone(U_3685)),U_3687)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3686),U_3687)) ) )
| ~ class_Groups_Ocomm__monoid__mult(U_3685) ),
inference(variable_rename,[status(thm)],[f_871_1]) ).
fof(f_871_3,plain,
( ! [U_3685,U_3686,U_3687,U_3688] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3686,U_3685),U_3688),U_3687) = c_Groups_Oone__class_Oone(U_3685)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3686),U_3687))
| ~ sP210(U_3685,U_3686,U_3687,U_3688) )
& ! [U_3685,U_3686,U_3687,U_3688] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3686,U_3685),U_3688),U_3687) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3685,U_3686,c_Groups_Otimes__class_Otimes(U_3685)),U_3688),c_Groups_Oone__class_Oone(U_3685)),U_3687)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3686),U_3687))
| ~ sP210(U_3685,U_3686,U_3687,U_3688) )
& ! [U_3685,U_3686,U_3687,U_3688] :
( sP210(U_3685,U_3686,U_3687,U_3688)
| ~ class_Groups_Ocomm__monoid__mult(U_3685) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210])],[f_871_2]) ).
cnf(f_871_4,plain,
( sP210(U_3685,U_3686,U_3687,U_3688)
| ~ class_Groups_Ocomm__monoid__mult(U_3685) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3686,U_3685),U_3688),U_3687) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3685,U_3686,c_Groups_Otimes__class_Otimes(U_3685)),U_3688),c_Groups_Oone__class_Oone(U_3685)),U_3687)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3686),U_3687))
| ~ sP210(U_3685,U_3686,U_3687,U_3688) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3686,U_3685),U_3688),U_3687) = c_Groups_Oone__class_Oone(U_3685)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_3686),U_3687))
| ~ sP210(U_3685,U_3686,U_3687,U_3688) ),
inference(clausify,[status(thm)],[f_871_3]) ).
fof(f_872_1,plain,
! [V_g_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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),c_Groups_Oone__class_Oone(T_d)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold]) ).
fof(f_872_2,plain,
! [U_3692,U_3691,U_3690,U_3689] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3690,U_3689),U_3692),U_3691) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3689,U_3690,c_Groups_Otimes__class_Otimes(U_3689)),U_3692),c_Groups_Oone__class_Oone(U_3689)),U_3691)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3690),U_3691))
| ~ class_Groups_Ocomm__monoid__mult(U_3689) ),
inference(variable_rename,[status(thm)],[f_872_1]) ).
fof(f_872_3,plain,
! [U_3691,U_3690,U_3689,U_3692] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3690,U_3689),U_3692),U_3691) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3689,U_3690,c_Groups_Otimes__class_Otimes(U_3689)),U_3692),c_Groups_Oone__class_Oone(U_3689)),U_3691)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3690),U_3691))
| ~ class_Groups_Ocomm__monoid__mult(U_3689) ),
inference(definitional_conversion,[status(esa)],[f_872_2]) ).
cnf(f_872_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3690,U_3689),U_3692),U_3691) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_3689,U_3690,c_Groups_Otimes__class_Otimes(U_3689)),U_3692),c_Groups_Oone__class_Oone(U_3689)),U_3691)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3690),U_3691))
| ~ class_Groups_Ocomm__monoid__mult(U_3689) ),
inference(clausify,[status(thm)],[f_872_3]) ).
fof(f_873_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),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_c),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)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oinsert__remove]) ).
fof(f_873_2,plain,
! [U_3695,U_3694,U_3693] :
( hAPP(c_Finite__Set_Ocard(U_3693),hAPP(hAPP(c_Set_Oinsert(U_3693),U_3695),U_3694)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3693),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3693,tc_HOL_Obool)),U_3694),hAPP(hAPP(c_Set_Oinsert(U_3693),U_3695),c_Orderings_Obot__class_Obot(tc_fun(U_3693,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3693),U_3694)) ),
inference(variable_rename,[status(thm)],[f_873_1]) ).
fof(f_873_3,plain,
! [U_3693,U_3694,U_3695] :
( hAPP(c_Finite__Set_Ocard(U_3693),hAPP(hAPP(c_Set_Oinsert(U_3693),U_3695),U_3694)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3693),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3693,tc_HOL_Obool)),U_3694),hAPP(hAPP(c_Set_Oinsert(U_3693),U_3695),c_Orderings_Obot__class_Obot(tc_fun(U_3693,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3693),U_3694)) ),
inference(definitional_conversion,[status(esa)],[f_873_2]) ).
cnf(f_873_4,plain,
( hAPP(c_Finite__Set_Ocard(U_3693),hAPP(hAPP(c_Set_Oinsert(U_3693),U_3695),U_3694)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3693),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3693,tc_HOL_Obool)),U_3694),hAPP(hAPP(c_Set_Oinsert(U_3693),U_3695),c_Orderings_Obot__class_Obot(tc_fun(U_3693,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3693),U_3694)) ),
inference(clausify,[status(thm)],[f_873_3]) ).
fof(f_874_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),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_c),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)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oremove]) ).
fof(f_874_2,plain,
! [U_3698,U_3697,U_3696] :
( hAPP(c_Finite__Set_Ocard(U_3696),U_3697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3696),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3696,tc_HOL_Obool)),U_3697),hAPP(hAPP(c_Set_Oinsert(U_3696),U_3698),c_Orderings_Obot__class_Obot(tc_fun(U_3696,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3696),U_3698),U_3697))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3696),U_3697)) ),
inference(variable_rename,[status(thm)],[f_874_1]) ).
fof(f_874_3,plain,
! [U_3696,U_3697,U_3698] :
( hAPP(c_Finite__Set_Ocard(U_3696),U_3697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3696),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3696,tc_HOL_Obool)),U_3697),hAPP(hAPP(c_Set_Oinsert(U_3696),U_3698),c_Orderings_Obot__class_Obot(tc_fun(U_3696,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3696),U_3698),U_3697))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3696),U_3697)) ),
inference(definitional_conversion,[status(esa)],[f_874_2]) ).
cnf(f_874_4,plain,
( hAPP(c_Finite__Set_Ocard(U_3696),U_3697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_3696),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3696,tc_HOL_Obool)),U_3697),hAPP(hAPP(c_Set_Oinsert(U_3696),U_3698),c_Orderings_Obot__class_Obot(tc_fun(U_3696,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3696),U_3698),U_3697))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3696),U_3697)) ),
inference(clausify,[status(thm)],[f_874_3]) ).
fof(f_875_1,plain,
! [V_B_2,V_a_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),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_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__insert]) ).
fof(f_875_2,plain,
! [U_3702,U_3701,U_3700,U_3699] :
( hAPP(c_Finite__Set_Ocard(U_3699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3699,tc_HOL_Obool)),U_3700),hAPP(hAPP(c_Set_Oinsert(U_3699),U_3701),U_3702))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3699,tc_HOL_Obool)),U_3700),U_3702))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(U_3699),U_3701),U_3702))
| ~ hBOOL(hAPP(hAPP(c_member(U_3699),U_3701),U_3700))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3699),U_3700)) ),
inference(variable_rename,[status(thm)],[f_875_1]) ).
fof(f_875_3,plain,
! [U_3699,U_3700,U_3701,U_3702] :
( hAPP(c_Finite__Set_Ocard(U_3699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3699,tc_HOL_Obool)),U_3700),hAPP(hAPP(c_Set_Oinsert(U_3699),U_3701),U_3702))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3699,tc_HOL_Obool)),U_3700),U_3702))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(U_3699),U_3701),U_3702))
| ~ hBOOL(hAPP(hAPP(c_member(U_3699),U_3701),U_3700))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3699),U_3700)) ),
inference(definitional_conversion,[status(esa)],[f_875_2]) ).
cnf(f_875_4,plain,
( hAPP(c_Finite__Set_Ocard(U_3699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3699,tc_HOL_Obool)),U_3700),hAPP(hAPP(c_Set_Oinsert(U_3699),U_3701),U_3702))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3699,tc_HOL_Obool)),U_3700),U_3702))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(U_3699),U_3701),U_3702))
| ~ hBOOL(hAPP(hAPP(c_member(U_3699),U_3701),U_3700))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3699),U_3700)) ),
inference(clausify,[status(thm)],[f_875_3]) ).
fof(f_876_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_876_2,plain,
! [U_3707,U_3706,U_3705,U_3704,U_3703] :
( ( ( 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_3703),U_3705)),U_3706)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3704),U_3705)),U_3707)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3706),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_3704),U_3703)),U_3705)),U_3707))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3706),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_3704),U_3703)),U_3705)),U_3707)))
| ~ 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_3703),U_3705)),U_3706)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3704),U_3705)),U_3707))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3703),U_3704)) ),
inference(variable_rename,[status(thm)],[f_876_1]) ).
fof(f_876_3,plain,
( ! [U_3703,U_3704,U_3705,U_3706,U_3707] :
( 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_3703),U_3705)),U_3706)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3704),U_3705)),U_3707)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3706),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_3704),U_3703)),U_3705)),U_3707)))
| ~ sP211(U_3703,U_3704,U_3705,U_3706,U_3707) )
& ! [U_3703,U_3704,U_3705,U_3706,U_3707] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3706),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_3704),U_3703)),U_3705)),U_3707)))
| ~ 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_3703),U_3705)),U_3706)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3704),U_3705)),U_3707)))
| ~ sP211(U_3703,U_3704,U_3705,U_3706,U_3707) )
& ! [U_3703,U_3704,U_3705,U_3706,U_3707] :
( sP211(U_3703,U_3704,U_3705,U_3706,U_3707)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3703),U_3704)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP211])],[f_876_2]) ).
cnf(f_876_4,plain,
( sP211(U_3703,U_3704,U_3705,U_3706,U_3707)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3703),U_3704)) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3706),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_3704),U_3703)),U_3705)),U_3707)))
| ~ 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_3703),U_3705)),U_3706)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3704),U_3705)),U_3707)))
| ~ sP211(U_3703,U_3704,U_3705,U_3706,U_3707) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_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_3703),U_3705)),U_3706)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3704),U_3705)),U_3707)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3706),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_3704),U_3703)),U_3705)),U_3707)))
| ~ sP211(U_3703,U_3704,U_3705,U_3706,U_3707) ),
inference(clausify,[status(thm)],[f_876_3]) ).
fof(f_877_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_877_2,plain,
! [U_3712,U_3711,U_3710,U_3709,U_3708] :
( ( ( 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_3709),U_3710)),U_3711)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3708),U_3710)),U_3712)))
| ~ 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_3709),U_3708)),U_3710)),U_3711)),U_3712)) )
& ( 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_3709),U_3708)),U_3710)),U_3711)),U_3712))
| ~ 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_3709),U_3710)),U_3711)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3708),U_3710)),U_3712))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3708),U_3709)) ),
inference(variable_rename,[status(thm)],[f_877_1]) ).
fof(f_877_3,plain,
( ! [U_3709,U_3708,U_3711,U_3710,U_3712] :
( 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_3709),U_3710)),U_3711)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3708),U_3710)),U_3712)))
| ~ 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_3709),U_3708)),U_3710)),U_3711)),U_3712))
| ~ sP212(U_3709,U_3708,U_3711,U_3710,U_3712) )
& ! [U_3709,U_3708,U_3711,U_3710,U_3712] :
( 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_3709),U_3708)),U_3710)),U_3711)),U_3712))
| ~ 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_3709),U_3710)),U_3711)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3708),U_3710)),U_3712)))
| ~ sP212(U_3709,U_3708,U_3711,U_3710,U_3712) )
& ! [U_3709,U_3708,U_3711,U_3710,U_3712] :
( sP212(U_3709,U_3708,U_3711,U_3710,U_3712)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3708),U_3709)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212])],[f_877_2]) ).
cnf(f_877_4,plain,
( sP212(U_3709,U_3708,U_3711,U_3710,U_3712)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3708),U_3709)) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_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_3709),U_3708)),U_3710)),U_3711)),U_3712))
| ~ 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_3709),U_3710)),U_3711)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3708),U_3710)),U_3712)))
| ~ sP212(U_3709,U_3708,U_3711,U_3710,U_3712) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_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_3709),U_3710)),U_3711)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3708),U_3710)),U_3712)))
| ~ 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_3709),U_3708)),U_3710)),U_3711)),U_3712))
| ~ sP212(U_3709,U_3708,U_3711,U_3710,U_3712) ),
inference(clausify,[status(thm)],[f_877_3]) ).
fof(f_878_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_878_2,plain,
! [U_3717,U_3716,U_3715,U_3714,U_3713] :
( ( ( 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_3714),U_3715)),U_3716)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3713),U_3715)),U_3717)))
| ~ 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_3714),U_3713)),U_3715)),U_3716)),U_3717)) )
& ( 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_3714),U_3713)),U_3715)),U_3716)),U_3717))
| ~ 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_3714),U_3715)),U_3716)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3713),U_3715)),U_3717))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3713),U_3714)) ),
inference(variable_rename,[status(thm)],[f_878_1]) ).
fof(f_878_3,plain,
( ! [U_3714,U_3713,U_3715,U_3716,U_3717] :
( 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_3714),U_3715)),U_3716)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3713),U_3715)),U_3717)))
| ~ 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_3714),U_3713)),U_3715)),U_3716)),U_3717))
| ~ sP213(U_3714,U_3713,U_3715,U_3716,U_3717) )
& ! [U_3714,U_3713,U_3715,U_3716,U_3717] :
( 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_3714),U_3713)),U_3715)),U_3716)),U_3717))
| ~ 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_3714),U_3715)),U_3716)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3713),U_3715)),U_3717)))
| ~ sP213(U_3714,U_3713,U_3715,U_3716,U_3717) )
& ! [U_3714,U_3713,U_3715,U_3716,U_3717] :
( sP213(U_3714,U_3713,U_3715,U_3716,U_3717)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3713),U_3714)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213])],[f_878_2]) ).
cnf(f_878_4,plain,
( sP213(U_3714,U_3713,U_3715,U_3716,U_3717)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3713),U_3714)) ),
inference(clausify,[status(thm)],[f_878_3]) ).
cnf(f_878_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_3714),U_3713)),U_3715)),U_3716)),U_3717))
| ~ 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_3714),U_3715)),U_3716)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3713),U_3715)),U_3717)))
| ~ sP213(U_3714,U_3713,U_3715,U_3716,U_3717) ),
inference(clausify,[status(thm)],[f_878_3]) ).
cnf(f_878_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_3714),U_3715)),U_3716)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3713),U_3715)),U_3717)))
| ~ 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_3714),U_3713)),U_3715)),U_3716)),U_3717))
| ~ sP213(U_3714,U_3713,U_3715,U_3716,U_3717) ),
inference(clausify,[status(thm)],[f_878_3]) ).
fof(f_879_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_879_2,plain,
! [U_3722,U_3721,U_3720,U_3719,U_3718] :
( 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_3719),U_3720)),U_3721)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3718),U_3720)),U_3722)) = 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_3719),U_3718)),U_3720)),U_3721)),U_3722)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3718),U_3719)) ),
inference(variable_rename,[status(thm)],[f_879_1]) ).
fof(f_879_3,plain,
! [U_3719,U_3718,U_3720,U_3721,U_3722] :
( 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_3719),U_3720)),U_3721)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3718),U_3720)),U_3722)) = 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_3719),U_3718)),U_3720)),U_3721)),U_3722)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3718),U_3719)) ),
inference(definitional_conversion,[status(esa)],[f_879_2]) ).
cnf(f_879_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_3719),U_3720)),U_3721)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3718),U_3720)),U_3722)) = 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_3719),U_3718)),U_3720)),U_3721)),U_3722)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3718),U_3719)) ),
inference(clausify,[status(thm)],[f_879_3]) ).
fof(f_880_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_880_2,plain,
! [U_3727,U_3726,U_3725,U_3724,U_3723] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3724),U_3725)),U_3726) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3723),U_3725)),U_3727)
| 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_3724),U_3723)),U_3725)),U_3726) != U_3727 )
& ( 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_3724),U_3723)),U_3725)),U_3726) = U_3727
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3724),U_3725)),U_3726) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3723),U_3725)),U_3727) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3723),U_3724)) ),
inference(variable_rename,[status(thm)],[f_880_1]) ).
fof(f_880_3,plain,
( ! [U_3723,U_3724,U_3725,U_3726,U_3727] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3724),U_3725)),U_3726) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3723),U_3725)),U_3727)
| 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_3724),U_3723)),U_3725)),U_3726) != U_3727
| ~ sP214(U_3723,U_3724,U_3725,U_3726,U_3727) )
& ! [U_3723,U_3724,U_3725,U_3726,U_3727] :
( 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_3724),U_3723)),U_3725)),U_3726) = U_3727
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3724),U_3725)),U_3726) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3723),U_3725)),U_3727)
| ~ sP214(U_3723,U_3724,U_3725,U_3726,U_3727) )
& ! [U_3723,U_3724,U_3725,U_3726,U_3727] :
( sP214(U_3723,U_3724,U_3725,U_3726,U_3727)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3723),U_3724)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214])],[f_880_2]) ).
cnf(f_880_4,plain,
( sP214(U_3723,U_3724,U_3725,U_3726,U_3727)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3723),U_3724)) ),
inference(clausify,[status(thm)],[f_880_3]) ).
cnf(f_880_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_3724),U_3723)),U_3725)),U_3726) = U_3727
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3724),U_3725)),U_3726) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3723),U_3725)),U_3727)
| ~ sP214(U_3723,U_3724,U_3725,U_3726,U_3727) ),
inference(clausify,[status(thm)],[f_880_3]) ).
cnf(f_880_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3724),U_3725)),U_3726) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3723),U_3725)),U_3727)
| 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_3724),U_3723)),U_3725)),U_3726) != U_3727
| ~ sP214(U_3723,U_3724,U_3725,U_3726,U_3727) ),
inference(clausify,[status(thm)],[f_880_3]) ).
fof(f_881_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_881_2,plain,
! [U_3732,U_3731,U_3730,U_3729,U_3728] :
( ( ( 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_3728),U_3730)),U_3731)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3729),U_3730)),U_3732)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3731),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_3729),U_3728)),U_3730)),U_3732))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3731),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_3729),U_3728)),U_3730)),U_3732)))
| ~ 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_3728),U_3730)),U_3731)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3729),U_3730)),U_3732))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3728),U_3729)) ),
inference(variable_rename,[status(thm)],[f_881_1]) ).
fof(f_881_3,plain,
( ! [U_3729,U_3728,U_3731,U_3730,U_3732] :
( 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_3728),U_3730)),U_3731)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3729),U_3730)),U_3732)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3731),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_3729),U_3728)),U_3730)),U_3732)))
| ~ sP215(U_3729,U_3728,U_3731,U_3730,U_3732) )
& ! [U_3729,U_3728,U_3731,U_3730,U_3732] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3731),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_3729),U_3728)),U_3730)),U_3732)))
| ~ 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_3728),U_3730)),U_3731)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3729),U_3730)),U_3732)))
| ~ sP215(U_3729,U_3728,U_3731,U_3730,U_3732) )
& ! [U_3729,U_3728,U_3731,U_3730,U_3732] :
( sP215(U_3729,U_3728,U_3731,U_3730,U_3732)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3728),U_3729)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215])],[f_881_2]) ).
cnf(f_881_4,plain,
( sP215(U_3729,U_3728,U_3731,U_3730,U_3732)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3728),U_3729)) ),
inference(clausify,[status(thm)],[f_881_3]) ).
cnf(f_881_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3731),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_3729),U_3728)),U_3730)),U_3732)))
| ~ 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_3728),U_3730)),U_3731)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3729),U_3730)),U_3732)))
| ~ sP215(U_3729,U_3728,U_3731,U_3730,U_3732) ),
inference(clausify,[status(thm)],[f_881_3]) ).
cnf(f_881_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_3728),U_3730)),U_3731)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3729),U_3730)),U_3732)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3731),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_3729),U_3728)),U_3730)),U_3732)))
| ~ sP215(U_3729,U_3728,U_3731,U_3730,U_3732) ),
inference(clausify,[status(thm)],[f_881_3]) ).
fof(f_882_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_882_2,plain,
! [U_3737,U_3736,U_3735,U_3734,U_3733] :
( 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_3733),U_3735)),U_3736)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3734),U_3735)),U_3737)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3736),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_3734),U_3733)),U_3735)),U_3737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3733),U_3734)) ),
inference(variable_rename,[status(thm)],[f_882_1]) ).
fof(f_882_3,plain,
! [U_3734,U_3735,U_3733,U_3736,U_3737] :
( 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_3733),U_3735)),U_3736)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3734),U_3735)),U_3737)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3736),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_3734),U_3733)),U_3735)),U_3737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3733),U_3734)) ),
inference(definitional_conversion,[status(esa)],[f_882_2]) ).
cnf(f_882_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_3733),U_3735)),U_3736)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3734),U_3735)),U_3737)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3736),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_3734),U_3733)),U_3735)),U_3737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3733),U_3734)) ),
inference(clausify,[status(thm)],[f_882_3]) ).
fof(f_883_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_883_2,plain,
! [U_3742,U_3741,U_3740,U_3739,U_3738] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3738),U_3740)),U_3741) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3739),U_3740)),U_3742)
| U_3741 != 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_3739),U_3738)),U_3740)),U_3742) )
& ( U_3741 = 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_3739),U_3738)),U_3740)),U_3742)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3738),U_3740)),U_3741) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3739),U_3740)),U_3742) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3738),U_3739)) ),
inference(variable_rename,[status(thm)],[f_883_1]) ).
fof(f_883_3,plain,
( ! [U_3738,U_3739,U_3740,U_3741,U_3742] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3738),U_3740)),U_3741) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3739),U_3740)),U_3742)
| U_3741 != 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_3739),U_3738)),U_3740)),U_3742)
| ~ sP216(U_3738,U_3739,U_3740,U_3741,U_3742) )
& ! [U_3738,U_3739,U_3740,U_3741,U_3742] :
( U_3741 = 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_3739),U_3738)),U_3740)),U_3742)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3738),U_3740)),U_3741) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3739),U_3740)),U_3742)
| ~ sP216(U_3738,U_3739,U_3740,U_3741,U_3742) )
& ! [U_3738,U_3739,U_3740,U_3741,U_3742] :
( sP216(U_3738,U_3739,U_3740,U_3741,U_3742)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3738),U_3739)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216])],[f_883_2]) ).
cnf(f_883_4,plain,
( sP216(U_3738,U_3739,U_3740,U_3741,U_3742)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3738),U_3739)) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_5,plain,
( U_3741 = 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_3739),U_3738)),U_3740)),U_3742)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3738),U_3740)),U_3741) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3739),U_3740)),U_3742)
| ~ sP216(U_3738,U_3739,U_3740,U_3741,U_3742) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3738),U_3740)),U_3741) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3739),U_3740)),U_3742)
| U_3741 != 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_3739),U_3738)),U_3740)),U_3742)
| ~ sP216(U_3738,U_3739,U_3740,U_3741,U_3742) ),
inference(clausify,[status(thm)],[f_883_3]) ).
fof(f_884_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_884_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_884_1]) ).
cnf(f_884_3,plain,
c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_884_2]) ).
fof(f_885_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_885_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_885_1]) ).
cnf(f_885_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_885_2]) ).
fof(f_886_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_886_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_886_1]) ).
fof(f_886_3,plain,
! [U_3744,U_3745,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(definitional_conversion,[status(esa)],[f_886_2]) ).
cnf(f_886_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_886_3]) ).
fof(f_887_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_887_2,plain,
! [U_3747,U_3746] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3746),U_3747) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3747),U_3746),
inference(variable_rename,[status(thm)],[f_887_1]) ).
fof(f_887_3,plain,
! [U_3746,U_3747] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3746),U_3747) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3747),U_3746),
inference(definitional_conversion,[status(esa)],[f_887_2]) ).
cnf(f_887_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3746),U_3747) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3747),U_3746),
inference(clausify,[status(thm)],[f_887_3]) ).
fof(f_888_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_888_2,plain,
! [U_3751,U_3750,U_3749,U_3748] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3748),U_3749)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3750),U_3749)),U_3751)) = 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_3748),U_3750)),U_3749)),U_3751),
inference(variable_rename,[status(thm)],[f_888_1]) ).
fof(f_888_3,plain,
! [U_3748,U_3749,U_3750,U_3751] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3748),U_3749)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3750),U_3749)),U_3751)) = 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_3748),U_3750)),U_3749)),U_3751),
inference(definitional_conversion,[status(esa)],[f_888_2]) ).
cnf(f_888_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3748),U_3749)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3750),U_3749)),U_3751)) = 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_3748),U_3750)),U_3749)),U_3751),
inference(clausify,[status(thm)],[f_888_3]) ).
fof(f_889_1,plain,
! [V_k_2,V_less__eq_2,V_i_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OatMost(T_c,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_c),V_i_2),c_SetInterval_Oord_OatMost(T_c,V_less__eq_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff]) ).
fof(f_889_2,plain,
! [U_3755,U_3754,U_3753,U_3752] :
( ( hBOOL(hAPP(hAPP(c_member(U_3752),U_3753),c_SetInterval_Oord_OatMost(U_3752,U_3754,U_3755)))
| ~ hBOOL(hAPP(hAPP(U_3754,U_3753),U_3755)) )
& ( hBOOL(hAPP(hAPP(U_3754,U_3753),U_3755))
| ~ hBOOL(hAPP(hAPP(c_member(U_3752),U_3753),c_SetInterval_Oord_OatMost(U_3752,U_3754,U_3755))) ) ),
inference(variable_rename,[status(thm)],[f_889_1]) ).
fof(f_889_3,plain,
( ! [U_3763,U_3761,U_3759] :
( ! [U_3757] : hBOOL(hAPP(hAPP(c_member(U_3757),U_3759),c_SetInterval_Oord_OatMost(U_3757,U_3761,U_3763)))
| ~ hBOOL(hAPP(hAPP(U_3761,U_3759),U_3763)) )
& ! [U_3762,U_3760,U_3758] :
( ! [U_3756] : ~ hBOOL(hAPP(hAPP(c_member(U_3756),U_3758),c_SetInterval_Oord_OatMost(U_3756,U_3760,U_3762)))
| hBOOL(hAPP(hAPP(U_3760,U_3758),U_3762)) ) ),
inference(miniscope,[status(thm)],[f_889_2]) ).
fof(f_889_4,plain,
( ! [U_3757,U_3763,U_3759,U_3761] :
( hBOOL(hAPP(hAPP(c_member(U_3757),U_3759),c_SetInterval_Oord_OatMost(U_3757,U_3761,U_3763)))
| ~ hBOOL(hAPP(hAPP(U_3761,U_3759),U_3763)) )
& ! [U_3758,U_3760,U_3756,U_3762] :
( ~ hBOOL(hAPP(hAPP(c_member(U_3756),U_3758),c_SetInterval_Oord_OatMost(U_3756,U_3760,U_3762)))
| hBOOL(hAPP(hAPP(U_3760,U_3758),U_3762)) ) ),
inference(definitional_conversion,[status(esa)],[f_889_3]) ).
cnf(f_889_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_3756),U_3758),c_SetInterval_Oord_OatMost(U_3756,U_3760,U_3762)))
| hBOOL(hAPP(hAPP(U_3760,U_3758),U_3762)) ),
inference(clausify,[status(thm)],[f_889_4]) ).
cnf(f_889_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3757),U_3759),c_SetInterval_Oord_OatMost(U_3757,U_3761,U_3763)))
| ~ hBOOL(hAPP(hAPP(U_3761,U_3759),U_3763)) ),
inference(clausify,[status(thm)],[f_889_4]) ).
fof(f_890_1,plain,
! [V_k_2,V_less__eq_2,V_i_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OatLeast(T_c,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_c),V_i_2),c_SetInterval_Oord_OatLeast(T_c,V_less__eq_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff]) ).
fof(f_890_2,plain,
! [U_3767,U_3766,U_3765,U_3764] :
( ( hBOOL(hAPP(hAPP(c_member(U_3764),U_3765),c_SetInterval_Oord_OatLeast(U_3764,U_3766,U_3767)))
| ~ hBOOL(hAPP(hAPP(U_3766,U_3767),U_3765)) )
& ( hBOOL(hAPP(hAPP(U_3766,U_3767),U_3765))
| ~ hBOOL(hAPP(hAPP(c_member(U_3764),U_3765),c_SetInterval_Oord_OatLeast(U_3764,U_3766,U_3767))) ) ),
inference(variable_rename,[status(thm)],[f_890_1]) ).
fof(f_890_3,plain,
( ! [U_3775,U_3773,U_3771] :
( ! [U_3769] : hBOOL(hAPP(hAPP(c_member(U_3769),U_3771),c_SetInterval_Oord_OatLeast(U_3769,U_3773,U_3775)))
| ~ hBOOL(hAPP(hAPP(U_3773,U_3775),U_3771)) )
& ! [U_3774,U_3772,U_3770] :
( ! [U_3768] : ~ hBOOL(hAPP(hAPP(c_member(U_3768),U_3770),c_SetInterval_Oord_OatLeast(U_3768,U_3772,U_3774)))
| hBOOL(hAPP(hAPP(U_3772,U_3774),U_3770)) ) ),
inference(miniscope,[status(thm)],[f_890_2]) ).
fof(f_890_4,plain,
( ! [U_3769,U_3771,U_3773,U_3775] :
( hBOOL(hAPP(hAPP(c_member(U_3769),U_3771),c_SetInterval_Oord_OatLeast(U_3769,U_3773,U_3775)))
| ~ hBOOL(hAPP(hAPP(U_3773,U_3775),U_3771)) )
& ! [U_3772,U_3770,U_3768,U_3774] :
( ~ hBOOL(hAPP(hAPP(c_member(U_3768),U_3770),c_SetInterval_Oord_OatLeast(U_3768,U_3772,U_3774)))
| hBOOL(hAPP(hAPP(U_3772,U_3774),U_3770)) ) ),
inference(definitional_conversion,[status(esa)],[f_890_3]) ).
cnf(f_890_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_3768),U_3770),c_SetInterval_Oord_OatLeast(U_3768,U_3772,U_3774)))
| hBOOL(hAPP(hAPP(U_3772,U_3774),U_3770)) ),
inference(clausify,[status(thm)],[f_890_4]) ).
cnf(f_890_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3769),U_3771),c_SetInterval_Oord_OatLeast(U_3769,U_3773,U_3775)))
| ~ hBOOL(hAPP(hAPP(U_3773,U_3775),U_3771)) ),
inference(clausify,[status(thm)],[f_890_4]) ).
fof(f_891_1,plain,
! [V_k_2,V_less_2,V_i_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OlessThan(T_c,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_c),V_i_2),c_SetInterval_Oord_OlessThan(T_c,V_less_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff]) ).
fof(f_891_2,plain,
! [U_3779,U_3778,U_3777,U_3776] :
( ( hBOOL(hAPP(hAPP(c_member(U_3776),U_3777),c_SetInterval_Oord_OlessThan(U_3776,U_3778,U_3779)))
| ~ hBOOL(hAPP(hAPP(U_3778,U_3777),U_3779)) )
& ( hBOOL(hAPP(hAPP(U_3778,U_3777),U_3779))
| ~ hBOOL(hAPP(hAPP(c_member(U_3776),U_3777),c_SetInterval_Oord_OlessThan(U_3776,U_3778,U_3779))) ) ),
inference(variable_rename,[status(thm)],[f_891_1]) ).
fof(f_891_3,plain,
( ! [U_3787,U_3785,U_3783] :
( ! [U_3781] : hBOOL(hAPP(hAPP(c_member(U_3781),U_3783),c_SetInterval_Oord_OlessThan(U_3781,U_3785,U_3787)))
| ~ hBOOL(hAPP(hAPP(U_3785,U_3783),U_3787)) )
& ! [U_3786,U_3784,U_3782] :
( ! [U_3780] : ~ hBOOL(hAPP(hAPP(c_member(U_3780),U_3782),c_SetInterval_Oord_OlessThan(U_3780,U_3784,U_3786)))
| hBOOL(hAPP(hAPP(U_3784,U_3782),U_3786)) ) ),
inference(miniscope,[status(thm)],[f_891_2]) ).
fof(f_891_4,plain,
( ! [U_3787,U_3781,U_3783,U_3785] :
( hBOOL(hAPP(hAPP(c_member(U_3781),U_3783),c_SetInterval_Oord_OlessThan(U_3781,U_3785,U_3787)))
| ~ hBOOL(hAPP(hAPP(U_3785,U_3783),U_3787)) )
& ! [U_3784,U_3782,U_3780,U_3786] :
( ~ hBOOL(hAPP(hAPP(c_member(U_3780),U_3782),c_SetInterval_Oord_OlessThan(U_3780,U_3784,U_3786)))
| hBOOL(hAPP(hAPP(U_3784,U_3782),U_3786)) ) ),
inference(definitional_conversion,[status(esa)],[f_891_3]) ).
cnf(f_891_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_3780),U_3782),c_SetInterval_Oord_OlessThan(U_3780,U_3784,U_3786)))
| hBOOL(hAPP(hAPP(U_3784,U_3782),U_3786)) ),
inference(clausify,[status(thm)],[f_891_4]) ).
cnf(f_891_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3781),U_3783),c_SetInterval_Oord_OlessThan(U_3781,U_3785,U_3787)))
| ~ hBOOL(hAPP(hAPP(U_3785,U_3783),U_3787)) ),
inference(clausify,[status(thm)],[f_891_4]) ).
fof(f_892_1,plain,
! [V_k_2,V_less_2,V_i_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OgreaterThan(T_c,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_c),V_i_2),c_SetInterval_Oord_OgreaterThan(T_c,V_less_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff]) ).
fof(f_892_2,plain,
! [U_3791,U_3790,U_3789,U_3788] :
( ( hBOOL(hAPP(hAPP(c_member(U_3788),U_3789),c_SetInterval_Oord_OgreaterThan(U_3788,U_3790,U_3791)))
| ~ hBOOL(hAPP(hAPP(U_3790,U_3791),U_3789)) )
& ( hBOOL(hAPP(hAPP(U_3790,U_3791),U_3789))
| ~ hBOOL(hAPP(hAPP(c_member(U_3788),U_3789),c_SetInterval_Oord_OgreaterThan(U_3788,U_3790,U_3791))) ) ),
inference(variable_rename,[status(thm)],[f_892_1]) ).
fof(f_892_3,plain,
( ! [U_3799,U_3797,U_3795] :
( ! [U_3793] : hBOOL(hAPP(hAPP(c_member(U_3793),U_3795),c_SetInterval_Oord_OgreaterThan(U_3793,U_3797,U_3799)))
| ~ hBOOL(hAPP(hAPP(U_3797,U_3799),U_3795)) )
& ! [U_3798,U_3796,U_3794] :
( ! [U_3792] : ~ hBOOL(hAPP(hAPP(c_member(U_3792),U_3794),c_SetInterval_Oord_OgreaterThan(U_3792,U_3796,U_3798)))
| hBOOL(hAPP(hAPP(U_3796,U_3798),U_3794)) ) ),
inference(miniscope,[status(thm)],[f_892_2]) ).
fof(f_892_4,plain,
( ! [U_3793,U_3795,U_3797,U_3799] :
( hBOOL(hAPP(hAPP(c_member(U_3793),U_3795),c_SetInterval_Oord_OgreaterThan(U_3793,U_3797,U_3799)))
| ~ hBOOL(hAPP(hAPP(U_3797,U_3799),U_3795)) )
& ! [U_3794,U_3792,U_3796,U_3798] :
( ~ hBOOL(hAPP(hAPP(c_member(U_3792),U_3794),c_SetInterval_Oord_OgreaterThan(U_3792,U_3796,U_3798)))
| hBOOL(hAPP(hAPP(U_3796,U_3798),U_3794)) ) ),
inference(definitional_conversion,[status(esa)],[f_892_3]) ).
cnf(f_892_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_3792),U_3794),c_SetInterval_Oord_OgreaterThan(U_3792,U_3796,U_3798)))
| hBOOL(hAPP(hAPP(U_3796,U_3798),U_3794)) ),
inference(clausify,[status(thm)],[f_892_4]) ).
cnf(f_892_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3793),U_3795),c_SetInterval_Oord_OgreaterThan(U_3793,U_3797,U_3799)))
| ~ hBOOL(hAPP(hAPP(U_3797,U_3799),U_3795)) ),
inference(clausify,[status(thm)],[f_892_4]) ).
fof(f_893_1,plain,
! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_c,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_c),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_c,V_less__eq_2,V_l_2,V_u_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff]) ).
fof(f_893_2,plain,
! [U_3804,U_3803,U_3802,U_3801,U_3800] :
( ( hBOOL(hAPP(hAPP(c_member(U_3800),U_3801),c_SetInterval_Oord_OatLeastAtMost(U_3800,U_3802,U_3803,U_3804)))
| ~ hBOOL(hAPP(hAPP(U_3802,U_3801),U_3804))
| ~ hBOOL(hAPP(hAPP(U_3802,U_3803),U_3801)) )
& ( ( hBOOL(hAPP(hAPP(U_3802,U_3801),U_3804))
& hBOOL(hAPP(hAPP(U_3802,U_3803),U_3801)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3800),U_3801),c_SetInterval_Oord_OatLeastAtMost(U_3800,U_3802,U_3803,U_3804))) ) ),
inference(variable_rename,[status(thm)],[f_893_1]) ).
fof(f_893_3,plain,
( ! [U_3814,U_3812,U_3810,U_3808] :
( ! [U_3806] : hBOOL(hAPP(hAPP(c_member(U_3806),U_3808),c_SetInterval_Oord_OatLeastAtMost(U_3806,U_3810,U_3812,U_3814)))
| ~ hBOOL(hAPP(hAPP(U_3810,U_3808),U_3814))
| ~ hBOOL(hAPP(hAPP(U_3810,U_3812),U_3808)) )
& ! [U_3813,U_3811,U_3809,U_3807] :
( ! [U_3805] : ~ hBOOL(hAPP(hAPP(c_member(U_3805),U_3807),c_SetInterval_Oord_OatLeastAtMost(U_3805,U_3809,U_3811,U_3813)))
| ( hBOOL(hAPP(hAPP(U_3809,U_3807),U_3813))
& hBOOL(hAPP(hAPP(U_3809,U_3811),U_3807)) ) ) ),
inference(miniscope,[status(thm)],[f_893_2]) ).
fof(f_893_4,plain,
( ! [U_3807,U_3809,U_3811,U_3813] :
( hBOOL(hAPP(hAPP(U_3809,U_3807),U_3813))
| ~ sP217(U_3807,U_3809,U_3811,U_3813) )
& ! [U_3807,U_3809,U_3811,U_3813] :
( hBOOL(hAPP(hAPP(U_3809,U_3811),U_3807))
| ~ sP217(U_3807,U_3809,U_3811,U_3813) )
& ! [U_3810,U_3808,U_3806,U_3812,U_3814] :
( hBOOL(hAPP(hAPP(c_member(U_3806),U_3808),c_SetInterval_Oord_OatLeastAtMost(U_3806,U_3810,U_3812,U_3814)))
| ~ hBOOL(hAPP(hAPP(U_3810,U_3808),U_3814))
| ~ hBOOL(hAPP(hAPP(U_3810,U_3812),U_3808)) )
& ! [U_3805,U_3807,U_3809,U_3811,U_3813] :
( ~ hBOOL(hAPP(hAPP(c_member(U_3805),U_3807),c_SetInterval_Oord_OatLeastAtMost(U_3805,U_3809,U_3811,U_3813)))
| sP217(U_3807,U_3809,U_3811,U_3813) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP217])],[f_893_3]) ).
cnf(f_893_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_3805),U_3807),c_SetInterval_Oord_OatLeastAtMost(U_3805,U_3809,U_3811,U_3813)))
| sP217(U_3807,U_3809,U_3811,U_3813) ),
inference(clausify,[status(thm)],[f_893_4]) ).
cnf(f_893_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3806),U_3808),c_SetInterval_Oord_OatLeastAtMost(U_3806,U_3810,U_3812,U_3814)))
| ~ hBOOL(hAPP(hAPP(U_3810,U_3808),U_3814))
| ~ hBOOL(hAPP(hAPP(U_3810,U_3812),U_3808)) ),
inference(clausify,[status(thm)],[f_893_4]) ).
cnf(f_893_7,plain,
( hBOOL(hAPP(hAPP(U_3809,U_3811),U_3807))
| ~ sP217(U_3807,U_3809,U_3811,U_3813) ),
inference(clausify,[status(thm)],[f_893_4]) ).
cnf(f_893_8,plain,
( hBOOL(hAPP(hAPP(U_3809,U_3807),U_3813))
| ~ sP217(U_3807,U_3809,U_3811,U_3813) ),
inference(clausify,[status(thm)],[f_893_4]) ).
fof(f_894_1,plain,
! [V_u_2,V_l_2,V_less_2,V_i_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_c,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_c),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_c,V_less_2,V_l_2,V_u_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff]) ).
fof(f_894_2,plain,
! [U_3819,U_3818,U_3817,U_3816,U_3815] :
( ( hBOOL(hAPP(hAPP(c_member(U_3815),U_3816),c_SetInterval_Oord_OgreaterThanLessThan(U_3815,U_3817,U_3818,U_3819)))
| ~ hBOOL(hAPP(hAPP(U_3817,U_3816),U_3819))
| ~ hBOOL(hAPP(hAPP(U_3817,U_3818),U_3816)) )
& ( ( hBOOL(hAPP(hAPP(U_3817,U_3816),U_3819))
& hBOOL(hAPP(hAPP(U_3817,U_3818),U_3816)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3815),U_3816),c_SetInterval_Oord_OgreaterThanLessThan(U_3815,U_3817,U_3818,U_3819))) ) ),
inference(variable_rename,[status(thm)],[f_894_1]) ).
fof(f_894_3,plain,
( ! [U_3829,U_3827,U_3825,U_3823] :
( ! [U_3821] : hBOOL(hAPP(hAPP(c_member(U_3821),U_3823),c_SetInterval_Oord_OgreaterThanLessThan(U_3821,U_3825,U_3827,U_3829)))
| ~ hBOOL(hAPP(hAPP(U_3825,U_3823),U_3829))
| ~ hBOOL(hAPP(hAPP(U_3825,U_3827),U_3823)) )
& ! [U_3828,U_3826,U_3824,U_3822] :
( ! [U_3820] : ~ hBOOL(hAPP(hAPP(c_member(U_3820),U_3822),c_SetInterval_Oord_OgreaterThanLessThan(U_3820,U_3824,U_3826,U_3828)))
| ( hBOOL(hAPP(hAPP(U_3824,U_3822),U_3828))
& hBOOL(hAPP(hAPP(U_3824,U_3826),U_3822)) ) ) ),
inference(miniscope,[status(thm)],[f_894_2]) ).
fof(f_894_4,plain,
( ! [U_3822,U_3824,U_3826,U_3828] :
( hBOOL(hAPP(hAPP(U_3824,U_3822),U_3828))
| ~ sP218(U_3822,U_3824,U_3826,U_3828) )
& ! [U_3822,U_3824,U_3826,U_3828] :
( hBOOL(hAPP(hAPP(U_3824,U_3826),U_3822))
| ~ sP218(U_3822,U_3824,U_3826,U_3828) )
& ! [U_3821,U_3827,U_3829,U_3823,U_3825] :
( hBOOL(hAPP(hAPP(c_member(U_3821),U_3823),c_SetInterval_Oord_OgreaterThanLessThan(U_3821,U_3825,U_3827,U_3829)))
| ~ hBOOL(hAPP(hAPP(U_3825,U_3823),U_3829))
| ~ hBOOL(hAPP(hAPP(U_3825,U_3827),U_3823)) )
& ! [U_3820,U_3822,U_3824,U_3826,U_3828] :
( ~ hBOOL(hAPP(hAPP(c_member(U_3820),U_3822),c_SetInterval_Oord_OgreaterThanLessThan(U_3820,U_3824,U_3826,U_3828)))
| sP218(U_3822,U_3824,U_3826,U_3828) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP218])],[f_894_3]) ).
cnf(f_894_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_3820),U_3822),c_SetInterval_Oord_OgreaterThanLessThan(U_3820,U_3824,U_3826,U_3828)))
| sP218(U_3822,U_3824,U_3826,U_3828) ),
inference(clausify,[status(thm)],[f_894_4]) ).
cnf(f_894_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3821),U_3823),c_SetInterval_Oord_OgreaterThanLessThan(U_3821,U_3825,U_3827,U_3829)))
| ~ hBOOL(hAPP(hAPP(U_3825,U_3823),U_3829))
| ~ hBOOL(hAPP(hAPP(U_3825,U_3827),U_3823)) ),
inference(clausify,[status(thm)],[f_894_4]) ).
cnf(f_894_7,plain,
( hBOOL(hAPP(hAPP(U_3824,U_3826),U_3822))
| ~ sP218(U_3822,U_3824,U_3826,U_3828) ),
inference(clausify,[status(thm)],[f_894_4]) ).
cnf(f_894_8,plain,
( hBOOL(hAPP(hAPP(U_3824,U_3822),U_3828))
| ~ sP218(U_3822,U_3824,U_3826,U_3828) ),
inference(clausify,[status(thm)],[f_894_4]) ).
fof(f_895_1,plain,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_c,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_c),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_c,V_less__eq_2,V_less_2,V_l_2,V_u_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff]) ).
fof(f_895_2,plain,
! [U_3835,U_3834,U_3833,U_3832,U_3831,U_3830] :
( ( hBOOL(hAPP(hAPP(c_member(U_3830),U_3831),c_SetInterval_Oord_OatLeastLessThan(U_3830,U_3832,U_3833,U_3834,U_3835)))
| ~ hBOOL(hAPP(hAPP(U_3833,U_3831),U_3835))
| ~ hBOOL(hAPP(hAPP(U_3832,U_3834),U_3831)) )
& ( ( hBOOL(hAPP(hAPP(U_3833,U_3831),U_3835))
& hBOOL(hAPP(hAPP(U_3832,U_3834),U_3831)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3830),U_3831),c_SetInterval_Oord_OatLeastLessThan(U_3830,U_3832,U_3833,U_3834,U_3835))) ) ),
inference(variable_rename,[status(thm)],[f_895_1]) ).
fof(f_895_3,plain,
( ! [U_3847,U_3845,U_3843,U_3841,U_3839] :
( ! [U_3837] : hBOOL(hAPP(hAPP(c_member(U_3837),U_3839),c_SetInterval_Oord_OatLeastLessThan(U_3837,U_3841,U_3843,U_3845,U_3847)))
| ~ hBOOL(hAPP(hAPP(U_3843,U_3839),U_3847))
| ~ hBOOL(hAPP(hAPP(U_3841,U_3845),U_3839)) )
& ! [U_3846,U_3844,U_3842,U_3840,U_3838] :
( ! [U_3836] : ~ hBOOL(hAPP(hAPP(c_member(U_3836),U_3838),c_SetInterval_Oord_OatLeastLessThan(U_3836,U_3840,U_3842,U_3844,U_3846)))
| ( hBOOL(hAPP(hAPP(U_3842,U_3838),U_3846))
& hBOOL(hAPP(hAPP(U_3840,U_3844),U_3838)) ) ) ),
inference(miniscope,[status(thm)],[f_895_2]) ).
fof(f_895_4,plain,
( ! [U_3838,U_3842,U_3840,U_3844,U_3846] :
( hBOOL(hAPP(hAPP(U_3842,U_3838),U_3846))
| ~ sP219(U_3838,U_3842,U_3840,U_3844,U_3846) )
& ! [U_3838,U_3842,U_3840,U_3844,U_3846] :
( hBOOL(hAPP(hAPP(U_3840,U_3844),U_3838))
| ~ sP219(U_3838,U_3842,U_3840,U_3844,U_3846) )
& ! [U_3841,U_3837,U_3843,U_3839,U_3847,U_3845] :
( hBOOL(hAPP(hAPP(c_member(U_3837),U_3839),c_SetInterval_Oord_OatLeastLessThan(U_3837,U_3841,U_3843,U_3845,U_3847)))
| ~ hBOOL(hAPP(hAPP(U_3843,U_3839),U_3847))
| ~ hBOOL(hAPP(hAPP(U_3841,U_3845),U_3839)) )
& ! [U_3838,U_3836,U_3842,U_3840,U_3844,U_3846] :
( ~ hBOOL(hAPP(hAPP(c_member(U_3836),U_3838),c_SetInterval_Oord_OatLeastLessThan(U_3836,U_3840,U_3842,U_3844,U_3846)))
| sP219(U_3838,U_3842,U_3840,U_3844,U_3846) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219])],[f_895_3]) ).
cnf(f_895_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_3836),U_3838),c_SetInterval_Oord_OatLeastLessThan(U_3836,U_3840,U_3842,U_3844,U_3846)))
| sP219(U_3838,U_3842,U_3840,U_3844,U_3846) ),
inference(clausify,[status(thm)],[f_895_4]) ).
cnf(f_895_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3837),U_3839),c_SetInterval_Oord_OatLeastLessThan(U_3837,U_3841,U_3843,U_3845,U_3847)))
| ~ hBOOL(hAPP(hAPP(U_3843,U_3839),U_3847))
| ~ hBOOL(hAPP(hAPP(U_3841,U_3845),U_3839)) ),
inference(clausify,[status(thm)],[f_895_4]) ).
cnf(f_895_7,plain,
( hBOOL(hAPP(hAPP(U_3840,U_3844),U_3838))
| ~ sP219(U_3838,U_3842,U_3840,U_3844,U_3846) ),
inference(clausify,[status(thm)],[f_895_4]) ).
cnf(f_895_8,plain,
( hBOOL(hAPP(hAPP(U_3842,U_3838),U_3846))
| ~ sP219(U_3838,U_3842,U_3840,U_3844,U_3846) ),
inference(clausify,[status(thm)],[f_895_4]) ).
fof(f_896_1,plain,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_c,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_c),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_c,V_less__eq_2,V_less_2,V_l_2,V_u_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff]) ).
fof(f_896_2,plain,
! [U_3853,U_3852,U_3851,U_3850,U_3849,U_3848] :
( ( hBOOL(hAPP(hAPP(c_member(U_3848),U_3849),c_SetInterval_Oord_OgreaterThanAtMost(U_3848,U_3850,U_3851,U_3852,U_3853)))
| ~ hBOOL(hAPP(hAPP(U_3850,U_3849),U_3853))
| ~ hBOOL(hAPP(hAPP(U_3851,U_3852),U_3849)) )
& ( ( hBOOL(hAPP(hAPP(U_3850,U_3849),U_3853))
& hBOOL(hAPP(hAPP(U_3851,U_3852),U_3849)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3848),U_3849),c_SetInterval_Oord_OgreaterThanAtMost(U_3848,U_3850,U_3851,U_3852,U_3853))) ) ),
inference(variable_rename,[status(thm)],[f_896_1]) ).
fof(f_896_3,plain,
( ! [U_3865,U_3863,U_3861,U_3859,U_3857] :
( ! [U_3855] : hBOOL(hAPP(hAPP(c_member(U_3855),U_3857),c_SetInterval_Oord_OgreaterThanAtMost(U_3855,U_3859,U_3861,U_3863,U_3865)))
| ~ hBOOL(hAPP(hAPP(U_3859,U_3857),U_3865))
| ~ hBOOL(hAPP(hAPP(U_3861,U_3863),U_3857)) )
& ! [U_3864,U_3862,U_3860,U_3858,U_3856] :
( ! [U_3854] : ~ hBOOL(hAPP(hAPP(c_member(U_3854),U_3856),c_SetInterval_Oord_OgreaterThanAtMost(U_3854,U_3858,U_3860,U_3862,U_3864)))
| ( hBOOL(hAPP(hAPP(U_3858,U_3856),U_3864))
& hBOOL(hAPP(hAPP(U_3860,U_3862),U_3856)) ) ) ),
inference(miniscope,[status(thm)],[f_896_2]) ).
fof(f_896_4,plain,
( ! [U_3856,U_3858,U_3860,U_3862,U_3864] :
( hBOOL(hAPP(hAPP(U_3858,U_3856),U_3864))
| ~ sP220(U_3856,U_3858,U_3860,U_3862,U_3864) )
& ! [U_3856,U_3858,U_3860,U_3862,U_3864] :
( hBOOL(hAPP(hAPP(U_3860,U_3862),U_3856))
| ~ sP220(U_3856,U_3858,U_3860,U_3862,U_3864) )
& ! [U_3859,U_3855,U_3861,U_3857,U_3865,U_3863] :
( hBOOL(hAPP(hAPP(c_member(U_3855),U_3857),c_SetInterval_Oord_OgreaterThanAtMost(U_3855,U_3859,U_3861,U_3863,U_3865)))
| ~ hBOOL(hAPP(hAPP(U_3859,U_3857),U_3865))
| ~ hBOOL(hAPP(hAPP(U_3861,U_3863),U_3857)) )
& ! [U_3856,U_3858,U_3860,U_3854,U_3862,U_3864] :
( ~ hBOOL(hAPP(hAPP(c_member(U_3854),U_3856),c_SetInterval_Oord_OgreaterThanAtMost(U_3854,U_3858,U_3860,U_3862,U_3864)))
| sP220(U_3856,U_3858,U_3860,U_3862,U_3864) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP220])],[f_896_3]) ).
cnf(f_896_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_3854),U_3856),c_SetInterval_Oord_OgreaterThanAtMost(U_3854,U_3858,U_3860,U_3862,U_3864)))
| sP220(U_3856,U_3858,U_3860,U_3862,U_3864) ),
inference(clausify,[status(thm)],[f_896_4]) ).
cnf(f_896_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3855),U_3857),c_SetInterval_Oord_OgreaterThanAtMost(U_3855,U_3859,U_3861,U_3863,U_3865)))
| ~ hBOOL(hAPP(hAPP(U_3859,U_3857),U_3865))
| ~ hBOOL(hAPP(hAPP(U_3861,U_3863),U_3857)) ),
inference(clausify,[status(thm)],[f_896_4]) ).
cnf(f_896_7,plain,
( hBOOL(hAPP(hAPP(U_3860,U_3862),U_3856))
| ~ sP220(U_3856,U_3858,U_3860,U_3862,U_3864) ),
inference(clausify,[status(thm)],[f_896_4]) ).
cnf(f_896_8,plain,
( hBOOL(hAPP(hAPP(U_3858,U_3856),U_3864))
| ~ sP220(U_3856,U_3858,U_3860,U_3862,U_3864) ),
inference(clausify,[status(thm)],[f_896_4]) ).
fof(f_897_1,plain,
! [V_c_2,V_b_2,V_a_2,V_S_2,T_c,T_d] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_d),V_c_2),hAPP(c_Finite__Set_Ocard(T_c),V_S_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_d),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__gen__delta]) ).
fof(f_897_2,plain,
! [U_3871,U_3870,U_3869,U_3868,U_3867,U_3866] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3867,U_3866),hAPP(hAPP(c_COMBC(U_3867,U_3866,U_3866),hAPP(hAPP(c_COMBS(U_3867,U_3866,tc_fun(U_3866,U_3866)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3866,tc_fun(U_3866,U_3866)),U_3867),c_If(U_3866)),hAPP(hAPP(c_COMBC(U_3867,U_3867,tc_HOL_Obool),c_fequal),U_3869))),U_3870)),U_3871)),U_3868) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3866),U_3871),hAPP(c_Finite__Set_Ocard(U_3867),U_3868))
| hBOOL(hAPP(hAPP(c_member(U_3867),U_3869),U_3868)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3867,U_3866),hAPP(hAPP(c_COMBC(U_3867,U_3866,U_3866),hAPP(hAPP(c_COMBS(U_3867,U_3866,tc_fun(U_3866,U_3866)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3866,tc_fun(U_3866,U_3866)),U_3867),c_If(U_3866)),hAPP(hAPP(c_COMBC(U_3867,U_3867,tc_HOL_Obool),c_fequal),U_3869))),U_3870)),U_3871)),U_3868) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3866),hAPP(U_3870,U_3869)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3866),U_3871),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3867),U_3868)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3867),U_3869),U_3868)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3867),U_3868))
| ~ class_Groups_Ocomm__monoid__mult(U_3866) ),
inference(variable_rename,[status(thm)],[f_897_1]) ).
fof(f_897_3,plain,
( ! [U_3866,U_3867,U_3868,U_3869,U_3870,U_3871] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3867,U_3866),hAPP(hAPP(c_COMBC(U_3867,U_3866,U_3866),hAPP(hAPP(c_COMBS(U_3867,U_3866,tc_fun(U_3866,U_3866)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3866,tc_fun(U_3866,U_3866)),U_3867),c_If(U_3866)),hAPP(hAPP(c_COMBC(U_3867,U_3867,tc_HOL_Obool),c_fequal),U_3869))),U_3870)),U_3871)),U_3868) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3866),U_3871),hAPP(c_Finite__Set_Ocard(U_3867),U_3868))
| hBOOL(hAPP(hAPP(c_member(U_3867),U_3869),U_3868))
| ~ sP221(U_3866,U_3867,U_3868,U_3869,U_3870,U_3871) )
& ! [U_3866,U_3867,U_3868,U_3869,U_3870,U_3871] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3867,U_3866),hAPP(hAPP(c_COMBC(U_3867,U_3866,U_3866),hAPP(hAPP(c_COMBS(U_3867,U_3866,tc_fun(U_3866,U_3866)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3866,tc_fun(U_3866,U_3866)),U_3867),c_If(U_3866)),hAPP(hAPP(c_COMBC(U_3867,U_3867,tc_HOL_Obool),c_fequal),U_3869))),U_3870)),U_3871)),U_3868) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3866),hAPP(U_3870,U_3869)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3866),U_3871),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3867),U_3868)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3867),U_3869),U_3868))
| ~ sP221(U_3866,U_3867,U_3868,U_3869,U_3870,U_3871) )
& ! [U_3866,U_3867,U_3868,U_3869,U_3870,U_3871] :
( sP221(U_3866,U_3867,U_3868,U_3869,U_3870,U_3871)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3867),U_3868))
| ~ class_Groups_Ocomm__monoid__mult(U_3866) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221])],[f_897_2]) ).
cnf(f_897_4,plain,
( sP221(U_3866,U_3867,U_3868,U_3869,U_3870,U_3871)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3867),U_3868))
| ~ class_Groups_Ocomm__monoid__mult(U_3866) ),
inference(clausify,[status(thm)],[f_897_3]) ).
cnf(f_897_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3867,U_3866),hAPP(hAPP(c_COMBC(U_3867,U_3866,U_3866),hAPP(hAPP(c_COMBS(U_3867,U_3866,tc_fun(U_3866,U_3866)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3866,tc_fun(U_3866,U_3866)),U_3867),c_If(U_3866)),hAPP(hAPP(c_COMBC(U_3867,U_3867,tc_HOL_Obool),c_fequal),U_3869))),U_3870)),U_3871)),U_3868) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3866),hAPP(U_3870,U_3869)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3866),U_3871),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_3867),U_3868)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(U_3867),U_3869),U_3868))
| ~ sP221(U_3866,U_3867,U_3868,U_3869,U_3870,U_3871) ),
inference(clausify,[status(thm)],[f_897_3]) ).
cnf(f_897_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3867,U_3866),hAPP(hAPP(c_COMBC(U_3867,U_3866,U_3866),hAPP(hAPP(c_COMBS(U_3867,U_3866,tc_fun(U_3866,U_3866)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_3866,tc_fun(U_3866,U_3866)),U_3867),c_If(U_3866)),hAPP(hAPP(c_COMBC(U_3867,U_3867,tc_HOL_Obool),c_fequal),U_3869))),U_3870)),U_3871)),U_3868) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3866),U_3871),hAPP(c_Finite__Set_Ocard(U_3867),U_3868))
| hBOOL(hAPP(hAPP(c_member(U_3867),U_3869),U_3868))
| ~ sP221(U_3866,U_3867,U_3868,U_3869,U_3870,U_3871) ),
inference(clausify,[status(thm)],[f_897_3]) ).
fof(f_898_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_898_2,plain,
! [U_3874,U_3873,U_3872] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3872),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3873),U_3874)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3872),U_3873)) ),
inference(variable_rename,[status(thm)],[f_898_1]) ).
fof(f_898_3,plain,
! [U_3873,U_3874,U_3872] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3872),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3873),U_3874)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3872),U_3873)) ),
inference(definitional_conversion,[status(esa)],[f_898_2]) ).
cnf(f_898_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3872),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3873),U_3874)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3872),U_3873)) ),
inference(clausify,[status(thm)],[f_898_3]) ).
fof(f_899_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_899_2,plain,
! [U_3877,U_3876,U_3875] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3877),U_3876)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3875),U_3876)) ),
inference(variable_rename,[status(thm)],[f_899_1]) ).
fof(f_899_3,plain,
! [U_3877,U_3875,U_3876] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3877),U_3876)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3875),U_3876)) ),
inference(definitional_conversion,[status(esa)],[f_899_2]) ).
cnf(f_899_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3875),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3877),U_3876)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3875),U_3876)) ),
inference(clausify,[status(thm)],[f_899_3]) ).
fof(f_900_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_900_2,plain,
! [U_3879,U_3878] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3878),U_3879))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3878),U_3879)) ),
inference(variable_rename,[status(thm)],[f_900_1]) ).
fof(f_900_3,plain,
! [U_3878,U_3879] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3878),U_3879))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3878),U_3879)) ),
inference(definitional_conversion,[status(esa)],[f_900_2]) ).
cnf(f_900_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3878),U_3879))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3878),U_3879)) ),
inference(clausify,[status(thm)],[f_900_3]) ).
fof(f_901_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_901_2,plain,
! [U_3882,U_3881,U_3880] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3880),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3882),U_3881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3880),U_3881)) ),
inference(variable_rename,[status(thm)],[f_901_1]) ).
fof(f_901_3,plain,
! [U_3880,U_3881,U_3882] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3880),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3882),U_3881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3880),U_3881)) ),
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_3880),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3882),U_3881)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3880),U_3881)) ),
inference(clausify,[status(thm)],[f_901_3]) ).
fof(f_902_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_902_2,plain,
! [U_3885,U_3884,U_3883] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3883),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3884),U_3885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3883),U_3884)) ),
inference(variable_rename,[status(thm)],[f_902_1]) ).
fof(f_902_3,plain,
! [U_3883,U_3884,U_3885] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3883),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3884),U_3885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3883),U_3884)) ),
inference(definitional_conversion,[status(esa)],[f_902_2]) ).
cnf(f_902_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3883),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3884),U_3885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3883),U_3884)) ),
inference(clausify,[status(thm)],[f_902_3]) ).
fof(f_903_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) = V_x_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)))) != 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))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove]) ).
fof(f_903_2,plain,
! [U_3888,U_3887,U_3886] :
( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_3886,U_3887) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3886),U_3888),c_Big__Operators_Olattice__class_OSup__fin(U_3886,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3886,tc_HOL_Obool)),U_3887),hAPP(hAPP(c_Set_Oinsert(U_3886),U_3888),c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3886,tc_HOL_Obool)),U_3887),hAPP(hAPP(c_Set_Oinsert(U_3886),U_3888),c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(U_3886,U_3887) = U_3888
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3886,tc_HOL_Obool)),U_3887),hAPP(hAPP(c_Set_Oinsert(U_3886),U_3888),c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_3886),U_3888),U_3887))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3886),U_3887))
| ~ class_Lattices_Olattice(U_3886) ),
inference(variable_rename,[status(thm)],[f_903_1]) ).
fof(f_903_3,plain,
( ! [U_3886,U_3887,U_3888] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3886,U_3887) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3886),U_3888),c_Big__Operators_Olattice__class_OSup__fin(U_3886,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3886,tc_HOL_Obool)),U_3887),hAPP(hAPP(c_Set_Oinsert(U_3886),U_3888),c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3886,tc_HOL_Obool)),U_3887),hAPP(hAPP(c_Set_Oinsert(U_3886),U_3888),c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool))
| ~ sP222(U_3886,U_3887,U_3888) )
& ! [U_3886,U_3887,U_3888] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3886,U_3887) = U_3888
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3886,tc_HOL_Obool)),U_3887),hAPP(hAPP(c_Set_Oinsert(U_3886),U_3888),c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool))
| ~ sP222(U_3886,U_3887,U_3888) )
& ! [U_3886,U_3887,U_3888] :
( sP222(U_3886,U_3887,U_3888)
| ~ hBOOL(hAPP(hAPP(c_member(U_3886),U_3888),U_3887))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3886),U_3887))
| ~ class_Lattices_Olattice(U_3886) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP222])],[f_903_2]) ).
cnf(f_903_4,plain,
( sP222(U_3886,U_3887,U_3888)
| ~ hBOOL(hAPP(hAPP(c_member(U_3886),U_3888),U_3887))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3886),U_3887))
| ~ class_Lattices_Olattice(U_3886) ),
inference(clausify,[status(thm)],[f_903_3]) ).
cnf(f_903_5,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3886,U_3887) = U_3888
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3886,tc_HOL_Obool)),U_3887),hAPP(hAPP(c_Set_Oinsert(U_3886),U_3888),c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool))
| ~ sP222(U_3886,U_3887,U_3888) ),
inference(clausify,[status(thm)],[f_903_3]) ).
cnf(f_903_6,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3886,U_3887) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3886),U_3888),c_Big__Operators_Olattice__class_OSup__fin(U_3886,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3886,tc_HOL_Obool)),U_3887),hAPP(hAPP(c_Set_Oinsert(U_3886),U_3888),c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3886,tc_HOL_Obool)),U_3887),hAPP(hAPP(c_Set_Oinsert(U_3886),U_3888),c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3886,tc_HOL_Obool))
| ~ sP222(U_3886,U_3887,U_3888) ),
inference(clausify,[status(thm)],[f_903_3]) ).
fof(f_904_1,plain,
! [V_x_2,T_c] : hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_iso__tuple__UNIV__I]) ).
fof(f_904_2,plain,
! [U_3890,U_3889] : hBOOL(hAPP(hAPP(c_member(U_3889),U_3890),c_Orderings_Otop__class_Otop(tc_fun(U_3889,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_904_1]) ).
fof(f_904_3,plain,
! [U_3890,U_3889] : hBOOL(hAPP(hAPP(c_member(U_3889),U_3890),c_Orderings_Otop__class_Otop(tc_fun(U_3889,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_904_2]) ).
cnf(f_904_4,plain,
hBOOL(hAPP(hAPP(c_member(U_3889),U_3890),c_Orderings_Otop__class_Otop(tc_fun(U_3889,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_904_3]) ).
fof(f_905_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_905_2,plain,
! [U_3894,U_3893,U_3892,U_3891] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3891),U_3892),U_3893)),U_3894) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3891),hAPP(hAPP(c_Power_Opower__class_Opower(U_3891),U_3892),U_3894)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3891),U_3893),U_3894))
| ~ class_Rings_Ocomm__semiring__1(U_3891) ),
inference(variable_rename,[status(thm)],[f_905_1]) ).
fof(f_905_3,plain,
! [U_3891,U_3892,U_3894,U_3893] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3891),U_3892),U_3893)),U_3894) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3891),hAPP(hAPP(c_Power_Opower__class_Opower(U_3891),U_3892),U_3894)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3891),U_3893),U_3894))
| ~ class_Rings_Ocomm__semiring__1(U_3891) ),
inference(definitional_conversion,[status(esa)],[f_905_2]) ).
cnf(f_905_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3891),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3891),U_3892),U_3893)),U_3894) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3891),hAPP(hAPP(c_Power_Opower__class_Opower(U_3891),U_3892),U_3894)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3891),U_3893),U_3894))
| ~ class_Rings_Ocomm__semiring__1(U_3891) ),
inference(clausify,[status(thm)],[f_905_3]) ).
fof(f_906_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_906_2,plain,
! [U_3898,U_3897,U_3896,U_3895] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3895),hAPP(hAPP(c_Power_Opower__class_Opower(U_3895),U_3896),U_3897)),U_3898) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3895),U_3896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3897),U_3898))
| ~ class_Rings_Ocomm__semiring__1(U_3895) ),
inference(variable_rename,[status(thm)],[f_906_1]) ).
fof(f_906_3,plain,
! [U_3895,U_3896,U_3897,U_3898] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3895),hAPP(hAPP(c_Power_Opower__class_Opower(U_3895),U_3896),U_3897)),U_3898) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3895),U_3896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3897),U_3898))
| ~ class_Rings_Ocomm__semiring__1(U_3895) ),
inference(definitional_conversion,[status(esa)],[f_906_2]) ).
cnf(f_906_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3895),hAPP(hAPP(c_Power_Opower__class_Opower(U_3895),U_3896),U_3897)),U_3898) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3895),U_3896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3897),U_3898))
| ~ class_Rings_Ocomm__semiring__1(U_3895) ),
inference(clausify,[status(thm)],[f_906_3]) ).
fof(f_907_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_907_2,plain,
! [U_3900,U_3899] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3899),U_3900),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3900
| ~ class_Rings_Ocomm__semiring__1(U_3899) ),
inference(variable_rename,[status(thm)],[f_907_1]) ).
fof(f_907_3,plain,
! [U_3900,U_3899] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3899),U_3900),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3900
| ~ class_Rings_Ocomm__semiring__1(U_3899) ),
inference(definitional_conversion,[status(esa)],[f_907_2]) ).
cnf(f_907_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3899),U_3900),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3900
| ~ class_Rings_Ocomm__semiring__1(U_3899) ),
inference(clausify,[status(thm)],[f_907_3]) ).
fof(f_908_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_908_2,plain,
! [U_3904,U_3903,U_3902,U_3901] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3901),hAPP(hAPP(c_Power_Opower__class_Opower(U_3901),U_3902),U_3903)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3901),U_3902),U_3904)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3901),U_3902),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3903),U_3904))
| ~ class_Rings_Ocomm__semiring__1(U_3901) ),
inference(variable_rename,[status(thm)],[f_908_1]) ).
fof(f_908_3,plain,
! [U_3901,U_3902,U_3903,U_3904] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3901),hAPP(hAPP(c_Power_Opower__class_Opower(U_3901),U_3902),U_3903)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3901),U_3902),U_3904)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3901),U_3902),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3903),U_3904))
| ~ class_Rings_Ocomm__semiring__1(U_3901) ),
inference(definitional_conversion,[status(esa)],[f_908_2]) ).
cnf(f_908_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3901),hAPP(hAPP(c_Power_Opower__class_Opower(U_3901),U_3902),U_3903)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3901),U_3902),U_3904)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3901),U_3902),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3903),U_3904))
| ~ class_Rings_Ocomm__semiring__1(U_3901) ),
inference(clausify,[status(thm)],[f_908_3]) ).
fof(f_909_1,plain,
! [V_x_2,T_c] :
( c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osingleton]) ).
fof(f_909_2,plain,
! [U_3906,U_3905] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3905,hAPP(hAPP(c_Set_Oinsert(U_3905),U_3906),c_Orderings_Obot__class_Obot(tc_fun(U_3905,tc_HOL_Obool)))) = U_3906
| ~ class_Lattices_Olattice(U_3905) ),
inference(variable_rename,[status(thm)],[f_909_1]) ).
fof(f_909_3,plain,
! [U_3905,U_3906] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3905,hAPP(hAPP(c_Set_Oinsert(U_3905),U_3906),c_Orderings_Obot__class_Obot(tc_fun(U_3905,tc_HOL_Obool)))) = U_3906
| ~ class_Lattices_Olattice(U_3905) ),
inference(definitional_conversion,[status(esa)],[f_909_2]) ).
cnf(f_909_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3905,hAPP(hAPP(c_Set_Oinsert(U_3905),U_3906),c_Orderings_Obot__class_Obot(tc_fun(U_3905,tc_HOL_Obool)))) = U_3906
| ~ class_Lattices_Olattice(U_3905) ),
inference(clausify,[status(thm)],[f_909_3]) ).
fof(f_910_1,plain,
! [V_y_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(c_COMBK(T_d,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_d),V_y_2),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__constant]) ).
fof(f_910_2,plain,
! [U_3910,U_3909,U_3908,U_3907] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3908,U_3907),hAPP(c_COMBK(U_3907,U_3908),U_3910)),U_3909) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3907),U_3910),hAPP(c_Finite__Set_Ocard(U_3908),U_3909))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3908),U_3909))
| ~ class_Groups_Ocomm__monoid__mult(U_3907) ),
inference(variable_rename,[status(thm)],[f_910_1]) ).
fof(f_910_3,plain,
! [U_3907,U_3908,U_3909,U_3910] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3908,U_3907),hAPP(c_COMBK(U_3907,U_3908),U_3910)),U_3909) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3907),U_3910),hAPP(c_Finite__Set_Ocard(U_3908),U_3909))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3908),U_3909))
| ~ class_Groups_Ocomm__monoid__mult(U_3907) ),
inference(definitional_conversion,[status(esa)],[f_910_2]) ).
cnf(f_910_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_3908,U_3907),hAPP(c_COMBK(U_3907,U_3908),U_3910)),U_3909) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3907),U_3910),hAPP(c_Finite__Set_Ocard(U_3908),U_3909))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3908),U_3909))
| ~ class_Groups_Ocomm__monoid__mult(U_3907) ),
inference(clausify,[status(thm)],[f_910_3]) ).
fof(f_911_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,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))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oin__idem]) ).
fof(f_911_2,plain,
! [U_3913,U_3912,U_3911] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3911),U_3913),c_Big__Operators_Olattice__class_OSup__fin(U_3911,U_3912)) = c_Big__Operators_Olattice__class_OSup__fin(U_3911,U_3912)
| ~ hBOOL(hAPP(hAPP(c_member(U_3911),U_3913),U_3912))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3911),U_3912))
| ~ class_Lattices_Olattice(U_3911) ),
inference(variable_rename,[status(thm)],[f_911_1]) ).
fof(f_911_3,plain,
! [U_3911,U_3912,U_3913] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3911),U_3913),c_Big__Operators_Olattice__class_OSup__fin(U_3911,U_3912)) = c_Big__Operators_Olattice__class_OSup__fin(U_3911,U_3912)
| ~ hBOOL(hAPP(hAPP(c_member(U_3911),U_3913),U_3912))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3911),U_3912))
| ~ class_Lattices_Olattice(U_3911) ),
inference(definitional_conversion,[status(esa)],[f_911_2]) ).
cnf(f_911_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3911),U_3913),c_Big__Operators_Olattice__class_OSup__fin(U_3911,U_3912)) = c_Big__Operators_Olattice__class_OSup__fin(U_3911,U_3912)
| ~ hBOOL(hAPP(hAPP(c_member(U_3911),U_3913),U_3912))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3911),U_3912))
| ~ class_Lattices_Olattice(U_3911) ),
inference(clausify,[status(thm)],[f_911_3]) ).
fof(f_912_1,plain,
! [V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq]) ).
fof(f_912_2,plain,
! [U_3915,U_3914] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3914,U_3915) = hAPP(c_Finite__Set_Ofold1(U_3914,c_Lattices_Osemilattice__sup__class_Osup(U_3914)),U_3915)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3914),U_3915))
| ~ class_Lattices_Olattice(U_3914) ),
inference(variable_rename,[status(thm)],[f_912_1]) ).
fof(f_912_3,plain,
! [U_3915,U_3914] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3914,U_3915) = hAPP(c_Finite__Set_Ofold1(U_3914,c_Lattices_Osemilattice__sup__class_Osup(U_3914)),U_3915)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3914),U_3915))
| ~ class_Lattices_Olattice(U_3914) ),
inference(definitional_conversion,[status(esa)],[f_912_2]) ).
cnf(f_912_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3914,U_3915) = hAPP(c_Finite__Set_Ofold1(U_3914,c_Lattices_Osemilattice__sup__class_Osup(U_3914)),U_3915)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3914),U_3915))
| ~ class_Lattices_Olattice(U_3914) ),
inference(clausify,[status(thm)],[f_912_3]) ).
fof(f_913_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__idem]) ).
fof(f_913_2,plain,
! [U_3918,U_3917,U_3916] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3916,hAPP(hAPP(c_Set_Oinsert(U_3916),U_3918),U_3917)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3916),U_3918),c_Big__Operators_Olattice__class_OSup__fin(U_3916,U_3917))
| U_3917 = c_Orderings_Obot__class_Obot(tc_fun(U_3916,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3916),U_3917))
| ~ class_Lattices_Olattice(U_3916) ),
inference(variable_rename,[status(thm)],[f_913_1]) ).
fof(f_913_3,plain,
! [U_3916,U_3917,U_3918] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3916,hAPP(hAPP(c_Set_Oinsert(U_3916),U_3918),U_3917)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3916),U_3918),c_Big__Operators_Olattice__class_OSup__fin(U_3916,U_3917))
| U_3917 = c_Orderings_Obot__class_Obot(tc_fun(U_3916,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3916),U_3917))
| ~ class_Lattices_Olattice(U_3916) ),
inference(definitional_conversion,[status(esa)],[f_913_2]) ).
cnf(f_913_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3916,hAPP(hAPP(c_Set_Oinsert(U_3916),U_3918),U_3917)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3916),U_3918),c_Big__Operators_Olattice__class_OSup__fin(U_3916,U_3917))
| U_3917 = c_Orderings_Obot__class_Obot(tc_fun(U_3916,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3916),U_3917))
| ~ class_Lattices_Olattice(U_3916) ),
inference(clausify,[status(thm)],[f_913_3]) ).
fof(f_914_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osubset__idem]) ).
fof(f_914_2,plain,
! [U_3921,U_3920,U_3919] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3919),c_Big__Operators_Olattice__class_OSup__fin(U_3919,U_3921)),c_Big__Operators_Olattice__class_OSup__fin(U_3919,U_3920)) = c_Big__Operators_Olattice__class_OSup__fin(U_3919,U_3920)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3919,tc_HOL_Obool)),U_3921),U_3920))
| U_3921 = c_Orderings_Obot__class_Obot(tc_fun(U_3919,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3919),U_3920))
| ~ class_Lattices_Olattice(U_3919) ),
inference(variable_rename,[status(thm)],[f_914_1]) ).
fof(f_914_3,plain,
! [U_3919,U_3920,U_3921] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3919),c_Big__Operators_Olattice__class_OSup__fin(U_3919,U_3921)),c_Big__Operators_Olattice__class_OSup__fin(U_3919,U_3920)) = c_Big__Operators_Olattice__class_OSup__fin(U_3919,U_3920)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3919,tc_HOL_Obool)),U_3921),U_3920))
| U_3921 = c_Orderings_Obot__class_Obot(tc_fun(U_3919,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3919),U_3920))
| ~ class_Lattices_Olattice(U_3919) ),
inference(definitional_conversion,[status(esa)],[f_914_2]) ).
cnf(f_914_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3919),c_Big__Operators_Olattice__class_OSup__fin(U_3919,U_3921)),c_Big__Operators_Olattice__class_OSup__fin(U_3919,U_3920)) = c_Big__Operators_Olattice__class_OSup__fin(U_3919,U_3920)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3919,tc_HOL_Obool)),U_3921),U_3920))
| U_3921 = c_Orderings_Obot__class_Obot(tc_fun(U_3919,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3919),U_3920))
| ~ class_Lattices_Olattice(U_3919) ),
inference(clausify,[status(thm)],[f_914_3]) ).
fof(f_915_1,plain,
! [V_B_2,V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OSup__fin(T_c,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(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,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_c),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__idem]) ).
fof(f_915_2,plain,
! [U_3924,U_3923,U_3922] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3922,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3922,tc_HOL_Obool)),U_3923),U_3924)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3922),c_Big__Operators_Olattice__class_OSup__fin(U_3922,U_3923)),c_Big__Operators_Olattice__class_OSup__fin(U_3922,U_3924))
| U_3924 = c_Orderings_Obot__class_Obot(tc_fun(U_3922,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3922),U_3924))
| U_3923 = c_Orderings_Obot__class_Obot(tc_fun(U_3922,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3922),U_3923))
| ~ class_Lattices_Olattice(U_3922) ),
inference(variable_rename,[status(thm)],[f_915_1]) ).
fof(f_915_3,plain,
! [U_3922,U_3923,U_3924] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3922,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3922,tc_HOL_Obool)),U_3923),U_3924)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3922),c_Big__Operators_Olattice__class_OSup__fin(U_3922,U_3923)),c_Big__Operators_Olattice__class_OSup__fin(U_3922,U_3924))
| U_3924 = c_Orderings_Obot__class_Obot(tc_fun(U_3922,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3922),U_3924))
| U_3923 = c_Orderings_Obot__class_Obot(tc_fun(U_3922,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3922),U_3923))
| ~ class_Lattices_Olattice(U_3922) ),
inference(definitional_conversion,[status(esa)],[f_915_2]) ).
cnf(f_915_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3922,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3922,tc_HOL_Obool)),U_3923),U_3924)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3922),c_Big__Operators_Olattice__class_OSup__fin(U_3922,U_3923)),c_Big__Operators_Olattice__class_OSup__fin(U_3922,U_3924))
| U_3924 = c_Orderings_Obot__class_Obot(tc_fun(U_3922,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3922),U_3924))
| U_3923 = c_Orderings_Obot__class_Obot(tc_fun(U_3922,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3922),U_3923))
| ~ class_Lattices_Olattice(U_3922) ),
inference(clausify,[status(thm)],[f_915_3]) ).
fof(f_916_1,plain,
! [V_a_2,V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H]) ).
fof(f_916_2,plain,
! [U_3927,U_3926,U_3925] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3925,hAPP(hAPP(c_Set_Oinsert(U_3925),U_3927),U_3926)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3925,U_3925,c_Lattices_Osemilattice__sup__class_Osup(U_3925)),U_3927),U_3926)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3925),U_3926))
| ~ class_Lattices_Olattice(U_3925) ),
inference(variable_rename,[status(thm)],[f_916_1]) ).
fof(f_916_3,plain,
! [U_3927,U_3926,U_3925] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3925,hAPP(hAPP(c_Set_Oinsert(U_3925),U_3927),U_3926)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3925,U_3925,c_Lattices_Osemilattice__sup__class_Osup(U_3925)),U_3927),U_3926)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3925),U_3926))
| ~ class_Lattices_Olattice(U_3925) ),
inference(definitional_conversion,[status(esa)],[f_916_2]) ).
cnf(f_916_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3925,hAPP(hAPP(c_Set_Oinsert(U_3925),U_3927),U_3926)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3925,U_3925,c_Lattices_Osemilattice__sup__class_Osup(U_3925)),U_3927),U_3926)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3925),U_3926))
| ~ class_Lattices_Olattice(U_3925) ),
inference(clausify,[status(thm)],[f_916_3]) ).
fof(f_917_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2))
| V_A_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))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert]) ).
fof(f_917_2,plain,
! [U_3930,U_3929,U_3928] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3928,hAPP(hAPP(c_Set_Oinsert(U_3928),U_3930),U_3929)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3928),U_3930),c_Big__Operators_Olattice__class_OSup__fin(U_3928,U_3929))
| U_3929 = c_Orderings_Obot__class_Obot(tc_fun(U_3928,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_3928),U_3930),U_3929))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3928),U_3929))
| ~ class_Lattices_Olattice(U_3928) ),
inference(variable_rename,[status(thm)],[f_917_1]) ).
fof(f_917_3,plain,
! [U_3928,U_3929,U_3930] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3928,hAPP(hAPP(c_Set_Oinsert(U_3928),U_3930),U_3929)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3928),U_3930),c_Big__Operators_Olattice__class_OSup__fin(U_3928,U_3929))
| U_3929 = c_Orderings_Obot__class_Obot(tc_fun(U_3928,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_3928),U_3930),U_3929))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3928),U_3929))
| ~ class_Lattices_Olattice(U_3928) ),
inference(definitional_conversion,[status(esa)],[f_917_2]) ).
cnf(f_917_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3928,hAPP(hAPP(c_Set_Oinsert(U_3928),U_3930),U_3929)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3928),U_3930),c_Big__Operators_Olattice__class_OSup__fin(U_3928,U_3929))
| U_3929 = c_Orderings_Obot__class_Obot(tc_fun(U_3928,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_3928),U_3930),U_3929))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3928),U_3929))
| ~ class_Lattices_Olattice(U_3928) ),
inference(clausify,[status(thm)],[f_917_3]) ).
fof(f_918_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__remove]) ).
fof(f_918_2,plain,
! [U_3933,U_3932,U_3931] :
( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_3931,hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),U_3932)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3931),U_3933),c_Big__Operators_Olattice__class_OSup__fin(U_3931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3931,tc_HOL_Obool)),U_3932),hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3931,tc_HOL_Obool)),U_3932),hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(U_3931,hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),U_3932)) = U_3933
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3931,tc_HOL_Obool)),U_3932),hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3931),U_3932))
| ~ class_Lattices_Olattice(U_3931) ),
inference(variable_rename,[status(thm)],[f_918_1]) ).
fof(f_918_3,plain,
( ! [U_3931,U_3932,U_3933] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3931,hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),U_3932)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3931),U_3933),c_Big__Operators_Olattice__class_OSup__fin(U_3931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3931,tc_HOL_Obool)),U_3932),hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3931,tc_HOL_Obool)),U_3932),hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool))
| ~ sP223(U_3931,U_3932,U_3933) )
& ! [U_3931,U_3932,U_3933] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3931,hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),U_3932)) = U_3933
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3931,tc_HOL_Obool)),U_3932),hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool))
| ~ sP223(U_3931,U_3932,U_3933) )
& ! [U_3931,U_3932,U_3933] :
( sP223(U_3931,U_3932,U_3933)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3931),U_3932))
| ~ class_Lattices_Olattice(U_3931) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP223])],[f_918_2]) ).
cnf(f_918_4,plain,
( sP223(U_3931,U_3932,U_3933)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3931),U_3932))
| ~ class_Lattices_Olattice(U_3931) ),
inference(clausify,[status(thm)],[f_918_3]) ).
cnf(f_918_5,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3931,hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),U_3932)) = U_3933
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3931,tc_HOL_Obool)),U_3932),hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool))
| ~ sP223(U_3931,U_3932,U_3933) ),
inference(clausify,[status(thm)],[f_918_3]) ).
cnf(f_918_6,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3931,hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),U_3932)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3931),U_3933),c_Big__Operators_Olattice__class_OSup__fin(U_3931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3931,tc_HOL_Obool)),U_3932),hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3931,tc_HOL_Obool)),U_3932),hAPP(hAPP(c_Set_Oinsert(U_3931),U_3933),c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3931,tc_HOL_Obool))
| ~ sP223(U_3931,U_3932,U_3933) ),
inference(clausify,[status(thm)],[f_918_3]) ).
fof(f_919_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_x_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))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold_H]) ).
fof(f_919_2,plain,
! [U_3936,U_3935,U_3934] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3934,hAPP(hAPP(c_Set_Oinsert(U_3934),U_3936),U_3935)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3934,U_3934,c_Lattices_Osemilattice__sup__class_Osup(U_3934)),U_3936),U_3935)
| hBOOL(hAPP(hAPP(c_member(U_3934),U_3936),U_3935))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3934),U_3935))
| ~ class_Lattices_Olattice(U_3934) ),
inference(variable_rename,[status(thm)],[f_919_1]) ).
fof(f_919_3,plain,
! [U_3934,U_3935,U_3936] :
( c_Big__Operators_Olattice__class_OSup__fin(U_3934,hAPP(hAPP(c_Set_Oinsert(U_3934),U_3936),U_3935)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3934,U_3934,c_Lattices_Osemilattice__sup__class_Osup(U_3934)),U_3936),U_3935)
| hBOOL(hAPP(hAPP(c_member(U_3934),U_3936),U_3935))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3934),U_3935))
| ~ class_Lattices_Olattice(U_3934) ),
inference(definitional_conversion,[status(esa)],[f_919_2]) ).
cnf(f_919_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_3934,hAPP(hAPP(c_Set_Oinsert(U_3934),U_3936),U_3935)) = hAPP(hAPP(c_Finite__Set_Ofold(U_3934,U_3934,c_Lattices_Osemilattice__sup__class_Osup(U_3934)),U_3936),U_3935)
| hBOOL(hAPP(hAPP(c_member(U_3934),U_3936),U_3935))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3934),U_3935))
| ~ class_Lattices_Olattice(U_3934) ),
inference(clausify,[status(thm)],[f_919_3]) ).
fof(f_920_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_920_2,plain,
! [U_3940,U_3939,U_3938,U_3937] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3939),U_3940))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3937),hAPP(hAPP(c_Power_Opower__class_Opower(U_3937),U_3938),U_3939)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3937),U_3938),U_3940)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3937),c_Groups_Oone__class_Oone(U_3937)),U_3938))
| ~ class_Rings_Olinordered__semidom(U_3937) ),
inference(variable_rename,[status(thm)],[f_920_1]) ).
fof(f_920_3,plain,
! [U_3937,U_3938,U_3939,U_3940] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3939),U_3940))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3937),hAPP(hAPP(c_Power_Opower__class_Opower(U_3937),U_3938),U_3939)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3937),U_3938),U_3940)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3937),c_Groups_Oone__class_Oone(U_3937)),U_3938))
| ~ class_Rings_Olinordered__semidom(U_3937) ),
inference(definitional_conversion,[status(esa)],[f_920_2]) ).
cnf(f_920_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3939),U_3940))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3937),hAPP(hAPP(c_Power_Opower__class_Opower(U_3937),U_3938),U_3939)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3937),U_3938),U_3940)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3937),c_Groups_Oone__class_Oone(U_3937)),U_3938))
| ~ class_Rings_Olinordered__semidom(U_3937) ),
inference(clausify,[status(thm)],[f_920_3]) ).
fof(f_921_1,plain,
! [V_y_2,V_x_2,V_b_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_b_2),V_y_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Oone__class_Oone(T_c)),V_b_2))
| ~ class_Rings_Olinordered__semidom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing__iff]) ).
fof(f_921_2,plain,
! [U_3944,U_3943,U_3942,U_3941] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3941),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3943)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3944)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3943),U_3944)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3943),U_3944))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3941),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3943)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3944))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3941),c_Groups_Oone__class_Oone(U_3941)),U_3942))
| ~ class_Rings_Olinordered__semidom(U_3941) ),
inference(variable_rename,[status(thm)],[f_921_1]) ).
fof(f_921_3,plain,
( ! [U_3942,U_3941,U_3943,U_3944] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3941),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3943)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3944)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3943),U_3944))
| ~ sP224(U_3942,U_3941,U_3943,U_3944) )
& ! [U_3942,U_3941,U_3943,U_3944] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3943),U_3944))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3941),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3943)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3944)))
| ~ sP224(U_3942,U_3941,U_3943,U_3944) )
& ! [U_3942,U_3941,U_3943,U_3944] :
( sP224(U_3942,U_3941,U_3943,U_3944)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3941),c_Groups_Oone__class_Oone(U_3941)),U_3942))
| ~ class_Rings_Olinordered__semidom(U_3941) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP224])],[f_921_2]) ).
cnf(f_921_4,plain,
( sP224(U_3942,U_3941,U_3943,U_3944)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3941),c_Groups_Oone__class_Oone(U_3941)),U_3942))
| ~ class_Rings_Olinordered__semidom(U_3941) ),
inference(clausify,[status(thm)],[f_921_3]) ).
cnf(f_921_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3943),U_3944))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3941),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3943)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3944)))
| ~ sP224(U_3942,U_3941,U_3943,U_3944) ),
inference(clausify,[status(thm)],[f_921_3]) ).
cnf(f_921_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3941),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3943)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3941),U_3942),U_3944)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3943),U_3944))
| ~ sP224(U_3942,U_3941,U_3943,U_3944) ),
inference(clausify,[status(thm)],[f_921_3]) ).
fof(f_922_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_922_2,plain,
! [U_3947,U_3946,U_3945] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3945),hAPP(c_Groups_Ouminus__class_Ouminus(U_3945),U_3946)),U_3947) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3945),hAPP(hAPP(c_Power_Opower__class_Opower(U_3945),hAPP(c_Groups_Ouminus__class_Ouminus(U_3945),c_Groups_Oone__class_Oone(U_3945))),U_3947)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3945),U_3946),U_3947))
| ~ class_Rings_Oring__1(U_3945) ),
inference(variable_rename,[status(thm)],[f_922_1]) ).
fof(f_922_3,plain,
! [U_3945,U_3946,U_3947] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3945),hAPP(c_Groups_Ouminus__class_Ouminus(U_3945),U_3946)),U_3947) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3945),hAPP(hAPP(c_Power_Opower__class_Opower(U_3945),hAPP(c_Groups_Ouminus__class_Ouminus(U_3945),c_Groups_Oone__class_Oone(U_3945))),U_3947)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3945),U_3946),U_3947))
| ~ class_Rings_Oring__1(U_3945) ),
inference(definitional_conversion,[status(esa)],[f_922_2]) ).
cnf(f_922_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3945),hAPP(c_Groups_Ouminus__class_Ouminus(U_3945),U_3946)),U_3947) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3945),hAPP(hAPP(c_Power_Opower__class_Opower(U_3945),hAPP(c_Groups_Ouminus__class_Ouminus(U_3945),c_Groups_Oone__class_Oone(U_3945))),U_3947)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3945),U_3946),U_3947))
| ~ class_Rings_Oring__1(U_3945) ),
inference(clausify,[status(thm)],[f_922_3]) ).
fof(f_923_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_923_2,plain,
! [U_3951,U_3950,U_3949,U_3948] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3948),hAPP(hAPP(c_Power_Opower__class_Opower(U_3948),U_3951),U_3949)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3948),U_3951),U_3950)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3948),c_Groups_Oone__class_Oone(U_3948)),U_3951))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3949),U_3950))
| ~ class_Rings_Olinordered__semidom(U_3948) ),
inference(variable_rename,[status(thm)],[f_923_1]) ).
fof(f_923_3,plain,
! [U_3948,U_3949,U_3950,U_3951] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3948),hAPP(hAPP(c_Power_Opower__class_Opower(U_3948),U_3951),U_3949)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3948),U_3951),U_3950)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3948),c_Groups_Oone__class_Oone(U_3948)),U_3951))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3949),U_3950))
| ~ class_Rings_Olinordered__semidom(U_3948) ),
inference(definitional_conversion,[status(esa)],[f_923_2]) ).
cnf(f_923_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3948),hAPP(hAPP(c_Power_Opower__class_Opower(U_3948),U_3951),U_3949)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3948),U_3951),U_3950)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3948),c_Groups_Oone__class_Oone(U_3948)),U_3951))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3949),U_3950))
| ~ class_Rings_Olinordered__semidom(U_3948) ),
inference(clausify,[status(thm)],[f_923_3]) ).
fof(f_924_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_924_2,plain,
! [U_3955,U_3954,U_3953,U_3952] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3952),hAPP(hAPP(c_Power_Opower__class_Opower(U_3952),U_3955),U_3953)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3952),U_3955),U_3954)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3952),c_Groups_Oone__class_Oone(U_3952)),U_3955))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3953),U_3954))
| ~ class_Rings_Olinordered__semidom(U_3952) ),
inference(variable_rename,[status(thm)],[f_924_1]) ).
fof(f_924_3,plain,
! [U_3952,U_3953,U_3954,U_3955] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3952),hAPP(hAPP(c_Power_Opower__class_Opower(U_3952),U_3955),U_3953)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3952),U_3955),U_3954)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3952),c_Groups_Oone__class_Oone(U_3952)),U_3955))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3953),U_3954))
| ~ class_Rings_Olinordered__semidom(U_3952) ),
inference(definitional_conversion,[status(esa)],[f_924_2]) ).
cnf(f_924_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3952),hAPP(hAPP(c_Power_Opower__class_Opower(U_3952),U_3955),U_3953)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3952),U_3955),U_3954)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3952),c_Groups_Oone__class_Oone(U_3952)),U_3955))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3953),U_3954))
| ~ class_Rings_Olinordered__semidom(U_3952) ),
inference(clausify,[status(thm)],[f_924_3]) ).
fof(f_925_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_925_2,plain,
! [U_3959,U_3958,U_3957,U_3956] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3958),U_3959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3956),hAPP(hAPP(c_Power_Opower__class_Opower(U_3956),U_3957),U_3958)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3956),U_3957),U_3959)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3956),c_Groups_Oone__class_Oone(U_3956)),U_3957))
| ~ class_Rings_Olinordered__semidom(U_3956) ),
inference(variable_rename,[status(thm)],[f_925_1]) ).
fof(f_925_3,plain,
! [U_3956,U_3957,U_3958,U_3959] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3958),U_3959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3956),hAPP(hAPP(c_Power_Opower__class_Opower(U_3956),U_3957),U_3958)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3956),U_3957),U_3959)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3956),c_Groups_Oone__class_Oone(U_3956)),U_3957))
| ~ class_Rings_Olinordered__semidom(U_3956) ),
inference(definitional_conversion,[status(esa)],[f_925_2]) ).
cnf(f_925_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3958),U_3959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3956),hAPP(hAPP(c_Power_Opower__class_Opower(U_3956),U_3957),U_3958)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3956),U_3957),U_3959)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3956),c_Groups_Oone__class_Oone(U_3956)),U_3957))
| ~ class_Rings_Olinordered__semidom(U_3956) ),
inference(clausify,[status(thm)],[f_925_3]) ).
fof(f_926_1,plain,
! [V_y_2,V_x_2,V_b_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_b_2),V_y_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Oone__class_Oone(T_c)),V_b_2))
| ~ class_Rings_Olinordered__semidom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff]) ).
fof(f_926_2,plain,
! [U_3963,U_3962,U_3961,U_3960] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3960),hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),U_3962)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),U_3963)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3962),U_3963)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3962),U_3963))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3960),hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),U_3962)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),U_3963))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3960),c_Groups_Oone__class_Oone(U_3960)),U_3961))
| ~ class_Rings_Olinordered__semidom(U_3960) ),
inference(variable_rename,[status(thm)],[f_926_1]) ).
fof(f_926_3,plain,
( ! [U_3960,U_3961,U_3962,U_3963] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3960),hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),U_3962)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),U_3963)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3962),U_3963))
| ~ sP225(U_3960,U_3961,U_3962,U_3963) )
& ! [U_3960,U_3961,U_3962,U_3963] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3962),U_3963))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3960),hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),U_3962)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),U_3963)))
| ~ sP225(U_3960,U_3961,U_3962,U_3963) )
& ! [U_3960,U_3961,U_3962,U_3963] :
( sP225(U_3960,U_3961,U_3962,U_3963)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3960),c_Groups_Oone__class_Oone(U_3960)),U_3961))
| ~ class_Rings_Olinordered__semidom(U_3960) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225])],[f_926_2]) ).
cnf(f_926_4,plain,
( sP225(U_3960,U_3961,U_3962,U_3963)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3960),c_Groups_Oone__class_Oone(U_3960)),U_3961))
| ~ class_Rings_Olinordered__semidom(U_3960) ),
inference(clausify,[status(thm)],[f_926_3]) ).
cnf(f_926_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3962),U_3963))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3960),hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),U_3962)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),U_3963)))
| ~ sP225(U_3960,U_3961,U_3962,U_3963) ),
inference(clausify,[status(thm)],[f_926_3]) ).
cnf(f_926_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3960),hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),U_3962)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),U_3963)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3962),U_3963))
| ~ sP225(U_3960,U_3961,U_3962,U_3963) ),
inference(clausify,[status(thm)],[f_926_3]) ).
fof(f_927_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_927_2,plain,
! [U_3966,U_3965,U_3964] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3964),hAPP(hAPP(c_Power_Opower__class_Opower(U_3964),U_3965),U_3966)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3964),U_3965),hAPP(hAPP(c_Power_Opower__class_Opower(U_3964),U_3965),U_3966))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3964),c_Groups_Oone__class_Oone(U_3964)),U_3965))
| ~ class_Rings_Olinordered__semidom(U_3964) ),
inference(variable_rename,[status(thm)],[f_927_1]) ).
fof(f_927_3,plain,
! [U_3964,U_3966,U_3965] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3964),hAPP(hAPP(c_Power_Opower__class_Opower(U_3964),U_3965),U_3966)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3964),U_3965),hAPP(hAPP(c_Power_Opower__class_Opower(U_3964),U_3965),U_3966))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3964),c_Groups_Oone__class_Oone(U_3964)),U_3965))
| ~ class_Rings_Olinordered__semidom(U_3964) ),
inference(definitional_conversion,[status(esa)],[f_927_2]) ).
cnf(f_927_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3964),hAPP(hAPP(c_Power_Opower__class_Opower(U_3964),U_3965),U_3966)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3964),U_3965),hAPP(hAPP(c_Power_Opower__class_Opower(U_3964),U_3965),U_3966))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3964),c_Groups_Oone__class_Oone(U_3964)),U_3965))
| ~ class_Rings_Olinordered__semidom(U_3964) ),
inference(clausify,[status(thm)],[f_927_3]) ).
fof(f_928_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_928_2,plain,
! [U_3969,U_3968,U_3967] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3967),hAPP(hAPP(c_Power_Opower__class_Opower(U_3967),U_3968),U_3969)),U_3968) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3967),U_3968),hAPP(hAPP(c_Power_Opower__class_Opower(U_3967),U_3968),U_3969))
| ~ class_Groups_Omonoid__mult(U_3967) ),
inference(variable_rename,[status(thm)],[f_928_1]) ).
fof(f_928_3,plain,
! [U_3967,U_3968,U_3969] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3967),hAPP(hAPP(c_Power_Opower__class_Opower(U_3967),U_3968),U_3969)),U_3968) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3967),U_3968),hAPP(hAPP(c_Power_Opower__class_Opower(U_3967),U_3968),U_3969))
| ~ class_Groups_Omonoid__mult(U_3967) ),
inference(definitional_conversion,[status(esa)],[f_928_2]) ).
cnf(f_928_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3967),hAPP(hAPP(c_Power_Opower__class_Opower(U_3967),U_3968),U_3969)),U_3968) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3967),U_3968),hAPP(hAPP(c_Power_Opower__class_Opower(U_3967),U_3968),U_3969))
| ~ class_Groups_Omonoid__mult(U_3967) ),
inference(clausify,[status(thm)],[f_928_3]) ).
fof(f_929_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_929_2,plain,
! [U_3973,U_3972,U_3971,U_3970] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3970),U_3971),U_3972)),U_3973) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3970),hAPP(hAPP(c_Power_Opower__class_Opower(U_3970),U_3971),U_3973)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3970),U_3972),U_3973))
| ~ class_Groups_Ocomm__monoid__mult(U_3970) ),
inference(variable_rename,[status(thm)],[f_929_1]) ).
fof(f_929_3,plain,
! [U_3970,U_3971,U_3972,U_3973] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3970),U_3971),U_3972)),U_3973) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3970),hAPP(hAPP(c_Power_Opower__class_Opower(U_3970),U_3971),U_3973)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3970),U_3972),U_3973))
| ~ class_Groups_Ocomm__monoid__mult(U_3970) ),
inference(definitional_conversion,[status(esa)],[f_929_2]) ).
cnf(f_929_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3970),U_3971),U_3972)),U_3973) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3970),hAPP(hAPP(c_Power_Opower__class_Opower(U_3970),U_3971),U_3973)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3970),U_3972),U_3973))
| ~ class_Groups_Ocomm__monoid__mult(U_3970) ),
inference(clausify,[status(thm)],[f_929_3]) ).
fof(f_930_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_930_2,plain,
! [U_3975,U_3974] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3974),c_Groups_Oone__class_Oone(U_3974)),U_3975) = c_Groups_Oone__class_Oone(U_3974)
| ~ class_Groups_Omonoid__mult(U_3974) ),
inference(variable_rename,[status(thm)],[f_930_1]) ).
fof(f_930_3,plain,
! [U_3975,U_3974] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3974),c_Groups_Oone__class_Oone(U_3974)),U_3975) = c_Groups_Oone__class_Oone(U_3974)
| ~ class_Groups_Omonoid__mult(U_3974) ),
inference(definitional_conversion,[status(esa)],[f_930_2]) ).
cnf(f_930_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3974),c_Groups_Oone__class_Oone(U_3974)),U_3975) = c_Groups_Oone__class_Oone(U_3974)
| ~ class_Groups_Omonoid__mult(U_3974) ),
inference(clausify,[status(thm)],[f_930_3]) ).
fof(f_931_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_931_2,plain,
! [U_3979,U_3978,U_3977,U_3976] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3976),U_3977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3978),U_3979)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3976),hAPP(hAPP(c_Power_Opower__class_Opower(U_3976),U_3977),U_3978)),U_3979)
| ~ class_Groups_Omonoid__mult(U_3976) ),
inference(variable_rename,[status(thm)],[f_931_1]) ).
fof(f_931_3,plain,
! [U_3976,U_3977,U_3978,U_3979] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3976),U_3977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3978),U_3979)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3976),hAPP(hAPP(c_Power_Opower__class_Opower(U_3976),U_3977),U_3978)),U_3979)
| ~ class_Groups_Omonoid__mult(U_3976) ),
inference(definitional_conversion,[status(esa)],[f_931_2]) ).
cnf(f_931_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3976),U_3977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3978),U_3979)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3976),hAPP(hAPP(c_Power_Opower__class_Opower(U_3976),U_3977),U_3978)),U_3979)
| ~ class_Groups_Omonoid__mult(U_3976) ),
inference(clausify,[status(thm)],[f_931_3]) ).
fof(f_932_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_932_2,plain,
! [U_3981,U_3980] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3980),U_3981),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3981
| ~ class_Groups_Omonoid__mult(U_3980) ),
inference(variable_rename,[status(thm)],[f_932_1]) ).
fof(f_932_3,plain,
! [U_3980,U_3981] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3980),U_3981),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3981
| ~ class_Groups_Omonoid__mult(U_3980) ),
inference(definitional_conversion,[status(esa)],[f_932_2]) ).
cnf(f_932_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3980),U_3981),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3981
| ~ class_Groups_Omonoid__mult(U_3980) ),
inference(clausify,[status(thm)],[f_932_3]) ).
fof(f_933_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_933_2,plain,
! [U_3984,U_3983,U_3982] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3982),c_Groups_Oone__class_Oone(U_3982)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3982),U_3983),U_3984)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3982),c_Groups_Oone__class_Oone(U_3982)),U_3983))
| ~ class_Rings_Olinordered__semidom(U_3982) ),
inference(variable_rename,[status(thm)],[f_933_1]) ).
fof(f_933_3,plain,
! [U_3982,U_3983,U_3984] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3982),c_Groups_Oone__class_Oone(U_3982)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3982),U_3983),U_3984)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3982),c_Groups_Oone__class_Oone(U_3982)),U_3983))
| ~ class_Rings_Olinordered__semidom(U_3982) ),
inference(definitional_conversion,[status(esa)],[f_933_2]) ).
cnf(f_933_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3982),c_Groups_Oone__class_Oone(U_3982)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3982),U_3983),U_3984)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3982),c_Groups_Oone__class_Oone(U_3982)),U_3983))
| ~ class_Rings_Olinordered__semidom(U_3982) ),
inference(clausify,[status(thm)],[f_933_3]) ).
fof(f_934_1,plain,
! [V_n_2,V_m_2,V_a_2,T_c] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),V_a_2),V_m_2) != hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_n_2) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Oone__class_Oone(T_c)),V_a_2))
| ~ class_Rings_Olinordered__semidom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_power__inject__exp]) ).
fof(f_934_2,plain,
! [U_3988,U_3987,U_3986,U_3985] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3985),U_3986),U_3987) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3985),U_3986),U_3988)
| U_3987 != U_3988 )
& ( U_3987 = U_3988
| hAPP(hAPP(c_Power_Opower__class_Opower(U_3985),U_3986),U_3987) != hAPP(hAPP(c_Power_Opower__class_Opower(U_3985),U_3986),U_3988) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3985),c_Groups_Oone__class_Oone(U_3985)),U_3986))
| ~ class_Rings_Olinordered__semidom(U_3985) ),
inference(variable_rename,[status(thm)],[f_934_1]) ).
fof(f_934_3,plain,
( ! [U_3985,U_3986,U_3987,U_3988] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3985),U_3986),U_3987) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3985),U_3986),U_3988)
| U_3987 != U_3988
| ~ sP226(U_3985,U_3986,U_3987,U_3988) )
& ! [U_3985,U_3986,U_3987,U_3988] :
( U_3987 = U_3988
| hAPP(hAPP(c_Power_Opower__class_Opower(U_3985),U_3986),U_3987) != hAPP(hAPP(c_Power_Opower__class_Opower(U_3985),U_3986),U_3988)
| ~ sP226(U_3985,U_3986,U_3987,U_3988) )
& ! [U_3985,U_3986,U_3987,U_3988] :
( sP226(U_3985,U_3986,U_3987,U_3988)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3985),c_Groups_Oone__class_Oone(U_3985)),U_3986))
| ~ class_Rings_Olinordered__semidom(U_3985) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226])],[f_934_2]) ).
cnf(f_934_4,plain,
( sP226(U_3985,U_3986,U_3987,U_3988)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3985),c_Groups_Oone__class_Oone(U_3985)),U_3986))
| ~ class_Rings_Olinordered__semidom(U_3985) ),
inference(clausify,[status(thm)],[f_934_3]) ).
cnf(f_934_5,plain,
( U_3987 = U_3988
| hAPP(hAPP(c_Power_Opower__class_Opower(U_3985),U_3986),U_3987) != hAPP(hAPP(c_Power_Opower__class_Opower(U_3985),U_3986),U_3988)
| ~ sP226(U_3985,U_3986,U_3987,U_3988) ),
inference(clausify,[status(thm)],[f_934_3]) ).
cnf(f_934_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3985),U_3986),U_3987) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3985),U_3986),U_3988)
| U_3987 != U_3988
| ~ sP226(U_3985,U_3986,U_3987,U_3988) ),
inference(clausify,[status(thm)],[f_934_3]) ).
fof(f_935_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_935_2,plain,
! [U_3992,U_3991,U_3990,U_3989] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3989),U_3990),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3991),U_3992)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3989),hAPP(hAPP(c_Power_Opower__class_Opower(U_3989),U_3990),U_3991)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3989),U_3990),U_3992))
| ~ class_Groups_Omonoid__mult(U_3989) ),
inference(variable_rename,[status(thm)],[f_935_1]) ).
fof(f_935_3,plain,
! [U_3991,U_3989,U_3990,U_3992] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3989),U_3990),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3991),U_3992)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3989),hAPP(hAPP(c_Power_Opower__class_Opower(U_3989),U_3990),U_3991)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3989),U_3990),U_3992))
| ~ class_Groups_Omonoid__mult(U_3989) ),
inference(definitional_conversion,[status(esa)],[f_935_2]) ).
cnf(f_935_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3989),U_3990),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3991),U_3992)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3989),hAPP(hAPP(c_Power_Opower__class_Opower(U_3989),U_3990),U_3991)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3989),U_3990),U_3992))
| ~ class_Groups_Omonoid__mult(U_3989) ),
inference(clausify,[status(thm)],[f_935_3]) ).
fof(f_936_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_936_2,plain,
! [U_3995,U_3994,U_3993] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),c_Groups_Oone__class_Oone(U_3993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3993),U_3994),hAPP(hAPP(c_Power_Opower__class_Opower(U_3993),U_3994),U_3995))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),c_Groups_Oone__class_Oone(U_3993)),U_3994))
| ~ class_Rings_Olinordered__semidom(U_3993) ),
inference(variable_rename,[status(thm)],[f_936_1]) ).
fof(f_936_3,plain,
! [U_3993,U_3994,U_3995] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),c_Groups_Oone__class_Oone(U_3993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3993),U_3994),hAPP(hAPP(c_Power_Opower__class_Opower(U_3993),U_3994),U_3995))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),c_Groups_Oone__class_Oone(U_3993)),U_3994))
| ~ class_Rings_Olinordered__semidom(U_3993) ),
inference(definitional_conversion,[status(esa)],[f_936_2]) ).
cnf(f_936_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),c_Groups_Oone__class_Oone(U_3993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3993),U_3994),hAPP(hAPP(c_Power_Opower__class_Opower(U_3993),U_3994),U_3995))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),c_Groups_Oone__class_Oone(U_3993)),U_3994))
| ~ class_Rings_Olinordered__semidom(U_3993) ),
inference(clausify,[status(thm)],[f_936_3]) ).
fof(f_937_1,plain,
! [T_c] :
( c_Power_Opower__class_Opower(T_c) = c_Power_Opower_Opower(T_c,c_Groups_Oone__class_Oone(T_c),c_Groups_Otimes__class_Otimes(T_c))
| ~ class_Power_Opower(T_c) ),
inference(fof_nnf,[status(thm)],[fact_power__power__power]) ).
fof(f_937_2,plain,
! [U_3996] :
( c_Power_Opower__class_Opower(U_3996) = c_Power_Opower_Opower(U_3996,c_Groups_Oone__class_Oone(U_3996),c_Groups_Otimes__class_Otimes(U_3996))
| ~ class_Power_Opower(U_3996) ),
inference(variable_rename,[status(thm)],[f_937_1]) ).
fof(f_937_3,plain,
! [U_3996] :
( c_Power_Opower__class_Opower(U_3996) = c_Power_Opower_Opower(U_3996,c_Groups_Oone__class_Oone(U_3996),c_Groups_Otimes__class_Otimes(U_3996))
| ~ class_Power_Opower(U_3996) ),
inference(definitional_conversion,[status(esa)],[f_937_2]) ).
cnf(f_937_4,plain,
( c_Power_Opower__class_Opower(U_3996) = c_Power_Opower_Opower(U_3996,c_Groups_Oone__class_Oone(U_3996),c_Groups_Otimes__class_Otimes(U_3996))
| ~ class_Power_Opower(U_3996) ),
inference(clausify,[status(thm)],[f_937_3]) ).
fof(f_938_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oclosed]) ).
fof(f_938_2,plain,
! [U_4000,U_3999] :
( hBOOL(hAPP(hAPP(c_member(U_3999),c_Big__Operators_Olattice__class_OSup__fin(U_3999,U_4000)),U_4000))
| ? [U_3998,U_3997] : ~ hBOOL(hAPP(hAPP(c_member(U_3999),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3999),U_3998),U_3997)),hAPP(hAPP(c_Set_Oinsert(U_3999),U_3998),hAPP(hAPP(c_Set_Oinsert(U_3999),U_3997),c_Orderings_Obot__class_Obot(tc_fun(U_3999,tc_HOL_Obool))))))
| U_4000 = c_Orderings_Obot__class_Obot(tc_fun(U_3999,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3999),U_4000))
| ~ class_Lattices_Olattice(U_3999) ),
inference(variable_rename,[status(thm)],[f_938_1]) ).
fof(f_938_3,plain,
! [U_4000,U_3999] :
( hBOOL(hAPP(hAPP(c_member(U_3999),c_Big__Operators_Olattice__class_OSup__fin(U_3999,U_4000)),U_4000))
| ? [U_3997] : ~ hBOOL(hAPP(hAPP(c_member(U_3999),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3999),sK82(U_4000,U_3999)),U_3997)),hAPP(hAPP(c_Set_Oinsert(U_3999),sK82(U_4000,U_3999)),hAPP(hAPP(c_Set_Oinsert(U_3999),U_3997),c_Orderings_Obot__class_Obot(tc_fun(U_3999,tc_HOL_Obool))))))
| U_4000 = c_Orderings_Obot__class_Obot(tc_fun(U_3999,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3999),U_4000))
| ~ class_Lattices_Olattice(U_3999) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_3998,sK82(U_4000,U_3999))],[f_938_2]) ).
fof(f_938_4,plain,
! [U_4000,U_3999] :
( hBOOL(hAPP(hAPP(c_member(U_3999),c_Big__Operators_Olattice__class_OSup__fin(U_3999,U_4000)),U_4000))
| ~ hBOOL(hAPP(hAPP(c_member(U_3999),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3999),sK82(U_4000,U_3999)),sK83(U_4000,U_3999))),hAPP(hAPP(c_Set_Oinsert(U_3999),sK82(U_4000,U_3999)),hAPP(hAPP(c_Set_Oinsert(U_3999),sK83(U_4000,U_3999)),c_Orderings_Obot__class_Obot(tc_fun(U_3999,tc_HOL_Obool))))))
| U_4000 = c_Orderings_Obot__class_Obot(tc_fun(U_3999,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3999),U_4000))
| ~ class_Lattices_Olattice(U_3999) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_3997,sK83(U_4000,U_3999))],[f_938_3]) ).
fof(f_938_5,plain,
! [U_3999,U_4000] :
( hBOOL(hAPP(hAPP(c_member(U_3999),c_Big__Operators_Olattice__class_OSup__fin(U_3999,U_4000)),U_4000))
| ~ hBOOL(hAPP(hAPP(c_member(U_3999),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3999),sK82(U_4000,U_3999)),sK83(U_4000,U_3999))),hAPP(hAPP(c_Set_Oinsert(U_3999),sK82(U_4000,U_3999)),hAPP(hAPP(c_Set_Oinsert(U_3999),sK83(U_4000,U_3999)),c_Orderings_Obot__class_Obot(tc_fun(U_3999,tc_HOL_Obool))))))
| U_4000 = c_Orderings_Obot__class_Obot(tc_fun(U_3999,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3999),U_4000))
| ~ class_Lattices_Olattice(U_3999) ),
inference(definitional_conversion,[status(esa)],[f_938_4]) ).
cnf(f_938_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_3999),c_Big__Operators_Olattice__class_OSup__fin(U_3999,U_4000)),U_4000))
| ~ hBOOL(hAPP(hAPP(c_member(U_3999),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3999),sK82(U_4000,U_3999)),sK83(U_4000,U_3999))),hAPP(hAPP(c_Set_Oinsert(U_3999),sK82(U_4000,U_3999)),hAPP(hAPP(c_Set_Oinsert(U_3999),sK83(U_4000,U_3999)),c_Orderings_Obot__class_Obot(tc_fun(U_3999,tc_HOL_Obool))))))
| U_4000 = c_Orderings_Obot__class_Obot(tc_fun(U_3999,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3999),U_4000))
| ~ class_Lattices_Olattice(U_3999) ),
inference(clausify,[status(thm)],[f_938_5]) ).
fof(f_939_1,plain,
! [V_a_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_c),c_HOL_OThe(T_c,hAPP(hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__vimage__singleton]) ).
fof(f_939_2,plain,
! [U_4004,U_4003,U_4002,U_4001] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4001,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4001,U_4002,U_4003),hAPP(hAPP(c_Set_Oinsert(U_4002),U_4004),c_Orderings_Obot__class_Obot(tc_fun(U_4002,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_4001),c_HOL_OThe(U_4001,hAPP(hAPP(c_COMBC(U_4001,U_4002,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_4002,tc_fun(U_4002,tc_HOL_Obool),U_4001),c_fequal),U_4003)),U_4004))),c_Orderings_Obot__class_Obot(tc_fun(U_4001,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_4001,U_4002,U_4003,c_Orderings_Otop__class_Otop(tc_fun(U_4001,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_939_1]) ).
fof(f_939_3,plain,
! [U_4002,U_4001,U_4003,U_4004] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4001,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4001,U_4002,U_4003),hAPP(hAPP(c_Set_Oinsert(U_4002),U_4004),c_Orderings_Obot__class_Obot(tc_fun(U_4002,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_4001),c_HOL_OThe(U_4001,hAPP(hAPP(c_COMBC(U_4001,U_4002,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_4002,tc_fun(U_4002,tc_HOL_Obool),U_4001),c_fequal),U_4003)),U_4004))),c_Orderings_Obot__class_Obot(tc_fun(U_4001,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_4001,U_4002,U_4003,c_Orderings_Otop__class_Otop(tc_fun(U_4001,tc_HOL_Obool))) ),
inference(definitional_conversion,[status(esa)],[f_939_2]) ).
cnf(f_939_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4001,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4001,U_4002,U_4003),hAPP(hAPP(c_Set_Oinsert(U_4002),U_4004),c_Orderings_Obot__class_Obot(tc_fun(U_4002,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_4001),c_HOL_OThe(U_4001,hAPP(hAPP(c_COMBC(U_4001,U_4002,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_4002,tc_fun(U_4002,tc_HOL_Obool),U_4001),c_fequal),U_4003)),U_4004))),c_Orderings_Obot__class_Obot(tc_fun(U_4001,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_4001,U_4002,U_4003,c_Orderings_Otop__class_Otop(tc_fun(U_4001,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_939_3]) ).
fof(f_940_1,plain,
! [V_N_2,V_h_2,T_c] :
( hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_c,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),B_x),B_y)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ohom__commute]) ).
fof(f_940_2,plain,
! [U_4009,U_4008,U_4007] :
( hAPP(U_4008,c_Big__Operators_Olattice__class_OSup__fin(U_4007,U_4009)) = c_Big__Operators_Olattice__class_OSup__fin(U_4007,hAPP(c_Set_Oimage(U_4007,U_4007,U_4008),U_4009))
| U_4009 = c_Orderings_Obot__class_Obot(tc_fun(U_4007,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4007),U_4009))
| ? [U_4006,U_4005] : hAPP(U_4008,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4007),U_4006),U_4005)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4007),hAPP(U_4008,U_4006)),hAPP(U_4008,U_4005))
| ~ class_Lattices_Olattice(U_4007) ),
inference(variable_rename,[status(thm)],[f_940_1]) ).
fof(f_940_3,plain,
! [U_4009,U_4008,U_4007] :
( hAPP(U_4008,c_Big__Operators_Olattice__class_OSup__fin(U_4007,U_4009)) = c_Big__Operators_Olattice__class_OSup__fin(U_4007,hAPP(c_Set_Oimage(U_4007,U_4007,U_4008),U_4009))
| U_4009 = c_Orderings_Obot__class_Obot(tc_fun(U_4007,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4007),U_4009))
| ? [U_4005] : hAPP(U_4008,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4007),sK84(U_4009,U_4008,U_4007)),U_4005)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4007),hAPP(U_4008,sK84(U_4009,U_4008,U_4007))),hAPP(U_4008,U_4005))
| ~ class_Lattices_Olattice(U_4007) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_4006,sK84(U_4009,U_4008,U_4007))],[f_940_2]) ).
fof(f_940_4,plain,
! [U_4009,U_4008,U_4007] :
( hAPP(U_4008,c_Big__Operators_Olattice__class_OSup__fin(U_4007,U_4009)) = c_Big__Operators_Olattice__class_OSup__fin(U_4007,hAPP(c_Set_Oimage(U_4007,U_4007,U_4008),U_4009))
| U_4009 = c_Orderings_Obot__class_Obot(tc_fun(U_4007,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4007),U_4009))
| hAPP(U_4008,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4007),sK84(U_4009,U_4008,U_4007)),sK85(U_4009,U_4008,U_4007))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4007),hAPP(U_4008,sK84(U_4009,U_4008,U_4007))),hAPP(U_4008,sK85(U_4009,U_4008,U_4007)))
| ~ class_Lattices_Olattice(U_4007) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_4005,sK85(U_4009,U_4008,U_4007))],[f_940_3]) ).
fof(f_940_5,plain,
! [U_4007,U_4008,U_4009] :
( hAPP(U_4008,c_Big__Operators_Olattice__class_OSup__fin(U_4007,U_4009)) = c_Big__Operators_Olattice__class_OSup__fin(U_4007,hAPP(c_Set_Oimage(U_4007,U_4007,U_4008),U_4009))
| U_4009 = c_Orderings_Obot__class_Obot(tc_fun(U_4007,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4007),U_4009))
| hAPP(U_4008,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4007),sK84(U_4009,U_4008,U_4007)),sK85(U_4009,U_4008,U_4007))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4007),hAPP(U_4008,sK84(U_4009,U_4008,U_4007))),hAPP(U_4008,sK85(U_4009,U_4008,U_4007)))
| ~ class_Lattices_Olattice(U_4007) ),
inference(definitional_conversion,[status(esa)],[f_940_4]) ).
cnf(f_940_6,plain,
( hAPP(U_4008,c_Big__Operators_Olattice__class_OSup__fin(U_4007,U_4009)) = c_Big__Operators_Olattice__class_OSup__fin(U_4007,hAPP(c_Set_Oimage(U_4007,U_4007,U_4008),U_4009))
| U_4009 = c_Orderings_Obot__class_Obot(tc_fun(U_4007,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4007),U_4009))
| hAPP(U_4008,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4007),sK84(U_4009,U_4008,U_4007)),sK85(U_4009,U_4008,U_4007))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4007),hAPP(U_4008,sK84(U_4009,U_4008,U_4007))),hAPP(U_4008,sK85(U_4009,U_4008,U_4007)))
| ~ class_Lattices_Olattice(U_4007) ),
inference(clausify,[status(thm)],[f_940_5]) ).
fof(f_941_1,plain,
! [V_f_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_d)),V_f_2)),c_Orderings_Obot__class_Obot(T_d)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_d) ),
inference(fof_nnf,[status(thm)],[fact_SUPR__fold__sup]) ).
fof(f_941_2,plain,
! [U_4013,U_4012,U_4011,U_4010] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4011,U_4010),U_4012),U_4013) = hAPP(hAPP(c_Finite__Set_Ofold(U_4011,U_4010,hAPP(hAPP(c_COMBB(U_4010,tc_fun(U_4010,U_4010),U_4011),c_Lattices_Osemilattice__sup__class_Osup(U_4010)),U_4013)),c_Orderings_Obot__class_Obot(U_4010)),U_4012)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4011),U_4012))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4010) ),
inference(variable_rename,[status(thm)],[f_941_1]) ).
fof(f_941_3,plain,
! [U_4011,U_4010,U_4012,U_4013] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4011,U_4010),U_4012),U_4013) = hAPP(hAPP(c_Finite__Set_Ofold(U_4011,U_4010,hAPP(hAPP(c_COMBB(U_4010,tc_fun(U_4010,U_4010),U_4011),c_Lattices_Osemilattice__sup__class_Osup(U_4010)),U_4013)),c_Orderings_Obot__class_Obot(U_4010)),U_4012)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4011),U_4012))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4010) ),
inference(definitional_conversion,[status(esa)],[f_941_2]) ).
cnf(f_941_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4011,U_4010),U_4012),U_4013) = hAPP(hAPP(c_Finite__Set_Ofold(U_4011,U_4010,hAPP(hAPP(c_COMBB(U_4010,tc_fun(U_4010,U_4010),U_4011),c_Lattices_Osemilattice__sup__class_Osup(U_4010)),U_4013)),c_Orderings_Obot__class_Obot(U_4010)),U_4012)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4011),U_4012))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4010) ),
inference(clausify,[status(thm)],[f_941_3]) ).
fof(f_942_1,plain,
! [V_f_2,V_S_2,V_T_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_S_2)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_d)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_T_2),V_S_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__right]) ).
fof(f_942_2,plain,
! [U_4019,U_4018,U_4017,U_4016,U_4015] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4016,U_4015),U_4019),U_4017) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4016,U_4015),U_4019),U_4018)
| ? [U_4014] :
( hAPP(U_4019,U_4014) != c_Groups_Oone__class_Oone(U_4015)
& hBOOL(hAPP(hAPP(c_member(U_4016),U_4014),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4016,tc_HOL_Obool)),U_4017),U_4018))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4016,tc_HOL_Obool)),U_4018),U_4017))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4016),U_4017))
| ~ class_Groups_Ocomm__monoid__mult(U_4015) ),
inference(variable_rename,[status(thm)],[f_942_1]) ).
fof(f_942_3,plain,
! [U_4019,U_4018,U_4017,U_4016,U_4015] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4016,U_4015),U_4019),U_4017) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4016,U_4015),U_4019),U_4018)
| ( hAPP(U_4019,sK86(U_4019,U_4018,U_4017,U_4016,U_4015)) != c_Groups_Oone__class_Oone(U_4015)
& hBOOL(hAPP(hAPP(c_member(U_4016),sK86(U_4019,U_4018,U_4017,U_4016,U_4015)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4016,tc_HOL_Obool)),U_4017),U_4018))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4016,tc_HOL_Obool)),U_4018),U_4017))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4016),U_4017))
| ~ class_Groups_Ocomm__monoid__mult(U_4015) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_4014,sK86(U_4019,U_4018,U_4017,U_4016,U_4015))],[f_942_2]) ).
fof(f_942_4,plain,
( ! [U_4015,U_4016,U_4017,U_4018,U_4019] :
( hAPP(U_4019,sK86(U_4019,U_4018,U_4017,U_4016,U_4015)) != c_Groups_Oone__class_Oone(U_4015)
| ~ sP227(U_4015,U_4016,U_4017,U_4018,U_4019) )
& ! [U_4015,U_4016,U_4017,U_4018,U_4019] :
( hBOOL(hAPP(hAPP(c_member(U_4016),sK86(U_4019,U_4018,U_4017,U_4016,U_4015)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4016,tc_HOL_Obool)),U_4017),U_4018)))
| ~ sP227(U_4015,U_4016,U_4017,U_4018,U_4019) )
& ! [U_4015,U_4016,U_4017,U_4018,U_4019] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4016,U_4015),U_4019),U_4017) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4016,U_4015),U_4019),U_4018)
| sP227(U_4015,U_4016,U_4017,U_4018,U_4019)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4016,tc_HOL_Obool)),U_4018),U_4017))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4016),U_4017))
| ~ class_Groups_Ocomm__monoid__mult(U_4015) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227])],[f_942_3]) ).
cnf(f_942_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4016,U_4015),U_4019),U_4017) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4016,U_4015),U_4019),U_4018)
| sP227(U_4015,U_4016,U_4017,U_4018,U_4019)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4016,tc_HOL_Obool)),U_4018),U_4017))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4016),U_4017))
| ~ class_Groups_Ocomm__monoid__mult(U_4015) ),
inference(clausify,[status(thm)],[f_942_4]) ).
cnf(f_942_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4016),sK86(U_4019,U_4018,U_4017,U_4016,U_4015)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4016,tc_HOL_Obool)),U_4017),U_4018)))
| ~ sP227(U_4015,U_4016,U_4017,U_4018,U_4019) ),
inference(clausify,[status(thm)],[f_942_4]) ).
cnf(f_942_7,plain,
( hAPP(U_4019,sK86(U_4019,U_4018,U_4017,U_4016,U_4015)) != c_Groups_Oone__class_Oone(U_4015)
| ~ sP227(U_4015,U_4016,U_4017,U_4018,U_4019) ),
inference(clausify,[status(thm)],[f_942_4]) ).
fof(f_943_1,plain,
! [V_f_2,V_S_2,V_T_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_T_2)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_d)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_T_2),V_S_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__left]) ).
fof(f_943_2,plain,
! [U_4025,U_4024,U_4023,U_4022,U_4021] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4022,U_4021),U_4025),U_4024) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4022,U_4021),U_4025),U_4023)
| ? [U_4020] :
( hAPP(U_4025,U_4020) != c_Groups_Oone__class_Oone(U_4021)
& hBOOL(hAPP(hAPP(c_member(U_4022),U_4020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4022,tc_HOL_Obool)),U_4023),U_4024))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4022,tc_HOL_Obool)),U_4024),U_4023))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4022),U_4023))
| ~ class_Groups_Ocomm__monoid__mult(U_4021) ),
inference(variable_rename,[status(thm)],[f_943_1]) ).
fof(f_943_3,plain,
! [U_4025,U_4024,U_4023,U_4022,U_4021] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4022,U_4021),U_4025),U_4024) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4022,U_4021),U_4025),U_4023)
| ( hAPP(U_4025,sK87(U_4025,U_4024,U_4023,U_4022,U_4021)) != c_Groups_Oone__class_Oone(U_4021)
& hBOOL(hAPP(hAPP(c_member(U_4022),sK87(U_4025,U_4024,U_4023,U_4022,U_4021)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4022,tc_HOL_Obool)),U_4023),U_4024))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4022,tc_HOL_Obool)),U_4024),U_4023))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4022),U_4023))
| ~ class_Groups_Ocomm__monoid__mult(U_4021) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_4020,sK87(U_4025,U_4024,U_4023,U_4022,U_4021))],[f_943_2]) ).
fof(f_943_4,plain,
( ! [U_4022,U_4025,U_4023,U_4024,U_4021] :
( hAPP(U_4025,sK87(U_4025,U_4024,U_4023,U_4022,U_4021)) != c_Groups_Oone__class_Oone(U_4021)
| ~ sP228(U_4022,U_4025,U_4023,U_4024,U_4021) )
& ! [U_4022,U_4025,U_4023,U_4024,U_4021] :
( hBOOL(hAPP(hAPP(c_member(U_4022),sK87(U_4025,U_4024,U_4023,U_4022,U_4021)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4022,tc_HOL_Obool)),U_4023),U_4024)))
| ~ sP228(U_4022,U_4025,U_4023,U_4024,U_4021) )
& ! [U_4022,U_4025,U_4023,U_4024,U_4021] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4022,U_4021),U_4025),U_4024) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4022,U_4021),U_4025),U_4023)
| sP228(U_4022,U_4025,U_4023,U_4024,U_4021)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4022,tc_HOL_Obool)),U_4024),U_4023))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4022),U_4023))
| ~ class_Groups_Ocomm__monoid__mult(U_4021) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228])],[f_943_3]) ).
cnf(f_943_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4022,U_4021),U_4025),U_4024) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4022,U_4021),U_4025),U_4023)
| sP228(U_4022,U_4025,U_4023,U_4024,U_4021)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4022,tc_HOL_Obool)),U_4024),U_4023))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4022),U_4023))
| ~ class_Groups_Ocomm__monoid__mult(U_4021) ),
inference(clausify,[status(thm)],[f_943_4]) ).
cnf(f_943_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4022),sK87(U_4025,U_4024,U_4023,U_4022,U_4021)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4022,tc_HOL_Obool)),U_4023),U_4024)))
| ~ sP228(U_4022,U_4025,U_4023,U_4024,U_4021) ),
inference(clausify,[status(thm)],[f_943_4]) ).
cnf(f_943_7,plain,
( hAPP(U_4025,sK87(U_4025,U_4024,U_4023,U_4022,U_4021)) != c_Groups_Oone__class_Oone(U_4021)
| ~ sP228(U_4022,U_4025,U_4023,U_4024,U_4021) ),
inference(clausify,[status(thm)],[f_943_4]) ).
fof(f_944_1,plain,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( 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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),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)),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),c_Groups_Oone__class_Oone(T_d)),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))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_fold__Un__disjoint]) ).
fof(f_944_2,plain,
! [U_4030,U_4029,U_4028,U_4027,U_4026] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4026,U_4027,c_Groups_Otimes__class_Otimes(U_4026)),U_4030),c_Groups_Oone__class_Oone(U_4026)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4027,tc_HOL_Obool)),U_4028),U_4029)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4026),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4026,U_4027,c_Groups_Otimes__class_Otimes(U_4026)),U_4030),c_Groups_Oone__class_Oone(U_4026)),U_4028)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4026,U_4027,c_Groups_Otimes__class_Otimes(U_4026)),U_4030),c_Groups_Oone__class_Oone(U_4026)),U_4029))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4027,tc_HOL_Obool)),U_4028),U_4029) != c_Orderings_Obot__class_Obot(tc_fun(U_4027,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4027),U_4029))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4027),U_4028))
| ~ class_Groups_Ocomm__monoid__mult(U_4026) ),
inference(variable_rename,[status(thm)],[f_944_1]) ).
fof(f_944_3,plain,
! [U_4028,U_4027,U_4029,U_4026,U_4030] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4026,U_4027,c_Groups_Otimes__class_Otimes(U_4026)),U_4030),c_Groups_Oone__class_Oone(U_4026)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4027,tc_HOL_Obool)),U_4028),U_4029)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4026),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4026,U_4027,c_Groups_Otimes__class_Otimes(U_4026)),U_4030),c_Groups_Oone__class_Oone(U_4026)),U_4028)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4026,U_4027,c_Groups_Otimes__class_Otimes(U_4026)),U_4030),c_Groups_Oone__class_Oone(U_4026)),U_4029))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4027,tc_HOL_Obool)),U_4028),U_4029) != c_Orderings_Obot__class_Obot(tc_fun(U_4027,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4027),U_4029))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4027),U_4028))
| ~ class_Groups_Ocomm__monoid__mult(U_4026) ),
inference(definitional_conversion,[status(esa)],[f_944_2]) ).
cnf(f_944_4,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4026,U_4027,c_Groups_Otimes__class_Otimes(U_4026)),U_4030),c_Groups_Oone__class_Oone(U_4026)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4027,tc_HOL_Obool)),U_4028),U_4029)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4026),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4026,U_4027,c_Groups_Otimes__class_Otimes(U_4026)),U_4030),c_Groups_Oone__class_Oone(U_4026)),U_4028)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4026,U_4027,c_Groups_Otimes__class_Otimes(U_4026)),U_4030),c_Groups_Oone__class_Oone(U_4026)),U_4029))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4027,tc_HOL_Obool)),U_4028),U_4029) != c_Orderings_Obot__class_Obot(tc_fun(U_4027,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4027),U_4029))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4027),U_4028))
| ~ class_Groups_Ocomm__monoid__mult(U_4026) ),
inference(clausify,[status(thm)],[f_944_3]) ).
fof(f_945_1,plain,
! [T_c,V_B_2,V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_945_2,plain,
! [U_4034,U_4033,U_4032,U_4031] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4034,tc_HOL_Obool)),U_4031),U_4033),U_4032))
| ~ hBOOL(hAPP(U_4033,U_4032))
| ~ hBOOL(hAPP(U_4031,U_4032)) ),
inference(variable_rename,[status(thm)],[f_945_1]) ).
fof(f_945_3,plain,
! [U_4033,U_4032,U_4034,U_4031] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4034,tc_HOL_Obool)),U_4031),U_4033),U_4032))
| ~ hBOOL(hAPP(U_4033,U_4032))
| ~ hBOOL(hAPP(U_4031,U_4032)) ),
inference(definitional_conversion,[status(esa)],[f_945_2]) ).
cnf(f_945_4,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4034,tc_HOL_Obool)),U_4031),U_4033),U_4032))
| ~ hBOOL(hAPP(U_4033,U_4032))
| ~ hBOOL(hAPP(U_4031,U_4032)) ),
inference(clausify,[status(thm)],[f_945_3]) ).
fof(f_946_1,plain,
! [V_x_2,V_B_2,V_A_2,T_c] :
( ( 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_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf1E]) ).
fof(f_946_2,plain,
! [U_4038,U_4037,U_4036,U_4035] :
( ( hBOOL(hAPP(U_4037,U_4038))
& hBOOL(hAPP(U_4036,U_4038)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4035,tc_HOL_Obool)),U_4036),U_4037),U_4038)) ),
inference(variable_rename,[status(thm)],[f_946_1]) ).
fof(f_946_3,plain,
! [U_4038,U_4037,U_4036] :
( ! [U_4035] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4035,tc_HOL_Obool)),U_4036),U_4037),U_4038))
| ( hBOOL(hAPP(U_4037,U_4038))
& hBOOL(hAPP(U_4036,U_4038)) ) ),
inference(miniscope,[status(thm)],[f_946_2]) ).
fof(f_946_4,plain,
( ! [U_4036,U_4037,U_4038] :
( hBOOL(hAPP(U_4037,U_4038))
| ~ sP229(U_4036,U_4037,U_4038) )
& ! [U_4036,U_4037,U_4038] :
( hBOOL(hAPP(U_4036,U_4038))
| ~ sP229(U_4036,U_4037,U_4038) )
& ! [U_4036,U_4035,U_4037,U_4038] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4035,tc_HOL_Obool)),U_4036),U_4037),U_4038))
| sP229(U_4036,U_4037,U_4038) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229])],[f_946_3]) ).
cnf(f_946_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4035,tc_HOL_Obool)),U_4036),U_4037),U_4038))
| sP229(U_4036,U_4037,U_4038) ),
inference(clausify,[status(thm)],[f_946_4]) ).
cnf(f_946_6,plain,
( hBOOL(hAPP(U_4036,U_4038))
| ~ sP229(U_4036,U_4037,U_4038) ),
inference(clausify,[status(thm)],[f_946_4]) ).
cnf(f_946_7,plain,
( hBOOL(hAPP(U_4037,U_4038))
| ~ sP229(U_4036,U_4037,U_4038) ),
inference(clausify,[status(thm)],[f_946_4]) ).
fof(f_947_1,plain,
! [T_d,V_b_2,V_B_2,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(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_b_2))
| ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_SUP1__I]) ).
fof(f_947_2,plain,
! [U_4044,U_4043,U_4042,U_4041,U_4040,U_4039] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4039,tc_fun(U_4044,tc_HOL_Obool)),U_4041),U_4042),U_4043))
| ~ hBOOL(hAPP(hAPP(U_4042,U_4040),U_4043))
| ~ hBOOL(hAPP(hAPP(c_member(U_4039),U_4040),U_4041)) ),
inference(variable_rename,[status(thm)],[f_947_1]) ).
fof(f_947_3,plain,
! [U_4039,U_4040,U_4041,U_4042,U_4043,U_4044] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4039,tc_fun(U_4044,tc_HOL_Obool)),U_4041),U_4042),U_4043))
| ~ hBOOL(hAPP(hAPP(U_4042,U_4040),U_4043))
| ~ hBOOL(hAPP(hAPP(c_member(U_4039),U_4040),U_4041)) ),
inference(definitional_conversion,[status(esa)],[f_947_2]) ).
cnf(f_947_4,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4039,tc_fun(U_4044,tc_HOL_Obool)),U_4041),U_4042),U_4043))
| ~ hBOOL(hAPP(hAPP(U_4042,U_4040),U_4043))
| ~ hBOOL(hAPP(hAPP(c_member(U_4039),U_4040),U_4041)) ),
inference(clausify,[status(thm)],[f_947_3]) ).
fof(f_948_1,plain,
! [T_e,T_d,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_SUP2__I]) ).
fof(f_948_2,plain,
! [U_4052,U_4051,U_4050,U_4049,U_4048,U_4047,U_4046,U_4045] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4045,tc_fun(U_4051,tc_fun(U_4052,tc_HOL_Obool))),U_4047),U_4048),U_4049),U_4050))
| ~ hBOOL(hAPP(hAPP(hAPP(U_4048,U_4046),U_4049),U_4050))
| ~ hBOOL(hAPP(hAPP(c_member(U_4045),U_4046),U_4047)) ),
inference(variable_rename,[status(thm)],[f_948_1]) ).
fof(f_948_3,plain,
! [U_4045,U_4046,U_4047,U_4048,U_4049,U_4050,U_4051,U_4052] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4045,tc_fun(U_4051,tc_fun(U_4052,tc_HOL_Obool))),U_4047),U_4048),U_4049),U_4050))
| ~ hBOOL(hAPP(hAPP(hAPP(U_4048,U_4046),U_4049),U_4050))
| ~ hBOOL(hAPP(hAPP(c_member(U_4045),U_4046),U_4047)) ),
inference(definitional_conversion,[status(esa)],[f_948_2]) ).
cnf(f_948_4,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4045,tc_fun(U_4051,tc_fun(U_4052,tc_HOL_Obool))),U_4047),U_4048),U_4049),U_4050))
| ~ hBOOL(hAPP(hAPP(hAPP(U_4048,U_4046),U_4049),U_4050))
| ~ hBOOL(hAPP(hAPP(c_member(U_4045),U_4046),U_4047)) ),
inference(clausify,[status(thm)],[f_948_3]) ).
fof(f_949_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_IntI]) ).
fof(f_949_2,plain,
! [U_4056,U_4055,U_4054,U_4053] :
( hBOOL(hAPP(hAPP(c_member(U_4053),U_4054),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4053,tc_HOL_Obool)),U_4055),U_4056)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4053),U_4054),U_4056))
| ~ hBOOL(hAPP(hAPP(c_member(U_4053),U_4054),U_4055)) ),
inference(variable_rename,[status(thm)],[f_949_1]) ).
fof(f_949_3,plain,
! [U_4053,U_4054,U_4055,U_4056] :
( hBOOL(hAPP(hAPP(c_member(U_4053),U_4054),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4053,tc_HOL_Obool)),U_4055),U_4056)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4053),U_4054),U_4056))
| ~ hBOOL(hAPP(hAPP(c_member(U_4053),U_4054),U_4055)) ),
inference(definitional_conversion,[status(esa)],[f_949_2]) ).
cnf(f_949_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_4053),U_4054),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4053,tc_HOL_Obool)),U_4055),U_4056)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4053),U_4054),U_4056))
| ~ hBOOL(hAPP(hAPP(c_member(U_4053),U_4054),U_4055)) ),
inference(clausify,[status(thm)],[f_949_3]) ).
fof(f_950_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntE]) ).
fof(f_950_2,plain,
! [U_4060,U_4059,U_4058,U_4057] :
( ( hBOOL(hAPP(hAPP(c_member(U_4057),U_4058),U_4060))
& hBOOL(hAPP(hAPP(c_member(U_4057),U_4058),U_4059)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4057),U_4058),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4057,tc_HOL_Obool)),U_4059),U_4060))) ),
inference(variable_rename,[status(thm)],[f_950_1]) ).
fof(f_950_3,plain,
( ! [U_4057,U_4058,U_4059,U_4060] :
( hBOOL(hAPP(hAPP(c_member(U_4057),U_4058),U_4060))
| ~ sP230(U_4057,U_4058,U_4059,U_4060) )
& ! [U_4057,U_4058,U_4059,U_4060] :
( hBOOL(hAPP(hAPP(c_member(U_4057),U_4058),U_4059))
| ~ sP230(U_4057,U_4058,U_4059,U_4060) )
& ! [U_4057,U_4058,U_4059,U_4060] :
( sP230(U_4057,U_4058,U_4059,U_4060)
| ~ hBOOL(hAPP(hAPP(c_member(U_4057),U_4058),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4057,tc_HOL_Obool)),U_4059),U_4060))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP230])],[f_950_2]) ).
cnf(f_950_4,plain,
( sP230(U_4057,U_4058,U_4059,U_4060)
| ~ hBOOL(hAPP(hAPP(c_member(U_4057),U_4058),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4057,tc_HOL_Obool)),U_4059),U_4060))) ),
inference(clausify,[status(thm)],[f_950_3]) ).
cnf(f_950_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_4057),U_4058),U_4059))
| ~ sP230(U_4057,U_4058,U_4059,U_4060) ),
inference(clausify,[status(thm)],[f_950_3]) ).
cnf(f_950_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4057),U_4058),U_4060))
| ~ sP230(U_4057,U_4058,U_4059,U_4060) ),
inference(clausify,[status(thm)],[f_950_3]) ).
fof(f_951_1,plain,
! [V_Ga_2,V_F_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_F_2),V_Ga_2)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_Ga_2))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Int]) ).
fof(f_951_2,plain,
! [U_4063,U_4062,U_4061] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4061),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4061,tc_HOL_Obool)),U_4062),U_4063)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4061),U_4063))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4061),U_4062)) ) ),
inference(variable_rename,[status(thm)],[f_951_1]) ).
fof(f_951_3,plain,
( ! [U_4061,U_4062,U_4063] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4061),U_4063))
| ~ sP231(U_4061,U_4062,U_4063) )
& ! [U_4061,U_4062,U_4063] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4061),U_4062))
| ~ sP231(U_4061,U_4062,U_4063) )
& ! [U_4061,U_4062,U_4063] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4061),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4061,tc_HOL_Obool)),U_4062),U_4063)))
| sP231(U_4061,U_4062,U_4063) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231])],[f_951_2]) ).
cnf(f_951_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4061),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4061,tc_HOL_Obool)),U_4062),U_4063)))
| sP231(U_4061,U_4062,U_4063) ),
inference(clausify,[status(thm)],[f_951_3]) ).
cnf(f_951_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4061),U_4062))
| ~ sP231(U_4061,U_4062,U_4063) ),
inference(clausify,[status(thm)],[f_951_3]) ).
cnf(f_951_6,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4061),U_4063))
| ~ sP231(U_4061,U_4062,U_4063) ),
inference(clausify,[status(thm)],[f_951_3]) ).
fof(f_952_1,plain,
! [T_d,V_B_2,T_c,V_b_2,V_a_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_B_2))
| hAPP(V_f_2,V_a_2) != V_b_2 ),
inference(fof_nnf,[status(thm)],[fact_vimageI]) ).
fof(f_952_2,plain,
! [U_4069,U_4068,U_4067,U_4066,U_4065,U_4064] :
( hBOOL(hAPP(hAPP(c_member(U_4069),U_4065),hAPP(c_Set_Ovimage(U_4069,U_4067,U_4064),U_4068)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4067),U_4066),U_4068))
| hAPP(U_4064,U_4065) != U_4066 ),
inference(variable_rename,[status(thm)],[f_952_1]) ).
fof(f_952_3,plain,
! [U_4064,U_4065,U_4066,U_4067,U_4068,U_4069] :
( hBOOL(hAPP(hAPP(c_member(U_4069),U_4065),hAPP(c_Set_Ovimage(U_4069,U_4067,U_4064),U_4068)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4067),U_4066),U_4068))
| hAPP(U_4064,U_4065) != U_4066 ),
inference(definitional_conversion,[status(esa)],[f_952_2]) ).
cnf(f_952_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_4069),U_4065),hAPP(c_Set_Ovimage(U_4069,U_4067,U_4064),U_4068)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4067),U_4066),U_4068))
| hAPP(U_4064,U_4065) != U_4066 ),
inference(clausify,[status(thm)],[f_952_3]) ).
fof(f_953_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_953_2,plain,
! [U_4071,U_4070] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4070),U_4071),U_4071) = U_4071
| ~ class_Lattices_Olattice(U_4070) ),
inference(variable_rename,[status(thm)],[f_953_1]) ).
fof(f_953_3,plain,
! [U_4071,U_4070] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4070),U_4071),U_4071) = U_4071
| ~ class_Lattices_Olattice(U_4070) ),
inference(definitional_conversion,[status(esa)],[f_953_2]) ).
cnf(f_953_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4070),U_4071),U_4071) = U_4071
| ~ class_Lattices_Olattice(U_4070) ),
inference(clausify,[status(thm)],[f_953_3]) ).
fof(f_954_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Int__absorb]) ).
fof(f_954_2,plain,
! [U_4073,U_4072] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4072,tc_HOL_Obool)),U_4073),U_4073) = U_4073,
inference(variable_rename,[status(thm)],[f_954_1]) ).
fof(f_954_3,plain,
! [U_4072,U_4073] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4072,tc_HOL_Obool)),U_4073),U_4073) = U_4073,
inference(definitional_conversion,[status(esa)],[f_954_2]) ).
cnf(f_954_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4072,tc_HOL_Obool)),U_4073),U_4073) = U_4073,
inference(clausify,[status(thm)],[f_954_3]) ).
fof(f_955_1,plain,
! [V_B_2,V_A_2,T_c] : 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_c,tc_HOL_Obool)),V_B_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_Int__commute]) ).
fof(f_955_2,plain,
! [U_4076,U_4075,U_4074] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4074,tc_HOL_Obool)),U_4075),U_4076) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4074,tc_HOL_Obool)),U_4076),U_4075),
inference(variable_rename,[status(thm)],[f_955_1]) ).
fof(f_955_3,plain,
! [U_4074,U_4075,U_4076] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4074,tc_HOL_Obool)),U_4075),U_4076) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4074,tc_HOL_Obool)),U_4076),U_4075),
inference(definitional_conversion,[status(esa)],[f_955_2]) ).
cnf(f_955_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4074,tc_HOL_Obool)),U_4075),U_4076) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4074,tc_HOL_Obool)),U_4076),U_4075),
inference(clausify,[status(thm)],[f_955_3]) ).
fof(f_956_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_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_c,tc_HOL_Obool)),V_A_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Int__left__absorb]) ).
fof(f_956_2,plain,
! [U_4079,U_4078,U_4077] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4077,tc_HOL_Obool)),U_4078),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4077,tc_HOL_Obool)),U_4078),U_4079)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4077,tc_HOL_Obool)),U_4078),U_4079),
inference(variable_rename,[status(thm)],[f_956_1]) ).
fof(f_956_3,plain,
! [U_4077,U_4078,U_4079] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4077,tc_HOL_Obool)),U_4078),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4077,tc_HOL_Obool)),U_4078),U_4079)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4077,tc_HOL_Obool)),U_4078),U_4079),
inference(definitional_conversion,[status(esa)],[f_956_2]) ).
cnf(f_956_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4077,tc_HOL_Obool)),U_4078),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4077,tc_HOL_Obool)),U_4078),U_4079)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4077,tc_HOL_Obool)),U_4078),U_4079),
inference(clausify,[status(thm)],[f_956_3]) ).
fof(f_957_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Int__left__commute]) ).
fof(f_957_2,plain,
! [U_4083,U_4082,U_4081,U_4080] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4081),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4082),U_4083)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4082),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4083)),
inference(variable_rename,[status(thm)],[f_957_1]) ).
fof(f_957_3,plain,
! [U_4080,U_4081,U_4082,U_4083] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4081),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4082),U_4083)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4082),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4083)),
inference(definitional_conversion,[status(esa)],[f_957_2]) ).
cnf(f_957_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4081),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4082),U_4083)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4082),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4080,tc_HOL_Obool)),U_4081),U_4083)),
inference(clausify,[status(thm)],[f_957_3]) ).
fof(f_958_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_Ovimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Int]) ).
fof(f_958_2,plain,
! [U_4088,U_4087,U_4086,U_4085,U_4084] : hAPP(c_Set_Ovimage(U_4084,U_4085,U_4086),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4085,tc_HOL_Obool)),U_4087),U_4088)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4084,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4084,U_4085,U_4086),U_4087)),hAPP(c_Set_Ovimage(U_4084,U_4085,U_4086),U_4088)),
inference(variable_rename,[status(thm)],[f_958_1]) ).
fof(f_958_3,plain,
! [U_4088,U_4084,U_4085,U_4086,U_4087] : hAPP(c_Set_Ovimage(U_4084,U_4085,U_4086),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4085,tc_HOL_Obool)),U_4087),U_4088)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4084,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4084,U_4085,U_4086),U_4087)),hAPP(c_Set_Ovimage(U_4084,U_4085,U_4086),U_4088)),
inference(definitional_conversion,[status(esa)],[f_958_2]) ).
cnf(f_958_4,plain,
hAPP(c_Set_Ovimage(U_4084,U_4085,U_4086),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4085,tc_HOL_Obool)),U_4087),U_4088)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4084,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4084,U_4085,U_4086),U_4087)),hAPP(c_Set_Ovimage(U_4084,U_4085,U_4086),U_4088)),
inference(clausify,[status(thm)],[f_958_3]) ).
fof(f_959_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Int__assoc]) ).
fof(f_959_2,plain,
! [U_4092,U_4091,U_4090,U_4089] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4089,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4089,tc_HOL_Obool)),U_4090),U_4091)),U_4092) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4089,tc_HOL_Obool)),U_4090),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4089,tc_HOL_Obool)),U_4091),U_4092)),
inference(variable_rename,[status(thm)],[f_959_1]) ).
fof(f_959_3,plain,
! [U_4089,U_4090,U_4091,U_4092] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4089,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4089,tc_HOL_Obool)),U_4090),U_4091)),U_4092) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4089,tc_HOL_Obool)),U_4090),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4089,tc_HOL_Obool)),U_4091),U_4092)),
inference(definitional_conversion,[status(esa)],[f_959_2]) ).
cnf(f_959_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4089,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4089,tc_HOL_Obool)),U_4090),U_4091)),U_4092) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4089,tc_HOL_Obool)),U_4090),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4089,tc_HOL_Obool)),U_4091),U_4092)),
inference(clausify,[status(thm)],[f_959_3]) ).
fof(f_960_1,plain,
! [V_x_2,V_A_2,V_f_2,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2),V_x_2))
| ~ hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) )
& ( hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_vimage__code]) ).
fof(f_960_2,plain,
! [U_4097,U_4096,U_4095,U_4094,U_4093] :
( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_4093,U_4094,U_4095),U_4096),U_4097))
| ~ hBOOL(hAPP(U_4096,hAPP(U_4095,U_4097))) )
& ( hBOOL(hAPP(U_4096,hAPP(U_4095,U_4097)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_4093,U_4094,U_4095),U_4096),U_4097)) ) ),
inference(variable_rename,[status(thm)],[f_960_1]) ).
fof(f_960_3,plain,
( ! [U_4107,U_4105,U_4103] :
( ! [U_4101,U_4099] : hBOOL(hAPP(hAPP(c_Set_Ovimage(U_4099,U_4101,U_4103),U_4105),U_4107))
| ~ hBOOL(hAPP(U_4105,hAPP(U_4103,U_4107))) )
& ! [U_4106,U_4104,U_4102] :
( ! [U_4100,U_4098] : ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_4098,U_4100,U_4102),U_4104),U_4106))
| hBOOL(hAPP(U_4104,hAPP(U_4102,U_4106))) ) ),
inference(miniscope,[status(thm)],[f_960_2]) ).
fof(f_960_4,plain,
( ! [U_4105,U_4099,U_4101,U_4103,U_4107] :
( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_4099,U_4101,U_4103),U_4105),U_4107))
| ~ hBOOL(hAPP(U_4105,hAPP(U_4103,U_4107))) )
& ! [U_4098,U_4104,U_4106,U_4102,U_4100] :
( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_4098,U_4100,U_4102),U_4104),U_4106))
| hBOOL(hAPP(U_4104,hAPP(U_4102,U_4106))) ) ),
inference(definitional_conversion,[status(esa)],[f_960_3]) ).
cnf(f_960_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_4098,U_4100,U_4102),U_4104),U_4106))
| hBOOL(hAPP(U_4104,hAPP(U_4102,U_4106))) ),
inference(clausify,[status(thm)],[f_960_4]) ).
cnf(f_960_6,plain,
( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_4099,U_4101,U_4103),U_4105),U_4107))
| ~ hBOOL(hAPP(U_4105,hAPP(U_4103,U_4107))) ),
inference(clausify,[status(thm)],[f_960_4]) ).
fof(f_961_1,plain,
! [V_x_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(V_A_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf1D1]) ).
fof(f_961_2,plain,
! [U_4111,U_4110,U_4109,U_4108] :
( hBOOL(hAPP(U_4109,U_4111))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4108,tc_HOL_Obool)),U_4109),U_4110),U_4111)) ),
inference(variable_rename,[status(thm)],[f_961_1]) ).
fof(f_961_3,plain,
! [U_4111,U_4110,U_4109] :
( ! [U_4108] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4108,tc_HOL_Obool)),U_4109),U_4110),U_4111))
| hBOOL(hAPP(U_4109,U_4111)) ),
inference(miniscope,[status(thm)],[f_961_2]) ).
fof(f_961_4,plain,
! [U_4108,U_4109,U_4110,U_4111] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4108,tc_HOL_Obool)),U_4109),U_4110),U_4111))
| hBOOL(hAPP(U_4109,U_4111)) ),
inference(definitional_conversion,[status(esa)],[f_961_3]) ).
cnf(f_961_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4108,tc_HOL_Obool)),U_4109),U_4110),U_4111))
| hBOOL(hAPP(U_4109,U_4111)) ),
inference(clausify,[status(thm)],[f_961_4]) ).
fof(f_962_1,plain,
! [V_x_2,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(V_B_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf1D2]) ).
fof(f_962_2,plain,
! [U_4115,U_4114,U_4113,U_4112] :
( hBOOL(hAPP(U_4114,U_4115))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4112,tc_HOL_Obool)),U_4113),U_4114),U_4115)) ),
inference(variable_rename,[status(thm)],[f_962_1]) ).
fof(f_962_3,plain,
! [U_4115,U_4114] :
( ! [U_4113,U_4112] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4112,tc_HOL_Obool)),U_4113),U_4114),U_4115))
| hBOOL(hAPP(U_4114,U_4115)) ),
inference(miniscope,[status(thm)],[f_962_2]) ).
fof(f_962_4,plain,
! [U_4112,U_4113,U_4114,U_4115] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4112,tc_HOL_Obool)),U_4113),U_4114),U_4115))
| hBOOL(hAPP(U_4114,U_4115)) ),
inference(definitional_conversion,[status(esa)],[f_962_3]) ).
cnf(f_962_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4112,tc_HOL_Obool)),U_4113),U_4114),U_4115))
| hBOOL(hAPP(U_4114,U_4115)) ),
inference(clausify,[status(thm)],[f_962_4]) ).
fof(f_963_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_963_2,plain,
! [U_4117,U_4116] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4116),U_4117),U_4117) = U_4117
| ~ class_Lattices_Osemilattice__inf(U_4116) ),
inference(variable_rename,[status(thm)],[f_963_1]) ).
fof(f_963_3,plain,
! [U_4116,U_4117] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4116),U_4117),U_4117) = U_4117
| ~ class_Lattices_Osemilattice__inf(U_4116) ),
inference(definitional_conversion,[status(esa)],[f_963_2]) ).
cnf(f_963_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4116),U_4117),U_4117) = U_4117
| ~ class_Lattices_Osemilattice__inf(U_4116) ),
inference(clausify,[status(thm)],[f_963_3]) ).
fof(f_964_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_964_2,plain,
! [U_4119,U_4118] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4118),U_4119),U_4119) = U_4119
| ~ class_Lattices_Osemilattice__inf(U_4118) ),
inference(variable_rename,[status(thm)],[f_964_1]) ).
fof(f_964_3,plain,
! [U_4118,U_4119] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4118),U_4119),U_4119) = U_4119
| ~ class_Lattices_Osemilattice__inf(U_4118) ),
inference(definitional_conversion,[status(esa)],[f_964_2]) ).
cnf(f_964_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4118),U_4119),U_4119) = U_4119
| ~ class_Lattices_Osemilattice__inf(U_4118) ),
inference(clausify,[status(thm)],[f_964_3]) ).
fof(f_965_1,plain,
! [V_x_2,V_g_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,T_c)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inf__fun__def]) ).
fof(f_965_2,plain,
! [U_4124,U_4123,U_4122,U_4121,U_4120] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4121,U_4120)),U_4122),U_4123),U_4124) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4120),hAPP(U_4122,U_4124)),hAPP(U_4123,U_4124))
| ~ class_Lattices_Olattice(U_4120) ),
inference(variable_rename,[status(thm)],[f_965_1]) ).
fof(f_965_3,plain,
! [U_4120,U_4121,U_4122,U_4123,U_4124] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4121,U_4120)),U_4122),U_4123),U_4124) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4120),hAPP(U_4122,U_4124)),hAPP(U_4123,U_4124))
| ~ class_Lattices_Olattice(U_4120) ),
inference(definitional_conversion,[status(esa)],[f_965_2]) ).
cnf(f_965_4,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4121,U_4120)),U_4122),U_4123),U_4124) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4120),hAPP(U_4122,U_4124)),hAPP(U_4123,U_4124))
| ~ class_Lattices_Olattice(U_4120) ),
inference(clausify,[status(thm)],[f_965_3]) ).
fof(f_966_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_966_2,plain,
! [U_4127,U_4126,U_4125] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4125),U_4126),U_4127) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4125),U_4127),U_4126)
| ~ class_Lattices_Osemilattice__inf(U_4125) ),
inference(variable_rename,[status(thm)],[f_966_1]) ).
fof(f_966_3,plain,
! [U_4125,U_4126,U_4127] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4125),U_4126),U_4127) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4125),U_4127),U_4126)
| ~ class_Lattices_Osemilattice__inf(U_4125) ),
inference(definitional_conversion,[status(esa)],[f_966_2]) ).
cnf(f_966_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4125),U_4126),U_4127) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4125),U_4127),U_4126)
| ~ class_Lattices_Osemilattice__inf(U_4125) ),
inference(clausify,[status(thm)],[f_966_3]) ).
fof(f_967_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_967_2,plain,
! [U_4130,U_4129,U_4128] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4128),U_4129),U_4130) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4128),U_4130),U_4129)
| ~ class_Lattices_Olattice(U_4128) ),
inference(variable_rename,[status(thm)],[f_967_1]) ).
fof(f_967_3,plain,
! [U_4128,U_4129,U_4130] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4128),U_4129),U_4130) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4128),U_4130),U_4129)
| ~ class_Lattices_Olattice(U_4128) ),
inference(definitional_conversion,[status(esa)],[f_967_2]) ).
cnf(f_967_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4128),U_4129),U_4130) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4128),U_4130),U_4129)
| ~ class_Lattices_Olattice(U_4128) ),
inference(clausify,[status(thm)],[f_967_3]) ).
fof(f_968_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_968_2,plain,
! [U_4133,U_4132,U_4131] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4131),U_4132),U_4133) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4131),U_4133),U_4132)
| ~ class_Lattices_Osemilattice__inf(U_4131) ),
inference(variable_rename,[status(thm)],[f_968_1]) ).
fof(f_968_3,plain,
! [U_4131,U_4132,U_4133] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4131),U_4132),U_4133) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4131),U_4133),U_4132)
| ~ class_Lattices_Osemilattice__inf(U_4131) ),
inference(definitional_conversion,[status(esa)],[f_968_2]) ).
cnf(f_968_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4131),U_4132),U_4133) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4131),U_4133),U_4132)
| ~ class_Lattices_Osemilattice__inf(U_4131) ),
inference(clausify,[status(thm)],[f_968_3]) ).
fof(f_969_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_969_2,plain,
! [U_4136,U_4135,U_4134] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4134),U_4135),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4134),U_4135),U_4136)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4134),U_4135),U_4136)
| ~ class_Lattices_Osemilattice__inf(U_4134) ),
inference(variable_rename,[status(thm)],[f_969_1]) ).
fof(f_969_3,plain,
! [U_4134,U_4135,U_4136] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4134),U_4135),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4134),U_4135),U_4136)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4134),U_4135),U_4136)
| ~ class_Lattices_Osemilattice__inf(U_4134) ),
inference(definitional_conversion,[status(esa)],[f_969_2]) ).
cnf(f_969_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4134),U_4135),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4134),U_4135),U_4136)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4134),U_4135),U_4136)
| ~ class_Lattices_Osemilattice__inf(U_4134) ),
inference(clausify,[status(thm)],[f_969_3]) ).
fof(f_970_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_970_2,plain,
! [U_4139,U_4138,U_4137] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4137),U_4138),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4137),U_4138),U_4139)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4137),U_4138),U_4139)
| ~ class_Lattices_Olattice(U_4137) ),
inference(variable_rename,[status(thm)],[f_970_1]) ).
fof(f_970_3,plain,
! [U_4137,U_4138,U_4139] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4137),U_4138),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4137),U_4138),U_4139)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4137),U_4138),U_4139)
| ~ class_Lattices_Olattice(U_4137) ),
inference(definitional_conversion,[status(esa)],[f_970_2]) ).
cnf(f_970_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4137),U_4138),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4137),U_4138),U_4139)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4137),U_4138),U_4139)
| ~ class_Lattices_Olattice(U_4137) ),
inference(clausify,[status(thm)],[f_970_3]) ).
fof(f_971_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_971_2,plain,
! [U_4142,U_4141,U_4140] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4140),U_4141),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4140),U_4141),U_4142)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4140),U_4141),U_4142)
| ~ class_Lattices_Osemilattice__inf(U_4140) ),
inference(variable_rename,[status(thm)],[f_971_1]) ).
fof(f_971_3,plain,
! [U_4140,U_4141,U_4142] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4140),U_4141),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4140),U_4141),U_4142)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4140),U_4141),U_4142)
| ~ class_Lattices_Osemilattice__inf(U_4140) ),
inference(definitional_conversion,[status(esa)],[f_971_2]) ).
cnf(f_971_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4140),U_4141),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4140),U_4141),U_4142)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4140),U_4141),U_4142)
| ~ class_Lattices_Osemilattice__inf(U_4140) ),
inference(clausify,[status(thm)],[f_971_3]) ).
fof(f_972_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_972_2,plain,
! [U_4146,U_4145,U_4144,U_4143] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4143),U_4144),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4143),U_4145),U_4146)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4143),U_4145),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4143),U_4144),U_4146))
| ~ class_Lattices_Osemilattice__inf(U_4143) ),
inference(variable_rename,[status(thm)],[f_972_1]) ).
fof(f_972_3,plain,
! [U_4143,U_4144,U_4145,U_4146] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4143),U_4144),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4143),U_4145),U_4146)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4143),U_4145),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4143),U_4144),U_4146))
| ~ class_Lattices_Osemilattice__inf(U_4143) ),
inference(definitional_conversion,[status(esa)],[f_972_2]) ).
cnf(f_972_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4143),U_4144),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4143),U_4145),U_4146)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4143),U_4145),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4143),U_4144),U_4146))
| ~ class_Lattices_Osemilattice__inf(U_4143) ),
inference(clausify,[status(thm)],[f_972_3]) ).
fof(f_973_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_973_2,plain,
! [U_4150,U_4149,U_4148,U_4147] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4147),U_4148),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4147),U_4149),U_4150)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4147),U_4149),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4147),U_4148),U_4150))
| ~ class_Lattices_Olattice(U_4147) ),
inference(variable_rename,[status(thm)],[f_973_1]) ).
fof(f_973_3,plain,
! [U_4147,U_4148,U_4149,U_4150] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4147),U_4148),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4147),U_4149),U_4150)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4147),U_4149),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4147),U_4148),U_4150))
| ~ class_Lattices_Olattice(U_4147) ),
inference(definitional_conversion,[status(esa)],[f_973_2]) ).
cnf(f_973_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4147),U_4148),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4147),U_4149),U_4150)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4147),U_4149),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4147),U_4148),U_4150))
| ~ class_Lattices_Olattice(U_4147) ),
inference(clausify,[status(thm)],[f_973_3]) ).
fof(f_974_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_974_2,plain,
! [U_4154,U_4153,U_4152,U_4151] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4151),U_4152),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4151),U_4153),U_4154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4151),U_4153),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4151),U_4152),U_4154))
| ~ class_Lattices_Osemilattice__inf(U_4151) ),
inference(variable_rename,[status(thm)],[f_974_1]) ).
fof(f_974_3,plain,
! [U_4151,U_4152,U_4153,U_4154] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4151),U_4152),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4151),U_4153),U_4154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4151),U_4153),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4151),U_4152),U_4154))
| ~ class_Lattices_Osemilattice__inf(U_4151) ),
inference(definitional_conversion,[status(esa)],[f_974_2]) ).
cnf(f_974_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4151),U_4152),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4151),U_4153),U_4154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4151),U_4153),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4151),U_4152),U_4154))
| ~ class_Lattices_Osemilattice__inf(U_4151) ),
inference(clausify,[status(thm)],[f_974_3]) ).
fof(f_975_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_975_2,plain,
! [U_4158,U_4157,U_4156,U_4155] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),U_4156),U_4157)),U_4158) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),U_4156),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),U_4157),U_4158))
| ~ class_Lattices_Osemilattice__inf(U_4155) ),
inference(variable_rename,[status(thm)],[f_975_1]) ).
fof(f_975_3,plain,
! [U_4155,U_4156,U_4157,U_4158] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),U_4156),U_4157)),U_4158) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),U_4156),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),U_4157),U_4158))
| ~ class_Lattices_Osemilattice__inf(U_4155) ),
inference(definitional_conversion,[status(esa)],[f_975_2]) ).
cnf(f_975_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),U_4156),U_4157)),U_4158) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),U_4156),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4155),U_4157),U_4158))
| ~ class_Lattices_Osemilattice__inf(U_4155) ),
inference(clausify,[status(thm)],[f_975_3]) ).
fof(f_976_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_976_2,plain,
! [U_4162,U_4161,U_4160,U_4159] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4159),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4159),U_4160),U_4161)),U_4162) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4159),U_4160),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4159),U_4161),U_4162))
| ~ class_Lattices_Olattice(U_4159) ),
inference(variable_rename,[status(thm)],[f_976_1]) ).
fof(f_976_3,plain,
! [U_4159,U_4160,U_4161,U_4162] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4159),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4159),U_4160),U_4161)),U_4162) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4159),U_4160),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4159),U_4161),U_4162))
| ~ class_Lattices_Olattice(U_4159) ),
inference(definitional_conversion,[status(esa)],[f_976_2]) ).
cnf(f_976_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4159),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4159),U_4160),U_4161)),U_4162) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4159),U_4160),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4159),U_4161),U_4162))
| ~ class_Lattices_Olattice(U_4159) ),
inference(clausify,[status(thm)],[f_976_3]) ).
fof(f_977_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_977_2,plain,
! [U_4166,U_4165,U_4164,U_4163] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4163),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4163),U_4164),U_4165)),U_4166) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4163),U_4164),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4163),U_4165),U_4166))
| ~ class_Lattices_Osemilattice__inf(U_4163) ),
inference(variable_rename,[status(thm)],[f_977_1]) ).
fof(f_977_3,plain,
! [U_4163,U_4164,U_4165,U_4166] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4163),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4163),U_4164),U_4165)),U_4166) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4163),U_4164),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4163),U_4165),U_4166))
| ~ class_Lattices_Osemilattice__inf(U_4163) ),
inference(definitional_conversion,[status(esa)],[f_977_2]) ).
cnf(f_977_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4163),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4163),U_4164),U_4165)),U_4166) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4163),U_4164),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4163),U_4165),U_4166))
| ~ class_Lattices_Osemilattice__inf(U_4163) ),
inference(clausify,[status(thm)],[f_977_3]) ).
fof(f_978_1,plain,
! [V_x_2,V_g_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,T_c)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inf__apply]) ).
fof(f_978_2,plain,
! [U_4171,U_4170,U_4169,U_4168,U_4167] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4168,U_4167)),U_4169),U_4170),U_4171) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4167),hAPP(U_4169,U_4171)),hAPP(U_4170,U_4171))
| ~ class_Lattices_Olattice(U_4167) ),
inference(variable_rename,[status(thm)],[f_978_1]) ).
fof(f_978_3,plain,
! [U_4167,U_4168,U_4169,U_4170,U_4171] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4168,U_4167)),U_4169),U_4170),U_4171) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4167),hAPP(U_4169,U_4171)),hAPP(U_4170,U_4171))
| ~ class_Lattices_Olattice(U_4167) ),
inference(definitional_conversion,[status(esa)],[f_978_2]) ).
cnf(f_978_4,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4168,U_4167)),U_4169),U_4170),U_4171) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4167),hAPP(U_4169,U_4171)),hAPP(U_4170,U_4171))
| ~ class_Lattices_Olattice(U_4167) ),
inference(clausify,[status(thm)],[f_978_3]) ).
fof(f_979_1,plain,
! [V_Y_2,T_c] : hAPP(c_Set_Ovimage(T_c,T_c,c_COMBI(T_c)),V_Y_2) = V_Y_2,
inference(fof_nnf,[status(thm)],[fact_vimage__ident]) ).
fof(f_979_2,plain,
! [U_4173,U_4172] : hAPP(c_Set_Ovimage(U_4172,U_4172,c_COMBI(U_4172)),U_4173) = U_4173,
inference(variable_rename,[status(thm)],[f_979_1]) ).
fof(f_979_3,plain,
! [U_4172,U_4173] : hAPP(c_Set_Ovimage(U_4172,U_4172,c_COMBI(U_4172)),U_4173) = U_4173,
inference(definitional_conversion,[status(esa)],[f_979_2]) ).
cnf(f_979_4,plain,
hAPP(c_Set_Ovimage(U_4172,U_4172,c_COMBI(U_4172)),U_4173) = U_4173,
inference(clausify,[status(thm)],[f_979_3]) ).
fof(f_980_1,plain,
! [V_A_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_image__vimage__eq]) ).
fof(f_980_2,plain,
! [U_4177,U_4176,U_4175,U_4174] : hAPP(c_Set_Oimage(U_4174,U_4175,U_4176),hAPP(c_Set_Ovimage(U_4174,U_4175,U_4176),U_4177)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4175,tc_HOL_Obool)),U_4177),hAPP(c_Set_Oimage(U_4174,U_4175,U_4176),c_Orderings_Otop__class_Otop(tc_fun(U_4174,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_980_1]) ).
fof(f_980_3,plain,
! [U_4174,U_4175,U_4176,U_4177] : hAPP(c_Set_Oimage(U_4174,U_4175,U_4176),hAPP(c_Set_Ovimage(U_4174,U_4175,U_4176),U_4177)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4175,tc_HOL_Obool)),U_4177),hAPP(c_Set_Oimage(U_4174,U_4175,U_4176),c_Orderings_Otop__class_Otop(tc_fun(U_4174,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_980_2]) ).
cnf(f_980_4,plain,
hAPP(c_Set_Oimage(U_4174,U_4175,U_4176),hAPP(c_Set_Ovimage(U_4174,U_4175,U_4176),U_4177)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4175,tc_HOL_Obool)),U_4177),hAPP(c_Set_Oimage(U_4174,U_4175,U_4176),c_Orderings_Otop__class_Otop(tc_fun(U_4174,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_980_3]) ).
fof(f_981_1,plain,
! [V_B_2,T_d,V_A_2,T_c] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__UN]) ).
fof(f_981_2,plain,
! [U_4183,U_4182,U_4181,U_4180] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4180,tc_fun(U_4182,tc_HOL_Obool)),U_4181),U_4183)))
| ? [U_4179] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(U_4183,U_4179)))
& hBOOL(hAPP(hAPP(c_member(U_4180),U_4179),U_4181)) ) )
& ( ! [U_4178] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(U_4183,U_4178)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4180),U_4178),U_4181)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4180,tc_fun(U_4182,tc_HOL_Obool)),U_4181),U_4183))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4180),U_4181)) ),
inference(variable_rename,[status(thm)],[f_981_1]) ).
fof(f_981_3,plain,
! [U_4183,U_4182,U_4181,U_4180] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4180,tc_fun(U_4182,tc_HOL_Obool)),U_4181),U_4183)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(U_4183,sK88(U_4183,U_4182,U_4181,U_4180))))
& hBOOL(hAPP(hAPP(c_member(U_4180),sK88(U_4183,U_4182,U_4181,U_4180)),U_4181)) ) )
& ( ! [U_4178] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(U_4183,U_4178)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4180),U_4178),U_4181)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4180,tc_fun(U_4182,tc_HOL_Obool)),U_4181),U_4183))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4180),U_4181)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_4179,sK88(U_4183,U_4182,U_4181,U_4180))],[f_981_2]) ).
fof(f_981_4,plain,
( ! [U_4180,U_4181,U_4182,U_4183] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(U_4183,sK88(U_4183,U_4182,U_4181,U_4180))))
| ~ sP232(U_4180,U_4181,U_4182,U_4183) )
& ! [U_4180,U_4181,U_4182,U_4183] :
( hBOOL(hAPP(hAPP(c_member(U_4180),sK88(U_4183,U_4182,U_4181,U_4180)),U_4181))
| ~ sP232(U_4180,U_4181,U_4182,U_4183) )
& ! [U_4178,U_4180,U_4181,U_4182,U_4183] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4180,tc_fun(U_4182,tc_HOL_Obool)),U_4181),U_4183)))
| sP232(U_4180,U_4181,U_4182,U_4183)
| ~ sP233(U_4178,U_4180,U_4181,U_4182,U_4183) )
& ! [U_4178,U_4180,U_4181,U_4182,U_4183] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(U_4183,U_4178)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4180),U_4178),U_4181))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4180,tc_fun(U_4182,tc_HOL_Obool)),U_4181),U_4183)))
| ~ sP233(U_4178,U_4180,U_4181,U_4182,U_4183) )
& ! [U_4178,U_4180,U_4181,U_4182,U_4183] :
( sP233(U_4178,U_4180,U_4181,U_4182,U_4183)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4180),U_4181)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP232,sP233])],[f_981_3]) ).
cnf(f_981_5,plain,
( sP233(U_4178,U_4180,U_4181,U_4182,U_4183)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4180),U_4181)) ),
inference(clausify,[status(thm)],[f_981_4]) ).
cnf(f_981_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(U_4183,U_4178)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4180),U_4178),U_4181))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4180,tc_fun(U_4182,tc_HOL_Obool)),U_4181),U_4183)))
| ~ sP233(U_4178,U_4180,U_4181,U_4182,U_4183) ),
inference(clausify,[status(thm)],[f_981_4]) ).
cnf(f_981_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4180,tc_fun(U_4182,tc_HOL_Obool)),U_4181),U_4183)))
| sP232(U_4180,U_4181,U_4182,U_4183)
| ~ sP233(U_4178,U_4180,U_4181,U_4182,U_4183) ),
inference(clausify,[status(thm)],[f_981_4]) ).
cnf(f_981_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_4180),sK88(U_4183,U_4182,U_4181,U_4180)),U_4181))
| ~ sP232(U_4180,U_4181,U_4182,U_4183) ),
inference(clausify,[status(thm)],[f_981_4]) ).
cnf(f_981_9,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4182),hAPP(U_4183,sK88(U_4183,U_4182,U_4181,U_4180))))
| ~ sP232(U_4180,U_4181,U_4182,U_4183) ),
inference(clausify,[status(thm)],[f_981_4]) ).
fof(f_982_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_982_2,plain,
! [U_4186,U_4185,U_4184] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4184),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4184),U_4185),U_4186)),U_4185))
| ~ class_Lattices_Olattice(U_4184) ),
inference(variable_rename,[status(thm)],[f_982_1]) ).
fof(f_982_3,plain,
! [U_4185,U_4184,U_4186] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4184),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4184),U_4185),U_4186)),U_4185))
| ~ class_Lattices_Olattice(U_4184) ),
inference(definitional_conversion,[status(esa)],[f_982_2]) ).
cnf(f_982_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4184),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4184),U_4185),U_4186)),U_4185))
| ~ class_Lattices_Olattice(U_4184) ),
inference(clausify,[status(thm)],[f_982_3]) ).
fof(f_983_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_983_2,plain,
! [U_4189,U_4188,U_4187] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4187),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4187),U_4188),U_4189)),U_4188))
| ~ class_Lattices_Osemilattice__inf(U_4187) ),
inference(variable_rename,[status(thm)],[f_983_1]) ).
fof(f_983_3,plain,
! [U_4187,U_4189,U_4188] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4187),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4187),U_4188),U_4189)),U_4188))
| ~ class_Lattices_Osemilattice__inf(U_4187) ),
inference(definitional_conversion,[status(esa)],[f_983_2]) ).
cnf(f_983_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4187),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4187),U_4188),U_4189)),U_4188))
| ~ class_Lattices_Osemilattice__inf(U_4187) ),
inference(clausify,[status(thm)],[f_983_3]) ).
fof(f_984_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_984_2,plain,
! [U_4192,U_4191,U_4190] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4190),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4190),U_4191),U_4192)),U_4192))
| ~ class_Lattices_Olattice(U_4190) ),
inference(variable_rename,[status(thm)],[f_984_1]) ).
fof(f_984_3,plain,
! [U_4190,U_4191,U_4192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4190),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4190),U_4191),U_4192)),U_4192))
| ~ class_Lattices_Olattice(U_4190) ),
inference(definitional_conversion,[status(esa)],[f_984_2]) ).
cnf(f_984_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4190),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4190),U_4191),U_4192)),U_4192))
| ~ class_Lattices_Olattice(U_4190) ),
inference(clausify,[status(thm)],[f_984_3]) ).
fof(f_985_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_985_2,plain,
! [U_4195,U_4194,U_4193] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4193),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4193),U_4194),U_4195)),U_4195))
| ~ class_Lattices_Osemilattice__inf(U_4193) ),
inference(variable_rename,[status(thm)],[f_985_1]) ).
fof(f_985_3,plain,
! [U_4193,U_4194,U_4195] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4193),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4193),U_4194),U_4195)),U_4195))
| ~ class_Lattices_Osemilattice__inf(U_4193) ),
inference(definitional_conversion,[status(esa)],[f_985_2]) ).
cnf(f_985_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4193),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4193),U_4194),U_4195)),U_4195))
| ~ class_Lattices_Osemilattice__inf(U_4193) ),
inference(clausify,[status(thm)],[f_985_3]) ).
fof(f_986_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),V_y_2) != V_x_2 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),V_y_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) ) )
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__inf]) ).
fof(f_986_2,plain,
! [U_4198,U_4197,U_4196] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4196),U_4197),U_4198))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4196),U_4197),U_4198) != U_4197 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4196),U_4197),U_4198) = U_4197
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4196),U_4197),U_4198)) ) )
| ~ class_Lattices_Osemilattice__inf(U_4196) ),
inference(variable_rename,[status(thm)],[f_986_1]) ).
fof(f_986_3,plain,
( ! [U_4196,U_4197,U_4198] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4196),U_4197),U_4198))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4196),U_4197),U_4198) != U_4197
| ~ sP234(U_4196,U_4197,U_4198) )
& ! [U_4196,U_4197,U_4198] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4196),U_4197),U_4198) = U_4197
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4196),U_4197),U_4198))
| ~ sP234(U_4196,U_4197,U_4198) )
& ! [U_4196,U_4197,U_4198] :
( sP234(U_4196,U_4197,U_4198)
| ~ class_Lattices_Osemilattice__inf(U_4196) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234])],[f_986_2]) ).
cnf(f_986_4,plain,
( sP234(U_4196,U_4197,U_4198)
| ~ class_Lattices_Osemilattice__inf(U_4196) ),
inference(clausify,[status(thm)],[f_986_3]) ).
cnf(f_986_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4196),U_4197),U_4198) = U_4197
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4196),U_4197),U_4198))
| ~ sP234(U_4196,U_4197,U_4198) ),
inference(clausify,[status(thm)],[f_986_3]) ).
cnf(f_986_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4196),U_4197),U_4198))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4196),U_4197),U_4198) != U_4197
| ~ sP234(U_4196,U_4197,U_4198) ),
inference(clausify,[status(thm)],[f_986_3]) ).
fof(f_987_1,plain,
! [V_z_2,V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_y_2),V_z_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_y_2),V_z_2))) ) )
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__inf__iff]) ).
fof(f_987_2,plain,
! [U_4202,U_4201,U_4200,U_4199] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4199),U_4201),U_4202)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),U_4202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),U_4201)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),U_4202))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),U_4201)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4199),U_4201),U_4202))) ) )
| ~ class_Lattices_Osemilattice__inf(U_4199) ),
inference(variable_rename,[status(thm)],[f_987_1]) ).
fof(f_987_3,plain,
( ! [U_4199,U_4200,U_4201,U_4202] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),U_4202))
| ~ sP235(U_4199,U_4200,U_4201,U_4202) )
& ! [U_4199,U_4200,U_4201,U_4202] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),U_4201))
| ~ sP235(U_4199,U_4200,U_4201,U_4202) )
& ! [U_4199,U_4200,U_4201,U_4202] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4199),U_4201),U_4202)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),U_4202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),U_4201))
| ~ sP236(U_4199,U_4200,U_4201,U_4202) )
& ! [U_4199,U_4200,U_4201,U_4202] :
( sP235(U_4199,U_4200,U_4201,U_4202)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4199),U_4201),U_4202)))
| ~ sP236(U_4199,U_4200,U_4201,U_4202) )
& ! [U_4199,U_4200,U_4201,U_4202] :
( sP236(U_4199,U_4200,U_4201,U_4202)
| ~ class_Lattices_Osemilattice__inf(U_4199) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP235,sP236])],[f_987_2]) ).
cnf(f_987_4,plain,
( sP236(U_4199,U_4200,U_4201,U_4202)
| ~ class_Lattices_Osemilattice__inf(U_4199) ),
inference(clausify,[status(thm)],[f_987_3]) ).
cnf(f_987_5,plain,
( sP235(U_4199,U_4200,U_4201,U_4202)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4199),U_4201),U_4202)))
| ~ sP236(U_4199,U_4200,U_4201,U_4202) ),
inference(clausify,[status(thm)],[f_987_3]) ).
cnf(f_987_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4199),U_4201),U_4202)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),U_4202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),U_4201))
| ~ sP236(U_4199,U_4200,U_4201,U_4202) ),
inference(clausify,[status(thm)],[f_987_3]) ).
cnf(f_987_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),U_4201))
| ~ sP235(U_4199,U_4200,U_4201,U_4202) ),
inference(clausify,[status(thm)],[f_987_3]) ).
cnf(f_987_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4199),U_4200),U_4202))
| ~ sP235(U_4199,U_4200,U_4201,U_4202) ),
inference(clausify,[status(thm)],[f_987_3]) ).
fof(f_988_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_988_2,plain,
! [U_4206,U_4205,U_4204,U_4203] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4203),U_4204),U_4206)),U_4205))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),U_4204),U_4205))
| ~ class_Lattices_Osemilattice__inf(U_4203) ),
inference(variable_rename,[status(thm)],[f_988_1]) ).
fof(f_988_3,plain,
! [U_4206,U_4205,U_4203,U_4204] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4203),U_4204),U_4206)),U_4205))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),U_4204),U_4205))
| ~ class_Lattices_Osemilattice__inf(U_4203) ),
inference(definitional_conversion,[status(esa)],[f_988_2]) ).
cnf(f_988_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4203),U_4204),U_4206)),U_4205))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),U_4204),U_4205))
| ~ class_Lattices_Osemilattice__inf(U_4203) ),
inference(clausify,[status(thm)],[f_988_3]) ).
fof(f_989_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_989_2,plain,
! [U_4210,U_4209,U_4208,U_4207] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4207),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4207),U_4210),U_4208)),U_4209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4207),U_4208),U_4209))
| ~ class_Lattices_Osemilattice__inf(U_4207) ),
inference(variable_rename,[status(thm)],[f_989_1]) ).
fof(f_989_3,plain,
! [U_4207,U_4208,U_4209,U_4210] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4207),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4207),U_4210),U_4208)),U_4209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4207),U_4208),U_4209))
| ~ class_Lattices_Osemilattice__inf(U_4207) ),
inference(definitional_conversion,[status(esa)],[f_989_2]) ).
cnf(f_989_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4207),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4207),U_4210),U_4208)),U_4209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4207),U_4208),U_4209))
| ~ class_Lattices_Osemilattice__inf(U_4207) ),
inference(clausify,[status(thm)],[f_989_3]) ).
fof(f_990_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_990_2,plain,
! [U_4213,U_4212,U_4211] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4211),U_4212),U_4213) = U_4212
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4211),U_4212),U_4213))
| ~ class_Lattices_Osemilattice__inf(U_4211) ),
inference(variable_rename,[status(thm)],[f_990_1]) ).
fof(f_990_3,plain,
! [U_4211,U_4212,U_4213] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4211),U_4212),U_4213) = U_4212
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4211),U_4212),U_4213))
| ~ class_Lattices_Osemilattice__inf(U_4211) ),
inference(definitional_conversion,[status(esa)],[f_990_2]) ).
cnf(f_990_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4211),U_4212),U_4213) = U_4212
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4211),U_4212),U_4213))
| ~ class_Lattices_Osemilattice__inf(U_4211) ),
inference(clausify,[status(thm)],[f_990_3]) ).
fof(f_991_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_991_2,plain,
! [U_4216,U_4215,U_4214] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4214),U_4216),U_4215) = U_4215
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4214),U_4215),U_4216))
| ~ class_Lattices_Osemilattice__inf(U_4214) ),
inference(variable_rename,[status(thm)],[f_991_1]) ).
fof(f_991_3,plain,
! [U_4214,U_4215,U_4216] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4214),U_4216),U_4215) = U_4215
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4214),U_4215),U_4216))
| ~ class_Lattices_Osemilattice__inf(U_4214) ),
inference(definitional_conversion,[status(esa)],[f_991_2]) ).
cnf(f_991_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4214),U_4216),U_4215) = U_4215
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4214),U_4215),U_4216))
| ~ class_Lattices_Osemilattice__inf(U_4214) ),
inference(clausify,[status(thm)],[f_991_3]) ).
fof(f_992_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_992_2,plain,
! [U_4220,U_4219,U_4218,U_4217] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4217),U_4218),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4217),U_4219),U_4220)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4217),U_4218),U_4220))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4217),U_4218),U_4219))
| ~ class_Lattices_Osemilattice__inf(U_4217) ),
inference(variable_rename,[status(thm)],[f_992_1]) ).
fof(f_992_3,plain,
! [U_4217,U_4218,U_4219,U_4220] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4217),U_4218),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4217),U_4219),U_4220)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4217),U_4218),U_4220))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4217),U_4218),U_4219))
| ~ class_Lattices_Osemilattice__inf(U_4217) ),
inference(definitional_conversion,[status(esa)],[f_992_2]) ).
cnf(f_992_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4217),U_4218),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4217),U_4219),U_4220)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4217),U_4218),U_4220))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4217),U_4218),U_4219))
| ~ class_Lattices_Osemilattice__inf(U_4217) ),
inference(clausify,[status(thm)],[f_992_3]) ).
fof(f_993_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_993_2,plain,
! [U_4224,U_4223,U_4222,U_4221] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4221),U_4222),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4221),U_4223),U_4224)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4221),U_4222),U_4224))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4221),U_4222),U_4223))
| ~ class_Lattices_Osemilattice__inf(U_4221) ),
inference(variable_rename,[status(thm)],[f_993_1]) ).
fof(f_993_3,plain,
! [U_4221,U_4222,U_4223,U_4224] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4221),U_4222),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4221),U_4223),U_4224)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4221),U_4222),U_4224))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4221),U_4222),U_4223))
| ~ class_Lattices_Osemilattice__inf(U_4221) ),
inference(definitional_conversion,[status(esa)],[f_993_2]) ).
cnf(f_993_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4221),U_4222),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4221),U_4223),U_4224)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4221),U_4222),U_4224))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4221),U_4222),U_4223))
| ~ class_Lattices_Osemilattice__inf(U_4221) ),
inference(clausify,[status(thm)],[f_993_3]) ).
fof(f_994_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_994_2,plain,
! [U_4229,U_4228,U_4227,U_4226,U_4225] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4225),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4225),U_4226),U_4228)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4225),U_4227),U_4229)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4225),U_4228),U_4229))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4225),U_4226),U_4227))
| ~ class_Lattices_Osemilattice__inf(U_4225) ),
inference(variable_rename,[status(thm)],[f_994_1]) ).
fof(f_994_3,plain,
! [U_4225,U_4226,U_4227,U_4228,U_4229] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4225),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4225),U_4226),U_4228)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4225),U_4227),U_4229)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4225),U_4228),U_4229))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4225),U_4226),U_4227))
| ~ class_Lattices_Osemilattice__inf(U_4225) ),
inference(definitional_conversion,[status(esa)],[f_994_2]) ).
cnf(f_994_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4225),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4225),U_4226),U_4228)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4225),U_4227),U_4229)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4225),U_4228),U_4229))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4225),U_4226),U_4227))
| ~ class_Lattices_Osemilattice__inf(U_4225) ),
inference(clausify,[status(thm)],[f_994_3]) ).
fof(f_995_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_995_2,plain,
! [U_4233,U_4232,U_4231,U_4230] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4230),U_4231),U_4233))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4230),U_4231),U_4232)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4230),U_4231),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4230),U_4232),U_4233)))
| ~ class_Lattices_Osemilattice__inf(U_4230) ),
inference(variable_rename,[status(thm)],[f_995_1]) ).
fof(f_995_3,plain,
( ! [U_4230,U_4231,U_4232,U_4233] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4230),U_4231),U_4233))
| ~ sP237(U_4230,U_4231,U_4232,U_4233) )
& ! [U_4230,U_4231,U_4232,U_4233] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4230),U_4231),U_4232))
| ~ sP237(U_4230,U_4231,U_4232,U_4233) )
& ! [U_4230,U_4231,U_4232,U_4233] :
( sP237(U_4230,U_4231,U_4232,U_4233)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4230),U_4231),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4230),U_4232),U_4233)))
| ~ class_Lattices_Osemilattice__inf(U_4230) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP237])],[f_995_2]) ).
cnf(f_995_4,plain,
( sP237(U_4230,U_4231,U_4232,U_4233)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4230),U_4231),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4230),U_4232),U_4233)))
| ~ class_Lattices_Osemilattice__inf(U_4230) ),
inference(clausify,[status(thm)],[f_995_3]) ).
cnf(f_995_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4230),U_4231),U_4232))
| ~ sP237(U_4230,U_4231,U_4232,U_4233) ),
inference(clausify,[status(thm)],[f_995_3]) ).
cnf(f_995_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4230),U_4231),U_4233))
| ~ sP237(U_4230,U_4231,U_4232,U_4233) ),
inference(clausify,[status(thm)],[f_995_3]) ).
fof(f_996_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_996_2,plain,
! [U_4237,U_4236,U_4235,U_4234] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4234),U_4235),U_4237)),U_4236))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),U_4235),U_4236))
| ~ class_Lattices_Osemilattice__inf(U_4234) ),
inference(variable_rename,[status(thm)],[f_996_1]) ).
fof(f_996_3,plain,
! [U_4234,U_4235,U_4236,U_4237] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4234),U_4235),U_4237)),U_4236))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),U_4235),U_4236))
| ~ class_Lattices_Osemilattice__inf(U_4234) ),
inference(definitional_conversion,[status(esa)],[f_996_2]) ).
cnf(f_996_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4234),U_4235),U_4237)),U_4236))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),U_4235),U_4236))
| ~ class_Lattices_Osemilattice__inf(U_4234) ),
inference(clausify,[status(thm)],[f_996_3]) ).
fof(f_997_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_997_2,plain,
! [U_4241,U_4240,U_4239,U_4238] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4238),U_4241),U_4239)),U_4240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),U_4239),U_4240))
| ~ class_Lattices_Osemilattice__inf(U_4238) ),
inference(variable_rename,[status(thm)],[f_997_1]) ).
fof(f_997_3,plain,
! [U_4238,U_4239,U_4240,U_4241] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4238),U_4241),U_4239)),U_4240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),U_4239),U_4240))
| ~ class_Lattices_Osemilattice__inf(U_4238) ),
inference(definitional_conversion,[status(esa)],[f_997_2]) ).
cnf(f_997_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4238),U_4241),U_4239)),U_4240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),U_4239),U_4240))
| ~ class_Lattices_Osemilattice__inf(U_4238) ),
inference(clausify,[status(thm)],[f_997_3]) ).
fof(f_998_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_998_2,plain,
! [U_4243,U_4242] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4242),c_Orderings_Obot__class_Obot(U_4242)),U_4243) = c_Orderings_Obot__class_Obot(U_4242)
| ~ class_Lattices_Obounded__lattice__bot(U_4242) ),
inference(variable_rename,[status(thm)],[f_998_1]) ).
fof(f_998_3,plain,
! [U_4242,U_4243] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4242),c_Orderings_Obot__class_Obot(U_4242)),U_4243) = c_Orderings_Obot__class_Obot(U_4242)
| ~ class_Lattices_Obounded__lattice__bot(U_4242) ),
inference(definitional_conversion,[status(esa)],[f_998_2]) ).
cnf(f_998_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4242),c_Orderings_Obot__class_Obot(U_4242)),U_4243) = c_Orderings_Obot__class_Obot(U_4242)
| ~ class_Lattices_Obounded__lattice__bot(U_4242) ),
inference(clausify,[status(thm)],[f_998_3]) ).
fof(f_999_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_999_2,plain,
! [U_4245,U_4244] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4244),U_4245),c_Orderings_Obot__class_Obot(U_4244)) = c_Orderings_Obot__class_Obot(U_4244)
| ~ class_Lattices_Obounded__lattice__bot(U_4244) ),
inference(variable_rename,[status(thm)],[f_999_1]) ).
fof(f_999_3,plain,
! [U_4244,U_4245] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4244),U_4245),c_Orderings_Obot__class_Obot(U_4244)) = c_Orderings_Obot__class_Obot(U_4244)
| ~ class_Lattices_Obounded__lattice__bot(U_4244) ),
inference(definitional_conversion,[status(esa)],[f_999_2]) ).
cnf(f_999_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4244),U_4245),c_Orderings_Obot__class_Obot(U_4244)) = c_Orderings_Obot__class_Obot(U_4244)
| ~ class_Lattices_Obounded__lattice__bot(U_4244) ),
inference(clausify,[status(thm)],[f_999_3]) ).
fof(f_1000_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_1000_2,plain,
! [U_4248,U_4247,U_4246] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4246),U_4247),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4246),U_4247),U_4248)) = U_4247
| ~ class_Lattices_Olattice(U_4246) ),
inference(variable_rename,[status(thm)],[f_1000_1]) ).
fof(f_1000_3,plain,
! [U_4246,U_4247,U_4248] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4246),U_4247),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4246),U_4247),U_4248)) = U_4247
| ~ class_Lattices_Olattice(U_4246) ),
inference(definitional_conversion,[status(esa)],[f_1000_2]) ).
cnf(f_1000_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4246),U_4247),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4246),U_4247),U_4248)) = U_4247
| ~ class_Lattices_Olattice(U_4246) ),
inference(clausify,[status(thm)],[f_1000_3]) ).
fof(f_1001_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_1001_2,plain,
! [U_4251,U_4250,U_4249] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4249),U_4250),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4249),U_4250),U_4251)) = U_4250
| ~ class_Lattices_Olattice(U_4249) ),
inference(variable_rename,[status(thm)],[f_1001_1]) ).
fof(f_1001_3,plain,
! [U_4249,U_4250,U_4251] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4249),U_4250),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4249),U_4250),U_4251)) = U_4250
| ~ class_Lattices_Olattice(U_4249) ),
inference(definitional_conversion,[status(esa)],[f_1001_2]) ).
cnf(f_1001_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4249),U_4250),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4249),U_4250),U_4251)) = U_4250
| ~ class_Lattices_Olattice(U_4249) ),
inference(clausify,[status(thm)],[f_1001_3]) ).
fof(f_1002_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_1002_2,plain,
! [U_4255,U_4254,U_4253,U_4252] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4252),U_4253),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4252),U_4254),U_4255)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4252),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4252),U_4253),U_4254)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4252),U_4253),U_4255))
| ~ class_Lattices_Odistrib__lattice(U_4252) ),
inference(variable_rename,[status(thm)],[f_1002_1]) ).
fof(f_1002_3,plain,
! [U_4252,U_4253,U_4254,U_4255] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4252),U_4253),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4252),U_4254),U_4255)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4252),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4252),U_4253),U_4254)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4252),U_4253),U_4255))
| ~ class_Lattices_Odistrib__lattice(U_4252) ),
inference(definitional_conversion,[status(esa)],[f_1002_2]) ).
cnf(f_1002_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4252),U_4253),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4252),U_4254),U_4255)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4252),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4252),U_4253),U_4254)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4252),U_4253),U_4255))
| ~ class_Lattices_Odistrib__lattice(U_4252) ),
inference(clausify,[status(thm)],[f_1002_3]) ).
fof(f_1003_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_1003_2,plain,
! [U_4259,U_4258,U_4257,U_4256] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4256),U_4257),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4256),U_4258),U_4259)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4256),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4256),U_4257),U_4258)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4256),U_4257),U_4259))
| ~ class_Lattices_Odistrib__lattice(U_4256) ),
inference(variable_rename,[status(thm)],[f_1003_1]) ).
fof(f_1003_3,plain,
! [U_4256,U_4257,U_4258,U_4259] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4256),U_4257),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4256),U_4258),U_4259)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4256),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4256),U_4257),U_4258)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4256),U_4257),U_4259))
| ~ class_Lattices_Odistrib__lattice(U_4256) ),
inference(definitional_conversion,[status(esa)],[f_1003_2]) ).
cnf(f_1003_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4256),U_4257),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4256),U_4258),U_4259)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4256),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4256),U_4257),U_4258)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4256),U_4257),U_4259))
| ~ class_Lattices_Odistrib__lattice(U_4256) ),
inference(clausify,[status(thm)],[f_1003_3]) ).
fof(f_1004_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_1004_2,plain,
! [U_4263,U_4262,U_4261,U_4260] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4260),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4260),U_4261),U_4262)),U_4263) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4260),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4260),U_4261),U_4263)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4260),U_4262),U_4263))
| ~ class_Lattices_Odistrib__lattice(U_4260) ),
inference(variable_rename,[status(thm)],[f_1004_1]) ).
fof(f_1004_3,plain,
! [U_4260,U_4261,U_4262,U_4263] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4260),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4260),U_4261),U_4262)),U_4263) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4260),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4260),U_4261),U_4263)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4260),U_4262),U_4263))
| ~ class_Lattices_Odistrib__lattice(U_4260) ),
inference(definitional_conversion,[status(esa)],[f_1004_2]) ).
cnf(f_1004_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4260),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4260),U_4261),U_4262)),U_4263) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4260),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4260),U_4261),U_4263)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4260),U_4262),U_4263))
| ~ class_Lattices_Odistrib__lattice(U_4260) ),
inference(clausify,[status(thm)],[f_1004_3]) ).
fof(f_1005_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_1005_2,plain,
! [U_4267,U_4266,U_4265,U_4264] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4264),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4264),U_4265),U_4266)),U_4267) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4264),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4264),U_4265),U_4267)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4264),U_4266),U_4267))
| ~ class_Lattices_Odistrib__lattice(U_4264) ),
inference(variable_rename,[status(thm)],[f_1005_1]) ).
fof(f_1005_3,plain,
! [U_4264,U_4265,U_4266,U_4267] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4264),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4264),U_4265),U_4266)),U_4267) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4264),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4264),U_4265),U_4267)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4264),U_4266),U_4267))
| ~ class_Lattices_Odistrib__lattice(U_4264) ),
inference(definitional_conversion,[status(esa)],[f_1005_2]) ).
cnf(f_1005_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4264),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4264),U_4265),U_4266)),U_4267) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4264),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4264),U_4265),U_4267)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4264),U_4266),U_4267))
| ~ class_Lattices_Odistrib__lattice(U_4264) ),
inference(clausify,[status(thm)],[f_1005_3]) ).
fof(f_1006_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_1006_2,plain,
! [U_4269,U_4268] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4268),c_Orderings_Otop__class_Otop(U_4268)),U_4269) = U_4269
| ~ class_Lattices_Obounded__lattice__top(U_4268) ),
inference(variable_rename,[status(thm)],[f_1006_1]) ).
fof(f_1006_3,plain,
! [U_4269,U_4268] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4268),c_Orderings_Otop__class_Otop(U_4268)),U_4269) = U_4269
| ~ class_Lattices_Obounded__lattice__top(U_4268) ),
inference(definitional_conversion,[status(esa)],[f_1006_2]) ).
cnf(f_1006_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4268),c_Orderings_Otop__class_Otop(U_4268)),U_4269) = U_4269
| ~ class_Lattices_Obounded__lattice__top(U_4268) ),
inference(clausify,[status(thm)],[f_1006_3]) ).
fof(f_1007_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_1007_2,plain,
! [U_4271,U_4270] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4270),U_4271),c_Orderings_Otop__class_Otop(U_4270)) = U_4271
| ~ class_Lattices_Obounded__lattice__top(U_4270) ),
inference(variable_rename,[status(thm)],[f_1007_1]) ).
fof(f_1007_3,plain,
! [U_4270,U_4271] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4270),U_4271),c_Orderings_Otop__class_Otop(U_4270)) = U_4271
| ~ class_Lattices_Obounded__lattice__top(U_4270) ),
inference(definitional_conversion,[status(esa)],[f_1007_2]) ).
cnf(f_1007_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4270),U_4271),c_Orderings_Otop__class_Otop(U_4270)) = U_4271
| ~ class_Lattices_Obounded__lattice__top(U_4270) ),
inference(clausify,[status(thm)],[f_1007_3]) ).
fof(f_1008_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_c)
| V_y_2 != c_Orderings_Otop__class_Otop(T_c)
| V_x_2 != c_Orderings_Otop__class_Otop(T_c) )
& ( ( V_y_2 = c_Orderings_Otop__class_Otop(T_c)
& V_x_2 = c_Orderings_Otop__class_Otop(T_c) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),V_y_2) != c_Orderings_Otop__class_Otop(T_c) ) )
| ~ class_Lattices_Obounded__lattice__top(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inf__eq__top__iff]) ).
fof(f_1008_2,plain,
! [U_4274,U_4273,U_4272] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4272),U_4273),U_4274) = c_Orderings_Otop__class_Otop(U_4272)
| U_4274 != c_Orderings_Otop__class_Otop(U_4272)
| U_4273 != c_Orderings_Otop__class_Otop(U_4272) )
& ( ( U_4274 = c_Orderings_Otop__class_Otop(U_4272)
& U_4273 = c_Orderings_Otop__class_Otop(U_4272) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4272),U_4273),U_4274) != c_Orderings_Otop__class_Otop(U_4272) ) )
| ~ class_Lattices_Obounded__lattice__top(U_4272) ),
inference(variable_rename,[status(thm)],[f_1008_1]) ).
fof(f_1008_3,plain,
( ! [U_4272,U_4273,U_4274] :
( U_4274 = c_Orderings_Otop__class_Otop(U_4272)
| ~ sP238(U_4272,U_4273,U_4274) )
& ! [U_4272,U_4273,U_4274] :
( U_4273 = c_Orderings_Otop__class_Otop(U_4272)
| ~ sP238(U_4272,U_4273,U_4274) )
& ! [U_4272,U_4273,U_4274] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4272),U_4273),U_4274) = c_Orderings_Otop__class_Otop(U_4272)
| U_4274 != c_Orderings_Otop__class_Otop(U_4272)
| U_4273 != c_Orderings_Otop__class_Otop(U_4272)
| ~ sP239(U_4272,U_4273,U_4274) )
& ! [U_4272,U_4273,U_4274] :
( sP238(U_4272,U_4273,U_4274)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4272),U_4273),U_4274) != c_Orderings_Otop__class_Otop(U_4272)
| ~ sP239(U_4272,U_4273,U_4274) )
& ! [U_4272,U_4273,U_4274] :
( sP239(U_4272,U_4273,U_4274)
| ~ class_Lattices_Obounded__lattice__top(U_4272) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP238,sP239])],[f_1008_2]) ).
cnf(f_1008_4,plain,
( sP239(U_4272,U_4273,U_4274)
| ~ class_Lattices_Obounded__lattice__top(U_4272) ),
inference(clausify,[status(thm)],[f_1008_3]) ).
cnf(f_1008_5,plain,
( sP238(U_4272,U_4273,U_4274)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4272),U_4273),U_4274) != c_Orderings_Otop__class_Otop(U_4272)
| ~ sP239(U_4272,U_4273,U_4274) ),
inference(clausify,[status(thm)],[f_1008_3]) ).
cnf(f_1008_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4272),U_4273),U_4274) = c_Orderings_Otop__class_Otop(U_4272)
| U_4274 != c_Orderings_Otop__class_Otop(U_4272)
| U_4273 != c_Orderings_Otop__class_Otop(U_4272)
| ~ sP239(U_4272,U_4273,U_4274) ),
inference(clausify,[status(thm)],[f_1008_3]) ).
cnf(f_1008_7,plain,
( U_4273 = c_Orderings_Otop__class_Otop(U_4272)
| ~ sP238(U_4272,U_4273,U_4274) ),
inference(clausify,[status(thm)],[f_1008_3]) ).
cnf(f_1008_8,plain,
( U_4274 = c_Orderings_Otop__class_Otop(U_4272)
| ~ sP238(U_4272,U_4273,U_4274) ),
inference(clausify,[status(thm)],[f_1008_3]) ).
fof(f_1009_1,plain,
! [V_B_2,V_f_2,T_d,V_a_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_d),hAPP(V_f_2,V_a_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_vimage__eq]) ).
fof(f_1009_2,plain,
! [U_4279,U_4278,U_4277,U_4276,U_4275] :
( ( hBOOL(hAPP(hAPP(c_member(U_4275),U_4276),hAPP(c_Set_Ovimage(U_4275,U_4277,U_4278),U_4279)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4277),hAPP(U_4278,U_4276)),U_4279)) )
& ( hBOOL(hAPP(hAPP(c_member(U_4277),hAPP(U_4278,U_4276)),U_4279))
| ~ hBOOL(hAPP(hAPP(c_member(U_4275),U_4276),hAPP(c_Set_Ovimage(U_4275,U_4277,U_4278),U_4279))) ) ),
inference(variable_rename,[status(thm)],[f_1009_1]) ).
fof(f_1009_3,plain,
( ! [U_4289,U_4287,U_4285,U_4283] :
( ! [U_4281] : hBOOL(hAPP(hAPP(c_member(U_4281),U_4283),hAPP(c_Set_Ovimage(U_4281,U_4285,U_4287),U_4289)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4285),hAPP(U_4287,U_4283)),U_4289)) )
& ! [U_4288,U_4286,U_4284,U_4282] :
( ! [U_4280] : ~ hBOOL(hAPP(hAPP(c_member(U_4280),U_4282),hAPP(c_Set_Ovimage(U_4280,U_4284,U_4286),U_4288)))
| hBOOL(hAPP(hAPP(c_member(U_4284),hAPP(U_4286,U_4282)),U_4288)) ) ),
inference(miniscope,[status(thm)],[f_1009_2]) ).
fof(f_1009_4,plain,
( ! [U_4281,U_4283,U_4285,U_4287,U_4289] :
( hBOOL(hAPP(hAPP(c_member(U_4281),U_4283),hAPP(c_Set_Ovimage(U_4281,U_4285,U_4287),U_4289)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4285),hAPP(U_4287,U_4283)),U_4289)) )
& ! [U_4280,U_4282,U_4284,U_4286,U_4288] :
( ~ hBOOL(hAPP(hAPP(c_member(U_4280),U_4282),hAPP(c_Set_Ovimage(U_4280,U_4284,U_4286),U_4288)))
| hBOOL(hAPP(hAPP(c_member(U_4284),hAPP(U_4286,U_4282)),U_4288)) ) ),
inference(definitional_conversion,[status(esa)],[f_1009_3]) ).
cnf(f_1009_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_4280),U_4282),hAPP(c_Set_Ovimage(U_4280,U_4284,U_4286),U_4288)))
| hBOOL(hAPP(hAPP(c_member(U_4284),hAPP(U_4286,U_4282)),U_4288)) ),
inference(clausify,[status(thm)],[f_1009_4]) ).
cnf(f_1009_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4281),U_4283),hAPP(c_Set_Ovimage(U_4281,U_4285,U_4287),U_4289)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4285),hAPP(U_4287,U_4283)),U_4289)) ),
inference(clausify,[status(thm)],[f_1009_4]) ).
fof(f_1010_1,plain,
! [V_A_2,V_f_2,T_d,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_d),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_d,V_f_2),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_vimageD]) ).
fof(f_1010_2,plain,
! [U_4294,U_4293,U_4292,U_4291,U_4290] :
( hBOOL(hAPP(hAPP(c_member(U_4292),hAPP(U_4293,U_4291)),U_4294))
| ~ hBOOL(hAPP(hAPP(c_member(U_4290),U_4291),hAPP(c_Set_Ovimage(U_4290,U_4292,U_4293),U_4294))) ),
inference(variable_rename,[status(thm)],[f_1010_1]) ).
fof(f_1010_3,plain,
! [U_4294,U_4293,U_4292,U_4291] :
( ! [U_4290] : ~ hBOOL(hAPP(hAPP(c_member(U_4290),U_4291),hAPP(c_Set_Ovimage(U_4290,U_4292,U_4293),U_4294)))
| hBOOL(hAPP(hAPP(c_member(U_4292),hAPP(U_4293,U_4291)),U_4294)) ),
inference(miniscope,[status(thm)],[f_1010_2]) ).
fof(f_1010_4,plain,
! [U_4290,U_4291,U_4292,U_4293,U_4294] :
( ~ hBOOL(hAPP(hAPP(c_member(U_4290),U_4291),hAPP(c_Set_Ovimage(U_4290,U_4292,U_4293),U_4294)))
| hBOOL(hAPP(hAPP(c_member(U_4292),hAPP(U_4293,U_4291)),U_4294)) ),
inference(definitional_conversion,[status(esa)],[f_1010_3]) ).
cnf(f_1010_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_4290),U_4291),hAPP(c_Set_Ovimage(U_4290,U_4292,U_4293),U_4294)))
| hBOOL(hAPP(hAPP(c_member(U_4292),hAPP(U_4293,U_4291)),U_4294)) ),
inference(clausify,[status(thm)],[f_1010_4]) ).
fof(f_1011_1,plain,
! [T_d,V_A_2,V_a_2,V_f_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),hAPP(c_Set_Ovimage(T_d,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)) ),
inference(fof_nnf,[status(thm)],[fact_vimageI2]) ).
fof(f_1011_2,plain,
! [U_4299,U_4298,U_4297,U_4296,U_4295] :
( hBOOL(hAPP(hAPP(c_member(U_4299),U_4297),hAPP(c_Set_Ovimage(U_4299,U_4295,U_4296),U_4298)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4295),hAPP(U_4296,U_4297)),U_4298)) ),
inference(variable_rename,[status(thm)],[f_1011_1]) ).
fof(f_1011_3,plain,
! [U_4296,U_4295,U_4297,U_4298,U_4299] :
( hBOOL(hAPP(hAPP(c_member(U_4299),U_4297),hAPP(c_Set_Ovimage(U_4299,U_4295,U_4296),U_4298)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4295),hAPP(U_4296,U_4297)),U_4298)) ),
inference(definitional_conversion,[status(esa)],[f_1011_2]) ).
cnf(f_1011_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_4299),U_4297),hAPP(c_Set_Ovimage(U_4299,U_4295,U_4296),U_4298)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4295),hAPP(U_4296,U_4297)),U_4298)) ),
inference(clausify,[status(thm)],[f_1011_3]) ).
fof(f_1012_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) )
& ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__iff]) ).
fof(f_1012_2,plain,
! [U_4303,U_4302,U_4301,U_4300] :
( ( hBOOL(hAPP(hAPP(c_member(U_4300),U_4301),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4300,tc_HOL_Obool)),U_4302),U_4303)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4300),U_4301),U_4303))
| ~ hBOOL(hAPP(hAPP(c_member(U_4300),U_4301),U_4302)) )
& ( ( hBOOL(hAPP(hAPP(c_member(U_4300),U_4301),U_4303))
& hBOOL(hAPP(hAPP(c_member(U_4300),U_4301),U_4302)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4300),U_4301),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4300,tc_HOL_Obool)),U_4302),U_4303))) ) ),
inference(variable_rename,[status(thm)],[f_1012_1]) ).
fof(f_1012_3,plain,
( ! [U_4311,U_4309,U_4307,U_4305] :
( hBOOL(hAPP(hAPP(c_member(U_4305),U_4307),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4305,tc_HOL_Obool)),U_4309),U_4311)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4305),U_4307),U_4311))
| ~ hBOOL(hAPP(hAPP(c_member(U_4305),U_4307),U_4309)) )
& ! [U_4310,U_4308,U_4306,U_4304] :
( ( hBOOL(hAPP(hAPP(c_member(U_4304),U_4306),U_4310))
& hBOOL(hAPP(hAPP(c_member(U_4304),U_4306),U_4308)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4304),U_4306),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4304,tc_HOL_Obool)),U_4308),U_4310))) ) ),
inference(miniscope,[status(thm)],[f_1012_2]) ).
fof(f_1012_4,plain,
( ! [U_4306,U_4310,U_4308,U_4304] :
( hBOOL(hAPP(hAPP(c_member(U_4304),U_4306),U_4310))
| ~ sP240(U_4306,U_4310,U_4308,U_4304) )
& ! [U_4306,U_4310,U_4308,U_4304] :
( hBOOL(hAPP(hAPP(c_member(U_4304),U_4306),U_4308))
| ~ sP240(U_4306,U_4310,U_4308,U_4304) )
& ! [U_4305,U_4311,U_4307,U_4309] :
( hBOOL(hAPP(hAPP(c_member(U_4305),U_4307),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4305,tc_HOL_Obool)),U_4309),U_4311)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4305),U_4307),U_4311))
| ~ hBOOL(hAPP(hAPP(c_member(U_4305),U_4307),U_4309)) )
& ! [U_4306,U_4310,U_4308,U_4304] :
( sP240(U_4306,U_4310,U_4308,U_4304)
| ~ hBOOL(hAPP(hAPP(c_member(U_4304),U_4306),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4304,tc_HOL_Obool)),U_4308),U_4310))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP240])],[f_1012_3]) ).
cnf(f_1012_5,plain,
( sP240(U_4306,U_4310,U_4308,U_4304)
| ~ hBOOL(hAPP(hAPP(c_member(U_4304),U_4306),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4304,tc_HOL_Obool)),U_4308),U_4310))) ),
inference(clausify,[status(thm)],[f_1012_4]) ).
cnf(f_1012_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4305),U_4307),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4305,tc_HOL_Obool)),U_4309),U_4311)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4305),U_4307),U_4311))
| ~ hBOOL(hAPP(hAPP(c_member(U_4305),U_4307),U_4309)) ),
inference(clausify,[status(thm)],[f_1012_4]) ).
cnf(f_1012_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_4304),U_4306),U_4308))
| ~ sP240(U_4306,U_4310,U_4308,U_4304) ),
inference(clausify,[status(thm)],[f_1012_4]) ).
cnf(f_1012_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_4304),U_4306),U_4310))
| ~ sP240(U_4306,U_4310,U_4308,U_4304) ),
inference(clausify,[status(thm)],[f_1012_4]) ).
fof(f_1013_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntD1]) ).
fof(f_1013_2,plain,
! [U_4315,U_4314,U_4313,U_4312] :
( hBOOL(hAPP(hAPP(c_member(U_4312),U_4313),U_4314))
| ~ hBOOL(hAPP(hAPP(c_member(U_4312),U_4313),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4312,tc_HOL_Obool)),U_4314),U_4315))) ),
inference(variable_rename,[status(thm)],[f_1013_1]) ).
fof(f_1013_3,plain,
! [U_4312,U_4313,U_4314,U_4315] :
( hBOOL(hAPP(hAPP(c_member(U_4312),U_4313),U_4314))
| ~ hBOOL(hAPP(hAPP(c_member(U_4312),U_4313),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4312,tc_HOL_Obool)),U_4314),U_4315))) ),
inference(definitional_conversion,[status(esa)],[f_1013_2]) ).
cnf(f_1013_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_4312),U_4313),U_4314))
| ~ hBOOL(hAPP(hAPP(c_member(U_4312),U_4313),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4312,tc_HOL_Obool)),U_4314),U_4315))) ),
inference(clausify,[status(thm)],[f_1013_3]) ).
fof(f_1014_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntD2]) ).
fof(f_1014_2,plain,
! [U_4319,U_4318,U_4317,U_4316] :
( hBOOL(hAPP(hAPP(c_member(U_4316),U_4317),U_4319))
| ~ hBOOL(hAPP(hAPP(c_member(U_4316),U_4317),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4316,tc_HOL_Obool)),U_4318),U_4319))) ),
inference(variable_rename,[status(thm)],[f_1014_1]) ).
fof(f_1014_3,plain,
! [U_4316,U_4317,U_4318,U_4319] :
( hBOOL(hAPP(hAPP(c_member(U_4316),U_4317),U_4319))
| ~ hBOOL(hAPP(hAPP(c_member(U_4316),U_4317),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4316,tc_HOL_Obool)),U_4318),U_4319))) ),
inference(definitional_conversion,[status(esa)],[f_1014_2]) ).
cnf(f_1014_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_4316),U_4317),U_4319))
| ~ hBOOL(hAPP(hAPP(c_member(U_4316),U_4317),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4316,tc_HOL_Obool)),U_4318),U_4319))) ),
inference(clausify,[status(thm)],[f_1014_3]) ).
fof(f_1015_1,plain,
! [T_c] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_c) = c_Orderings_Oord__class_Omin(T_c)
| ~ class_Orderings_Olinorder(T_c)
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inf__min]) ).
fof(f_1015_2,plain,
! [U_4320] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_4320) = c_Orderings_Oord__class_Omin(U_4320)
| ~ class_Orderings_Olinorder(U_4320)
| ~ class_Lattices_Osemilattice__inf(U_4320) ),
inference(variable_rename,[status(thm)],[f_1015_1]) ).
fof(f_1015_3,plain,
! [U_4320] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_4320) = c_Orderings_Oord__class_Omin(U_4320)
| ~ class_Orderings_Olinorder(U_4320)
| ~ class_Lattices_Osemilattice__inf(U_4320) ),
inference(definitional_conversion,[status(esa)],[f_1015_2]) ).
cnf(f_1015_4,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_4320) = c_Orderings_Oord__class_Omin(U_4320)
| ~ class_Orderings_Olinorder(U_4320)
| ~ class_Lattices_Osemilattice__inf(U_4320) ),
inference(clausify,[status(thm)],[f_1015_3]) ).
fof(f_1016_1,plain,
! [V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_vimage__empty]) ).
fof(f_1016_2,plain,
! [U_4323,U_4322,U_4321] : hAPP(c_Set_Ovimage(U_4321,U_4322,U_4323),c_Orderings_Obot__class_Obot(tc_fun(U_4322,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_4321,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1016_1]) ).
fof(f_1016_3,plain,
! [U_4322,U_4321,U_4323] : hAPP(c_Set_Ovimage(U_4321,U_4322,U_4323),c_Orderings_Obot__class_Obot(tc_fun(U_4322,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_4321,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1016_2]) ).
cnf(f_1016_4,plain,
hAPP(c_Set_Ovimage(U_4321,U_4322,U_4323),c_Orderings_Obot__class_Obot(tc_fun(U_4322,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_4321,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1016_3]) ).
fof(f_1017_1,plain,
! [V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Int__empty__left]) ).
fof(f_1017_2,plain,
! [U_4325,U_4324] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4324,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_4324,tc_HOL_Obool))),U_4325) = c_Orderings_Obot__class_Obot(tc_fun(U_4324,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1017_1]) ).
fof(f_1017_3,plain,
! [U_4324,U_4325] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4324,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_4324,tc_HOL_Obool))),U_4325) = c_Orderings_Obot__class_Obot(tc_fun(U_4324,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1017_2]) ).
cnf(f_1017_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4324,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_4324,tc_HOL_Obool))),U_4325) = c_Orderings_Obot__class_Obot(tc_fun(U_4324,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1017_3]) ).
fof(f_1018_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Int__empty__right]) ).
fof(f_1018_2,plain,
! [U_4327,U_4326] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4326,tc_HOL_Obool)),U_4327),c_Orderings_Obot__class_Obot(tc_fun(U_4326,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_4326,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1018_1]) ).
fof(f_1018_3,plain,
! [U_4326,U_4327] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4326,tc_HOL_Obool)),U_4327),c_Orderings_Obot__class_Obot(tc_fun(U_4326,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_4326,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1018_2]) ).
cnf(f_1018_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4326,tc_HOL_Obool)),U_4327),c_Orderings_Obot__class_Obot(tc_fun(U_4326,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_4326,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1018_3]) ).
fof(f_1019_1,plain,
! [V_B_2,V_A_2,T_c] :
( ( 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))
| ? [B_x] :
( ? [B_xa] :
( B_x = B_xa
& hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_B_2)) )
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( ! [B_xa] :
( B_x != B_xa
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_xa),V_B_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_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)) ) ),
inference(fof_nnf,[status(thm)],[fact_disjoint__iff__not__equal]) ).
fof(f_1019_2,plain,
! [U_4334,U_4333,U_4332] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4332,tc_HOL_Obool)),U_4333),U_4334) = c_Orderings_Obot__class_Obot(tc_fun(U_4332,tc_HOL_Obool))
| ? [U_4331] :
( ? [U_4330] :
( U_4331 = U_4330
& hBOOL(hAPP(hAPP(c_member(U_4332),U_4330),U_4334)) )
& hBOOL(hAPP(hAPP(c_member(U_4332),U_4331),U_4333)) ) )
& ( ! [U_4329] :
( ! [U_4328] :
( U_4329 != U_4328
| ~ hBOOL(hAPP(hAPP(c_member(U_4332),U_4328),U_4334)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4332),U_4329),U_4333)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4332,tc_HOL_Obool)),U_4333),U_4334) != c_Orderings_Obot__class_Obot(tc_fun(U_4332,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1019_1]) ).
fof(f_1019_3,plain,
( ! [U_4340,U_4338,U_4336] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4336,tc_HOL_Obool)),U_4338),U_4340) = c_Orderings_Obot__class_Obot(tc_fun(U_4336,tc_HOL_Obool))
| ? [U_4331] :
( ? [U_4330] :
( U_4331 = U_4330
& hBOOL(hAPP(hAPP(c_member(U_4336),U_4330),U_4340)) )
& hBOOL(hAPP(hAPP(c_member(U_4336),U_4331),U_4338)) ) )
& ! [U_4339,U_4337,U_4335] :
( ! [U_4329] :
( ! [U_4328] :
( U_4329 != U_4328
| ~ hBOOL(hAPP(hAPP(c_member(U_4335),U_4328),U_4339)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4335),U_4329),U_4337)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4335,tc_HOL_Obool)),U_4337),U_4339) != c_Orderings_Obot__class_Obot(tc_fun(U_4335,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1019_2]) ).
fof(f_1019_4,plain,
( ! [U_4340,U_4338,U_4336] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4336,tc_HOL_Obool)),U_4338),U_4340) = c_Orderings_Obot__class_Obot(tc_fun(U_4336,tc_HOL_Obool))
| ( ? [U_4330] :
( sK89(U_4340,U_4338,U_4336) = U_4330
& hBOOL(hAPP(hAPP(c_member(U_4336),U_4330),U_4340)) )
& hBOOL(hAPP(hAPP(c_member(U_4336),sK89(U_4340,U_4338,U_4336)),U_4338)) ) )
& ! [U_4339,U_4337,U_4335] :
( ! [U_4329] :
( ! [U_4328] :
( U_4329 != U_4328
| ~ hBOOL(hAPP(hAPP(c_member(U_4335),U_4328),U_4339)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4335),U_4329),U_4337)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4335,tc_HOL_Obool)),U_4337),U_4339) != c_Orderings_Obot__class_Obot(tc_fun(U_4335,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_4331,sK89(U_4340,U_4338,U_4336))],[f_1019_3]) ).
fof(f_1019_5,plain,
( ! [U_4340,U_4338,U_4336] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4336,tc_HOL_Obool)),U_4338),U_4340) = c_Orderings_Obot__class_Obot(tc_fun(U_4336,tc_HOL_Obool))
| ( sK89(U_4340,U_4338,U_4336) = sK90(U_4340,U_4338,U_4336)
& hBOOL(hAPP(hAPP(c_member(U_4336),sK90(U_4340,U_4338,U_4336)),U_4340))
& hBOOL(hAPP(hAPP(c_member(U_4336),sK89(U_4340,U_4338,U_4336)),U_4338)) ) )
& ! [U_4339,U_4337,U_4335] :
( ! [U_4329] :
( ! [U_4328] :
( U_4329 != U_4328
| ~ hBOOL(hAPP(hAPP(c_member(U_4335),U_4328),U_4339)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4335),U_4329),U_4337)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4335,tc_HOL_Obool)),U_4337),U_4339) != c_Orderings_Obot__class_Obot(tc_fun(U_4335,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_4330,sK90(U_4340,U_4338,U_4336))],[f_1019_4]) ).
fof(f_1019_6,plain,
( ! [U_4340,U_4336,U_4338] :
( sK89(U_4340,U_4338,U_4336) = sK90(U_4340,U_4338,U_4336)
| ~ sP241(U_4340,U_4336,U_4338) )
& ! [U_4340,U_4336,U_4338] :
( hBOOL(hAPP(hAPP(c_member(U_4336),sK90(U_4340,U_4338,U_4336)),U_4340))
| ~ sP241(U_4340,U_4336,U_4338) )
& ! [U_4340,U_4336,U_4338] :
( hBOOL(hAPP(hAPP(c_member(U_4336),sK89(U_4340,U_4338,U_4336)),U_4338))
| ~ sP241(U_4340,U_4336,U_4338) )
& ! [U_4340,U_4336,U_4338] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4336,tc_HOL_Obool)),U_4338),U_4340) = c_Orderings_Obot__class_Obot(tc_fun(U_4336,tc_HOL_Obool))
| sP241(U_4340,U_4336,U_4338) )
& ! [U_4339,U_4328,U_4337,U_4329,U_4335] :
( U_4329 != U_4328
| ~ hBOOL(hAPP(hAPP(c_member(U_4335),U_4328),U_4339))
| ~ hBOOL(hAPP(hAPP(c_member(U_4335),U_4329),U_4337))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4335,tc_HOL_Obool)),U_4337),U_4339) != c_Orderings_Obot__class_Obot(tc_fun(U_4335,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP241])],[f_1019_5]) ).
cnf(f_1019_7,plain,
( U_4329 != U_4328
| ~ hBOOL(hAPP(hAPP(c_member(U_4335),U_4328),U_4339))
| ~ hBOOL(hAPP(hAPP(c_member(U_4335),U_4329),U_4337))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4335,tc_HOL_Obool)),U_4337),U_4339) != c_Orderings_Obot__class_Obot(tc_fun(U_4335,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1019_6]) ).
cnf(f_1019_8,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4336,tc_HOL_Obool)),U_4338),U_4340) = c_Orderings_Obot__class_Obot(tc_fun(U_4336,tc_HOL_Obool))
| sP241(U_4340,U_4336,U_4338) ),
inference(clausify,[status(thm)],[f_1019_6]) ).
cnf(f_1019_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_4336),sK89(U_4340,U_4338,U_4336)),U_4338))
| ~ sP241(U_4340,U_4336,U_4338) ),
inference(clausify,[status(thm)],[f_1019_6]) ).
cnf(f_1019_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_4336),sK90(U_4340,U_4338,U_4336)),U_4340))
| ~ sP241(U_4340,U_4336,U_4338) ),
inference(clausify,[status(thm)],[f_1019_6]) ).
cnf(f_1019_11,plain,
( sK89(U_4340,U_4338,U_4336) = sK90(U_4340,U_4338,U_4336)
| ~ sP241(U_4340,U_4336,U_4338) ),
inference(clausify,[status(thm)],[f_1019_6]) ).
fof(f_1020_1,plain,
! [V_f_2,T_d,V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_vimage__mono]) ).
fof(f_1020_2,plain,
! [U_4345,U_4344,U_4343,U_4342,U_4341] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4344,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4344,U_4341,U_4345),U_4342)),hAPP(c_Set_Ovimage(U_4344,U_4341,U_4345),U_4343)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4341,tc_HOL_Obool)),U_4342),U_4343)) ),
inference(variable_rename,[status(thm)],[f_1020_1]) ).
fof(f_1020_3,plain,
! [U_4345,U_4342,U_4343,U_4341,U_4344] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4344,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4344,U_4341,U_4345),U_4342)),hAPP(c_Set_Ovimage(U_4344,U_4341,U_4345),U_4343)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4341,tc_HOL_Obool)),U_4342),U_4343)) ),
inference(definitional_conversion,[status(esa)],[f_1020_2]) ).
cnf(f_1020_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4344,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4344,U_4341,U_4345),U_4342)),hAPP(c_Set_Ovimage(U_4344,U_4341,U_4345),U_4343)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4341,tc_HOL_Obool)),U_4342),U_4343)) ),
inference(clausify,[status(thm)],[f_1020_3]) ).
fof(f_1021_1,plain,
! [V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_vimage__UNIV]) ).
fof(f_1021_2,plain,
! [U_4348,U_4347,U_4346] : hAPP(c_Set_Ovimage(U_4346,U_4347,U_4348),c_Orderings_Otop__class_Otop(tc_fun(U_4347,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_4346,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1021_1]) ).
fof(f_1021_3,plain,
! [U_4346,U_4347,U_4348] : hAPP(c_Set_Ovimage(U_4346,U_4347,U_4348),c_Orderings_Otop__class_Otop(tc_fun(U_4347,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_4346,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1021_2]) ).
cnf(f_1021_4,plain,
hAPP(c_Set_Ovimage(U_4346,U_4347,U_4348),c_Orderings_Otop__class_Otop(tc_fun(U_4347,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_4346,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1021_3]) ).
fof(f_1022_1,plain,
! [V_B_2,V_A_2,V_a_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_insert__inter__insert]) ).
fof(f_1022_2,plain,
! [U_4352,U_4351,U_4350,U_4349] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4349,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4349),U_4350),U_4351)),hAPP(hAPP(c_Set_Oinsert(U_4349),U_4350),U_4352)) = hAPP(hAPP(c_Set_Oinsert(U_4349),U_4350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4349,tc_HOL_Obool)),U_4351),U_4352)),
inference(variable_rename,[status(thm)],[f_1022_1]) ).
fof(f_1022_3,plain,
! [U_4349,U_4350,U_4351,U_4352] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4349,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4349),U_4350),U_4351)),hAPP(hAPP(c_Set_Oinsert(U_4349),U_4350),U_4352)) = hAPP(hAPP(c_Set_Oinsert(U_4349),U_4350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4349,tc_HOL_Obool)),U_4351),U_4352)),
inference(definitional_conversion,[status(esa)],[f_1022_2]) ).
cnf(f_1022_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4349,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4349),U_4350),U_4351)),hAPP(hAPP(c_Set_Oinsert(U_4349),U_4350),U_4352)) = hAPP(hAPP(c_Set_Oinsert(U_4349),U_4350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4349,tc_HOL_Obool)),U_4351),U_4352)),
inference(clausify,[status(thm)],[f_1022_3]) ).
fof(f_1023_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Un]) ).
fof(f_1023_2,plain,
! [U_4357,U_4356,U_4355,U_4354,U_4353] : hAPP(c_Set_Ovimage(U_4353,U_4354,U_4355),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4354,tc_HOL_Obool)),U_4356),U_4357)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4353,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4353,U_4354,U_4355),U_4356)),hAPP(c_Set_Ovimage(U_4353,U_4354,U_4355),U_4357)),
inference(variable_rename,[status(thm)],[f_1023_1]) ).
fof(f_1023_3,plain,
! [U_4353,U_4354,U_4355,U_4356,U_4357] : hAPP(c_Set_Ovimage(U_4353,U_4354,U_4355),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4354,tc_HOL_Obool)),U_4356),U_4357)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4353,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4353,U_4354,U_4355),U_4356)),hAPP(c_Set_Ovimage(U_4353,U_4354,U_4355),U_4357)),
inference(definitional_conversion,[status(esa)],[f_1023_2]) ).
cnf(f_1023_4,plain,
hAPP(c_Set_Ovimage(U_4353,U_4354,U_4355),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4354,tc_HOL_Obool)),U_4356),U_4357)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4353,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4353,U_4354,U_4355),U_4356)),hAPP(c_Set_Ovimage(U_4353,U_4354,U_4355),U_4357)),
inference(clausify,[status(thm)],[f_1023_3]) ).
fof(f_1024_1,plain,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Int__lower1]) ).
fof(f_1024_2,plain,
! [U_4360,U_4359,U_4358] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4358,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4358,tc_HOL_Obool)),U_4359),U_4360)),U_4359)),
inference(variable_rename,[status(thm)],[f_1024_1]) ).
fof(f_1024_3,plain,
! [U_4358,U_4359,U_4360] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4358,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4358,tc_HOL_Obool)),U_4359),U_4360)),U_4359)),
inference(definitional_conversion,[status(esa)],[f_1024_2]) ).
cnf(f_1024_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4358,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4358,tc_HOL_Obool)),U_4359),U_4360)),U_4359)),
inference(clausify,[status(thm)],[f_1024_3]) ).
fof(f_1025_1,plain,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Int__lower2]) ).
fof(f_1025_2,plain,
! [U_4363,U_4362,U_4361] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4361,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4361,tc_HOL_Obool)),U_4362),U_4363)),U_4363)),
inference(variable_rename,[status(thm)],[f_1025_1]) ).
fof(f_1025_3,plain,
! [U_4361,U_4362,U_4363] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4361,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4361,tc_HOL_Obool)),U_4362),U_4363)),U_4363)),
inference(definitional_conversion,[status(esa)],[f_1025_2]) ).
cnf(f_1025_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4361,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4361,tc_HOL_Obool)),U_4362),U_4363)),U_4363)),
inference(clausify,[status(thm)],[f_1025_3]) ).
fof(f_1026_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__absorb2]) ).
fof(f_1026_2,plain,
! [U_4366,U_4365,U_4364] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4364,tc_HOL_Obool)),U_4365),U_4366) = U_4365
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4364,tc_HOL_Obool)),U_4365),U_4366)) ),
inference(variable_rename,[status(thm)],[f_1026_1]) ).
fof(f_1026_3,plain,
! [U_4365,U_4366,U_4364] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4364,tc_HOL_Obool)),U_4365),U_4366) = U_4365
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4364,tc_HOL_Obool)),U_4365),U_4366)) ),
inference(definitional_conversion,[status(esa)],[f_1026_2]) ).
cnf(f_1026_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4364,tc_HOL_Obool)),U_4365),U_4366) = U_4365
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4364,tc_HOL_Obool)),U_4365),U_4366)) ),
inference(clausify,[status(thm)],[f_1026_3]) ).
fof(f_1027_1,plain,
! [V_A_2,V_B_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__absorb1]) ).
fof(f_1027_2,plain,
! [U_4369,U_4368,U_4367] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4367,tc_HOL_Obool)),U_4369),U_4368) = U_4368
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4367,tc_HOL_Obool)),U_4368),U_4369)) ),
inference(variable_rename,[status(thm)],[f_1027_1]) ).
fof(f_1027_3,plain,
! [U_4367,U_4368,U_4369] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4367,tc_HOL_Obool)),U_4369),U_4368) = U_4368
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4367,tc_HOL_Obool)),U_4368),U_4369)) ),
inference(definitional_conversion,[status(esa)],[f_1027_2]) ).
cnf(f_1027_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4367,tc_HOL_Obool)),U_4369),U_4368) = U_4368
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4367,tc_HOL_Obool)),U_4368),U_4369)) ),
inference(clausify,[status(thm)],[f_1027_3]) ).
fof(f_1028_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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)),V_C_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__greatest]) ).
fof(f_1028_2,plain,
! [U_4373,U_4372,U_4371,U_4370] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4370,tc_HOL_Obool)),U_4371),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4370,tc_HOL_Obool)),U_4372),U_4373)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4370,tc_HOL_Obool)),U_4371),U_4373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4370,tc_HOL_Obool)),U_4371),U_4372)) ),
inference(variable_rename,[status(thm)],[f_1028_1]) ).
fof(f_1028_3,plain,
! [U_4370,U_4371,U_4372,U_4373] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4370,tc_HOL_Obool)),U_4371),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4370,tc_HOL_Obool)),U_4372),U_4373)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4370,tc_HOL_Obool)),U_4371),U_4373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4370,tc_HOL_Obool)),U_4371),U_4372)) ),
inference(definitional_conversion,[status(esa)],[f_1028_2]) ).
cnf(f_1028_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4370,tc_HOL_Obool)),U_4371),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4370,tc_HOL_Obool)),U_4372),U_4373)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4370,tc_HOL_Obool)),U_4371),U_4373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4370,tc_HOL_Obool)),U_4371),U_4372)) ),
inference(clausify,[status(thm)],[f_1028_3]) ).
fof(f_1029_1,plain,
! [V_D_2,V_B_2,V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_C_2),V_D_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__mono]) ).
fof(f_1029_2,plain,
! [U_4378,U_4377,U_4376,U_4375,U_4374] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4374,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4374,tc_HOL_Obool)),U_4375),U_4377)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4374,tc_HOL_Obool)),U_4376),U_4378)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4374,tc_HOL_Obool)),U_4377),U_4378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4374,tc_HOL_Obool)),U_4375),U_4376)) ),
inference(variable_rename,[status(thm)],[f_1029_1]) ).
fof(f_1029_3,plain,
! [U_4374,U_4375,U_4376,U_4377,U_4378] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4374,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4374,tc_HOL_Obool)),U_4375),U_4377)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4374,tc_HOL_Obool)),U_4376),U_4378)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4374,tc_HOL_Obool)),U_4377),U_4378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4374,tc_HOL_Obool)),U_4375),U_4376)) ),
inference(definitional_conversion,[status(esa)],[f_1029_2]) ).
cnf(f_1029_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4374,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4374,tc_HOL_Obool)),U_4375),U_4377)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4374,tc_HOL_Obool)),U_4376),U_4378)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4374,tc_HOL_Obool)),U_4377),U_4378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4374,tc_HOL_Obool)),U_4375),U_4376)) ),
inference(clausify,[status(thm)],[f_1029_3]) ).
fof(f_1030_1,plain,
! [V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = V_B_2,
inference(fof_nnf,[status(thm)],[fact_Int__UNIV__left]) ).
fof(f_1030_2,plain,
! [U_4380,U_4379] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4379,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4379,tc_HOL_Obool))),U_4380) = U_4380,
inference(variable_rename,[status(thm)],[f_1030_1]) ).
fof(f_1030_3,plain,
! [U_4380,U_4379] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4379,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4379,tc_HOL_Obool))),U_4380) = U_4380,
inference(definitional_conversion,[status(esa)],[f_1030_2]) ).
cnf(f_1030_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4379,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4379,tc_HOL_Obool))),U_4380) = U_4380,
inference(clausify,[status(thm)],[f_1030_3]) ).
fof(f_1031_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Int__UNIV__right]) ).
fof(f_1031_2,plain,
! [U_4382,U_4381] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4381,tc_HOL_Obool)),U_4382),c_Orderings_Otop__class_Otop(tc_fun(U_4381,tc_HOL_Obool))) = U_4382,
inference(variable_rename,[status(thm)],[f_1031_1]) ).
fof(f_1031_3,plain,
! [U_4381,U_4382] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4381,tc_HOL_Obool)),U_4382),c_Orderings_Otop__class_Otop(tc_fun(U_4381,tc_HOL_Obool))) = U_4382,
inference(definitional_conversion,[status(esa)],[f_1031_2]) ).
cnf(f_1031_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4381,tc_HOL_Obool)),U_4382),c_Orderings_Otop__class_Otop(tc_fun(U_4381,tc_HOL_Obool))) = U_4382,
inference(clausify,[status(thm)],[f_1031_3]) ).
fof(f_1032_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_A_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Int__Un__distrib]) ).
fof(f_1032_2,plain,
! [U_4386,U_4385,U_4384,U_4383] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4383,tc_HOL_Obool)),U_4384),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4383,tc_HOL_Obool)),U_4385),U_4386)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4383,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4383,tc_HOL_Obool)),U_4384),U_4385)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4383,tc_HOL_Obool)),U_4384),U_4386)),
inference(variable_rename,[status(thm)],[f_1032_1]) ).
fof(f_1032_3,plain,
! [U_4383,U_4384,U_4385,U_4386] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4383,tc_HOL_Obool)),U_4384),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4383,tc_HOL_Obool)),U_4385),U_4386)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4383,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4383,tc_HOL_Obool)),U_4384),U_4385)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4383,tc_HOL_Obool)),U_4384),U_4386)),
inference(definitional_conversion,[status(esa)],[f_1032_2]) ).
cnf(f_1032_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4383,tc_HOL_Obool)),U_4384),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4383,tc_HOL_Obool)),U_4385),U_4386)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4383,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4383,tc_HOL_Obool)),U_4384),U_4385)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4383,tc_HOL_Obool)),U_4384),U_4386)),
inference(clausify,[status(thm)],[f_1032_3]) ).
fof(f_1033_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_A_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Un__Int__distrib]) ).
fof(f_1033_2,plain,
! [U_4390,U_4389,U_4388,U_4387] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4387,tc_HOL_Obool)),U_4388),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4387,tc_HOL_Obool)),U_4389),U_4390)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4387,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4387,tc_HOL_Obool)),U_4388),U_4389)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4387,tc_HOL_Obool)),U_4388),U_4390)),
inference(variable_rename,[status(thm)],[f_1033_1]) ).
fof(f_1033_3,plain,
! [U_4387,U_4388,U_4389,U_4390] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4387,tc_HOL_Obool)),U_4388),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4387,tc_HOL_Obool)),U_4389),U_4390)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4387,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4387,tc_HOL_Obool)),U_4388),U_4389)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4387,tc_HOL_Obool)),U_4388),U_4390)),
inference(definitional_conversion,[status(esa)],[f_1033_2]) ).
cnf(f_1033_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4387,tc_HOL_Obool)),U_4388),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4387,tc_HOL_Obool)),U_4389),U_4390)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4387,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4387,tc_HOL_Obool)),U_4388),U_4389)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4387,tc_HOL_Obool)),U_4388),U_4390)),
inference(clausify,[status(thm)],[f_1033_3]) ).
fof(f_1034_1,plain,
! [V_A_2,V_C_2,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Int__Un__distrib2]) ).
fof(f_1034_2,plain,
! [U_4394,U_4393,U_4392,U_4391] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4391,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4391,tc_HOL_Obool)),U_4392),U_4393)),U_4394) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4391,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4391,tc_HOL_Obool)),U_4392),U_4394)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4391,tc_HOL_Obool)),U_4393),U_4394)),
inference(variable_rename,[status(thm)],[f_1034_1]) ).
fof(f_1034_3,plain,
! [U_4391,U_4392,U_4393,U_4394] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4391,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4391,tc_HOL_Obool)),U_4392),U_4393)),U_4394) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4391,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4391,tc_HOL_Obool)),U_4392),U_4394)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4391,tc_HOL_Obool)),U_4393),U_4394)),
inference(definitional_conversion,[status(esa)],[f_1034_2]) ).
cnf(f_1034_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4391,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4391,tc_HOL_Obool)),U_4392),U_4393)),U_4394) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4391,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4391,tc_HOL_Obool)),U_4392),U_4394)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4391,tc_HOL_Obool)),U_4393),U_4394)),
inference(clausify,[status(thm)],[f_1034_3]) ).
fof(f_1035_1,plain,
! [V_A_2,V_C_2,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Un__Int__distrib2]) ).
fof(f_1035_2,plain,
! [U_4398,U_4397,U_4396,U_4395] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4395,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4395,tc_HOL_Obool)),U_4396),U_4397)),U_4398) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4395,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4395,tc_HOL_Obool)),U_4396),U_4398)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4395,tc_HOL_Obool)),U_4397),U_4398)),
inference(variable_rename,[status(thm)],[f_1035_1]) ).
fof(f_1035_3,plain,
! [U_4395,U_4396,U_4397,U_4398] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4395,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4395,tc_HOL_Obool)),U_4396),U_4397)),U_4398) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4395,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4395,tc_HOL_Obool)),U_4396),U_4398)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4395,tc_HOL_Obool)),U_4397),U_4398)),
inference(definitional_conversion,[status(esa)],[f_1035_2]) ).
cnf(f_1035_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4395,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4395,tc_HOL_Obool)),U_4396),U_4397)),U_4398) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4395,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4395,tc_HOL_Obool)),U_4396),U_4398)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4395,tc_HOL_Obool)),U_4397),U_4398)),
inference(clausify,[status(thm)],[f_1035_3]) ).
fof(f_1036_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Un__Int__crazy]) ).
fof(f_1036_2,plain,
! [U_4402,U_4401,U_4400,U_4399] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),U_4400),U_4401)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),U_4401),U_4402))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),U_4402),U_4400)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),U_4400),U_4401)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),U_4401),U_4402))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),U_4402),U_4400)),
inference(variable_rename,[status(thm)],[f_1036_1]) ).
fof(f_1036_3,plain,
! [U_4399,U_4400,U_4401,U_4402] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),U_4400),U_4401)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),U_4401),U_4402))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),U_4402),U_4400)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),U_4400),U_4401)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),U_4401),U_4402))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),U_4402),U_4400)),
inference(definitional_conversion,[status(esa)],[f_1036_2]) ).
cnf(f_1036_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),U_4400),U_4401)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),U_4401),U_4402))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),U_4402),U_4400)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4399,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),U_4400),U_4401)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),U_4401),U_4402))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4399,tc_HOL_Obool)),U_4402),U_4400)),
inference(clausify,[status(thm)],[f_1036_3]) ).
fof(f_1037_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,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_Ovimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Diff]) ).
fof(f_1037_2,plain,
! [U_4407,U_4406,U_4405,U_4404,U_4403] : hAPP(c_Set_Ovimage(U_4403,U_4404,U_4405),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4404,tc_HOL_Obool)),U_4406),U_4407)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4403,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4403,U_4404,U_4405),U_4406)),hAPP(c_Set_Ovimage(U_4403,U_4404,U_4405),U_4407)),
inference(variable_rename,[status(thm)],[f_1037_1]) ).
fof(f_1037_3,plain,
! [U_4403,U_4404,U_4405,U_4406,U_4407] : hAPP(c_Set_Ovimage(U_4403,U_4404,U_4405),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4404,tc_HOL_Obool)),U_4406),U_4407)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4403,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4403,U_4404,U_4405),U_4406)),hAPP(c_Set_Ovimage(U_4403,U_4404,U_4405),U_4407)),
inference(definitional_conversion,[status(esa)],[f_1037_2]) ).
cnf(f_1037_4,plain,
hAPP(c_Set_Ovimage(U_4403,U_4404,U_4405),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4404,tc_HOL_Obool)),U_4406),U_4407)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4403,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4403,U_4404,U_4405),U_4406)),hAPP(c_Set_Ovimage(U_4403,U_4404,U_4405),U_4407)),
inference(clausify,[status(thm)],[f_1037_3]) ).
fof(f_1038_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_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_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Diff__Int__distrib]) ).
fof(f_1038_2,plain,
! [U_4411,U_4410,U_4409,U_4408] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4408,tc_HOL_Obool)),U_4409),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4408,tc_HOL_Obool)),U_4410),U_4411)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4408,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4408,tc_HOL_Obool)),U_4409),U_4410)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4408,tc_HOL_Obool)),U_4409),U_4411)),
inference(variable_rename,[status(thm)],[f_1038_1]) ).
fof(f_1038_3,plain,
! [U_4408,U_4409,U_4410,U_4411] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4408,tc_HOL_Obool)),U_4409),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4408,tc_HOL_Obool)),U_4410),U_4411)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4408,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4408,tc_HOL_Obool)),U_4409),U_4410)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4408,tc_HOL_Obool)),U_4409),U_4411)),
inference(definitional_conversion,[status(esa)],[f_1038_2]) ).
cnf(f_1038_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4408,tc_HOL_Obool)),U_4409),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4408,tc_HOL_Obool)),U_4410),U_4411)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4408,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4408,tc_HOL_Obool)),U_4409),U_4410)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4408,tc_HOL_Obool)),U_4409),U_4411)),
inference(clausify,[status(thm)],[f_1038_3]) ).
fof(f_1039_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Int__Diff]) ).
fof(f_1039_2,plain,
! [U_4415,U_4414,U_4413,U_4412] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4412,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4412,tc_HOL_Obool)),U_4413),U_4414)),U_4415) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4412,tc_HOL_Obool)),U_4413),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4412,tc_HOL_Obool)),U_4414),U_4415)),
inference(variable_rename,[status(thm)],[f_1039_1]) ).
fof(f_1039_3,plain,
! [U_4412,U_4413,U_4414,U_4415] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4412,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4412,tc_HOL_Obool)),U_4413),U_4414)),U_4415) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4412,tc_HOL_Obool)),U_4413),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4412,tc_HOL_Obool)),U_4414),U_4415)),
inference(definitional_conversion,[status(esa)],[f_1039_2]) ).
cnf(f_1039_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4412,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4412,tc_HOL_Obool)),U_4413),U_4414)),U_4415) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4412,tc_HOL_Obool)),U_4413),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4412,tc_HOL_Obool)),U_4414),U_4415)),
inference(clausify,[status(thm)],[f_1039_3]) ).
fof(f_1040_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Diff__Int__distrib2]) ).
fof(f_1040_2,plain,
! [U_4419,U_4418,U_4417,U_4416] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4416,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4416,tc_HOL_Obool)),U_4417),U_4418)),U_4419) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4416,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4416,tc_HOL_Obool)),U_4417),U_4419)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4416,tc_HOL_Obool)),U_4418),U_4419)),
inference(variable_rename,[status(thm)],[f_1040_1]) ).
fof(f_1040_3,plain,
! [U_4416,U_4417,U_4418,U_4419] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4416,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4416,tc_HOL_Obool)),U_4417),U_4418)),U_4419) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4416,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4416,tc_HOL_Obool)),U_4417),U_4419)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4416,tc_HOL_Obool)),U_4418),U_4419)),
inference(definitional_conversion,[status(esa)],[f_1040_2]) ).
cnf(f_1040_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4416,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4416,tc_HOL_Obool)),U_4417),U_4418)),U_4419) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4416,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4416,tc_HOL_Obool)),U_4417),U_4419)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4416,tc_HOL_Obool)),U_4418),U_4419)),
inference(clausify,[status(thm)],[f_1040_3]) ).
fof(f_1041_1,plain,
! [V_B_2,V_C_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Diff__Int2]) ).
fof(f_1041_2,plain,
! [U_4423,U_4422,U_4421,U_4420] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4420,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4420,tc_HOL_Obool)),U_4421),U_4422)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4420,tc_HOL_Obool)),U_4423),U_4422)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4420,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4420,tc_HOL_Obool)),U_4421),U_4422)),U_4423),
inference(variable_rename,[status(thm)],[f_1041_1]) ).
fof(f_1041_3,plain,
! [U_4420,U_4421,U_4422,U_4423] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4420,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4420,tc_HOL_Obool)),U_4421),U_4422)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4420,tc_HOL_Obool)),U_4423),U_4422)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4420,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4420,tc_HOL_Obool)),U_4421),U_4422)),U_4423),
inference(definitional_conversion,[status(esa)],[f_1041_2]) ).
cnf(f_1041_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4420,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4420,tc_HOL_Obool)),U_4421),U_4422)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4420,tc_HOL_Obool)),U_4423),U_4422)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4420,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4420,tc_HOL_Obool)),U_4421),U_4422)),U_4423),
inference(clausify,[status(thm)],[f_1041_3]) ).
fof(f_1042_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2)
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__Int]) ).
fof(f_1042_2,plain,
! [U_4428,U_4427,U_4426,U_4425,U_4424] :
( c_Fun_Oinj__on(U_4424,U_4425,U_4426,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4424,tc_HOL_Obool)),U_4427),U_4428))
| ~ c_Fun_Oinj__on(U_4424,U_4425,U_4426,U_4428)
| ~ c_Fun_Oinj__on(U_4424,U_4425,U_4426,U_4427) ),
inference(variable_rename,[status(thm)],[f_1042_1]) ).
fof(f_1042_3,plain,
! [U_4424,U_4425,U_4426,U_4427,U_4428] :
( c_Fun_Oinj__on(U_4424,U_4425,U_4426,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4424,tc_HOL_Obool)),U_4427),U_4428))
| ~ c_Fun_Oinj__on(U_4424,U_4425,U_4426,U_4428)
| ~ c_Fun_Oinj__on(U_4424,U_4425,U_4426,U_4427) ),
inference(definitional_conversion,[status(esa)],[f_1042_2]) ).
cnf(f_1042_4,plain,
( c_Fun_Oinj__on(U_4424,U_4425,U_4426,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4424,tc_HOL_Obool)),U_4427),U_4428))
| ~ c_Fun_Oinj__on(U_4424,U_4425,U_4426,U_4428)
| ~ c_Fun_Oinj__on(U_4424,U_4425,U_4426,U_4427) ),
inference(clausify,[status(thm)],[f_1042_3]) ).
fof(f_1043_1,plain,
! [V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Compl]) ).
fof(f_1043_2,plain,
! [U_4432,U_4431,U_4430,U_4429] : hAPP(c_Set_Ovimage(U_4429,U_4430,U_4431),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4430,tc_HOL_Obool)),U_4432)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4429,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4429,U_4430,U_4431),U_4432)),
inference(variable_rename,[status(thm)],[f_1043_1]) ).
fof(f_1043_3,plain,
! [U_4429,U_4430,U_4431,U_4432] : hAPP(c_Set_Ovimage(U_4429,U_4430,U_4431),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4430,tc_HOL_Obool)),U_4432)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4429,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4429,U_4430,U_4431),U_4432)),
inference(definitional_conversion,[status(esa)],[f_1043_2]) ).
cnf(f_1043_4,plain,
hAPP(c_Set_Ovimage(U_4429,U_4430,U_4431),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4430,tc_HOL_Obool)),U_4432)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4429,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4429,U_4430,U_4431),U_4432)),
inference(clausify,[status(thm)],[f_1043_3]) ).
fof(f_1044_1,plain,
! [T_c] :
( c_Finite__Set_Ofun__left__comm__idem(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c))
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf]) ).
fof(f_1044_2,plain,
! [U_4433] :
( c_Finite__Set_Ofun__left__comm__idem(U_4433,U_4433,c_Lattices_Osemilattice__inf__class_Oinf(U_4433))
| ~ class_Lattices_Osemilattice__inf(U_4433) ),
inference(variable_rename,[status(thm)],[f_1044_1]) ).
fof(f_1044_3,plain,
! [U_4433] :
( c_Finite__Set_Ofun__left__comm__idem(U_4433,U_4433,c_Lattices_Osemilattice__inf__class_Oinf(U_4433))
| ~ class_Lattices_Osemilattice__inf(U_4433) ),
inference(definitional_conversion,[status(esa)],[f_1044_2]) ).
cnf(f_1044_4,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_4433,U_4433,c_Lattices_Osemilattice__inf__class_Oinf(U_4433))
| ~ class_Lattices_Osemilattice__inf(U_4433) ),
inference(clausify,[status(thm)],[f_1044_3]) ).
fof(f_1045_1,plain,
! [V_x_2,V_S_2,V_R_2,T_c] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_R_2),V_S_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_R_2),V_S_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_R_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_S_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_inf__Int__eq]) ).
fof(f_1045_2,plain,
! [U_4437,U_4436,U_4435,U_4434] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4434,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_4434,tc_fun(U_4434,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4434)),U_4435)),hAPP(hAPP(c_COMBC(U_4434,tc_fun(U_4434,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4434)),U_4436)),U_4437))
| ~ hBOOL(hAPP(hAPP(c_member(U_4434),U_4437),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4434,tc_HOL_Obool)),U_4435),U_4436))) )
& ( hBOOL(hAPP(hAPP(c_member(U_4434),U_4437),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4434,tc_HOL_Obool)),U_4435),U_4436)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4434,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_4434,tc_fun(U_4434,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4434)),U_4435)),hAPP(hAPP(c_COMBC(U_4434,tc_fun(U_4434,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4434)),U_4436)),U_4437)) ) ),
inference(variable_rename,[status(thm)],[f_1045_1]) ).
fof(f_1045_3,plain,
( ! [U_4445,U_4443,U_4441,U_4439] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4439,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_4439,tc_fun(U_4439,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4439)),U_4441)),hAPP(hAPP(c_COMBC(U_4439,tc_fun(U_4439,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4439)),U_4443)),U_4445))
| ~ hBOOL(hAPP(hAPP(c_member(U_4439),U_4445),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4439,tc_HOL_Obool)),U_4441),U_4443))) )
& ! [U_4444,U_4442,U_4440,U_4438] :
( hBOOL(hAPP(hAPP(c_member(U_4438),U_4444),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4438,tc_HOL_Obool)),U_4440),U_4442)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4438,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_4438,tc_fun(U_4438,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4438)),U_4440)),hAPP(hAPP(c_COMBC(U_4438,tc_fun(U_4438,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4438)),U_4442)),U_4444)) ) ),
inference(miniscope,[status(thm)],[f_1045_2]) ).
fof(f_1045_4,plain,
( ! [U_4439,U_4441,U_4443,U_4445] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4439,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_4439,tc_fun(U_4439,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4439)),U_4441)),hAPP(hAPP(c_COMBC(U_4439,tc_fun(U_4439,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4439)),U_4443)),U_4445))
| ~ hBOOL(hAPP(hAPP(c_member(U_4439),U_4445),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4439,tc_HOL_Obool)),U_4441),U_4443))) )
& ! [U_4442,U_4440,U_4444,U_4438] :
( hBOOL(hAPP(hAPP(c_member(U_4438),U_4444),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4438,tc_HOL_Obool)),U_4440),U_4442)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4438,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_4438,tc_fun(U_4438,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4438)),U_4440)),hAPP(hAPP(c_COMBC(U_4438,tc_fun(U_4438,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4438)),U_4442)),U_4444)) ) ),
inference(definitional_conversion,[status(esa)],[f_1045_3]) ).
cnf(f_1045_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_4438),U_4444),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4438,tc_HOL_Obool)),U_4440),U_4442)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4438,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_4438,tc_fun(U_4438,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4438)),U_4440)),hAPP(hAPP(c_COMBC(U_4438,tc_fun(U_4438,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4438)),U_4442)),U_4444)) ),
inference(clausify,[status(thm)],[f_1045_4]) ).
cnf(f_1045_6,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4439,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_4439,tc_fun(U_4439,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4439)),U_4441)),hAPP(hAPP(c_COMBC(U_4439,tc_fun(U_4439,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4439)),U_4443)),U_4445))
| ~ hBOOL(hAPP(hAPP(c_member(U_4439),U_4445),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4439,tc_HOL_Obool)),U_4441),U_4443))) ),
inference(clausify,[status(thm)],[f_1045_4]) ).
fof(f_1046_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_1046_2,plain,
! [U_4449,U_4448,U_4447,U_4446] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4446),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4446),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4446),U_4447),U_4448)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4446),U_4447),U_4449))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4446),U_4447),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4446),U_4448),U_4449))))
| ~ class_Lattices_Olattice(U_4446) ),
inference(variable_rename,[status(thm)],[f_1046_1]) ).
fof(f_1046_3,plain,
! [U_4446,U_4447,U_4448,U_4449] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4446),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4446),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4446),U_4447),U_4448)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4446),U_4447),U_4449))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4446),U_4447),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4446),U_4448),U_4449))))
| ~ class_Lattices_Olattice(U_4446) ),
inference(definitional_conversion,[status(esa)],[f_1046_2]) ).
cnf(f_1046_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4446),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4446),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4446),U_4447),U_4448)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4446),U_4447),U_4449))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4446),U_4447),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4446),U_4448),U_4449))))
| ~ class_Lattices_Olattice(U_4446) ),
inference(clausify,[status(thm)],[f_1046_3]) ).
fof(f_1047_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_1047_2,plain,
! [U_4453,U_4452,U_4451,U_4450] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4450),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4450),U_4451),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4450),U_4452),U_4453))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4450),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4450),U_4451),U_4452)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4450),U_4451),U_4453))))
| ~ class_Lattices_Olattice(U_4450) ),
inference(variable_rename,[status(thm)],[f_1047_1]) ).
fof(f_1047_3,plain,
! [U_4450,U_4451,U_4452,U_4453] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4450),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4450),U_4451),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4450),U_4452),U_4453))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4450),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4450),U_4451),U_4452)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4450),U_4451),U_4453))))
| ~ class_Lattices_Olattice(U_4450) ),
inference(definitional_conversion,[status(esa)],[f_1047_2]) ).
cnf(f_1047_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4450),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4450),U_4451),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4450),U_4452),U_4453))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4450),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4450),U_4451),U_4452)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4450),U_4451),U_4453))))
| ~ class_Lattices_Olattice(U_4450) ),
inference(clausify,[status(thm)],[f_1047_3]) ).
fof(f_1048_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_1048_2,plain,
! [U_4455,U_4454] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4454),U_4455),hAPP(c_Groups_Ouminus__class_Ouminus(U_4454),U_4455)) = c_Orderings_Obot__class_Obot(U_4454)
| ~ class_Lattices_Oboolean__algebra(U_4454) ),
inference(variable_rename,[status(thm)],[f_1048_1]) ).
fof(f_1048_3,plain,
! [U_4454,U_4455] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4454),U_4455),hAPP(c_Groups_Ouminus__class_Ouminus(U_4454),U_4455)) = c_Orderings_Obot__class_Obot(U_4454)
| ~ class_Lattices_Oboolean__algebra(U_4454) ),
inference(definitional_conversion,[status(esa)],[f_1048_2]) ).
cnf(f_1048_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4454),U_4455),hAPP(c_Groups_Ouminus__class_Ouminus(U_4454),U_4455)) = c_Orderings_Obot__class_Obot(U_4454)
| ~ class_Lattices_Oboolean__algebra(U_4454) ),
inference(clausify,[status(thm)],[f_1048_3]) ).
fof(f_1049_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_1049_2,plain,
! [U_4457,U_4456] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4456),hAPP(c_Groups_Ouminus__class_Ouminus(U_4456),U_4457)),U_4457) = c_Orderings_Obot__class_Obot(U_4456)
| ~ class_Lattices_Oboolean__algebra(U_4456) ),
inference(variable_rename,[status(thm)],[f_1049_1]) ).
fof(f_1049_3,plain,
! [U_4456,U_4457] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4456),hAPP(c_Groups_Ouminus__class_Ouminus(U_4456),U_4457)),U_4457) = c_Orderings_Obot__class_Obot(U_4456)
| ~ class_Lattices_Oboolean__algebra(U_4456) ),
inference(definitional_conversion,[status(esa)],[f_1049_2]) ).
cnf(f_1049_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4456),hAPP(c_Groups_Ouminus__class_Ouminus(U_4456),U_4457)),U_4457) = c_Orderings_Obot__class_Obot(U_4456)
| ~ class_Lattices_Oboolean__algebra(U_4456) ),
inference(clausify,[status(thm)],[f_1049_3]) ).
fof(f_1050_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_1050_2,plain,
! [U_4460,U_4459,U_4458] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4458),U_4459),U_4460) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4458),U_4459),hAPP(c_Groups_Ouminus__class_Ouminus(U_4458),U_4460))
| ~ class_Lattices_Oboolean__algebra(U_4458) ),
inference(variable_rename,[status(thm)],[f_1050_1]) ).
fof(f_1050_3,plain,
! [U_4458,U_4459,U_4460] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4458),U_4459),U_4460) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4458),U_4459),hAPP(c_Groups_Ouminus__class_Ouminus(U_4458),U_4460))
| ~ class_Lattices_Oboolean__algebra(U_4458) ),
inference(definitional_conversion,[status(esa)],[f_1050_2]) ).
cnf(f_1050_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4458),U_4459),U_4460) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4458),U_4459),hAPP(c_Groups_Ouminus__class_Ouminus(U_4458),U_4460))
| ~ class_Lattices_Oboolean__algebra(U_4458) ),
inference(clausify,[status(thm)],[f_1050_3]) ).
fof(f_1051_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_1051_2,plain,
! [U_4463,U_4462,U_4461] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4461),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4461),U_4462),U_4463)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4461),hAPP(c_Groups_Ouminus__class_Ouminus(U_4461),U_4462)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4461),U_4463))
| ~ class_Lattices_Oboolean__algebra(U_4461) ),
inference(variable_rename,[status(thm)],[f_1051_1]) ).
fof(f_1051_3,plain,
! [U_4461,U_4462,U_4463] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4461),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4461),U_4462),U_4463)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4461),hAPP(c_Groups_Ouminus__class_Ouminus(U_4461),U_4462)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4461),U_4463))
| ~ class_Lattices_Oboolean__algebra(U_4461) ),
inference(definitional_conversion,[status(esa)],[f_1051_2]) ).
cnf(f_1051_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4461),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4461),U_4462),U_4463)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4461),hAPP(c_Groups_Ouminus__class_Ouminus(U_4461),U_4462)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4461),U_4463))
| ~ class_Lattices_Oboolean__algebra(U_4461) ),
inference(clausify,[status(thm)],[f_1051_3]) ).
fof(f_1052_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_1052_2,plain,
! [U_4466,U_4465,U_4464] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4464),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4464),U_4465),U_4466)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4464),hAPP(c_Groups_Ouminus__class_Ouminus(U_4464),U_4465)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4464),U_4466))
| ~ class_Lattices_Oboolean__algebra(U_4464) ),
inference(variable_rename,[status(thm)],[f_1052_1]) ).
fof(f_1052_3,plain,
! [U_4464,U_4465,U_4466] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4464),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4464),U_4465),U_4466)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4464),hAPP(c_Groups_Ouminus__class_Ouminus(U_4464),U_4465)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4464),U_4466))
| ~ class_Lattices_Oboolean__algebra(U_4464) ),
inference(definitional_conversion,[status(esa)],[f_1052_2]) ).
cnf(f_1052_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4464),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4464),U_4465),U_4466)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4464),hAPP(c_Groups_Ouminus__class_Ouminus(U_4464),U_4465)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4464),U_4466))
| ~ class_Lattices_Oboolean__algebra(U_4464) ),
inference(clausify,[status(thm)],[f_1052_3]) ).
fof(f_1053_1,plain,
! [V_B_2,V_A_2,V_a_2,T_c] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_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)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__right]) ).
fof(f_1053_2,plain,
! [U_4470,U_4469,U_4468,U_4467] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4467,tc_HOL_Obool)),U_4469),hAPP(hAPP(c_Set_Oinsert(U_4467),U_4468),U_4470)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4467,tc_HOL_Obool)),U_4469),U_4470)
| hBOOL(hAPP(hAPP(c_member(U_4467),U_4468),U_4469)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4467,tc_HOL_Obool)),U_4469),hAPP(hAPP(c_Set_Oinsert(U_4467),U_4468),U_4470)) = hAPP(hAPP(c_Set_Oinsert(U_4467),U_4468),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4467,tc_HOL_Obool)),U_4469),U_4470))
| ~ hBOOL(hAPP(hAPP(c_member(U_4467),U_4468),U_4469)) ) ),
inference(variable_rename,[status(thm)],[f_1053_1]) ).
fof(f_1053_3,plain,
( ! [U_4478,U_4476,U_4474,U_4472] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4472,tc_HOL_Obool)),U_4476),hAPP(hAPP(c_Set_Oinsert(U_4472),U_4474),U_4478)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4472,tc_HOL_Obool)),U_4476),U_4478)
| hBOOL(hAPP(hAPP(c_member(U_4472),U_4474),U_4476)) )
& ! [U_4477,U_4475,U_4473,U_4471] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4471,tc_HOL_Obool)),U_4475),hAPP(hAPP(c_Set_Oinsert(U_4471),U_4473),U_4477)) = hAPP(hAPP(c_Set_Oinsert(U_4471),U_4473),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4471,tc_HOL_Obool)),U_4475),U_4477))
| ~ hBOOL(hAPP(hAPP(c_member(U_4471),U_4473),U_4475)) ) ),
inference(miniscope,[status(thm)],[f_1053_2]) ).
fof(f_1053_4,plain,
( ! [U_4472,U_4474,U_4476,U_4478] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4472,tc_HOL_Obool)),U_4476),hAPP(hAPP(c_Set_Oinsert(U_4472),U_4474),U_4478)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4472,tc_HOL_Obool)),U_4476),U_4478)
| hBOOL(hAPP(hAPP(c_member(U_4472),U_4474),U_4476)) )
& ! [U_4477,U_4473,U_4471,U_4475] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4471,tc_HOL_Obool)),U_4475),hAPP(hAPP(c_Set_Oinsert(U_4471),U_4473),U_4477)) = hAPP(hAPP(c_Set_Oinsert(U_4471),U_4473),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4471,tc_HOL_Obool)),U_4475),U_4477))
| ~ hBOOL(hAPP(hAPP(c_member(U_4471),U_4473),U_4475)) ) ),
inference(definitional_conversion,[status(esa)],[f_1053_3]) ).
cnf(f_1053_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4471,tc_HOL_Obool)),U_4475),hAPP(hAPP(c_Set_Oinsert(U_4471),U_4473),U_4477)) = hAPP(hAPP(c_Set_Oinsert(U_4471),U_4473),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4471,tc_HOL_Obool)),U_4475),U_4477))
| ~ hBOOL(hAPP(hAPP(c_member(U_4471),U_4473),U_4475)) ),
inference(clausify,[status(thm)],[f_1053_4]) ).
cnf(f_1053_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4472,tc_HOL_Obool)),U_4476),hAPP(hAPP(c_Set_Oinsert(U_4472),U_4474),U_4478)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4472,tc_HOL_Obool)),U_4476),U_4478)
| hBOOL(hAPP(hAPP(c_member(U_4472),U_4474),U_4476)) ),
inference(clausify,[status(thm)],[f_1053_4]) ).
fof(f_1054_1,plain,
! [V_B_2,V_C_2,V_a_2,T_c] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_C_2)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_C_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__left]) ).
fof(f_1054_2,plain,
! [U_4482,U_4481,U_4480,U_4479] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4479,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4479),U_4480),U_4482)),U_4481) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4479,tc_HOL_Obool)),U_4482),U_4481)
| hBOOL(hAPP(hAPP(c_member(U_4479),U_4480),U_4481)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4479,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4479),U_4480),U_4482)),U_4481) = hAPP(hAPP(c_Set_Oinsert(U_4479),U_4480),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4479,tc_HOL_Obool)),U_4482),U_4481))
| ~ hBOOL(hAPP(hAPP(c_member(U_4479),U_4480),U_4481)) ) ),
inference(variable_rename,[status(thm)],[f_1054_1]) ).
fof(f_1054_3,plain,
( ! [U_4490,U_4488,U_4486,U_4484] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4484,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4484),U_4486),U_4490)),U_4488) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4484,tc_HOL_Obool)),U_4490),U_4488)
| hBOOL(hAPP(hAPP(c_member(U_4484),U_4486),U_4488)) )
& ! [U_4489,U_4487,U_4485,U_4483] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4483,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4483),U_4485),U_4489)),U_4487) = hAPP(hAPP(c_Set_Oinsert(U_4483),U_4485),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4483,tc_HOL_Obool)),U_4489),U_4487))
| ~ hBOOL(hAPP(hAPP(c_member(U_4483),U_4485),U_4487)) ) ),
inference(miniscope,[status(thm)],[f_1054_2]) ).
fof(f_1054_4,plain,
( ! [U_4484,U_4486,U_4488,U_4490] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4484,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4484),U_4486),U_4490)),U_4488) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4484,tc_HOL_Obool)),U_4490),U_4488)
| hBOOL(hAPP(hAPP(c_member(U_4484),U_4486),U_4488)) )
& ! [U_4487,U_4489,U_4485,U_4483] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4483,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4483),U_4485),U_4489)),U_4487) = hAPP(hAPP(c_Set_Oinsert(U_4483),U_4485),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4483,tc_HOL_Obool)),U_4489),U_4487))
| ~ hBOOL(hAPP(hAPP(c_member(U_4483),U_4485),U_4487)) ) ),
inference(definitional_conversion,[status(esa)],[f_1054_3]) ).
cnf(f_1054_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4483,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4483),U_4485),U_4489)),U_4487) = hAPP(hAPP(c_Set_Oinsert(U_4483),U_4485),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4483,tc_HOL_Obool)),U_4489),U_4487))
| ~ hBOOL(hAPP(hAPP(c_member(U_4483),U_4485),U_4487)) ),
inference(clausify,[status(thm)],[f_1054_4]) ).
cnf(f_1054_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4484,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4484),U_4486),U_4490)),U_4488) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4484,tc_HOL_Obool)),U_4490),U_4488)
| hBOOL(hAPP(hAPP(c_member(U_4484),U_4486),U_4488)) ),
inference(clausify,[status(thm)],[f_1054_4]) ).
fof(f_1055_1,plain,
! [V_B_2,V_A_2,V_a_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_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)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if0]) ).
fof(f_1055_2,plain,
! [U_4494,U_4493,U_4492,U_4491] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4491,tc_HOL_Obool)),U_4493),hAPP(hAPP(c_Set_Oinsert(U_4491),U_4492),U_4494)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4491,tc_HOL_Obool)),U_4493),U_4494)
| hBOOL(hAPP(hAPP(c_member(U_4491),U_4492),U_4493)) ),
inference(variable_rename,[status(thm)],[f_1055_1]) ).
fof(f_1055_3,plain,
! [U_4491,U_4492,U_4493,U_4494] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4491,tc_HOL_Obool)),U_4493),hAPP(hAPP(c_Set_Oinsert(U_4491),U_4492),U_4494)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4491,tc_HOL_Obool)),U_4493),U_4494)
| hBOOL(hAPP(hAPP(c_member(U_4491),U_4492),U_4493)) ),
inference(definitional_conversion,[status(esa)],[f_1055_2]) ).
cnf(f_1055_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4491,tc_HOL_Obool)),U_4493),hAPP(hAPP(c_Set_Oinsert(U_4491),U_4492),U_4494)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4491,tc_HOL_Obool)),U_4493),U_4494)
| hBOOL(hAPP(hAPP(c_member(U_4491),U_4492),U_4493)) ),
inference(clausify,[status(thm)],[f_1055_3]) ).
fof(f_1056_1,plain,
! [V_B_2,V_C_2,V_a_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if0]) ).
fof(f_1056_2,plain,
! [U_4498,U_4497,U_4496,U_4495] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4495,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4495),U_4496),U_4498)),U_4497) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4495,tc_HOL_Obool)),U_4498),U_4497)
| hBOOL(hAPP(hAPP(c_member(U_4495),U_4496),U_4497)) ),
inference(variable_rename,[status(thm)],[f_1056_1]) ).
fof(f_1056_3,plain,
! [U_4495,U_4496,U_4497,U_4498] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4495,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4495),U_4496),U_4498)),U_4497) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4495,tc_HOL_Obool)),U_4498),U_4497)
| hBOOL(hAPP(hAPP(c_member(U_4495),U_4496),U_4497)) ),
inference(definitional_conversion,[status(esa)],[f_1056_2]) ).
cnf(f_1056_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4495,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4495),U_4496),U_4498)),U_4497) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4495,tc_HOL_Obool)),U_4498),U_4497)
| hBOOL(hAPP(hAPP(c_member(U_4495),U_4496),U_4497)) ),
inference(clausify,[status(thm)],[f_1056_3]) ).
fof(f_1057_1,plain,
! [V_B_2,V_A_2,V_a_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1]) ).
fof(f_1057_2,plain,
! [U_4502,U_4501,U_4500,U_4499] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4499,tc_HOL_Obool)),U_4501),hAPP(hAPP(c_Set_Oinsert(U_4499),U_4500),U_4502)) = hAPP(hAPP(c_Set_Oinsert(U_4499),U_4500),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4499,tc_HOL_Obool)),U_4501),U_4502))
| ~ hBOOL(hAPP(hAPP(c_member(U_4499),U_4500),U_4501)) ),
inference(variable_rename,[status(thm)],[f_1057_1]) ).
fof(f_1057_3,plain,
! [U_4499,U_4500,U_4501,U_4502] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4499,tc_HOL_Obool)),U_4501),hAPP(hAPP(c_Set_Oinsert(U_4499),U_4500),U_4502)) = hAPP(hAPP(c_Set_Oinsert(U_4499),U_4500),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4499,tc_HOL_Obool)),U_4501),U_4502))
| ~ hBOOL(hAPP(hAPP(c_member(U_4499),U_4500),U_4501)) ),
inference(definitional_conversion,[status(esa)],[f_1057_2]) ).
cnf(f_1057_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4499,tc_HOL_Obool)),U_4501),hAPP(hAPP(c_Set_Oinsert(U_4499),U_4500),U_4502)) = hAPP(hAPP(c_Set_Oinsert(U_4499),U_4500),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4499,tc_HOL_Obool)),U_4501),U_4502))
| ~ hBOOL(hAPP(hAPP(c_member(U_4499),U_4500),U_4501)) ),
inference(clausify,[status(thm)],[f_1057_3]) ).
fof(f_1058_1,plain,
! [V_B_2,V_C_2,V_a_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1]) ).
fof(f_1058_2,plain,
! [U_4506,U_4505,U_4504,U_4503] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4503,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4503),U_4504),U_4506)),U_4505) = hAPP(hAPP(c_Set_Oinsert(U_4503),U_4504),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4503,tc_HOL_Obool)),U_4506),U_4505))
| ~ hBOOL(hAPP(hAPP(c_member(U_4503),U_4504),U_4505)) ),
inference(variable_rename,[status(thm)],[f_1058_1]) ).
fof(f_1058_3,plain,
! [U_4503,U_4504,U_4505,U_4506] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4503,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4503),U_4504),U_4506)),U_4505) = hAPP(hAPP(c_Set_Oinsert(U_4503),U_4504),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4503,tc_HOL_Obool)),U_4506),U_4505))
| ~ hBOOL(hAPP(hAPP(c_member(U_4503),U_4504),U_4505)) ),
inference(definitional_conversion,[status(esa)],[f_1058_2]) ).
cnf(f_1058_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4503,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4503),U_4504),U_4506)),U_4505) = hAPP(hAPP(c_Set_Oinsert(U_4503),U_4504),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4503,tc_HOL_Obool)),U_4506),U_4505))
| ~ hBOOL(hAPP(hAPP(c_member(U_4503),U_4504),U_4505)) ),
inference(clausify,[status(thm)],[f_1058_3]) ).
fof(f_1059_1,plain,
! [V_A_2,V_f_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2))),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_image__vimage__subset]) ).
fof(f_1059_2,plain,
! [U_4510,U_4509,U_4508,U_4507] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4507,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4508,U_4507,U_4509),hAPP(c_Set_Ovimage(U_4508,U_4507,U_4509),U_4510))),U_4510)),
inference(variable_rename,[status(thm)],[f_1059_1]) ).
fof(f_1059_3,plain,
! [U_4507,U_4508,U_4509,U_4510] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4507,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4508,U_4507,U_4509),hAPP(c_Set_Ovimage(U_4508,U_4507,U_4509),U_4510))),U_4510)),
inference(definitional_conversion,[status(esa)],[f_1059_2]) ).
cnf(f_1059_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4507,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4508,U_4507,U_4509),hAPP(c_Set_Ovimage(U_4508,U_4507,U_4509),U_4510))),U_4510)),
inference(clausify,[status(thm)],[f_1059_3]) ).
fof(f_1060_1,plain,
! [V_A_2,V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_A_2)) = V_A_2
| hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq]) ).
fof(f_1060_2,plain,
! [U_4514,U_4513,U_4512,U_4511] :
( hAPP(c_Set_Oimage(U_4511,U_4512,U_4513),hAPP(c_Set_Ovimage(U_4511,U_4512,U_4513),U_4514)) = U_4514
| hAPP(c_Set_Oimage(U_4511,U_4512,U_4513),c_Orderings_Otop__class_Otop(tc_fun(U_4511,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_4512,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_1060_1]) ).
fof(f_1060_3,plain,
! [U_4511,U_4512,U_4513,U_4514] :
( hAPP(c_Set_Oimage(U_4511,U_4512,U_4513),hAPP(c_Set_Ovimage(U_4511,U_4512,U_4513),U_4514)) = U_4514
| hAPP(c_Set_Oimage(U_4511,U_4512,U_4513),c_Orderings_Otop__class_Otop(tc_fun(U_4511,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_4512,tc_HOL_Obool)) ),
inference(definitional_conversion,[status(esa)],[f_1060_2]) ).
cnf(f_1060_4,plain,
( hAPP(c_Set_Oimage(U_4511,U_4512,U_4513),hAPP(c_Set_Ovimage(U_4511,U_4512,U_4513),U_4514)) = U_4514
| hAPP(c_Set_Oimage(U_4511,U_4512,U_4513),c_Orderings_Otop__class_Otop(tc_fun(U_4511,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_4512,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1060_3]) ).
fof(f_1061_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_d,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_image__Int__subset]) ).
fof(f_1061_2,plain,
! [U_4519,U_4518,U_4517,U_4516,U_4515] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4515,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4516,U_4515,U_4517),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4516,tc_HOL_Obool)),U_4518),U_4519))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4515,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4516,U_4515,U_4517),U_4518)),hAPP(c_Set_Oimage(U_4516,U_4515,U_4517),U_4519)))),
inference(variable_rename,[status(thm)],[f_1061_1]) ).
fof(f_1061_3,plain,
! [U_4515,U_4516,U_4517,U_4518,U_4519] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4515,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4516,U_4515,U_4517),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4516,tc_HOL_Obool)),U_4518),U_4519))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4515,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4516,U_4515,U_4517),U_4518)),hAPP(c_Set_Oimage(U_4516,U_4515,U_4517),U_4519)))),
inference(definitional_conversion,[status(esa)],[f_1061_2]) ).
cnf(f_1061_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4515,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4516,U_4515,U_4517),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4516,tc_HOL_Obool)),U_4518),U_4519))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4515,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4516,U_4515,U_4517),U_4518)),hAPP(c_Set_Oimage(U_4516,U_4515,U_4517),U_4519)))),
inference(clausify,[status(thm)],[f_1061_3]) ).
fof(f_1062_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_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)) ),
inference(fof_nnf,[status(thm)],[fact_Diff__triv]) ).
fof(f_1062_2,plain,
! [U_4522,U_4521,U_4520] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4520,tc_HOL_Obool)),U_4521),U_4522) = U_4521
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4520,tc_HOL_Obool)),U_4521),U_4522) != c_Orderings_Obot__class_Obot(tc_fun(U_4520,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_1062_1]) ).
fof(f_1062_3,plain,
! [U_4520,U_4521,U_4522] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4520,tc_HOL_Obool)),U_4521),U_4522) = U_4521
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4520,tc_HOL_Obool)),U_4521),U_4522) != c_Orderings_Obot__class_Obot(tc_fun(U_4520,tc_HOL_Obool)) ),
inference(definitional_conversion,[status(esa)],[f_1062_2]) ).
cnf(f_1062_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4520,tc_HOL_Obool)),U_4521),U_4522) = U_4521
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4520,tc_HOL_Obool)),U_4521),U_4522) != c_Orderings_Obot__class_Obot(tc_fun(U_4520,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1062_3]) ).
fof(f_1063_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Diff__disjoint]) ).
fof(f_1063_2,plain,
! [U_4525,U_4524,U_4523] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4523,tc_HOL_Obool)),U_4524),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4523,tc_HOL_Obool)),U_4525),U_4524)) = c_Orderings_Obot__class_Obot(tc_fun(U_4523,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1063_1]) ).
fof(f_1063_3,plain,
! [U_4523,U_4524,U_4525] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4523,tc_HOL_Obool)),U_4524),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4523,tc_HOL_Obool)),U_4525),U_4524)) = c_Orderings_Obot__class_Obot(tc_fun(U_4523,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1063_2]) ).
cnf(f_1063_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4523,tc_HOL_Obool)),U_4524),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4523,tc_HOL_Obool)),U_4525),U_4524)) = c_Orderings_Obot__class_Obot(tc_fun(U_4523,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1063_3]) ).
fof(f_1064_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq]) ).
fof(f_1064_2,plain,
! [U_4529,U_4528,U_4527,U_4526] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4526,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4526,tc_HOL_Obool)),U_4527),U_4528)),U_4529) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4526,tc_HOL_Obool)),U_4527),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4526,tc_HOL_Obool)),U_4528),U_4529))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4526,tc_HOL_Obool)),U_4529),U_4527)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4526,tc_HOL_Obool)),U_4529),U_4527))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4526,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4526,tc_HOL_Obool)),U_4527),U_4528)),U_4529) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4526,tc_HOL_Obool)),U_4527),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4526,tc_HOL_Obool)),U_4528),U_4529)) ) ),
inference(variable_rename,[status(thm)],[f_1064_1]) ).
fof(f_1064_3,plain,
( ! [U_4537,U_4535,U_4533,U_4531] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4531,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4531,tc_HOL_Obool)),U_4533),U_4535)),U_4537) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4531,tc_HOL_Obool)),U_4533),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4531,tc_HOL_Obool)),U_4535),U_4537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4531,tc_HOL_Obool)),U_4537),U_4533)) )
& ! [U_4536,U_4534,U_4532,U_4530] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4530,tc_HOL_Obool)),U_4536),U_4532))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4530,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4530,tc_HOL_Obool)),U_4532),U_4534)),U_4536) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4530,tc_HOL_Obool)),U_4532),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4530,tc_HOL_Obool)),U_4534),U_4536)) ) ),
inference(miniscope,[status(thm)],[f_1064_2]) ).
fof(f_1064_4,plain,
( ! [U_4531,U_4533,U_4535,U_4537] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4531,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4531,tc_HOL_Obool)),U_4533),U_4535)),U_4537) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4531,tc_HOL_Obool)),U_4533),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4531,tc_HOL_Obool)),U_4535),U_4537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4531,tc_HOL_Obool)),U_4537),U_4533)) )
& ! [U_4536,U_4532,U_4534,U_4530] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4530,tc_HOL_Obool)),U_4536),U_4532))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4530,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4530,tc_HOL_Obool)),U_4532),U_4534)),U_4536) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4530,tc_HOL_Obool)),U_4532),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4530,tc_HOL_Obool)),U_4534),U_4536)) ) ),
inference(definitional_conversion,[status(esa)],[f_1064_3]) ).
cnf(f_1064_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4530,tc_HOL_Obool)),U_4536),U_4532))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4530,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4530,tc_HOL_Obool)),U_4532),U_4534)),U_4536) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4530,tc_HOL_Obool)),U_4532),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4530,tc_HOL_Obool)),U_4534),U_4536)) ),
inference(clausify,[status(thm)],[f_1064_4]) ).
cnf(f_1064_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4531,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4531,tc_HOL_Obool)),U_4533),U_4535)),U_4537) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4531,tc_HOL_Obool)),U_4533),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4531,tc_HOL_Obool)),U_4535),U_4537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4531,tc_HOL_Obool)),U_4537),U_4533)) ),
inference(clausify,[status(thm)],[f_1064_4]) ).
fof(f_1065_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),V_B_2)) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Un__Diff__Int]) ).
fof(f_1065_2,plain,
! [U_4540,U_4539,U_4538] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4538,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4538,tc_HOL_Obool)),U_4539),U_4540)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4538,tc_HOL_Obool)),U_4539),U_4540)) = U_4539,
inference(variable_rename,[status(thm)],[f_1065_1]) ).
fof(f_1065_3,plain,
! [U_4538,U_4539,U_4540] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4538,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4538,tc_HOL_Obool)),U_4539),U_4540)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4538,tc_HOL_Obool)),U_4539),U_4540)) = U_4539,
inference(definitional_conversion,[status(esa)],[f_1065_2]) ).
cnf(f_1065_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4538,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4538,tc_HOL_Obool)),U_4539),U_4540)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4538,tc_HOL_Obool)),U_4539),U_4540)) = U_4539,
inference(clausify,[status(thm)],[f_1065_3]) ).
fof(f_1066_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_A_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Diff__Un]) ).
fof(f_1066_2,plain,
! [U_4544,U_4543,U_4542,U_4541] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4541,tc_HOL_Obool)),U_4542),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4541,tc_HOL_Obool)),U_4543),U_4544)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4541,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4541,tc_HOL_Obool)),U_4542),U_4543)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4541,tc_HOL_Obool)),U_4542),U_4544)),
inference(variable_rename,[status(thm)],[f_1066_1]) ).
fof(f_1066_3,plain,
! [U_4541,U_4542,U_4543,U_4544] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4541,tc_HOL_Obool)),U_4542),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4541,tc_HOL_Obool)),U_4543),U_4544)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4541,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4541,tc_HOL_Obool)),U_4542),U_4543)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4541,tc_HOL_Obool)),U_4542),U_4544)),
inference(definitional_conversion,[status(esa)],[f_1066_2]) ).
cnf(f_1066_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4541,tc_HOL_Obool)),U_4542),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4541,tc_HOL_Obool)),U_4543),U_4544)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4541,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4541,tc_HOL_Obool)),U_4542),U_4543)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4541,tc_HOL_Obool)),U_4542),U_4544)),
inference(clausify,[status(thm)],[f_1066_3]) ).
fof(f_1067_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_A_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Diff__Int]) ).
fof(f_1067_2,plain,
! [U_4548,U_4547,U_4546,U_4545] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4545,tc_HOL_Obool)),U_4546),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4545,tc_HOL_Obool)),U_4547),U_4548)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4545,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4545,tc_HOL_Obool)),U_4546),U_4547)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4545,tc_HOL_Obool)),U_4546),U_4548)),
inference(variable_rename,[status(thm)],[f_1067_1]) ).
fof(f_1067_3,plain,
! [U_4545,U_4546,U_4547,U_4548] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4545,tc_HOL_Obool)),U_4546),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4545,tc_HOL_Obool)),U_4547),U_4548)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4545,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4545,tc_HOL_Obool)),U_4546),U_4547)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4545,tc_HOL_Obool)),U_4546),U_4548)),
inference(definitional_conversion,[status(esa)],[f_1067_2]) ).
cnf(f_1067_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4545,tc_HOL_Obool)),U_4546),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4545,tc_HOL_Obool)),U_4547),U_4548)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4545,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4545,tc_HOL_Obool)),U_4546),U_4547)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4545,tc_HOL_Obool)),U_4546),U_4548)),
inference(clausify,[status(thm)],[f_1067_3]) ).
fof(f_1068_1,plain,
! [V_x_2,V_r_2,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d))),V_r_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d))),V_r_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq]) ).
fof(f_1068_2,plain,
! [U_4552,U_4551,U_4550,U_4549] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4549,tc_fun(U_4550,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4549,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_4550,tc_HOL_Obool),tc_fun(U_4550,tc_HOL_Obool),U_4549),hAPP(c_COMBC(U_4550,tc_fun(U_4550,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4550))),U_4551)),U_4552))
| ~ hBOOL(hAPP(hAPP(c_member(U_4550),U_4552),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4549,tc_fun(U_4550,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4549,tc_HOL_Obool))),U_4551))) )
& ( hBOOL(hAPP(hAPP(c_member(U_4550),U_4552),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4549,tc_fun(U_4550,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4549,tc_HOL_Obool))),U_4551)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4549,tc_fun(U_4550,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4549,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_4550,tc_HOL_Obool),tc_fun(U_4550,tc_HOL_Obool),U_4549),hAPP(c_COMBC(U_4550,tc_fun(U_4550,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4550))),U_4551)),U_4552)) ) ),
inference(variable_rename,[status(thm)],[f_1068_1]) ).
fof(f_1068_3,plain,
( ! [U_4560,U_4558,U_4556,U_4554] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4554,tc_fun(U_4556,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4554,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_4556,tc_HOL_Obool),tc_fun(U_4556,tc_HOL_Obool),U_4554),hAPP(c_COMBC(U_4556,tc_fun(U_4556,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4556))),U_4558)),U_4560))
| ~ hBOOL(hAPP(hAPP(c_member(U_4556),U_4560),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4554,tc_fun(U_4556,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4554,tc_HOL_Obool))),U_4558))) )
& ! [U_4559,U_4557,U_4555,U_4553] :
( hBOOL(hAPP(hAPP(c_member(U_4555),U_4559),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4553,tc_fun(U_4555,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4553,tc_HOL_Obool))),U_4557)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4553,tc_fun(U_4555,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4553,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_4555,tc_HOL_Obool),tc_fun(U_4555,tc_HOL_Obool),U_4553),hAPP(c_COMBC(U_4555,tc_fun(U_4555,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4555))),U_4557)),U_4559)) ) ),
inference(miniscope,[status(thm)],[f_1068_2]) ).
fof(f_1068_4,plain,
( ! [U_4554,U_4556,U_4558,U_4560] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4554,tc_fun(U_4556,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4554,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_4556,tc_HOL_Obool),tc_fun(U_4556,tc_HOL_Obool),U_4554),hAPP(c_COMBC(U_4556,tc_fun(U_4556,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4556))),U_4558)),U_4560))
| ~ hBOOL(hAPP(hAPP(c_member(U_4556),U_4560),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4554,tc_fun(U_4556,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4554,tc_HOL_Obool))),U_4558))) )
& ! [U_4555,U_4559,U_4553,U_4557] :
( hBOOL(hAPP(hAPP(c_member(U_4555),U_4559),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4553,tc_fun(U_4555,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4553,tc_HOL_Obool))),U_4557)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4553,tc_fun(U_4555,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4553,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_4555,tc_HOL_Obool),tc_fun(U_4555,tc_HOL_Obool),U_4553),hAPP(c_COMBC(U_4555,tc_fun(U_4555,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4555))),U_4557)),U_4559)) ) ),
inference(definitional_conversion,[status(esa)],[f_1068_3]) ).
cnf(f_1068_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_4555),U_4559),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4553,tc_fun(U_4555,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4553,tc_HOL_Obool))),U_4557)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4553,tc_fun(U_4555,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4553,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_4555,tc_HOL_Obool),tc_fun(U_4555,tc_HOL_Obool),U_4553),hAPP(c_COMBC(U_4555,tc_fun(U_4555,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4555))),U_4557)),U_4559)) ),
inference(clausify,[status(thm)],[f_1068_4]) ).
cnf(f_1068_6,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4554,tc_fun(U_4556,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4554,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_4556,tc_HOL_Obool),tc_fun(U_4556,tc_HOL_Obool),U_4554),hAPP(c_COMBC(U_4556,tc_fun(U_4556,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4556))),U_4558)),U_4560))
| ~ hBOOL(hAPP(hAPP(c_member(U_4556),U_4560),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4554,tc_fun(U_4556,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_4554,tc_HOL_Obool))),U_4558))) ),
inference(clausify,[status(thm)],[f_1068_4]) ).
fof(f_1069_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Compl__disjoint]) ).
fof(f_1069_2,plain,
! [U_4562,U_4561] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4561,tc_HOL_Obool)),U_4562),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4561,tc_HOL_Obool)),U_4562)) = c_Orderings_Obot__class_Obot(tc_fun(U_4561,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1069_1]) ).
fof(f_1069_3,plain,
! [U_4561,U_4562] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4561,tc_HOL_Obool)),U_4562),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4561,tc_HOL_Obool)),U_4562)) = c_Orderings_Obot__class_Obot(tc_fun(U_4561,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1069_2]) ).
cnf(f_1069_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4561,tc_HOL_Obool)),U_4562),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4561,tc_HOL_Obool)),U_4562)) = c_Orderings_Obot__class_Obot(tc_fun(U_4561,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1069_3]) ).
fof(f_1070_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Compl__disjoint2]) ).
fof(f_1070_2,plain,
! [U_4564,U_4563] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4563,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4563,tc_HOL_Obool)),U_4564)),U_4564) = c_Orderings_Obot__class_Obot(tc_fun(U_4563,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1070_1]) ).
fof(f_1070_3,plain,
! [U_4563,U_4564] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4563,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4563,tc_HOL_Obool)),U_4564)),U_4564) = c_Orderings_Obot__class_Obot(tc_fun(U_4563,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1070_2]) ).
cnf(f_1070_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4563,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4563,tc_HOL_Obool)),U_4564)),U_4564) = c_Orderings_Obot__class_Obot(tc_fun(U_4563,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1070_3]) ).
fof(f_1071_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),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__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Compl__Int]) ).
fof(f_1071_2,plain,
! [U_4567,U_4566,U_4565] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4565,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4565,tc_HOL_Obool)),U_4566),U_4567)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4565,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4565,tc_HOL_Obool)),U_4566)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4565,tc_HOL_Obool)),U_4567)),
inference(variable_rename,[status(thm)],[f_1071_1]) ).
fof(f_1071_3,plain,
! [U_4565,U_4566,U_4567] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4565,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4565,tc_HOL_Obool)),U_4566),U_4567)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4565,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4565,tc_HOL_Obool)),U_4566)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4565,tc_HOL_Obool)),U_4567)),
inference(definitional_conversion,[status(esa)],[f_1071_2]) ).
cnf(f_1071_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4565,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4565,tc_HOL_Obool)),U_4566),U_4567)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4565,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4565,tc_HOL_Obool)),U_4566)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4565,tc_HOL_Obool)),U_4567)),
inference(clausify,[status(thm)],[f_1071_3]) ).
fof(f_1072_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),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__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),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_c,tc_HOL_Obool)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Compl__Un]) ).
fof(f_1072_2,plain,
! [U_4570,U_4569,U_4568] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4568,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4568,tc_HOL_Obool)),U_4569),U_4570)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4568,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4568,tc_HOL_Obool)),U_4569)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4568,tc_HOL_Obool)),U_4570)),
inference(variable_rename,[status(thm)],[f_1072_1]) ).
fof(f_1072_3,plain,
! [U_4568,U_4569,U_4570] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4568,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4568,tc_HOL_Obool)),U_4569),U_4570)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4568,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4568,tc_HOL_Obool)),U_4569)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4568,tc_HOL_Obool)),U_4570)),
inference(definitional_conversion,[status(esa)],[f_1072_2]) ).
cnf(f_1072_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4568,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4568,tc_HOL_Obool)),U_4569),U_4570)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4568,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4568,tc_HOL_Obool)),U_4569)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4568,tc_HOL_Obool)),U_4570)),
inference(clausify,[status(thm)],[f_1072_3]) ).
fof(f_1073_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Diff__Compl]) ).
fof(f_1073_2,plain,
! [U_4573,U_4572,U_4571] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4571,tc_HOL_Obool)),U_4572),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4571,tc_HOL_Obool)),U_4573)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4571,tc_HOL_Obool)),U_4572),U_4573),
inference(variable_rename,[status(thm)],[f_1073_1]) ).
fof(f_1073_3,plain,
! [U_4571,U_4572,U_4573] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4571,tc_HOL_Obool)),U_4572),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4571,tc_HOL_Obool)),U_4573)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4571,tc_HOL_Obool)),U_4572),U_4573),
inference(definitional_conversion,[status(esa)],[f_1073_2]) ).
cnf(f_1073_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4571,tc_HOL_Obool)),U_4572),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4571,tc_HOL_Obool)),U_4573)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4571,tc_HOL_Obool)),U_4572),U_4573),
inference(clausify,[status(thm)],[f_1073_3]) ).
fof(f_1074_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Diff__eq]) ).
fof(f_1074_2,plain,
! [U_4576,U_4575,U_4574] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4574,tc_HOL_Obool)),U_4575),U_4576) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4574,tc_HOL_Obool)),U_4575),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4574,tc_HOL_Obool)),U_4576)),
inference(variable_rename,[status(thm)],[f_1074_1]) ).
fof(f_1074_3,plain,
! [U_4574,U_4575,U_4576] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4574,tc_HOL_Obool)),U_4575),U_4576) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4574,tc_HOL_Obool)),U_4575),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4574,tc_HOL_Obool)),U_4576)),
inference(definitional_conversion,[status(esa)],[f_1074_2]) ).
cnf(f_1074_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4574,tc_HOL_Obool)),U_4575),U_4576) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4574,tc_HOL_Obool)),U_4575),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4574,tc_HOL_Obool)),U_4576)),
inference(clausify,[status(thm)],[f_1074_3]) ).
fof(f_1075_1,plain,
! [V_b_2,V_f_2,T_d,V_a_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))))
| hAPP(V_f_2,V_a_2) != V_b_2 )
& ( hAPP(V_f_2,V_a_2) = V_b_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))) ) ),
inference(fof_nnf,[status(thm)],[fact_vimage__singleton__eq]) ).
fof(f_1075_2,plain,
! [U_4581,U_4580,U_4579,U_4578,U_4577] :
( ( hBOOL(hAPP(hAPP(c_member(U_4577),U_4578),hAPP(c_Set_Ovimage(U_4577,U_4579,U_4580),hAPP(hAPP(c_Set_Oinsert(U_4579),U_4581),c_Orderings_Obot__class_Obot(tc_fun(U_4579,tc_HOL_Obool))))))
| hAPP(U_4580,U_4578) != U_4581 )
& ( hAPP(U_4580,U_4578) = U_4581
| ~ hBOOL(hAPP(hAPP(c_member(U_4577),U_4578),hAPP(c_Set_Ovimage(U_4577,U_4579,U_4580),hAPP(hAPP(c_Set_Oinsert(U_4579),U_4581),c_Orderings_Obot__class_Obot(tc_fun(U_4579,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[f_1075_1]) ).
fof(f_1075_3,plain,
( ! [U_4591,U_4589,U_4587,U_4585] :
( ! [U_4583] : hBOOL(hAPP(hAPP(c_member(U_4583),U_4585),hAPP(c_Set_Ovimage(U_4583,U_4587,U_4589),hAPP(hAPP(c_Set_Oinsert(U_4587),U_4591),c_Orderings_Obot__class_Obot(tc_fun(U_4587,tc_HOL_Obool))))))
| hAPP(U_4589,U_4585) != U_4591 )
& ! [U_4590,U_4588,U_4586,U_4584] :
( ! [U_4582] : ~ hBOOL(hAPP(hAPP(c_member(U_4582),U_4584),hAPP(c_Set_Ovimage(U_4582,U_4586,U_4588),hAPP(hAPP(c_Set_Oinsert(U_4586),U_4590),c_Orderings_Obot__class_Obot(tc_fun(U_4586,tc_HOL_Obool))))))
| hAPP(U_4588,U_4584) = U_4590 ) ),
inference(miniscope,[status(thm)],[f_1075_2]) ).
fof(f_1075_4,plain,
( ! [U_4583,U_4585,U_4587,U_4589,U_4591] :
( hBOOL(hAPP(hAPP(c_member(U_4583),U_4585),hAPP(c_Set_Ovimage(U_4583,U_4587,U_4589),hAPP(hAPP(c_Set_Oinsert(U_4587),U_4591),c_Orderings_Obot__class_Obot(tc_fun(U_4587,tc_HOL_Obool))))))
| hAPP(U_4589,U_4585) != U_4591 )
& ! [U_4588,U_4584,U_4582,U_4586,U_4590] :
( ~ hBOOL(hAPP(hAPP(c_member(U_4582),U_4584),hAPP(c_Set_Ovimage(U_4582,U_4586,U_4588),hAPP(hAPP(c_Set_Oinsert(U_4586),U_4590),c_Orderings_Obot__class_Obot(tc_fun(U_4586,tc_HOL_Obool))))))
| hAPP(U_4588,U_4584) = U_4590 ) ),
inference(definitional_conversion,[status(esa)],[f_1075_3]) ).
cnf(f_1075_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_4582),U_4584),hAPP(c_Set_Ovimage(U_4582,U_4586,U_4588),hAPP(hAPP(c_Set_Oinsert(U_4586),U_4590),c_Orderings_Obot__class_Obot(tc_fun(U_4586,tc_HOL_Obool))))))
| hAPP(U_4588,U_4584) = U_4590 ),
inference(clausify,[status(thm)],[f_1075_4]) ).
cnf(f_1075_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4583),U_4585),hAPP(c_Set_Ovimage(U_4583,U_4587,U_4589),hAPP(hAPP(c_Set_Oinsert(U_4587),U_4591),c_Orderings_Obot__class_Obot(tc_fun(U_4587,tc_HOL_Obool))))))
| hAPP(U_4589,U_4585) != U_4591 ),
inference(clausify,[status(thm)],[f_1075_4]) ).
fof(f_1076_1,plain,
! [V_a_2,V_b_2,V_A_2,T_c] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_b_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__inf__insert]) ).
fof(f_1076_2,plain,
! [U_4595,U_4594,U_4593,U_4592] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_4592,U_4592,c_Lattices_Osemilattice__inf__class_Oinf(U_4592)),U_4594),hAPP(hAPP(c_Set_Oinsert(U_4592),U_4595),U_4593)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4592),U_4595),hAPP(hAPP(c_Finite__Set_Ofold(U_4592,U_4592,c_Lattices_Osemilattice__inf__class_Oinf(U_4592)),U_4594),U_4593))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4592),U_4593))
| ~ class_Lattices_Osemilattice__inf(U_4592) ),
inference(variable_rename,[status(thm)],[f_1076_1]) ).
fof(f_1076_3,plain,
! [U_4593,U_4592,U_4594,U_4595] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_4592,U_4592,c_Lattices_Osemilattice__inf__class_Oinf(U_4592)),U_4594),hAPP(hAPP(c_Set_Oinsert(U_4592),U_4595),U_4593)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4592),U_4595),hAPP(hAPP(c_Finite__Set_Ofold(U_4592,U_4592,c_Lattices_Osemilattice__inf__class_Oinf(U_4592)),U_4594),U_4593))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4592),U_4593))
| ~ class_Lattices_Osemilattice__inf(U_4592) ),
inference(definitional_conversion,[status(esa)],[f_1076_2]) ).
cnf(f_1076_4,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_4592,U_4592,c_Lattices_Osemilattice__inf__class_Oinf(U_4592)),U_4594),hAPP(hAPP(c_Set_Oinsert(U_4592),U_4595),U_4593)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4592),U_4595),hAPP(hAPP(c_Finite__Set_Ofold(U_4592,U_4592,c_Lattices_Osemilattice__inf__class_Oinf(U_4592)),U_4594),U_4593))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4592),U_4593))
| ~ class_Lattices_Osemilattice__inf(U_4592) ),
inference(clausify,[status(thm)],[f_1076_3]) ).
fof(f_1077_1,plain,
! [V_a_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) = V_a_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inf__Sup__absorb]) ).
fof(f_1077_2,plain,
! [U_4598,U_4597,U_4596] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4596),U_4598),c_Big__Operators_Olattice__class_OSup__fin(U_4596,U_4597)) = U_4598
| ~ hBOOL(hAPP(hAPP(c_member(U_4596),U_4598),U_4597))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4596),U_4597))
| ~ class_Lattices_Olattice(U_4596) ),
inference(variable_rename,[status(thm)],[f_1077_1]) ).
fof(f_1077_3,plain,
! [U_4596,U_4597,U_4598] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4596),U_4598),c_Big__Operators_Olattice__class_OSup__fin(U_4596,U_4597)) = U_4598
| ~ hBOOL(hAPP(hAPP(c_member(U_4596),U_4598),U_4597))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4596),U_4597))
| ~ class_Lattices_Olattice(U_4596) ),
inference(definitional_conversion,[status(esa)],[f_1077_2]) ).
cnf(f_1077_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4596),U_4598),c_Big__Operators_Olattice__class_OSup__fin(U_4596,U_4597)) = U_4598
| ~ hBOOL(hAPP(hAPP(c_member(U_4596),U_4598),U_4597))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4596),U_4597))
| ~ class_Lattices_Olattice(U_4596) ),
inference(clausify,[status(thm)],[f_1077_3]) ).
fof(f_1078_1,plain,
! [V_B_2,V_a_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__insert]) ).
fof(f_1078_2,plain,
! [U_4603,U_4602,U_4601,U_4600,U_4599] : hAPP(c_Set_Ovimage(U_4599,U_4600,U_4601),hAPP(hAPP(c_Set_Oinsert(U_4600),U_4602),U_4603)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4599,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4599,U_4600,U_4601),hAPP(hAPP(c_Set_Oinsert(U_4600),U_4602),c_Orderings_Obot__class_Obot(tc_fun(U_4600,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_4599,U_4600,U_4601),U_4603)),
inference(variable_rename,[status(thm)],[f_1078_1]) ).
fof(f_1078_3,plain,
! [U_4600,U_4599,U_4601,U_4602,U_4603] : hAPP(c_Set_Ovimage(U_4599,U_4600,U_4601),hAPP(hAPP(c_Set_Oinsert(U_4600),U_4602),U_4603)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4599,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4599,U_4600,U_4601),hAPP(hAPP(c_Set_Oinsert(U_4600),U_4602),c_Orderings_Obot__class_Obot(tc_fun(U_4600,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_4599,U_4600,U_4601),U_4603)),
inference(definitional_conversion,[status(esa)],[f_1078_2]) ).
cnf(f_1078_4,plain,
hAPP(c_Set_Ovimage(U_4599,U_4600,U_4601),hAPP(hAPP(c_Set_Oinsert(U_4600),U_4602),U_4603)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4599,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4599,U_4600,U_4601),hAPP(hAPP(c_Set_Oinsert(U_4600),U_4602),c_Orderings_Obot__class_Obot(tc_fun(U_4600,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_4599,U_4600,U_4601),U_4603)),
inference(clausify,[status(thm)],[f_1078_3]) ).
fof(f_1079_1,plain,
! [V_F_2,V_h_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_F_2))
| hAPP(c_Set_Oimage(T_c,T_d,V_h_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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_d,V_h_2),V_F_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__vimageD]) ).
fof(f_1079_2,plain,
! [U_4607,U_4606,U_4605,U_4604] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4605),U_4607))
| hAPP(c_Set_Oimage(U_4604,U_4605,U_4606),c_Orderings_Otop__class_Otop(tc_fun(U_4604,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_4605,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4604),hAPP(c_Set_Ovimage(U_4604,U_4605,U_4606),U_4607))) ),
inference(variable_rename,[status(thm)],[f_1079_1]) ).
fof(f_1079_3,plain,
! [U_4605,U_4604,U_4606,U_4607] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4605),U_4607))
| hAPP(c_Set_Oimage(U_4604,U_4605,U_4606),c_Orderings_Otop__class_Otop(tc_fun(U_4604,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_4605,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4604),hAPP(c_Set_Ovimage(U_4604,U_4605,U_4606),U_4607))) ),
inference(definitional_conversion,[status(esa)],[f_1079_2]) ).
cnf(f_1079_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4605),U_4607))
| hAPP(c_Set_Oimage(U_4604,U_4605,U_4606),c_Orderings_Otop__class_Otop(tc_fun(U_4604,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_4605,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4604),hAPP(c_Set_Ovimage(U_4604,U_4605,U_4606),U_4607))) ),
inference(clausify,[status(thm)],[f_1079_3]) ).
fof(f_1080_1,plain,
! [V_A_2,V_B_2,V_f_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_d,T_c,V_f_2),V_B_2)),V_A_2))
| hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_vimage__subsetD]) ).
fof(f_1080_2,plain,
! [U_4612,U_4611,U_4610,U_4609,U_4608] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4609,tc_HOL_Obool)),U_4611),hAPP(c_Set_Oimage(U_4608,U_4609,U_4610),U_4612)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4608,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4608,U_4609,U_4610),U_4611)),U_4612))
| hAPP(c_Set_Oimage(U_4608,U_4609,U_4610),c_Orderings_Otop__class_Otop(tc_fun(U_4608,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_4609,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_1080_1]) ).
fof(f_1080_3,plain,
! [U_4610,U_4608,U_4609,U_4611,U_4612] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4609,tc_HOL_Obool)),U_4611),hAPP(c_Set_Oimage(U_4608,U_4609,U_4610),U_4612)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4608,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4608,U_4609,U_4610),U_4611)),U_4612))
| hAPP(c_Set_Oimage(U_4608,U_4609,U_4610),c_Orderings_Otop__class_Otop(tc_fun(U_4608,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_4609,tc_HOL_Obool)) ),
inference(definitional_conversion,[status(esa)],[f_1080_2]) ).
cnf(f_1080_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4609,tc_HOL_Obool)),U_4611),hAPP(c_Set_Oimage(U_4608,U_4609,U_4610),U_4612)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4608,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4608,U_4609,U_4610),U_4611)),U_4612))
| hAPP(c_Set_Oimage(U_4608,U_4609,U_4610),c_Orderings_Otop__class_Otop(tc_fun(U_4608,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_4609,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1080_3]) ).
fof(f_1081_1,plain,
! [V_h_2,T_d,V_F_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Ovimage(T_d,T_c,V_h_2),V_F_2)))
| ~ c_Fun_Oinj__on(T_d,T_c,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__vimageI]) ).
fof(f_1081_2,plain,
! [U_4616,U_4615,U_4614,U_4613] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4615),hAPP(c_Set_Ovimage(U_4615,U_4613,U_4616),U_4614)))
| ~ c_Fun_Oinj__on(U_4615,U_4613,U_4616,c_Orderings_Otop__class_Otop(tc_fun(U_4615,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4613),U_4614)) ),
inference(variable_rename,[status(thm)],[f_1081_1]) ).
fof(f_1081_3,plain,
! [U_4614,U_4613,U_4615,U_4616] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4615),hAPP(c_Set_Ovimage(U_4615,U_4613,U_4616),U_4614)))
| ~ c_Fun_Oinj__on(U_4615,U_4613,U_4616,c_Orderings_Otop__class_Otop(tc_fun(U_4615,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4613),U_4614)) ),
inference(definitional_conversion,[status(esa)],[f_1081_2]) ).
cnf(f_1081_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4615),hAPP(c_Set_Ovimage(U_4615,U_4613,U_4616),U_4614)))
| ~ c_Fun_Oinj__on(U_4615,U_4613,U_4616,c_Orderings_Otop__class_Otop(tc_fun(U_4615,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4613),U_4614)) ),
inference(clausify,[status(thm)],[f_1081_3]) ).
fof(f_1082_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)) = V_A_2
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__vimage__image__eq]) ).
fof(f_1082_2,plain,
! [U_4620,U_4619,U_4618,U_4617] :
( hAPP(c_Set_Ovimage(U_4617,U_4618,U_4619),hAPP(c_Set_Oimage(U_4617,U_4618,U_4619),U_4620)) = U_4620
| ~ c_Fun_Oinj__on(U_4617,U_4618,U_4619,c_Orderings_Otop__class_Otop(tc_fun(U_4617,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_1082_1]) ).
fof(f_1082_3,plain,
! [U_4617,U_4618,U_4619,U_4620] :
( hAPP(c_Set_Ovimage(U_4617,U_4618,U_4619),hAPP(c_Set_Oimage(U_4617,U_4618,U_4619),U_4620)) = U_4620
| ~ c_Fun_Oinj__on(U_4617,U_4618,U_4619,c_Orderings_Otop__class_Otop(tc_fun(U_4617,tc_HOL_Obool))) ),
inference(definitional_conversion,[status(esa)],[f_1082_2]) ).
cnf(f_1082_4,plain,
( hAPP(c_Set_Ovimage(U_4617,U_4618,U_4619),hAPP(c_Set_Oimage(U_4617,U_4618,U_4619),U_4620)) = U_4620
| ~ c_Fun_Oinj__on(U_4617,U_4618,U_4619,c_Orderings_Otop__class_Otop(tc_fun(U_4617,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_1082_3]) ).
fof(f_1083_1,plain,
! [V_B_2,V_A_2,V_C_2,V_f_2,T_d,T_c] :
( hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_C_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__image__Int]) ).
fof(f_1083_2,plain,
! [U_4626,U_4625,U_4624,U_4623,U_4622,U_4621] :
( hAPP(c_Set_Oimage(U_4621,U_4622,U_4623),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4621,tc_HOL_Obool)),U_4625),U_4626)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4622,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4621,U_4622,U_4623),U_4625)),hAPP(c_Set_Oimage(U_4621,U_4622,U_4623),U_4626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4621,tc_HOL_Obool)),U_4626),U_4624))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4621,tc_HOL_Obool)),U_4625),U_4624))
| ~ c_Fun_Oinj__on(U_4621,U_4622,U_4623,U_4624) ),
inference(variable_rename,[status(thm)],[f_1083_1]) ).
fof(f_1083_3,plain,
! [U_4621,U_4622,U_4623,U_4624,U_4625,U_4626] :
( hAPP(c_Set_Oimage(U_4621,U_4622,U_4623),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4621,tc_HOL_Obool)),U_4625),U_4626)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4622,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4621,U_4622,U_4623),U_4625)),hAPP(c_Set_Oimage(U_4621,U_4622,U_4623),U_4626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4621,tc_HOL_Obool)),U_4626),U_4624))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4621,tc_HOL_Obool)),U_4625),U_4624))
| ~ c_Fun_Oinj__on(U_4621,U_4622,U_4623,U_4624) ),
inference(definitional_conversion,[status(esa)],[f_1083_2]) ).
cnf(f_1083_4,plain,
( hAPP(c_Set_Oimage(U_4621,U_4622,U_4623),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4621,tc_HOL_Obool)),U_4625),U_4626)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4622,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4621,U_4622,U_4623),U_4625)),hAPP(c_Set_Oimage(U_4621,U_4622,U_4623),U_4626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4621,tc_HOL_Obool)),U_4626),U_4624))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4621,tc_HOL_Obool)),U_4625),U_4624))
| ~ c_Fun_Oinj__on(U_4621,U_4622,U_4623,U_4624) ),
inference(clausify,[status(thm)],[f_1083_3]) ).
fof(f_1084_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Set_Oimage(T_c,T_d,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_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_B_2))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_image__Int]) ).
fof(f_1084_2,plain,
! [U_4631,U_4630,U_4629,U_4628,U_4627] :
( hAPP(c_Set_Oimage(U_4627,U_4628,U_4629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4627,tc_HOL_Obool)),U_4630),U_4631)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4628,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4627,U_4628,U_4629),U_4630)),hAPP(c_Set_Oimage(U_4627,U_4628,U_4629),U_4631))
| ~ c_Fun_Oinj__on(U_4627,U_4628,U_4629,c_Orderings_Otop__class_Otop(tc_fun(U_4627,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_1084_1]) ).
fof(f_1084_3,plain,
! [U_4627,U_4628,U_4629,U_4630,U_4631] :
( hAPP(c_Set_Oimage(U_4627,U_4628,U_4629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4627,tc_HOL_Obool)),U_4630),U_4631)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4628,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4627,U_4628,U_4629),U_4630)),hAPP(c_Set_Oimage(U_4627,U_4628,U_4629),U_4631))
| ~ c_Fun_Oinj__on(U_4627,U_4628,U_4629,c_Orderings_Otop__class_Otop(tc_fun(U_4627,tc_HOL_Obool))) ),
inference(definitional_conversion,[status(esa)],[f_1084_2]) ).
cnf(f_1084_4,plain,
( hAPP(c_Set_Oimage(U_4627,U_4628,U_4629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4627,tc_HOL_Obool)),U_4630),U_4631)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4628,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4627,U_4628,U_4629),U_4630)),hAPP(c_Set_Oimage(U_4627,U_4628,U_4629),U_4631))
| ~ c_Fun_Oinj__on(U_4627,U_4628,U_4629,c_Orderings_Otop__class_Otop(tc_fun(U_4627,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_1084_3]) ).
fof(f_1085_1,plain,
! [V_B_2,V_A_2,T_c] :
( ( 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(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)),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)),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)) ) ),
inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl]) ).
fof(f_1085_2,plain,
! [U_4634,U_4633,U_4632] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4632,tc_HOL_Obool)),U_4633),U_4634) = c_Orderings_Obot__class_Obot(tc_fun(U_4632,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4632,tc_HOL_Obool)),U_4633),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4632,tc_HOL_Obool)),U_4634))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4632,tc_HOL_Obool)),U_4633),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4632,tc_HOL_Obool)),U_4634)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4632,tc_HOL_Obool)),U_4633),U_4634) != c_Orderings_Obot__class_Obot(tc_fun(U_4632,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1085_1]) ).
fof(f_1085_3,plain,
( ! [U_4640,U_4638,U_4636] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4636,tc_HOL_Obool)),U_4638),U_4640) = c_Orderings_Obot__class_Obot(tc_fun(U_4636,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4636,tc_HOL_Obool)),U_4638),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4636,tc_HOL_Obool)),U_4640))) )
& ! [U_4639,U_4637,U_4635] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4635,tc_HOL_Obool)),U_4637),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4635,tc_HOL_Obool)),U_4639)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4635,tc_HOL_Obool)),U_4637),U_4639) != c_Orderings_Obot__class_Obot(tc_fun(U_4635,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1085_2]) ).
fof(f_1085_4,plain,
( ! [U_4636,U_4638,U_4640] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4636,tc_HOL_Obool)),U_4638),U_4640) = c_Orderings_Obot__class_Obot(tc_fun(U_4636,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4636,tc_HOL_Obool)),U_4638),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4636,tc_HOL_Obool)),U_4640))) )
& ! [U_4637,U_4635,U_4639] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4635,tc_HOL_Obool)),U_4637),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4635,tc_HOL_Obool)),U_4639)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4635,tc_HOL_Obool)),U_4637),U_4639) != c_Orderings_Obot__class_Obot(tc_fun(U_4635,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1085_3]) ).
cnf(f_1085_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4635,tc_HOL_Obool)),U_4637),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4635,tc_HOL_Obool)),U_4639)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4635,tc_HOL_Obool)),U_4637),U_4639) != c_Orderings_Obot__class_Obot(tc_fun(U_4635,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1085_4]) ).
cnf(f_1085_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4636,tc_HOL_Obool)),U_4638),U_4640) = c_Orderings_Obot__class_Obot(tc_fun(U_4636,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4636,tc_HOL_Obool)),U_4638),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4636,tc_HOL_Obool)),U_4640))) ),
inference(clausify,[status(thm)],[f_1085_4]) ).
fof(f_1086_1,plain,
! [T_d,V_A_2,V_c_2,T_c] :
( ( hAPP(c_Set_Ovimage(T_d,T_c,hAPP(c_COMBK(T_c,T_d),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) )
& ( hAPP(c_Set_Ovimage(T_d,T_c,hAPP(c_COMBK(T_c,T_d),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_vimage__const]) ).
fof(f_1086_2,plain,
! [U_4644,U_4643,U_4642,U_4641] :
( ( hAPP(c_Set_Ovimage(U_4644,U_4641,hAPP(c_COMBK(U_4641,U_4644),U_4642)),U_4643) = c_Orderings_Obot__class_Obot(tc_fun(U_4644,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_4641),U_4642),U_4643)) )
& ( hAPP(c_Set_Ovimage(U_4644,U_4641,hAPP(c_COMBK(U_4641,U_4644),U_4642)),U_4643) = c_Orderings_Otop__class_Otop(tc_fun(U_4644,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4641),U_4642),U_4643)) ) ),
inference(variable_rename,[status(thm)],[f_1086_1]) ).
fof(f_1086_3,plain,
( ! [U_4652,U_4650,U_4648,U_4646] :
( hAPP(c_Set_Ovimage(U_4652,U_4646,hAPP(c_COMBK(U_4646,U_4652),U_4648)),U_4650) = c_Orderings_Obot__class_Obot(tc_fun(U_4652,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_4646),U_4648),U_4650)) )
& ! [U_4651,U_4649,U_4647,U_4645] :
( hAPP(c_Set_Ovimage(U_4651,U_4645,hAPP(c_COMBK(U_4645,U_4651),U_4647)),U_4649) = c_Orderings_Otop__class_Otop(tc_fun(U_4651,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4645),U_4647),U_4649)) ) ),
inference(miniscope,[status(thm)],[f_1086_2]) ).
fof(f_1086_4,plain,
( ! [U_4646,U_4648,U_4650,U_4652] :
( hAPP(c_Set_Ovimage(U_4652,U_4646,hAPP(c_COMBK(U_4646,U_4652),U_4648)),U_4650) = c_Orderings_Obot__class_Obot(tc_fun(U_4652,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_4646),U_4648),U_4650)) )
& ! [U_4651,U_4647,U_4645,U_4649] :
( hAPP(c_Set_Ovimage(U_4651,U_4645,hAPP(c_COMBK(U_4645,U_4651),U_4647)),U_4649) = c_Orderings_Otop__class_Otop(tc_fun(U_4651,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4645),U_4647),U_4649)) ) ),
inference(definitional_conversion,[status(esa)],[f_1086_3]) ).
cnf(f_1086_5,plain,
( hAPP(c_Set_Ovimage(U_4651,U_4645,hAPP(c_COMBK(U_4645,U_4651),U_4647)),U_4649) = c_Orderings_Otop__class_Otop(tc_fun(U_4651,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4645),U_4647),U_4649)) ),
inference(clausify,[status(thm)],[f_1086_4]) ).
cnf(f_1086_6,plain,
( hAPP(c_Set_Ovimage(U_4652,U_4646,hAPP(c_COMBK(U_4646,U_4652),U_4648)),U_4650) = c_Orderings_Obot__class_Obot(tc_fun(U_4652,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_4646),U_4648),U_4650)) ),
inference(clausify,[status(thm)],[f_1086_4]) ).
fof(f_1087_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_d),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_c,T_d,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_1087_2,plain,
! [U_4660,U_4659,U_4658,U_4657,U_4656,U_4655,U_4654,U_4653] :
( hAPP(hAPP(U_4655,hAPP(U_4658,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4654,tc_HOL_Obool)),U_4659),U_4660))),hAPP(U_4658,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4654,tc_HOL_Obool)),U_4659),U_4660))) = hAPP(hAPP(U_4655,hAPP(U_4658,U_4659)),hAPP(U_4658,U_4660))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4654),U_4660))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4654),U_4659))
| ~ c_Finite__Set_Ofolding__image__simple(U_4653,U_4654,U_4655,U_4656,U_4657,U_4658) ),
inference(variable_rename,[status(thm)],[f_1087_1]) ).
fof(f_1087_3,plain,
! [U_4660,U_4659,U_4658,U_4657,U_4656,U_4655,U_4654] :
( ! [U_4653] : ~ c_Finite__Set_Ofolding__image__simple(U_4653,U_4654,U_4655,U_4656,U_4657,U_4658)
| hAPP(hAPP(U_4655,hAPP(U_4658,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4654,tc_HOL_Obool)),U_4659),U_4660))),hAPP(U_4658,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4654,tc_HOL_Obool)),U_4659),U_4660))) = hAPP(hAPP(U_4655,hAPP(U_4658,U_4659)),hAPP(U_4658,U_4660))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4654),U_4660))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4654),U_4659)) ),
inference(miniscope,[status(thm)],[f_1087_2]) ).
fof(f_1087_4,plain,
! [U_4653,U_4654,U_4655,U_4656,U_4657,U_4658,U_4659,U_4660] :
( ~ c_Finite__Set_Ofolding__image__simple(U_4653,U_4654,U_4655,U_4656,U_4657,U_4658)
| hAPP(hAPP(U_4655,hAPP(U_4658,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4654,tc_HOL_Obool)),U_4659),U_4660))),hAPP(U_4658,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4654,tc_HOL_Obool)),U_4659),U_4660))) = hAPP(hAPP(U_4655,hAPP(U_4658,U_4659)),hAPP(U_4658,U_4660))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4654),U_4660))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4654),U_4659)) ),
inference(definitional_conversion,[status(esa)],[f_1087_3]) ).
cnf(f_1087_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_4653,U_4654,U_4655,U_4656,U_4657,U_4658)
| hAPP(hAPP(U_4655,hAPP(U_4658,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4654,tc_HOL_Obool)),U_4659),U_4660))),hAPP(U_4658,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4654,tc_HOL_Obool)),U_4659),U_4660))) = hAPP(hAPP(U_4655,hAPP(U_4658,U_4659)),hAPP(U_4658,U_4660))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4654),U_4660))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4654),U_4659)) ),
inference(clausify,[status(thm)],[f_1087_4]) ).
fof(f_1088_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_1088_2,plain,
! [U_4663,U_4662,U_4661] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4661),U_4662) = U_4663
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4661),U_4662),U_4663) != c_Orderings_Otop__class_Otop(U_4661)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4661),U_4662),U_4663) != c_Orderings_Obot__class_Obot(U_4661)
| ~ class_Lattices_Oboolean__algebra(U_4661) ),
inference(variable_rename,[status(thm)],[f_1088_1]) ).
fof(f_1088_3,plain,
! [U_4662,U_4661,U_4663] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4661),U_4662) = U_4663
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4661),U_4662),U_4663) != c_Orderings_Otop__class_Otop(U_4661)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4661),U_4662),U_4663) != c_Orderings_Obot__class_Obot(U_4661)
| ~ class_Lattices_Oboolean__algebra(U_4661) ),
inference(definitional_conversion,[status(esa)],[f_1088_2]) ).
cnf(f_1088_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4661),U_4662) = U_4663
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4661),U_4662),U_4663) != c_Orderings_Otop__class_Otop(U_4661)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4661),U_4662),U_4663) != c_Orderings_Obot__class_Obot(U_4661)
| ~ class_Lattices_Oboolean__algebra(U_4661) ),
inference(clausify,[status(thm)],[f_1088_3]) ).
fof(f_1089_1,plain,
! [V_b_2,V_a_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__inf__le__inf]) ).
fof(f_1089_2,plain,
! [U_4667,U_4666,U_4665,U_4664] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4664),hAPP(hAPP(c_Finite__Set_Ofold(U_4664,U_4664,c_Lattices_Osemilattice__inf__class_Oinf(U_4664)),U_4667),U_4665)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4664),U_4666),U_4667)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4664),U_4666),U_4665))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4664),U_4665))
| ~ class_Lattices_Osemilattice__inf(U_4664) ),
inference(variable_rename,[status(thm)],[f_1089_1]) ).
fof(f_1089_3,plain,
! [U_4664,U_4665,U_4666,U_4667] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4664),hAPP(hAPP(c_Finite__Set_Ofold(U_4664,U_4664,c_Lattices_Osemilattice__inf__class_Oinf(U_4664)),U_4667),U_4665)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4664),U_4666),U_4667)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4664),U_4666),U_4665))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4664),U_4665))
| ~ class_Lattices_Osemilattice__inf(U_4664) ),
inference(definitional_conversion,[status(esa)],[f_1089_2]) ).
cnf(f_1089_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4664),hAPP(hAPP(c_Finite__Set_Ofold(U_4664,U_4664,c_Lattices_Osemilattice__inf__class_Oinf(U_4664)),U_4667),U_4665)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4664),U_4666),U_4667)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4664),U_4666),U_4665))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4664),U_4665))
| ~ class_Lattices_Osemilattice__inf(U_4664) ),
inference(clausify,[status(thm)],[f_1089_3]) ).
fof(f_1090_1,plain,
! [V_a_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_A_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold1__belowI]) ).
fof(f_1090_2,plain,
! [U_4670,U_4669,U_4668] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4668),hAPP(c_Finite__Set_Ofold1(U_4668,c_Lattices_Osemilattice__inf__class_Oinf(U_4668)),U_4669)),U_4670))
| ~ hBOOL(hAPP(hAPP(c_member(U_4668),U_4670),U_4669))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4668),U_4669))
| ~ class_Lattices_Osemilattice__inf(U_4668) ),
inference(variable_rename,[status(thm)],[f_1090_1]) ).
fof(f_1090_3,plain,
! [U_4668,U_4669,U_4670] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4668),hAPP(c_Finite__Set_Ofold1(U_4668,c_Lattices_Osemilattice__inf__class_Oinf(U_4668)),U_4669)),U_4670))
| ~ hBOOL(hAPP(hAPP(c_member(U_4668),U_4670),U_4669))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4668),U_4669))
| ~ class_Lattices_Osemilattice__inf(U_4668) ),
inference(definitional_conversion,[status(esa)],[f_1090_2]) ).
cnf(f_1090_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4668),hAPP(c_Finite__Set_Ofold1(U_4668,c_Lattices_Osemilattice__inf__class_Oinf(U_4668)),U_4669)),U_4670))
| ~ hBOOL(hAPP(hAPP(c_member(U_4668),U_4670),U_4669))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4668),U_4669))
| ~ class_Lattices_Osemilattice__inf(U_4668) ),
inference(clausify,[status(thm)],[f_1090_3]) ).
fof(f_1091_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_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_c),V_x_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_c),V_x_2),hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_A_2))) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_below__fold1__iff]) ).
fof(f_1091_2,plain,
! [U_4675,U_4674,U_4673] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),hAPP(c_Finite__Set_Ofold1(U_4673,c_Lattices_Osemilattice__inf__class_Oinf(U_4673)),U_4674)))
| ? [U_4672] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),U_4672))
& hBOOL(hAPP(hAPP(c_member(U_4673),U_4672),U_4674)) ) )
& ( ! [U_4671] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),U_4671))
| ~ hBOOL(hAPP(hAPP(c_member(U_4673),U_4671),U_4674)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),hAPP(c_Finite__Set_Ofold1(U_4673,c_Lattices_Osemilattice__inf__class_Oinf(U_4673)),U_4674))) ) )
| U_4674 = c_Orderings_Obot__class_Obot(tc_fun(U_4673,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4673),U_4674))
| ~ class_Lattices_Osemilattice__inf(U_4673) ),
inference(variable_rename,[status(thm)],[f_1091_1]) ).
fof(f_1091_3,plain,
! [U_4675,U_4674,U_4673] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),hAPP(c_Finite__Set_Ofold1(U_4673,c_Lattices_Osemilattice__inf__class_Oinf(U_4673)),U_4674)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),sK91(U_4675,U_4674,U_4673)))
& hBOOL(hAPP(hAPP(c_member(U_4673),sK91(U_4675,U_4674,U_4673)),U_4674)) ) )
& ( ! [U_4671] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),U_4671))
| ~ hBOOL(hAPP(hAPP(c_member(U_4673),U_4671),U_4674)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),hAPP(c_Finite__Set_Ofold1(U_4673,c_Lattices_Osemilattice__inf__class_Oinf(U_4673)),U_4674))) ) )
| U_4674 = c_Orderings_Obot__class_Obot(tc_fun(U_4673,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4673),U_4674))
| ~ class_Lattices_Osemilattice__inf(U_4673) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_4672,sK91(U_4675,U_4674,U_4673))],[f_1091_2]) ).
fof(f_1091_4,plain,
( ! [U_4673,U_4674,U_4675] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),sK91(U_4675,U_4674,U_4673)))
| ~ sP242(U_4673,U_4674,U_4675) )
& ! [U_4673,U_4674,U_4675] :
( hBOOL(hAPP(hAPP(c_member(U_4673),sK91(U_4675,U_4674,U_4673)),U_4674))
| ~ sP242(U_4673,U_4674,U_4675) )
& ! [U_4671,U_4673,U_4674,U_4675] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),hAPP(c_Finite__Set_Ofold1(U_4673,c_Lattices_Osemilattice__inf__class_Oinf(U_4673)),U_4674)))
| sP242(U_4673,U_4674,U_4675)
| ~ sP243(U_4671,U_4673,U_4674,U_4675) )
& ! [U_4671,U_4673,U_4674,U_4675] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),U_4671))
| ~ hBOOL(hAPP(hAPP(c_member(U_4673),U_4671),U_4674))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),hAPP(c_Finite__Set_Ofold1(U_4673,c_Lattices_Osemilattice__inf__class_Oinf(U_4673)),U_4674)))
| ~ sP243(U_4671,U_4673,U_4674,U_4675) )
& ! [U_4671,U_4673,U_4674,U_4675] :
( sP243(U_4671,U_4673,U_4674,U_4675)
| U_4674 = c_Orderings_Obot__class_Obot(tc_fun(U_4673,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4673),U_4674))
| ~ class_Lattices_Osemilattice__inf(U_4673) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP242,sP243])],[f_1091_3]) ).
cnf(f_1091_5,plain,
( sP243(U_4671,U_4673,U_4674,U_4675)
| U_4674 = c_Orderings_Obot__class_Obot(tc_fun(U_4673,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4673),U_4674))
| ~ class_Lattices_Osemilattice__inf(U_4673) ),
inference(clausify,[status(thm)],[f_1091_4]) ).
cnf(f_1091_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),U_4671))
| ~ hBOOL(hAPP(hAPP(c_member(U_4673),U_4671),U_4674))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),hAPP(c_Finite__Set_Ofold1(U_4673,c_Lattices_Osemilattice__inf__class_Oinf(U_4673)),U_4674)))
| ~ sP243(U_4671,U_4673,U_4674,U_4675) ),
inference(clausify,[status(thm)],[f_1091_4]) ).
cnf(f_1091_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),hAPP(c_Finite__Set_Ofold1(U_4673,c_Lattices_Osemilattice__inf__class_Oinf(U_4673)),U_4674)))
| sP242(U_4673,U_4674,U_4675)
| ~ sP243(U_4671,U_4673,U_4674,U_4675) ),
inference(clausify,[status(thm)],[f_1091_4]) ).
cnf(f_1091_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_4673),sK91(U_4675,U_4674,U_4673)),U_4674))
| ~ sP242(U_4673,U_4674,U_4675) ),
inference(clausify,[status(thm)],[f_1091_4]) ).
cnf(f_1091_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4673),U_4675),sK91(U_4675,U_4674,U_4673)))
| ~ sP242(U_4673,U_4674,U_4675) ),
inference(clausify,[status(thm)],[f_1091_4]) ).
fof(f_1092_1,plain,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un__Int]) ).
fof(f_1092_2,plain,
! [U_4680,U_4679,U_4678,U_4677,U_4676] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4676),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4677,U_4676),U_4680),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4677,tc_HOL_Obool)),U_4678),U_4679))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4677,U_4676),U_4680),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4677,tc_HOL_Obool)),U_4678),U_4679))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4676),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4677,U_4676),U_4680),U_4678)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4677,U_4676),U_4680),U_4679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4677),U_4679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4677),U_4678))
| ~ class_Groups_Ocomm__monoid__add(U_4676) ),
inference(variable_rename,[status(thm)],[f_1092_1]) ).
fof(f_1092_3,plain,
! [U_4677,U_4680,U_4679,U_4676,U_4678] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4676),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4677,U_4676),U_4680),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4677,tc_HOL_Obool)),U_4678),U_4679))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4677,U_4676),U_4680),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4677,tc_HOL_Obool)),U_4678),U_4679))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4676),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4677,U_4676),U_4680),U_4678)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4677,U_4676),U_4680),U_4679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4677),U_4679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4677),U_4678))
| ~ class_Groups_Ocomm__monoid__add(U_4676) ),
inference(definitional_conversion,[status(esa)],[f_1092_2]) ).
cnf(f_1092_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4676),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4677,U_4676),U_4680),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4677,tc_HOL_Obool)),U_4678),U_4679))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4677,U_4676),U_4680),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4677,tc_HOL_Obool)),U_4678),U_4679))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4676),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4677,U_4676),U_4680),U_4678)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4677,U_4676),U_4680),U_4679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4677),U_4679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4677),U_4678))
| ~ class_Groups_Ocomm__monoid__add(U_4676) ),
inference(clausify,[status(thm)],[f_1092_3]) ).
fof(f_1093_1,plain,
! [V_A_2,V_B_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2)),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_vimage__subsetI]) ).
fof(f_1093_2,plain,
! [U_4685,U_4684,U_4683,U_4682,U_4681] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4681,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4681,U_4682,U_4683),U_4684)),U_4685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4682,tc_HOL_Obool)),U_4684),hAPP(c_Set_Oimage(U_4681,U_4682,U_4683),U_4685)))
| ~ c_Fun_Oinj__on(U_4681,U_4682,U_4683,c_Orderings_Otop__class_Otop(tc_fun(U_4681,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_1093_1]) ).
fof(f_1093_3,plain,
! [U_4681,U_4682,U_4683,U_4684,U_4685] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4681,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4681,U_4682,U_4683),U_4684)),U_4685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4682,tc_HOL_Obool)),U_4684),hAPP(c_Set_Oimage(U_4681,U_4682,U_4683),U_4685)))
| ~ c_Fun_Oinj__on(U_4681,U_4682,U_4683,c_Orderings_Otop__class_Otop(tc_fun(U_4681,tc_HOL_Obool))) ),
inference(definitional_conversion,[status(esa)],[f_1093_2]) ).
cnf(f_1093_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4681,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_4681,U_4682,U_4683),U_4684)),U_4685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4682,tc_HOL_Obool)),U_4684),hAPP(c_Set_Oimage(U_4681,U_4682,U_4683),U_4685)))
| ~ c_Fun_Oinj__on(U_4681,U_4682,U_4683,c_Orderings_Otop__class_Otop(tc_fun(U_4681,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_1093_3]) ).
fof(f_1094_1,plain,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter]) ).
fof(f_1094_2,plain,
! [U_4690,U_4689,U_4688,U_4687,U_4686] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4686),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4687,U_4686),U_4690),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4687,tc_HOL_Obool)),U_4688),U_4689))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4687,U_4686),U_4690),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4687,tc_HOL_Obool)),U_4688),U_4689))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4686),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4687,U_4686),U_4690),U_4688)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4687,U_4686),U_4690),U_4689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4687),U_4689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4687),U_4688))
| ~ class_Groups_Ocomm__monoid__mult(U_4686) ),
inference(variable_rename,[status(thm)],[f_1094_1]) ).
fof(f_1094_3,plain,
! [U_4686,U_4687,U_4688,U_4689,U_4690] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4686),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4687,U_4686),U_4690),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4687,tc_HOL_Obool)),U_4688),U_4689))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4687,U_4686),U_4690),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4687,tc_HOL_Obool)),U_4688),U_4689))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4686),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4687,U_4686),U_4690),U_4688)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4687,U_4686),U_4690),U_4689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4687),U_4689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4687),U_4688))
| ~ class_Groups_Ocomm__monoid__mult(U_4686) ),
inference(definitional_conversion,[status(esa)],[f_1094_2]) ).
cnf(f_1094_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4686),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4687,U_4686),U_4690),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4687,tc_HOL_Obool)),U_4688),U_4689))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4687,U_4686),U_4690),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4687,tc_HOL_Obool)),U_4688),U_4689))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4686),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4687,U_4686),U_4690),U_4688)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4687,U_4686),U_4690),U_4689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4687),U_4689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4687),U_4688))
| ~ class_Groups_Ocomm__monoid__mult(U_4686) ),
inference(clausify,[status(thm)],[f_1094_3]) ).
fof(f_1095_1,plain,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int]) ).
fof(f_1095_2,plain,
! [U_4695,U_4694,U_4693,U_4692,U_4691] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4691),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,U_4691),U_4695),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4692,tc_HOL_Obool)),U_4693),U_4694))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,U_4691),U_4695),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4692,tc_HOL_Obool)),U_4693),U_4694))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4691),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,U_4691),U_4695),U_4693)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,U_4691),U_4695),U_4694))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4694))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4693))
| ~ class_Groups_Ocomm__monoid__mult(U_4691) ),
inference(variable_rename,[status(thm)],[f_1095_1]) ).
fof(f_1095_3,plain,
! [U_4692,U_4691,U_4693,U_4694,U_4695] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4691),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,U_4691),U_4695),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4692,tc_HOL_Obool)),U_4693),U_4694))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,U_4691),U_4695),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4692,tc_HOL_Obool)),U_4693),U_4694))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4691),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,U_4691),U_4695),U_4693)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,U_4691),U_4695),U_4694))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4694))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4693))
| ~ class_Groups_Ocomm__monoid__mult(U_4691) ),
inference(definitional_conversion,[status(esa)],[f_1095_2]) ).
cnf(f_1095_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4691),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,U_4691),U_4695),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4692,tc_HOL_Obool)),U_4693),U_4694))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,U_4691),U_4695),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4692,tc_HOL_Obool)),U_4693),U_4694))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4691),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,U_4691),U_4695),U_4693)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,U_4691),U_4695),U_4694))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4694))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4693))
| ~ class_Groups_Ocomm__monoid__mult(U_4691) ),
inference(clausify,[status(thm)],[f_1095_3]) ).
fof(f_1096_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_c),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_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter]) ).
fof(f_1096_2,plain,
! [U_4698,U_4697,U_4696] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4696),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4696,tc_HOL_Obool)),U_4697),U_4698))),hAPP(c_Finite__Set_Ocard(U_4696),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4696,tc_HOL_Obool)),U_4697),U_4698))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4696),U_4697)),hAPP(c_Finite__Set_Ocard(U_4696),U_4698))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4696),U_4698))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4696),U_4697)) ),
inference(variable_rename,[status(thm)],[f_1096_1]) ).
fof(f_1096_3,plain,
! [U_4696,U_4697,U_4698] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4696),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4696,tc_HOL_Obool)),U_4697),U_4698))),hAPP(c_Finite__Set_Ocard(U_4696),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4696,tc_HOL_Obool)),U_4697),U_4698))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4696),U_4697)),hAPP(c_Finite__Set_Ocard(U_4696),U_4698))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4696),U_4698))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4696),U_4697)) ),
inference(definitional_conversion,[status(esa)],[f_1096_2]) ).
cnf(f_1096_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4696),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4696,tc_HOL_Obool)),U_4697),U_4698))),hAPP(c_Finite__Set_Ocard(U_4696),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4696,tc_HOL_Obool)),U_4697),U_4698))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4696),U_4697)),hAPP(c_Finite__Set_Ocard(U_4696),U_4698))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4696),U_4698))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4696),U_4697)) ),
inference(clausify,[status(thm)],[f_1096_3]) ).
fof(f_1097_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_c),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)) ),
inference(fof_nnf,[status(thm)],[fact_card__Un__Int]) ).
fof(f_1097_2,plain,
! [U_4701,U_4700,U_4699] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4699),U_4700)),hAPP(c_Finite__Set_Ocard(U_4699),U_4701)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4699),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4699,tc_HOL_Obool)),U_4700),U_4701))),hAPP(c_Finite__Set_Ocard(U_4699),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4699,tc_HOL_Obool)),U_4700),U_4701)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4699),U_4701))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4699),U_4700)) ),
inference(variable_rename,[status(thm)],[f_1097_1]) ).
fof(f_1097_3,plain,
! [U_4699,U_4700,U_4701] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4699),U_4700)),hAPP(c_Finite__Set_Ocard(U_4699),U_4701)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4699),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4699,tc_HOL_Obool)),U_4700),U_4701))),hAPP(c_Finite__Set_Ocard(U_4699),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4699,tc_HOL_Obool)),U_4700),U_4701)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4699),U_4701))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4699),U_4700)) ),
inference(definitional_conversion,[status(esa)],[f_1097_2]) ).
cnf(f_1097_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4699),U_4700)),hAPP(c_Finite__Set_Ocard(U_4699),U_4701)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4699),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4699,tc_HOL_Obool)),U_4700),U_4701))),hAPP(c_Finite__Set_Ocard(U_4699),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4699,tc_HOL_Obool)),U_4700),U_4701)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4699),U_4701))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4699),U_4700)) ),
inference(clausify,[status(thm)],[f_1097_3]) ).
fof(f_1098_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),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_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),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),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__subset__Int]) ).
fof(f_1098_2,plain,
! [U_4704,U_4703,U_4702] :
( hAPP(c_Finite__Set_Ocard(U_4702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4702,tc_HOL_Obool)),U_4703),U_4704)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4702),U_4703)),hAPP(c_Finite__Set_Ocard(U_4702),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4702,tc_HOL_Obool)),U_4703),U_4704)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4702),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4702,tc_HOL_Obool)),U_4703),U_4704))) ),
inference(variable_rename,[status(thm)],[f_1098_1]) ).
fof(f_1098_3,plain,
! [U_4702,U_4703,U_4704] :
( hAPP(c_Finite__Set_Ocard(U_4702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4702,tc_HOL_Obool)),U_4703),U_4704)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4702),U_4703)),hAPP(c_Finite__Set_Ocard(U_4702),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4702,tc_HOL_Obool)),U_4703),U_4704)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4702),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4702,tc_HOL_Obool)),U_4703),U_4704))) ),
inference(definitional_conversion,[status(esa)],[f_1098_2]) ).
cnf(f_1098_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4702,tc_HOL_Obool)),U_4703),U_4704)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4702),U_4703)),hAPP(c_Finite__Set_Ocard(U_4702),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4702,tc_HOL_Obool)),U_4703),U_4704)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4702),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4702,tc_HOL_Obool)),U_4703),U_4704))) ),
inference(clausify,[status(thm)],[f_1098_3]) ).
fof(f_1099_1,plain,
! [V_B_2,T_d,V_d_2,V_A_2,V_c_2,T_c] :
( ( ( ( hAPP(c_Set_Ovimage(T_d,T_c,hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBC(T_d,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_d),c_If(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_c),V_d_2),V_A_2)) )
& ( hAPP(c_Set_Ovimage(T_d,T_c,hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBC(T_d,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_d),c_If(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_d,tc_HOL_Obool)),V_B_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_d_2),V_A_2)) ) )
| hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) )
& ( ( ( hAPP(c_Set_Ovimage(T_d,T_c,hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBC(T_d,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_d),c_If(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2
| hBOOL(hAPP(hAPP(c_member(T_c),V_d_2),V_A_2)) )
& ( hAPP(c_Set_Ovimage(T_d,T_c,hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBC(T_d,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_d),c_If(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_d_2),V_A_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_c_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_vimage__if]) ).
fof(f_1099_2,plain,
! [U_4710,U_4709,U_4708,U_4707,U_4706,U_4705] :
( ( ( ( hAPP(c_Set_Ovimage(U_4709,U_4705,hAPP(hAPP(c_COMBC(U_4709,U_4705,U_4705),hAPP(hAPP(c_COMBC(U_4709,U_4705,tc_fun(U_4705,U_4705)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4705,tc_fun(U_4705,U_4705)),U_4709),c_If(U_4705)),hAPP(hAPP(c_COMBC(U_4709,tc_fun(U_4709,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4709)),U_4710))),U_4706)),U_4708)),U_4707) = c_Orderings_Obot__class_Obot(tc_fun(U_4709,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_4705),U_4708),U_4707)) )
& ( hAPP(c_Set_Ovimage(U_4709,U_4705,hAPP(hAPP(c_COMBC(U_4709,U_4705,U_4705),hAPP(hAPP(c_COMBC(U_4709,U_4705,tc_fun(U_4705,U_4705)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4705,tc_fun(U_4705,U_4705)),U_4709),c_If(U_4705)),hAPP(hAPP(c_COMBC(U_4709,tc_fun(U_4709,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4709)),U_4710))),U_4706)),U_4708)),U_4707) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4709,tc_HOL_Obool)),U_4710)
| ~ hBOOL(hAPP(hAPP(c_member(U_4705),U_4708),U_4707)) ) )
| hBOOL(hAPP(hAPP(c_member(U_4705),U_4706),U_4707)) )
& ( ( ( hAPP(c_Set_Ovimage(U_4709,U_4705,hAPP(hAPP(c_COMBC(U_4709,U_4705,U_4705),hAPP(hAPP(c_COMBC(U_4709,U_4705,tc_fun(U_4705,U_4705)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4705,tc_fun(U_4705,U_4705)),U_4709),c_If(U_4705)),hAPP(hAPP(c_COMBC(U_4709,tc_fun(U_4709,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4709)),U_4710))),U_4706)),U_4708)),U_4707) = U_4710
| hBOOL(hAPP(hAPP(c_member(U_4705),U_4708),U_4707)) )
& ( hAPP(c_Set_Ovimage(U_4709,U_4705,hAPP(hAPP(c_COMBC(U_4709,U_4705,U_4705),hAPP(hAPP(c_COMBC(U_4709,U_4705,tc_fun(U_4705,U_4705)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4705,tc_fun(U_4705,U_4705)),U_4709),c_If(U_4705)),hAPP(hAPP(c_COMBC(U_4709,tc_fun(U_4709,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4709)),U_4710))),U_4706)),U_4708)),U_4707) = c_Orderings_Otop__class_Otop(tc_fun(U_4709,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4705),U_4708),U_4707)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4705),U_4706),U_4707)) ) ),
inference(variable_rename,[status(thm)],[f_1099_1]) ).
fof(f_1099_3,plain,
( ! [U_4722,U_4720,U_4718,U_4716,U_4714,U_4712] :
( ( ( hAPP(c_Set_Ovimage(U_4720,U_4712,hAPP(hAPP(c_COMBC(U_4720,U_4712,U_4712),hAPP(hAPP(c_COMBC(U_4720,U_4712,tc_fun(U_4712,U_4712)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4712,tc_fun(U_4712,U_4712)),U_4720),c_If(U_4712)),hAPP(hAPP(c_COMBC(U_4720,tc_fun(U_4720,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4720)),U_4722))),U_4714)),U_4718)),U_4716) = c_Orderings_Obot__class_Obot(tc_fun(U_4720,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_4712),U_4718),U_4716)) )
& ( hAPP(c_Set_Ovimage(U_4720,U_4712,hAPP(hAPP(c_COMBC(U_4720,U_4712,U_4712),hAPP(hAPP(c_COMBC(U_4720,U_4712,tc_fun(U_4712,U_4712)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4712,tc_fun(U_4712,U_4712)),U_4720),c_If(U_4712)),hAPP(hAPP(c_COMBC(U_4720,tc_fun(U_4720,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4720)),U_4722))),U_4714)),U_4718)),U_4716) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4720,tc_HOL_Obool)),U_4722)
| ~ hBOOL(hAPP(hAPP(c_member(U_4712),U_4718),U_4716)) ) )
| hBOOL(hAPP(hAPP(c_member(U_4712),U_4714),U_4716)) )
& ! [U_4721,U_4719,U_4717,U_4715,U_4713,U_4711] :
( ( ( hAPP(c_Set_Ovimage(U_4719,U_4711,hAPP(hAPP(c_COMBC(U_4719,U_4711,U_4711),hAPP(hAPP(c_COMBC(U_4719,U_4711,tc_fun(U_4711,U_4711)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4711,tc_fun(U_4711,U_4711)),U_4719),c_If(U_4711)),hAPP(hAPP(c_COMBC(U_4719,tc_fun(U_4719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4719)),U_4721))),U_4713)),U_4717)),U_4715) = U_4721
| hBOOL(hAPP(hAPP(c_member(U_4711),U_4717),U_4715)) )
& ( hAPP(c_Set_Ovimage(U_4719,U_4711,hAPP(hAPP(c_COMBC(U_4719,U_4711,U_4711),hAPP(hAPP(c_COMBC(U_4719,U_4711,tc_fun(U_4711,U_4711)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4711,tc_fun(U_4711,U_4711)),U_4719),c_If(U_4711)),hAPP(hAPP(c_COMBC(U_4719,tc_fun(U_4719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4719)),U_4721))),U_4713)),U_4717)),U_4715) = c_Orderings_Otop__class_Otop(tc_fun(U_4719,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4711),U_4717),U_4715)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4711),U_4713),U_4715)) ) ),
inference(miniscope,[status(thm)],[f_1099_2]) ).
fof(f_1099_4,plain,
( ! [U_4722,U_4712,U_4714,U_4718,U_4716,U_4720] :
( hAPP(c_Set_Ovimage(U_4720,U_4712,hAPP(hAPP(c_COMBC(U_4720,U_4712,U_4712),hAPP(hAPP(c_COMBC(U_4720,U_4712,tc_fun(U_4712,U_4712)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4712,tc_fun(U_4712,U_4712)),U_4720),c_If(U_4712)),hAPP(hAPP(c_COMBC(U_4720,tc_fun(U_4720,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4720)),U_4722))),U_4714)),U_4718)),U_4716) = c_Orderings_Obot__class_Obot(tc_fun(U_4720,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_4712),U_4718),U_4716))
| ~ sP245(U_4722,U_4712,U_4714,U_4718,U_4716,U_4720) )
& ! [U_4722,U_4712,U_4714,U_4718,U_4716,U_4720] :
( hAPP(c_Set_Ovimage(U_4720,U_4712,hAPP(hAPP(c_COMBC(U_4720,U_4712,U_4712),hAPP(hAPP(c_COMBC(U_4720,U_4712,tc_fun(U_4712,U_4712)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4712,tc_fun(U_4712,U_4712)),U_4720),c_If(U_4712)),hAPP(hAPP(c_COMBC(U_4720,tc_fun(U_4720,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4720)),U_4722))),U_4714)),U_4718)),U_4716) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4720,tc_HOL_Obool)),U_4722)
| ~ hBOOL(hAPP(hAPP(c_member(U_4712),U_4718),U_4716))
| ~ sP245(U_4722,U_4712,U_4714,U_4718,U_4716,U_4720) )
& ! [U_4711,U_4713,U_4715,U_4717,U_4721,U_4719] :
( hAPP(c_Set_Ovimage(U_4719,U_4711,hAPP(hAPP(c_COMBC(U_4719,U_4711,U_4711),hAPP(hAPP(c_COMBC(U_4719,U_4711,tc_fun(U_4711,U_4711)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4711,tc_fun(U_4711,U_4711)),U_4719),c_If(U_4711)),hAPP(hAPP(c_COMBC(U_4719,tc_fun(U_4719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4719)),U_4721))),U_4713)),U_4717)),U_4715) = U_4721
| hBOOL(hAPP(hAPP(c_member(U_4711),U_4717),U_4715))
| ~ sP244(U_4711,U_4713,U_4715,U_4717,U_4721,U_4719) )
& ! [U_4711,U_4713,U_4715,U_4717,U_4721,U_4719] :
( hAPP(c_Set_Ovimage(U_4719,U_4711,hAPP(hAPP(c_COMBC(U_4719,U_4711,U_4711),hAPP(hAPP(c_COMBC(U_4719,U_4711,tc_fun(U_4711,U_4711)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4711,tc_fun(U_4711,U_4711)),U_4719),c_If(U_4711)),hAPP(hAPP(c_COMBC(U_4719,tc_fun(U_4719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4719)),U_4721))),U_4713)),U_4717)),U_4715) = c_Orderings_Otop__class_Otop(tc_fun(U_4719,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4711),U_4717),U_4715))
| ~ sP244(U_4711,U_4713,U_4715,U_4717,U_4721,U_4719) )
& ! [U_4722,U_4712,U_4714,U_4718,U_4716,U_4720] :
( sP245(U_4722,U_4712,U_4714,U_4718,U_4716,U_4720)
| hBOOL(hAPP(hAPP(c_member(U_4712),U_4714),U_4716)) )
& ! [U_4711,U_4713,U_4715,U_4717,U_4721,U_4719] :
( sP244(U_4711,U_4713,U_4715,U_4717,U_4721,U_4719)
| ~ hBOOL(hAPP(hAPP(c_member(U_4711),U_4713),U_4715)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP244,sP245])],[f_1099_3]) ).
cnf(f_1099_5,plain,
( sP244(U_4711,U_4713,U_4715,U_4717,U_4721,U_4719)
| ~ hBOOL(hAPP(hAPP(c_member(U_4711),U_4713),U_4715)) ),
inference(clausify,[status(thm)],[f_1099_4]) ).
cnf(f_1099_6,plain,
( sP245(U_4722,U_4712,U_4714,U_4718,U_4716,U_4720)
| hBOOL(hAPP(hAPP(c_member(U_4712),U_4714),U_4716)) ),
inference(clausify,[status(thm)],[f_1099_4]) ).
cnf(f_1099_7,plain,
( hAPP(c_Set_Ovimage(U_4719,U_4711,hAPP(hAPP(c_COMBC(U_4719,U_4711,U_4711),hAPP(hAPP(c_COMBC(U_4719,U_4711,tc_fun(U_4711,U_4711)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4711,tc_fun(U_4711,U_4711)),U_4719),c_If(U_4711)),hAPP(hAPP(c_COMBC(U_4719,tc_fun(U_4719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4719)),U_4721))),U_4713)),U_4717)),U_4715) = c_Orderings_Otop__class_Otop(tc_fun(U_4719,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4711),U_4717),U_4715))
| ~ sP244(U_4711,U_4713,U_4715,U_4717,U_4721,U_4719) ),
inference(clausify,[status(thm)],[f_1099_4]) ).
cnf(f_1099_8,plain,
( hAPP(c_Set_Ovimage(U_4719,U_4711,hAPP(hAPP(c_COMBC(U_4719,U_4711,U_4711),hAPP(hAPP(c_COMBC(U_4719,U_4711,tc_fun(U_4711,U_4711)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4711,tc_fun(U_4711,U_4711)),U_4719),c_If(U_4711)),hAPP(hAPP(c_COMBC(U_4719,tc_fun(U_4719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4719)),U_4721))),U_4713)),U_4717)),U_4715) = U_4721
| hBOOL(hAPP(hAPP(c_member(U_4711),U_4717),U_4715))
| ~ sP244(U_4711,U_4713,U_4715,U_4717,U_4721,U_4719) ),
inference(clausify,[status(thm)],[f_1099_4]) ).
cnf(f_1099_9,plain,
( hAPP(c_Set_Ovimage(U_4720,U_4712,hAPP(hAPP(c_COMBC(U_4720,U_4712,U_4712),hAPP(hAPP(c_COMBC(U_4720,U_4712,tc_fun(U_4712,U_4712)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4712,tc_fun(U_4712,U_4712)),U_4720),c_If(U_4712)),hAPP(hAPP(c_COMBC(U_4720,tc_fun(U_4720,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4720)),U_4722))),U_4714)),U_4718)),U_4716) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4720,tc_HOL_Obool)),U_4722)
| ~ hBOOL(hAPP(hAPP(c_member(U_4712),U_4718),U_4716))
| ~ sP245(U_4722,U_4712,U_4714,U_4718,U_4716,U_4720) ),
inference(clausify,[status(thm)],[f_1099_4]) ).
cnf(f_1099_10,plain,
( hAPP(c_Set_Ovimage(U_4720,U_4712,hAPP(hAPP(c_COMBC(U_4720,U_4712,U_4712),hAPP(hAPP(c_COMBC(U_4720,U_4712,tc_fun(U_4712,U_4712)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4712,tc_fun(U_4712,U_4712)),U_4720),c_If(U_4712)),hAPP(hAPP(c_COMBC(U_4720,tc_fun(U_4720,tc_HOL_Obool),tc_HOL_Obool),c_member(U_4720)),U_4722))),U_4714)),U_4718)),U_4716) = c_Orderings_Obot__class_Obot(tc_fun(U_4720,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_4712),U_4718),U_4716))
| ~ sP245(U_4722,U_4712,U_4714,U_4718,U_4716,U_4720) ),
inference(clausify,[status(thm)],[f_1099_4]) ).
fof(f_1100_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c] :
( 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))
| 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__one(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__inter]) ).
fof(f_1100_2,plain,
! [U_4727,U_4726,U_4725,U_4724,U_4723] :
( hAPP(hAPP(U_4724,hAPP(U_4725,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4723,tc_HOL_Obool)),U_4726),U_4727))),hAPP(U_4725,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4723,tc_HOL_Obool)),U_4726),U_4727))) = hAPP(hAPP(U_4724,hAPP(U_4725,U_4726)),hAPP(U_4725,U_4727))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4723,tc_HOL_Obool)),U_4726),U_4727) = c_Orderings_Obot__class_Obot(tc_fun(U_4723,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4723),U_4727))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4723),U_4726))
| ~ c_Finite__Set_Ofolding__one(U_4723,U_4724,U_4725) ),
inference(variable_rename,[status(thm)],[f_1100_1]) ).
fof(f_1100_3,plain,
! [U_4724,U_4723,U_4727,U_4726,U_4725] :
( hAPP(hAPP(U_4724,hAPP(U_4725,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4723,tc_HOL_Obool)),U_4726),U_4727))),hAPP(U_4725,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4723,tc_HOL_Obool)),U_4726),U_4727))) = hAPP(hAPP(U_4724,hAPP(U_4725,U_4726)),hAPP(U_4725,U_4727))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4723,tc_HOL_Obool)),U_4726),U_4727) = c_Orderings_Obot__class_Obot(tc_fun(U_4723,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4723),U_4727))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4723),U_4726))
| ~ c_Finite__Set_Ofolding__one(U_4723,U_4724,U_4725) ),
inference(definitional_conversion,[status(esa)],[f_1100_2]) ).
cnf(f_1100_4,plain,
( hAPP(hAPP(U_4724,hAPP(U_4725,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4723,tc_HOL_Obool)),U_4726),U_4727))),hAPP(U_4725,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4723,tc_HOL_Obool)),U_4726),U_4727))) = hAPP(hAPP(U_4724,hAPP(U_4725,U_4726)),hAPP(U_4725,U_4727))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4723,tc_HOL_Obool)),U_4726),U_4727) = c_Orderings_Obot__class_Obot(tc_fun(U_4723,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4723),U_4727))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4723),U_4726))
| ~ c_Finite__Set_Ofolding__one(U_4723,U_4724,U_4725) ),
inference(clausify,[status(thm)],[f_1100_3]) ).
fof(f_1101_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c] :
( 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))
| 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))
| V_A_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__one(T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint]) ).
fof(f_1101_2,plain,
! [U_4732,U_4731,U_4730,U_4729,U_4728] :
( hAPP(U_4730,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4728,tc_HOL_Obool)),U_4731),U_4732)) = hAPP(hAPP(U_4729,hAPP(U_4730,U_4731)),hAPP(U_4730,U_4732))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4728,tc_HOL_Obool)),U_4731),U_4732) != c_Orderings_Obot__class_Obot(tc_fun(U_4728,tc_HOL_Obool))
| U_4732 = c_Orderings_Obot__class_Obot(tc_fun(U_4728,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4728),U_4732))
| U_4731 = c_Orderings_Obot__class_Obot(tc_fun(U_4728,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4728),U_4731))
| ~ c_Finite__Set_Ofolding__one(U_4728,U_4729,U_4730) ),
inference(variable_rename,[status(thm)],[f_1101_1]) ).
fof(f_1101_3,plain,
! [U_4729,U_4730,U_4728,U_4731,U_4732] :
( hAPP(U_4730,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4728,tc_HOL_Obool)),U_4731),U_4732)) = hAPP(hAPP(U_4729,hAPP(U_4730,U_4731)),hAPP(U_4730,U_4732))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4728,tc_HOL_Obool)),U_4731),U_4732) != c_Orderings_Obot__class_Obot(tc_fun(U_4728,tc_HOL_Obool))
| U_4732 = c_Orderings_Obot__class_Obot(tc_fun(U_4728,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4728),U_4732))
| U_4731 = c_Orderings_Obot__class_Obot(tc_fun(U_4728,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4728),U_4731))
| ~ c_Finite__Set_Ofolding__one(U_4728,U_4729,U_4730) ),
inference(definitional_conversion,[status(esa)],[f_1101_2]) ).
cnf(f_1101_4,plain,
( hAPP(U_4730,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4728,tc_HOL_Obool)),U_4731),U_4732)) = hAPP(hAPP(U_4729,hAPP(U_4730,U_4731)),hAPP(U_4730,U_4732))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4728,tc_HOL_Obool)),U_4731),U_4732) != c_Orderings_Obot__class_Obot(tc_fun(U_4728,tc_HOL_Obool))
| U_4732 = c_Orderings_Obot__class_Obot(tc_fun(U_4728,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4728),U_4732))
| U_4731 = c_Orderings_Obot__class_Obot(tc_fun(U_4728,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4728),U_4731))
| ~ c_Finite__Set_Ofolding__one(U_4728,U_4729,U_4730) ),
inference(clausify,[status(thm)],[f_1101_3]) ).
fof(f_1102_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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_d,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_c,T_d,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_1102_2,plain,
! [U_4740,U_4739,U_4738,U_4737,U_4736,U_4735,U_4734,U_4733] :
( hAPP(U_4738,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4734,tc_HOL_Obool)),U_4739),U_4740)) = hAPP(hAPP(U_4735,hAPP(U_4738,U_4739)),hAPP(U_4738,U_4740))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4734,tc_HOL_Obool)),U_4739),U_4740) != c_Orderings_Obot__class_Obot(tc_fun(U_4734,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4734),U_4740))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4734),U_4739))
| ~ c_Finite__Set_Ofolding__image__simple(U_4733,U_4734,U_4735,U_4736,U_4737,U_4738) ),
inference(variable_rename,[status(thm)],[f_1102_1]) ).
fof(f_1102_3,plain,
! [U_4740,U_4739,U_4738,U_4737,U_4736,U_4735,U_4734] :
( ! [U_4733] : ~ c_Finite__Set_Ofolding__image__simple(U_4733,U_4734,U_4735,U_4736,U_4737,U_4738)
| hAPP(U_4738,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4734,tc_HOL_Obool)),U_4739),U_4740)) = hAPP(hAPP(U_4735,hAPP(U_4738,U_4739)),hAPP(U_4738,U_4740))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4734,tc_HOL_Obool)),U_4739),U_4740) != c_Orderings_Obot__class_Obot(tc_fun(U_4734,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4734),U_4740))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4734),U_4739)) ),
inference(miniscope,[status(thm)],[f_1102_2]) ).
fof(f_1102_4,plain,
! [U_4736,U_4739,U_4735,U_4734,U_4737,U_4738,U_4733,U_4740] :
( ~ c_Finite__Set_Ofolding__image__simple(U_4733,U_4734,U_4735,U_4736,U_4737,U_4738)
| hAPP(U_4738,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4734,tc_HOL_Obool)),U_4739),U_4740)) = hAPP(hAPP(U_4735,hAPP(U_4738,U_4739)),hAPP(U_4738,U_4740))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4734,tc_HOL_Obool)),U_4739),U_4740) != c_Orderings_Obot__class_Obot(tc_fun(U_4734,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4734),U_4740))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4734),U_4739)) ),
inference(definitional_conversion,[status(esa)],[f_1102_3]) ).
cnf(f_1102_5,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_4733,U_4734,U_4735,U_4736,U_4737,U_4738)
| hAPP(U_4738,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4734,tc_HOL_Obool)),U_4739),U_4740)) = hAPP(hAPP(U_4735,hAPP(U_4738,U_4739)),hAPP(U_4738,U_4740))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4734,tc_HOL_Obool)),U_4739),U_4740) != c_Orderings_Obot__class_Obot(tc_fun(U_4734,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4734),U_4740))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4734),U_4739)) ),
inference(clausify,[status(thm)],[f_1102_4]) ).
fof(f_1103_1,plain,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_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))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un__disjoint]) ).
fof(f_1103_2,plain,
! [U_4745,U_4744,U_4743,U_4742,U_4741] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4742,U_4741),U_4745),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4742,tc_HOL_Obool)),U_4743),U_4744)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4741),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4742,U_4741),U_4745),U_4743)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4742,U_4741),U_4745),U_4744))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4742,tc_HOL_Obool)),U_4743),U_4744) != c_Orderings_Obot__class_Obot(tc_fun(U_4742,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4742),U_4744))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4742),U_4743))
| ~ class_Groups_Ocomm__monoid__add(U_4741) ),
inference(variable_rename,[status(thm)],[f_1103_1]) ).
fof(f_1103_3,plain,
! [U_4742,U_4743,U_4741,U_4744,U_4745] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4742,U_4741),U_4745),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4742,tc_HOL_Obool)),U_4743),U_4744)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4741),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4742,U_4741),U_4745),U_4743)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4742,U_4741),U_4745),U_4744))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4742,tc_HOL_Obool)),U_4743),U_4744) != c_Orderings_Obot__class_Obot(tc_fun(U_4742,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4742),U_4744))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4742),U_4743))
| ~ class_Groups_Ocomm__monoid__add(U_4741) ),
inference(definitional_conversion,[status(esa)],[f_1103_2]) ).
cnf(f_1103_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4742,U_4741),U_4745),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4742,tc_HOL_Obool)),U_4743),U_4744)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4741),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4742,U_4741),U_4745),U_4743)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4742,U_4741),U_4745),U_4744))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4742,tc_HOL_Obool)),U_4743),U_4744) != c_Orderings_Obot__class_Obot(tc_fun(U_4742,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4742),U_4744))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4742),U_4743))
| ~ class_Groups_Ocomm__monoid__add(U_4741) ),
inference(clausify,[status(thm)],[f_1103_3]) ).
fof(f_1104_1,plain,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_Groups_Ominus__class_Ominus(T_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),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))
| ~ class_Groups_Oab__group__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un]) ).
fof(f_1104_2,plain,
! [U_4750,U_4749,U_4748,U_4747,U_4746] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4747,U_4746),U_4750),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4747,tc_HOL_Obool)),U_4748),U_4749)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4746),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4746),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4747,U_4746),U_4750),U_4748)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4747,U_4746),U_4750),U_4749))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4747,U_4746),U_4750),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4747,tc_HOL_Obool)),U_4748),U_4749)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4747),U_4749))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4747),U_4748))
| ~ class_Groups_Oab__group__add(U_4746) ),
inference(variable_rename,[status(thm)],[f_1104_1]) ).
fof(f_1104_3,plain,
! [U_4747,U_4746,U_4748,U_4749,U_4750] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4747,U_4746),U_4750),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4747,tc_HOL_Obool)),U_4748),U_4749)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4746),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4746),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4747,U_4746),U_4750),U_4748)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4747,U_4746),U_4750),U_4749))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4747,U_4746),U_4750),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4747,tc_HOL_Obool)),U_4748),U_4749)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4747),U_4749))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4747),U_4748))
| ~ class_Groups_Oab__group__add(U_4746) ),
inference(definitional_conversion,[status(esa)],[f_1104_2]) ).
cnf(f_1104_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4747,U_4746),U_4750),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4747,tc_HOL_Obool)),U_4748),U_4749)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4746),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4746),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4747,U_4746),U_4750),U_4748)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4747,U_4746),U_4750),U_4749))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4747,U_4746),U_4750),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4747,tc_HOL_Obool)),U_4748),U_4749)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4747),U_4749))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4747),U_4748))
| ~ class_Groups_Oab__group__add(U_4746) ),
inference(clausify,[status(thm)],[f_1104_3]) ).
fof(f_1105_1,plain,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Un__disjoint]) ).
fof(f_1105_2,plain,
! [U_4755,U_4754,U_4753,U_4752,U_4751] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4752,U_4751),U_4755),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4752,tc_HOL_Obool)),U_4753),U_4754)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4751),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4752,U_4751),U_4755),U_4753)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4752,U_4751),U_4755),U_4754))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4752,tc_HOL_Obool)),U_4753),U_4754) != c_Orderings_Obot__class_Obot(tc_fun(U_4752,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4752),U_4754))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4752),U_4753))
| ~ class_Groups_Ocomm__monoid__mult(U_4751) ),
inference(variable_rename,[status(thm)],[f_1105_1]) ).
fof(f_1105_3,plain,
! [U_4751,U_4752,U_4753,U_4754,U_4755] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4752,U_4751),U_4755),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4752,tc_HOL_Obool)),U_4753),U_4754)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4751),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4752,U_4751),U_4755),U_4753)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4752,U_4751),U_4755),U_4754))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4752,tc_HOL_Obool)),U_4753),U_4754) != c_Orderings_Obot__class_Obot(tc_fun(U_4752,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4752),U_4754))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4752),U_4753))
| ~ class_Groups_Ocomm__monoid__mult(U_4751) ),
inference(definitional_conversion,[status(esa)],[f_1105_2]) ).
cnf(f_1105_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4752,U_4751),U_4755),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4752,tc_HOL_Obool)),U_4753),U_4754)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4751),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4752,U_4751),U_4755),U_4753)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4752,U_4751),U_4755),U_4754))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4752,tc_HOL_Obool)),U_4753),U_4754) != c_Orderings_Obot__class_Obot(tc_fun(U_4752,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4752),U_4754))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4752),U_4753))
| ~ class_Groups_Ocomm__monoid__mult(U_4751) ),
inference(clausify,[status(thm)],[f_1105_3]) ).
fof(f_1106_1,plain,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__disjoint]) ).
fof(f_1106_2,plain,
! [U_4760,U_4759,U_4758,U_4757,U_4756] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4757,U_4756),U_4760),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4757,tc_HOL_Obool)),U_4758),U_4759)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4756),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4757,U_4756),U_4760),U_4758)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4757,U_4756),U_4760),U_4759))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4757,tc_HOL_Obool)),U_4758),U_4759) != c_Orderings_Obot__class_Obot(tc_fun(U_4757,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4757),U_4759))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4757),U_4758))
| ~ class_Groups_Ocomm__monoid__mult(U_4756) ),
inference(variable_rename,[status(thm)],[f_1106_1]) ).
fof(f_1106_3,plain,
! [U_4756,U_4757,U_4758,U_4759,U_4760] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4757,U_4756),U_4760),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4757,tc_HOL_Obool)),U_4758),U_4759)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4756),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4757,U_4756),U_4760),U_4758)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4757,U_4756),U_4760),U_4759))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4757,tc_HOL_Obool)),U_4758),U_4759) != c_Orderings_Obot__class_Obot(tc_fun(U_4757,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4757),U_4759))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4757),U_4758))
| ~ class_Groups_Ocomm__monoid__mult(U_4756) ),
inference(definitional_conversion,[status(esa)],[f_1106_2]) ).
cnf(f_1106_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4757,U_4756),U_4760),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4757,tc_HOL_Obool)),U_4758),U_4759)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4756),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4757,U_4756),U_4760),U_4758)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4757,U_4756),U_4760),U_4759))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4757,tc_HOL_Obool)),U_4758),U_4759) != c_Orderings_Obot__class_Obot(tc_fun(U_4757,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4757),U_4759))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4757),U_4758))
| ~ class_Groups_Ocomm__monoid__mult(U_4756) ),
inference(clausify,[status(thm)],[f_1106_3]) ).
fof(f_1107_1,plain,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_d),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_d)),V_f_2)),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_d) ),
inference(fof_nnf,[status(thm)],[fact_sup__SUPR__fold__sup]) ).
fof(f_1107_2,plain,
! [U_4765,U_4764,U_4763,U_4762,U_4761] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4761),U_4764),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4762,U_4761),U_4763),U_4765)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4762,U_4761,hAPP(hAPP(c_COMBB(U_4761,tc_fun(U_4761,U_4761),U_4762),c_Lattices_Osemilattice__sup__class_Osup(U_4761)),U_4765)),U_4764),U_4763)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4762),U_4763))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4761) ),
inference(variable_rename,[status(thm)],[f_1107_1]) ).
fof(f_1107_3,plain,
! [U_4762,U_4761,U_4763,U_4764,U_4765] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4761),U_4764),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4762,U_4761),U_4763),U_4765)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4762,U_4761,hAPP(hAPP(c_COMBB(U_4761,tc_fun(U_4761,U_4761),U_4762),c_Lattices_Osemilattice__sup__class_Osup(U_4761)),U_4765)),U_4764),U_4763)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4762),U_4763))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4761) ),
inference(definitional_conversion,[status(esa)],[f_1107_2]) ).
cnf(f_1107_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4761),U_4764),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4762,U_4761),U_4763),U_4765)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4762,U_4761,hAPP(hAPP(c_COMBB(U_4761,tc_fun(U_4761,U_4761),U_4762),c_Lattices_Osemilattice__sup__class_Osup(U_4761)),U_4765)),U_4764),U_4763)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4762),U_4763))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4761) ),
inference(clausify,[status(thm)],[f_1107_3]) ).
fof(f_1108_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint]) ).
fof(f_1108_2,plain,
! [U_4768,U_4767,U_4766] :
( hAPP(c_Finite__Set_Ocard(U_4766),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4766,tc_HOL_Obool)),U_4767),U_4768)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4766),U_4767)),hAPP(c_Finite__Set_Ocard(U_4766),U_4768))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4766,tc_HOL_Obool)),U_4767),U_4768) != c_Orderings_Obot__class_Obot(tc_fun(U_4766,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4766),U_4768))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4766),U_4767)) ),
inference(variable_rename,[status(thm)],[f_1108_1]) ).
fof(f_1108_3,plain,
! [U_4766,U_4767,U_4768] :
( hAPP(c_Finite__Set_Ocard(U_4766),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4766,tc_HOL_Obool)),U_4767),U_4768)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4766),U_4767)),hAPP(c_Finite__Set_Ocard(U_4766),U_4768))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4766,tc_HOL_Obool)),U_4767),U_4768) != c_Orderings_Obot__class_Obot(tc_fun(U_4766,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4766),U_4768))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4766),U_4767)) ),
inference(definitional_conversion,[status(esa)],[f_1108_2]) ).
cnf(f_1108_4,plain,
( hAPP(c_Finite__Set_Ocard(U_4766),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4766,tc_HOL_Obool)),U_4767),U_4768)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4766),U_4767)),hAPP(c_Finite__Set_Ocard(U_4766),U_4768))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4766,tc_HOL_Obool)),U_4767),U_4768) != c_Orderings_Obot__class_Obot(tc_fun(U_4766,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4766),U_4768))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4766),U_4767)) ),
inference(clausify,[status(thm)],[f_1108_3]) ).
fof(f_1109_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( ( c_Fun_Oinj__on(T_c,T_d,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__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))) != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2)
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) )
& ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
& c_Fun_Oinj__on(T_c,T_d,V_f_2,V_B_2)
& c_Fun_Oinj__on(T_c,T_d,V_f_2,V_A_2) )
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__Un]) ).
fof(f_1109_2,plain,
! [U_4773,U_4772,U_4771,U_4770,U_4769] :
( ( c_Fun_Oinj__on(U_4769,U_4770,U_4771,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4769,tc_HOL_Obool)),U_4772),U_4773))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4770,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4769,U_4770,U_4771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4769,tc_HOL_Obool)),U_4772),U_4773))),hAPP(c_Set_Oimage(U_4769,U_4770,U_4771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4769,tc_HOL_Obool)),U_4773),U_4772))) != c_Orderings_Obot__class_Obot(tc_fun(U_4770,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_4769,U_4770,U_4771,U_4773)
| ~ c_Fun_Oinj__on(U_4769,U_4770,U_4771,U_4772) )
& ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4770,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4769,U_4770,U_4771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4769,tc_HOL_Obool)),U_4772),U_4773))),hAPP(c_Set_Oimage(U_4769,U_4770,U_4771),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4769,tc_HOL_Obool)),U_4773),U_4772))) = c_Orderings_Obot__class_Obot(tc_fun(U_4770,tc_HOL_Obool))
& c_Fun_Oinj__on(U_4769,U_4770,U_4771,U_4773)
& c_Fun_Oinj__on(U_4769,U_4770,U_4771,U_4772) )
| ~ c_Fun_Oinj__on(U_4769,U_4770,U_4771,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4769,tc_HOL_Obool)),U_4772),U_4773)) ) ),
inference(variable_rename,[status(thm)],[f_1109_1]) ).
fof(f_1109_3,plain,
( ! [U_4783,U_4781,U_4779,U_4777,U_4775] :
( c_Fun_Oinj__on(U_4775,U_4777,U_4779,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4775,tc_HOL_Obool)),U_4781),U_4783))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4777,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4775,U_4777,U_4779),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4775,tc_HOL_Obool)),U_4781),U_4783))),hAPP(c_Set_Oimage(U_4775,U_4777,U_4779),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4775,tc_HOL_Obool)),U_4783),U_4781))) != c_Orderings_Obot__class_Obot(tc_fun(U_4777,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_4775,U_4777,U_4779,U_4783)
| ~ c_Fun_Oinj__on(U_4775,U_4777,U_4779,U_4781) )
& ! [U_4782,U_4780,U_4778,U_4776,U_4774] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4776,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4774,U_4776,U_4778),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4774,tc_HOL_Obool)),U_4780),U_4782))),hAPP(c_Set_Oimage(U_4774,U_4776,U_4778),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4774,tc_HOL_Obool)),U_4782),U_4780))) = c_Orderings_Obot__class_Obot(tc_fun(U_4776,tc_HOL_Obool))
& c_Fun_Oinj__on(U_4774,U_4776,U_4778,U_4782)
& c_Fun_Oinj__on(U_4774,U_4776,U_4778,U_4780) )
| ~ c_Fun_Oinj__on(U_4774,U_4776,U_4778,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4774,tc_HOL_Obool)),U_4780),U_4782)) ) ),
inference(miniscope,[status(thm)],[f_1109_2]) ).
fof(f_1109_4,plain,
( ! [U_4778,U_4776,U_4774,U_4780,U_4782] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4776,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4774,U_4776,U_4778),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4774,tc_HOL_Obool)),U_4780),U_4782))),hAPP(c_Set_Oimage(U_4774,U_4776,U_4778),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4774,tc_HOL_Obool)),U_4782),U_4780))) = c_Orderings_Obot__class_Obot(tc_fun(U_4776,tc_HOL_Obool))
| ~ sP246(U_4778,U_4776,U_4774,U_4780,U_4782) )
& ! [U_4778,U_4776,U_4774,U_4780,U_4782] :
( c_Fun_Oinj__on(U_4774,U_4776,U_4778,U_4782)
| ~ sP246(U_4778,U_4776,U_4774,U_4780,U_4782) )
& ! [U_4778,U_4776,U_4774,U_4780,U_4782] :
( c_Fun_Oinj__on(U_4774,U_4776,U_4778,U_4780)
| ~ sP246(U_4778,U_4776,U_4774,U_4780,U_4782) )
& ! [U_4777,U_4775,U_4779,U_4781,U_4783] :
( c_Fun_Oinj__on(U_4775,U_4777,U_4779,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4775,tc_HOL_Obool)),U_4781),U_4783))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4777,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4775,U_4777,U_4779),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4775,tc_HOL_Obool)),U_4781),U_4783))),hAPP(c_Set_Oimage(U_4775,U_4777,U_4779),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4775,tc_HOL_Obool)),U_4783),U_4781))) != c_Orderings_Obot__class_Obot(tc_fun(U_4777,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_4775,U_4777,U_4779,U_4783)
| ~ c_Fun_Oinj__on(U_4775,U_4777,U_4779,U_4781) )
& ! [U_4778,U_4776,U_4774,U_4780,U_4782] :
( sP246(U_4778,U_4776,U_4774,U_4780,U_4782)
| ~ c_Fun_Oinj__on(U_4774,U_4776,U_4778,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4774,tc_HOL_Obool)),U_4780),U_4782)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP246])],[f_1109_3]) ).
cnf(f_1109_5,plain,
( sP246(U_4778,U_4776,U_4774,U_4780,U_4782)
| ~ c_Fun_Oinj__on(U_4774,U_4776,U_4778,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4774,tc_HOL_Obool)),U_4780),U_4782)) ),
inference(clausify,[status(thm)],[f_1109_4]) ).
cnf(f_1109_6,plain,
( c_Fun_Oinj__on(U_4775,U_4777,U_4779,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4775,tc_HOL_Obool)),U_4781),U_4783))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4777,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4775,U_4777,U_4779),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4775,tc_HOL_Obool)),U_4781),U_4783))),hAPP(c_Set_Oimage(U_4775,U_4777,U_4779),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4775,tc_HOL_Obool)),U_4783),U_4781))) != c_Orderings_Obot__class_Obot(tc_fun(U_4777,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_4775,U_4777,U_4779,U_4783)
| ~ c_Fun_Oinj__on(U_4775,U_4777,U_4779,U_4781) ),
inference(clausify,[status(thm)],[f_1109_4]) ).
cnf(f_1109_7,plain,
( c_Fun_Oinj__on(U_4774,U_4776,U_4778,U_4780)
| ~ sP246(U_4778,U_4776,U_4774,U_4780,U_4782) ),
inference(clausify,[status(thm)],[f_1109_4]) ).
cnf(f_1109_8,plain,
( c_Fun_Oinj__on(U_4774,U_4776,U_4778,U_4782)
| ~ sP246(U_4778,U_4776,U_4774,U_4780,U_4782) ),
inference(clausify,[status(thm)],[f_1109_4]) ).
cnf(f_1109_9,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4776,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4774,U_4776,U_4778),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4774,tc_HOL_Obool)),U_4780),U_4782))),hAPP(c_Set_Oimage(U_4774,U_4776,U_4778),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4774,tc_HOL_Obool)),U_4782),U_4780))) = c_Orderings_Obot__class_Obot(tc_fun(U_4776,tc_HOL_Obool))
| ~ sP246(U_4778,U_4776,U_4774,U_4780,U_4782) ),
inference(clausify,[status(thm)],[f_1109_4]) ).
fof(f_1110_1,plain,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),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)),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),c_Groups_Oone__class_Oone(T_d)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),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_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))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int]) ).
fof(f_1110_2,plain,
! [U_4788,U_4787,U_4786,U_4785,U_4784] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4784),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4784,U_4785,c_Groups_Otimes__class_Otimes(U_4784)),U_4788),c_Groups_Oone__class_Oone(U_4784)),U_4786)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4784,U_4785,c_Groups_Otimes__class_Otimes(U_4784)),U_4788),c_Groups_Oone__class_Oone(U_4784)),U_4787)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4784),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4784,U_4785,c_Groups_Otimes__class_Otimes(U_4784)),U_4788),c_Groups_Oone__class_Oone(U_4784)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4785,tc_HOL_Obool)),U_4786),U_4787))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4784,U_4785,c_Groups_Otimes__class_Otimes(U_4784)),U_4788),c_Groups_Oone__class_Oone(U_4784)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4785,tc_HOL_Obool)),U_4786),U_4787)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4785),U_4787))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4785),U_4786))
| ~ class_Groups_Ocomm__monoid__mult(U_4784) ),
inference(variable_rename,[status(thm)],[f_1110_1]) ).
fof(f_1110_3,plain,
! [U_4784,U_4786,U_4787,U_4788,U_4785] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4784),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4784,U_4785,c_Groups_Otimes__class_Otimes(U_4784)),U_4788),c_Groups_Oone__class_Oone(U_4784)),U_4786)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4784,U_4785,c_Groups_Otimes__class_Otimes(U_4784)),U_4788),c_Groups_Oone__class_Oone(U_4784)),U_4787)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4784),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4784,U_4785,c_Groups_Otimes__class_Otimes(U_4784)),U_4788),c_Groups_Oone__class_Oone(U_4784)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4785,tc_HOL_Obool)),U_4786),U_4787))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4784,U_4785,c_Groups_Otimes__class_Otimes(U_4784)),U_4788),c_Groups_Oone__class_Oone(U_4784)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4785,tc_HOL_Obool)),U_4786),U_4787)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4785),U_4787))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4785),U_4786))
| ~ class_Groups_Ocomm__monoid__mult(U_4784) ),
inference(definitional_conversion,[status(esa)],[f_1110_2]) ).
cnf(f_1110_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4784),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4784,U_4785,c_Groups_Otimes__class_Otimes(U_4784)),U_4788),c_Groups_Oone__class_Oone(U_4784)),U_4786)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4784,U_4785,c_Groups_Otimes__class_Otimes(U_4784)),U_4788),c_Groups_Oone__class_Oone(U_4784)),U_4787)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4784),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4784,U_4785,c_Groups_Otimes__class_Otimes(U_4784)),U_4788),c_Groups_Oone__class_Oone(U_4784)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4785,tc_HOL_Obool)),U_4786),U_4787))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_4784,U_4785,c_Groups_Otimes__class_Otimes(U_4784)),U_4788),c_Groups_Oone__class_Oone(U_4784)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4785,tc_HOL_Obool)),U_4786),U_4787)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4785),U_4787))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4785),U_4786))
| ~ class_Groups_Ocomm__monoid__mult(U_4784) ),
inference(clausify,[status(thm)],[f_1110_3]) ).
fof(f_1111_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(T_c)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_c,c_Groups_Otimes__class_Otimes(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))
| 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold1__Un]) ).
fof(f_1111_2,plain,
! [U_4791,U_4790,U_4789] :
( hAPP(c_Finite__Set_Ofold1(U_4789,c_Groups_Otimes__class_Otimes(U_4789)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4789,tc_HOL_Obool)),U_4790),U_4791)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4789),hAPP(c_Finite__Set_Ofold1(U_4789,c_Groups_Otimes__class_Otimes(U_4789)),U_4790)),hAPP(c_Finite__Set_Ofold1(U_4789,c_Groups_Otimes__class_Otimes(U_4789)),U_4791))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4789,tc_HOL_Obool)),U_4790),U_4791) != c_Orderings_Obot__class_Obot(tc_fun(U_4789,tc_HOL_Obool))
| U_4791 = c_Orderings_Obot__class_Obot(tc_fun(U_4789,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4789),U_4791))
| U_4790 = c_Orderings_Obot__class_Obot(tc_fun(U_4789,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4789),U_4790))
| ~ class_Groups_Oab__semigroup__mult(U_4789) ),
inference(variable_rename,[status(thm)],[f_1111_1]) ).
fof(f_1111_3,plain,
! [U_4789,U_4791,U_4790] :
( hAPP(c_Finite__Set_Ofold1(U_4789,c_Groups_Otimes__class_Otimes(U_4789)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4789,tc_HOL_Obool)),U_4790),U_4791)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4789),hAPP(c_Finite__Set_Ofold1(U_4789,c_Groups_Otimes__class_Otimes(U_4789)),U_4790)),hAPP(c_Finite__Set_Ofold1(U_4789,c_Groups_Otimes__class_Otimes(U_4789)),U_4791))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4789,tc_HOL_Obool)),U_4790),U_4791) != c_Orderings_Obot__class_Obot(tc_fun(U_4789,tc_HOL_Obool))
| U_4791 = c_Orderings_Obot__class_Obot(tc_fun(U_4789,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4789),U_4791))
| U_4790 = c_Orderings_Obot__class_Obot(tc_fun(U_4789,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4789),U_4790))
| ~ class_Groups_Oab__semigroup__mult(U_4789) ),
inference(definitional_conversion,[status(esa)],[f_1111_2]) ).
cnf(f_1111_4,plain,
( hAPP(c_Finite__Set_Ofold1(U_4789,c_Groups_Otimes__class_Otimes(U_4789)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4789,tc_HOL_Obool)),U_4790),U_4791)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4789),hAPP(c_Finite__Set_Ofold1(U_4789,c_Groups_Otimes__class_Otimes(U_4789)),U_4790)),hAPP(c_Finite__Set_Ofold1(U_4789,c_Groups_Otimes__class_Otimes(U_4789)),U_4791))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4789,tc_HOL_Obool)),U_4790),U_4791) != c_Orderings_Obot__class_Obot(tc_fun(U_4789,tc_HOL_Obool))
| U_4791 = c_Orderings_Obot__class_Obot(tc_fun(U_4789,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4789),U_4791))
| U_4790 = c_Orderings_Obot__class_Obot(tc_fun(U_4789,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4789),U_4790))
| ~ class_Groups_Oab__semigroup__mult(U_4789) ),
inference(clausify,[status(thm)],[f_1111_3]) ).
fof(f_1112_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_c,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__sup__class_Osup(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__inter]) ).
fof(f_1112_2,plain,
! [U_4794,U_4793,U_4792] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4792),c_Big__Operators_Olattice__class_OSup__fin(U_4792,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4792,tc_HOL_Obool)),U_4793),U_4794))),c_Big__Operators_Olattice__class_OSup__fin(U_4792,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4792,tc_HOL_Obool)),U_4793),U_4794))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4792),c_Big__Operators_Olattice__class_OSup__fin(U_4792,U_4793)),c_Big__Operators_Olattice__class_OSup__fin(U_4792,U_4794))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4792,tc_HOL_Obool)),U_4793),U_4794) = c_Orderings_Obot__class_Obot(tc_fun(U_4792,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4792),U_4794))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4792),U_4793))
| ~ class_Lattices_Olattice(U_4792) ),
inference(variable_rename,[status(thm)],[f_1112_1]) ).
fof(f_1112_3,plain,
! [U_4794,U_4793,U_4792] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4792),c_Big__Operators_Olattice__class_OSup__fin(U_4792,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4792,tc_HOL_Obool)),U_4793),U_4794))),c_Big__Operators_Olattice__class_OSup__fin(U_4792,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4792,tc_HOL_Obool)),U_4793),U_4794))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4792),c_Big__Operators_Olattice__class_OSup__fin(U_4792,U_4793)),c_Big__Operators_Olattice__class_OSup__fin(U_4792,U_4794))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4792,tc_HOL_Obool)),U_4793),U_4794) = c_Orderings_Obot__class_Obot(tc_fun(U_4792,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4792),U_4794))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4792),U_4793))
| ~ class_Lattices_Olattice(U_4792) ),
inference(definitional_conversion,[status(esa)],[f_1112_2]) ).
cnf(f_1112_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4792),c_Big__Operators_Olattice__class_OSup__fin(U_4792,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4792,tc_HOL_Obool)),U_4793),U_4794))),c_Big__Operators_Olattice__class_OSup__fin(U_4792,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4792,tc_HOL_Obool)),U_4793),U_4794))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4792),c_Big__Operators_Olattice__class_OSup__fin(U_4792,U_4793)),c_Big__Operators_Olattice__class_OSup__fin(U_4792,U_4794))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4792,tc_HOL_Obool)),U_4793),U_4794) = c_Orderings_Obot__class_Obot(tc_fun(U_4792,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4792),U_4794))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4792),U_4793))
| ~ class_Lattices_Olattice(U_4792) ),
inference(clausify,[status(thm)],[f_1112_3]) ).
fof(f_1113_1,plain,
! [V_B_2,V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OSup__fin(T_c,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(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(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))
| 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__disjoint]) ).
fof(f_1113_2,plain,
! [U_4797,U_4796,U_4795] :
( c_Big__Operators_Olattice__class_OSup__fin(U_4795,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4795,tc_HOL_Obool)),U_4796),U_4797)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4795),c_Big__Operators_Olattice__class_OSup__fin(U_4795,U_4796)),c_Big__Operators_Olattice__class_OSup__fin(U_4795,U_4797))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4795,tc_HOL_Obool)),U_4796),U_4797) != c_Orderings_Obot__class_Obot(tc_fun(U_4795,tc_HOL_Obool))
| U_4797 = c_Orderings_Obot__class_Obot(tc_fun(U_4795,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4795),U_4797))
| U_4796 = c_Orderings_Obot__class_Obot(tc_fun(U_4795,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4795),U_4796))
| ~ class_Lattices_Olattice(U_4795) ),
inference(variable_rename,[status(thm)],[f_1113_1]) ).
fof(f_1113_3,plain,
! [U_4795,U_4796,U_4797] :
( c_Big__Operators_Olattice__class_OSup__fin(U_4795,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4795,tc_HOL_Obool)),U_4796),U_4797)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4795),c_Big__Operators_Olattice__class_OSup__fin(U_4795,U_4796)),c_Big__Operators_Olattice__class_OSup__fin(U_4795,U_4797))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4795,tc_HOL_Obool)),U_4796),U_4797) != c_Orderings_Obot__class_Obot(tc_fun(U_4795,tc_HOL_Obool))
| U_4797 = c_Orderings_Obot__class_Obot(tc_fun(U_4795,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4795),U_4797))
| U_4796 = c_Orderings_Obot__class_Obot(tc_fun(U_4795,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4795),U_4796))
| ~ class_Lattices_Olattice(U_4795) ),
inference(definitional_conversion,[status(esa)],[f_1113_2]) ).
cnf(f_1113_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_4795,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4795,tc_HOL_Obool)),U_4796),U_4797)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4795),c_Big__Operators_Olattice__class_OSup__fin(U_4795,U_4796)),c_Big__Operators_Olattice__class_OSup__fin(U_4795,U_4797))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4795,tc_HOL_Obool)),U_4796),U_4797) != c_Orderings_Obot__class_Obot(tc_fun(U_4795,tc_HOL_Obool))
| U_4797 = c_Orderings_Obot__class_Obot(tc_fun(U_4795,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4795),U_4797))
| U_4796 = c_Orderings_Obot__class_Obot(tc_fun(U_4795,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4795),U_4796))
| ~ class_Lattices_Olattice(U_4795) ),
inference(clausify,[status(thm)],[f_1113_3]) ).
fof(f_1114_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMin(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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_Ounion__inter]) ).
fof(f_1114_2,plain,
! [U_4800,U_4799,U_4798] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4798),c_Big__Operators_Olinorder__class_OMin(U_4798,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4798,tc_HOL_Obool)),U_4799),U_4800))),c_Big__Operators_Olinorder__class_OMin(U_4798,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4798,tc_HOL_Obool)),U_4799),U_4800))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4798),c_Big__Operators_Olinorder__class_OMin(U_4798,U_4799)),c_Big__Operators_Olinorder__class_OMin(U_4798,U_4800))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4798,tc_HOL_Obool)),U_4799),U_4800) = c_Orderings_Obot__class_Obot(tc_fun(U_4798,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4798),U_4800))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4798),U_4799))
| ~ class_Orderings_Olinorder(U_4798) ),
inference(variable_rename,[status(thm)],[f_1114_1]) ).
fof(f_1114_3,plain,
! [U_4798,U_4799,U_4800] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4798),c_Big__Operators_Olinorder__class_OMin(U_4798,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4798,tc_HOL_Obool)),U_4799),U_4800))),c_Big__Operators_Olinorder__class_OMin(U_4798,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4798,tc_HOL_Obool)),U_4799),U_4800))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4798),c_Big__Operators_Olinorder__class_OMin(U_4798,U_4799)),c_Big__Operators_Olinorder__class_OMin(U_4798,U_4800))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4798,tc_HOL_Obool)),U_4799),U_4800) = c_Orderings_Obot__class_Obot(tc_fun(U_4798,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4798),U_4800))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4798),U_4799))
| ~ class_Orderings_Olinorder(U_4798) ),
inference(definitional_conversion,[status(esa)],[f_1114_2]) ).
cnf(f_1114_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4798),c_Big__Operators_Olinorder__class_OMin(U_4798,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4798,tc_HOL_Obool)),U_4799),U_4800))),c_Big__Operators_Olinorder__class_OMin(U_4798,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4798,tc_HOL_Obool)),U_4799),U_4800))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4798),c_Big__Operators_Olinorder__class_OMin(U_4798,U_4799)),c_Big__Operators_Olinorder__class_OMin(U_4798,U_4800))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4798,tc_HOL_Obool)),U_4799),U_4800) = c_Orderings_Obot__class_Obot(tc_fun(U_4798,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4798),U_4800))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4798),U_4799))
| ~ class_Orderings_Olinorder(U_4798) ),
inference(clausify,[status(thm)],[f_1114_3]) ).
fof(f_1115_1,plain,
! [V_B_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olinorder__class_OMin(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMin(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))
| 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Min_Ounion__disjoint]) ).
fof(f_1115_2,plain,
! [U_4803,U_4802,U_4801] :
( c_Big__Operators_Olinorder__class_OMin(U_4801,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4801,tc_HOL_Obool)),U_4802),U_4803)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4801),c_Big__Operators_Olinorder__class_OMin(U_4801,U_4802)),c_Big__Operators_Olinorder__class_OMin(U_4801,U_4803))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4801,tc_HOL_Obool)),U_4802),U_4803) != c_Orderings_Obot__class_Obot(tc_fun(U_4801,tc_HOL_Obool))
| U_4803 = c_Orderings_Obot__class_Obot(tc_fun(U_4801,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4801),U_4803))
| U_4802 = c_Orderings_Obot__class_Obot(tc_fun(U_4801,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4801),U_4802))
| ~ class_Orderings_Olinorder(U_4801) ),
inference(variable_rename,[status(thm)],[f_1115_1]) ).
fof(f_1115_3,plain,
! [U_4801,U_4802,U_4803] :
( c_Big__Operators_Olinorder__class_OMin(U_4801,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4801,tc_HOL_Obool)),U_4802),U_4803)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4801),c_Big__Operators_Olinorder__class_OMin(U_4801,U_4802)),c_Big__Operators_Olinorder__class_OMin(U_4801,U_4803))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4801,tc_HOL_Obool)),U_4802),U_4803) != c_Orderings_Obot__class_Obot(tc_fun(U_4801,tc_HOL_Obool))
| U_4803 = c_Orderings_Obot__class_Obot(tc_fun(U_4801,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4801),U_4803))
| U_4802 = c_Orderings_Obot__class_Obot(tc_fun(U_4801,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4801),U_4802))
| ~ class_Orderings_Olinorder(U_4801) ),
inference(definitional_conversion,[status(esa)],[f_1115_2]) ).
cnf(f_1115_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_4801,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4801,tc_HOL_Obool)),U_4802),U_4803)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4801),c_Big__Operators_Olinorder__class_OMin(U_4801,U_4802)),c_Big__Operators_Olinorder__class_OMin(U_4801,U_4803))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4801,tc_HOL_Obool)),U_4802),U_4803) != c_Orderings_Obot__class_Obot(tc_fun(U_4801,tc_HOL_Obool))
| U_4803 = c_Orderings_Obot__class_Obot(tc_fun(U_4801,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4801),U_4803))
| U_4802 = c_Orderings_Obot__class_Obot(tc_fun(U_4801,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4801),U_4802))
| ~ class_Orderings_Olinorder(U_4801) ),
inference(clausify,[status(thm)],[f_1115_3]) ).
fof(f_1116_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMax(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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_Ounion__inter]) ).
fof(f_1116_2,plain,
! [U_4806,U_4805,U_4804] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4804),c_Big__Operators_Olinorder__class_OMax(U_4804,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4804,tc_HOL_Obool)),U_4805),U_4806))),c_Big__Operators_Olinorder__class_OMax(U_4804,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4804,tc_HOL_Obool)),U_4805),U_4806))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4804),c_Big__Operators_Olinorder__class_OMax(U_4804,U_4805)),c_Big__Operators_Olinorder__class_OMax(U_4804,U_4806))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4804,tc_HOL_Obool)),U_4805),U_4806) = c_Orderings_Obot__class_Obot(tc_fun(U_4804,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4804),U_4806))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4804),U_4805))
| ~ class_Orderings_Olinorder(U_4804) ),
inference(variable_rename,[status(thm)],[f_1116_1]) ).
fof(f_1116_3,plain,
! [U_4804,U_4805,U_4806] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4804),c_Big__Operators_Olinorder__class_OMax(U_4804,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4804,tc_HOL_Obool)),U_4805),U_4806))),c_Big__Operators_Olinorder__class_OMax(U_4804,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4804,tc_HOL_Obool)),U_4805),U_4806))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4804),c_Big__Operators_Olinorder__class_OMax(U_4804,U_4805)),c_Big__Operators_Olinorder__class_OMax(U_4804,U_4806))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4804,tc_HOL_Obool)),U_4805),U_4806) = c_Orderings_Obot__class_Obot(tc_fun(U_4804,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4804),U_4806))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4804),U_4805))
| ~ class_Orderings_Olinorder(U_4804) ),
inference(definitional_conversion,[status(esa)],[f_1116_2]) ).
cnf(f_1116_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4804),c_Big__Operators_Olinorder__class_OMax(U_4804,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4804,tc_HOL_Obool)),U_4805),U_4806))),c_Big__Operators_Olinorder__class_OMax(U_4804,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4804,tc_HOL_Obool)),U_4805),U_4806))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4804),c_Big__Operators_Olinorder__class_OMax(U_4804,U_4805)),c_Big__Operators_Olinorder__class_OMax(U_4804,U_4806))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4804,tc_HOL_Obool)),U_4805),U_4806) = c_Orderings_Obot__class_Obot(tc_fun(U_4804,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4804),U_4806))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4804),U_4805))
| ~ class_Orderings_Olinorder(U_4804) ),
inference(clausify,[status(thm)],[f_1116_3]) ).
fof(f_1117_1,plain,
! [V_B_2,V_A_2,T_c] :
( c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olinorder__class_OMax(T_c,V_A_2)),c_Big__Operators_Olinorder__class_OMax(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))
| 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Max_Ounion__disjoint]) ).
fof(f_1117_2,plain,
! [U_4809,U_4808,U_4807] :
( c_Big__Operators_Olinorder__class_OMax(U_4807,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4807,tc_HOL_Obool)),U_4808),U_4809)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4807),c_Big__Operators_Olinorder__class_OMax(U_4807,U_4808)),c_Big__Operators_Olinorder__class_OMax(U_4807,U_4809))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4807,tc_HOL_Obool)),U_4808),U_4809) != c_Orderings_Obot__class_Obot(tc_fun(U_4807,tc_HOL_Obool))
| U_4809 = c_Orderings_Obot__class_Obot(tc_fun(U_4807,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4807),U_4809))
| U_4808 = c_Orderings_Obot__class_Obot(tc_fun(U_4807,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4807),U_4808))
| ~ class_Orderings_Olinorder(U_4807) ),
inference(variable_rename,[status(thm)],[f_1117_1]) ).
fof(f_1117_3,plain,
! [U_4808,U_4807,U_4809] :
( c_Big__Operators_Olinorder__class_OMax(U_4807,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4807,tc_HOL_Obool)),U_4808),U_4809)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4807),c_Big__Operators_Olinorder__class_OMax(U_4807,U_4808)),c_Big__Operators_Olinorder__class_OMax(U_4807,U_4809))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4807,tc_HOL_Obool)),U_4808),U_4809) != c_Orderings_Obot__class_Obot(tc_fun(U_4807,tc_HOL_Obool))
| U_4809 = c_Orderings_Obot__class_Obot(tc_fun(U_4807,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4807),U_4809))
| U_4808 = c_Orderings_Obot__class_Obot(tc_fun(U_4807,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4807),U_4808))
| ~ class_Orderings_Olinorder(U_4807) ),
inference(definitional_conversion,[status(esa)],[f_1117_2]) ).
cnf(f_1117_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_4807,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4807,tc_HOL_Obool)),U_4808),U_4809)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4807),c_Big__Operators_Olinorder__class_OMax(U_4807,U_4808)),c_Big__Operators_Olinorder__class_OMax(U_4807,U_4809))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4807,tc_HOL_Obool)),U_4808),U_4809) != c_Orderings_Obot__class_Obot(tc_fun(U_4807,tc_HOL_Obool))
| U_4809 = c_Orderings_Obot__class_Obot(tc_fun(U_4807,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4807),U_4809))
| U_4808 = c_Orderings_Obot__class_Obot(tc_fun(U_4807,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4807),U_4808))
| ~ class_Orderings_Olinorder(U_4807) ),
inference(clausify,[status(thm)],[f_1117_3]) ).
fof(f_1118_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter]) ).
fof(f_1118_2,plain,
! [U_4812,U_4811,U_4810] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4810),c_Big__Operators_Olattice_OInf__fin(U_4810,c_Orderings_Oord__class_Omin(U_4810),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4810,tc_HOL_Obool)),U_4811),U_4812))),c_Big__Operators_Olattice_OInf__fin(U_4810,c_Orderings_Oord__class_Omin(U_4810),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4810,tc_HOL_Obool)),U_4811),U_4812))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4810),c_Big__Operators_Olattice_OInf__fin(U_4810,c_Orderings_Oord__class_Omin(U_4810),U_4811)),c_Big__Operators_Olattice_OInf__fin(U_4810,c_Orderings_Oord__class_Omin(U_4810),U_4812))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4810,tc_HOL_Obool)),U_4811),U_4812) = c_Orderings_Obot__class_Obot(tc_fun(U_4810,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4810),U_4812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4810),U_4811))
| ~ class_Orderings_Olinorder(U_4810) ),
inference(variable_rename,[status(thm)],[f_1118_1]) ).
fof(f_1118_3,plain,
! [U_4810,U_4811,U_4812] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4810),c_Big__Operators_Olattice_OInf__fin(U_4810,c_Orderings_Oord__class_Omin(U_4810),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4810,tc_HOL_Obool)),U_4811),U_4812))),c_Big__Operators_Olattice_OInf__fin(U_4810,c_Orderings_Oord__class_Omin(U_4810),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4810,tc_HOL_Obool)),U_4811),U_4812))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4810),c_Big__Operators_Olattice_OInf__fin(U_4810,c_Orderings_Oord__class_Omin(U_4810),U_4811)),c_Big__Operators_Olattice_OInf__fin(U_4810,c_Orderings_Oord__class_Omin(U_4810),U_4812))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4810,tc_HOL_Obool)),U_4811),U_4812) = c_Orderings_Obot__class_Obot(tc_fun(U_4810,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4810),U_4812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4810),U_4811))
| ~ class_Orderings_Olinorder(U_4810) ),
inference(definitional_conversion,[status(esa)],[f_1118_2]) ).
cnf(f_1118_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4810),c_Big__Operators_Olattice_OInf__fin(U_4810,c_Orderings_Oord__class_Omin(U_4810),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4810,tc_HOL_Obool)),U_4811),U_4812))),c_Big__Operators_Olattice_OInf__fin(U_4810,c_Orderings_Oord__class_Omin(U_4810),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4810,tc_HOL_Obool)),U_4811),U_4812))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4810),c_Big__Operators_Olattice_OInf__fin(U_4810,c_Orderings_Oord__class_Omin(U_4810),U_4811)),c_Big__Operators_Olattice_OInf__fin(U_4810,c_Orderings_Oord__class_Omin(U_4810),U_4812))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4810,tc_HOL_Obool)),U_4811),U_4812) = c_Orderings_Obot__class_Obot(tc_fun(U_4810,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4810),U_4812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4810),U_4811))
| ~ class_Orderings_Olinorder(U_4810) ),
inference(clausify,[status(thm)],[f_1118_3]) ).
fof(f_1119_1,plain,
! [V_B_2,V_A_2,T_c] :
( c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(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))
| 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__disjoint]) ).
fof(f_1119_2,plain,
! [U_4815,U_4814,U_4813] :
( c_Big__Operators_Olattice_OInf__fin(U_4813,c_Orderings_Oord__class_Omin(U_4813),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4813,tc_HOL_Obool)),U_4814),U_4815)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4813),c_Big__Operators_Olattice_OInf__fin(U_4813,c_Orderings_Oord__class_Omin(U_4813),U_4814)),c_Big__Operators_Olattice_OInf__fin(U_4813,c_Orderings_Oord__class_Omin(U_4813),U_4815))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4813,tc_HOL_Obool)),U_4814),U_4815) != c_Orderings_Obot__class_Obot(tc_fun(U_4813,tc_HOL_Obool))
| U_4815 = c_Orderings_Obot__class_Obot(tc_fun(U_4813,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4813),U_4815))
| U_4814 = c_Orderings_Obot__class_Obot(tc_fun(U_4813,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4813),U_4814))
| ~ class_Orderings_Olinorder(U_4813) ),
inference(variable_rename,[status(thm)],[f_1119_1]) ).
fof(f_1119_3,plain,
! [U_4814,U_4813,U_4815] :
( c_Big__Operators_Olattice_OInf__fin(U_4813,c_Orderings_Oord__class_Omin(U_4813),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4813,tc_HOL_Obool)),U_4814),U_4815)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4813),c_Big__Operators_Olattice_OInf__fin(U_4813,c_Orderings_Oord__class_Omin(U_4813),U_4814)),c_Big__Operators_Olattice_OInf__fin(U_4813,c_Orderings_Oord__class_Omin(U_4813),U_4815))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4813,tc_HOL_Obool)),U_4814),U_4815) != c_Orderings_Obot__class_Obot(tc_fun(U_4813,tc_HOL_Obool))
| U_4815 = c_Orderings_Obot__class_Obot(tc_fun(U_4813,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4813),U_4815))
| U_4814 = c_Orderings_Obot__class_Obot(tc_fun(U_4813,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4813),U_4814))
| ~ class_Orderings_Olinorder(U_4813) ),
inference(definitional_conversion,[status(esa)],[f_1119_2]) ).
cnf(f_1119_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_4813,c_Orderings_Oord__class_Omin(U_4813),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4813,tc_HOL_Obool)),U_4814),U_4815)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4813),c_Big__Operators_Olattice_OInf__fin(U_4813,c_Orderings_Oord__class_Omin(U_4813),U_4814)),c_Big__Operators_Olattice_OInf__fin(U_4813,c_Orderings_Oord__class_Omin(U_4813),U_4815))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4813,tc_HOL_Obool)),U_4814),U_4815) != c_Orderings_Obot__class_Obot(tc_fun(U_4813,tc_HOL_Obool))
| U_4815 = c_Orderings_Obot__class_Obot(tc_fun(U_4813,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4813),U_4815))
| U_4814 = c_Orderings_Obot__class_Obot(tc_fun(U_4813,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4813),U_4814))
| ~ class_Orderings_Olinorder(U_4813) ),
inference(clausify,[status(thm)],[f_1119_3]) ).
fof(f_1120_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter]) ).
fof(f_1120_2,plain,
! [U_4818,U_4817,U_4816] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4816),c_Big__Operators_Olattice_OSup__fin(U_4816,c_Orderings_Oord__class_Omax(U_4816),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4816,tc_HOL_Obool)),U_4817),U_4818))),c_Big__Operators_Olattice_OSup__fin(U_4816,c_Orderings_Oord__class_Omax(U_4816),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4816,tc_HOL_Obool)),U_4817),U_4818))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4816),c_Big__Operators_Olattice_OSup__fin(U_4816,c_Orderings_Oord__class_Omax(U_4816),U_4817)),c_Big__Operators_Olattice_OSup__fin(U_4816,c_Orderings_Oord__class_Omax(U_4816),U_4818))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4816,tc_HOL_Obool)),U_4817),U_4818) = c_Orderings_Obot__class_Obot(tc_fun(U_4816,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4816),U_4818))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4816),U_4817))
| ~ class_Orderings_Olinorder(U_4816) ),
inference(variable_rename,[status(thm)],[f_1120_1]) ).
fof(f_1120_3,plain,
! [U_4817,U_4816,U_4818] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4816),c_Big__Operators_Olattice_OSup__fin(U_4816,c_Orderings_Oord__class_Omax(U_4816),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4816,tc_HOL_Obool)),U_4817),U_4818))),c_Big__Operators_Olattice_OSup__fin(U_4816,c_Orderings_Oord__class_Omax(U_4816),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4816,tc_HOL_Obool)),U_4817),U_4818))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4816),c_Big__Operators_Olattice_OSup__fin(U_4816,c_Orderings_Oord__class_Omax(U_4816),U_4817)),c_Big__Operators_Olattice_OSup__fin(U_4816,c_Orderings_Oord__class_Omax(U_4816),U_4818))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4816,tc_HOL_Obool)),U_4817),U_4818) = c_Orderings_Obot__class_Obot(tc_fun(U_4816,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4816),U_4818))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4816),U_4817))
| ~ class_Orderings_Olinorder(U_4816) ),
inference(definitional_conversion,[status(esa)],[f_1120_2]) ).
cnf(f_1120_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4816),c_Big__Operators_Olattice_OSup__fin(U_4816,c_Orderings_Oord__class_Omax(U_4816),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4816,tc_HOL_Obool)),U_4817),U_4818))),c_Big__Operators_Olattice_OSup__fin(U_4816,c_Orderings_Oord__class_Omax(U_4816),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4816,tc_HOL_Obool)),U_4817),U_4818))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4816),c_Big__Operators_Olattice_OSup__fin(U_4816,c_Orderings_Oord__class_Omax(U_4816),U_4817)),c_Big__Operators_Olattice_OSup__fin(U_4816,c_Orderings_Oord__class_Omax(U_4816),U_4818))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4816,tc_HOL_Obool)),U_4817),U_4818) = c_Orderings_Obot__class_Obot(tc_fun(U_4816,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4816),U_4818))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4816),U_4817))
| ~ class_Orderings_Olinorder(U_4816) ),
inference(clausify,[status(thm)],[f_1120_3]) ).
fof(f_1121_1,plain,
! [V_B_2,V_A_2,T_c] :
( c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(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))
| 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__disjoint]) ).
fof(f_1121_2,plain,
! [U_4821,U_4820,U_4819] :
( c_Big__Operators_Olattice_OSup__fin(U_4819,c_Orderings_Oord__class_Omax(U_4819),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4819,tc_HOL_Obool)),U_4820),U_4821)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4819),c_Big__Operators_Olattice_OSup__fin(U_4819,c_Orderings_Oord__class_Omax(U_4819),U_4820)),c_Big__Operators_Olattice_OSup__fin(U_4819,c_Orderings_Oord__class_Omax(U_4819),U_4821))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4819,tc_HOL_Obool)),U_4820),U_4821) != c_Orderings_Obot__class_Obot(tc_fun(U_4819,tc_HOL_Obool))
| U_4821 = c_Orderings_Obot__class_Obot(tc_fun(U_4819,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4819),U_4821))
| U_4820 = c_Orderings_Obot__class_Obot(tc_fun(U_4819,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4819),U_4820))
| ~ class_Orderings_Olinorder(U_4819) ),
inference(variable_rename,[status(thm)],[f_1121_1]) ).
fof(f_1121_3,plain,
! [U_4820,U_4819,U_4821] :
( c_Big__Operators_Olattice_OSup__fin(U_4819,c_Orderings_Oord__class_Omax(U_4819),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4819,tc_HOL_Obool)),U_4820),U_4821)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4819),c_Big__Operators_Olattice_OSup__fin(U_4819,c_Orderings_Oord__class_Omax(U_4819),U_4820)),c_Big__Operators_Olattice_OSup__fin(U_4819,c_Orderings_Oord__class_Omax(U_4819),U_4821))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4819,tc_HOL_Obool)),U_4820),U_4821) != c_Orderings_Obot__class_Obot(tc_fun(U_4819,tc_HOL_Obool))
| U_4821 = c_Orderings_Obot__class_Obot(tc_fun(U_4819,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4819),U_4821))
| U_4820 = c_Orderings_Obot__class_Obot(tc_fun(U_4819,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4819),U_4820))
| ~ class_Orderings_Olinorder(U_4819) ),
inference(definitional_conversion,[status(esa)],[f_1121_2]) ).
cnf(f_1121_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_4819,c_Orderings_Oord__class_Omax(U_4819),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4819,tc_HOL_Obool)),U_4820),U_4821)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4819),c_Big__Operators_Olattice_OSup__fin(U_4819,c_Orderings_Oord__class_Omax(U_4819),U_4820)),c_Big__Operators_Olattice_OSup__fin(U_4819,c_Orderings_Oord__class_Omax(U_4819),U_4821))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4819,tc_HOL_Obool)),U_4820),U_4821) != c_Orderings_Obot__class_Obot(tc_fun(U_4819,tc_HOL_Obool))
| U_4821 = c_Orderings_Obot__class_Obot(tc_fun(U_4819,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4819),U_4821))
| U_4820 = c_Orderings_Obot__class_Obot(tc_fun(U_4819,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4819),U_4820))
| ~ class_Orderings_Olinorder(U_4819) ),
inference(clausify,[status(thm)],[f_1121_3]) ).
fof(f_1122_1,plain,
! [V_f_2,V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),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_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_c,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),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)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un__nat]) ).
fof(f_1122_2,plain,
! [U_4825,U_4824,U_4823,U_4822] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4822,tc_Nat_Onat),U_4825),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4822,tc_HOL_Obool)),U_4823),U_4824)) = 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_4822,tc_Nat_Onat),U_4825),U_4823)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4822,tc_Nat_Onat),U_4825),U_4824))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4822,tc_Nat_Onat),U_4825),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4822,tc_HOL_Obool)),U_4823),U_4824)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4822),U_4824))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4822),U_4823)) ),
inference(variable_rename,[status(thm)],[f_1122_1]) ).
fof(f_1122_3,plain,
! [U_4823,U_4824,U_4822,U_4825] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4822,tc_Nat_Onat),U_4825),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4822,tc_HOL_Obool)),U_4823),U_4824)) = 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_4822,tc_Nat_Onat),U_4825),U_4823)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4822,tc_Nat_Onat),U_4825),U_4824))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4822,tc_Nat_Onat),U_4825),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4822,tc_HOL_Obool)),U_4823),U_4824)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4822),U_4824))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4822),U_4823)) ),
inference(definitional_conversion,[status(esa)],[f_1122_2]) ).
cnf(f_1122_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4822,tc_Nat_Onat),U_4825),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4822,tc_HOL_Obool)),U_4823),U_4824)) = 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_4822,tc_Nat_Onat),U_4825),U_4823)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4822,tc_Nat_Onat),U_4825),U_4824))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4822,tc_Nat_Onat),U_4825),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4822,tc_HOL_Obool)),U_4823),U_4824)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4822),U_4824))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4822),U_4823)) ),
inference(clausify,[status(thm)],[f_1122_3]) ).
fof(f_1123_1,plain,
! [V_B_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Ovimage(T_c,T_d,V_f_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),c_Set_Oinsert(T_d)),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_vimage__eq__UN]) ).
fof(f_1123_2,plain,
! [U_4829,U_4828,U_4827,U_4826] : hAPP(c_Set_Ovimage(U_4826,U_4827,U_4828),U_4829) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4827,tc_fun(U_4826,tc_HOL_Obool)),U_4829),hAPP(hAPP(c_COMBB(tc_fun(U_4827,tc_HOL_Obool),tc_fun(U_4826,tc_HOL_Obool),U_4827),c_Set_Ovimage(U_4826,U_4827,U_4828)),hAPP(hAPP(c_COMBC(U_4827,tc_fun(U_4827,tc_HOL_Obool),tc_fun(U_4827,tc_HOL_Obool)),c_Set_Oinsert(U_4827)),c_Orderings_Obot__class_Obot(tc_fun(U_4827,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_1123_1]) ).
fof(f_1123_3,plain,
! [U_4826,U_4827,U_4828,U_4829] : hAPP(c_Set_Ovimage(U_4826,U_4827,U_4828),U_4829) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4827,tc_fun(U_4826,tc_HOL_Obool)),U_4829),hAPP(hAPP(c_COMBB(tc_fun(U_4827,tc_HOL_Obool),tc_fun(U_4826,tc_HOL_Obool),U_4827),c_Set_Ovimage(U_4826,U_4827,U_4828)),hAPP(hAPP(c_COMBC(U_4827,tc_fun(U_4827,tc_HOL_Obool),tc_fun(U_4827,tc_HOL_Obool)),c_Set_Oinsert(U_4827)),c_Orderings_Obot__class_Obot(tc_fun(U_4827,tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_1123_2]) ).
cnf(f_1123_4,plain,
hAPP(c_Set_Ovimage(U_4826,U_4827,U_4828),U_4829) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4827,tc_fun(U_4826,tc_HOL_Obool)),U_4829),hAPP(hAPP(c_COMBB(tc_fun(U_4827,tc_HOL_Obool),tc_fun(U_4826,tc_HOL_Obool),U_4827),c_Set_Ovimage(U_4826,U_4827,U_4828)),hAPP(hAPP(c_COMBC(U_4827,tc_fun(U_4827,tc_HOL_Obool),tc_fun(U_4827,tc_HOL_Obool)),c_Set_Oinsert(U_4827)),c_Orderings_Obot__class_Obot(tc_fun(U_4827,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_1123_3]) ).
fof(f_1124_1,plain,
! [V_A_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,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_d),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_image__eq__UN]) ).
fof(f_1124_2,plain,
! [U_4833,U_4832,U_4831,U_4830] : hAPP(c_Set_Oimage(U_4830,U_4831,U_4832),U_4833) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4830,tc_fun(U_4831,tc_HOL_Obool)),U_4833),hAPP(hAPP(c_COMBC(U_4830,tc_fun(U_4831,tc_HOL_Obool),tc_fun(U_4831,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_4831,tc_fun(tc_fun(U_4831,tc_HOL_Obool),tc_fun(U_4831,tc_HOL_Obool)),U_4830),c_Set_Oinsert(U_4831)),U_4832)),c_Orderings_Obot__class_Obot(tc_fun(U_4831,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_1124_1]) ).
fof(f_1124_3,plain,
! [U_4830,U_4831,U_4832,U_4833] : hAPP(c_Set_Oimage(U_4830,U_4831,U_4832),U_4833) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4830,tc_fun(U_4831,tc_HOL_Obool)),U_4833),hAPP(hAPP(c_COMBC(U_4830,tc_fun(U_4831,tc_HOL_Obool),tc_fun(U_4831,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_4831,tc_fun(tc_fun(U_4831,tc_HOL_Obool),tc_fun(U_4831,tc_HOL_Obool)),U_4830),c_Set_Oinsert(U_4831)),U_4832)),c_Orderings_Obot__class_Obot(tc_fun(U_4831,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_1124_2]) ).
cnf(f_1124_4,plain,
hAPP(c_Set_Oimage(U_4830,U_4831,U_4832),U_4833) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4830,tc_fun(U_4831,tc_HOL_Obool)),U_4833),hAPP(hAPP(c_COMBC(U_4830,tc_fun(U_4831,tc_HOL_Obool),tc_fun(U_4831,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_4831,tc_fun(tc_fun(U_4831,tc_HOL_Obool),tc_fun(U_4831,tc_HOL_Obool)),U_4830),c_Set_Oinsert(U_4831)),U_4832)),c_Orderings_Obot__class_Obot(tc_fun(U_4831,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_1124_3]) ).
fof(f_1125_1,plain,
! [V_B_2,V_b_2,T_d,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(V_B_2,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__I]) ).
fof(f_1125_2,plain,
! [U_4839,U_4838,U_4837,U_4836,U_4835,U_4834] :
( hBOOL(hAPP(hAPP(c_member(U_4837),U_4838),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4834,tc_fun(U_4837,tc_HOL_Obool)),U_4836),U_4839)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4837),U_4838),hAPP(U_4839,U_4835)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4834),U_4835),U_4836)) ),
inference(variable_rename,[status(thm)],[f_1125_1]) ).
fof(f_1125_3,plain,
! [U_4834,U_4835,U_4836,U_4837,U_4838,U_4839] :
( hBOOL(hAPP(hAPP(c_member(U_4837),U_4838),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4834,tc_fun(U_4837,tc_HOL_Obool)),U_4836),U_4839)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4837),U_4838),hAPP(U_4839,U_4835)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4834),U_4835),U_4836)) ),
inference(definitional_conversion,[status(esa)],[f_1125_2]) ).
cnf(f_1125_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_4837),U_4838),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4834,tc_fun(U_4837,tc_HOL_Obool)),U_4836),U_4839)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4837),U_4838),hAPP(U_4839,U_4835)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4834),U_4835),U_4836)) ),
inference(clausify,[status(thm)],[f_1125_3]) ).
fof(f_1126_1,plain,
! [V_M_2,V_A_2,V_i_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),V_M_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_d) ),
inference(fof_nnf,[status(thm)],[fact_le__SUPI]) ).
fof(f_1126_2,plain,
! [U_4844,U_4843,U_4842,U_4841,U_4840] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4840),hAPP(U_4844,U_4842)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4841,U_4840),U_4843),U_4844)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4841),U_4842),U_4843))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4840) ),
inference(variable_rename,[status(thm)],[f_1126_1]) ).
fof(f_1126_3,plain,
! [U_4841,U_4840,U_4842,U_4843,U_4844] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4840),hAPP(U_4844,U_4842)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4841,U_4840),U_4843),U_4844)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4841),U_4842),U_4843))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4840) ),
inference(definitional_conversion,[status(esa)],[f_1126_2]) ).
cnf(f_1126_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4840),hAPP(U_4844,U_4842)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4841,U_4840),U_4843),U_4844)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4841),U_4842),U_4843))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4840) ),
inference(clausify,[status(thm)],[f_1126_3]) ).
fof(f_1127_1,plain,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_B_2),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_d) ),
inference(fof_nnf,[status(thm)],[fact_SUP__subset]) ).
fof(f_1127_2,plain,
! [U_4849,U_4848,U_4847,U_4846,U_4845] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4845),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4846,U_4845),U_4847),U_4849)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4846,U_4845),U_4848),U_4849)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4846,tc_HOL_Obool)),U_4847),U_4848))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4845) ),
inference(variable_rename,[status(thm)],[f_1127_1]) ).
fof(f_1127_3,plain,
! [U_4845,U_4846,U_4847,U_4848,U_4849] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4845),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4846,U_4845),U_4847),U_4849)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4846,U_4845),U_4848),U_4849)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4846,tc_HOL_Obool)),U_4847),U_4848))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4845) ),
inference(definitional_conversion,[status(esa)],[f_1127_2]) ).
cnf(f_1127_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4845),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4846,U_4845),U_4847),U_4849)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4846,U_4845),U_4848),U_4849)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4846,tc_HOL_Obool)),U_4847),U_4848))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4845) ),
inference(clausify,[status(thm)],[f_1127_3]) ).
fof(f_1128_1,plain,
! [V_M_2,T_c,V_A_2,T_d] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_d),V_A_2),hAPP(c_COMBK(T_d,T_c),V_M_2)) = V_M_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_d) ),
inference(fof_nnf,[status(thm)],[fact_SUP__const]) ).
fof(f_1128_2,plain,
! [U_4853,U_4852,U_4851,U_4850] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4852,U_4850),U_4851),hAPP(c_COMBK(U_4850,U_4852),U_4853)) = U_4853
| U_4851 = c_Orderings_Obot__class_Obot(tc_fun(U_4852,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4850) ),
inference(variable_rename,[status(thm)],[f_1128_1]) ).
fof(f_1128_3,plain,
! [U_4850,U_4851,U_4852,U_4853] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4852,U_4850),U_4851),hAPP(c_COMBK(U_4850,U_4852),U_4853)) = U_4853
| U_4851 = c_Orderings_Obot__class_Obot(tc_fun(U_4852,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4850) ),
inference(definitional_conversion,[status(esa)],[f_1128_2]) ).
cnf(f_1128_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4852,U_4850),U_4851),hAPP(c_COMBK(U_4850,U_4852),U_4853)) = U_4853
| U_4851 = c_Orderings_Obot__class_Obot(tc_fun(U_4852,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4850) ),
inference(clausify,[status(thm)],[f_1128_3]) ).
fof(f_1129_1,plain,
! [V_B_2,V_A_2,V_a_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_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)),
inference(fof_nnf,[status(thm)],[fact_UN__insert]) ).
fof(f_1129_2,plain,
! [U_4858,U_4857,U_4856,U_4855,U_4854] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4854,tc_fun(U_4855,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4854),U_4856),U_4857)),U_4858) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4855,tc_HOL_Obool)),hAPP(U_4858,U_4856)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4854,tc_fun(U_4855,tc_HOL_Obool)),U_4857),U_4858)),
inference(variable_rename,[status(thm)],[f_1129_1]) ).
fof(f_1129_3,plain,
! [U_4854,U_4855,U_4856,U_4857,U_4858] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4854,tc_fun(U_4855,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4854),U_4856),U_4857)),U_4858) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4855,tc_HOL_Obool)),hAPP(U_4858,U_4856)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4854,tc_fun(U_4855,tc_HOL_Obool)),U_4857),U_4858)),
inference(definitional_conversion,[status(esa)],[f_1129_2]) ).
cnf(f_1129_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4854,tc_fun(U_4855,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_4854),U_4856),U_4857)),U_4858) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4855,tc_HOL_Obool)),hAPP(U_4858,U_4856)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4854,tc_fun(U_4855,tc_HOL_Obool)),U_4857),U_4858)),
inference(clausify,[status(thm)],[f_1129_3]) ).
fof(f_1130_1,plain,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J]) ).
fof(f_1130_2,plain,
! [U_4863,U_4862,U_4861,U_4860,U_4859] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4860,tc_fun(U_4861,tc_HOL_Obool)),U_4859),hAPP(hAPP(c_COMBB(tc_fun(U_4861,tc_HOL_Obool),tc_fun(U_4861,tc_HOL_Obool),U_4860),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4861,tc_HOL_Obool)),U_4862)),U_4863)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4861,tc_HOL_Obool)),U_4862),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4860,tc_fun(U_4861,tc_HOL_Obool)),U_4859),U_4863))
| U_4859 = c_Orderings_Obot__class_Obot(tc_fun(U_4860,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4860,tc_fun(U_4861,tc_HOL_Obool)),U_4859),hAPP(hAPP(c_COMBB(tc_fun(U_4861,tc_HOL_Obool),tc_fun(U_4861,tc_HOL_Obool),U_4860),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4861,tc_HOL_Obool)),U_4862)),U_4863)) = c_Orderings_Obot__class_Obot(tc_fun(U_4861,tc_HOL_Obool))
| U_4859 != c_Orderings_Obot__class_Obot(tc_fun(U_4860,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1130_1]) ).
fof(f_1130_3,plain,
( ! [U_4873,U_4871,U_4869,U_4867,U_4865] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4867,tc_fun(U_4869,tc_HOL_Obool)),U_4865),hAPP(hAPP(c_COMBB(tc_fun(U_4869,tc_HOL_Obool),tc_fun(U_4869,tc_HOL_Obool),U_4867),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4869,tc_HOL_Obool)),U_4871)),U_4873)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4869,tc_HOL_Obool)),U_4871),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4867,tc_fun(U_4869,tc_HOL_Obool)),U_4865),U_4873))
| U_4865 = c_Orderings_Obot__class_Obot(tc_fun(U_4867,tc_HOL_Obool)) )
& ! [U_4872,U_4870,U_4868,U_4866,U_4864] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4866,tc_fun(U_4868,tc_HOL_Obool)),U_4864),hAPP(hAPP(c_COMBB(tc_fun(U_4868,tc_HOL_Obool),tc_fun(U_4868,tc_HOL_Obool),U_4866),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4868,tc_HOL_Obool)),U_4870)),U_4872)) = c_Orderings_Obot__class_Obot(tc_fun(U_4868,tc_HOL_Obool))
| U_4864 != c_Orderings_Obot__class_Obot(tc_fun(U_4866,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1130_2]) ).
fof(f_1130_4,plain,
( ! [U_4865,U_4867,U_4869,U_4871,U_4873] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4867,tc_fun(U_4869,tc_HOL_Obool)),U_4865),hAPP(hAPP(c_COMBB(tc_fun(U_4869,tc_HOL_Obool),tc_fun(U_4869,tc_HOL_Obool),U_4867),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4869,tc_HOL_Obool)),U_4871)),U_4873)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4869,tc_HOL_Obool)),U_4871),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4867,tc_fun(U_4869,tc_HOL_Obool)),U_4865),U_4873))
| U_4865 = c_Orderings_Obot__class_Obot(tc_fun(U_4867,tc_HOL_Obool)) )
& ! [U_4868,U_4866,U_4870,U_4864,U_4872] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4866,tc_fun(U_4868,tc_HOL_Obool)),U_4864),hAPP(hAPP(c_COMBB(tc_fun(U_4868,tc_HOL_Obool),tc_fun(U_4868,tc_HOL_Obool),U_4866),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4868,tc_HOL_Obool)),U_4870)),U_4872)) = c_Orderings_Obot__class_Obot(tc_fun(U_4868,tc_HOL_Obool))
| U_4864 != c_Orderings_Obot__class_Obot(tc_fun(U_4866,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1130_3]) ).
cnf(f_1130_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4866,tc_fun(U_4868,tc_HOL_Obool)),U_4864),hAPP(hAPP(c_COMBB(tc_fun(U_4868,tc_HOL_Obool),tc_fun(U_4868,tc_HOL_Obool),U_4866),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4868,tc_HOL_Obool)),U_4870)),U_4872)) = c_Orderings_Obot__class_Obot(tc_fun(U_4868,tc_HOL_Obool))
| U_4864 != c_Orderings_Obot__class_Obot(tc_fun(U_4866,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1130_4]) ).
cnf(f_1130_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4867,tc_fun(U_4869,tc_HOL_Obool)),U_4865),hAPP(hAPP(c_COMBB(tc_fun(U_4869,tc_HOL_Obool),tc_fun(U_4869,tc_HOL_Obool),U_4867),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4869,tc_HOL_Obool)),U_4871)),U_4873)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4869,tc_HOL_Obool)),U_4871),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4867,tc_fun(U_4869,tc_HOL_Obool)),U_4865),U_4873))
| U_4865 = c_Orderings_Obot__class_Obot(tc_fun(U_4867,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1130_4]) ).
fof(f_1131_1,plain,
! [V_C_2,V_B_2,V_A_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_e),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_UN__UN__flatten]) ).
fof(f_1131_2,plain,
! [U_4879,U_4878,U_4877,U_4876,U_4875,U_4874] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4874,tc_fun(U_4875,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4876,tc_fun(U_4874,tc_HOL_Obool)),U_4877),U_4878)),U_4879) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4876,tc_fun(U_4875,tc_HOL_Obool)),U_4877),hAPP(hAPP(c_COMBC(U_4876,tc_fun(U_4874,tc_fun(U_4875,tc_HOL_Obool)),tc_fun(U_4875,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_4874,tc_HOL_Obool),tc_fun(tc_fun(U_4874,tc_fun(U_4875,tc_HOL_Obool)),tc_fun(U_4875,tc_HOL_Obool)),U_4876),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4874,tc_fun(U_4875,tc_HOL_Obool))),U_4878)),U_4879)),
inference(variable_rename,[status(thm)],[f_1131_1]) ).
fof(f_1131_3,plain,
! [U_4875,U_4874,U_4876,U_4877,U_4878,U_4879] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4874,tc_fun(U_4875,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4876,tc_fun(U_4874,tc_HOL_Obool)),U_4877),U_4878)),U_4879) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4876,tc_fun(U_4875,tc_HOL_Obool)),U_4877),hAPP(hAPP(c_COMBC(U_4876,tc_fun(U_4874,tc_fun(U_4875,tc_HOL_Obool)),tc_fun(U_4875,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_4874,tc_HOL_Obool),tc_fun(tc_fun(U_4874,tc_fun(U_4875,tc_HOL_Obool)),tc_fun(U_4875,tc_HOL_Obool)),U_4876),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4874,tc_fun(U_4875,tc_HOL_Obool))),U_4878)),U_4879)),
inference(definitional_conversion,[status(esa)],[f_1131_2]) ).
cnf(f_1131_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4874,tc_fun(U_4875,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4876,tc_fun(U_4874,tc_HOL_Obool)),U_4877),U_4878)),U_4879) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4876,tc_fun(U_4875,tc_HOL_Obool)),U_4877),hAPP(hAPP(c_COMBC(U_4876,tc_fun(U_4874,tc_fun(U_4875,tc_HOL_Obool)),tc_fun(U_4875,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_4874,tc_HOL_Obool),tc_fun(tc_fun(U_4874,tc_fun(U_4875,tc_HOL_Obool)),tc_fun(U_4875,tc_HOL_Obool)),U_4876),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4874,tc_fun(U_4875,tc_HOL_Obool))),U_4878)),U_4879)),
inference(clausify,[status(thm)],[f_1131_3]) ).
fof(f_1132_1,plain,
! [V_C_2,V_B_2,V_A_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_e),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I9_J]) ).
fof(f_1132_2,plain,
! [U_4885,U_4884,U_4883,U_4882,U_4881,U_4880] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4880,tc_fun(U_4881,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4882,tc_fun(U_4880,tc_HOL_Obool)),U_4883),U_4884)),U_4885) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4882,tc_fun(U_4881,tc_HOL_Obool)),U_4883),hAPP(hAPP(c_COMBC(U_4882,tc_fun(U_4880,tc_fun(U_4881,tc_HOL_Obool)),tc_fun(U_4881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_4880,tc_HOL_Obool),tc_fun(tc_fun(U_4880,tc_fun(U_4881,tc_HOL_Obool)),tc_fun(U_4881,tc_HOL_Obool)),U_4882),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4880,tc_fun(U_4881,tc_HOL_Obool))),U_4884)),U_4885)),
inference(variable_rename,[status(thm)],[f_1132_1]) ).
fof(f_1132_3,plain,
! [U_4880,U_4881,U_4882,U_4883,U_4884,U_4885] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4880,tc_fun(U_4881,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4882,tc_fun(U_4880,tc_HOL_Obool)),U_4883),U_4884)),U_4885) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4882,tc_fun(U_4881,tc_HOL_Obool)),U_4883),hAPP(hAPP(c_COMBC(U_4882,tc_fun(U_4880,tc_fun(U_4881,tc_HOL_Obool)),tc_fun(U_4881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_4880,tc_HOL_Obool),tc_fun(tc_fun(U_4880,tc_fun(U_4881,tc_HOL_Obool)),tc_fun(U_4881,tc_HOL_Obool)),U_4882),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4880,tc_fun(U_4881,tc_HOL_Obool))),U_4884)),U_4885)),
inference(definitional_conversion,[status(esa)],[f_1132_2]) ).
cnf(f_1132_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4880,tc_fun(U_4881,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4882,tc_fun(U_4880,tc_HOL_Obool)),U_4883),U_4884)),U_4885) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4882,tc_fun(U_4881,tc_HOL_Obool)),U_4883),hAPP(hAPP(c_COMBC(U_4882,tc_fun(U_4880,tc_fun(U_4881,tc_HOL_Obool)),tc_fun(U_4881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_4880,tc_HOL_Obool),tc_fun(tc_fun(U_4880,tc_fun(U_4881,tc_HOL_Obool)),tc_fun(U_4881,tc_HOL_Obool)),U_4882),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4880,tc_fun(U_4881,tc_HOL_Obool))),U_4884)),U_4885)),
inference(clausify,[status(thm)],[f_1132_3]) ).
fof(f_1133_1,plain,
! [V_Pa_2,V_B_2,V_A_2,T_d,T_c] :
( ( ! [B_x] :
( hBOOL(hAPP(V_Pa_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,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_c),B_xa),hAPP(V_B_2,B_x))) )
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ! [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(V_Pa_2,B_xa))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_xa),hAPP(V_B_2,B_x))) )
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_Pa_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ball__UN]) ).
fof(f_1133_2,plain,
! [U_4896,U_4895,U_4894,U_4893,U_4892] :
( ( ! [U_4891] :
( hBOOL(hAPP(U_4896,U_4891))
| ~ hBOOL(hAPP(hAPP(c_member(U_4892),U_4891),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4893,tc_fun(U_4892,tc_HOL_Obool)),U_4894),U_4895))) )
| ? [U_4890] :
( ? [U_4889] :
( ~ hBOOL(hAPP(U_4896,U_4889))
& hBOOL(hAPP(hAPP(c_member(U_4892),U_4889),hAPP(U_4895,U_4890))) )
& hBOOL(hAPP(hAPP(c_member(U_4893),U_4890),U_4894)) ) )
& ( ! [U_4888] :
( ! [U_4887] :
( hBOOL(hAPP(U_4896,U_4887))
| ~ hBOOL(hAPP(hAPP(c_member(U_4892),U_4887),hAPP(U_4895,U_4888))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4893),U_4888),U_4894)) )
| ? [U_4886] :
( ~ hBOOL(hAPP(U_4896,U_4886))
& hBOOL(hAPP(hAPP(c_member(U_4892),U_4886),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4893,tc_fun(U_4892,tc_HOL_Obool)),U_4894),U_4895))) ) ) ),
inference(variable_rename,[status(thm)],[f_1133_1]) ).
fof(f_1133_3,plain,
( ! [U_4906,U_4904,U_4902,U_4900,U_4898] :
( ! [U_4891] :
( hBOOL(hAPP(U_4906,U_4891))
| ~ hBOOL(hAPP(hAPP(c_member(U_4898),U_4891),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4900,tc_fun(U_4898,tc_HOL_Obool)),U_4902),U_4904))) )
| ? [U_4890] :
( ? [U_4889] :
( ~ hBOOL(hAPP(U_4906,U_4889))
& hBOOL(hAPP(hAPP(c_member(U_4898),U_4889),hAPP(U_4904,U_4890))) )
& hBOOL(hAPP(hAPP(c_member(U_4900),U_4890),U_4902)) ) )
& ! [U_4905,U_4903,U_4901,U_4899,U_4897] :
( ! [U_4888] :
( ! [U_4887] :
( hBOOL(hAPP(U_4905,U_4887))
| ~ hBOOL(hAPP(hAPP(c_member(U_4897),U_4887),hAPP(U_4903,U_4888))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4899),U_4888),U_4901)) )
| ? [U_4886] :
( ~ hBOOL(hAPP(U_4905,U_4886))
& hBOOL(hAPP(hAPP(c_member(U_4897),U_4886),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4899,tc_fun(U_4897,tc_HOL_Obool)),U_4901),U_4903))) ) ) ),
inference(miniscope,[status(thm)],[f_1133_2]) ).
fof(f_1133_4,plain,
( ! [U_4906,U_4904,U_4902,U_4900,U_4898] :
( ! [U_4891] :
( hBOOL(hAPP(U_4906,U_4891))
| ~ hBOOL(hAPP(hAPP(c_member(U_4898),U_4891),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4900,tc_fun(U_4898,tc_HOL_Obool)),U_4902),U_4904))) )
| ? [U_4890] :
( ? [U_4889] :
( ~ hBOOL(hAPP(U_4906,U_4889))
& hBOOL(hAPP(hAPP(c_member(U_4898),U_4889),hAPP(U_4904,U_4890))) )
& hBOOL(hAPP(hAPP(c_member(U_4900),U_4890),U_4902)) ) )
& ! [U_4905,U_4903,U_4901,U_4899,U_4897] :
( ! [U_4888] :
( ! [U_4887] :
( hBOOL(hAPP(U_4905,U_4887))
| ~ hBOOL(hAPP(hAPP(c_member(U_4897),U_4887),hAPP(U_4903,U_4888))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4899),U_4888),U_4901)) )
| ( ~ hBOOL(hAPP(U_4905,sK92(U_4905,U_4903,U_4901,U_4899,U_4897)))
& hBOOL(hAPP(hAPP(c_member(U_4897),sK92(U_4905,U_4903,U_4901,U_4899,U_4897)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4899,tc_fun(U_4897,tc_HOL_Obool)),U_4901),U_4903))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_4886,sK92(U_4905,U_4903,U_4901,U_4899,U_4897))],[f_1133_3]) ).
fof(f_1133_5,plain,
( ! [U_4906,U_4904,U_4902,U_4900,U_4898] :
( ! [U_4891] :
( hBOOL(hAPP(U_4906,U_4891))
| ~ hBOOL(hAPP(hAPP(c_member(U_4898),U_4891),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4900,tc_fun(U_4898,tc_HOL_Obool)),U_4902),U_4904))) )
| ( ? [U_4889] :
( ~ hBOOL(hAPP(U_4906,U_4889))
& hBOOL(hAPP(hAPP(c_member(U_4898),U_4889),hAPP(U_4904,sK93(U_4906,U_4904,U_4902,U_4900,U_4898)))) )
& hBOOL(hAPP(hAPP(c_member(U_4900),sK93(U_4906,U_4904,U_4902,U_4900,U_4898)),U_4902)) ) )
& ! [U_4905,U_4903,U_4901,U_4899,U_4897] :
( ! [U_4888] :
( ! [U_4887] :
( hBOOL(hAPP(U_4905,U_4887))
| ~ hBOOL(hAPP(hAPP(c_member(U_4897),U_4887),hAPP(U_4903,U_4888))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4899),U_4888),U_4901)) )
| ( ~ hBOOL(hAPP(U_4905,sK92(U_4905,U_4903,U_4901,U_4899,U_4897)))
& hBOOL(hAPP(hAPP(c_member(U_4897),sK92(U_4905,U_4903,U_4901,U_4899,U_4897)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4899,tc_fun(U_4897,tc_HOL_Obool)),U_4901),U_4903))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_4890,sK93(U_4906,U_4904,U_4902,U_4900,U_4898))],[f_1133_4]) ).
fof(f_1133_6,plain,
( ! [U_4906,U_4904,U_4902,U_4900,U_4898] :
( ! [U_4891] :
( hBOOL(hAPP(U_4906,U_4891))
| ~ hBOOL(hAPP(hAPP(c_member(U_4898),U_4891),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4900,tc_fun(U_4898,tc_HOL_Obool)),U_4902),U_4904))) )
| ( ~ hBOOL(hAPP(U_4906,sK94(U_4906,U_4904,U_4902,U_4900,U_4898)))
& hBOOL(hAPP(hAPP(c_member(U_4898),sK94(U_4906,U_4904,U_4902,U_4900,U_4898)),hAPP(U_4904,sK93(U_4906,U_4904,U_4902,U_4900,U_4898))))
& hBOOL(hAPP(hAPP(c_member(U_4900),sK93(U_4906,U_4904,U_4902,U_4900,U_4898)),U_4902)) ) )
& ! [U_4905,U_4903,U_4901,U_4899,U_4897] :
( ! [U_4888] :
( ! [U_4887] :
( hBOOL(hAPP(U_4905,U_4887))
| ~ hBOOL(hAPP(hAPP(c_member(U_4897),U_4887),hAPP(U_4903,U_4888))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4899),U_4888),U_4901)) )
| ( ~ hBOOL(hAPP(U_4905,sK92(U_4905,U_4903,U_4901,U_4899,U_4897)))
& hBOOL(hAPP(hAPP(c_member(U_4897),sK92(U_4905,U_4903,U_4901,U_4899,U_4897)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4899,tc_fun(U_4897,tc_HOL_Obool)),U_4901),U_4903))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_4889,sK94(U_4906,U_4904,U_4902,U_4900,U_4898))],[f_1133_5]) ).
fof(f_1133_7,plain,
( ! [U_4900,U_4898,U_4902,U_4904,U_4906] :
( ~ hBOOL(hAPP(U_4906,sK94(U_4906,U_4904,U_4902,U_4900,U_4898)))
| ~ sP248(U_4900,U_4898,U_4902,U_4904,U_4906) )
& ! [U_4900,U_4898,U_4902,U_4904,U_4906] :
( hBOOL(hAPP(hAPP(c_member(U_4898),sK94(U_4906,U_4904,U_4902,U_4900,U_4898)),hAPP(U_4904,sK93(U_4906,U_4904,U_4902,U_4900,U_4898))))
| ~ sP248(U_4900,U_4898,U_4902,U_4904,U_4906) )
& ! [U_4900,U_4898,U_4902,U_4904,U_4906] :
( hBOOL(hAPP(hAPP(c_member(U_4900),sK93(U_4906,U_4904,U_4902,U_4900,U_4898)),U_4902))
| ~ sP248(U_4900,U_4898,U_4902,U_4904,U_4906) )
& ! [U_4903,U_4901,U_4897,U_4899,U_4905] :
( ~ hBOOL(hAPP(U_4905,sK92(U_4905,U_4903,U_4901,U_4899,U_4897)))
| ~ sP247(U_4903,U_4901,U_4897,U_4899,U_4905) )
& ! [U_4903,U_4901,U_4897,U_4899,U_4905] :
( hBOOL(hAPP(hAPP(c_member(U_4897),sK92(U_4905,U_4903,U_4901,U_4899,U_4897)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4899,tc_fun(U_4897,tc_HOL_Obool)),U_4901),U_4903)))
| ~ sP247(U_4903,U_4901,U_4897,U_4899,U_4905) )
& ! [U_4900,U_4898,U_4902,U_4891,U_4904,U_4906] :
( hBOOL(hAPP(U_4906,U_4891))
| ~ hBOOL(hAPP(hAPP(c_member(U_4898),U_4891),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4900,tc_fun(U_4898,tc_HOL_Obool)),U_4902),U_4904)))
| sP248(U_4900,U_4898,U_4902,U_4904,U_4906) )
& ! [U_4903,U_4887,U_4901,U_4888,U_4897,U_4899,U_4905] :
( hBOOL(hAPP(U_4905,U_4887))
| ~ hBOOL(hAPP(hAPP(c_member(U_4897),U_4887),hAPP(U_4903,U_4888)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4899),U_4888),U_4901))
| sP247(U_4903,U_4901,U_4897,U_4899,U_4905) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP247,sP248])],[f_1133_6]) ).
cnf(f_1133_8,plain,
( hBOOL(hAPP(U_4905,U_4887))
| ~ hBOOL(hAPP(hAPP(c_member(U_4897),U_4887),hAPP(U_4903,U_4888)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4899),U_4888),U_4901))
| sP247(U_4903,U_4901,U_4897,U_4899,U_4905) ),
inference(clausify,[status(thm)],[f_1133_7]) ).
cnf(f_1133_9,plain,
( hBOOL(hAPP(U_4906,U_4891))
| ~ hBOOL(hAPP(hAPP(c_member(U_4898),U_4891),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4900,tc_fun(U_4898,tc_HOL_Obool)),U_4902),U_4904)))
| sP248(U_4900,U_4898,U_4902,U_4904,U_4906) ),
inference(clausify,[status(thm)],[f_1133_7]) ).
cnf(f_1133_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_4897),sK92(U_4905,U_4903,U_4901,U_4899,U_4897)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4899,tc_fun(U_4897,tc_HOL_Obool)),U_4901),U_4903)))
| ~ sP247(U_4903,U_4901,U_4897,U_4899,U_4905) ),
inference(clausify,[status(thm)],[f_1133_7]) ).
cnf(f_1133_11,plain,
( ~ hBOOL(hAPP(U_4905,sK92(U_4905,U_4903,U_4901,U_4899,U_4897)))
| ~ sP247(U_4903,U_4901,U_4897,U_4899,U_4905) ),
inference(clausify,[status(thm)],[f_1133_7]) ).
cnf(f_1133_12,plain,
( hBOOL(hAPP(hAPP(c_member(U_4900),sK93(U_4906,U_4904,U_4902,U_4900,U_4898)),U_4902))
| ~ sP248(U_4900,U_4898,U_4902,U_4904,U_4906) ),
inference(clausify,[status(thm)],[f_1133_7]) ).
cnf(f_1133_13,plain,
( hBOOL(hAPP(hAPP(c_member(U_4898),sK94(U_4906,U_4904,U_4902,U_4900,U_4898)),hAPP(U_4904,sK93(U_4906,U_4904,U_4902,U_4900,U_4898))))
| ~ sP248(U_4900,U_4898,U_4902,U_4904,U_4906) ),
inference(clausify,[status(thm)],[f_1133_7]) ).
cnf(f_1133_14,plain,
( ~ hBOOL(hAPP(U_4906,sK94(U_4906,U_4904,U_4902,U_4900,U_4898)))
| ~ sP248(U_4900,U_4898,U_4902,U_4904,U_4906) ),
inference(clausify,[status(thm)],[f_1133_7]) ).
fof(f_1134_1,plain,
! [V_C_2,V_B_2,T_e,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,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_1134_2,plain,
! [U_4912,U_4911,U_4910,U_4909,U_4908,U_4907] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4907,tc_fun(U_4908,tc_HOL_Obool)),U_4909),hAPP(hAPP(c_COMBC(U_4907,tc_fun(U_4910,tc_fun(U_4908,tc_HOL_Obool)),tc_fun(U_4908,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_4910,tc_HOL_Obool),tc_fun(tc_fun(U_4910,tc_fun(U_4908,tc_HOL_Obool)),tc_fun(U_4908,tc_HOL_Obool)),U_4907),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4910,tc_fun(U_4908,tc_HOL_Obool))),U_4911)),U_4912)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4910,tc_fun(U_4908,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4907,tc_fun(U_4910,tc_HOL_Obool)),U_4909),U_4911)),U_4912),
inference(variable_rename,[status(thm)],[f_1134_1]) ).
fof(f_1134_3,plain,
! [U_4908,U_4910,U_4909,U_4907,U_4911,U_4912] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4907,tc_fun(U_4908,tc_HOL_Obool)),U_4909),hAPP(hAPP(c_COMBC(U_4907,tc_fun(U_4910,tc_fun(U_4908,tc_HOL_Obool)),tc_fun(U_4908,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_4910,tc_HOL_Obool),tc_fun(tc_fun(U_4910,tc_fun(U_4908,tc_HOL_Obool)),tc_fun(U_4908,tc_HOL_Obool)),U_4907),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4910,tc_fun(U_4908,tc_HOL_Obool))),U_4911)),U_4912)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4910,tc_fun(U_4908,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4907,tc_fun(U_4910,tc_HOL_Obool)),U_4909),U_4911)),U_4912),
inference(definitional_conversion,[status(esa)],[f_1134_2]) ).
cnf(f_1134_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4907,tc_fun(U_4908,tc_HOL_Obool)),U_4909),hAPP(hAPP(c_COMBC(U_4907,tc_fun(U_4910,tc_fun(U_4908,tc_HOL_Obool)),tc_fun(U_4908,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_4910,tc_HOL_Obool),tc_fun(tc_fun(U_4910,tc_fun(U_4908,tc_HOL_Obool)),tc_fun(U_4908,tc_HOL_Obool)),U_4907),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4910,tc_fun(U_4908,tc_HOL_Obool))),U_4911)),U_4912)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4910,tc_fun(U_4908,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4907,tc_fun(U_4910,tc_HOL_Obool)),U_4909),U_4911)),U_4912),
inference(clausify,[status(thm)],[f_1134_3]) ).
fof(f_1135_1,plain,
! [V_b_2,V_B_2,V_A_2,T_d,T_c] :
( ( hBOOL(hAPP(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_b_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(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_b_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP1__iff]) ).
fof(f_1135_2,plain,
! [U_4919,U_4918,U_4917,U_4916,U_4915] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4915,tc_fun(U_4916,tc_HOL_Obool)),U_4917),U_4918),U_4919))
| ! [U_4914] :
( ~ hBOOL(hAPP(hAPP(U_4918,U_4914),U_4919))
| ~ hBOOL(hAPP(hAPP(c_member(U_4915),U_4914),U_4917)) ) )
& ( ? [U_4913] :
( hBOOL(hAPP(hAPP(U_4918,U_4913),U_4919))
& hBOOL(hAPP(hAPP(c_member(U_4915),U_4913),U_4917)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4915,tc_fun(U_4916,tc_HOL_Obool)),U_4917),U_4918),U_4919)) ) ),
inference(variable_rename,[status(thm)],[f_1135_1]) ).
fof(f_1135_3,plain,
( ! [U_4929,U_4927,U_4925,U_4923,U_4921] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4921,tc_fun(U_4923,tc_HOL_Obool)),U_4925),U_4927),U_4929))
| ! [U_4914] :
( ~ hBOOL(hAPP(hAPP(U_4927,U_4914),U_4929))
| ~ hBOOL(hAPP(hAPP(c_member(U_4921),U_4914),U_4925)) ) )
& ! [U_4928,U_4926,U_4924,U_4922,U_4920] :
( ? [U_4913] :
( hBOOL(hAPP(hAPP(U_4926,U_4913),U_4928))
& hBOOL(hAPP(hAPP(c_member(U_4920),U_4913),U_4924)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4920,tc_fun(U_4922,tc_HOL_Obool)),U_4924),U_4926),U_4928)) ) ),
inference(miniscope,[status(thm)],[f_1135_2]) ).
fof(f_1135_4,plain,
( ! [U_4929,U_4927,U_4925,U_4923,U_4921] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4921,tc_fun(U_4923,tc_HOL_Obool)),U_4925),U_4927),U_4929))
| ! [U_4914] :
( ~ hBOOL(hAPP(hAPP(U_4927,U_4914),U_4929))
| ~ hBOOL(hAPP(hAPP(c_member(U_4921),U_4914),U_4925)) ) )
& ! [U_4928,U_4926,U_4924,U_4922,U_4920] :
( ( hBOOL(hAPP(hAPP(U_4926,sK95(U_4928,U_4926,U_4924,U_4922,U_4920)),U_4928))
& hBOOL(hAPP(hAPP(c_member(U_4920),sK95(U_4928,U_4926,U_4924,U_4922,U_4920)),U_4924)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4920,tc_fun(U_4922,tc_HOL_Obool)),U_4924),U_4926),U_4928)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_4913,sK95(U_4928,U_4926,U_4924,U_4922,U_4920))],[f_1135_3]) ).
fof(f_1135_5,plain,
( ! [U_4926,U_4924,U_4922,U_4920,U_4928] :
( hBOOL(hAPP(hAPP(U_4926,sK95(U_4928,U_4926,U_4924,U_4922,U_4920)),U_4928))
| ~ sP249(U_4926,U_4924,U_4922,U_4920,U_4928) )
& ! [U_4926,U_4924,U_4922,U_4920,U_4928] :
( hBOOL(hAPP(hAPP(c_member(U_4920),sK95(U_4928,U_4926,U_4924,U_4922,U_4920)),U_4924))
| ~ sP249(U_4926,U_4924,U_4922,U_4920,U_4928) )
& ! [U_4914,U_4921,U_4923,U_4927,U_4925,U_4929] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4921,tc_fun(U_4923,tc_HOL_Obool)),U_4925),U_4927),U_4929))
| ~ hBOOL(hAPP(hAPP(U_4927,U_4914),U_4929))
| ~ hBOOL(hAPP(hAPP(c_member(U_4921),U_4914),U_4925)) )
& ! [U_4926,U_4924,U_4922,U_4920,U_4928] :
( sP249(U_4926,U_4924,U_4922,U_4920,U_4928)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4920,tc_fun(U_4922,tc_HOL_Obool)),U_4924),U_4926),U_4928)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP249])],[f_1135_4]) ).
cnf(f_1135_6,plain,
( sP249(U_4926,U_4924,U_4922,U_4920,U_4928)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4920,tc_fun(U_4922,tc_HOL_Obool)),U_4924),U_4926),U_4928)) ),
inference(clausify,[status(thm)],[f_1135_5]) ).
cnf(f_1135_7,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4921,tc_fun(U_4923,tc_HOL_Obool)),U_4925),U_4927),U_4929))
| ~ hBOOL(hAPP(hAPP(U_4927,U_4914),U_4929))
| ~ hBOOL(hAPP(hAPP(c_member(U_4921),U_4914),U_4925)) ),
inference(clausify,[status(thm)],[f_1135_5]) ).
cnf(f_1135_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_4920),sK95(U_4928,U_4926,U_4924,U_4922,U_4920)),U_4924))
| ~ sP249(U_4926,U_4924,U_4922,U_4920,U_4928) ),
inference(clausify,[status(thm)],[f_1135_5]) ).
cnf(f_1135_9,plain,
( hBOOL(hAPP(hAPP(U_4926,sK95(U_4928,U_4926,U_4924,U_4922,U_4920)),U_4928))
| ~ sP249(U_4926,U_4924,U_4922,U_4920,U_4928) ),
inference(clausify,[status(thm)],[f_1135_5]) ).
fof(f_1136_1,plain,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP2__iff]) ).
fof(f_1136_2,plain,
! [U_4938,U_4937,U_4936,U_4935,U_4934,U_4933,U_4932] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4932,tc_fun(U_4933,tc_fun(U_4934,tc_HOL_Obool))),U_4935),U_4936),U_4937),U_4938))
| ! [U_4931] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_4936,U_4931),U_4937),U_4938))
| ~ hBOOL(hAPP(hAPP(c_member(U_4932),U_4931),U_4935)) ) )
& ( ? [U_4930] :
( hBOOL(hAPP(hAPP(hAPP(U_4936,U_4930),U_4937),U_4938))
& hBOOL(hAPP(hAPP(c_member(U_4932),U_4930),U_4935)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4932,tc_fun(U_4933,tc_fun(U_4934,tc_HOL_Obool))),U_4935),U_4936),U_4937),U_4938)) ) ),
inference(variable_rename,[status(thm)],[f_1136_1]) ).
fof(f_1136_3,plain,
( ! [U_4952,U_4950,U_4948,U_4946,U_4944,U_4942,U_4940] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4940,tc_fun(U_4942,tc_fun(U_4944,tc_HOL_Obool))),U_4946),U_4948),U_4950),U_4952))
| ! [U_4931] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_4948,U_4931),U_4950),U_4952))
| ~ hBOOL(hAPP(hAPP(c_member(U_4940),U_4931),U_4946)) ) )
& ! [U_4951,U_4949,U_4947,U_4945,U_4943,U_4941,U_4939] :
( ? [U_4930] :
( hBOOL(hAPP(hAPP(hAPP(U_4947,U_4930),U_4949),U_4951))
& hBOOL(hAPP(hAPP(c_member(U_4939),U_4930),U_4945)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4939,tc_fun(U_4941,tc_fun(U_4943,tc_HOL_Obool))),U_4945),U_4947),U_4949),U_4951)) ) ),
inference(miniscope,[status(thm)],[f_1136_2]) ).
fof(f_1136_4,plain,
( ! [U_4952,U_4950,U_4948,U_4946,U_4944,U_4942,U_4940] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4940,tc_fun(U_4942,tc_fun(U_4944,tc_HOL_Obool))),U_4946),U_4948),U_4950),U_4952))
| ! [U_4931] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_4948,U_4931),U_4950),U_4952))
| ~ hBOOL(hAPP(hAPP(c_member(U_4940),U_4931),U_4946)) ) )
& ! [U_4951,U_4949,U_4947,U_4945,U_4943,U_4941,U_4939] :
( ( hBOOL(hAPP(hAPP(hAPP(U_4947,sK96(U_4951,U_4949,U_4947,U_4945,U_4943,U_4941,U_4939)),U_4949),U_4951))
& hBOOL(hAPP(hAPP(c_member(U_4939),sK96(U_4951,U_4949,U_4947,U_4945,U_4943,U_4941,U_4939)),U_4945)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4939,tc_fun(U_4941,tc_fun(U_4943,tc_HOL_Obool))),U_4945),U_4947),U_4949),U_4951)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_4930,sK96(U_4951,U_4949,U_4947,U_4945,U_4943,U_4941,U_4939))],[f_1136_3]) ).
fof(f_1136_5,plain,
( ! [U_4943,U_4941,U_4939,U_4947,U_4951,U_4945,U_4949] :
( hBOOL(hAPP(hAPP(hAPP(U_4947,sK96(U_4951,U_4949,U_4947,U_4945,U_4943,U_4941,U_4939)),U_4949),U_4951))
| ~ sP250(U_4943,U_4941,U_4939,U_4947,U_4951,U_4945,U_4949) )
& ! [U_4943,U_4941,U_4939,U_4947,U_4951,U_4945,U_4949] :
( hBOOL(hAPP(hAPP(c_member(U_4939),sK96(U_4951,U_4949,U_4947,U_4945,U_4943,U_4941,U_4939)),U_4945))
| ~ sP250(U_4943,U_4941,U_4939,U_4947,U_4951,U_4945,U_4949) )
& ! [U_4931,U_4940,U_4942,U_4944,U_4946,U_4950,U_4948,U_4952] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4940,tc_fun(U_4942,tc_fun(U_4944,tc_HOL_Obool))),U_4946),U_4948),U_4950),U_4952))
| ~ hBOOL(hAPP(hAPP(hAPP(U_4948,U_4931),U_4950),U_4952))
| ~ hBOOL(hAPP(hAPP(c_member(U_4940),U_4931),U_4946)) )
& ! [U_4943,U_4941,U_4939,U_4947,U_4951,U_4945,U_4949] :
( sP250(U_4943,U_4941,U_4939,U_4947,U_4951,U_4945,U_4949)
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4939,tc_fun(U_4941,tc_fun(U_4943,tc_HOL_Obool))),U_4945),U_4947),U_4949),U_4951)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP250])],[f_1136_4]) ).
cnf(f_1136_6,plain,
( sP250(U_4943,U_4941,U_4939,U_4947,U_4951,U_4945,U_4949)
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4939,tc_fun(U_4941,tc_fun(U_4943,tc_HOL_Obool))),U_4945),U_4947),U_4949),U_4951)) ),
inference(clausify,[status(thm)],[f_1136_5]) ).
cnf(f_1136_7,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4940,tc_fun(U_4942,tc_fun(U_4944,tc_HOL_Obool))),U_4946),U_4948),U_4950),U_4952))
| ~ hBOOL(hAPP(hAPP(hAPP(U_4948,U_4931),U_4950),U_4952))
| ~ hBOOL(hAPP(hAPP(c_member(U_4940),U_4931),U_4946)) ),
inference(clausify,[status(thm)],[f_1136_5]) ).
cnf(f_1136_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_4939),sK96(U_4951,U_4949,U_4947,U_4945,U_4943,U_4941,U_4939)),U_4945))
| ~ sP250(U_4943,U_4941,U_4939,U_4947,U_4951,U_4945,U_4949) ),
inference(clausify,[status(thm)],[f_1136_5]) ).
cnf(f_1136_9,plain,
( hBOOL(hAPP(hAPP(hAPP(U_4947,sK96(U_4951,U_4949,U_4947,U_4945,U_4943,U_4941,U_4939)),U_4949),U_4951))
| ~ sP250(U_4943,U_4941,U_4939,U_4947,U_4951,U_4945,U_4949) ),
inference(clausify,[status(thm)],[f_1136_5]) ).
fof(f_1137_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_1137_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_1137_1]) ).
cnf(f_1137_3,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1137_2]) ).
fof(f_1138_1,plain,
! [V_B_2,V_A_2,T_d,V_b_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_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)))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_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))) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__iff]) ).
fof(f_1138_2,plain,
! [U_4959,U_4958,U_4957,U_4956,U_4955] :
( ( hBOOL(hAPP(hAPP(c_member(U_4955),U_4956),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4957,tc_fun(U_4955,tc_HOL_Obool)),U_4958),U_4959)))
| ! [U_4954] :
( ~ hBOOL(hAPP(hAPP(c_member(U_4955),U_4956),hAPP(U_4959,U_4954)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4957),U_4954),U_4958)) ) )
& ( ? [U_4953] :
( hBOOL(hAPP(hAPP(c_member(U_4955),U_4956),hAPP(U_4959,U_4953)))
& hBOOL(hAPP(hAPP(c_member(U_4957),U_4953),U_4958)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4955),U_4956),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4957,tc_fun(U_4955,tc_HOL_Obool)),U_4958),U_4959))) ) ),
inference(variable_rename,[status(thm)],[f_1138_1]) ).
fof(f_1138_3,plain,
( ! [U_4969,U_4967,U_4965,U_4963,U_4961] :
( hBOOL(hAPP(hAPP(c_member(U_4961),U_4963),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4965,tc_fun(U_4961,tc_HOL_Obool)),U_4967),U_4969)))
| ! [U_4954] :
( ~ hBOOL(hAPP(hAPP(c_member(U_4961),U_4963),hAPP(U_4969,U_4954)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4965),U_4954),U_4967)) ) )
& ! [U_4968,U_4966,U_4964,U_4962,U_4960] :
( ? [U_4953] :
( hBOOL(hAPP(hAPP(c_member(U_4960),U_4962),hAPP(U_4968,U_4953)))
& hBOOL(hAPP(hAPP(c_member(U_4964),U_4953),U_4966)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4960),U_4962),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4964,tc_fun(U_4960,tc_HOL_Obool)),U_4966),U_4968))) ) ),
inference(miniscope,[status(thm)],[f_1138_2]) ).
fof(f_1138_4,plain,
( ! [U_4969,U_4967,U_4965,U_4963,U_4961] :
( hBOOL(hAPP(hAPP(c_member(U_4961),U_4963),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4965,tc_fun(U_4961,tc_HOL_Obool)),U_4967),U_4969)))
| ! [U_4954] :
( ~ hBOOL(hAPP(hAPP(c_member(U_4961),U_4963),hAPP(U_4969,U_4954)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4965),U_4954),U_4967)) ) )
& ! [U_4968,U_4966,U_4964,U_4962,U_4960] :
( ( hBOOL(hAPP(hAPP(c_member(U_4960),U_4962),hAPP(U_4968,sK97(U_4968,U_4966,U_4964,U_4962,U_4960))))
& hBOOL(hAPP(hAPP(c_member(U_4964),sK97(U_4968,U_4966,U_4964,U_4962,U_4960)),U_4966)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_4960),U_4962),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4964,tc_fun(U_4960,tc_HOL_Obool)),U_4966),U_4968))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_4953,sK97(U_4968,U_4966,U_4964,U_4962,U_4960))],[f_1138_3]) ).
fof(f_1138_5,plain,
( ! [U_4964,U_4962,U_4960,U_4968,U_4966] :
( hBOOL(hAPP(hAPP(c_member(U_4960),U_4962),hAPP(U_4968,sK97(U_4968,U_4966,U_4964,U_4962,U_4960))))
| ~ sP251(U_4964,U_4962,U_4960,U_4968,U_4966) )
& ! [U_4964,U_4962,U_4960,U_4968,U_4966] :
( hBOOL(hAPP(hAPP(c_member(U_4964),sK97(U_4968,U_4966,U_4964,U_4962,U_4960)),U_4966))
| ~ sP251(U_4964,U_4962,U_4960,U_4968,U_4966) )
& ! [U_4954,U_4963,U_4961,U_4967,U_4965,U_4969] :
( hBOOL(hAPP(hAPP(c_member(U_4961),U_4963),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4965,tc_fun(U_4961,tc_HOL_Obool)),U_4967),U_4969)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4961),U_4963),hAPP(U_4969,U_4954)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4965),U_4954),U_4967)) )
& ! [U_4964,U_4962,U_4960,U_4968,U_4966] :
( sP251(U_4964,U_4962,U_4960,U_4968,U_4966)
| ~ hBOOL(hAPP(hAPP(c_member(U_4960),U_4962),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4964,tc_fun(U_4960,tc_HOL_Obool)),U_4966),U_4968))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP251])],[f_1138_4]) ).
cnf(f_1138_6,plain,
( sP251(U_4964,U_4962,U_4960,U_4968,U_4966)
| ~ hBOOL(hAPP(hAPP(c_member(U_4960),U_4962),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4964,tc_fun(U_4960,tc_HOL_Obool)),U_4966),U_4968))) ),
inference(clausify,[status(thm)],[f_1138_5]) ).
cnf(f_1138_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_4961),U_4963),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4965,tc_fun(U_4961,tc_HOL_Obool)),U_4967),U_4969)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4961),U_4963),hAPP(U_4969,U_4954)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4965),U_4954),U_4967)) ),
inference(clausify,[status(thm)],[f_1138_5]) ).
cnf(f_1138_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_4964),sK97(U_4968,U_4966,U_4964,U_4962,U_4960)),U_4966))
| ~ sP251(U_4964,U_4962,U_4960,U_4968,U_4966) ),
inference(clausify,[status(thm)],[f_1138_5]) ).
cnf(f_1138_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_4960),U_4962),hAPP(U_4968,sK97(U_4968,U_4966,U_4964,U_4962,U_4960))))
| ~ sP251(U_4964,U_4962,U_4960,U_4968,U_4966) ),
inference(clausify,[status(thm)],[f_1138_5]) ).
fof(f_1139_1,plain,
! [V_B_2,V_A_2,T_c,T_d] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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))
| ? [B_x] :
( hAPP(V_B_2,B_x) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_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) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I2_J]) ).
fof(f_1139_2,plain,
! [U_4975,U_4974,U_4973,U_4972] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4972,tc_fun(U_4973,tc_HOL_Obool)),U_4974),U_4975) = c_Orderings_Obot__class_Obot(tc_fun(U_4973,tc_HOL_Obool))
| ? [U_4971] :
( hAPP(U_4975,U_4971) != c_Orderings_Obot__class_Obot(tc_fun(U_4973,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_4972),U_4971),U_4974)) ) )
& ( ! [U_4970] :
( hAPP(U_4975,U_4970) = c_Orderings_Obot__class_Obot(tc_fun(U_4973,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4972),U_4970),U_4974)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4972,tc_fun(U_4973,tc_HOL_Obool)),U_4974),U_4975) != c_Orderings_Obot__class_Obot(tc_fun(U_4973,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1139_1]) ).
fof(f_1139_3,plain,
( ! [U_4983,U_4981,U_4979,U_4977] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4977,tc_fun(U_4979,tc_HOL_Obool)),U_4981),U_4983) = c_Orderings_Obot__class_Obot(tc_fun(U_4979,tc_HOL_Obool))
| ? [U_4971] :
( hAPP(U_4983,U_4971) != c_Orderings_Obot__class_Obot(tc_fun(U_4979,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_4977),U_4971),U_4981)) ) )
& ! [U_4982,U_4980,U_4978,U_4976] :
( ! [U_4970] :
( hAPP(U_4982,U_4970) = c_Orderings_Obot__class_Obot(tc_fun(U_4978,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4976),U_4970),U_4980)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4976,tc_fun(U_4978,tc_HOL_Obool)),U_4980),U_4982) != c_Orderings_Obot__class_Obot(tc_fun(U_4978,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1139_2]) ).
fof(f_1139_4,plain,
( ! [U_4983,U_4981,U_4979,U_4977] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4977,tc_fun(U_4979,tc_HOL_Obool)),U_4981),U_4983) = c_Orderings_Obot__class_Obot(tc_fun(U_4979,tc_HOL_Obool))
| ( hAPP(U_4983,sK98(U_4983,U_4981,U_4979,U_4977)) != c_Orderings_Obot__class_Obot(tc_fun(U_4979,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_4977),sK98(U_4983,U_4981,U_4979,U_4977)),U_4981)) ) )
& ! [U_4982,U_4980,U_4978,U_4976] :
( ! [U_4970] :
( hAPP(U_4982,U_4970) = c_Orderings_Obot__class_Obot(tc_fun(U_4978,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4976),U_4970),U_4980)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4976,tc_fun(U_4978,tc_HOL_Obool)),U_4980),U_4982) != c_Orderings_Obot__class_Obot(tc_fun(U_4978,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_4971,sK98(U_4983,U_4981,U_4979,U_4977))],[f_1139_3]) ).
fof(f_1139_5,plain,
( ! [U_4977,U_4979,U_4983,U_4981] :
( hAPP(U_4983,sK98(U_4983,U_4981,U_4979,U_4977)) != c_Orderings_Obot__class_Obot(tc_fun(U_4979,tc_HOL_Obool))
| ~ sP252(U_4977,U_4979,U_4983,U_4981) )
& ! [U_4977,U_4979,U_4983,U_4981] :
( hBOOL(hAPP(hAPP(c_member(U_4977),sK98(U_4983,U_4981,U_4979,U_4977)),U_4981))
| ~ sP252(U_4977,U_4979,U_4983,U_4981) )
& ! [U_4977,U_4979,U_4983,U_4981] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4977,tc_fun(U_4979,tc_HOL_Obool)),U_4981),U_4983) = c_Orderings_Obot__class_Obot(tc_fun(U_4979,tc_HOL_Obool))
| sP252(U_4977,U_4979,U_4983,U_4981) )
& ! [U_4970,U_4980,U_4978,U_4982,U_4976] :
( hAPP(U_4982,U_4970) = c_Orderings_Obot__class_Obot(tc_fun(U_4978,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4976),U_4970),U_4980))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4976,tc_fun(U_4978,tc_HOL_Obool)),U_4980),U_4982) != c_Orderings_Obot__class_Obot(tc_fun(U_4978,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP252])],[f_1139_4]) ).
cnf(f_1139_6,plain,
( hAPP(U_4982,U_4970) = c_Orderings_Obot__class_Obot(tc_fun(U_4978,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_4976),U_4970),U_4980))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4976,tc_fun(U_4978,tc_HOL_Obool)),U_4980),U_4982) != c_Orderings_Obot__class_Obot(tc_fun(U_4978,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1139_5]) ).
cnf(f_1139_7,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4977,tc_fun(U_4979,tc_HOL_Obool)),U_4981),U_4983) = c_Orderings_Obot__class_Obot(tc_fun(U_4979,tc_HOL_Obool))
| sP252(U_4977,U_4979,U_4983,U_4981) ),
inference(clausify,[status(thm)],[f_1139_5]) ).
cnf(f_1139_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_4977),sK98(U_4983,U_4981,U_4979,U_4977)),U_4981))
| ~ sP252(U_4977,U_4979,U_4983,U_4981) ),
inference(clausify,[status(thm)],[f_1139_5]) ).
cnf(f_1139_9,plain,
( hAPP(U_4983,sK98(U_4983,U_4981,U_4979,U_4977)) != c_Orderings_Obot__class_Obot(tc_fun(U_4979,tc_HOL_Obool))
| ~ sP252(U_4977,U_4979,U_4983,U_4981) ),
inference(clausify,[status(thm)],[f_1139_5]) ).
fof(f_1140_1,plain,
! [V_c_2,T_d,T_c,V_A_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_c_2)) = V_c_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__constant]) ).
fof(f_1140_2,plain,
! [U_4987,U_4986,U_4985,U_4984] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4985,tc_fun(U_4986,tc_HOL_Obool)),U_4984),hAPP(c_COMBK(tc_fun(U_4986,tc_HOL_Obool),U_4985),U_4987)) = U_4987
| U_4984 = c_Orderings_Obot__class_Obot(tc_fun(U_4985,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4985,tc_fun(U_4986,tc_HOL_Obool)),U_4984),hAPP(c_COMBK(tc_fun(U_4986,tc_HOL_Obool),U_4985),U_4987)) = c_Orderings_Obot__class_Obot(tc_fun(U_4986,tc_HOL_Obool))
| U_4984 != c_Orderings_Obot__class_Obot(tc_fun(U_4985,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1140_1]) ).
fof(f_1140_3,plain,
( ! [U_4995,U_4993,U_4991,U_4989] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4991,tc_fun(U_4993,tc_HOL_Obool)),U_4989),hAPP(c_COMBK(tc_fun(U_4993,tc_HOL_Obool),U_4991),U_4995)) = U_4995
| U_4989 = c_Orderings_Obot__class_Obot(tc_fun(U_4991,tc_HOL_Obool)) )
& ! [U_4994,U_4992,U_4990,U_4988] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4990,tc_fun(U_4992,tc_HOL_Obool)),U_4988),hAPP(c_COMBK(tc_fun(U_4992,tc_HOL_Obool),U_4990),U_4994)) = c_Orderings_Obot__class_Obot(tc_fun(U_4992,tc_HOL_Obool))
| U_4988 != c_Orderings_Obot__class_Obot(tc_fun(U_4990,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1140_2]) ).
fof(f_1140_4,plain,
( ! [U_4989,U_4991,U_4993,U_4995] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4991,tc_fun(U_4993,tc_HOL_Obool)),U_4989),hAPP(c_COMBK(tc_fun(U_4993,tc_HOL_Obool),U_4991),U_4995)) = U_4995
| U_4989 = c_Orderings_Obot__class_Obot(tc_fun(U_4991,tc_HOL_Obool)) )
& ! [U_4988,U_4992,U_4990,U_4994] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4990,tc_fun(U_4992,tc_HOL_Obool)),U_4988),hAPP(c_COMBK(tc_fun(U_4992,tc_HOL_Obool),U_4990),U_4994)) = c_Orderings_Obot__class_Obot(tc_fun(U_4992,tc_HOL_Obool))
| U_4988 != c_Orderings_Obot__class_Obot(tc_fun(U_4990,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1140_3]) ).
cnf(f_1140_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4990,tc_fun(U_4992,tc_HOL_Obool)),U_4988),hAPP(c_COMBK(tc_fun(U_4992,tc_HOL_Obool),U_4990),U_4994)) = c_Orderings_Obot__class_Obot(tc_fun(U_4992,tc_HOL_Obool))
| U_4988 != c_Orderings_Obot__class_Obot(tc_fun(U_4990,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1140_4]) ).
cnf(f_1140_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4991,tc_fun(U_4993,tc_HOL_Obool)),U_4989),hAPP(c_COMBK(tc_fun(U_4993,tc_HOL_Obool),U_4991),U_4995)) = U_4995
| U_4989 = c_Orderings_Obot__class_Obot(tc_fun(U_4991,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1140_4]) ).
fof(f_1141_1,plain,
! [V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_d),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_UN__empty2]) ).
fof(f_1141_2,plain,
! [U_4998,U_4997,U_4996] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4996,tc_fun(U_4997,tc_HOL_Obool)),U_4998),hAPP(c_COMBK(tc_fun(U_4997,tc_HOL_Obool),U_4996),c_Orderings_Obot__class_Obot(tc_fun(U_4997,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_4997,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1141_1]) ).
fof(f_1141_3,plain,
! [U_4996,U_4997,U_4998] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4996,tc_fun(U_4997,tc_HOL_Obool)),U_4998),hAPP(c_COMBK(tc_fun(U_4997,tc_HOL_Obool),U_4996),c_Orderings_Obot__class_Obot(tc_fun(U_4997,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_4997,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1141_2]) ).
cnf(f_1141_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_4996,tc_fun(U_4997,tc_HOL_Obool)),U_4998),hAPP(c_COMBK(tc_fun(U_4997,tc_HOL_Obool),U_4996),c_Orderings_Obot__class_Obot(tc_fun(U_4997,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_4997,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1141_3]) ).
fof(f_1142_1,plain,
! [V_B_2,V_A_2,T_d,T_c] :
( ( c_Orderings_Obot__class_Obot(tc_fun(T_c,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)
| ? [B_x] :
( hAPP(V_B_2,B_x) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
| c_Orderings_Obot__class_Obot(tc_fun(T_c,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) ) ),
inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I1_J]) ).
fof(f_1142_2,plain,
! [U_5004,U_5003,U_5002,U_5001] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_5001,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5002,tc_fun(U_5001,tc_HOL_Obool)),U_5003),U_5004)
| ? [U_5000] :
( hAPP(U_5004,U_5000) != c_Orderings_Obot__class_Obot(tc_fun(U_5001,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_5002),U_5000),U_5003)) ) )
& ( ! [U_4999] :
( hAPP(U_5004,U_4999) = c_Orderings_Obot__class_Obot(tc_fun(U_5001,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5002),U_4999),U_5003)) )
| c_Orderings_Obot__class_Obot(tc_fun(U_5001,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5002,tc_fun(U_5001,tc_HOL_Obool)),U_5003),U_5004) ) ),
inference(variable_rename,[status(thm)],[f_1142_1]) ).
fof(f_1142_3,plain,
( ! [U_5012,U_5010,U_5008,U_5006] :
( c_Orderings_Obot__class_Obot(tc_fun(U_5006,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5008,tc_fun(U_5006,tc_HOL_Obool)),U_5010),U_5012)
| ? [U_5000] :
( hAPP(U_5012,U_5000) != c_Orderings_Obot__class_Obot(tc_fun(U_5006,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_5008),U_5000),U_5010)) ) )
& ! [U_5011,U_5009,U_5007,U_5005] :
( ! [U_4999] :
( hAPP(U_5011,U_4999) = c_Orderings_Obot__class_Obot(tc_fun(U_5005,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5007),U_4999),U_5009)) )
| c_Orderings_Obot__class_Obot(tc_fun(U_5005,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5007,tc_fun(U_5005,tc_HOL_Obool)),U_5009),U_5011) ) ),
inference(miniscope,[status(thm)],[f_1142_2]) ).
fof(f_1142_4,plain,
( ! [U_5012,U_5010,U_5008,U_5006] :
( c_Orderings_Obot__class_Obot(tc_fun(U_5006,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5008,tc_fun(U_5006,tc_HOL_Obool)),U_5010),U_5012)
| ( hAPP(U_5012,sK99(U_5012,U_5010,U_5008,U_5006)) != c_Orderings_Obot__class_Obot(tc_fun(U_5006,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_5008),sK99(U_5012,U_5010,U_5008,U_5006)),U_5010)) ) )
& ! [U_5011,U_5009,U_5007,U_5005] :
( ! [U_4999] :
( hAPP(U_5011,U_4999) = c_Orderings_Obot__class_Obot(tc_fun(U_5005,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5007),U_4999),U_5009)) )
| c_Orderings_Obot__class_Obot(tc_fun(U_5005,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5007,tc_fun(U_5005,tc_HOL_Obool)),U_5009),U_5011) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_5000,sK99(U_5012,U_5010,U_5008,U_5006))],[f_1142_3]) ).
fof(f_1142_5,plain,
( ! [U_5010,U_5008,U_5006,U_5012] :
( hAPP(U_5012,sK99(U_5012,U_5010,U_5008,U_5006)) != c_Orderings_Obot__class_Obot(tc_fun(U_5006,tc_HOL_Obool))
| ~ sP253(U_5010,U_5008,U_5006,U_5012) )
& ! [U_5010,U_5008,U_5006,U_5012] :
( hBOOL(hAPP(hAPP(c_member(U_5008),sK99(U_5012,U_5010,U_5008,U_5006)),U_5010))
| ~ sP253(U_5010,U_5008,U_5006,U_5012) )
& ! [U_5010,U_5008,U_5006,U_5012] :
( c_Orderings_Obot__class_Obot(tc_fun(U_5006,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5008,tc_fun(U_5006,tc_HOL_Obool)),U_5010),U_5012)
| sP253(U_5010,U_5008,U_5006,U_5012) )
& ! [U_5011,U_4999,U_5005,U_5009,U_5007] :
( hAPP(U_5011,U_4999) = c_Orderings_Obot__class_Obot(tc_fun(U_5005,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5007),U_4999),U_5009))
| c_Orderings_Obot__class_Obot(tc_fun(U_5005,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5007,tc_fun(U_5005,tc_HOL_Obool)),U_5009),U_5011) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP253])],[f_1142_4]) ).
cnf(f_1142_6,plain,
( hAPP(U_5011,U_4999) = c_Orderings_Obot__class_Obot(tc_fun(U_5005,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5007),U_4999),U_5009))
| c_Orderings_Obot__class_Obot(tc_fun(U_5005,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5007,tc_fun(U_5005,tc_HOL_Obool)),U_5009),U_5011) ),
inference(clausify,[status(thm)],[f_1142_5]) ).
cnf(f_1142_7,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_5006,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5008,tc_fun(U_5006,tc_HOL_Obool)),U_5010),U_5012)
| sP253(U_5010,U_5008,U_5006,U_5012) ),
inference(clausify,[status(thm)],[f_1142_5]) ).
cnf(f_1142_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_5008),sK99(U_5012,U_5010,U_5008,U_5006)),U_5010))
| ~ sP253(U_5010,U_5008,U_5006,U_5012) ),
inference(clausify,[status(thm)],[f_1142_5]) ).
cnf(f_1142_9,plain,
( hAPP(U_5012,sK99(U_5012,U_5010,U_5008,U_5006)) != c_Orderings_Obot__class_Obot(tc_fun(U_5006,tc_HOL_Obool))
| ~ sP253(U_5010,U_5008,U_5006,U_5012) ),
inference(clausify,[status(thm)],[f_1142_5]) ).
fof(f_1143_1,plain,
! [V_B_2,V_A_2,V_I_2,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,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_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_I_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_I_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_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__subset__iff]) ).
fof(f_1143_2,plain,
! [U_5019,U_5018,U_5017,U_5016,U_5015] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5015,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5016,tc_fun(U_5015,tc_HOL_Obool)),U_5017),U_5018)),U_5019))
| ? [U_5014] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5015,tc_HOL_Obool)),hAPP(U_5018,U_5014)),U_5019))
& hBOOL(hAPP(hAPP(c_member(U_5016),U_5014),U_5017)) ) )
& ( ! [U_5013] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5015,tc_HOL_Obool)),hAPP(U_5018,U_5013)),U_5019))
| ~ hBOOL(hAPP(hAPP(c_member(U_5016),U_5013),U_5017)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5015,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5016,tc_fun(U_5015,tc_HOL_Obool)),U_5017),U_5018)),U_5019)) ) ),
inference(variable_rename,[status(thm)],[f_1143_1]) ).
fof(f_1143_3,plain,
( ! [U_5029,U_5027,U_5025,U_5023,U_5021] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5021,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5023,tc_fun(U_5021,tc_HOL_Obool)),U_5025),U_5027)),U_5029))
| ? [U_5014] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5021,tc_HOL_Obool)),hAPP(U_5027,U_5014)),U_5029))
& hBOOL(hAPP(hAPP(c_member(U_5023),U_5014),U_5025)) ) )
& ! [U_5028,U_5026,U_5024,U_5022,U_5020] :
( ! [U_5013] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5020,tc_HOL_Obool)),hAPP(U_5026,U_5013)),U_5028))
| ~ hBOOL(hAPP(hAPP(c_member(U_5022),U_5013),U_5024)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5020,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5022,tc_fun(U_5020,tc_HOL_Obool)),U_5024),U_5026)),U_5028)) ) ),
inference(miniscope,[status(thm)],[f_1143_2]) ).
fof(f_1143_4,plain,
( ! [U_5029,U_5027,U_5025,U_5023,U_5021] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5021,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5023,tc_fun(U_5021,tc_HOL_Obool)),U_5025),U_5027)),U_5029))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5021,tc_HOL_Obool)),hAPP(U_5027,sK100(U_5029,U_5027,U_5025,U_5023,U_5021))),U_5029))
& hBOOL(hAPP(hAPP(c_member(U_5023),sK100(U_5029,U_5027,U_5025,U_5023,U_5021)),U_5025)) ) )
& ! [U_5028,U_5026,U_5024,U_5022,U_5020] :
( ! [U_5013] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5020,tc_HOL_Obool)),hAPP(U_5026,U_5013)),U_5028))
| ~ hBOOL(hAPP(hAPP(c_member(U_5022),U_5013),U_5024)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5020,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5022,tc_fun(U_5020,tc_HOL_Obool)),U_5024),U_5026)),U_5028)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_5014,sK100(U_5029,U_5027,U_5025,U_5023,U_5021))],[f_1143_3]) ).
fof(f_1143_5,plain,
( ! [U_5025,U_5021,U_5023,U_5027,U_5029] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5021,tc_HOL_Obool)),hAPP(U_5027,sK100(U_5029,U_5027,U_5025,U_5023,U_5021))),U_5029))
| ~ sP254(U_5025,U_5021,U_5023,U_5027,U_5029) )
& ! [U_5025,U_5021,U_5023,U_5027,U_5029] :
( hBOOL(hAPP(hAPP(c_member(U_5023),sK100(U_5029,U_5027,U_5025,U_5023,U_5021)),U_5025))
| ~ sP254(U_5025,U_5021,U_5023,U_5027,U_5029) )
& ! [U_5025,U_5021,U_5023,U_5027,U_5029] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5021,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5023,tc_fun(U_5021,tc_HOL_Obool)),U_5025),U_5027)),U_5029))
| sP254(U_5025,U_5021,U_5023,U_5027,U_5029) )
& ! [U_5013,U_5022,U_5026,U_5020,U_5028,U_5024] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5020,tc_HOL_Obool)),hAPP(U_5026,U_5013)),U_5028))
| ~ hBOOL(hAPP(hAPP(c_member(U_5022),U_5013),U_5024))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5020,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5022,tc_fun(U_5020,tc_HOL_Obool)),U_5024),U_5026)),U_5028)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP254])],[f_1143_4]) ).
cnf(f_1143_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5020,tc_HOL_Obool)),hAPP(U_5026,U_5013)),U_5028))
| ~ hBOOL(hAPP(hAPP(c_member(U_5022),U_5013),U_5024))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5020,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5022,tc_fun(U_5020,tc_HOL_Obool)),U_5024),U_5026)),U_5028)) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
cnf(f_1143_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5021,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5023,tc_fun(U_5021,tc_HOL_Obool)),U_5025),U_5027)),U_5029))
| sP254(U_5025,U_5021,U_5023,U_5027,U_5029) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
cnf(f_1143_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_5023),sK100(U_5029,U_5027,U_5025,U_5023,U_5021)),U_5025))
| ~ sP254(U_5025,U_5021,U_5023,U_5027,U_5029) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
cnf(f_1143_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5021,tc_HOL_Obool)),hAPP(U_5027,sK100(U_5029,U_5027,U_5025,U_5023,U_5021))),U_5029))
| ~ sP254(U_5025,U_5021,U_5023,U_5027,U_5029) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
fof(f_1144_1,plain,
! [V_B_2,V_A_2,V_f_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_e,T_d,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_c,tc_HOL_Obool),T_e),V_B_2),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I10_J]) ).
fof(f_1144_2,plain,
! [U_5035,U_5034,U_5033,U_5032,U_5031,U_5030] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5030,tc_fun(U_5031,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5032,U_5030,U_5033),U_5034)),U_5035) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5032,tc_fun(U_5031,tc_HOL_Obool)),U_5034),hAPP(hAPP(c_COMBB(U_5030,tc_fun(U_5031,tc_HOL_Obool),U_5032),U_5035),U_5033)),
inference(variable_rename,[status(thm)],[f_1144_1]) ).
fof(f_1144_3,plain,
! [U_5030,U_5031,U_5032,U_5033,U_5034,U_5035] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5030,tc_fun(U_5031,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5032,U_5030,U_5033),U_5034)),U_5035) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5032,tc_fun(U_5031,tc_HOL_Obool)),U_5034),hAPP(hAPP(c_COMBB(U_5030,tc_fun(U_5031,tc_HOL_Obool),U_5032),U_5035),U_5033)),
inference(definitional_conversion,[status(esa)],[f_1144_2]) ).
cnf(f_1144_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5030,tc_fun(U_5031,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5032,U_5030,U_5033),U_5034)),U_5035) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5032,tc_fun(U_5031,tc_HOL_Obool)),U_5034),hAPP(hAPP(c_COMBB(U_5030,tc_fun(U_5031,tc_HOL_Obool),U_5032),U_5035),U_5033)),
inference(clausify,[status(thm)],[f_1144_3]) ).
fof(f_1145_1,plain,
! [V_B_2,V_A_2,T_e,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Set_Oimage(T_d,T_c,V_f_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_image__UN]) ).
fof(f_1145_2,plain,
! [U_5041,U_5040,U_5039,U_5038,U_5037,U_5036] : hAPP(c_Set_Oimage(U_5036,U_5037,U_5038),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5039,tc_fun(U_5036,tc_HOL_Obool)),U_5040),U_5041)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5039,tc_fun(U_5037,tc_HOL_Obool)),U_5040),hAPP(hAPP(c_COMBB(tc_fun(U_5036,tc_HOL_Obool),tc_fun(U_5037,tc_HOL_Obool),U_5039),c_Set_Oimage(U_5036,U_5037,U_5038)),U_5041)),
inference(variable_rename,[status(thm)],[f_1145_1]) ).
fof(f_1145_3,plain,
! [U_5036,U_5037,U_5038,U_5039,U_5040,U_5041] : hAPP(c_Set_Oimage(U_5036,U_5037,U_5038),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5039,tc_fun(U_5036,tc_HOL_Obool)),U_5040),U_5041)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5039,tc_fun(U_5037,tc_HOL_Obool)),U_5040),hAPP(hAPP(c_COMBB(tc_fun(U_5036,tc_HOL_Obool),tc_fun(U_5037,tc_HOL_Obool),U_5039),c_Set_Oimage(U_5036,U_5037,U_5038)),U_5041)),
inference(definitional_conversion,[status(esa)],[f_1145_2]) ).
cnf(f_1145_4,plain,
hAPP(c_Set_Oimage(U_5036,U_5037,U_5038),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5039,tc_fun(U_5036,tc_HOL_Obool)),U_5040),U_5041)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5039,tc_fun(U_5037,tc_HOL_Obool)),U_5040),hAPP(hAPP(c_COMBB(tc_fun(U_5036,tc_HOL_Obool),tc_fun(U_5037,tc_HOL_Obool),U_5039),c_Set_Oimage(U_5036,U_5037,U_5038)),U_5041)),
inference(clausify,[status(thm)],[f_1145_3]) ).
fof(f_1146_1,plain,
! [V_f_2,V_B_2,T_e,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,tc_HOL_Obool),T_d),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_e,V_f_2),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I10_J]) ).
fof(f_1146_2,plain,
! [U_5047,U_5046,U_5045,U_5044,U_5043,U_5042] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5042,tc_fun(U_5043,tc_HOL_Obool)),U_5044),hAPP(hAPP(c_COMBB(U_5045,tc_fun(U_5043,tc_HOL_Obool),U_5042),U_5046),U_5047)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5045,tc_fun(U_5043,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5042,U_5045,U_5047),U_5044)),U_5046),
inference(variable_rename,[status(thm)],[f_1146_1]) ).
fof(f_1146_3,plain,
! [U_5042,U_5043,U_5044,U_5045,U_5046,U_5047] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5042,tc_fun(U_5043,tc_HOL_Obool)),U_5044),hAPP(hAPP(c_COMBB(U_5045,tc_fun(U_5043,tc_HOL_Obool),U_5042),U_5046),U_5047)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5045,tc_fun(U_5043,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5042,U_5045,U_5047),U_5044)),U_5046),
inference(definitional_conversion,[status(esa)],[f_1146_2]) ).
cnf(f_1146_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5042,tc_fun(U_5043,tc_HOL_Obool)),U_5044),hAPP(hAPP(c_COMBB(U_5045,tc_fun(U_5043,tc_HOL_Obool),U_5042),U_5046),U_5047)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5045,tc_fun(U_5043,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5042,U_5045,U_5047),U_5044)),U_5046),
inference(clausify,[status(thm)],[f_1146_3]) ).
fof(f_1147_1,plain,
! [V_B_2,V_A_2,V_I_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_d,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_d),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_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__Un__distrib]) ).
fof(f_1147_2,plain,
! [U_5052,U_5051,U_5050,U_5049,U_5048] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5048,tc_fun(U_5049,tc_HOL_Obool)),U_5050),hAPP(hAPP(c_COMBS(U_5048,tc_fun(U_5049,tc_HOL_Obool),tc_fun(U_5049,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5049,tc_HOL_Obool),tc_fun(tc_fun(U_5049,tc_HOL_Obool),tc_fun(U_5049,tc_HOL_Obool)),U_5048),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5049,tc_HOL_Obool))),U_5051)),U_5052)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5049,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5048,tc_fun(U_5049,tc_HOL_Obool)),U_5050),U_5051)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5048,tc_fun(U_5049,tc_HOL_Obool)),U_5050),U_5052)),
inference(variable_rename,[status(thm)],[f_1147_1]) ).
fof(f_1147_3,plain,
! [U_5048,U_5049,U_5050,U_5051,U_5052] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5048,tc_fun(U_5049,tc_HOL_Obool)),U_5050),hAPP(hAPP(c_COMBS(U_5048,tc_fun(U_5049,tc_HOL_Obool),tc_fun(U_5049,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5049,tc_HOL_Obool),tc_fun(tc_fun(U_5049,tc_HOL_Obool),tc_fun(U_5049,tc_HOL_Obool)),U_5048),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5049,tc_HOL_Obool))),U_5051)),U_5052)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5049,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5048,tc_fun(U_5049,tc_HOL_Obool)),U_5050),U_5051)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5048,tc_fun(U_5049,tc_HOL_Obool)),U_5050),U_5052)),
inference(definitional_conversion,[status(esa)],[f_1147_2]) ).
cnf(f_1147_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5048,tc_fun(U_5049,tc_HOL_Obool)),U_5050),hAPP(hAPP(c_COMBS(U_5048,tc_fun(U_5049,tc_HOL_Obool),tc_fun(U_5049,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5049,tc_HOL_Obool),tc_fun(tc_fun(U_5049,tc_HOL_Obool),tc_fun(U_5049,tc_HOL_Obool)),U_5048),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5049,tc_HOL_Obool))),U_5051)),U_5052)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5049,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5048,tc_fun(U_5049,tc_HOL_Obool)),U_5050),U_5051)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5048,tc_fun(U_5049,tc_HOL_Obool)),U_5050),U_5052)),
inference(clausify,[status(thm)],[f_1147_3]) ).
fof(f_1148_1,plain,
! [V_M_2,V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_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_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_M_2)),
inference(fof_nnf,[status(thm)],[fact_UN__Un]) ).
fof(f_1148_2,plain,
! [U_5057,U_5056,U_5055,U_5054,U_5053] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5053,tc_fun(U_5054,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5053,tc_HOL_Obool)),U_5055),U_5056)),U_5057) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5054,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5053,tc_fun(U_5054,tc_HOL_Obool)),U_5055),U_5057)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5053,tc_fun(U_5054,tc_HOL_Obool)),U_5056),U_5057)),
inference(variable_rename,[status(thm)],[f_1148_1]) ).
fof(f_1148_3,plain,
! [U_5053,U_5054,U_5055,U_5056,U_5057] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5053,tc_fun(U_5054,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5053,tc_HOL_Obool)),U_5055),U_5056)),U_5057) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5054,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5053,tc_fun(U_5054,tc_HOL_Obool)),U_5055),U_5057)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5053,tc_fun(U_5054,tc_HOL_Obool)),U_5056),U_5057)),
inference(definitional_conversion,[status(esa)],[f_1148_2]) ).
cnf(f_1148_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5053,tc_fun(U_5054,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5053,tc_HOL_Obool)),U_5055),U_5056)),U_5057) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5054,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5053,tc_fun(U_5054,tc_HOL_Obool)),U_5055),U_5057)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5053,tc_fun(U_5054,tc_HOL_Obool)),U_5056),U_5057)),
inference(clausify,[status(thm)],[f_1148_3]) ).
fof(f_1149_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d),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_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I5_J]) ).
fof(f_1149_2,plain,
! [U_5062,U_5061,U_5060,U_5059,U_5058] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5058,tc_fun(U_5059,tc_HOL_Obool)),U_5060),hAPP(hAPP(c_COMBB(tc_fun(U_5059,tc_HOL_Obool),tc_fun(U_5059,tc_HOL_Obool),U_5058),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5059,tc_HOL_Obool)),U_5061)),U_5062)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5059,tc_HOL_Obool)),U_5061),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5058,tc_fun(U_5059,tc_HOL_Obool)),U_5060),U_5062)),
inference(variable_rename,[status(thm)],[f_1149_1]) ).
fof(f_1149_3,plain,
! [U_5058,U_5059,U_5060,U_5061,U_5062] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5058,tc_fun(U_5059,tc_HOL_Obool)),U_5060),hAPP(hAPP(c_COMBB(tc_fun(U_5059,tc_HOL_Obool),tc_fun(U_5059,tc_HOL_Obool),U_5058),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5059,tc_HOL_Obool)),U_5061)),U_5062)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5059,tc_HOL_Obool)),U_5061),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5058,tc_fun(U_5059,tc_HOL_Obool)),U_5060),U_5062)),
inference(definitional_conversion,[status(esa)],[f_1149_2]) ).
cnf(f_1149_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5058,tc_fun(U_5059,tc_HOL_Obool)),U_5060),hAPP(hAPP(c_COMBB(tc_fun(U_5059,tc_HOL_Obool),tc_fun(U_5059,tc_HOL_Obool),U_5058),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5059,tc_HOL_Obool)),U_5061)),U_5062)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5059,tc_HOL_Obool)),U_5061),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5058,tc_fun(U_5059,tc_HOL_Obool)),U_5060),U_5062)),
inference(clausify,[status(thm)],[f_1149_3]) ).
fof(f_1150_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),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_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I4_J]) ).
fof(f_1150_2,plain,
! [U_5067,U_5066,U_5065,U_5064,U_5063] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5063,tc_fun(U_5064,tc_HOL_Obool)),U_5065),hAPP(hAPP(c_COMBC(U_5063,tc_fun(U_5064,tc_HOL_Obool),tc_fun(U_5064,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5064,tc_HOL_Obool),tc_fun(tc_fun(U_5064,tc_HOL_Obool),tc_fun(U_5064,tc_HOL_Obool)),U_5063),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5064,tc_HOL_Obool))),U_5066)),U_5067)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5064,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5063,tc_fun(U_5064,tc_HOL_Obool)),U_5065),U_5066)),U_5067),
inference(variable_rename,[status(thm)],[f_1150_1]) ).
fof(f_1150_3,plain,
! [U_5063,U_5064,U_5065,U_5066,U_5067] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5063,tc_fun(U_5064,tc_HOL_Obool)),U_5065),hAPP(hAPP(c_COMBC(U_5063,tc_fun(U_5064,tc_HOL_Obool),tc_fun(U_5064,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5064,tc_HOL_Obool),tc_fun(tc_fun(U_5064,tc_HOL_Obool),tc_fun(U_5064,tc_HOL_Obool)),U_5063),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5064,tc_HOL_Obool))),U_5066)),U_5067)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5064,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5063,tc_fun(U_5064,tc_HOL_Obool)),U_5065),U_5066)),U_5067),
inference(definitional_conversion,[status(esa)],[f_1150_2]) ).
cnf(f_1150_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5063,tc_fun(U_5064,tc_HOL_Obool)),U_5065),hAPP(hAPP(c_COMBC(U_5063,tc_fun(U_5064,tc_HOL_Obool),tc_fun(U_5064,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5064,tc_HOL_Obool),tc_fun(tc_fun(U_5064,tc_HOL_Obool),tc_fun(U_5064,tc_HOL_Obool)),U_5063),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5064,tc_HOL_Obool))),U_5066)),U_5067)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5064,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5063,tc_fun(U_5064,tc_HOL_Obool)),U_5065),U_5066)),U_5067),
inference(clausify,[status(thm)],[f_1150_3]) ).
fof(f_1151_1,plain,
! [V_B_2,V_C_2,T_d,V_A_2,T_c] : 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_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I5_J]) ).
fof(f_1151_2,plain,
! [U_5072,U_5071,U_5070,U_5069,U_5068] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5068,tc_HOL_Obool)),U_5069),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5070,tc_fun(U_5068,tc_HOL_Obool)),U_5071),U_5072)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5070,tc_fun(U_5068,tc_HOL_Obool)),U_5071),hAPP(hAPP(c_COMBB(tc_fun(U_5068,tc_HOL_Obool),tc_fun(U_5068,tc_HOL_Obool),U_5070),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5068,tc_HOL_Obool)),U_5069)),U_5072)),
inference(variable_rename,[status(thm)],[f_1151_1]) ).
fof(f_1151_3,plain,
! [U_5068,U_5069,U_5070,U_5071,U_5072] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5068,tc_HOL_Obool)),U_5069),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5070,tc_fun(U_5068,tc_HOL_Obool)),U_5071),U_5072)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5070,tc_fun(U_5068,tc_HOL_Obool)),U_5071),hAPP(hAPP(c_COMBB(tc_fun(U_5068,tc_HOL_Obool),tc_fun(U_5068,tc_HOL_Obool),U_5070),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5068,tc_HOL_Obool)),U_5069)),U_5072)),
inference(definitional_conversion,[status(esa)],[f_1151_2]) ).
cnf(f_1151_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5068,tc_HOL_Obool)),U_5069),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5070,tc_fun(U_5068,tc_HOL_Obool)),U_5071),U_5072)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5070,tc_fun(U_5068,tc_HOL_Obool)),U_5071),hAPP(hAPP(c_COMBB(tc_fun(U_5068,tc_HOL_Obool),tc_fun(U_5068,tc_HOL_Obool),U_5070),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5068,tc_HOL_Obool)),U_5069)),U_5072)),
inference(clausify,[status(thm)],[f_1151_3]) ).
fof(f_1152_1,plain,
! [V_A_2,V_I_2,T_d,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Int__UN__distrib]) ).
fof(f_1152_2,plain,
! [U_5077,U_5076,U_5075,U_5074,U_5073] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5073,tc_HOL_Obool)),U_5074),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5075,tc_fun(U_5073,tc_HOL_Obool)),U_5076),U_5077)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5075,tc_fun(U_5073,tc_HOL_Obool)),U_5076),hAPP(hAPP(c_COMBB(tc_fun(U_5073,tc_HOL_Obool),tc_fun(U_5073,tc_HOL_Obool),U_5075),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5073,tc_HOL_Obool)),U_5074)),U_5077)),
inference(variable_rename,[status(thm)],[f_1152_1]) ).
fof(f_1152_3,plain,
! [U_5073,U_5074,U_5075,U_5076,U_5077] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5073,tc_HOL_Obool)),U_5074),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5075,tc_fun(U_5073,tc_HOL_Obool)),U_5076),U_5077)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5075,tc_fun(U_5073,tc_HOL_Obool)),U_5076),hAPP(hAPP(c_COMBB(tc_fun(U_5073,tc_HOL_Obool),tc_fun(U_5073,tc_HOL_Obool),U_5075),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5073,tc_HOL_Obool)),U_5074)),U_5077)),
inference(definitional_conversion,[status(esa)],[f_1152_2]) ).
cnf(f_1152_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5073,tc_HOL_Obool)),U_5074),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5075,tc_fun(U_5073,tc_HOL_Obool)),U_5076),U_5077)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5075,tc_fun(U_5073,tc_HOL_Obool)),U_5076),hAPP(hAPP(c_COMBB(tc_fun(U_5073,tc_HOL_Obool),tc_fun(U_5073,tc_HOL_Obool),U_5075),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5073,tc_HOL_Obool)),U_5074)),U_5077)),
inference(clausify,[status(thm)],[f_1152_3]) ).
fof(f_1153_1,plain,
! [V_B_2,V_A_2,V_C_2,T_d,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I4_J]) ).
fof(f_1153_2,plain,
! [U_5082,U_5081,U_5080,U_5079,U_5078] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5078,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5079,tc_fun(U_5078,tc_HOL_Obool)),U_5080),U_5081)),U_5082) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5079,tc_fun(U_5078,tc_HOL_Obool)),U_5080),hAPP(hAPP(c_COMBC(U_5079,tc_fun(U_5078,tc_HOL_Obool),tc_fun(U_5078,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5078,tc_HOL_Obool),tc_fun(tc_fun(U_5078,tc_HOL_Obool),tc_fun(U_5078,tc_HOL_Obool)),U_5079),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5078,tc_HOL_Obool))),U_5081)),U_5082)),
inference(variable_rename,[status(thm)],[f_1153_1]) ).
fof(f_1153_3,plain,
! [U_5078,U_5079,U_5080,U_5081,U_5082] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5078,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5079,tc_fun(U_5078,tc_HOL_Obool)),U_5080),U_5081)),U_5082) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5079,tc_fun(U_5078,tc_HOL_Obool)),U_5080),hAPP(hAPP(c_COMBC(U_5079,tc_fun(U_5078,tc_HOL_Obool),tc_fun(U_5078,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5078,tc_HOL_Obool),tc_fun(tc_fun(U_5078,tc_HOL_Obool),tc_fun(U_5078,tc_HOL_Obool)),U_5079),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5078,tc_HOL_Obool))),U_5081)),U_5082)),
inference(definitional_conversion,[status(esa)],[f_1153_2]) ).
cnf(f_1153_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5078,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5079,tc_fun(U_5078,tc_HOL_Obool)),U_5080),U_5081)),U_5082) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5079,tc_fun(U_5078,tc_HOL_Obool)),U_5080),hAPP(hAPP(c_COMBC(U_5079,tc_fun(U_5078,tc_HOL_Obool),tc_fun(U_5078,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5078,tc_HOL_Obool),tc_fun(tc_fun(U_5078,tc_HOL_Obool),tc_fun(U_5078,tc_HOL_Obool)),U_5079),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5078,tc_HOL_Obool))),U_5081)),U_5082)),
inference(clausify,[status(thm)],[f_1153_3]) ).
fof(f_1154_1,plain,
! [V_B_2,V_J_2,T_e,V_A_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e)),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_d),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2))),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Int__UN__distrib2]) ).
fof(f_1154_2,plain,
! [U_5089,U_5088,U_5087,U_5086,U_5085,U_5084,U_5083] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5083,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5084,tc_fun(U_5083,tc_HOL_Obool)),U_5085),U_5086)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5087,tc_fun(U_5083,tc_HOL_Obool)),U_5088),U_5089)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5084,tc_fun(U_5083,tc_HOL_Obool)),U_5085),hAPP(hAPP(c_COMBB(tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool)),tc_fun(U_5083,tc_HOL_Obool),U_5084),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5087,tc_fun(U_5083,tc_HOL_Obool)),U_5088)),hAPP(hAPP(c_COMBC(U_5084,tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool)),tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5083,tc_HOL_Obool),tc_fun(U_5083,tc_HOL_Obool)),tc_fun(tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool)),tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool))),U_5084),c_COMBB(tc_fun(U_5083,tc_HOL_Obool),tc_fun(U_5083,tc_HOL_Obool),U_5087)),hAPP(hAPP(c_COMBB(tc_fun(U_5083,tc_HOL_Obool),tc_fun(tc_fun(U_5083,tc_HOL_Obool),tc_fun(U_5083,tc_HOL_Obool)),U_5084),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5083,tc_HOL_Obool))),U_5086))),U_5089))),
inference(variable_rename,[status(thm)],[f_1154_1]) ).
fof(f_1154_3,plain,
! [U_5083,U_5084,U_5085,U_5086,U_5087,U_5088,U_5089] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5083,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5084,tc_fun(U_5083,tc_HOL_Obool)),U_5085),U_5086)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5087,tc_fun(U_5083,tc_HOL_Obool)),U_5088),U_5089)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5084,tc_fun(U_5083,tc_HOL_Obool)),U_5085),hAPP(hAPP(c_COMBB(tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool)),tc_fun(U_5083,tc_HOL_Obool),U_5084),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5087,tc_fun(U_5083,tc_HOL_Obool)),U_5088)),hAPP(hAPP(c_COMBC(U_5084,tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool)),tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5083,tc_HOL_Obool),tc_fun(U_5083,tc_HOL_Obool)),tc_fun(tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool)),tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool))),U_5084),c_COMBB(tc_fun(U_5083,tc_HOL_Obool),tc_fun(U_5083,tc_HOL_Obool),U_5087)),hAPP(hAPP(c_COMBB(tc_fun(U_5083,tc_HOL_Obool),tc_fun(tc_fun(U_5083,tc_HOL_Obool),tc_fun(U_5083,tc_HOL_Obool)),U_5084),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5083,tc_HOL_Obool))),U_5086))),U_5089))),
inference(definitional_conversion,[status(esa)],[f_1154_2]) ).
cnf(f_1154_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5083,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5084,tc_fun(U_5083,tc_HOL_Obool)),U_5085),U_5086)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5087,tc_fun(U_5083,tc_HOL_Obool)),U_5088),U_5089)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5084,tc_fun(U_5083,tc_HOL_Obool)),U_5085),hAPP(hAPP(c_COMBB(tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool)),tc_fun(U_5083,tc_HOL_Obool),U_5084),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5087,tc_fun(U_5083,tc_HOL_Obool)),U_5088)),hAPP(hAPP(c_COMBC(U_5084,tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool)),tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5083,tc_HOL_Obool),tc_fun(U_5083,tc_HOL_Obool)),tc_fun(tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool)),tc_fun(U_5087,tc_fun(U_5083,tc_HOL_Obool))),U_5084),c_COMBB(tc_fun(U_5083,tc_HOL_Obool),tc_fun(U_5083,tc_HOL_Obool),U_5087)),hAPP(hAPP(c_COMBB(tc_fun(U_5083,tc_HOL_Obool),tc_fun(tc_fun(U_5083,tc_HOL_Obool),tc_fun(U_5083,tc_HOL_Obool)),U_5084),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5083,tc_HOL_Obool))),U_5086))),U_5089))),
inference(clausify,[status(thm)],[f_1154_3]) ).
fof(f_1155_1,plain,
! [V_f_2,V_B_2,T_e,V_A_2,T_d,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),T_c,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,T_c),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,T_c),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),T_c,T_e),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2)),hAPP(c_COMBC(T_d,T_e,T_c),V_f_2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_SUP__commute]) ).
fof(f_1155_2,plain,
! [U_5095,U_5094,U_5093,U_5092,U_5091,U_5090] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5091,U_5090),U_5092),hAPP(hAPP(c_COMBB(tc_fun(U_5093,U_5090),U_5090,U_5091),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5093,U_5090),U_5094)),U_5095)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5093,U_5090),U_5094),hAPP(hAPP(c_COMBB(tc_fun(U_5091,U_5090),U_5090,U_5093),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5091,U_5090),U_5092)),hAPP(c_COMBC(U_5091,U_5093,U_5090),U_5095)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5090) ),
inference(variable_rename,[status(thm)],[f_1155_1]) ).
fof(f_1155_3,plain,
! [U_5090,U_5091,U_5092,U_5093,U_5094,U_5095] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5091,U_5090),U_5092),hAPP(hAPP(c_COMBB(tc_fun(U_5093,U_5090),U_5090,U_5091),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5093,U_5090),U_5094)),U_5095)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5093,U_5090),U_5094),hAPP(hAPP(c_COMBB(tc_fun(U_5091,U_5090),U_5090,U_5093),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5091,U_5090),U_5092)),hAPP(c_COMBC(U_5091,U_5093,U_5090),U_5095)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5090) ),
inference(definitional_conversion,[status(esa)],[f_1155_2]) ).
cnf(f_1155_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5091,U_5090),U_5092),hAPP(hAPP(c_COMBB(tc_fun(U_5093,U_5090),U_5090,U_5091),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5093,U_5090),U_5094)),U_5095)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5093,U_5090),U_5094),hAPP(hAPP(c_COMBB(tc_fun(U_5091,U_5090),U_5090,U_5093),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5091,U_5090),U_5092)),hAPP(c_COMBC(U_5091,U_5093,U_5090),U_5095)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5090) ),
inference(clausify,[status(thm)],[f_1155_3]) ).
fof(f_1156_1,plain,
! [V_x_2,V_f_2,V_A_2,T_e,T_d,T_c] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,T_c)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),hAPP(hAPP(c_COMBC(T_d,T_e,T_c),V_f_2),V_x_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_SUPR__apply]) ).
fof(f_1156_2,plain,
! [U_5101,U_5100,U_5099,U_5098,U_5097,U_5096] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5097,tc_fun(U_5098,U_5096)),U_5099),U_5100),U_5101) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5097,U_5096),U_5099),hAPP(hAPP(c_COMBC(U_5097,U_5098,U_5096),U_5100),U_5101))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5096) ),
inference(variable_rename,[status(thm)],[f_1156_1]) ).
fof(f_1156_3,plain,
! [U_5096,U_5097,U_5098,U_5099,U_5100,U_5101] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5097,tc_fun(U_5098,U_5096)),U_5099),U_5100),U_5101) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5097,U_5096),U_5099),hAPP(hAPP(c_COMBC(U_5097,U_5098,U_5096),U_5100),U_5101))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5096) ),
inference(definitional_conversion,[status(esa)],[f_1156_2]) ).
cnf(f_1156_4,plain,
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5097,tc_fun(U_5098,U_5096)),U_5099),U_5100),U_5101) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5097,U_5096),U_5099),hAPP(hAPP(c_COMBC(U_5097,U_5098,U_5096),U_5100),U_5101))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5096) ),
inference(clausify,[status(thm)],[f_1156_3]) ).
fof(f_1157_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),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_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I6_J]) ).
fof(f_1157_2,plain,
! [U_5106,U_5105,U_5104,U_5103,U_5102] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5102,tc_fun(U_5103,tc_HOL_Obool)),U_5104),hAPP(hAPP(c_COMBC(U_5102,tc_fun(U_5103,tc_HOL_Obool),tc_fun(U_5103,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5103,tc_HOL_Obool),tc_fun(tc_fun(U_5103,tc_HOL_Obool),tc_fun(U_5103,tc_HOL_Obool)),U_5102),c_Groups_Ominus__class_Ominus(tc_fun(U_5103,tc_HOL_Obool))),U_5105)),U_5106)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5103,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5102,tc_fun(U_5103,tc_HOL_Obool)),U_5104),U_5105)),U_5106),
inference(variable_rename,[status(thm)],[f_1157_1]) ).
fof(f_1157_3,plain,
! [U_5102,U_5103,U_5104,U_5105,U_5106] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5102,tc_fun(U_5103,tc_HOL_Obool)),U_5104),hAPP(hAPP(c_COMBC(U_5102,tc_fun(U_5103,tc_HOL_Obool),tc_fun(U_5103,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5103,tc_HOL_Obool),tc_fun(tc_fun(U_5103,tc_HOL_Obool),tc_fun(U_5103,tc_HOL_Obool)),U_5102),c_Groups_Ominus__class_Ominus(tc_fun(U_5103,tc_HOL_Obool))),U_5105)),U_5106)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5103,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5102,tc_fun(U_5103,tc_HOL_Obool)),U_5104),U_5105)),U_5106),
inference(definitional_conversion,[status(esa)],[f_1157_2]) ).
cnf(f_1157_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5102,tc_fun(U_5103,tc_HOL_Obool)),U_5104),hAPP(hAPP(c_COMBC(U_5102,tc_fun(U_5103,tc_HOL_Obool),tc_fun(U_5103,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5103,tc_HOL_Obool),tc_fun(tc_fun(U_5103,tc_HOL_Obool),tc_fun(U_5103,tc_HOL_Obool)),U_5102),c_Groups_Ominus__class_Ominus(tc_fun(U_5103,tc_HOL_Obool))),U_5105)),U_5106)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5103,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5102,tc_fun(U_5103,tc_HOL_Obool)),U_5104),U_5105)),U_5106),
inference(clausify,[status(thm)],[f_1157_3]) ).
fof(f_1158_1,plain,
! [V_B_2,V_A_2,V_C_2,T_d,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I6_J]) ).
fof(f_1158_2,plain,
! [U_5111,U_5110,U_5109,U_5108,U_5107] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5107,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5108,tc_fun(U_5107,tc_HOL_Obool)),U_5109),U_5110)),U_5111) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5108,tc_fun(U_5107,tc_HOL_Obool)),U_5109),hAPP(hAPP(c_COMBC(U_5108,tc_fun(U_5107,tc_HOL_Obool),tc_fun(U_5107,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5107,tc_HOL_Obool),tc_fun(tc_fun(U_5107,tc_HOL_Obool),tc_fun(U_5107,tc_HOL_Obool)),U_5108),c_Groups_Ominus__class_Ominus(tc_fun(U_5107,tc_HOL_Obool))),U_5110)),U_5111)),
inference(variable_rename,[status(thm)],[f_1158_1]) ).
fof(f_1158_3,plain,
! [U_5107,U_5108,U_5109,U_5110,U_5111] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5107,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5108,tc_fun(U_5107,tc_HOL_Obool)),U_5109),U_5110)),U_5111) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5108,tc_fun(U_5107,tc_HOL_Obool)),U_5109),hAPP(hAPP(c_COMBC(U_5108,tc_fun(U_5107,tc_HOL_Obool),tc_fun(U_5107,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5107,tc_HOL_Obool),tc_fun(tc_fun(U_5107,tc_HOL_Obool),tc_fun(U_5107,tc_HOL_Obool)),U_5108),c_Groups_Ominus__class_Ominus(tc_fun(U_5107,tc_HOL_Obool))),U_5110)),U_5111)),
inference(definitional_conversion,[status(esa)],[f_1158_2]) ).
cnf(f_1158_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5107,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5108,tc_fun(U_5107,tc_HOL_Obool)),U_5109),U_5110)),U_5111) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5108,tc_fun(U_5107,tc_HOL_Obool)),U_5109),hAPP(hAPP(c_COMBC(U_5108,tc_fun(U_5107,tc_HOL_Obool),tc_fun(U_5107,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5107,tc_HOL_Obool),tc_fun(tc_fun(U_5107,tc_HOL_Obool),tc_fun(U_5107,tc_HOL_Obool)),U_5108),c_Groups_Ominus__class_Ominus(tc_fun(U_5107,tc_HOL_Obool))),U_5110)),U_5111)),
inference(clausify,[status(thm)],[f_1158_3]) ).
fof(f_1159_1,plain,
! [V_B_2,V_A_2,T_e,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Set_Ovimage(T_c,T_d,V_f_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__UN]) ).
fof(f_1159_2,plain,
! [U_5117,U_5116,U_5115,U_5114,U_5113,U_5112] : hAPP(c_Set_Ovimage(U_5112,U_5113,U_5114),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5115,tc_fun(U_5113,tc_HOL_Obool)),U_5116),U_5117)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5115,tc_fun(U_5112,tc_HOL_Obool)),U_5116),hAPP(hAPP(c_COMBB(tc_fun(U_5113,tc_HOL_Obool),tc_fun(U_5112,tc_HOL_Obool),U_5115),c_Set_Ovimage(U_5112,U_5113,U_5114)),U_5117)),
inference(variable_rename,[status(thm)],[f_1159_1]) ).
fof(f_1159_3,plain,
! [U_5112,U_5113,U_5114,U_5115,U_5116,U_5117] : hAPP(c_Set_Ovimage(U_5112,U_5113,U_5114),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5115,tc_fun(U_5113,tc_HOL_Obool)),U_5116),U_5117)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5115,tc_fun(U_5112,tc_HOL_Obool)),U_5116),hAPP(hAPP(c_COMBB(tc_fun(U_5113,tc_HOL_Obool),tc_fun(U_5112,tc_HOL_Obool),U_5115),c_Set_Ovimage(U_5112,U_5113,U_5114)),U_5117)),
inference(definitional_conversion,[status(esa)],[f_1159_2]) ).
cnf(f_1159_4,plain,
hAPP(c_Set_Ovimage(U_5112,U_5113,U_5114),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5115,tc_fun(U_5113,tc_HOL_Obool)),U_5116),U_5117)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5115,tc_fun(U_5112,tc_HOL_Obool)),U_5116),hAPP(hAPP(c_COMBB(tc_fun(U_5113,tc_HOL_Obool),tc_fun(U_5112,tc_HOL_Obool),U_5115),c_Set_Ovimage(U_5112,U_5113,U_5114)),U_5117)),
inference(clausify,[status(thm)],[f_1159_3]) ).
fof(f_1160_1,plain,
! [V_B_2,V_a_2,T_d,V_A_2,V_u_2,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_u_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib]) ).
fof(f_1160_2,plain,
! [U_5123,U_5122,U_5121,U_5120,U_5119,U_5118] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5118,tc_fun(U_5121,tc_HOL_Obool)),U_5120),hAPP(hAPP(c_COMBB(tc_fun(U_5121,tc_HOL_Obool),tc_fun(U_5121,tc_HOL_Obool),U_5118),hAPP(c_Set_Oinsert(U_5121),U_5122)),U_5123)) = hAPP(hAPP(c_Set_Oinsert(U_5121),U_5122),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5118,tc_fun(U_5121,tc_HOL_Obool)),U_5120),U_5123))
| ~ hBOOL(hAPP(hAPP(c_member(U_5118),U_5119),U_5120)) ),
inference(variable_rename,[status(thm)],[f_1160_1]) ).
fof(f_1160_3,plain,
! [U_5118,U_5119,U_5120,U_5121,U_5122,U_5123] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5118,tc_fun(U_5121,tc_HOL_Obool)),U_5120),hAPP(hAPP(c_COMBB(tc_fun(U_5121,tc_HOL_Obool),tc_fun(U_5121,tc_HOL_Obool),U_5118),hAPP(c_Set_Oinsert(U_5121),U_5122)),U_5123)) = hAPP(hAPP(c_Set_Oinsert(U_5121),U_5122),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5118,tc_fun(U_5121,tc_HOL_Obool)),U_5120),U_5123))
| ~ hBOOL(hAPP(hAPP(c_member(U_5118),U_5119),U_5120)) ),
inference(definitional_conversion,[status(esa)],[f_1160_2]) ).
cnf(f_1160_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5118,tc_fun(U_5121,tc_HOL_Obool)),U_5120),hAPP(hAPP(c_COMBB(tc_fun(U_5121,tc_HOL_Obool),tc_fun(U_5121,tc_HOL_Obool),U_5118),hAPP(c_Set_Oinsert(U_5121),U_5122)),U_5123)) = hAPP(hAPP(c_Set_Oinsert(U_5121),U_5122),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5118,tc_fun(U_5121,tc_HOL_Obool)),U_5120),U_5123))
| ~ hBOOL(hAPP(hAPP(c_member(U_5118),U_5119),U_5120)) ),
inference(clausify,[status(thm)],[f_1160_3]) ).
fof(f_1161_1,plain,
! [V_B_2,T_d,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__upper]) ).
fof(f_1161_2,plain,
! [U_5128,U_5127,U_5126,U_5125,U_5124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5127,tc_HOL_Obool)),hAPP(U_5128,U_5125)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5124,tc_fun(U_5127,tc_HOL_Obool)),U_5126),U_5128)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5124),U_5125),U_5126)) ),
inference(variable_rename,[status(thm)],[f_1161_1]) ).
fof(f_1161_3,plain,
! [U_5124,U_5125,U_5126,U_5127,U_5128] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5127,tc_HOL_Obool)),hAPP(U_5128,U_5125)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5124,tc_fun(U_5127,tc_HOL_Obool)),U_5126),U_5128)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5124),U_5125),U_5126)) ),
inference(definitional_conversion,[status(esa)],[f_1161_2]) ).
cnf(f_1161_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5127,tc_HOL_Obool)),hAPP(U_5128,U_5125)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5124,tc_fun(U_5127,tc_HOL_Obool)),U_5126),U_5128)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5124),U_5125),U_5126)) ),
inference(clausify,[status(thm)],[f_1161_3]) ).
fof(f_1162_1,plain,
! [V_A_2,T_d,V_I_2,V_k_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_k_2),V_I_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__absorb]) ).
fof(f_1162_2,plain,
! [U_5133,U_5132,U_5131,U_5130,U_5129] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5132,tc_HOL_Obool)),hAPP(U_5133,U_5130)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5129,tc_fun(U_5132,tc_HOL_Obool)),U_5131),U_5133)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5129,tc_fun(U_5132,tc_HOL_Obool)),U_5131),U_5133)
| ~ hBOOL(hAPP(hAPP(c_member(U_5129),U_5130),U_5131)) ),
inference(variable_rename,[status(thm)],[f_1162_1]) ).
fof(f_1162_3,plain,
! [U_5129,U_5130,U_5131,U_5132,U_5133] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5132,tc_HOL_Obool)),hAPP(U_5133,U_5130)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5129,tc_fun(U_5132,tc_HOL_Obool)),U_5131),U_5133)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5129,tc_fun(U_5132,tc_HOL_Obool)),U_5131),U_5133)
| ~ hBOOL(hAPP(hAPP(c_member(U_5129),U_5130),U_5131)) ),
inference(definitional_conversion,[status(esa)],[f_1162_2]) ).
cnf(f_1162_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5132,tc_HOL_Obool)),hAPP(U_5133,U_5130)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5129,tc_fun(U_5132,tc_HOL_Obool)),U_5131),U_5133)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5129,tc_fun(U_5132,tc_HOL_Obool)),U_5131),U_5133)
| ~ hBOOL(hAPP(hAPP(c_member(U_5129),U_5130),U_5131)) ),
inference(clausify,[status(thm)],[f_1162_3]) ).
fof(f_1163_1,plain,
! [V_B_2,V_a_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J]) ).
fof(f_1163_2,plain,
! [U_5138,U_5137,U_5136,U_5135,U_5134] :
( ( hAPP(hAPP(c_Set_Oinsert(U_5136),U_5137),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5135,tc_fun(U_5136,tc_HOL_Obool)),U_5134),U_5138)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5135,tc_fun(U_5136,tc_HOL_Obool)),U_5134),hAPP(hAPP(c_COMBB(tc_fun(U_5136,tc_HOL_Obool),tc_fun(U_5136,tc_HOL_Obool),U_5135),hAPP(c_Set_Oinsert(U_5136),U_5137)),U_5138))
| U_5134 = c_Orderings_Obot__class_Obot(tc_fun(U_5135,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Set_Oinsert(U_5136),U_5137),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5135,tc_fun(U_5136,tc_HOL_Obool)),U_5134),U_5138)) = hAPP(hAPP(c_Set_Oinsert(U_5136),U_5137),c_Orderings_Obot__class_Obot(tc_fun(U_5136,tc_HOL_Obool)))
| U_5134 != c_Orderings_Obot__class_Obot(tc_fun(U_5135,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1163_1]) ).
fof(f_1163_3,plain,
( ! [U_5148,U_5146,U_5144,U_5142,U_5140] :
( hAPP(hAPP(c_Set_Oinsert(U_5144),U_5146),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5142,tc_fun(U_5144,tc_HOL_Obool)),U_5140),U_5148)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5142,tc_fun(U_5144,tc_HOL_Obool)),U_5140),hAPP(hAPP(c_COMBB(tc_fun(U_5144,tc_HOL_Obool),tc_fun(U_5144,tc_HOL_Obool),U_5142),hAPP(c_Set_Oinsert(U_5144),U_5146)),U_5148))
| U_5140 = c_Orderings_Obot__class_Obot(tc_fun(U_5142,tc_HOL_Obool)) )
& ! [U_5147,U_5145,U_5143,U_5141,U_5139] :
( hAPP(hAPP(c_Set_Oinsert(U_5143),U_5145),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5141,tc_fun(U_5143,tc_HOL_Obool)),U_5139),U_5147)) = hAPP(hAPP(c_Set_Oinsert(U_5143),U_5145),c_Orderings_Obot__class_Obot(tc_fun(U_5143,tc_HOL_Obool)))
| U_5139 != c_Orderings_Obot__class_Obot(tc_fun(U_5141,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1163_2]) ).
fof(f_1163_4,plain,
( ! [U_5140,U_5142,U_5144,U_5146,U_5148] :
( hAPP(hAPP(c_Set_Oinsert(U_5144),U_5146),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5142,tc_fun(U_5144,tc_HOL_Obool)),U_5140),U_5148)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5142,tc_fun(U_5144,tc_HOL_Obool)),U_5140),hAPP(hAPP(c_COMBB(tc_fun(U_5144,tc_HOL_Obool),tc_fun(U_5144,tc_HOL_Obool),U_5142),hAPP(c_Set_Oinsert(U_5144),U_5146)),U_5148))
| U_5140 = c_Orderings_Obot__class_Obot(tc_fun(U_5142,tc_HOL_Obool)) )
& ! [U_5141,U_5139,U_5143,U_5145,U_5147] :
( hAPP(hAPP(c_Set_Oinsert(U_5143),U_5145),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5141,tc_fun(U_5143,tc_HOL_Obool)),U_5139),U_5147)) = hAPP(hAPP(c_Set_Oinsert(U_5143),U_5145),c_Orderings_Obot__class_Obot(tc_fun(U_5143,tc_HOL_Obool)))
| U_5139 != c_Orderings_Obot__class_Obot(tc_fun(U_5141,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1163_3]) ).
cnf(f_1163_5,plain,
( hAPP(hAPP(c_Set_Oinsert(U_5143),U_5145),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5141,tc_fun(U_5143,tc_HOL_Obool)),U_5139),U_5147)) = hAPP(hAPP(c_Set_Oinsert(U_5143),U_5145),c_Orderings_Obot__class_Obot(tc_fun(U_5143,tc_HOL_Obool)))
| U_5139 != c_Orderings_Obot__class_Obot(tc_fun(U_5141,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1163_4]) ).
cnf(f_1163_6,plain,
( hAPP(hAPP(c_Set_Oinsert(U_5144),U_5146),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5142,tc_fun(U_5144,tc_HOL_Obool)),U_5140),U_5148)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5142,tc_fun(U_5144,tc_HOL_Obool)),U_5140),hAPP(hAPP(c_COMBB(tc_fun(U_5144,tc_HOL_Obool),tc_fun(U_5144,tc_HOL_Obool),U_5142),hAPP(c_Set_Oinsert(U_5144),U_5146)),U_5148))
| U_5140 = c_Orderings_Obot__class_Obot(tc_fun(U_5142,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1163_4]) ).
fof(f_1164_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_c,tc_HOL_Obool)),V_A_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)))) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_UN__singleton]) ).
fof(f_1164_2,plain,
! [U_5150,U_5149] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5149,tc_fun(U_5149,tc_HOL_Obool)),U_5150),hAPP(hAPP(c_COMBC(U_5149,tc_fun(U_5149,tc_HOL_Obool),tc_fun(U_5149,tc_HOL_Obool)),c_Set_Oinsert(U_5149)),c_Orderings_Obot__class_Obot(tc_fun(U_5149,tc_HOL_Obool)))) = U_5150,
inference(variable_rename,[status(thm)],[f_1164_1]) ).
fof(f_1164_3,plain,
! [U_5150,U_5149] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5149,tc_fun(U_5149,tc_HOL_Obool)),U_5150),hAPP(hAPP(c_COMBC(U_5149,tc_fun(U_5149,tc_HOL_Obool),tc_fun(U_5149,tc_HOL_Obool)),c_Set_Oinsert(U_5149)),c_Orderings_Obot__class_Obot(tc_fun(U_5149,tc_HOL_Obool)))) = U_5150,
inference(definitional_conversion,[status(esa)],[f_1164_2]) ).
cnf(f_1164_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5149,tc_fun(U_5149,tc_HOL_Obool)),U_5150),hAPP(hAPP(c_COMBC(U_5149,tc_fun(U_5149,tc_HOL_Obool),tc_fun(U_5149,tc_HOL_Obool)),c_Set_Oinsert(U_5149)),c_Orderings_Obot__class_Obot(tc_fun(U_5149,tc_HOL_Obool)))) = U_5150,
inference(clausify,[status(thm)],[f_1164_3]) ).
fof(f_1165_1,plain,
! [V_B_2,V_a_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I1_J]) ).
fof(f_1165_2,plain,
! [U_5155,U_5154,U_5153,U_5152,U_5151] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5152,tc_fun(U_5153,tc_HOL_Obool)),U_5151),hAPP(hAPP(c_COMBB(tc_fun(U_5153,tc_HOL_Obool),tc_fun(U_5153,tc_HOL_Obool),U_5152),hAPP(c_Set_Oinsert(U_5153),U_5154)),U_5155)) = hAPP(hAPP(c_Set_Oinsert(U_5153),U_5154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5152,tc_fun(U_5153,tc_HOL_Obool)),U_5151),U_5155))
| U_5151 = c_Orderings_Obot__class_Obot(tc_fun(U_5152,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5152,tc_fun(U_5153,tc_HOL_Obool)),U_5151),hAPP(hAPP(c_COMBB(tc_fun(U_5153,tc_HOL_Obool),tc_fun(U_5153,tc_HOL_Obool),U_5152),hAPP(c_Set_Oinsert(U_5153),U_5154)),U_5155)) = c_Orderings_Obot__class_Obot(tc_fun(U_5153,tc_HOL_Obool))
| U_5151 != c_Orderings_Obot__class_Obot(tc_fun(U_5152,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1165_1]) ).
fof(f_1165_3,plain,
( ! [U_5165,U_5163,U_5161,U_5159,U_5157] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5159,tc_fun(U_5161,tc_HOL_Obool)),U_5157),hAPP(hAPP(c_COMBB(tc_fun(U_5161,tc_HOL_Obool),tc_fun(U_5161,tc_HOL_Obool),U_5159),hAPP(c_Set_Oinsert(U_5161),U_5163)),U_5165)) = hAPP(hAPP(c_Set_Oinsert(U_5161),U_5163),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5159,tc_fun(U_5161,tc_HOL_Obool)),U_5157),U_5165))
| U_5157 = c_Orderings_Obot__class_Obot(tc_fun(U_5159,tc_HOL_Obool)) )
& ! [U_5164,U_5162,U_5160,U_5158,U_5156] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5158,tc_fun(U_5160,tc_HOL_Obool)),U_5156),hAPP(hAPP(c_COMBB(tc_fun(U_5160,tc_HOL_Obool),tc_fun(U_5160,tc_HOL_Obool),U_5158),hAPP(c_Set_Oinsert(U_5160),U_5162)),U_5164)) = c_Orderings_Obot__class_Obot(tc_fun(U_5160,tc_HOL_Obool))
| U_5156 != c_Orderings_Obot__class_Obot(tc_fun(U_5158,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1165_2]) ).
fof(f_1165_4,plain,
( ! [U_5157,U_5159,U_5161,U_5163,U_5165] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5159,tc_fun(U_5161,tc_HOL_Obool)),U_5157),hAPP(hAPP(c_COMBB(tc_fun(U_5161,tc_HOL_Obool),tc_fun(U_5161,tc_HOL_Obool),U_5159),hAPP(c_Set_Oinsert(U_5161),U_5163)),U_5165)) = hAPP(hAPP(c_Set_Oinsert(U_5161),U_5163),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5159,tc_fun(U_5161,tc_HOL_Obool)),U_5157),U_5165))
| U_5157 = c_Orderings_Obot__class_Obot(tc_fun(U_5159,tc_HOL_Obool)) )
& ! [U_5162,U_5158,U_5156,U_5160,U_5164] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5158,tc_fun(U_5160,tc_HOL_Obool)),U_5156),hAPP(hAPP(c_COMBB(tc_fun(U_5160,tc_HOL_Obool),tc_fun(U_5160,tc_HOL_Obool),U_5158),hAPP(c_Set_Oinsert(U_5160),U_5162)),U_5164)) = c_Orderings_Obot__class_Obot(tc_fun(U_5160,tc_HOL_Obool))
| U_5156 != c_Orderings_Obot__class_Obot(tc_fun(U_5158,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1165_3]) ).
cnf(f_1165_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5158,tc_fun(U_5160,tc_HOL_Obool)),U_5156),hAPP(hAPP(c_COMBB(tc_fun(U_5160,tc_HOL_Obool),tc_fun(U_5160,tc_HOL_Obool),U_5158),hAPP(c_Set_Oinsert(U_5160),U_5162)),U_5164)) = c_Orderings_Obot__class_Obot(tc_fun(U_5160,tc_HOL_Obool))
| U_5156 != c_Orderings_Obot__class_Obot(tc_fun(U_5158,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1165_4]) ).
cnf(f_1165_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5159,tc_fun(U_5161,tc_HOL_Obool)),U_5157),hAPP(hAPP(c_COMBB(tc_fun(U_5161,tc_HOL_Obool),tc_fun(U_5161,tc_HOL_Obool),U_5159),hAPP(c_Set_Oinsert(U_5161),U_5163)),U_5165)) = hAPP(hAPP(c_Set_Oinsert(U_5161),U_5163),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5159,tc_fun(U_5161,tc_HOL_Obool)),U_5157),U_5165))
| U_5157 = c_Orderings_Obot__class_Obot(tc_fun(U_5159,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1165_4]) ).
fof(f_1166_1,plain,
! [V_u_2,V_M_2,V_A_2,T_d,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),V_M_2)),V_u_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,B_x)),V_u_2))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,B_x)),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),V_M_2)),V_u_2)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_SUP__le__iff]) ).
fof(f_1166_2,plain,
! [U_5172,U_5171,U_5170,U_5169,U_5168] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5169,U_5168),U_5170),U_5171)),U_5172))
| ? [U_5167] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(U_5171,U_5167)),U_5172))
& hBOOL(hAPP(hAPP(c_member(U_5169),U_5167),U_5170)) ) )
& ( ! [U_5166] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(U_5171,U_5166)),U_5172))
| ~ hBOOL(hAPP(hAPP(c_member(U_5169),U_5166),U_5170)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5169,U_5168),U_5170),U_5171)),U_5172)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5168) ),
inference(variable_rename,[status(thm)],[f_1166_1]) ).
fof(f_1166_3,plain,
! [U_5172,U_5171,U_5170,U_5169,U_5168] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5169,U_5168),U_5170),U_5171)),U_5172))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(U_5171,sK101(U_5172,U_5171,U_5170,U_5169,U_5168))),U_5172))
& hBOOL(hAPP(hAPP(c_member(U_5169),sK101(U_5172,U_5171,U_5170,U_5169,U_5168)),U_5170)) ) )
& ( ! [U_5166] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(U_5171,U_5166)),U_5172))
| ~ hBOOL(hAPP(hAPP(c_member(U_5169),U_5166),U_5170)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5169,U_5168),U_5170),U_5171)),U_5172)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5168) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_5167,sK101(U_5172,U_5171,U_5170,U_5169,U_5168))],[f_1166_2]) ).
fof(f_1166_4,plain,
( ! [U_5168,U_5169,U_5170,U_5171,U_5172] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(U_5171,sK101(U_5172,U_5171,U_5170,U_5169,U_5168))),U_5172))
| ~ sP255(U_5168,U_5169,U_5170,U_5171,U_5172) )
& ! [U_5168,U_5169,U_5170,U_5171,U_5172] :
( hBOOL(hAPP(hAPP(c_member(U_5169),sK101(U_5172,U_5171,U_5170,U_5169,U_5168)),U_5170))
| ~ sP255(U_5168,U_5169,U_5170,U_5171,U_5172) )
& ! [U_5166,U_5168,U_5169,U_5170,U_5171,U_5172] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5169,U_5168),U_5170),U_5171)),U_5172))
| sP255(U_5168,U_5169,U_5170,U_5171,U_5172)
| ~ sP256(U_5166,U_5168,U_5169,U_5170,U_5171,U_5172) )
& ! [U_5166,U_5168,U_5169,U_5170,U_5171,U_5172] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(U_5171,U_5166)),U_5172))
| ~ hBOOL(hAPP(hAPP(c_member(U_5169),U_5166),U_5170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5169,U_5168),U_5170),U_5171)),U_5172))
| ~ sP256(U_5166,U_5168,U_5169,U_5170,U_5171,U_5172) )
& ! [U_5166,U_5168,U_5169,U_5170,U_5171,U_5172] :
( sP256(U_5166,U_5168,U_5169,U_5170,U_5171,U_5172)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5168) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP255,sP256])],[f_1166_3]) ).
cnf(f_1166_5,plain,
( sP256(U_5166,U_5168,U_5169,U_5170,U_5171,U_5172)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5168) ),
inference(clausify,[status(thm)],[f_1166_4]) ).
cnf(f_1166_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(U_5171,U_5166)),U_5172))
| ~ hBOOL(hAPP(hAPP(c_member(U_5169),U_5166),U_5170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5169,U_5168),U_5170),U_5171)),U_5172))
| ~ sP256(U_5166,U_5168,U_5169,U_5170,U_5171,U_5172) ),
inference(clausify,[status(thm)],[f_1166_4]) ).
cnf(f_1166_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5169,U_5168),U_5170),U_5171)),U_5172))
| sP255(U_5168,U_5169,U_5170,U_5171,U_5172)
| ~ sP256(U_5166,U_5168,U_5169,U_5170,U_5171,U_5172) ),
inference(clausify,[status(thm)],[f_1166_4]) ).
cnf(f_1166_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_5169),sK101(U_5172,U_5171,U_5170,U_5169,U_5168)),U_5170))
| ~ sP255(U_5168,U_5169,U_5170,U_5171,U_5172) ),
inference(clausify,[status(thm)],[f_1166_4]) ).
cnf(f_1166_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5168),hAPP(U_5171,sK101(U_5172,U_5171,U_5170,U_5169,U_5168))),U_5172))
| ~ sP255(U_5168,U_5169,U_5170,U_5171,U_5172) ),
inference(clausify,[status(thm)],[f_1166_4]) ).
fof(f_1167_1,plain,
! [V_f_2,V_A_2,T_d,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),V_f_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(V_f_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_c),V_A_2),V_f_2))) ) )
| ~ class_Orderings_Olinorder(T_c)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__SUP__iff]) ).
fof(f_1167_2,plain,
! [U_5179,U_5178,U_5177,U_5176,U_5175] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5177,U_5175),U_5178),U_5179)))
| ! [U_5174] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(U_5179,U_5174)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5177),U_5174),U_5178)) ) )
& ( ? [U_5173] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(U_5179,U_5173)))
& hBOOL(hAPP(hAPP(c_member(U_5177),U_5173),U_5178)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5177,U_5175),U_5178),U_5179))) ) )
| ~ class_Orderings_Olinorder(U_5175)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5175) ),
inference(variable_rename,[status(thm)],[f_1167_1]) ).
fof(f_1167_3,plain,
! [U_5179,U_5178,U_5177,U_5176,U_5175] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5177,U_5175),U_5178),U_5179)))
| ! [U_5174] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(U_5179,U_5174)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5177),U_5174),U_5178)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(U_5179,sK102(U_5179,U_5178,U_5177,U_5176,U_5175))))
& hBOOL(hAPP(hAPP(c_member(U_5177),sK102(U_5179,U_5178,U_5177,U_5176,U_5175)),U_5178)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5177,U_5175),U_5178),U_5179))) ) )
| ~ class_Orderings_Olinorder(U_5175)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5175) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_5173,sK102(U_5179,U_5178,U_5177,U_5176,U_5175))],[f_1167_2]) ).
fof(f_1167_4,plain,
( ! [U_5179,U_5178,U_5175,U_5176,U_5177] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(U_5179,sK102(U_5179,U_5178,U_5177,U_5176,U_5175))))
| ~ sP257(U_5179,U_5178,U_5175,U_5176,U_5177) )
& ! [U_5179,U_5178,U_5175,U_5176,U_5177] :
( hBOOL(hAPP(hAPP(c_member(U_5177),sK102(U_5179,U_5178,U_5177,U_5176,U_5175)),U_5178))
| ~ sP257(U_5179,U_5178,U_5175,U_5176,U_5177) )
& ! [U_5174,U_5179,U_5178,U_5175,U_5176,U_5177] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5177,U_5175),U_5178),U_5179)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(U_5179,U_5174)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5177),U_5174),U_5178))
| ~ sP258(U_5174,U_5179,U_5178,U_5175,U_5176,U_5177) )
& ! [U_5174,U_5179,U_5178,U_5175,U_5176,U_5177] :
( sP257(U_5179,U_5178,U_5175,U_5176,U_5177)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5177,U_5175),U_5178),U_5179)))
| ~ sP258(U_5174,U_5179,U_5178,U_5175,U_5176,U_5177) )
& ! [U_5174,U_5179,U_5178,U_5175,U_5176,U_5177] :
( sP258(U_5174,U_5179,U_5178,U_5175,U_5176,U_5177)
| ~ class_Orderings_Olinorder(U_5175)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5175) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP257,sP258])],[f_1167_3]) ).
cnf(f_1167_5,plain,
( sP258(U_5174,U_5179,U_5178,U_5175,U_5176,U_5177)
| ~ class_Orderings_Olinorder(U_5175)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5175) ),
inference(clausify,[status(thm)],[f_1167_4]) ).
cnf(f_1167_6,plain,
( sP257(U_5179,U_5178,U_5175,U_5176,U_5177)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5177,U_5175),U_5178),U_5179)))
| ~ sP258(U_5174,U_5179,U_5178,U_5175,U_5176,U_5177) ),
inference(clausify,[status(thm)],[f_1167_4]) ).
cnf(f_1167_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5177,U_5175),U_5178),U_5179)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(U_5179,U_5174)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5177),U_5174),U_5178))
| ~ sP258(U_5174,U_5179,U_5178,U_5175,U_5176,U_5177) ),
inference(clausify,[status(thm)],[f_1167_4]) ).
cnf(f_1167_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_5177),sK102(U_5179,U_5178,U_5177,U_5176,U_5175)),U_5178))
| ~ sP257(U_5179,U_5178,U_5175,U_5176,U_5177) ),
inference(clausify,[status(thm)],[f_1167_4]) ).
cnf(f_1167_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5175),U_5176),hAPP(U_5179,sK102(U_5179,U_5178,U_5177,U_5176,U_5175))))
| ~ sP257(U_5179,U_5178,U_5175,U_5176,U_5177) ),
inference(clausify,[status(thm)],[f_1167_4]) ).
fof(f_1168_1,plain,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,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_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,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_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J]) ).
fof(f_1168_2,plain,
! [U_5184,U_5183,U_5182,U_5181,U_5180] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5182,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5181,tc_fun(U_5182,tc_HOL_Obool)),U_5180),U_5183)),U_5184) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5181,tc_fun(U_5182,tc_HOL_Obool)),U_5180),hAPP(hAPP(c_COMBC(U_5181,tc_fun(U_5182,tc_HOL_Obool),tc_fun(U_5182,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5182,tc_HOL_Obool),tc_fun(tc_fun(U_5182,tc_HOL_Obool),tc_fun(U_5182,tc_HOL_Obool)),U_5181),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5182,tc_HOL_Obool))),U_5183)),U_5184))
| U_5180 = c_Orderings_Obot__class_Obot(tc_fun(U_5181,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5182,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5181,tc_fun(U_5182,tc_HOL_Obool)),U_5180),U_5183)),U_5184) = U_5184
| U_5180 != c_Orderings_Obot__class_Obot(tc_fun(U_5181,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1168_1]) ).
fof(f_1168_3,plain,
( ! [U_5194,U_5192,U_5190,U_5188,U_5186] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5190,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5188,tc_fun(U_5190,tc_HOL_Obool)),U_5186),U_5192)),U_5194) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5188,tc_fun(U_5190,tc_HOL_Obool)),U_5186),hAPP(hAPP(c_COMBC(U_5188,tc_fun(U_5190,tc_HOL_Obool),tc_fun(U_5190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5190,tc_HOL_Obool),tc_fun(tc_fun(U_5190,tc_HOL_Obool),tc_fun(U_5190,tc_HOL_Obool)),U_5188),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5190,tc_HOL_Obool))),U_5192)),U_5194))
| U_5186 = c_Orderings_Obot__class_Obot(tc_fun(U_5188,tc_HOL_Obool)) )
& ! [U_5193,U_5191,U_5189,U_5187,U_5185] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5189,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5187,tc_fun(U_5189,tc_HOL_Obool)),U_5185),U_5191)),U_5193) = U_5193
| U_5185 != c_Orderings_Obot__class_Obot(tc_fun(U_5187,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1168_2]) ).
fof(f_1168_4,plain,
( ! [U_5194,U_5186,U_5188,U_5190,U_5192] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5190,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5188,tc_fun(U_5190,tc_HOL_Obool)),U_5186),U_5192)),U_5194) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5188,tc_fun(U_5190,tc_HOL_Obool)),U_5186),hAPP(hAPP(c_COMBC(U_5188,tc_fun(U_5190,tc_HOL_Obool),tc_fun(U_5190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5190,tc_HOL_Obool),tc_fun(tc_fun(U_5190,tc_HOL_Obool),tc_fun(U_5190,tc_HOL_Obool)),U_5188),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5190,tc_HOL_Obool))),U_5192)),U_5194))
| U_5186 = c_Orderings_Obot__class_Obot(tc_fun(U_5188,tc_HOL_Obool)) )
& ! [U_5185,U_5189,U_5187,U_5191,U_5193] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5189,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5187,tc_fun(U_5189,tc_HOL_Obool)),U_5185),U_5191)),U_5193) = U_5193
| U_5185 != c_Orderings_Obot__class_Obot(tc_fun(U_5187,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1168_3]) ).
cnf(f_1168_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5189,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5187,tc_fun(U_5189,tc_HOL_Obool)),U_5185),U_5191)),U_5193) = U_5193
| U_5185 != c_Orderings_Obot__class_Obot(tc_fun(U_5187,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1168_4]) ).
cnf(f_1168_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5190,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5188,tc_fun(U_5190,tc_HOL_Obool)),U_5186),U_5192)),U_5194) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5188,tc_fun(U_5190,tc_HOL_Obool)),U_5186),hAPP(hAPP(c_COMBC(U_5188,tc_fun(U_5190,tc_HOL_Obool),tc_fun(U_5190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5190,tc_HOL_Obool),tc_fun(tc_fun(U_5190,tc_HOL_Obool),tc_fun(U_5190,tc_HOL_Obool)),U_5188),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5190,tc_HOL_Obool))),U_5192)),U_5194))
| U_5186 = c_Orderings_Obot__class_Obot(tc_fun(U_5188,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1168_4]) ).
fof(f_1169_1,plain,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J]) ).
fof(f_1169_2,plain,
! [U_5199,U_5198,U_5197,U_5196,U_5195] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5197,tc_HOL_Obool)),U_5198),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5196,tc_fun(U_5197,tc_HOL_Obool)),U_5195),U_5199)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5196,tc_fun(U_5197,tc_HOL_Obool)),U_5195),hAPP(hAPP(c_COMBB(tc_fun(U_5197,tc_HOL_Obool),tc_fun(U_5197,tc_HOL_Obool),U_5196),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5197,tc_HOL_Obool)),U_5198)),U_5199))
| U_5195 = c_Orderings_Obot__class_Obot(tc_fun(U_5196,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5197,tc_HOL_Obool)),U_5198),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5196,tc_fun(U_5197,tc_HOL_Obool)),U_5195),U_5199)) = U_5198
| U_5195 != c_Orderings_Obot__class_Obot(tc_fun(U_5196,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1169_1]) ).
fof(f_1169_3,plain,
( ! [U_5209,U_5207,U_5205,U_5203,U_5201] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5205,tc_HOL_Obool)),U_5207),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5203,tc_fun(U_5205,tc_HOL_Obool)),U_5201),U_5209)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5203,tc_fun(U_5205,tc_HOL_Obool)),U_5201),hAPP(hAPP(c_COMBB(tc_fun(U_5205,tc_HOL_Obool),tc_fun(U_5205,tc_HOL_Obool),U_5203),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5205,tc_HOL_Obool)),U_5207)),U_5209))
| U_5201 = c_Orderings_Obot__class_Obot(tc_fun(U_5203,tc_HOL_Obool)) )
& ! [U_5208,U_5206,U_5204,U_5202,U_5200] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5204,tc_HOL_Obool)),U_5206),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5202,tc_fun(U_5204,tc_HOL_Obool)),U_5200),U_5208)) = U_5206
| U_5200 != c_Orderings_Obot__class_Obot(tc_fun(U_5202,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1169_2]) ).
fof(f_1169_4,plain,
( ! [U_5201,U_5203,U_5205,U_5207,U_5209] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5205,tc_HOL_Obool)),U_5207),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5203,tc_fun(U_5205,tc_HOL_Obool)),U_5201),U_5209)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5203,tc_fun(U_5205,tc_HOL_Obool)),U_5201),hAPP(hAPP(c_COMBB(tc_fun(U_5205,tc_HOL_Obool),tc_fun(U_5205,tc_HOL_Obool),U_5203),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5205,tc_HOL_Obool)),U_5207)),U_5209))
| U_5201 = c_Orderings_Obot__class_Obot(tc_fun(U_5203,tc_HOL_Obool)) )
& ! [U_5204,U_5206,U_5202,U_5200,U_5208] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5204,tc_HOL_Obool)),U_5206),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5202,tc_fun(U_5204,tc_HOL_Obool)),U_5200),U_5208)) = U_5206
| U_5200 != c_Orderings_Obot__class_Obot(tc_fun(U_5202,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1169_3]) ).
cnf(f_1169_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5204,tc_HOL_Obool)),U_5206),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5202,tc_fun(U_5204,tc_HOL_Obool)),U_5200),U_5208)) = U_5206
| U_5200 != c_Orderings_Obot__class_Obot(tc_fun(U_5202,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1169_4]) ).
cnf(f_1169_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5205,tc_HOL_Obool)),U_5207),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5203,tc_fun(U_5205,tc_HOL_Obool)),U_5201),U_5209)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5203,tc_fun(U_5205,tc_HOL_Obool)),U_5201),hAPP(hAPP(c_COMBB(tc_fun(U_5205,tc_HOL_Obool),tc_fun(U_5205,tc_HOL_Obool),U_5203),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5205,tc_HOL_Obool)),U_5207)),U_5209))
| U_5201 = c_Orderings_Obot__class_Obot(tc_fun(U_5203,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1169_4]) ).
fof(f_1170_1,plain,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J]) ).
fof(f_1170_2,plain,
! [U_5214,U_5213,U_5212,U_5211,U_5210] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5211,tc_fun(U_5212,tc_HOL_Obool)),U_5210),hAPP(hAPP(c_COMBC(U_5211,tc_fun(U_5212,tc_HOL_Obool),tc_fun(U_5212,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5212,tc_HOL_Obool),tc_fun(tc_fun(U_5212,tc_HOL_Obool),tc_fun(U_5212,tc_HOL_Obool)),U_5211),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5212,tc_HOL_Obool))),U_5213)),U_5214)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5212,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5211,tc_fun(U_5212,tc_HOL_Obool)),U_5210),U_5213)),U_5214)
| U_5210 = c_Orderings_Obot__class_Obot(tc_fun(U_5211,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5211,tc_fun(U_5212,tc_HOL_Obool)),U_5210),hAPP(hAPP(c_COMBC(U_5211,tc_fun(U_5212,tc_HOL_Obool),tc_fun(U_5212,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5212,tc_HOL_Obool),tc_fun(tc_fun(U_5212,tc_HOL_Obool),tc_fun(U_5212,tc_HOL_Obool)),U_5211),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5212,tc_HOL_Obool))),U_5213)),U_5214)) = c_Orderings_Obot__class_Obot(tc_fun(U_5212,tc_HOL_Obool))
| U_5210 != c_Orderings_Obot__class_Obot(tc_fun(U_5211,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1170_1]) ).
fof(f_1170_3,plain,
( ! [U_5224,U_5222,U_5220,U_5218,U_5216] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5218,tc_fun(U_5220,tc_HOL_Obool)),U_5216),hAPP(hAPP(c_COMBC(U_5218,tc_fun(U_5220,tc_HOL_Obool),tc_fun(U_5220,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5220,tc_HOL_Obool),tc_fun(tc_fun(U_5220,tc_HOL_Obool),tc_fun(U_5220,tc_HOL_Obool)),U_5218),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5220,tc_HOL_Obool))),U_5222)),U_5224)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5220,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5218,tc_fun(U_5220,tc_HOL_Obool)),U_5216),U_5222)),U_5224)
| U_5216 = c_Orderings_Obot__class_Obot(tc_fun(U_5218,tc_HOL_Obool)) )
& ! [U_5223,U_5221,U_5219,U_5217,U_5215] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5217,tc_fun(U_5219,tc_HOL_Obool)),U_5215),hAPP(hAPP(c_COMBC(U_5217,tc_fun(U_5219,tc_HOL_Obool),tc_fun(U_5219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5219,tc_HOL_Obool),tc_fun(tc_fun(U_5219,tc_HOL_Obool),tc_fun(U_5219,tc_HOL_Obool)),U_5217),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5219,tc_HOL_Obool))),U_5221)),U_5223)) = c_Orderings_Obot__class_Obot(tc_fun(U_5219,tc_HOL_Obool))
| U_5215 != c_Orderings_Obot__class_Obot(tc_fun(U_5217,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1170_2]) ).
fof(f_1170_4,plain,
( ! [U_5216,U_5218,U_5220,U_5222,U_5224] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5218,tc_fun(U_5220,tc_HOL_Obool)),U_5216),hAPP(hAPP(c_COMBC(U_5218,tc_fun(U_5220,tc_HOL_Obool),tc_fun(U_5220,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5220,tc_HOL_Obool),tc_fun(tc_fun(U_5220,tc_HOL_Obool),tc_fun(U_5220,tc_HOL_Obool)),U_5218),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5220,tc_HOL_Obool))),U_5222)),U_5224)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5220,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5218,tc_fun(U_5220,tc_HOL_Obool)),U_5216),U_5222)),U_5224)
| U_5216 = c_Orderings_Obot__class_Obot(tc_fun(U_5218,tc_HOL_Obool)) )
& ! [U_5221,U_5217,U_5215,U_5223,U_5219] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5217,tc_fun(U_5219,tc_HOL_Obool)),U_5215),hAPP(hAPP(c_COMBC(U_5217,tc_fun(U_5219,tc_HOL_Obool),tc_fun(U_5219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5219,tc_HOL_Obool),tc_fun(tc_fun(U_5219,tc_HOL_Obool),tc_fun(U_5219,tc_HOL_Obool)),U_5217),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5219,tc_HOL_Obool))),U_5221)),U_5223)) = c_Orderings_Obot__class_Obot(tc_fun(U_5219,tc_HOL_Obool))
| U_5215 != c_Orderings_Obot__class_Obot(tc_fun(U_5217,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1170_3]) ).
cnf(f_1170_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5217,tc_fun(U_5219,tc_HOL_Obool)),U_5215),hAPP(hAPP(c_COMBC(U_5217,tc_fun(U_5219,tc_HOL_Obool),tc_fun(U_5219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5219,tc_HOL_Obool),tc_fun(tc_fun(U_5219,tc_HOL_Obool),tc_fun(U_5219,tc_HOL_Obool)),U_5217),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5219,tc_HOL_Obool))),U_5221)),U_5223)) = c_Orderings_Obot__class_Obot(tc_fun(U_5219,tc_HOL_Obool))
| U_5215 != c_Orderings_Obot__class_Obot(tc_fun(U_5217,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1170_4]) ).
cnf(f_1170_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5218,tc_fun(U_5220,tc_HOL_Obool)),U_5216),hAPP(hAPP(c_COMBC(U_5218,tc_fun(U_5220,tc_HOL_Obool),tc_fun(U_5220,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5220,tc_HOL_Obool),tc_fun(tc_fun(U_5220,tc_HOL_Obool),tc_fun(U_5220,tc_HOL_Obool)),U_5218),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5220,tc_HOL_Obool))),U_5222)),U_5224)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5220,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5218,tc_fun(U_5220,tc_HOL_Obool)),U_5216),U_5222)),U_5224)
| U_5216 = c_Orderings_Obot__class_Obot(tc_fun(U_5218,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1170_4]) ).
fof(f_1171_1,plain,
! [V_f_2,V_T_2,V_S_2,T_c,T_d] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_f_2),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_f_2),c_Groups_Oone__class_Oone(T_d)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_f_2),c_Groups_Oone__class_Oone(T_d)),V_T_2))
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_d)
& 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_S_2),V_T_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__Un__one]) ).
fof(f_1171_2,plain,
! [U_5230,U_5229,U_5228,U_5227,U_5226] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5226,U_5227,c_Groups_Otimes__class_Otimes(U_5226)),U_5230),c_Groups_Oone__class_Oone(U_5226)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5227,tc_HOL_Obool)),U_5228),U_5229)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5226,U_5227,c_Groups_Otimes__class_Otimes(U_5226)),U_5230),c_Groups_Oone__class_Oone(U_5226)),U_5228)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5226,U_5227,c_Groups_Otimes__class_Otimes(U_5226)),U_5230),c_Groups_Oone__class_Oone(U_5226)),U_5229))
| ? [U_5225] :
( hAPP(U_5230,U_5225) != c_Groups_Oone__class_Oone(U_5226)
& hBOOL(hAPP(hAPP(c_member(U_5227),U_5225),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5227,tc_HOL_Obool)),U_5228),U_5229))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5227),U_5229))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5227),U_5228))
| ~ class_Groups_Ocomm__monoid__mult(U_5226) ),
inference(variable_rename,[status(thm)],[f_1171_1]) ).
fof(f_1171_3,plain,
! [U_5230,U_5229,U_5228,U_5227,U_5226] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5226,U_5227,c_Groups_Otimes__class_Otimes(U_5226)),U_5230),c_Groups_Oone__class_Oone(U_5226)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5227,tc_HOL_Obool)),U_5228),U_5229)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5226,U_5227,c_Groups_Otimes__class_Otimes(U_5226)),U_5230),c_Groups_Oone__class_Oone(U_5226)),U_5228)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5226,U_5227,c_Groups_Otimes__class_Otimes(U_5226)),U_5230),c_Groups_Oone__class_Oone(U_5226)),U_5229))
| ( hAPP(U_5230,sK103(U_5230,U_5229,U_5228,U_5227,U_5226)) != c_Groups_Oone__class_Oone(U_5226)
& hBOOL(hAPP(hAPP(c_member(U_5227),sK103(U_5230,U_5229,U_5228,U_5227,U_5226)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5227,tc_HOL_Obool)),U_5228),U_5229))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5227),U_5229))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5227),U_5228))
| ~ class_Groups_Ocomm__monoid__mult(U_5226) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_5225,sK103(U_5230,U_5229,U_5228,U_5227,U_5226))],[f_1171_2]) ).
fof(f_1171_4,plain,
( ! [U_5227,U_5226,U_5228,U_5229,U_5230] :
( hAPP(U_5230,sK103(U_5230,U_5229,U_5228,U_5227,U_5226)) != c_Groups_Oone__class_Oone(U_5226)
| ~ sP259(U_5227,U_5226,U_5228,U_5229,U_5230) )
& ! [U_5227,U_5226,U_5228,U_5229,U_5230] :
( hBOOL(hAPP(hAPP(c_member(U_5227),sK103(U_5230,U_5229,U_5228,U_5227,U_5226)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5227,tc_HOL_Obool)),U_5228),U_5229)))
| ~ sP259(U_5227,U_5226,U_5228,U_5229,U_5230) )
& ! [U_5227,U_5226,U_5228,U_5229,U_5230] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5226,U_5227,c_Groups_Otimes__class_Otimes(U_5226)),U_5230),c_Groups_Oone__class_Oone(U_5226)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5227,tc_HOL_Obool)),U_5228),U_5229)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5226,U_5227,c_Groups_Otimes__class_Otimes(U_5226)),U_5230),c_Groups_Oone__class_Oone(U_5226)),U_5228)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5226,U_5227,c_Groups_Otimes__class_Otimes(U_5226)),U_5230),c_Groups_Oone__class_Oone(U_5226)),U_5229))
| sP259(U_5227,U_5226,U_5228,U_5229,U_5230)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5227),U_5229))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5227),U_5228))
| ~ class_Groups_Ocomm__monoid__mult(U_5226) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP259])],[f_1171_3]) ).
cnf(f_1171_5,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5226,U_5227,c_Groups_Otimes__class_Otimes(U_5226)),U_5230),c_Groups_Oone__class_Oone(U_5226)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5227,tc_HOL_Obool)),U_5228),U_5229)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5226,U_5227,c_Groups_Otimes__class_Otimes(U_5226)),U_5230),c_Groups_Oone__class_Oone(U_5226)),U_5228)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5226,U_5227,c_Groups_Otimes__class_Otimes(U_5226)),U_5230),c_Groups_Oone__class_Oone(U_5226)),U_5229))
| sP259(U_5227,U_5226,U_5228,U_5229,U_5230)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5227),U_5229))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5227),U_5228))
| ~ class_Groups_Ocomm__monoid__mult(U_5226) ),
inference(clausify,[status(thm)],[f_1171_4]) ).
cnf(f_1171_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5227),sK103(U_5230,U_5229,U_5228,U_5227,U_5226)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5227,tc_HOL_Obool)),U_5228),U_5229)))
| ~ sP259(U_5227,U_5226,U_5228,U_5229,U_5230) ),
inference(clausify,[status(thm)],[f_1171_4]) ).
cnf(f_1171_7,plain,
( hAPP(U_5230,sK103(U_5230,U_5229,U_5228,U_5227,U_5226)) != c_Groups_Oone__class_Oone(U_5226)
| ~ sP259(U_5227,U_5226,U_5228,U_5229,U_5230) ),
inference(clausify,[status(thm)],[f_1171_4]) ).
fof(f_1172_1,plain,
! [V_f_2,V_T_2,V_S_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_T_2))
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_d)
& 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_S_2),V_T_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Un__one]) ).
fof(f_1172_2,plain,
! [U_5236,U_5235,U_5234,U_5233,U_5232] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5233,U_5232),U_5236),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5233,tc_HOL_Obool)),U_5234),U_5235)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5232),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5233,U_5232),U_5236),U_5234)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5233,U_5232),U_5236),U_5235))
| ? [U_5231] :
( hAPP(U_5236,U_5231) != c_Groups_Oone__class_Oone(U_5232)
& hBOOL(hAPP(hAPP(c_member(U_5233),U_5231),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5233,tc_HOL_Obool)),U_5234),U_5235))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5233),U_5235))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5233),U_5234))
| ~ class_Groups_Ocomm__monoid__mult(U_5232) ),
inference(variable_rename,[status(thm)],[f_1172_1]) ).
fof(f_1172_3,plain,
! [U_5236,U_5235,U_5234,U_5233,U_5232] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5233,U_5232),U_5236),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5233,tc_HOL_Obool)),U_5234),U_5235)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5232),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5233,U_5232),U_5236),U_5234)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5233,U_5232),U_5236),U_5235))
| ( hAPP(U_5236,sK104(U_5236,U_5235,U_5234,U_5233,U_5232)) != c_Groups_Oone__class_Oone(U_5232)
& hBOOL(hAPP(hAPP(c_member(U_5233),sK104(U_5236,U_5235,U_5234,U_5233,U_5232)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5233,tc_HOL_Obool)),U_5234),U_5235))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5233),U_5235))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5233),U_5234))
| ~ class_Groups_Ocomm__monoid__mult(U_5232) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_5231,sK104(U_5236,U_5235,U_5234,U_5233,U_5232))],[f_1172_2]) ).
fof(f_1172_4,plain,
( ! [U_5232,U_5235,U_5234,U_5233,U_5236] :
( hAPP(U_5236,sK104(U_5236,U_5235,U_5234,U_5233,U_5232)) != c_Groups_Oone__class_Oone(U_5232)
| ~ sP260(U_5232,U_5235,U_5234,U_5233,U_5236) )
& ! [U_5232,U_5235,U_5234,U_5233,U_5236] :
( hBOOL(hAPP(hAPP(c_member(U_5233),sK104(U_5236,U_5235,U_5234,U_5233,U_5232)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5233,tc_HOL_Obool)),U_5234),U_5235)))
| ~ sP260(U_5232,U_5235,U_5234,U_5233,U_5236) )
& ! [U_5232,U_5235,U_5234,U_5233,U_5236] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5233,U_5232),U_5236),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5233,tc_HOL_Obool)),U_5234),U_5235)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5232),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5233,U_5232),U_5236),U_5234)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5233,U_5232),U_5236),U_5235))
| sP260(U_5232,U_5235,U_5234,U_5233,U_5236)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5233),U_5235))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5233),U_5234))
| ~ class_Groups_Ocomm__monoid__mult(U_5232) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP260])],[f_1172_3]) ).
cnf(f_1172_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5233,U_5232),U_5236),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5233,tc_HOL_Obool)),U_5234),U_5235)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5232),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5233,U_5232),U_5236),U_5234)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5233,U_5232),U_5236),U_5235))
| sP260(U_5232,U_5235,U_5234,U_5233,U_5236)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5233),U_5235))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5233),U_5234))
| ~ class_Groups_Ocomm__monoid__mult(U_5232) ),
inference(clausify,[status(thm)],[f_1172_4]) ).
cnf(f_1172_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5233),sK104(U_5236,U_5235,U_5234,U_5233,U_5232)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5233,tc_HOL_Obool)),U_5234),U_5235)))
| ~ sP260(U_5232,U_5235,U_5234,U_5233,U_5236) ),
inference(clausify,[status(thm)],[f_1172_4]) ).
cnf(f_1172_7,plain,
( hAPP(U_5236,sK104(U_5236,U_5235,U_5234,U_5233,U_5232)) != c_Groups_Oone__class_Oone(U_5232)
| ~ sP260(U_5232,U_5235,U_5234,U_5233,U_5236) ),
inference(clausify,[status(thm)],[f_1172_4]) ).
fof(f_1173_1,plain,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_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_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_B_2))
| ? [B_x] :
( hAPP(V_g_2,B_x) != c_Groups_Oone__class_Oone(T_d)
& 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))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter__neutral]) ).
fof(f_1173_2,plain,
! [U_5242,U_5241,U_5240,U_5239,U_5238] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5239,U_5238),U_5242),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5239,tc_HOL_Obool)),U_5240),U_5241)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5238),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5239,U_5238),U_5242),U_5240)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5239,U_5238),U_5242),U_5241))
| ? [U_5237] :
( hAPP(U_5242,U_5237) != c_Groups_Oone__class_Oone(U_5238)
& hBOOL(hAPP(hAPP(c_member(U_5239),U_5237),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5239,tc_HOL_Obool)),U_5240),U_5241))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5239),U_5241))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5239),U_5240))
| ~ class_Groups_Ocomm__monoid__mult(U_5238) ),
inference(variable_rename,[status(thm)],[f_1173_1]) ).
fof(f_1173_3,plain,
! [U_5242,U_5241,U_5240,U_5239,U_5238] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5239,U_5238),U_5242),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5239,tc_HOL_Obool)),U_5240),U_5241)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5238),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5239,U_5238),U_5242),U_5240)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5239,U_5238),U_5242),U_5241))
| ( hAPP(U_5242,sK105(U_5242,U_5241,U_5240,U_5239,U_5238)) != c_Groups_Oone__class_Oone(U_5238)
& hBOOL(hAPP(hAPP(c_member(U_5239),sK105(U_5242,U_5241,U_5240,U_5239,U_5238)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5239,tc_HOL_Obool)),U_5240),U_5241))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5239),U_5241))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5239),U_5240))
| ~ class_Groups_Ocomm__monoid__mult(U_5238) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_5237,sK105(U_5242,U_5241,U_5240,U_5239,U_5238))],[f_1173_2]) ).
fof(f_1173_4,plain,
( ! [U_5239,U_5238,U_5240,U_5241,U_5242] :
( hAPP(U_5242,sK105(U_5242,U_5241,U_5240,U_5239,U_5238)) != c_Groups_Oone__class_Oone(U_5238)
| ~ sP261(U_5239,U_5238,U_5240,U_5241,U_5242) )
& ! [U_5239,U_5238,U_5240,U_5241,U_5242] :
( hBOOL(hAPP(hAPP(c_member(U_5239),sK105(U_5242,U_5241,U_5240,U_5239,U_5238)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5239,tc_HOL_Obool)),U_5240),U_5241)))
| ~ sP261(U_5239,U_5238,U_5240,U_5241,U_5242) )
& ! [U_5239,U_5238,U_5240,U_5241,U_5242] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5239,U_5238),U_5242),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5239,tc_HOL_Obool)),U_5240),U_5241)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5238),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5239,U_5238),U_5242),U_5240)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5239,U_5238),U_5242),U_5241))
| sP261(U_5239,U_5238,U_5240,U_5241,U_5242)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5239),U_5241))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5239),U_5240))
| ~ class_Groups_Ocomm__monoid__mult(U_5238) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP261])],[f_1173_3]) ).
cnf(f_1173_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5239,U_5238),U_5242),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5239,tc_HOL_Obool)),U_5240),U_5241)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5238),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5239,U_5238),U_5242),U_5240)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5239,U_5238),U_5242),U_5241))
| sP261(U_5239,U_5238,U_5240,U_5241,U_5242)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5239),U_5241))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5239),U_5240))
| ~ class_Groups_Ocomm__monoid__mult(U_5238) ),
inference(clausify,[status(thm)],[f_1173_4]) ).
cnf(f_1173_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5239),sK105(U_5242,U_5241,U_5240,U_5239,U_5238)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5239,tc_HOL_Obool)),U_5240),U_5241)))
| ~ sP261(U_5239,U_5238,U_5240,U_5241,U_5242) ),
inference(clausify,[status(thm)],[f_1173_4]) ).
cnf(f_1173_7,plain,
( hAPP(U_5242,sK105(U_5242,U_5241,U_5240,U_5239,U_5238)) != c_Groups_Oone__class_Oone(U_5238)
| ~ sP261(U_5239,U_5238,U_5240,U_5241,U_5242) ),
inference(clausify,[status(thm)],[f_1173_4]) ).
fof(f_1174_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) = V_x_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)))) != 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))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oremove]) ).
fof(f_1174_2,plain,
! [U_5245,U_5244,U_5243] :
( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_5243,U_5244) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5243),U_5245),c_Big__Operators_Olattice__class_OInf__fin(U_5243,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5243,tc_HOL_Obool)),U_5244),hAPP(hAPP(c_Set_Oinsert(U_5243),U_5245),c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5243,tc_HOL_Obool)),U_5244),hAPP(hAPP(c_Set_Oinsert(U_5243),U_5245),c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(U_5243,U_5244) = U_5245
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5243,tc_HOL_Obool)),U_5244),hAPP(hAPP(c_Set_Oinsert(U_5243),U_5245),c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_5243),U_5245),U_5244))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5243),U_5244))
| ~ class_Lattices_Olattice(U_5243) ),
inference(variable_rename,[status(thm)],[f_1174_1]) ).
fof(f_1174_3,plain,
( ! [U_5243,U_5244,U_5245] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5243,U_5244) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5243),U_5245),c_Big__Operators_Olattice__class_OInf__fin(U_5243,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5243,tc_HOL_Obool)),U_5244),hAPP(hAPP(c_Set_Oinsert(U_5243),U_5245),c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5243,tc_HOL_Obool)),U_5244),hAPP(hAPP(c_Set_Oinsert(U_5243),U_5245),c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool))
| ~ sP262(U_5243,U_5244,U_5245) )
& ! [U_5243,U_5244,U_5245] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5243,U_5244) = U_5245
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5243,tc_HOL_Obool)),U_5244),hAPP(hAPP(c_Set_Oinsert(U_5243),U_5245),c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool))
| ~ sP262(U_5243,U_5244,U_5245) )
& ! [U_5243,U_5244,U_5245] :
( sP262(U_5243,U_5244,U_5245)
| ~ hBOOL(hAPP(hAPP(c_member(U_5243),U_5245),U_5244))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5243),U_5244))
| ~ class_Lattices_Olattice(U_5243) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP262])],[f_1174_2]) ).
cnf(f_1174_4,plain,
( sP262(U_5243,U_5244,U_5245)
| ~ hBOOL(hAPP(hAPP(c_member(U_5243),U_5245),U_5244))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5243),U_5244))
| ~ class_Lattices_Olattice(U_5243) ),
inference(clausify,[status(thm)],[f_1174_3]) ).
cnf(f_1174_5,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5243,U_5244) = U_5245
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5243,tc_HOL_Obool)),U_5244),hAPP(hAPP(c_Set_Oinsert(U_5243),U_5245),c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool))
| ~ sP262(U_5243,U_5244,U_5245) ),
inference(clausify,[status(thm)],[f_1174_3]) ).
cnf(f_1174_6,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5243,U_5244) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5243),U_5245),c_Big__Operators_Olattice__class_OInf__fin(U_5243,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5243,tc_HOL_Obool)),U_5244),hAPP(hAPP(c_Set_Oinsert(U_5243),U_5245),c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5243,tc_HOL_Obool)),U_5244),hAPP(hAPP(c_Set_Oinsert(U_5243),U_5245),c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_5243,tc_HOL_Obool))
| ~ sP262(U_5243,U_5244,U_5245) ),
inference(clausify,[status(thm)],[f_1174_3]) ).
fof(f_1175_1,plain,
! [V_f_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_d)),V_f_2)),c_Orderings_Otop__class_Otop(T_d)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_d) ),
inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf]) ).
fof(f_1175_2,plain,
! [U_5249,U_5248,U_5247,U_5246] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5247,U_5246),U_5248),U_5249) = hAPP(hAPP(c_Finite__Set_Ofold(U_5247,U_5246,hAPP(hAPP(c_COMBB(U_5246,tc_fun(U_5246,U_5246),U_5247),c_Lattices_Osemilattice__inf__class_Oinf(U_5246)),U_5249)),c_Orderings_Otop__class_Otop(U_5246)),U_5248)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5247),U_5248))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5246) ),
inference(variable_rename,[status(thm)],[f_1175_1]) ).
fof(f_1175_3,plain,
! [U_5247,U_5249,U_5248,U_5246] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5247,U_5246),U_5248),U_5249) = hAPP(hAPP(c_Finite__Set_Ofold(U_5247,U_5246,hAPP(hAPP(c_COMBB(U_5246,tc_fun(U_5246,U_5246),U_5247),c_Lattices_Osemilattice__inf__class_Oinf(U_5246)),U_5249)),c_Orderings_Otop__class_Otop(U_5246)),U_5248)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5247),U_5248))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5246) ),
inference(definitional_conversion,[status(esa)],[f_1175_2]) ).
cnf(f_1175_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5247,U_5246),U_5248),U_5249) = hAPP(hAPP(c_Finite__Set_Ofold(U_5247,U_5246,hAPP(hAPP(c_COMBB(U_5246,tc_fun(U_5246,U_5246),U_5247),c_Lattices_Osemilattice__inf__class_Oinf(U_5246)),U_5249)),c_Orderings_Otop__class_Otop(U_5246)),U_5248)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5247),U_5248))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5246) ),
inference(clausify,[status(thm)],[f_1175_3]) ).
fof(f_1176_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_c),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)))))) = hAPP(c_Finite__Set_Ocard(T_c),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)) ),
inference(fof_nnf,[status(thm)],[fact_card__Suc__Diff1]) ).
fof(f_1176_2,plain,
! [U_5252,U_5251,U_5250] :
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5250),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5250,tc_HOL_Obool)),U_5251),hAPP(hAPP(c_Set_Oinsert(U_5250),U_5252),c_Orderings_Obot__class_Obot(tc_fun(U_5250,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_5250),U_5251)
| ~ hBOOL(hAPP(hAPP(c_member(U_5250),U_5252),U_5251))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5250),U_5251)) ),
inference(variable_rename,[status(thm)],[f_1176_1]) ).
fof(f_1176_3,plain,
! [U_5250,U_5251,U_5252] :
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5250),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5250,tc_HOL_Obool)),U_5251),hAPP(hAPP(c_Set_Oinsert(U_5250),U_5252),c_Orderings_Obot__class_Obot(tc_fun(U_5250,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_5250),U_5251)
| ~ hBOOL(hAPP(hAPP(c_member(U_5250),U_5252),U_5251))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5250),U_5251)) ),
inference(definitional_conversion,[status(esa)],[f_1176_2]) ).
cnf(f_1176_4,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5250),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5250,tc_HOL_Obool)),U_5251),hAPP(hAPP(c_Set_Oinsert(U_5250),U_5252),c_Orderings_Obot__class_Obot(tc_fun(U_5250,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_5250),U_5251)
| ~ hBOOL(hAPP(hAPP(c_member(U_5250),U_5252),U_5251))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5250),U_5251)) ),
inference(clausify,[status(thm)],[f_1176_3]) ).
fof(f_1177_1,plain,
! [V_A_2,T_c] :
( c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),c_Orderings_Otop__class_Otop(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fold__inf]) ).
fof(f_1177_2,plain,
! [U_5254,U_5253] :
( c_Complete__Lattice_OInf__class_OInf(U_5253,U_5254) = hAPP(hAPP(c_Finite__Set_Ofold(U_5253,U_5253,c_Lattices_Osemilattice__inf__class_Oinf(U_5253)),c_Orderings_Otop__class_Otop(U_5253)),U_5254)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5253),U_5254))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5253) ),
inference(variable_rename,[status(thm)],[f_1177_1]) ).
fof(f_1177_3,plain,
! [U_5253,U_5254] :
( c_Complete__Lattice_OInf__class_OInf(U_5253,U_5254) = hAPP(hAPP(c_Finite__Set_Ofold(U_5253,U_5253,c_Lattices_Osemilattice__inf__class_Oinf(U_5253)),c_Orderings_Otop__class_Otop(U_5253)),U_5254)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5253),U_5254))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5253) ),
inference(definitional_conversion,[status(esa)],[f_1177_2]) ).
cnf(f_1177_4,plain,
( c_Complete__Lattice_OInf__class_OInf(U_5253,U_5254) = hAPP(hAPP(c_Finite__Set_Ofold(U_5253,U_5253,c_Lattices_Osemilattice__inf__class_Oinf(U_5253)),c_Orderings_Otop__class_Otop(U_5253)),U_5254)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5253),U_5254))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5253) ),
inference(clausify,[status(thm)],[f_1177_3]) ).
fof(f_1178_1,plain,
! [V_X_2,V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_C_2))) ),
inference(fof_nnf,[status(thm)],[fact_InterE]) ).
fof(f_1178_2,plain,
! [U_5258,U_5257,U_5256,U_5255] :
( hBOOL(hAPP(hAPP(c_member(U_5255),U_5256),U_5258))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5255,tc_HOL_Obool)),U_5258),U_5257))
| ~ hBOOL(hAPP(hAPP(c_member(U_5255),U_5256),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5255,tc_HOL_Obool),U_5257))) ),
inference(variable_rename,[status(thm)],[f_1178_1]) ).
fof(f_1178_3,plain,
! [U_5255,U_5256,U_5257,U_5258] :
( hBOOL(hAPP(hAPP(c_member(U_5255),U_5256),U_5258))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5255,tc_HOL_Obool)),U_5258),U_5257))
| ~ hBOOL(hAPP(hAPP(c_member(U_5255),U_5256),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5255,tc_HOL_Obool),U_5257))) ),
inference(definitional_conversion,[status(esa)],[f_1178_2]) ).
cnf(f_1178_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_5255),U_5256),U_5258))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5255,tc_HOL_Obool)),U_5258),U_5257))
| ~ hBOOL(hAPP(hAPP(c_member(U_5255),U_5256),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5255,tc_HOL_Obool),U_5257))) ),
inference(clausify,[status(thm)],[f_1178_3]) ).
fof(f_1179_1,plain,
! [V_X_2,V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_C_2))) ),
inference(fof_nnf,[status(thm)],[fact_InterD]) ).
fof(f_1179_2,plain,
! [U_5262,U_5261,U_5260,U_5259] :
( hBOOL(hAPP(hAPP(c_member(U_5259),U_5260),U_5262))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5259,tc_HOL_Obool)),U_5262),U_5261))
| ~ hBOOL(hAPP(hAPP(c_member(U_5259),U_5260),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5259,tc_HOL_Obool),U_5261))) ),
inference(variable_rename,[status(thm)],[f_1179_1]) ).
fof(f_1179_3,plain,
! [U_5259,U_5260,U_5261,U_5262] :
( hBOOL(hAPP(hAPP(c_member(U_5259),U_5260),U_5262))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5259,tc_HOL_Obool)),U_5262),U_5261))
| ~ hBOOL(hAPP(hAPP(c_member(U_5259),U_5260),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5259,tc_HOL_Obool),U_5261))) ),
inference(definitional_conversion,[status(esa)],[f_1179_2]) ).
cnf(f_1179_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_5259),U_5260),U_5262))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5259,tc_HOL_Obool)),U_5262),U_5261))
| ~ hBOOL(hAPP(hAPP(c_member(U_5259),U_5260),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5259,tc_HOL_Obool),U_5261))) ),
inference(clausify,[status(thm)],[f_1179_3]) ).
fof(f_1180_1,plain,
! [V_M_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_M_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_x),V_M_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Inter]) ).
fof(f_1180_2,plain,
! [U_5265,U_5264] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5264),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5264,tc_HOL_Obool),U_5265)))
| ! [U_5263] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5264),U_5263))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5264,tc_HOL_Obool)),U_5263),U_5265)) ) ),
inference(variable_rename,[status(thm)],[f_1180_1]) ).
fof(f_1180_3,plain,
! [U_5264,U_5263,U_5265] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5264),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5264,tc_HOL_Obool),U_5265)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5264),U_5263))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5264,tc_HOL_Obool)),U_5263),U_5265)) ),
inference(definitional_conversion,[status(esa)],[f_1180_2]) ).
cnf(f_1180_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5264),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5264,tc_HOL_Obool),U_5265)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5264),U_5263))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5264,tc_HOL_Obool)),U_5263),U_5265)) ),
inference(clausify,[status(thm)],[f_1180_3]) ).
fof(f_1181_1,plain,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_INF1__D]) ).
fof(f_1181_2,plain,
! [U_5271,U_5270,U_5269,U_5268,U_5267,U_5266] :
( hBOOL(hAPP(hAPP(U_5269,U_5271),U_5270))
| ~ hBOOL(hAPP(hAPP(c_member(U_5266),U_5271),U_5268))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5266,tc_fun(U_5267,tc_HOL_Obool)),U_5268),U_5269),U_5270)) ),
inference(variable_rename,[status(thm)],[f_1181_1]) ).
fof(f_1181_3,plain,
! [U_5266,U_5267,U_5268,U_5269,U_5270,U_5271] :
( hBOOL(hAPP(hAPP(U_5269,U_5271),U_5270))
| ~ hBOOL(hAPP(hAPP(c_member(U_5266),U_5271),U_5268))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5266,tc_fun(U_5267,tc_HOL_Obool)),U_5268),U_5269),U_5270)) ),
inference(definitional_conversion,[status(esa)],[f_1181_2]) ).
cnf(f_1181_4,plain,
( hBOOL(hAPP(hAPP(U_5269,U_5271),U_5270))
| ~ hBOOL(hAPP(hAPP(c_member(U_5266),U_5271),U_5268))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5266,tc_fun(U_5267,tc_HOL_Obool)),U_5268),U_5269),U_5270)) ),
inference(clausify,[status(thm)],[f_1181_3]) ).
fof(f_1182_1,plain,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_d,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),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_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_INF1__E]) ).
fof(f_1182_2,plain,
! [U_5277,U_5276,U_5275,U_5274,U_5273,U_5272] :
( ~ hBOOL(hAPP(hAPP(c_member(U_5272),U_5277),U_5274))
| hBOOL(hAPP(hAPP(U_5275,U_5277),U_5276))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5272,tc_fun(U_5273,tc_HOL_Obool)),U_5274),U_5275),U_5276)) ),
inference(variable_rename,[status(thm)],[f_1182_1]) ).
fof(f_1182_3,plain,
! [U_5272,U_5273,U_5274,U_5275,U_5276,U_5277] :
( ~ hBOOL(hAPP(hAPP(c_member(U_5272),U_5277),U_5274))
| hBOOL(hAPP(hAPP(U_5275,U_5277),U_5276))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5272,tc_fun(U_5273,tc_HOL_Obool)),U_5274),U_5275),U_5276)) ),
inference(definitional_conversion,[status(esa)],[f_1182_2]) ).
cnf(f_1182_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_5272),U_5277),U_5274))
| hBOOL(hAPP(hAPP(U_5275,U_5277),U_5276))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5272,tc_fun(U_5273,tc_HOL_Obool)),U_5274),U_5275),U_5276)) ),
inference(clausify,[status(thm)],[f_1182_3]) ).
fof(f_1183_1,plain,
! [V_a_2,V_B_2,V_A_2,T_d,V_b_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_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))) ),
inference(fof_nnf,[status(thm)],[fact_INT__D]) ).
fof(f_1183_2,plain,
! [U_5283,U_5282,U_5281,U_5280,U_5279,U_5278] :
( hBOOL(hAPP(hAPP(c_member(U_5278),U_5279),hAPP(U_5282,U_5283)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5280),U_5283),U_5281))
| ~ hBOOL(hAPP(hAPP(c_member(U_5278),U_5279),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5280,tc_fun(U_5278,tc_HOL_Obool)),U_5281),U_5282))) ),
inference(variable_rename,[status(thm)],[f_1183_1]) ).
fof(f_1183_3,plain,
! [U_5278,U_5279,U_5280,U_5281,U_5282,U_5283] :
( hBOOL(hAPP(hAPP(c_member(U_5278),U_5279),hAPP(U_5282,U_5283)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5280),U_5283),U_5281))
| ~ hBOOL(hAPP(hAPP(c_member(U_5278),U_5279),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5280,tc_fun(U_5278,tc_HOL_Obool)),U_5281),U_5282))) ),
inference(definitional_conversion,[status(esa)],[f_1183_2]) ).
cnf(f_1183_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_5278),U_5279),hAPP(U_5282,U_5283)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5280),U_5283),U_5281))
| ~ hBOOL(hAPP(hAPP(c_member(U_5278),U_5279),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5280,tc_fun(U_5278,tc_HOL_Obool)),U_5281),U_5282))) ),
inference(clausify,[status(thm)],[f_1183_3]) ).
fof(f_1184_1,plain,
! [V_a_2,V_B_2,V_A_2,T_d,V_b_2,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_d),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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_INT__E]) ).
fof(f_1184_2,plain,
! [U_5289,U_5288,U_5287,U_5286,U_5285,U_5284] :
( ~ hBOOL(hAPP(hAPP(c_member(U_5286),U_5289),U_5287))
| hBOOL(hAPP(hAPP(c_member(U_5284),U_5285),hAPP(U_5288,U_5289)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5284),U_5285),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5286,tc_fun(U_5284,tc_HOL_Obool)),U_5287),U_5288))) ),
inference(variable_rename,[status(thm)],[f_1184_1]) ).
fof(f_1184_3,plain,
! [U_5287,U_5284,U_5285,U_5286,U_5288,U_5289] :
( ~ hBOOL(hAPP(hAPP(c_member(U_5286),U_5289),U_5287))
| hBOOL(hAPP(hAPP(c_member(U_5284),U_5285),hAPP(U_5288,U_5289)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5284),U_5285),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5286,tc_fun(U_5284,tc_HOL_Obool)),U_5287),U_5288))) ),
inference(definitional_conversion,[status(esa)],[f_1184_2]) ).
cnf(f_1184_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_5286),U_5289),U_5287))
| hBOOL(hAPP(hAPP(c_member(U_5284),U_5285),hAPP(U_5288,U_5289)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5284),U_5285),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5286,tc_fun(U_5284,tc_HOL_Obool)),U_5287),U_5288))) ),
inference(clausify,[status(thm)],[f_1184_3]) ).
fof(f_1185_1,plain,
! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
inference(fof_nnf,[status(thm)],[fact_INF2__D]) ).
fof(f_1185_2,plain,
! [U_5297,U_5296,U_5295,U_5294,U_5293,U_5292,U_5291,U_5290] :
( hBOOL(hAPP(hAPP(hAPP(U_5294,U_5297),U_5295),U_5296))
| ~ hBOOL(hAPP(hAPP(c_member(U_5290),U_5297),U_5293))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5290,tc_fun(U_5291,tc_fun(U_5292,tc_HOL_Obool))),U_5293),U_5294),U_5295),U_5296)) ),
inference(variable_rename,[status(thm)],[f_1185_1]) ).
fof(f_1185_3,plain,
! [U_5290,U_5291,U_5292,U_5293,U_5294,U_5295,U_5296,U_5297] :
( hBOOL(hAPP(hAPP(hAPP(U_5294,U_5297),U_5295),U_5296))
| ~ hBOOL(hAPP(hAPP(c_member(U_5290),U_5297),U_5293))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5290,tc_fun(U_5291,tc_fun(U_5292,tc_HOL_Obool))),U_5293),U_5294),U_5295),U_5296)) ),
inference(definitional_conversion,[status(esa)],[f_1185_2]) ).
cnf(f_1185_4,plain,
( hBOOL(hAPP(hAPP(hAPP(U_5294,U_5297),U_5295),U_5296))
| ~ hBOOL(hAPP(hAPP(c_member(U_5290),U_5297),U_5293))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5290,tc_fun(U_5291,tc_fun(U_5292,tc_HOL_Obool))),U_5293),U_5294),U_5295),U_5296)) ),
inference(clausify,[status(thm)],[f_1185_3]) ).
fof(f_1186_1,plain,
! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
inference(fof_nnf,[status(thm)],[fact_INF2__E]) ).
fof(f_1186_2,plain,
! [U_5305,U_5304,U_5303,U_5302,U_5301,U_5300,U_5299,U_5298] :
( ~ hBOOL(hAPP(hAPP(c_member(U_5298),U_5305),U_5301))
| hBOOL(hAPP(hAPP(hAPP(U_5302,U_5305),U_5303),U_5304))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5298,tc_fun(U_5299,tc_fun(U_5300,tc_HOL_Obool))),U_5301),U_5302),U_5303),U_5304)) ),
inference(variable_rename,[status(thm)],[f_1186_1]) ).
fof(f_1186_3,plain,
! [U_5298,U_5299,U_5300,U_5301,U_5302,U_5303,U_5304,U_5305] :
( ~ hBOOL(hAPP(hAPP(c_member(U_5298),U_5305),U_5301))
| hBOOL(hAPP(hAPP(hAPP(U_5302,U_5305),U_5303),U_5304))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5298,tc_fun(U_5299,tc_fun(U_5300,tc_HOL_Obool))),U_5301),U_5302),U_5303),U_5304)) ),
inference(definitional_conversion,[status(esa)],[f_1186_2]) ).
cnf(f_1186_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_5298),U_5305),U_5301))
| hBOOL(hAPP(hAPP(hAPP(U_5302,U_5305),U_5303),U_5304))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5298,tc_fun(U_5299,tc_fun(U_5300,tc_HOL_Obool))),U_5301),U_5302),U_5303),U_5304)) ),
inference(clausify,[status(thm)],[f_1186_3]) ).
fof(f_1187_1,plain,
! [V_A_2,T_d,V_I_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_A_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__INT]) ).
fof(f_1187_2,plain,
! [U_5310,U_5309,U_5308,U_5307] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5309),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5307,tc_fun(U_5309,tc_HOL_Obool)),U_5308),U_5310)))
| ! [U_5306] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5309),hAPP(U_5310,U_5306)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5307),U_5306),U_5308)) ) ),
inference(variable_rename,[status(thm)],[f_1187_1]) ).
fof(f_1187_3,plain,
! [U_5307,U_5306,U_5308,U_5309,U_5310] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5309),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5307,tc_fun(U_5309,tc_HOL_Obool)),U_5308),U_5310)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5309),hAPP(U_5310,U_5306)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5307),U_5306),U_5308)) ),
inference(definitional_conversion,[status(esa)],[f_1187_2]) ).
cnf(f_1187_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5309),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5307,tc_fun(U_5309,tc_HOL_Obool)),U_5308),U_5310)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5309),hAPP(U_5310,U_5306)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5307),U_5306),U_5308)) ),
inference(clausify,[status(thm)],[f_1187_3]) ).
fof(f_1188_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_1188_2,plain,
! [U_5312,U_5311] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5311)),hAPP(c_Nat_OSuc,U_5312)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5311),U_5312)) ),
inference(variable_rename,[status(thm)],[f_1188_1]) ).
fof(f_1188_3,plain,
! [U_5312,U_5311] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5311)),hAPP(c_Nat_OSuc,U_5312)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5311),U_5312)) ),
inference(definitional_conversion,[status(esa)],[f_1188_2]) ).
cnf(f_1188_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5311)),hAPP(c_Nat_OSuc,U_5312)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5311),U_5312)) ),
inference(clausify,[status(thm)],[f_1188_3]) ).
fof(f_1189_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_1189_2,plain,
! [U_5313] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5313),hAPP(c_Nat_OSuc,U_5313))),
inference(variable_rename,[status(thm)],[f_1189_1]) ).
fof(f_1189_3,plain,
! [U_5313] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5313),hAPP(c_Nat_OSuc,U_5313))),
inference(definitional_conversion,[status(esa)],[f_1189_2]) ).
cnf(f_1189_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5313),hAPP(c_Nat_OSuc,U_5313))),
inference(clausify,[status(thm)],[f_1189_3]) ).
fof(f_1190_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_d,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_d),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)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_C_2))),
inference(fof_nnf,[status(thm)],[fact_Int__Inter__image]) ).
fof(f_1190_2,plain,
! [U_5318,U_5317,U_5316,U_5315,U_5314] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5314,tc_fun(U_5315,tc_HOL_Obool)),U_5316),hAPP(hAPP(c_COMBS(U_5314,tc_fun(U_5315,tc_HOL_Obool),tc_fun(U_5315,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5315,tc_HOL_Obool),tc_fun(tc_fun(U_5315,tc_HOL_Obool),tc_fun(U_5315,tc_HOL_Obool)),U_5314),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5315,tc_HOL_Obool))),U_5317)),U_5318)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5315,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5315,tc_HOL_Obool),hAPP(c_Set_Oimage(U_5314,tc_fun(U_5315,tc_HOL_Obool),U_5317),U_5316))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5315,tc_HOL_Obool),hAPP(c_Set_Oimage(U_5314,tc_fun(U_5315,tc_HOL_Obool),U_5318),U_5316))),
inference(variable_rename,[status(thm)],[f_1190_1]) ).
fof(f_1190_3,plain,
! [U_5314,U_5315,U_5316,U_5317,U_5318] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5314,tc_fun(U_5315,tc_HOL_Obool)),U_5316),hAPP(hAPP(c_COMBS(U_5314,tc_fun(U_5315,tc_HOL_Obool),tc_fun(U_5315,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5315,tc_HOL_Obool),tc_fun(tc_fun(U_5315,tc_HOL_Obool),tc_fun(U_5315,tc_HOL_Obool)),U_5314),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5315,tc_HOL_Obool))),U_5317)),U_5318)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5315,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5315,tc_HOL_Obool),hAPP(c_Set_Oimage(U_5314,tc_fun(U_5315,tc_HOL_Obool),U_5317),U_5316))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5315,tc_HOL_Obool),hAPP(c_Set_Oimage(U_5314,tc_fun(U_5315,tc_HOL_Obool),U_5318),U_5316))),
inference(definitional_conversion,[status(esa)],[f_1190_2]) ).
cnf(f_1190_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5314,tc_fun(U_5315,tc_HOL_Obool)),U_5316),hAPP(hAPP(c_COMBS(U_5314,tc_fun(U_5315,tc_HOL_Obool),tc_fun(U_5315,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5315,tc_HOL_Obool),tc_fun(tc_fun(U_5315,tc_HOL_Obool),tc_fun(U_5315,tc_HOL_Obool)),U_5314),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5315,tc_HOL_Obool))),U_5317)),U_5318)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5315,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5315,tc_HOL_Obool),hAPP(c_Set_Oimage(U_5314,tc_fun(U_5315,tc_HOL_Obool),U_5317),U_5316))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5315,tc_HOL_Obool),hAPP(c_Set_Oimage(U_5314,tc_fun(U_5315,tc_HOL_Obool),U_5318),U_5316))),
inference(clausify,[status(thm)],[f_1190_3]) ).
fof(f_1191_1,plain,
! [V_x_2,V_f_2,V_A_2,T_e,T_d,T_c] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_e,T_c)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),hAPP(hAPP(c_COMBC(T_d,T_e,T_c),V_f_2),V_x_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_INFI__apply]) ).
fof(f_1191_2,plain,
! [U_5324,U_5323,U_5322,U_5321,U_5320,U_5319] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5320,tc_fun(U_5321,U_5319)),U_5322),U_5323),U_5324) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5320,U_5319),U_5322),hAPP(hAPP(c_COMBC(U_5320,U_5321,U_5319),U_5323),U_5324))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5319) ),
inference(variable_rename,[status(thm)],[f_1191_1]) ).
fof(f_1191_3,plain,
! [U_5319,U_5320,U_5321,U_5322,U_5323,U_5324] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5320,tc_fun(U_5321,U_5319)),U_5322),U_5323),U_5324) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5320,U_5319),U_5322),hAPP(hAPP(c_COMBC(U_5320,U_5321,U_5319),U_5323),U_5324))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5319) ),
inference(definitional_conversion,[status(esa)],[f_1191_2]) ).
cnf(f_1191_4,plain,
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5320,tc_fun(U_5321,U_5319)),U_5322),U_5323),U_5324) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5320,U_5319),U_5322),hAPP(hAPP(c_COMBC(U_5320,U_5321,U_5319),U_5323),U_5324))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5319) ),
inference(clausify,[status(thm)],[f_1191_3]) ).
fof(f_1192_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Un__Inter]) ).
fof(f_1192_2,plain,
! [U_5327,U_5326,U_5325] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5325,tc_HOL_Obool)),U_5326),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5325,tc_HOL_Obool),U_5327)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_5325,tc_HOL_Obool),tc_fun(U_5325,tc_HOL_Obool)),U_5327),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5325,tc_HOL_Obool)),U_5326)),
inference(variable_rename,[status(thm)],[f_1192_1]) ).
fof(f_1192_3,plain,
! [U_5326,U_5325,U_5327] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5325,tc_HOL_Obool)),U_5326),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5325,tc_HOL_Obool),U_5327)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_5325,tc_HOL_Obool),tc_fun(U_5325,tc_HOL_Obool)),U_5327),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5325,tc_HOL_Obool)),U_5326)),
inference(definitional_conversion,[status(esa)],[f_1192_2]) ).
cnf(f_1192_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5325,tc_HOL_Obool)),U_5326),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5325,tc_HOL_Obool),U_5327)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_5325,tc_HOL_Obool),tc_fun(U_5325,tc_HOL_Obool)),U_5327),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5325,tc_HOL_Obool)),U_5326)),
inference(clausify,[status(thm)],[f_1192_3]) ).
fof(f_1193_1,plain,
! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).
fof(f_1193_2,plain,
! [U_5328] : U_5328 != hAPP(c_Nat_OSuc,U_5328),
inference(variable_rename,[status(thm)],[f_1193_1]) ).
fof(f_1193_3,plain,
! [U_5328] : U_5328 != hAPP(c_Nat_OSuc,U_5328),
inference(definitional_conversion,[status(esa)],[f_1193_2]) ).
cnf(f_1193_4,plain,
U_5328 != hAPP(c_Nat_OSuc,U_5328),
inference(clausify,[status(thm)],[f_1193_3]) ).
fof(f_1194_1,plain,
! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).
fof(f_1194_2,plain,
! [U_5329] : hAPP(c_Nat_OSuc,U_5329) != U_5329,
inference(variable_rename,[status(thm)],[f_1194_1]) ).
fof(f_1194_3,plain,
! [U_5329] : hAPP(c_Nat_OSuc,U_5329) != U_5329,
inference(definitional_conversion,[status(esa)],[f_1194_2]) ).
cnf(f_1194_4,plain,
hAPP(c_Nat_OSuc,U_5329) != U_5329,
inference(clausify,[status(thm)],[f_1194_3]) ).
fof(f_1195_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_1195_2,plain,
! [U_5331,U_5330] :
( ( hAPP(c_Nat_OSuc,U_5330) = hAPP(c_Nat_OSuc,U_5331)
| U_5330 != U_5331 )
& ( U_5330 = U_5331
| hAPP(c_Nat_OSuc,U_5330) != hAPP(c_Nat_OSuc,U_5331) ) ),
inference(variable_rename,[status(thm)],[f_1195_1]) ).
fof(f_1195_3,plain,
( ! [U_5335,U_5333] :
( hAPP(c_Nat_OSuc,U_5333) = hAPP(c_Nat_OSuc,U_5335)
| U_5333 != U_5335 )
& ! [U_5334,U_5332] :
( U_5332 = U_5334
| hAPP(c_Nat_OSuc,U_5332) != hAPP(c_Nat_OSuc,U_5334) ) ),
inference(miniscope,[status(thm)],[f_1195_2]) ).
fof(f_1195_4,plain,
( ! [U_5335,U_5333] :
( hAPP(c_Nat_OSuc,U_5333) = hAPP(c_Nat_OSuc,U_5335)
| U_5333 != U_5335 )
& ! [U_5334,U_5332] :
( U_5332 = U_5334
| hAPP(c_Nat_OSuc,U_5332) != hAPP(c_Nat_OSuc,U_5334) ) ),
inference(definitional_conversion,[status(esa)],[f_1195_3]) ).
cnf(f_1195_5,plain,
( U_5332 = U_5334
| hAPP(c_Nat_OSuc,U_5332) != hAPP(c_Nat_OSuc,U_5334) ),
inference(clausify,[status(thm)],[f_1195_4]) ).
cnf(f_1195_6,plain,
( hAPP(c_Nat_OSuc,U_5333) = hAPP(c_Nat_OSuc,U_5335)
| U_5333 != U_5335 ),
inference(clausify,[status(thm)],[f_1195_4]) ).
fof(f_1196_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_1196_2,plain,
! [U_5337,U_5336] :
( U_5336 = U_5337
| hAPP(c_Nat_OSuc,U_5336) != hAPP(c_Nat_OSuc,U_5337) ),
inference(variable_rename,[status(thm)],[f_1196_1]) ).
fof(f_1196_3,plain,
! [U_5336,U_5337] :
( U_5336 = U_5337
| hAPP(c_Nat_OSuc,U_5336) != hAPP(c_Nat_OSuc,U_5337) ),
inference(definitional_conversion,[status(esa)],[f_1196_2]) ).
cnf(f_1196_4,plain,
( U_5336 = U_5337
| hAPP(c_Nat_OSuc,U_5336) != hAPP(c_Nat_OSuc,U_5337) ),
inference(clausify,[status(thm)],[f_1196_3]) ).
fof(f_1197_1,plain,
! [V_f_2,V_B_2,T_e,V_A_2,T_d,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_e,T_c),T_c,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,T_c),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,T_c),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_c),T_c,T_e),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2)),hAPP(c_COMBC(T_d,T_e,T_c),V_f_2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_INF__commute]) ).
fof(f_1197_2,plain,
! [U_5343,U_5342,U_5341,U_5340,U_5339,U_5338] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5339,U_5338),U_5340),hAPP(hAPP(c_COMBB(tc_fun(U_5341,U_5338),U_5338,U_5339),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5341,U_5338),U_5342)),U_5343)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5341,U_5338),U_5342),hAPP(hAPP(c_COMBB(tc_fun(U_5339,U_5338),U_5338,U_5341),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5339,U_5338),U_5340)),hAPP(c_COMBC(U_5339,U_5341,U_5338),U_5343)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5338) ),
inference(variable_rename,[status(thm)],[f_1197_1]) ).
fof(f_1197_3,plain,
! [U_5338,U_5339,U_5340,U_5341,U_5342,U_5343] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5339,U_5338),U_5340),hAPP(hAPP(c_COMBB(tc_fun(U_5341,U_5338),U_5338,U_5339),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5341,U_5338),U_5342)),U_5343)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5341,U_5338),U_5342),hAPP(hAPP(c_COMBB(tc_fun(U_5339,U_5338),U_5338,U_5341),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5339,U_5338),U_5340)),hAPP(c_COMBC(U_5339,U_5341,U_5338),U_5343)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5338) ),
inference(definitional_conversion,[status(esa)],[f_1197_2]) ).
cnf(f_1197_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5339,U_5338),U_5340),hAPP(hAPP(c_COMBB(tc_fun(U_5341,U_5338),U_5338,U_5339),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5341,U_5338),U_5342)),U_5343)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5341,U_5338),U_5342),hAPP(hAPP(c_COMBB(tc_fun(U_5339,U_5338),U_5338,U_5341),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5339,U_5338),U_5340)),hAPP(c_COMBC(U_5339,U_5341,U_5338),U_5343)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5338) ),
inference(clausify,[status(thm)],[f_1197_3]) ).
fof(f_1198_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_1198_2,plain,
! [U_5345,U_5344] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5344),U_5345))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5344)),hAPP(c_Nat_OSuc,U_5345))) ),
inference(variable_rename,[status(thm)],[f_1198_1]) ).
fof(f_1198_3,plain,
! [U_5344,U_5345] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5344),U_5345))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5344)),hAPP(c_Nat_OSuc,U_5345))) ),
inference(definitional_conversion,[status(esa)],[f_1198_2]) ).
cnf(f_1198_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5344),U_5345))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5344)),hAPP(c_Nat_OSuc,U_5345))) ),
inference(clausify,[status(thm)],[f_1198_3]) ).
fof(f_1199_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_1199_2,plain,
! [U_5347,U_5346] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5346),U_5347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5346)),U_5347)) ),
inference(variable_rename,[status(thm)],[f_1199_1]) ).
fof(f_1199_3,plain,
! [U_5346,U_5347] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5346),U_5347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5346)),U_5347)) ),
inference(definitional_conversion,[status(esa)],[f_1199_2]) ).
cnf(f_1199_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5346),U_5347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5346)),U_5347)) ),
inference(clausify,[status(thm)],[f_1199_3]) ).
fof(f_1200_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_1200_2,plain,
! [U_5349,U_5348] :
( U_5348 = U_5349
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5348),U_5349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5348),hAPP(c_Nat_OSuc,U_5349))) ),
inference(variable_rename,[status(thm)],[f_1200_1]) ).
fof(f_1200_3,plain,
! [U_5348,U_5349] :
( U_5348 = U_5349
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5348),U_5349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5348),hAPP(c_Nat_OSuc,U_5349))) ),
inference(definitional_conversion,[status(esa)],[f_1200_2]) ).
cnf(f_1200_4,plain,
( U_5348 = U_5349
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5348),U_5349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5348),hAPP(c_Nat_OSuc,U_5349))) ),
inference(clausify,[status(thm)],[f_1200_3]) ).
fof(f_1201_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_1201_2,plain,
! [U_5352,U_5351,U_5350] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5350)),U_5352))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5351),U_5352))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5350),U_5351)) ),
inference(variable_rename,[status(thm)],[f_1201_1]) ).
fof(f_1201_3,plain,
! [U_5350,U_5351,U_5352] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5350)),U_5352))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5351),U_5352))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5350),U_5351)) ),
inference(definitional_conversion,[status(esa)],[f_1201_2]) ).
cnf(f_1201_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5350)),U_5352))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5351),U_5352))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5350),U_5351)) ),
inference(clausify,[status(thm)],[f_1201_3]) ).
fof(f_1202_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_1202_2,plain,
! [U_5354,U_5353] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5353)),U_5354))
| hAPP(c_Nat_OSuc,U_5353) = U_5354
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5353),U_5354)) ),
inference(variable_rename,[status(thm)],[f_1202_1]) ).
fof(f_1202_3,plain,
! [U_5353,U_5354] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5353)),U_5354))
| hAPP(c_Nat_OSuc,U_5353) = U_5354
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5353),U_5354)) ),
inference(definitional_conversion,[status(esa)],[f_1202_2]) ).
cnf(f_1202_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5353)),U_5354))
| hAPP(c_Nat_OSuc,U_5353) = U_5354
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5353),U_5354)) ),
inference(clausify,[status(thm)],[f_1202_3]) ).
fof(f_1203_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_1203_2,plain,
! [U_5356,U_5355] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5355),hAPP(c_Nat_OSuc,U_5356)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5355),U_5356)) ),
inference(variable_rename,[status(thm)],[f_1203_1]) ).
fof(f_1203_3,plain,
! [U_5356,U_5355] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5355),hAPP(c_Nat_OSuc,U_5356)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5355),U_5356)) ),
inference(definitional_conversion,[status(esa)],[f_1203_2]) ).
cnf(f_1203_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5355),hAPP(c_Nat_OSuc,U_5356)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5355),U_5356)) ),
inference(clausify,[status(thm)],[f_1203_3]) ).
fof(f_1204_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_1204_2,plain,
! [U_5358,U_5357] :
( U_5358 = U_5357
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5357),hAPP(c_Nat_OSuc,U_5358)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5357),U_5358)) ),
inference(variable_rename,[status(thm)],[f_1204_1]) ).
fof(f_1204_3,plain,
! [U_5357,U_5358] :
( U_5358 = U_5357
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5357),hAPP(c_Nat_OSuc,U_5358)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5357),U_5358)) ),
inference(definitional_conversion,[status(esa)],[f_1204_2]) ).
cnf(f_1204_4,plain,
( U_5358 = U_5357
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5357),hAPP(c_Nat_OSuc,U_5358)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5357),U_5358)) ),
inference(clausify,[status(thm)],[f_1204_3]) ).
fof(f_1205_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_1205_2,plain,
! [U_5360,U_5359] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5359),hAPP(c_Nat_OSuc,U_5360)))
| U_5359 != U_5360 )
& ( U_5359 = U_5360
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5359),hAPP(c_Nat_OSuc,U_5360))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5359),U_5360)) ),
inference(variable_rename,[status(thm)],[f_1205_1]) ).
fof(f_1205_3,plain,
( ! [U_5360,U_5359] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5359),hAPP(c_Nat_OSuc,U_5360)))
| U_5359 != U_5360
| ~ sP263(U_5360,U_5359) )
& ! [U_5360,U_5359] :
( U_5359 = U_5360
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5359),hAPP(c_Nat_OSuc,U_5360)))
| ~ sP263(U_5360,U_5359) )
& ! [U_5360,U_5359] :
( sP263(U_5360,U_5359)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5359),U_5360)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP263])],[f_1205_2]) ).
cnf(f_1205_4,plain,
( sP263(U_5360,U_5359)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5359),U_5360)) ),
inference(clausify,[status(thm)],[f_1205_3]) ).
cnf(f_1205_5,plain,
( U_5359 = U_5360
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5359),hAPP(c_Nat_OSuc,U_5360)))
| ~ sP263(U_5360,U_5359) ),
inference(clausify,[status(thm)],[f_1205_3]) ).
cnf(f_1205_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5359),hAPP(c_Nat_OSuc,U_5360)))
| U_5359 != U_5360
| ~ sP263(U_5360,U_5359) ),
inference(clausify,[status(thm)],[f_1205_3]) ).
fof(f_1206_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_1206_2,plain,
! [U_5362,U_5361] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5361)),hAPP(c_Nat_OSuc,U_5362)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5361),U_5362)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5361),U_5362))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5361)),hAPP(c_Nat_OSuc,U_5362))) ) ),
inference(variable_rename,[status(thm)],[f_1206_1]) ).
fof(f_1206_3,plain,
( ! [U_5366,U_5364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5364)),hAPP(c_Nat_OSuc,U_5366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5364),U_5366)) )
& ! [U_5365,U_5363] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5363),U_5365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5363)),hAPP(c_Nat_OSuc,U_5365))) ) ),
inference(miniscope,[status(thm)],[f_1206_2]) ).
fof(f_1206_4,plain,
( ! [U_5364,U_5366] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5364)),hAPP(c_Nat_OSuc,U_5366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5364),U_5366)) )
& ! [U_5365,U_5363] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5363),U_5365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5363)),hAPP(c_Nat_OSuc,U_5365))) ) ),
inference(definitional_conversion,[status(esa)],[f_1206_3]) ).
cnf(f_1206_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5363),U_5365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5363)),hAPP(c_Nat_OSuc,U_5365))) ),
inference(clausify,[status(thm)],[f_1206_4]) ).
cnf(f_1206_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5364)),hAPP(c_Nat_OSuc,U_5366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5364),U_5366)) ),
inference(clausify,[status(thm)],[f_1206_4]) ).
fof(f_1207_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_1207_2,plain,
! [U_5368,U_5367] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5367),hAPP(c_Nat_OSuc,U_5368)))
| ( U_5367 != U_5368
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5367),U_5368)) ) )
& ( U_5367 = U_5368
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5367),U_5368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5367),hAPP(c_Nat_OSuc,U_5368))) ) ),
inference(variable_rename,[status(thm)],[f_1207_1]) ).
fof(f_1207_3,plain,
( ! [U_5372,U_5370] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5370),hAPP(c_Nat_OSuc,U_5372)))
| ( U_5370 != U_5372
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5370),U_5372)) ) )
& ! [U_5371,U_5369] :
( U_5369 = U_5371
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5369),U_5371))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5369),hAPP(c_Nat_OSuc,U_5371))) ) ),
inference(miniscope,[status(thm)],[f_1207_2]) ).
fof(f_1207_4,plain,
( ! [U_5372,U_5370] :
( U_5370 != U_5372
| ~ sP264(U_5372,U_5370) )
& ! [U_5372,U_5370] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5370),U_5372))
| ~ sP264(U_5372,U_5370) )
& ! [U_5372,U_5370] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5370),hAPP(c_Nat_OSuc,U_5372)))
| sP264(U_5372,U_5370) )
& ! [U_5371,U_5369] :
( U_5369 = U_5371
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5369),U_5371))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5369),hAPP(c_Nat_OSuc,U_5371))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP264])],[f_1207_3]) ).
cnf(f_1207_5,plain,
( U_5369 = U_5371
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5369),U_5371))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5369),hAPP(c_Nat_OSuc,U_5371))) ),
inference(clausify,[status(thm)],[f_1207_4]) ).
cnf(f_1207_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5370),hAPP(c_Nat_OSuc,U_5372)))
| sP264(U_5372,U_5370) ),
inference(clausify,[status(thm)],[f_1207_4]) ).
cnf(f_1207_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5370),U_5372))
| ~ sP264(U_5372,U_5370) ),
inference(clausify,[status(thm)],[f_1207_4]) ).
cnf(f_1207_8,plain,
( U_5370 != U_5372
| ~ sP264(U_5372,U_5370) ),
inference(clausify,[status(thm)],[f_1207_4]) ).
fof(f_1208_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_1208_2,plain,
! [U_5374,U_5373] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5373),U_5374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5374),hAPP(c_Nat_OSuc,U_5373))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5374),hAPP(c_Nat_OSuc,U_5373)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5373),U_5374)) ) ),
inference(variable_rename,[status(thm)],[f_1208_1]) ).
fof(f_1208_3,plain,
( ! [U_5378,U_5376] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5376),U_5378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5378),hAPP(c_Nat_OSuc,U_5376))) )
& ! [U_5377,U_5375] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5377),hAPP(c_Nat_OSuc,U_5375)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5375),U_5377)) ) ),
inference(miniscope,[status(thm)],[f_1208_2]) ).
fof(f_1208_4,plain,
( ! [U_5376,U_5378] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5376),U_5378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5378),hAPP(c_Nat_OSuc,U_5376))) )
& ! [U_5377,U_5375] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5377),hAPP(c_Nat_OSuc,U_5375)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5375),U_5377)) ) ),
inference(definitional_conversion,[status(esa)],[f_1208_3]) ).
cnf(f_1208_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5377),hAPP(c_Nat_OSuc,U_5375)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5375),U_5377)) ),
inference(clausify,[status(thm)],[f_1208_4]) ).
cnf(f_1208_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5376),U_5378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5378),hAPP(c_Nat_OSuc,U_5376))) ),
inference(clausify,[status(thm)],[f_1208_4]) ).
fof(f_1209_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_1209_2,plain,
! [U_5380,U_5379] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5379),hAPP(c_Nat_OSuc,U_5380)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5379),U_5380)),
inference(variable_rename,[status(thm)],[f_1209_1]) ).
fof(f_1209_3,plain,
! [U_5380,U_5379] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5379),hAPP(c_Nat_OSuc,U_5380)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5379),U_5380)),
inference(definitional_conversion,[status(esa)],[f_1209_2]) ).
cnf(f_1209_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5379),hAPP(c_Nat_OSuc,U_5380)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5379),U_5380)),
inference(clausify,[status(thm)],[f_1209_3]) ).
fof(f_1210_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_1210_2,plain,
! [U_5382,U_5381] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5381)),U_5382) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5381),U_5382)),
inference(variable_rename,[status(thm)],[f_1210_1]) ).
fof(f_1210_3,plain,
! [U_5381,U_5382] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5381)),U_5382) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5381),U_5382)),
inference(definitional_conversion,[status(esa)],[f_1210_2]) ).
cnf(f_1210_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5381)),U_5382) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5381),U_5382)),
inference(clausify,[status(thm)],[f_1210_3]) ).
fof(f_1211_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_1211_2,plain,
! [U_5384,U_5383] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5383)),U_5384) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5383),hAPP(c_Nat_OSuc,U_5384)),
inference(variable_rename,[status(thm)],[f_1211_1]) ).
fof(f_1211_3,plain,
! [U_5383,U_5384] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5383)),U_5384) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5383),hAPP(c_Nat_OSuc,U_5384)),
inference(definitional_conversion,[status(esa)],[f_1211_2]) ).
cnf(f_1211_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5383)),U_5384) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5383),hAPP(c_Nat_OSuc,U_5384)),
inference(clausify,[status(thm)],[f_1211_3]) ).
fof(f_1212_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_1212_2,plain,
! [U_5386,U_5385] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5385),U_5386))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5385)),U_5386)) ),
inference(variable_rename,[status(thm)],[f_1212_1]) ).
fof(f_1212_3,plain,
! [U_5385,U_5386] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5385),U_5386))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5385)),U_5386)) ),
inference(definitional_conversion,[status(esa)],[f_1212_2]) ).
cnf(f_1212_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5385),U_5386))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5385)),U_5386)) ),
inference(clausify,[status(thm)],[f_1212_3]) ).
fof(f_1213_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_1213_2,plain,
! [U_5388,U_5387] :
( U_5387 = hAPP(c_Nat_OSuc,U_5388)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5387),U_5388))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5387),hAPP(c_Nat_OSuc,U_5388))) ),
inference(variable_rename,[status(thm)],[f_1213_1]) ).
fof(f_1213_3,plain,
! [U_5387,U_5388] :
( U_5387 = hAPP(c_Nat_OSuc,U_5388)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5387),U_5388))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5387),hAPP(c_Nat_OSuc,U_5388))) ),
inference(definitional_conversion,[status(esa)],[f_1213_2]) ).
cnf(f_1213_4,plain,
( U_5387 = hAPP(c_Nat_OSuc,U_5388)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5387),U_5388))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5387),hAPP(c_Nat_OSuc,U_5388))) ),
inference(clausify,[status(thm)],[f_1213_3]) ).
fof(f_1214_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_1214_2,plain,
! [U_5390,U_5389] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5389),hAPP(c_Nat_OSuc,U_5390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5389),U_5390)) ),
inference(variable_rename,[status(thm)],[f_1214_1]) ).
fof(f_1214_3,plain,
! [U_5390,U_5389] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5389),hAPP(c_Nat_OSuc,U_5390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5389),U_5390)) ),
inference(definitional_conversion,[status(esa)],[f_1214_2]) ).
cnf(f_1214_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5389),hAPP(c_Nat_OSuc,U_5390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5389),U_5390)) ),
inference(clausify,[status(thm)],[f_1214_3]) ).
fof(f_1215_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_1215_2,plain,
! [U_5392,U_5391] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5391)),hAPP(c_Nat_OSuc,U_5392)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5391),U_5392)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5391),U_5392))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5391)),hAPP(c_Nat_OSuc,U_5392))) ) ),
inference(variable_rename,[status(thm)],[f_1215_1]) ).
fof(f_1215_3,plain,
( ! [U_5396,U_5394] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5394)),hAPP(c_Nat_OSuc,U_5396)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5394),U_5396)) )
& ! [U_5395,U_5393] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5393),U_5395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5393)),hAPP(c_Nat_OSuc,U_5395))) ) ),
inference(miniscope,[status(thm)],[f_1215_2]) ).
fof(f_1215_4,plain,
( ! [U_5394,U_5396] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5394)),hAPP(c_Nat_OSuc,U_5396)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5394),U_5396)) )
& ! [U_5395,U_5393] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5393),U_5395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5393)),hAPP(c_Nat_OSuc,U_5395))) ) ),
inference(definitional_conversion,[status(esa)],[f_1215_3]) ).
cnf(f_1215_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5393),U_5395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5393)),hAPP(c_Nat_OSuc,U_5395))) ),
inference(clausify,[status(thm)],[f_1215_4]) ).
cnf(f_1215_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5394)),hAPP(c_Nat_OSuc,U_5396)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5394),U_5396)) ),
inference(clausify,[status(thm)],[f_1215_4]) ).
fof(f_1216_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_1216_2,plain,
! [U_5398,U_5397] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5397),hAPP(c_Nat_OSuc,U_5398)))
| ( U_5397 != hAPP(c_Nat_OSuc,U_5398)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5397),U_5398)) ) )
& ( U_5397 = hAPP(c_Nat_OSuc,U_5398)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5397),U_5398))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5397),hAPP(c_Nat_OSuc,U_5398))) ) ),
inference(variable_rename,[status(thm)],[f_1216_1]) ).
fof(f_1216_3,plain,
( ! [U_5402,U_5400] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5400),hAPP(c_Nat_OSuc,U_5402)))
| ( U_5400 != hAPP(c_Nat_OSuc,U_5402)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5400),U_5402)) ) )
& ! [U_5401,U_5399] :
( U_5399 = hAPP(c_Nat_OSuc,U_5401)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5399),U_5401))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5399),hAPP(c_Nat_OSuc,U_5401))) ) ),
inference(miniscope,[status(thm)],[f_1216_2]) ).
fof(f_1216_4,plain,
( ! [U_5402,U_5400] :
( U_5400 != hAPP(c_Nat_OSuc,U_5402)
| ~ sP265(U_5402,U_5400) )
& ! [U_5402,U_5400] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5400),U_5402))
| ~ sP265(U_5402,U_5400) )
& ! [U_5402,U_5400] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5400),hAPP(c_Nat_OSuc,U_5402)))
| sP265(U_5402,U_5400) )
& ! [U_5401,U_5399] :
( U_5399 = hAPP(c_Nat_OSuc,U_5401)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5399),U_5401))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5399),hAPP(c_Nat_OSuc,U_5401))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP265])],[f_1216_3]) ).
cnf(f_1216_5,plain,
( U_5399 = hAPP(c_Nat_OSuc,U_5401)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5399),U_5401))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5399),hAPP(c_Nat_OSuc,U_5401))) ),
inference(clausify,[status(thm)],[f_1216_4]) ).
cnf(f_1216_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5400),hAPP(c_Nat_OSuc,U_5402)))
| sP265(U_5402,U_5400) ),
inference(clausify,[status(thm)],[f_1216_4]) ).
cnf(f_1216_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5400),U_5402))
| ~ sP265(U_5402,U_5400) ),
inference(clausify,[status(thm)],[f_1216_4]) ).
cnf(f_1216_8,plain,
( U_5400 != hAPP(c_Nat_OSuc,U_5402)
| ~ sP265(U_5402,U_5400) ),
inference(clausify,[status(thm)],[f_1216_4]) ).
fof(f_1217_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_1217_2,plain,
! [U_5404,U_5403] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5403),U_5404))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5404)),U_5403)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5404)),U_5403))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5403),U_5404)) ) ),
inference(variable_rename,[status(thm)],[f_1217_1]) ).
fof(f_1217_3,plain,
( ! [U_5408,U_5406] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5406),U_5408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5408)),U_5406)) )
& ! [U_5407,U_5405] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5407)),U_5405))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5405),U_5407)) ) ),
inference(miniscope,[status(thm)],[f_1217_2]) ).
fof(f_1217_4,plain,
( ! [U_5406,U_5408] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5406),U_5408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5408)),U_5406)) )
& ! [U_5407,U_5405] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5407)),U_5405))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5405),U_5407)) ) ),
inference(definitional_conversion,[status(esa)],[f_1217_3]) ).
cnf(f_1217_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5407)),U_5405))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5405),U_5407)) ),
inference(clausify,[status(thm)],[f_1217_4]) ).
cnf(f_1217_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5406),U_5408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5408)),U_5406)) ),
inference(clausify,[status(thm)],[f_1217_4]) ).
fof(f_1218_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_1218_2,plain,
! [U_5409] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5409)),U_5409)),
inference(variable_rename,[status(thm)],[f_1218_1]) ).
fof(f_1218_3,plain,
! [U_5409] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5409)),U_5409)),
inference(definitional_conversion,[status(esa)],[f_1218_2]) ).
cnf(f_1218_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5409)),U_5409)),
inference(clausify,[status(thm)],[f_1218_3]) ).
fof(f_1219_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_1219_2,plain,
! [U_5412,U_5411,U_5410] : 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_5410)),U_5411)),hAPP(c_Nat_OSuc,U_5412)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5410),U_5411)),U_5412),
inference(variable_rename,[status(thm)],[f_1219_1]) ).
fof(f_1219_3,plain,
! [U_5410,U_5411,U_5412] : 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_5410)),U_5411)),hAPP(c_Nat_OSuc,U_5412)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5410),U_5411)),U_5412),
inference(definitional_conversion,[status(esa)],[f_1219_2]) ).
cnf(f_1219_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_5410)),U_5411)),hAPP(c_Nat_OSuc,U_5412)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5410),U_5411)),U_5412),
inference(clausify,[status(thm)],[f_1219_3]) ).
fof(f_1220_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_1220_2,plain,
! [U_5414,U_5413] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5413)),hAPP(c_Nat_OSuc,U_5414)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5413),U_5414),
inference(variable_rename,[status(thm)],[f_1220_1]) ).
fof(f_1220_3,plain,
! [U_5413,U_5414] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5413)),hAPP(c_Nat_OSuc,U_5414)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5413),U_5414),
inference(definitional_conversion,[status(esa)],[f_1220_2]) ).
cnf(f_1220_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5413)),hAPP(c_Nat_OSuc,U_5414)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5413),U_5414),
inference(clausify,[status(thm)],[f_1220_3]) ).
fof(f_1221_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_1221_2,plain,
! [U_5417,U_5416,U_5415] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5415)),U_5416) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5415)),U_5417)
| U_5416 != U_5417 )
& ( U_5416 = U_5417
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5415)),U_5416) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5415)),U_5417) ) ),
inference(variable_rename,[status(thm)],[f_1221_1]) ).
fof(f_1221_3,plain,
( ! [U_5423,U_5421] :
( ! [U_5419] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5419)),U_5421) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5419)),U_5423)
| U_5421 != U_5423 )
& ! [U_5422,U_5420] :
( ! [U_5418] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5418)),U_5420) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5418)),U_5422)
| U_5420 = U_5422 ) ),
inference(miniscope,[status(thm)],[f_1221_2]) ).
fof(f_1221_4,plain,
( ! [U_5423,U_5419,U_5421] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5419)),U_5421) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5419)),U_5423)
| U_5421 != U_5423 )
& ! [U_5422,U_5420,U_5418] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5418)),U_5420) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5418)),U_5422)
| U_5420 = U_5422 ) ),
inference(definitional_conversion,[status(esa)],[f_1221_3]) ).
cnf(f_1221_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5418)),U_5420) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5418)),U_5422)
| U_5420 = U_5422 ),
inference(clausify,[status(thm)],[f_1221_4]) ).
cnf(f_1221_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5419)),U_5421) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5419)),U_5423)
| U_5421 != U_5423 ),
inference(clausify,[status(thm)],[f_1221_4]) ).
fof(f_1222_1,plain,
! [T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Inter__UNIV]) ).
fof(f_1222_2,plain,
! [U_5424] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5424,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_5424,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_5424,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1222_1]) ).
fof(f_1222_3,plain,
! [U_5424] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5424,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_5424,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_5424,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1222_2]) ).
cnf(f_1222_4,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5424,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_5424,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_5424,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1222_3]) ).
fof(f_1223_1,plain,
! [V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2)
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf]) ).
fof(f_1223_2,plain,
! [U_5426,U_5425] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5425,U_5426) = c_Complete__Lattice_OInf__class_OInf(U_5425,U_5426)
| U_5426 = c_Orderings_Obot__class_Obot(tc_fun(U_5425,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5425),U_5426))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5425) ),
inference(variable_rename,[status(thm)],[f_1223_1]) ).
fof(f_1223_3,plain,
! [U_5425,U_5426] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5425,U_5426) = c_Complete__Lattice_OInf__class_OInf(U_5425,U_5426)
| U_5426 = c_Orderings_Obot__class_Obot(tc_fun(U_5425,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5425),U_5426))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5425) ),
inference(definitional_conversion,[status(esa)],[f_1223_2]) ).
cnf(f_1223_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5425,U_5426) = c_Complete__Lattice_OInf__class_OInf(U_5425,U_5426)
| U_5426 = c_Orderings_Obot__class_Obot(tc_fun(U_5425,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5425),U_5426))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5425) ),
inference(clausify,[status(thm)],[f_1223_3]) ).
fof(f_1224_1,plain,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono]) ).
fof(f_1224_2,plain,
! [U_5429,U_5428,U_5427] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5427,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5427,tc_HOL_Obool),U_5429)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5427,tc_HOL_Obool),U_5428)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_5427,tc_HOL_Obool),tc_HOL_Obool)),U_5428),U_5429)) ),
inference(variable_rename,[status(thm)],[f_1224_1]) ).
fof(f_1224_3,plain,
! [U_5428,U_5427,U_5429] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5427,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5427,tc_HOL_Obool),U_5429)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5427,tc_HOL_Obool),U_5428)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_5427,tc_HOL_Obool),tc_HOL_Obool)),U_5428),U_5429)) ),
inference(definitional_conversion,[status(esa)],[f_1224_2]) ).
cnf(f_1224_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5427,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5427,tc_HOL_Obool),U_5429)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5427,tc_HOL_Obool),U_5428)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_5427,tc_HOL_Obool),tc_HOL_Obool)),U_5428),U_5429)) ),
inference(clausify,[status(thm)],[f_1224_3]) ).
fof(f_1225_1,plain,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Inter__lower]) ).
fof(f_1225_2,plain,
! [U_5432,U_5431,U_5430] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5430,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5430,tc_HOL_Obool),U_5432)),U_5431))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5430,tc_HOL_Obool)),U_5431),U_5432)) ),
inference(variable_rename,[status(thm)],[f_1225_1]) ).
fof(f_1225_3,plain,
! [U_5430,U_5431,U_5432] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5430,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5430,tc_HOL_Obool),U_5432)),U_5431))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5430,tc_HOL_Obool)),U_5431),U_5432)) ),
inference(definitional_conversion,[status(esa)],[f_1225_2]) ).
cnf(f_1225_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5430,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5430,tc_HOL_Obool),U_5432)),U_5431))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_5430,tc_HOL_Obool)),U_5431),U_5432)) ),
inference(clausify,[status(thm)],[f_1225_3]) ).
fof(f_1226_1,plain,
! [T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Inter__empty]) ).
fof(f_1226_2,plain,
! [U_5433] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5433,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_5433,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_5433,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1226_1]) ).
fof(f_1226_3,plain,
! [U_5433] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5433,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_5433,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_5433,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1226_2]) ).
cnf(f_1226_4,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5433,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_5433,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_5433,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1226_3]) ).
fof(f_1227_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_Int__eq__Inter]) ).
fof(f_1227_2,plain,
! [U_5436,U_5435,U_5434] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5434,tc_HOL_Obool)),U_5435),U_5436) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5434,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_5434,tc_HOL_Obool)),U_5435),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_5434,tc_HOL_Obool)),U_5436),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_5434,tc_HOL_Obool),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_1227_1]) ).
fof(f_1227_3,plain,
! [U_5434,U_5435,U_5436] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5434,tc_HOL_Obool)),U_5435),U_5436) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5434,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_5434,tc_HOL_Obool)),U_5435),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_5434,tc_HOL_Obool)),U_5436),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_5434,tc_HOL_Obool),tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_1227_2]) ).
cnf(f_1227_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5434,tc_HOL_Obool)),U_5435),U_5436) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5434,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_5434,tc_HOL_Obool)),U_5435),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_5434,tc_HOL_Obool)),U_5436),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_5434,tc_HOL_Obool),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_1227_3]) ).
fof(f_1228_1,plain,
! [V_B_2,V_a_2,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(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),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Inter__insert]) ).
fof(f_1228_2,plain,
! [U_5439,U_5438,U_5437] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5437,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_5437,tc_HOL_Obool)),U_5438),U_5439)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5437,tc_HOL_Obool)),U_5438),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5437,tc_HOL_Obool),U_5439)),
inference(variable_rename,[status(thm)],[f_1228_1]) ).
fof(f_1228_3,plain,
! [U_5437,U_5438,U_5439] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5437,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_5437,tc_HOL_Obool)),U_5438),U_5439)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5437,tc_HOL_Obool)),U_5438),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5437,tc_HOL_Obool),U_5439)),
inference(definitional_conversion,[status(esa)],[f_1228_2]) ).
cnf(f_1228_4,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5437,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_5437,tc_HOL_Obool)),U_5438),U_5439)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5437,tc_HOL_Obool)),U_5438),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5437,tc_HOL_Obool),U_5439)),
inference(clausify,[status(thm)],[f_1228_3]) ).
fof(f_1229_1,plain,
! [V_B_2,V_A_2,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Inter__Un__distrib]) ).
fof(f_1229_2,plain,
! [U_5442,U_5441,U_5440] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5440,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_5440,tc_HOL_Obool),tc_HOL_Obool)),U_5441),U_5442)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5440,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5440,tc_HOL_Obool),U_5441)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5440,tc_HOL_Obool),U_5442)),
inference(variable_rename,[status(thm)],[f_1229_1]) ).
fof(f_1229_3,plain,
! [U_5440,U_5441,U_5442] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5440,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_5440,tc_HOL_Obool),tc_HOL_Obool)),U_5441),U_5442)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5440,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5440,tc_HOL_Obool),U_5441)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5440,tc_HOL_Obool),U_5442)),
inference(definitional_conversion,[status(esa)],[f_1229_2]) ).
cnf(f_1229_4,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5440,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_5440,tc_HOL_Obool),tc_HOL_Obool)),U_5441),U_5442)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5440,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5440,tc_HOL_Obool),U_5441)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5440,tc_HOL_Obool),U_5442)),
inference(clausify,[status(thm)],[f_1229_3]) ).
fof(f_1230_1,plain,
! [V_B_2,V_A_2,T_d,V_b_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_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)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_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))) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__iff]) ).
fof(f_1230_2,plain,
! [U_5449,U_5448,U_5447,U_5446,U_5445] :
( ( hBOOL(hAPP(hAPP(c_member(U_5445),U_5446),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5447,tc_fun(U_5445,tc_HOL_Obool)),U_5448),U_5449)))
| ? [U_5444] :
( ~ hBOOL(hAPP(hAPP(c_member(U_5445),U_5446),hAPP(U_5449,U_5444)))
& hBOOL(hAPP(hAPP(c_member(U_5447),U_5444),U_5448)) ) )
& ( ! [U_5443] :
( hBOOL(hAPP(hAPP(c_member(U_5445),U_5446),hAPP(U_5449,U_5443)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5447),U_5443),U_5448)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_5445),U_5446),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5447,tc_fun(U_5445,tc_HOL_Obool)),U_5448),U_5449))) ) ),
inference(variable_rename,[status(thm)],[f_1230_1]) ).
fof(f_1230_3,plain,
( ! [U_5459,U_5457,U_5455,U_5453,U_5451] :
( hBOOL(hAPP(hAPP(c_member(U_5451),U_5453),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5455,tc_fun(U_5451,tc_HOL_Obool)),U_5457),U_5459)))
| ? [U_5444] :
( ~ hBOOL(hAPP(hAPP(c_member(U_5451),U_5453),hAPP(U_5459,U_5444)))
& hBOOL(hAPP(hAPP(c_member(U_5455),U_5444),U_5457)) ) )
& ! [U_5458,U_5456,U_5454,U_5452,U_5450] :
( ! [U_5443] :
( hBOOL(hAPP(hAPP(c_member(U_5450),U_5452),hAPP(U_5458,U_5443)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5454),U_5443),U_5456)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_5450),U_5452),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5454,tc_fun(U_5450,tc_HOL_Obool)),U_5456),U_5458))) ) ),
inference(miniscope,[status(thm)],[f_1230_2]) ).
fof(f_1230_4,plain,
( ! [U_5459,U_5457,U_5455,U_5453,U_5451] :
( hBOOL(hAPP(hAPP(c_member(U_5451),U_5453),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5455,tc_fun(U_5451,tc_HOL_Obool)),U_5457),U_5459)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_5451),U_5453),hAPP(U_5459,sK106(U_5459,U_5457,U_5455,U_5453,U_5451))))
& hBOOL(hAPP(hAPP(c_member(U_5455),sK106(U_5459,U_5457,U_5455,U_5453,U_5451)),U_5457)) ) )
& ! [U_5458,U_5456,U_5454,U_5452,U_5450] :
( ! [U_5443] :
( hBOOL(hAPP(hAPP(c_member(U_5450),U_5452),hAPP(U_5458,U_5443)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5454),U_5443),U_5456)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_5450),U_5452),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5454,tc_fun(U_5450,tc_HOL_Obool)),U_5456),U_5458))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_5444,sK106(U_5459,U_5457,U_5455,U_5453,U_5451))],[f_1230_3]) ).
fof(f_1230_5,plain,
( ! [U_5453,U_5451,U_5457,U_5459,U_5455] :
( ~ hBOOL(hAPP(hAPP(c_member(U_5451),U_5453),hAPP(U_5459,sK106(U_5459,U_5457,U_5455,U_5453,U_5451))))
| ~ sP266(U_5453,U_5451,U_5457,U_5459,U_5455) )
& ! [U_5453,U_5451,U_5457,U_5459,U_5455] :
( hBOOL(hAPP(hAPP(c_member(U_5455),sK106(U_5459,U_5457,U_5455,U_5453,U_5451)),U_5457))
| ~ sP266(U_5453,U_5451,U_5457,U_5459,U_5455) )
& ! [U_5453,U_5451,U_5457,U_5459,U_5455] :
( hBOOL(hAPP(hAPP(c_member(U_5451),U_5453),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5455,tc_fun(U_5451,tc_HOL_Obool)),U_5457),U_5459)))
| sP266(U_5453,U_5451,U_5457,U_5459,U_5455) )
& ! [U_5452,U_5454,U_5443,U_5450,U_5458,U_5456] :
( hBOOL(hAPP(hAPP(c_member(U_5450),U_5452),hAPP(U_5458,U_5443)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5454),U_5443),U_5456))
| ~ hBOOL(hAPP(hAPP(c_member(U_5450),U_5452),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5454,tc_fun(U_5450,tc_HOL_Obool)),U_5456),U_5458))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP266])],[f_1230_4]) ).
cnf(f_1230_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5450),U_5452),hAPP(U_5458,U_5443)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5454),U_5443),U_5456))
| ~ hBOOL(hAPP(hAPP(c_member(U_5450),U_5452),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5454,tc_fun(U_5450,tc_HOL_Obool)),U_5456),U_5458))) ),
inference(clausify,[status(thm)],[f_1230_5]) ).
cnf(f_1230_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_5451),U_5453),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5455,tc_fun(U_5451,tc_HOL_Obool)),U_5457),U_5459)))
| sP266(U_5453,U_5451,U_5457,U_5459,U_5455) ),
inference(clausify,[status(thm)],[f_1230_5]) ).
cnf(f_1230_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_5455),sK106(U_5459,U_5457,U_5455,U_5453,U_5451)),U_5457))
| ~ sP266(U_5453,U_5451,U_5457,U_5459,U_5455) ),
inference(clausify,[status(thm)],[f_1230_5]) ).
cnf(f_1230_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_5451),U_5453),hAPP(U_5459,sK106(U_5459,U_5457,U_5455,U_5453,U_5451))))
| ~ sP266(U_5453,U_5451,U_5457,U_5459,U_5455) ),
inference(clausify,[status(thm)],[f_1230_5]) ).
fof(f_1231_1,plain,
! [V_B_2,V_a_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d),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_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I5_J]) ).
fof(f_1231_2,plain,
! [U_5464,U_5463,U_5462,U_5461,U_5460] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5460,tc_fun(U_5461,tc_HOL_Obool)),U_5462),hAPP(hAPP(c_COMBB(tc_fun(U_5461,tc_HOL_Obool),tc_fun(U_5461,tc_HOL_Obool),U_5460),hAPP(c_Set_Oinsert(U_5461),U_5463)),U_5464)) = hAPP(hAPP(c_Set_Oinsert(U_5461),U_5463),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5460,tc_fun(U_5461,tc_HOL_Obool)),U_5462),U_5464)),
inference(variable_rename,[status(thm)],[f_1231_1]) ).
fof(f_1231_3,plain,
! [U_5460,U_5462,U_5463,U_5461,U_5464] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5460,tc_fun(U_5461,tc_HOL_Obool)),U_5462),hAPP(hAPP(c_COMBB(tc_fun(U_5461,tc_HOL_Obool),tc_fun(U_5461,tc_HOL_Obool),U_5460),hAPP(c_Set_Oinsert(U_5461),U_5463)),U_5464)) = hAPP(hAPP(c_Set_Oinsert(U_5461),U_5463),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5460,tc_fun(U_5461,tc_HOL_Obool)),U_5462),U_5464)),
inference(definitional_conversion,[status(esa)],[f_1231_2]) ).
cnf(f_1231_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5460,tc_fun(U_5461,tc_HOL_Obool)),U_5462),hAPP(hAPP(c_COMBB(tc_fun(U_5461,tc_HOL_Obool),tc_fun(U_5461,tc_HOL_Obool),U_5460),hAPP(c_Set_Oinsert(U_5461),U_5463)),U_5464)) = hAPP(hAPP(c_Set_Oinsert(U_5461),U_5463),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5460,tc_fun(U_5461,tc_HOL_Obool)),U_5462),U_5464)),
inference(clausify,[status(thm)],[f_1231_3]) ).
fof(f_1232_1,plain,
! [V_B_2,V_C_2,T_d,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I5_J]) ).
fof(f_1232_2,plain,
! [U_5469,U_5468,U_5467,U_5466,U_5465] : hAPP(hAPP(c_Set_Oinsert(U_5465),U_5466),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5467,tc_fun(U_5465,tc_HOL_Obool)),U_5468),U_5469)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5467,tc_fun(U_5465,tc_HOL_Obool)),U_5468),hAPP(hAPP(c_COMBB(tc_fun(U_5465,tc_HOL_Obool),tc_fun(U_5465,tc_HOL_Obool),U_5467),hAPP(c_Set_Oinsert(U_5465),U_5466)),U_5469)),
inference(variable_rename,[status(thm)],[f_1232_1]) ).
fof(f_1232_3,plain,
! [U_5465,U_5466,U_5467,U_5468,U_5469] : hAPP(hAPP(c_Set_Oinsert(U_5465),U_5466),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5467,tc_fun(U_5465,tc_HOL_Obool)),U_5468),U_5469)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5467,tc_fun(U_5465,tc_HOL_Obool)),U_5468),hAPP(hAPP(c_COMBB(tc_fun(U_5465,tc_HOL_Obool),tc_fun(U_5465,tc_HOL_Obool),U_5467),hAPP(c_Set_Oinsert(U_5465),U_5466)),U_5469)),
inference(definitional_conversion,[status(esa)],[f_1232_2]) ).
cnf(f_1232_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_5465),U_5466),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5467,tc_fun(U_5465,tc_HOL_Obool)),U_5468),U_5469)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5467,tc_fun(U_5465,tc_HOL_Obool)),U_5468),hAPP(hAPP(c_COMBB(tc_fun(U_5465,tc_HOL_Obool),tc_fun(U_5465,tc_HOL_Obool),U_5467),hAPP(c_Set_Oinsert(U_5465),U_5466)),U_5469)),
inference(clausify,[status(thm)],[f_1232_3]) ).
fof(f_1233_1,plain,
! [V_A_2,V_I_2,T_d,V_B_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_I_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_I_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__subset__iff]) ).
fof(f_1233_2,plain,
! [U_5476,U_5475,U_5474,U_5473,U_5472] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5472,tc_HOL_Obool)),U_5473),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5474,tc_fun(U_5472,tc_HOL_Obool)),U_5475),U_5476)))
| ? [U_5471] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5472,tc_HOL_Obool)),U_5473),hAPP(U_5476,U_5471)))
& hBOOL(hAPP(hAPP(c_member(U_5474),U_5471),U_5475)) ) )
& ( ! [U_5470] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5472,tc_HOL_Obool)),U_5473),hAPP(U_5476,U_5470)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5474),U_5470),U_5475)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5472,tc_HOL_Obool)),U_5473),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5474,tc_fun(U_5472,tc_HOL_Obool)),U_5475),U_5476))) ) ),
inference(variable_rename,[status(thm)],[f_1233_1]) ).
fof(f_1233_3,plain,
( ! [U_5486,U_5484,U_5482,U_5480,U_5478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5478,tc_HOL_Obool)),U_5480),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5482,tc_fun(U_5478,tc_HOL_Obool)),U_5484),U_5486)))
| ? [U_5471] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5478,tc_HOL_Obool)),U_5480),hAPP(U_5486,U_5471)))
& hBOOL(hAPP(hAPP(c_member(U_5482),U_5471),U_5484)) ) )
& ! [U_5485,U_5483,U_5481,U_5479,U_5477] :
( ! [U_5470] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5477,tc_HOL_Obool)),U_5479),hAPP(U_5485,U_5470)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5481),U_5470),U_5483)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5477,tc_HOL_Obool)),U_5479),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5481,tc_fun(U_5477,tc_HOL_Obool)),U_5483),U_5485))) ) ),
inference(miniscope,[status(thm)],[f_1233_2]) ).
fof(f_1233_4,plain,
( ! [U_5486,U_5484,U_5482,U_5480,U_5478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5478,tc_HOL_Obool)),U_5480),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5482,tc_fun(U_5478,tc_HOL_Obool)),U_5484),U_5486)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5478,tc_HOL_Obool)),U_5480),hAPP(U_5486,sK107(U_5486,U_5484,U_5482,U_5480,U_5478))))
& hBOOL(hAPP(hAPP(c_member(U_5482),sK107(U_5486,U_5484,U_5482,U_5480,U_5478)),U_5484)) ) )
& ! [U_5485,U_5483,U_5481,U_5479,U_5477] :
( ! [U_5470] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5477,tc_HOL_Obool)),U_5479),hAPP(U_5485,U_5470)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5481),U_5470),U_5483)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5477,tc_HOL_Obool)),U_5479),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5481,tc_fun(U_5477,tc_HOL_Obool)),U_5483),U_5485))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_5471,sK107(U_5486,U_5484,U_5482,U_5480,U_5478))],[f_1233_3]) ).
fof(f_1233_5,plain,
( ! [U_5478,U_5480,U_5484,U_5486,U_5482] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5478,tc_HOL_Obool)),U_5480),hAPP(U_5486,sK107(U_5486,U_5484,U_5482,U_5480,U_5478))))
| ~ sP267(U_5478,U_5480,U_5484,U_5486,U_5482) )
& ! [U_5478,U_5480,U_5484,U_5486,U_5482] :
( hBOOL(hAPP(hAPP(c_member(U_5482),sK107(U_5486,U_5484,U_5482,U_5480,U_5478)),U_5484))
| ~ sP267(U_5478,U_5480,U_5484,U_5486,U_5482) )
& ! [U_5478,U_5480,U_5484,U_5486,U_5482] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5478,tc_HOL_Obool)),U_5480),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5482,tc_fun(U_5478,tc_HOL_Obool)),U_5484),U_5486)))
| sP267(U_5478,U_5480,U_5484,U_5486,U_5482) )
& ! [U_5481,U_5470,U_5477,U_5479,U_5485,U_5483] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5477,tc_HOL_Obool)),U_5479),hAPP(U_5485,U_5470)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5481),U_5470),U_5483))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5477,tc_HOL_Obool)),U_5479),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5481,tc_fun(U_5477,tc_HOL_Obool)),U_5483),U_5485))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP267])],[f_1233_4]) ).
cnf(f_1233_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5477,tc_HOL_Obool)),U_5479),hAPP(U_5485,U_5470)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5481),U_5470),U_5483))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5477,tc_HOL_Obool)),U_5479),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5481,tc_fun(U_5477,tc_HOL_Obool)),U_5483),U_5485))) ),
inference(clausify,[status(thm)],[f_1233_5]) ).
cnf(f_1233_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5478,tc_HOL_Obool)),U_5480),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5482,tc_fun(U_5478,tc_HOL_Obool)),U_5484),U_5486)))
| sP267(U_5478,U_5480,U_5484,U_5486,U_5482) ),
inference(clausify,[status(thm)],[f_1233_5]) ).
cnf(f_1233_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_5482),sK107(U_5486,U_5484,U_5482,U_5480,U_5478)),U_5484))
| ~ sP267(U_5478,U_5480,U_5484,U_5486,U_5482) ),
inference(clausify,[status(thm)],[f_1233_5]) ).
cnf(f_1233_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5478,tc_HOL_Obool)),U_5480),hAPP(U_5486,sK107(U_5486,U_5484,U_5482,U_5480,U_5478))))
| ~ sP267(U_5478,U_5480,U_5484,U_5486,U_5482) ),
inference(clausify,[status(thm)],[f_1233_5]) ).
fof(f_1234_1,plain,
! [V_B_2,V_A_2,T_c,T_d] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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))
| ? [B_x] :
( hAPP(V_B_2,B_x) != c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_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) != c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I2_J]) ).
fof(f_1234_2,plain,
! [U_5492,U_5491,U_5490,U_5489] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5489,tc_fun(U_5490,tc_HOL_Obool)),U_5491),U_5492) = c_Orderings_Otop__class_Otop(tc_fun(U_5490,tc_HOL_Obool))
| ? [U_5488] :
( hAPP(U_5492,U_5488) != c_Orderings_Otop__class_Otop(tc_fun(U_5490,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_5489),U_5488),U_5491)) ) )
& ( ! [U_5487] :
( hAPP(U_5492,U_5487) = c_Orderings_Otop__class_Otop(tc_fun(U_5490,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5489),U_5487),U_5491)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5489,tc_fun(U_5490,tc_HOL_Obool)),U_5491),U_5492) != c_Orderings_Otop__class_Otop(tc_fun(U_5490,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1234_1]) ).
fof(f_1234_3,plain,
( ! [U_5500,U_5498,U_5496,U_5494] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5494,tc_fun(U_5496,tc_HOL_Obool)),U_5498),U_5500) = c_Orderings_Otop__class_Otop(tc_fun(U_5496,tc_HOL_Obool))
| ? [U_5488] :
( hAPP(U_5500,U_5488) != c_Orderings_Otop__class_Otop(tc_fun(U_5496,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_5494),U_5488),U_5498)) ) )
& ! [U_5499,U_5497,U_5495,U_5493] :
( ! [U_5487] :
( hAPP(U_5499,U_5487) = c_Orderings_Otop__class_Otop(tc_fun(U_5495,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5493),U_5487),U_5497)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5493,tc_fun(U_5495,tc_HOL_Obool)),U_5497),U_5499) != c_Orderings_Otop__class_Otop(tc_fun(U_5495,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1234_2]) ).
fof(f_1234_4,plain,
( ! [U_5500,U_5498,U_5496,U_5494] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5494,tc_fun(U_5496,tc_HOL_Obool)),U_5498),U_5500) = c_Orderings_Otop__class_Otop(tc_fun(U_5496,tc_HOL_Obool))
| ( hAPP(U_5500,sK108(U_5500,U_5498,U_5496,U_5494)) != c_Orderings_Otop__class_Otop(tc_fun(U_5496,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_5494),sK108(U_5500,U_5498,U_5496,U_5494)),U_5498)) ) )
& ! [U_5499,U_5497,U_5495,U_5493] :
( ! [U_5487] :
( hAPP(U_5499,U_5487) = c_Orderings_Otop__class_Otop(tc_fun(U_5495,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5493),U_5487),U_5497)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5493,tc_fun(U_5495,tc_HOL_Obool)),U_5497),U_5499) != c_Orderings_Otop__class_Otop(tc_fun(U_5495,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_5488,sK108(U_5500,U_5498,U_5496,U_5494))],[f_1234_3]) ).
fof(f_1234_5,plain,
( ! [U_5494,U_5496,U_5500,U_5498] :
( hAPP(U_5500,sK108(U_5500,U_5498,U_5496,U_5494)) != c_Orderings_Otop__class_Otop(tc_fun(U_5496,tc_HOL_Obool))
| ~ sP268(U_5494,U_5496,U_5500,U_5498) )
& ! [U_5494,U_5496,U_5500,U_5498] :
( hBOOL(hAPP(hAPP(c_member(U_5494),sK108(U_5500,U_5498,U_5496,U_5494)),U_5498))
| ~ sP268(U_5494,U_5496,U_5500,U_5498) )
& ! [U_5494,U_5496,U_5500,U_5498] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5494,tc_fun(U_5496,tc_HOL_Obool)),U_5498),U_5500) = c_Orderings_Otop__class_Otop(tc_fun(U_5496,tc_HOL_Obool))
| sP268(U_5494,U_5496,U_5500,U_5498) )
& ! [U_5493,U_5487,U_5497,U_5499,U_5495] :
( hAPP(U_5499,U_5487) = c_Orderings_Otop__class_Otop(tc_fun(U_5495,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5493),U_5487),U_5497))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5493,tc_fun(U_5495,tc_HOL_Obool)),U_5497),U_5499) != c_Orderings_Otop__class_Otop(tc_fun(U_5495,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP268])],[f_1234_4]) ).
cnf(f_1234_6,plain,
( hAPP(U_5499,U_5487) = c_Orderings_Otop__class_Otop(tc_fun(U_5495,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5493),U_5487),U_5497))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5493,tc_fun(U_5495,tc_HOL_Obool)),U_5497),U_5499) != c_Orderings_Otop__class_Otop(tc_fun(U_5495,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1234_5]) ).
cnf(f_1234_7,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5494,tc_fun(U_5496,tc_HOL_Obool)),U_5498),U_5500) = c_Orderings_Otop__class_Otop(tc_fun(U_5496,tc_HOL_Obool))
| sP268(U_5494,U_5496,U_5500,U_5498) ),
inference(clausify,[status(thm)],[f_1234_5]) ).
cnf(f_1234_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_5494),sK108(U_5500,U_5498,U_5496,U_5494)),U_5498))
| ~ sP268(U_5494,U_5496,U_5500,U_5498) ),
inference(clausify,[status(thm)],[f_1234_5]) ).
cnf(f_1234_9,plain,
( hAPP(U_5500,sK108(U_5500,U_5498,U_5496,U_5494)) != c_Orderings_Otop__class_Otop(tc_fun(U_5496,tc_HOL_Obool))
| ~ sP268(U_5494,U_5496,U_5500,U_5498) ),
inference(clausify,[status(thm)],[f_1234_5]) ).
fof(f_1235_1,plain,
! [V_B_2,V_A_2,T_d,T_c] :
( ( c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,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_c,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
| c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I1_J]) ).
fof(f_1235_2,plain,
! [U_5506,U_5505,U_5504,U_5503] :
( ( c_Orderings_Otop__class_Otop(tc_fun(U_5503,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5504,tc_fun(U_5503,tc_HOL_Obool)),U_5505),U_5506)
| ? [U_5502] :
( hAPP(U_5506,U_5502) != c_Orderings_Otop__class_Otop(tc_fun(U_5503,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_5504),U_5502),U_5505)) ) )
& ( ! [U_5501] :
( hAPP(U_5506,U_5501) = c_Orderings_Otop__class_Otop(tc_fun(U_5503,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5504),U_5501),U_5505)) )
| c_Orderings_Otop__class_Otop(tc_fun(U_5503,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5504,tc_fun(U_5503,tc_HOL_Obool)),U_5505),U_5506) ) ),
inference(variable_rename,[status(thm)],[f_1235_1]) ).
fof(f_1235_3,plain,
( ! [U_5514,U_5512,U_5510,U_5508] :
( c_Orderings_Otop__class_Otop(tc_fun(U_5508,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5510,tc_fun(U_5508,tc_HOL_Obool)),U_5512),U_5514)
| ? [U_5502] :
( hAPP(U_5514,U_5502) != c_Orderings_Otop__class_Otop(tc_fun(U_5508,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_5510),U_5502),U_5512)) ) )
& ! [U_5513,U_5511,U_5509,U_5507] :
( ! [U_5501] :
( hAPP(U_5513,U_5501) = c_Orderings_Otop__class_Otop(tc_fun(U_5507,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5509),U_5501),U_5511)) )
| c_Orderings_Otop__class_Otop(tc_fun(U_5507,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5509,tc_fun(U_5507,tc_HOL_Obool)),U_5511),U_5513) ) ),
inference(miniscope,[status(thm)],[f_1235_2]) ).
fof(f_1235_4,plain,
( ! [U_5514,U_5512,U_5510,U_5508] :
( c_Orderings_Otop__class_Otop(tc_fun(U_5508,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5510,tc_fun(U_5508,tc_HOL_Obool)),U_5512),U_5514)
| ( hAPP(U_5514,sK109(U_5514,U_5512,U_5510,U_5508)) != c_Orderings_Otop__class_Otop(tc_fun(U_5508,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_5510),sK109(U_5514,U_5512,U_5510,U_5508)),U_5512)) ) )
& ! [U_5513,U_5511,U_5509,U_5507] :
( ! [U_5501] :
( hAPP(U_5513,U_5501) = c_Orderings_Otop__class_Otop(tc_fun(U_5507,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5509),U_5501),U_5511)) )
| c_Orderings_Otop__class_Otop(tc_fun(U_5507,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5509,tc_fun(U_5507,tc_HOL_Obool)),U_5511),U_5513) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_5502,sK109(U_5514,U_5512,U_5510,U_5508))],[f_1235_3]) ).
fof(f_1235_5,plain,
( ! [U_5508,U_5514,U_5510,U_5512] :
( hAPP(U_5514,sK109(U_5514,U_5512,U_5510,U_5508)) != c_Orderings_Otop__class_Otop(tc_fun(U_5508,tc_HOL_Obool))
| ~ sP269(U_5508,U_5514,U_5510,U_5512) )
& ! [U_5508,U_5514,U_5510,U_5512] :
( hBOOL(hAPP(hAPP(c_member(U_5510),sK109(U_5514,U_5512,U_5510,U_5508)),U_5512))
| ~ sP269(U_5508,U_5514,U_5510,U_5512) )
& ! [U_5508,U_5514,U_5510,U_5512] :
( c_Orderings_Otop__class_Otop(tc_fun(U_5508,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5510,tc_fun(U_5508,tc_HOL_Obool)),U_5512),U_5514)
| sP269(U_5508,U_5514,U_5510,U_5512) )
& ! [U_5501,U_5509,U_5513,U_5511,U_5507] :
( hAPP(U_5513,U_5501) = c_Orderings_Otop__class_Otop(tc_fun(U_5507,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5509),U_5501),U_5511))
| c_Orderings_Otop__class_Otop(tc_fun(U_5507,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5509,tc_fun(U_5507,tc_HOL_Obool)),U_5511),U_5513) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP269])],[f_1235_4]) ).
cnf(f_1235_6,plain,
( hAPP(U_5513,U_5501) = c_Orderings_Otop__class_Otop(tc_fun(U_5507,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_5509),U_5501),U_5511))
| c_Orderings_Otop__class_Otop(tc_fun(U_5507,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5509,tc_fun(U_5507,tc_HOL_Obool)),U_5511),U_5513) ),
inference(clausify,[status(thm)],[f_1235_5]) ).
cnf(f_1235_7,plain,
( c_Orderings_Otop__class_Otop(tc_fun(U_5508,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5510,tc_fun(U_5508,tc_HOL_Obool)),U_5512),U_5514)
| sP269(U_5508,U_5514,U_5510,U_5512) ),
inference(clausify,[status(thm)],[f_1235_5]) ).
cnf(f_1235_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_5510),sK109(U_5514,U_5512,U_5510,U_5508)),U_5512))
| ~ sP269(U_5508,U_5514,U_5510,U_5512) ),
inference(clausify,[status(thm)],[f_1235_5]) ).
cnf(f_1235_9,plain,
( hAPP(U_5514,sK109(U_5514,U_5512,U_5510,U_5508)) != c_Orderings_Otop__class_Otop(tc_fun(U_5508,tc_HOL_Obool))
| ~ sP269(U_5508,U_5514,U_5510,U_5512) ),
inference(clausify,[status(thm)],[f_1235_5]) ).
fof(f_1236_1,plain,
! [V_f_2,V_B_2,T_e,V_A_2,T_c,T_d] : 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(T_e,tc_fun(T_c,tc_HOL_Obool),T_d),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_e,V_f_2),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I10_J]) ).
fof(f_1236_2,plain,
! [U_5520,U_5519,U_5518,U_5517,U_5516,U_5515] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5515,tc_fun(U_5516,tc_HOL_Obool)),U_5517),hAPP(hAPP(c_COMBB(U_5518,tc_fun(U_5516,tc_HOL_Obool),U_5515),U_5519),U_5520)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5518,tc_fun(U_5516,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5515,U_5518,U_5520),U_5517)),U_5519),
inference(variable_rename,[status(thm)],[f_1236_1]) ).
fof(f_1236_3,plain,
! [U_5516,U_5515,U_5517,U_5518,U_5519,U_5520] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5515,tc_fun(U_5516,tc_HOL_Obool)),U_5517),hAPP(hAPP(c_COMBB(U_5518,tc_fun(U_5516,tc_HOL_Obool),U_5515),U_5519),U_5520)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5518,tc_fun(U_5516,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5515,U_5518,U_5520),U_5517)),U_5519),
inference(definitional_conversion,[status(esa)],[f_1236_2]) ).
cnf(f_1236_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5515,tc_fun(U_5516,tc_HOL_Obool)),U_5517),hAPP(hAPP(c_COMBB(U_5518,tc_fun(U_5516,tc_HOL_Obool),U_5515),U_5519),U_5520)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5518,tc_fun(U_5516,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5515,U_5518,U_5520),U_5517)),U_5519),
inference(clausify,[status(thm)],[f_1236_3]) ).
fof(f_1237_1,plain,
! [V_B_2,V_A_2,V_f_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_e,T_d,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_c,tc_HOL_Obool),T_e),V_B_2),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I10_J]) ).
fof(f_1237_2,plain,
! [U_5526,U_5525,U_5524,U_5523,U_5522,U_5521] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5521,tc_fun(U_5522,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5523,U_5521,U_5524),U_5525)),U_5526) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5523,tc_fun(U_5522,tc_HOL_Obool)),U_5525),hAPP(hAPP(c_COMBB(U_5521,tc_fun(U_5522,tc_HOL_Obool),U_5523),U_5526),U_5524)),
inference(variable_rename,[status(thm)],[f_1237_1]) ).
fof(f_1237_3,plain,
! [U_5521,U_5522,U_5523,U_5524,U_5525,U_5526] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5521,tc_fun(U_5522,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5523,U_5521,U_5524),U_5525)),U_5526) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5523,tc_fun(U_5522,tc_HOL_Obool)),U_5525),hAPP(hAPP(c_COMBB(U_5521,tc_fun(U_5522,tc_HOL_Obool),U_5523),U_5526),U_5524)),
inference(definitional_conversion,[status(esa)],[f_1237_2]) ).
cnf(f_1237_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5521,tc_fun(U_5522,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_5523,U_5521,U_5524),U_5525)),U_5526) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5523,tc_fun(U_5522,tc_HOL_Obool)),U_5525),hAPP(hAPP(c_COMBB(U_5521,tc_fun(U_5522,tc_HOL_Obool),U_5523),U_5526),U_5524)),
inference(clausify,[status(thm)],[f_1237_3]) ).
fof(f_1238_1,plain,
! [V_B_2,V_J_2,T_e,V_A_2,V_I_2,T_d,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e)),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_d),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2))),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Un__INT__distrib2]) ).
fof(f_1238_2,plain,
! [U_5533,U_5532,U_5531,U_5530,U_5529,U_5528,U_5527] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5527,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5528,tc_fun(U_5527,tc_HOL_Obool)),U_5529),U_5530)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5531,tc_fun(U_5527,tc_HOL_Obool)),U_5532),U_5533)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5528,tc_fun(U_5527,tc_HOL_Obool)),U_5529),hAPP(hAPP(c_COMBB(tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool)),tc_fun(U_5527,tc_HOL_Obool),U_5528),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5531,tc_fun(U_5527,tc_HOL_Obool)),U_5532)),hAPP(hAPP(c_COMBC(U_5528,tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool)),tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5527,tc_HOL_Obool),tc_fun(U_5527,tc_HOL_Obool)),tc_fun(tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool)),tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool))),U_5528),c_COMBB(tc_fun(U_5527,tc_HOL_Obool),tc_fun(U_5527,tc_HOL_Obool),U_5531)),hAPP(hAPP(c_COMBB(tc_fun(U_5527,tc_HOL_Obool),tc_fun(tc_fun(U_5527,tc_HOL_Obool),tc_fun(U_5527,tc_HOL_Obool)),U_5528),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5527,tc_HOL_Obool))),U_5530))),U_5533))),
inference(variable_rename,[status(thm)],[f_1238_1]) ).
fof(f_1238_3,plain,
! [U_5527,U_5528,U_5529,U_5530,U_5531,U_5532,U_5533] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5527,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5528,tc_fun(U_5527,tc_HOL_Obool)),U_5529),U_5530)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5531,tc_fun(U_5527,tc_HOL_Obool)),U_5532),U_5533)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5528,tc_fun(U_5527,tc_HOL_Obool)),U_5529),hAPP(hAPP(c_COMBB(tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool)),tc_fun(U_5527,tc_HOL_Obool),U_5528),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5531,tc_fun(U_5527,tc_HOL_Obool)),U_5532)),hAPP(hAPP(c_COMBC(U_5528,tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool)),tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5527,tc_HOL_Obool),tc_fun(U_5527,tc_HOL_Obool)),tc_fun(tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool)),tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool))),U_5528),c_COMBB(tc_fun(U_5527,tc_HOL_Obool),tc_fun(U_5527,tc_HOL_Obool),U_5531)),hAPP(hAPP(c_COMBB(tc_fun(U_5527,tc_HOL_Obool),tc_fun(tc_fun(U_5527,tc_HOL_Obool),tc_fun(U_5527,tc_HOL_Obool)),U_5528),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5527,tc_HOL_Obool))),U_5530))),U_5533))),
inference(definitional_conversion,[status(esa)],[f_1238_2]) ).
cnf(f_1238_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5527,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5528,tc_fun(U_5527,tc_HOL_Obool)),U_5529),U_5530)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5531,tc_fun(U_5527,tc_HOL_Obool)),U_5532),U_5533)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5528,tc_fun(U_5527,tc_HOL_Obool)),U_5529),hAPP(hAPP(c_COMBB(tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool)),tc_fun(U_5527,tc_HOL_Obool),U_5528),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5531,tc_fun(U_5527,tc_HOL_Obool)),U_5532)),hAPP(hAPP(c_COMBC(U_5528,tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool)),tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5527,tc_HOL_Obool),tc_fun(U_5527,tc_HOL_Obool)),tc_fun(tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool)),tc_fun(U_5531,tc_fun(U_5527,tc_HOL_Obool))),U_5528),c_COMBB(tc_fun(U_5527,tc_HOL_Obool),tc_fun(U_5527,tc_HOL_Obool),U_5531)),hAPP(hAPP(c_COMBB(tc_fun(U_5527,tc_HOL_Obool),tc_fun(tc_fun(U_5527,tc_HOL_Obool),tc_fun(U_5527,tc_HOL_Obool)),U_5528),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5527,tc_HOL_Obool))),U_5530))),U_5533))),
inference(clausify,[status(thm)],[f_1238_3]) ).
fof(f_1239_1,plain,
! [V_B_2,V_A_2,V_C_2,T_d,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I6_J]) ).
fof(f_1239_2,plain,
! [U_5538,U_5537,U_5536,U_5535,U_5534] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5534,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5535,tc_fun(U_5534,tc_HOL_Obool)),U_5536),U_5537)),U_5538) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5535,tc_fun(U_5534,tc_HOL_Obool)),U_5536),hAPP(hAPP(c_COMBC(U_5535,tc_fun(U_5534,tc_HOL_Obool),tc_fun(U_5534,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5534,tc_HOL_Obool),tc_fun(tc_fun(U_5534,tc_HOL_Obool),tc_fun(U_5534,tc_HOL_Obool)),U_5535),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5534,tc_HOL_Obool))),U_5537)),U_5538)),
inference(variable_rename,[status(thm)],[f_1239_1]) ).
fof(f_1239_3,plain,
! [U_5534,U_5535,U_5536,U_5537,U_5538] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5534,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5535,tc_fun(U_5534,tc_HOL_Obool)),U_5536),U_5537)),U_5538) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5535,tc_fun(U_5534,tc_HOL_Obool)),U_5536),hAPP(hAPP(c_COMBC(U_5535,tc_fun(U_5534,tc_HOL_Obool),tc_fun(U_5534,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5534,tc_HOL_Obool),tc_fun(tc_fun(U_5534,tc_HOL_Obool),tc_fun(U_5534,tc_HOL_Obool)),U_5535),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5534,tc_HOL_Obool))),U_5537)),U_5538)),
inference(definitional_conversion,[status(esa)],[f_1239_2]) ).
cnf(f_1239_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5534,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5535,tc_fun(U_5534,tc_HOL_Obool)),U_5536),U_5537)),U_5538) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5535,tc_fun(U_5534,tc_HOL_Obool)),U_5536),hAPP(hAPP(c_COMBC(U_5535,tc_fun(U_5534,tc_HOL_Obool),tc_fun(U_5534,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5534,tc_HOL_Obool),tc_fun(tc_fun(U_5534,tc_HOL_Obool),tc_fun(U_5534,tc_HOL_Obool)),U_5535),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5534,tc_HOL_Obool))),U_5537)),U_5538)),
inference(clausify,[status(thm)],[f_1239_3]) ).
fof(f_1240_1,plain,
! [V_A_2,V_I_2,T_d,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Un__INT__distrib]) ).
fof(f_1240_2,plain,
! [U_5543,U_5542,U_5541,U_5540,U_5539] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5539,tc_HOL_Obool)),U_5540),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5541,tc_fun(U_5539,tc_HOL_Obool)),U_5542),U_5543)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5541,tc_fun(U_5539,tc_HOL_Obool)),U_5542),hAPP(hAPP(c_COMBB(tc_fun(U_5539,tc_HOL_Obool),tc_fun(U_5539,tc_HOL_Obool),U_5541),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5539,tc_HOL_Obool)),U_5540)),U_5543)),
inference(variable_rename,[status(thm)],[f_1240_1]) ).
fof(f_1240_3,plain,
! [U_5539,U_5540,U_5541,U_5542,U_5543] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5539,tc_HOL_Obool)),U_5540),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5541,tc_fun(U_5539,tc_HOL_Obool)),U_5542),U_5543)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5541,tc_fun(U_5539,tc_HOL_Obool)),U_5542),hAPP(hAPP(c_COMBB(tc_fun(U_5539,tc_HOL_Obool),tc_fun(U_5539,tc_HOL_Obool),U_5541),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5539,tc_HOL_Obool)),U_5540)),U_5543)),
inference(definitional_conversion,[status(esa)],[f_1240_2]) ).
cnf(f_1240_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5539,tc_HOL_Obool)),U_5540),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5541,tc_fun(U_5539,tc_HOL_Obool)),U_5542),U_5543)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5541,tc_fun(U_5539,tc_HOL_Obool)),U_5542),hAPP(hAPP(c_COMBB(tc_fun(U_5539,tc_HOL_Obool),tc_fun(U_5539,tc_HOL_Obool),U_5541),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5539,tc_HOL_Obool)),U_5540)),U_5543)),
inference(clausify,[status(thm)],[f_1240_3]) ).
fof(f_1241_1,plain,
! [V_B_2,V_C_2,T_d,V_A_2,T_c] : 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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I7_J]) ).
fof(f_1241_2,plain,
! [U_5548,U_5547,U_5546,U_5545,U_5544] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5544,tc_HOL_Obool)),U_5545),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5546,tc_fun(U_5544,tc_HOL_Obool)),U_5547),U_5548)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5546,tc_fun(U_5544,tc_HOL_Obool)),U_5547),hAPP(hAPP(c_COMBB(tc_fun(U_5544,tc_HOL_Obool),tc_fun(U_5544,tc_HOL_Obool),U_5546),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5544,tc_HOL_Obool)),U_5545)),U_5548)),
inference(variable_rename,[status(thm)],[f_1241_1]) ).
fof(f_1241_3,plain,
! [U_5544,U_5545,U_5546,U_5547,U_5548] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5544,tc_HOL_Obool)),U_5545),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5546,tc_fun(U_5544,tc_HOL_Obool)),U_5547),U_5548)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5546,tc_fun(U_5544,tc_HOL_Obool)),U_5547),hAPP(hAPP(c_COMBB(tc_fun(U_5544,tc_HOL_Obool),tc_fun(U_5544,tc_HOL_Obool),U_5546),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5544,tc_HOL_Obool)),U_5545)),U_5548)),
inference(definitional_conversion,[status(esa)],[f_1241_2]) ).
cnf(f_1241_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5544,tc_HOL_Obool)),U_5545),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5546,tc_fun(U_5544,tc_HOL_Obool)),U_5547),U_5548)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5546,tc_fun(U_5544,tc_HOL_Obool)),U_5547),hAPP(hAPP(c_COMBB(tc_fun(U_5544,tc_HOL_Obool),tc_fun(U_5544,tc_HOL_Obool),U_5546),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5544,tc_HOL_Obool)),U_5545)),U_5548)),
inference(clausify,[status(thm)],[f_1241_3]) ).
fof(f_1242_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_d,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_d),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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I6_J]) ).
fof(f_1242_2,plain,
! [U_5553,U_5552,U_5551,U_5550,U_5549] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5549,tc_fun(U_5550,tc_HOL_Obool)),U_5551),hAPP(hAPP(c_COMBC(U_5549,tc_fun(U_5550,tc_HOL_Obool),tc_fun(U_5550,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5550,tc_HOL_Obool),tc_fun(tc_fun(U_5550,tc_HOL_Obool),tc_fun(U_5550,tc_HOL_Obool)),U_5549),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5550,tc_HOL_Obool))),U_5552)),U_5553)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5550,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5549,tc_fun(U_5550,tc_HOL_Obool)),U_5551),U_5552)),U_5553),
inference(variable_rename,[status(thm)],[f_1242_1]) ).
fof(f_1242_3,plain,
! [U_5549,U_5550,U_5551,U_5552,U_5553] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5549,tc_fun(U_5550,tc_HOL_Obool)),U_5551),hAPP(hAPP(c_COMBC(U_5549,tc_fun(U_5550,tc_HOL_Obool),tc_fun(U_5550,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5550,tc_HOL_Obool),tc_fun(tc_fun(U_5550,tc_HOL_Obool),tc_fun(U_5550,tc_HOL_Obool)),U_5549),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5550,tc_HOL_Obool))),U_5552)),U_5553)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5550,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5549,tc_fun(U_5550,tc_HOL_Obool)),U_5551),U_5552)),U_5553),
inference(definitional_conversion,[status(esa)],[f_1242_2]) ).
cnf(f_1242_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5549,tc_fun(U_5550,tc_HOL_Obool)),U_5551),hAPP(hAPP(c_COMBC(U_5549,tc_fun(U_5550,tc_HOL_Obool),tc_fun(U_5550,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5550,tc_HOL_Obool),tc_fun(tc_fun(U_5550,tc_HOL_Obool),tc_fun(U_5550,tc_HOL_Obool)),U_5549),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5550,tc_HOL_Obool))),U_5552)),U_5553)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5550,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5549,tc_fun(U_5550,tc_HOL_Obool)),U_5551),U_5552)),U_5553),
inference(clausify,[status(thm)],[f_1242_3]) ).
fof(f_1243_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,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_d),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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I7_J]) ).
fof(f_1243_2,plain,
! [U_5558,U_5557,U_5556,U_5555,U_5554] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5554,tc_fun(U_5555,tc_HOL_Obool)),U_5556),hAPP(hAPP(c_COMBB(tc_fun(U_5555,tc_HOL_Obool),tc_fun(U_5555,tc_HOL_Obool),U_5554),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5555,tc_HOL_Obool)),U_5557)),U_5558)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5555,tc_HOL_Obool)),U_5557),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5554,tc_fun(U_5555,tc_HOL_Obool)),U_5556),U_5558)),
inference(variable_rename,[status(thm)],[f_1243_1]) ).
fof(f_1243_3,plain,
! [U_5554,U_5555,U_5556,U_5557,U_5558] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5554,tc_fun(U_5555,tc_HOL_Obool)),U_5556),hAPP(hAPP(c_COMBB(tc_fun(U_5555,tc_HOL_Obool),tc_fun(U_5555,tc_HOL_Obool),U_5554),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5555,tc_HOL_Obool)),U_5557)),U_5558)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5555,tc_HOL_Obool)),U_5557),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5554,tc_fun(U_5555,tc_HOL_Obool)),U_5556),U_5558)),
inference(definitional_conversion,[status(esa)],[f_1243_2]) ).
cnf(f_1243_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5554,tc_fun(U_5555,tc_HOL_Obool)),U_5556),hAPP(hAPP(c_COMBB(tc_fun(U_5555,tc_HOL_Obool),tc_fun(U_5555,tc_HOL_Obool),U_5554),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5555,tc_HOL_Obool)),U_5557)),U_5558)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5555,tc_HOL_Obool)),U_5557),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5554,tc_fun(U_5555,tc_HOL_Obool)),U_5556),U_5558)),
inference(clausify,[status(thm)],[f_1243_3]) ).
fof(f_1244_1,plain,
! [V_B_2,V_A_2,V_I_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_d,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_d),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_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__Int__distrib]) ).
fof(f_1244_2,plain,
! [U_5563,U_5562,U_5561,U_5560,U_5559] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5559,tc_fun(U_5560,tc_HOL_Obool)),U_5561),hAPP(hAPP(c_COMBS(U_5559,tc_fun(U_5560,tc_HOL_Obool),tc_fun(U_5560,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5560,tc_HOL_Obool),tc_fun(tc_fun(U_5560,tc_HOL_Obool),tc_fun(U_5560,tc_HOL_Obool)),U_5559),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5560,tc_HOL_Obool))),U_5562)),U_5563)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5560,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5559,tc_fun(U_5560,tc_HOL_Obool)),U_5561),U_5562)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5559,tc_fun(U_5560,tc_HOL_Obool)),U_5561),U_5563)),
inference(variable_rename,[status(thm)],[f_1244_1]) ).
fof(f_1244_3,plain,
! [U_5559,U_5560,U_5561,U_5562,U_5563] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5559,tc_fun(U_5560,tc_HOL_Obool)),U_5561),hAPP(hAPP(c_COMBS(U_5559,tc_fun(U_5560,tc_HOL_Obool),tc_fun(U_5560,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5560,tc_HOL_Obool),tc_fun(tc_fun(U_5560,tc_HOL_Obool),tc_fun(U_5560,tc_HOL_Obool)),U_5559),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5560,tc_HOL_Obool))),U_5562)),U_5563)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5560,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5559,tc_fun(U_5560,tc_HOL_Obool)),U_5561),U_5562)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5559,tc_fun(U_5560,tc_HOL_Obool)),U_5561),U_5563)),
inference(definitional_conversion,[status(esa)],[f_1244_2]) ).
cnf(f_1244_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5559,tc_fun(U_5560,tc_HOL_Obool)),U_5561),hAPP(hAPP(c_COMBS(U_5559,tc_fun(U_5560,tc_HOL_Obool),tc_fun(U_5560,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5560,tc_HOL_Obool),tc_fun(tc_fun(U_5560,tc_HOL_Obool),tc_fun(U_5560,tc_HOL_Obool)),U_5559),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5560,tc_HOL_Obool))),U_5562)),U_5563)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5560,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5559,tc_fun(U_5560,tc_HOL_Obool)),U_5561),U_5562)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5559,tc_fun(U_5560,tc_HOL_Obool)),U_5561),U_5563)),
inference(clausify,[status(thm)],[f_1244_3]) ).
fof(f_1245_1,plain,
! [V_C_2,V_B_2,T_e,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_HOL_Obool),tc_fun(tc_fun(T_e,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,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_1245_2,plain,
! [U_5569,U_5568,U_5567,U_5566,U_5565,U_5564] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5564,tc_fun(U_5565,tc_HOL_Obool)),U_5566),hAPP(hAPP(c_COMBC(U_5564,tc_fun(U_5567,tc_fun(U_5565,tc_HOL_Obool)),tc_fun(U_5565,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5567,tc_HOL_Obool),tc_fun(tc_fun(U_5567,tc_fun(U_5565,tc_HOL_Obool)),tc_fun(U_5565,tc_HOL_Obool)),U_5564),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5567,tc_fun(U_5565,tc_HOL_Obool))),U_5568)),U_5569)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5567,tc_fun(U_5565,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5564,tc_fun(U_5567,tc_HOL_Obool)),U_5566),U_5568)),U_5569),
inference(variable_rename,[status(thm)],[f_1245_1]) ).
fof(f_1245_3,plain,
! [U_5564,U_5565,U_5566,U_5567,U_5568,U_5569] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5564,tc_fun(U_5565,tc_HOL_Obool)),U_5566),hAPP(hAPP(c_COMBC(U_5564,tc_fun(U_5567,tc_fun(U_5565,tc_HOL_Obool)),tc_fun(U_5565,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5567,tc_HOL_Obool),tc_fun(tc_fun(U_5567,tc_fun(U_5565,tc_HOL_Obool)),tc_fun(U_5565,tc_HOL_Obool)),U_5564),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5567,tc_fun(U_5565,tc_HOL_Obool))),U_5568)),U_5569)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5567,tc_fun(U_5565,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5564,tc_fun(U_5567,tc_HOL_Obool)),U_5566),U_5568)),U_5569),
inference(definitional_conversion,[status(esa)],[f_1245_2]) ).
cnf(f_1245_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5564,tc_fun(U_5565,tc_HOL_Obool)),U_5566),hAPP(hAPP(c_COMBC(U_5564,tc_fun(U_5567,tc_fun(U_5565,tc_HOL_Obool)),tc_fun(U_5565,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5567,tc_HOL_Obool),tc_fun(tc_fun(U_5567,tc_fun(U_5565,tc_HOL_Obool)),tc_fun(U_5565,tc_HOL_Obool)),U_5564),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5567,tc_fun(U_5565,tc_HOL_Obool))),U_5568)),U_5569)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5567,tc_fun(U_5565,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5564,tc_fun(U_5567,tc_HOL_Obool)),U_5566),U_5568)),U_5569),
inference(clausify,[status(thm)],[f_1245_3]) ).
fof(f_1246_1,plain,
! [V_C_2,V_B_2,V_A_2,T_e,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_e),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I9_J]) ).
fof(f_1246_2,plain,
! [U_5575,U_5574,U_5573,U_5572,U_5571,U_5570] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5570,tc_fun(U_5571,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5572,tc_fun(U_5570,tc_HOL_Obool)),U_5573),U_5574)),U_5575) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5572,tc_fun(U_5571,tc_HOL_Obool)),U_5573),hAPP(hAPP(c_COMBC(U_5572,tc_fun(U_5570,tc_fun(U_5571,tc_HOL_Obool)),tc_fun(U_5571,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5570,tc_HOL_Obool),tc_fun(tc_fun(U_5570,tc_fun(U_5571,tc_HOL_Obool)),tc_fun(U_5571,tc_HOL_Obool)),U_5572),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5570,tc_fun(U_5571,tc_HOL_Obool))),U_5574)),U_5575)),
inference(variable_rename,[status(thm)],[f_1246_1]) ).
fof(f_1246_3,plain,
! [U_5570,U_5571,U_5572,U_5573,U_5574,U_5575] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5570,tc_fun(U_5571,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5572,tc_fun(U_5570,tc_HOL_Obool)),U_5573),U_5574)),U_5575) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5572,tc_fun(U_5571,tc_HOL_Obool)),U_5573),hAPP(hAPP(c_COMBC(U_5572,tc_fun(U_5570,tc_fun(U_5571,tc_HOL_Obool)),tc_fun(U_5571,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5570,tc_HOL_Obool),tc_fun(tc_fun(U_5570,tc_fun(U_5571,tc_HOL_Obool)),tc_fun(U_5571,tc_HOL_Obool)),U_5572),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5570,tc_fun(U_5571,tc_HOL_Obool))),U_5574)),U_5575)),
inference(definitional_conversion,[status(esa)],[f_1246_2]) ).
cnf(f_1246_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5570,tc_fun(U_5571,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5572,tc_fun(U_5570,tc_HOL_Obool)),U_5573),U_5574)),U_5575) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5572,tc_fun(U_5571,tc_HOL_Obool)),U_5573),hAPP(hAPP(c_COMBC(U_5572,tc_fun(U_5570,tc_fun(U_5571,tc_HOL_Obool)),tc_fun(U_5571,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5570,tc_HOL_Obool),tc_fun(tc_fun(U_5570,tc_fun(U_5571,tc_HOL_Obool)),tc_fun(U_5571,tc_HOL_Obool)),U_5572),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5570,tc_fun(U_5571,tc_HOL_Obool))),U_5574)),U_5575)),
inference(clausify,[status(thm)],[f_1246_3]) ).
fof(f_1247_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_1247_2,plain,
! [U_5577,U_5576] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5576)),hAPP(c_Nat_OSuc,U_5577)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5576),U_5577)),
inference(variable_rename,[status(thm)],[f_1247_1]) ).
fof(f_1247_3,plain,
! [U_5576,U_5577] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5576)),hAPP(c_Nat_OSuc,U_5577)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5576),U_5577)),
inference(definitional_conversion,[status(esa)],[f_1247_2]) ).
cnf(f_1247_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5576)),hAPP(c_Nat_OSuc,U_5577)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5576),U_5577)),
inference(clausify,[status(thm)],[f_1247_3]) ).
fof(f_1248_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_1248_2,plain,
! [U_5579,U_5578] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5578)),hAPP(c_Nat_OSuc,U_5579)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5578),U_5579)),
inference(variable_rename,[status(thm)],[f_1248_1]) ).
fof(f_1248_3,plain,
! [U_5578,U_5579] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5578)),hAPP(c_Nat_OSuc,U_5579)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5578),U_5579)),
inference(definitional_conversion,[status(esa)],[f_1248_2]) ).
cnf(f_1248_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5578)),hAPP(c_Nat_OSuc,U_5579)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5578),U_5579)),
inference(clausify,[status(thm)],[f_1248_3]) ).
fof(f_1249_1,plain,
! [V_B_2,V_A_2,T_e,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Set_Ovimage(T_c,T_d,V_f_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__INT]) ).
fof(f_1249_2,plain,
! [U_5585,U_5584,U_5583,U_5582,U_5581,U_5580] : hAPP(c_Set_Ovimage(U_5580,U_5581,U_5582),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5583,tc_fun(U_5581,tc_HOL_Obool)),U_5584),U_5585)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5583,tc_fun(U_5580,tc_HOL_Obool)),U_5584),hAPP(hAPP(c_COMBB(tc_fun(U_5581,tc_HOL_Obool),tc_fun(U_5580,tc_HOL_Obool),U_5583),c_Set_Ovimage(U_5580,U_5581,U_5582)),U_5585)),
inference(variable_rename,[status(thm)],[f_1249_1]) ).
fof(f_1249_3,plain,
! [U_5580,U_5581,U_5582,U_5583,U_5584,U_5585] : hAPP(c_Set_Ovimage(U_5580,U_5581,U_5582),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5583,tc_fun(U_5581,tc_HOL_Obool)),U_5584),U_5585)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5583,tc_fun(U_5580,tc_HOL_Obool)),U_5584),hAPP(hAPP(c_COMBB(tc_fun(U_5581,tc_HOL_Obool),tc_fun(U_5580,tc_HOL_Obool),U_5583),c_Set_Ovimage(U_5580,U_5581,U_5582)),U_5585)),
inference(definitional_conversion,[status(esa)],[f_1249_2]) ).
cnf(f_1249_4,plain,
hAPP(c_Set_Ovimage(U_5580,U_5581,U_5582),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5583,tc_fun(U_5581,tc_HOL_Obool)),U_5584),U_5585)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5583,tc_fun(U_5580,tc_HOL_Obool)),U_5584),hAPP(hAPP(c_COMBB(tc_fun(U_5581,tc_HOL_Obool),tc_fun(U_5580,tc_HOL_Obool),U_5583),c_Set_Ovimage(U_5580,U_5581,U_5582)),U_5585)),
inference(clausify,[status(thm)],[f_1249_3]) ).
fof(f_1250_1,plain,
! [V_A_2,V_b_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_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_c),V_b_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_c),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__Inf__iff]) ).
fof(f_1250_2,plain,
! [U_5590,U_5589,U_5588] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),c_Complete__Lattice_OInf__class_OInf(U_5588,U_5590)))
| ? [U_5587] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),U_5587))
& hBOOL(hAPP(hAPP(c_member(U_5588),U_5587),U_5590)) ) )
& ( ! [U_5586] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),U_5586))
| ~ hBOOL(hAPP(hAPP(c_member(U_5588),U_5586),U_5590)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),c_Complete__Lattice_OInf__class_OInf(U_5588,U_5590))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5588) ),
inference(variable_rename,[status(thm)],[f_1250_1]) ).
fof(f_1250_3,plain,
! [U_5590,U_5589,U_5588] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),c_Complete__Lattice_OInf__class_OInf(U_5588,U_5590)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),sK110(U_5590,U_5589,U_5588)))
& hBOOL(hAPP(hAPP(c_member(U_5588),sK110(U_5590,U_5589,U_5588)),U_5590)) ) )
& ( ! [U_5586] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),U_5586))
| ~ hBOOL(hAPP(hAPP(c_member(U_5588),U_5586),U_5590)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),c_Complete__Lattice_OInf__class_OInf(U_5588,U_5590))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5588) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_5587,sK110(U_5590,U_5589,U_5588))],[f_1250_2]) ).
fof(f_1250_4,plain,
( ! [U_5588,U_5589,U_5590] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),sK110(U_5590,U_5589,U_5588)))
| ~ sP270(U_5588,U_5589,U_5590) )
& ! [U_5588,U_5589,U_5590] :
( hBOOL(hAPP(hAPP(c_member(U_5588),sK110(U_5590,U_5589,U_5588)),U_5590))
| ~ sP270(U_5588,U_5589,U_5590) )
& ! [U_5586,U_5588,U_5589,U_5590] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),c_Complete__Lattice_OInf__class_OInf(U_5588,U_5590)))
| sP270(U_5588,U_5589,U_5590)
| ~ sP271(U_5586,U_5588,U_5589,U_5590) )
& ! [U_5586,U_5588,U_5589,U_5590] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),U_5586))
| ~ hBOOL(hAPP(hAPP(c_member(U_5588),U_5586),U_5590))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),c_Complete__Lattice_OInf__class_OInf(U_5588,U_5590)))
| ~ sP271(U_5586,U_5588,U_5589,U_5590) )
& ! [U_5586,U_5588,U_5589,U_5590] :
( sP271(U_5586,U_5588,U_5589,U_5590)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5588) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP270,sP271])],[f_1250_3]) ).
cnf(f_1250_5,plain,
( sP271(U_5586,U_5588,U_5589,U_5590)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5588) ),
inference(clausify,[status(thm)],[f_1250_4]) ).
cnf(f_1250_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),U_5586))
| ~ hBOOL(hAPP(hAPP(c_member(U_5588),U_5586),U_5590))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),c_Complete__Lattice_OInf__class_OInf(U_5588,U_5590)))
| ~ sP271(U_5586,U_5588,U_5589,U_5590) ),
inference(clausify,[status(thm)],[f_1250_4]) ).
cnf(f_1250_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),c_Complete__Lattice_OInf__class_OInf(U_5588,U_5590)))
| sP270(U_5588,U_5589,U_5590)
| ~ sP271(U_5586,U_5588,U_5589,U_5590) ),
inference(clausify,[status(thm)],[f_1250_4]) ).
cnf(f_1250_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_5588),sK110(U_5590,U_5589,U_5588)),U_5590))
| ~ sP270(U_5588,U_5589,U_5590) ),
inference(clausify,[status(thm)],[f_1250_4]) ).
cnf(f_1250_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5588),U_5589),sK110(U_5590,U_5589,U_5588)))
| ~ sP270(U_5588,U_5589,U_5590) ),
inference(clausify,[status(thm)],[f_1250_4]) ).
fof(f_1251_1,plain,
! [V_a_2,V_S_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Complete__Lattice_OInf__class_OInf(T_c,V_S_2)),V_a_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),B_x),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),B_x),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Complete__Lattice_OInf__class_OInf(T_c,V_S_2)),V_a_2)) ) )
| ~ class_Orderings_Olinorder(T_c)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__less__iff]) ).
fof(f_1251_2,plain,
! [U_5595,U_5594,U_5593] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),c_Complete__Lattice_OInf__class_OInf(U_5593,U_5594)),U_5595))
| ! [U_5592] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),U_5592),U_5595))
| ~ hBOOL(hAPP(hAPP(c_member(U_5593),U_5592),U_5594)) ) )
& ( ? [U_5591] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),U_5591),U_5595))
& hBOOL(hAPP(hAPP(c_member(U_5593),U_5591),U_5594)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),c_Complete__Lattice_OInf__class_OInf(U_5593,U_5594)),U_5595)) ) )
| ~ class_Orderings_Olinorder(U_5593)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5593) ),
inference(variable_rename,[status(thm)],[f_1251_1]) ).
fof(f_1251_3,plain,
! [U_5595,U_5594,U_5593] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),c_Complete__Lattice_OInf__class_OInf(U_5593,U_5594)),U_5595))
| ! [U_5592] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),U_5592),U_5595))
| ~ hBOOL(hAPP(hAPP(c_member(U_5593),U_5592),U_5594)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),sK111(U_5595,U_5594,U_5593)),U_5595))
& hBOOL(hAPP(hAPP(c_member(U_5593),sK111(U_5595,U_5594,U_5593)),U_5594)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),c_Complete__Lattice_OInf__class_OInf(U_5593,U_5594)),U_5595)) ) )
| ~ class_Orderings_Olinorder(U_5593)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5593) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_5591,sK111(U_5595,U_5594,U_5593))],[f_1251_2]) ).
fof(f_1251_4,plain,
( ! [U_5595,U_5594,U_5593] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),sK111(U_5595,U_5594,U_5593)),U_5595))
| ~ sP272(U_5595,U_5594,U_5593) )
& ! [U_5595,U_5594,U_5593] :
( hBOOL(hAPP(hAPP(c_member(U_5593),sK111(U_5595,U_5594,U_5593)),U_5594))
| ~ sP272(U_5595,U_5594,U_5593) )
& ! [U_5595,U_5594,U_5592,U_5593] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),c_Complete__Lattice_OInf__class_OInf(U_5593,U_5594)),U_5595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),U_5592),U_5595))
| ~ hBOOL(hAPP(hAPP(c_member(U_5593),U_5592),U_5594))
| ~ sP273(U_5595,U_5594,U_5592,U_5593) )
& ! [U_5595,U_5594,U_5592,U_5593] :
( sP272(U_5595,U_5594,U_5593)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),c_Complete__Lattice_OInf__class_OInf(U_5593,U_5594)),U_5595))
| ~ sP273(U_5595,U_5594,U_5592,U_5593) )
& ! [U_5595,U_5594,U_5592,U_5593] :
( sP273(U_5595,U_5594,U_5592,U_5593)
| ~ class_Orderings_Olinorder(U_5593)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5593) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP272,sP273])],[f_1251_3]) ).
cnf(f_1251_5,plain,
( sP273(U_5595,U_5594,U_5592,U_5593)
| ~ class_Orderings_Olinorder(U_5593)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5593) ),
inference(clausify,[status(thm)],[f_1251_4]) ).
cnf(f_1251_6,plain,
( sP272(U_5595,U_5594,U_5593)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),c_Complete__Lattice_OInf__class_OInf(U_5593,U_5594)),U_5595))
| ~ sP273(U_5595,U_5594,U_5592,U_5593) ),
inference(clausify,[status(thm)],[f_1251_4]) ).
cnf(f_1251_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),c_Complete__Lattice_OInf__class_OInf(U_5593,U_5594)),U_5595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),U_5592),U_5595))
| ~ hBOOL(hAPP(hAPP(c_member(U_5593),U_5592),U_5594))
| ~ sP273(U_5595,U_5594,U_5592,U_5593) ),
inference(clausify,[status(thm)],[f_1251_4]) ).
cnf(f_1251_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_5593),sK111(U_5595,U_5594,U_5593)),U_5594))
| ~ sP272(U_5595,U_5594,U_5593) ),
inference(clausify,[status(thm)],[f_1251_4]) ).
cnf(f_1251_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5593),sK111(U_5595,U_5594,U_5593)),U_5595))
| ~ sP272(U_5595,U_5594,U_5593) ),
inference(clausify,[status(thm)],[f_1251_4]) ).
fof(f_1252_1,plain,
! [V_n_2,V_a_2,V_times_2,V_one_2,T_c] : hAPP(hAPP(c_Power_Opower_Opower(T_c,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_c,V_one_2,V_times_2),V_a_2),V_n_2)),
inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__Suc]) ).
fof(f_1252_2,plain,
! [U_5600,U_5599,U_5598,U_5597,U_5596] : hAPP(hAPP(c_Power_Opower_Opower(U_5596,U_5597,U_5598),U_5599),hAPP(c_Nat_OSuc,U_5600)) = hAPP(hAPP(U_5598,U_5599),hAPP(hAPP(c_Power_Opower_Opower(U_5596,U_5597,U_5598),U_5599),U_5600)),
inference(variable_rename,[status(thm)],[f_1252_1]) ).
fof(f_1252_3,plain,
! [U_5600,U_5598,U_5597,U_5599,U_5596] : hAPP(hAPP(c_Power_Opower_Opower(U_5596,U_5597,U_5598),U_5599),hAPP(c_Nat_OSuc,U_5600)) = hAPP(hAPP(U_5598,U_5599),hAPP(hAPP(c_Power_Opower_Opower(U_5596,U_5597,U_5598),U_5599),U_5600)),
inference(definitional_conversion,[status(esa)],[f_1252_2]) ).
cnf(f_1252_4,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_5596,U_5597,U_5598),U_5599),hAPP(c_Nat_OSuc,U_5600)) = hAPP(hAPP(U_5598,U_5599),hAPP(hAPP(c_Power_Opower_Opower(U_5596,U_5597,U_5598),U_5599),U_5600)),
inference(clausify,[status(thm)],[f_1252_3]) ).
fof(f_1253_1,plain,
! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2),
inference(fof_nnf,[status(thm)],[fact_inj__Suc]) ).
fof(f_1253_2,plain,
! [U_5601] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_5601),
inference(variable_rename,[status(thm)],[f_1253_1]) ).
fof(f_1253_3,plain,
! [U_5601] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_5601),
inference(definitional_conversion,[status(esa)],[f_1253_2]) ).
cnf(f_1253_4,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_5601),
inference(clausify,[status(thm)],[f_1253_3]) ).
fof(f_1254_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_1254_2,plain,
! [U_5604,U_5603,U_5602] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5602),U_5603),hAPP(c_Nat_OSuc,U_5604)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5602),U_5603),hAPP(hAPP(c_Power_Opower__class_Opower(U_5602),U_5603),U_5604))
| ~ class_Rings_Ocomm__semiring__1(U_5602) ),
inference(variable_rename,[status(thm)],[f_1254_1]) ).
fof(f_1254_3,plain,
! [U_5602,U_5603,U_5604] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5602),U_5603),hAPP(c_Nat_OSuc,U_5604)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5602),U_5603),hAPP(hAPP(c_Power_Opower__class_Opower(U_5602),U_5603),U_5604))
| ~ class_Rings_Ocomm__semiring__1(U_5602) ),
inference(definitional_conversion,[status(esa)],[f_1254_2]) ).
cnf(f_1254_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5602),U_5603),hAPP(c_Nat_OSuc,U_5604)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5602),U_5603),hAPP(hAPP(c_Power_Opower__class_Opower(U_5602),U_5603),U_5604))
| ~ class_Rings_Ocomm__semiring__1(U_5602) ),
inference(clausify,[status(thm)],[f_1254_3]) ).
fof(f_1255_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_1255_2,plain,
! [U_5607,U_5606,U_5605] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5605),U_5606),hAPP(hAPP(c_Power_Opower__class_Opower(U_5605),U_5606),U_5607)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5605),U_5606),hAPP(c_Nat_OSuc,U_5607))
| ~ class_Rings_Ocomm__semiring__1(U_5605) ),
inference(variable_rename,[status(thm)],[f_1255_1]) ).
fof(f_1255_3,plain,
! [U_5605,U_5606,U_5607] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5605),U_5606),hAPP(hAPP(c_Power_Opower__class_Opower(U_5605),U_5606),U_5607)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5605),U_5606),hAPP(c_Nat_OSuc,U_5607))
| ~ class_Rings_Ocomm__semiring__1(U_5605) ),
inference(definitional_conversion,[status(esa)],[f_1255_2]) ).
cnf(f_1255_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5605),U_5606),hAPP(hAPP(c_Power_Opower__class_Opower(U_5605),U_5606),U_5607)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5605),U_5606),hAPP(c_Nat_OSuc,U_5607))
| ~ class_Rings_Ocomm__semiring__1(U_5605) ),
inference(clausify,[status(thm)],[f_1255_3]) ).
fof(f_1256_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_1256_2,plain,
! [U_5610,U_5609,U_5608] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5608),hAPP(hAPP(c_Power_Opower__class_Opower(U_5608),U_5609),U_5610)),U_5609) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5608),U_5609),hAPP(c_Nat_OSuc,U_5610))
| ~ class_Rings_Ocomm__semiring__1(U_5608) ),
inference(variable_rename,[status(thm)],[f_1256_1]) ).
fof(f_1256_3,plain,
! [U_5608,U_5609,U_5610] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5608),hAPP(hAPP(c_Power_Opower__class_Opower(U_5608),U_5609),U_5610)),U_5609) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5608),U_5609),hAPP(c_Nat_OSuc,U_5610))
| ~ class_Rings_Ocomm__semiring__1(U_5608) ),
inference(definitional_conversion,[status(esa)],[f_1256_2]) ).
cnf(f_1256_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5608),hAPP(hAPP(c_Power_Opower__class_Opower(U_5608),U_5609),U_5610)),U_5609) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5608),U_5609),hAPP(c_Nat_OSuc,U_5610))
| ~ class_Rings_Ocomm__semiring__1(U_5608) ),
inference(clausify,[status(thm)],[f_1256_3]) ).
fof(f_1257_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_1257_2,plain,
! [U_5613,U_5612,U_5611] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5611),U_5612),hAPP(c_Nat_OSuc,U_5613)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5611),hAPP(hAPP(c_Power_Opower__class_Opower(U_5611),U_5612),U_5613)),U_5612)
| ~ class_Groups_Omonoid__mult(U_5611) ),
inference(variable_rename,[status(thm)],[f_1257_1]) ).
fof(f_1257_3,plain,
! [U_5611,U_5612,U_5613] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5611),U_5612),hAPP(c_Nat_OSuc,U_5613)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5611),hAPP(hAPP(c_Power_Opower__class_Opower(U_5611),U_5612),U_5613)),U_5612)
| ~ class_Groups_Omonoid__mult(U_5611) ),
inference(definitional_conversion,[status(esa)],[f_1257_2]) ).
cnf(f_1257_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5611),U_5612),hAPP(c_Nat_OSuc,U_5613)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5611),hAPP(hAPP(c_Power_Opower__class_Opower(U_5611),U_5612),U_5613)),U_5612)
| ~ class_Groups_Omonoid__mult(U_5611) ),
inference(clausify,[status(thm)],[f_1257_3]) ).
fof(f_1258_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_1258_2,plain,
! [U_5616,U_5615,U_5614] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5614),U_5615),hAPP(c_Nat_OSuc,U_5616)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5614),U_5615),hAPP(hAPP(c_Power_Opower__class_Opower(U_5614),U_5615),U_5616))
| ~ class_Power_Opower(U_5614) ),
inference(variable_rename,[status(thm)],[f_1258_1]) ).
fof(f_1258_3,plain,
! [U_5614,U_5615,U_5616] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5614),U_5615),hAPP(c_Nat_OSuc,U_5616)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5614),U_5615),hAPP(hAPP(c_Power_Opower__class_Opower(U_5614),U_5615),U_5616))
| ~ class_Power_Opower(U_5614) ),
inference(definitional_conversion,[status(esa)],[f_1258_2]) ).
cnf(f_1258_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5614),U_5615),hAPP(c_Nat_OSuc,U_5616)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5614),U_5615),hAPP(hAPP(c_Power_Opower__class_Opower(U_5614),U_5615),U_5616))
| ~ class_Power_Opower(U_5614) ),
inference(clausify,[status(thm)],[f_1258_3]) ).
fof(f_1259_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_1259_2,plain,
! [U_5618,U_5617] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5617),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5617),U_5618)))),
inference(variable_rename,[status(thm)],[f_1259_1]) ).
fof(f_1259_3,plain,
! [U_5617,U_5618] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5617),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5617),U_5618)))),
inference(definitional_conversion,[status(esa)],[f_1259_2]) ).
cnf(f_1259_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5617),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5617),U_5618)))),
inference(clausify,[status(thm)],[f_1259_3]) ).
fof(f_1260_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_1260_2,plain,
! [U_5620,U_5619] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5619),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5620),U_5619)))),
inference(variable_rename,[status(thm)],[f_1260_1]) ).
fof(f_1260_3,plain,
! [U_5619,U_5620] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5619),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5620),U_5619)))),
inference(definitional_conversion,[status(esa)],[f_1260_2]) ).
cnf(f_1260_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5619),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5620),U_5619)))),
inference(clausify,[status(thm)],[f_1260_3]) ).
fof(f_1261_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_1261_2,plain,
! [U_5624,U_5623] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5623),U_5624))
| ! [U_5622] : U_5624 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5623),U_5622)) )
& ( ? [U_5621] : U_5624 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5623),U_5621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5623),U_5624)) ) ),
inference(variable_rename,[status(thm)],[f_1261_1]) ).
fof(f_1261_3,plain,
( ! [U_5628,U_5626] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5626),U_5628))
| ! [U_5622] : U_5628 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5626),U_5622)) )
& ! [U_5627,U_5625] :
( ? [U_5621] : U_5627 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5625),U_5621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5625),U_5627)) ) ),
inference(miniscope,[status(thm)],[f_1261_2]) ).
fof(f_1261_4,plain,
( ! [U_5628,U_5626] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5626),U_5628))
| ! [U_5622] : U_5628 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5626),U_5622)) )
& ! [U_5627,U_5625] :
( U_5627 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5625),sK112(U_5627,U_5625)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5625),U_5627)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_5621,sK112(U_5627,U_5625))],[f_1261_3]) ).
fof(f_1261_5,plain,
( ! [U_5622,U_5626,U_5628] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5626),U_5628))
| U_5628 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5626),U_5622)) )
& ! [U_5627,U_5625] :
( U_5627 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5625),sK112(U_5627,U_5625)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5625),U_5627)) ) ),
inference(definitional_conversion,[status(esa)],[f_1261_4]) ).
cnf(f_1261_6,plain,
( U_5627 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5625),sK112(U_5627,U_5625)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5625),U_5627)) ),
inference(clausify,[status(thm)],[f_1261_5]) ).
cnf(f_1261_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5626),U_5628))
| U_5628 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5626),U_5622)) ),
inference(clausify,[status(thm)],[f_1261_5]) ).
fof(f_1262_1,plain,
! [V_M_2,V_A_2,T_d,V_u_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),V_M_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_u_2),hAPP(V_M_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_u_2),hAPP(V_M_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),V_M_2))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__INF__iff]) ).
fof(f_1262_2,plain,
! [U_5635,U_5634,U_5633,U_5632,U_5631] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5633,U_5631),U_5634),U_5635)))
| ? [U_5630] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(U_5635,U_5630)))
& hBOOL(hAPP(hAPP(c_member(U_5633),U_5630),U_5634)) ) )
& ( ! [U_5629] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(U_5635,U_5629)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5633),U_5629),U_5634)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5633,U_5631),U_5634),U_5635))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5631) ),
inference(variable_rename,[status(thm)],[f_1262_1]) ).
fof(f_1262_3,plain,
! [U_5635,U_5634,U_5633,U_5632,U_5631] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5633,U_5631),U_5634),U_5635)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(U_5635,sK113(U_5635,U_5634,U_5633,U_5632,U_5631))))
& hBOOL(hAPP(hAPP(c_member(U_5633),sK113(U_5635,U_5634,U_5633,U_5632,U_5631)),U_5634)) ) )
& ( ! [U_5629] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(U_5635,U_5629)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5633),U_5629),U_5634)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5633,U_5631),U_5634),U_5635))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5631) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_5630,sK113(U_5635,U_5634,U_5633,U_5632,U_5631))],[f_1262_2]) ).
fof(f_1262_4,plain,
( ! [U_5631,U_5632,U_5633,U_5634,U_5635] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(U_5635,sK113(U_5635,U_5634,U_5633,U_5632,U_5631))))
| ~ sP274(U_5631,U_5632,U_5633,U_5634,U_5635) )
& ! [U_5631,U_5632,U_5633,U_5634,U_5635] :
( hBOOL(hAPP(hAPP(c_member(U_5633),sK113(U_5635,U_5634,U_5633,U_5632,U_5631)),U_5634))
| ~ sP274(U_5631,U_5632,U_5633,U_5634,U_5635) )
& ! [U_5629,U_5631,U_5632,U_5633,U_5634,U_5635] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5633,U_5631),U_5634),U_5635)))
| sP274(U_5631,U_5632,U_5633,U_5634,U_5635)
| ~ sP275(U_5629,U_5631,U_5632,U_5633,U_5634,U_5635) )
& ! [U_5629,U_5631,U_5632,U_5633,U_5634,U_5635] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(U_5635,U_5629)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5633),U_5629),U_5634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5633,U_5631),U_5634),U_5635)))
| ~ sP275(U_5629,U_5631,U_5632,U_5633,U_5634,U_5635) )
& ! [U_5629,U_5631,U_5632,U_5633,U_5634,U_5635] :
( sP275(U_5629,U_5631,U_5632,U_5633,U_5634,U_5635)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5631) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP274,sP275])],[f_1262_3]) ).
cnf(f_1262_5,plain,
( sP275(U_5629,U_5631,U_5632,U_5633,U_5634,U_5635)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5631) ),
inference(clausify,[status(thm)],[f_1262_4]) ).
cnf(f_1262_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(U_5635,U_5629)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5633),U_5629),U_5634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5633,U_5631),U_5634),U_5635)))
| ~ sP275(U_5629,U_5631,U_5632,U_5633,U_5634,U_5635) ),
inference(clausify,[status(thm)],[f_1262_4]) ).
cnf(f_1262_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5633,U_5631),U_5634),U_5635)))
| sP274(U_5631,U_5632,U_5633,U_5634,U_5635)
| ~ sP275(U_5629,U_5631,U_5632,U_5633,U_5634,U_5635) ),
inference(clausify,[status(thm)],[f_1262_4]) ).
cnf(f_1262_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_5633),sK113(U_5635,U_5634,U_5633,U_5632,U_5631)),U_5634))
| ~ sP274(U_5631,U_5632,U_5633,U_5634,U_5635) ),
inference(clausify,[status(thm)],[f_1262_4]) ).
cnf(f_1262_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5631),U_5632),hAPP(U_5635,sK113(U_5635,U_5634,U_5633,U_5632,U_5631))))
| ~ sP274(U_5631,U_5632,U_5633,U_5634,U_5635) ),
inference(clausify,[status(thm)],[f_1262_4]) ).
fof(f_1263_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_1263_2,plain,
! [U_5637,U_5636] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5636),U_5637))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5636)),U_5637)) ),
inference(variable_rename,[status(thm)],[f_1263_1]) ).
fof(f_1263_3,plain,
! [U_5637,U_5636] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5636),U_5637))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5636)),U_5637)) ),
inference(definitional_conversion,[status(esa)],[f_1263_2]) ).
cnf(f_1263_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5636),U_5637))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5636)),U_5637)) ),
inference(clausify,[status(thm)],[f_1263_3]) ).
fof(f_1264_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_1264_2,plain,
! [U_5639,U_5638] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5639),hAPP(c_Nat_OSuc,U_5638)))
| U_5639 != U_5638 )
& ( U_5639 = U_5638
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5639),hAPP(c_Nat_OSuc,U_5638))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5638),U_5639)) ),
inference(variable_rename,[status(thm)],[f_1264_1]) ).
fof(f_1264_3,plain,
( ! [U_5638,U_5639] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5639),hAPP(c_Nat_OSuc,U_5638)))
| U_5639 != U_5638
| ~ sP276(U_5638,U_5639) )
& ! [U_5638,U_5639] :
( U_5639 = U_5638
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5639),hAPP(c_Nat_OSuc,U_5638)))
| ~ sP276(U_5638,U_5639) )
& ! [U_5638,U_5639] :
( sP276(U_5638,U_5639)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5638),U_5639)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP276])],[f_1264_2]) ).
cnf(f_1264_4,plain,
( sP276(U_5638,U_5639)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5638),U_5639)) ),
inference(clausify,[status(thm)],[f_1264_3]) ).
cnf(f_1264_5,plain,
( U_5639 = U_5638
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5639),hAPP(c_Nat_OSuc,U_5638)))
| ~ sP276(U_5638,U_5639) ),
inference(clausify,[status(thm)],[f_1264_3]) ).
cnf(f_1264_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5639),hAPP(c_Nat_OSuc,U_5638)))
| U_5639 != U_5638
| ~ sP276(U_5638,U_5639) ),
inference(clausify,[status(thm)],[f_1264_3]) ).
fof(f_1265_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_1265_2,plain,
! [U_5641,U_5640] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5640)),U_5641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5640),U_5641)) ),
inference(variable_rename,[status(thm)],[f_1265_1]) ).
fof(f_1265_3,plain,
! [U_5641,U_5640] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5640)),U_5641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5640),U_5641)) ),
inference(definitional_conversion,[status(esa)],[f_1265_2]) ).
cnf(f_1265_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5640)),U_5641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5640),U_5641)) ),
inference(clausify,[status(thm)],[f_1265_3]) ).
fof(f_1266_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_1266_2,plain,
! [U_5643,U_5642] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5642),hAPP(c_Nat_OSuc,U_5643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5642),U_5643)) ),
inference(variable_rename,[status(thm)],[f_1266_1]) ).
fof(f_1266_3,plain,
! [U_5643,U_5642] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5642),hAPP(c_Nat_OSuc,U_5643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5642),U_5643)) ),
inference(definitional_conversion,[status(esa)],[f_1266_2]) ).
cnf(f_1266_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5642),hAPP(c_Nat_OSuc,U_5643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5642),U_5643)) ),
inference(clausify,[status(thm)],[f_1266_3]) ).
fof(f_1267_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_1267_2,plain,
! [U_5645,U_5644] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5644)),U_5645))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5644),U_5645)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5644),U_5645))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5644)),U_5645)) ) ),
inference(variable_rename,[status(thm)],[f_1267_1]) ).
fof(f_1267_3,plain,
( ! [U_5649,U_5647] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5647)),U_5649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5647),U_5649)) )
& ! [U_5648,U_5646] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5646),U_5648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5646)),U_5648)) ) ),
inference(miniscope,[status(thm)],[f_1267_2]) ).
fof(f_1267_4,plain,
( ! [U_5647,U_5649] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5647)),U_5649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5647),U_5649)) )
& ! [U_5648,U_5646] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5646),U_5648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5646)),U_5648)) ) ),
inference(definitional_conversion,[status(esa)],[f_1267_3]) ).
cnf(f_1267_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5646),U_5648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5646)),U_5648)) ),
inference(clausify,[status(thm)],[f_1267_4]) ).
cnf(f_1267_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5647)),U_5649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5647),U_5649)) ),
inference(clausify,[status(thm)],[f_1267_4]) ).
fof(f_1268_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_1268_2,plain,
! [U_5651,U_5650] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5650),hAPP(c_Nat_OSuc,U_5651)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5650),U_5651)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5650),U_5651))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5650),hAPP(c_Nat_OSuc,U_5651))) ) ),
inference(variable_rename,[status(thm)],[f_1268_1]) ).
fof(f_1268_3,plain,
( ! [U_5655,U_5653] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5653),hAPP(c_Nat_OSuc,U_5655)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5653),U_5655)) )
& ! [U_5654,U_5652] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5652),U_5654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5652),hAPP(c_Nat_OSuc,U_5654))) ) ),
inference(miniscope,[status(thm)],[f_1268_2]) ).
fof(f_1268_4,plain,
( ! [U_5653,U_5655] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5653),hAPP(c_Nat_OSuc,U_5655)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5653),U_5655)) )
& ! [U_5654,U_5652] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5652),U_5654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5652),hAPP(c_Nat_OSuc,U_5654))) ) ),
inference(definitional_conversion,[status(esa)],[f_1268_3]) ).
cnf(f_1268_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5652),U_5654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5652),hAPP(c_Nat_OSuc,U_5654))) ),
inference(clausify,[status(thm)],[f_1268_4]) ).
cnf(f_1268_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5653),hAPP(c_Nat_OSuc,U_5655)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5653),U_5655)) ),
inference(clausify,[status(thm)],[f_1268_4]) ).
fof(f_1269_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_1269_2,plain,
! [U_5657,U_5656] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5656),U_5657))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5656)),U_5657)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5656)),U_5657))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5656),U_5657)) ) ),
inference(variable_rename,[status(thm)],[f_1269_1]) ).
fof(f_1269_3,plain,
( ! [U_5661,U_5659] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5659),U_5661))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5659)),U_5661)) )
& ! [U_5660,U_5658] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5658)),U_5660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5658),U_5660)) ) ),
inference(miniscope,[status(thm)],[f_1269_2]) ).
fof(f_1269_4,plain,
( ! [U_5659,U_5661] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5659),U_5661))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5659)),U_5661)) )
& ! [U_5660,U_5658] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5658)),U_5660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5658),U_5660)) ) ),
inference(definitional_conversion,[status(esa)],[f_1269_3]) ).
cnf(f_1269_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5658)),U_5660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5658),U_5660)) ),
inference(clausify,[status(thm)],[f_1269_4]) ).
cnf(f_1269_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5659),U_5661))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5659)),U_5661)) ),
inference(clausify,[status(thm)],[f_1269_4]) ).
fof(f_1270_1,plain,
! [V_a_2,V_f_2,V_A_2,T_d,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),V_f_2)),V_a_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_c),V_A_2),V_f_2)),V_a_2)) ) )
| ~ class_Orderings_Olinorder(T_c)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_INF__less__iff]) ).
fof(f_1270_2,plain,
! [U_5668,U_5667,U_5666,U_5665,U_5664] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5665,U_5664),U_5666),U_5667)),U_5668))
| ! [U_5663] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(U_5667,U_5663)),U_5668))
| ~ hBOOL(hAPP(hAPP(c_member(U_5665),U_5663),U_5666)) ) )
& ( ? [U_5662] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(U_5667,U_5662)),U_5668))
& hBOOL(hAPP(hAPP(c_member(U_5665),U_5662),U_5666)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5665,U_5664),U_5666),U_5667)),U_5668)) ) )
| ~ class_Orderings_Olinorder(U_5664)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5664) ),
inference(variable_rename,[status(thm)],[f_1270_1]) ).
fof(f_1270_3,plain,
! [U_5668,U_5667,U_5666,U_5665,U_5664] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5665,U_5664),U_5666),U_5667)),U_5668))
| ! [U_5663] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(U_5667,U_5663)),U_5668))
| ~ hBOOL(hAPP(hAPP(c_member(U_5665),U_5663),U_5666)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(U_5667,sK114(U_5668,U_5667,U_5666,U_5665,U_5664))),U_5668))
& hBOOL(hAPP(hAPP(c_member(U_5665),sK114(U_5668,U_5667,U_5666,U_5665,U_5664)),U_5666)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5665,U_5664),U_5666),U_5667)),U_5668)) ) )
| ~ class_Orderings_Olinorder(U_5664)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5664) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_5662,sK114(U_5668,U_5667,U_5666,U_5665,U_5664))],[f_1270_2]) ).
fof(f_1270_4,plain,
( ! [U_5664,U_5665,U_5666,U_5667,U_5668] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(U_5667,sK114(U_5668,U_5667,U_5666,U_5665,U_5664))),U_5668))
| ~ sP277(U_5664,U_5665,U_5666,U_5667,U_5668) )
& ! [U_5664,U_5665,U_5666,U_5667,U_5668] :
( hBOOL(hAPP(hAPP(c_member(U_5665),sK114(U_5668,U_5667,U_5666,U_5665,U_5664)),U_5666))
| ~ sP277(U_5664,U_5665,U_5666,U_5667,U_5668) )
& ! [U_5663,U_5664,U_5665,U_5666,U_5667,U_5668] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5665,U_5664),U_5666),U_5667)),U_5668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(U_5667,U_5663)),U_5668))
| ~ hBOOL(hAPP(hAPP(c_member(U_5665),U_5663),U_5666))
| ~ sP278(U_5663,U_5664,U_5665,U_5666,U_5667,U_5668) )
& ! [U_5663,U_5664,U_5665,U_5666,U_5667,U_5668] :
( sP277(U_5664,U_5665,U_5666,U_5667,U_5668)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5665,U_5664),U_5666),U_5667)),U_5668))
| ~ sP278(U_5663,U_5664,U_5665,U_5666,U_5667,U_5668) )
& ! [U_5663,U_5664,U_5665,U_5666,U_5667,U_5668] :
( sP278(U_5663,U_5664,U_5665,U_5666,U_5667,U_5668)
| ~ class_Orderings_Olinorder(U_5664)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5664) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP277,sP278])],[f_1270_3]) ).
cnf(f_1270_5,plain,
( sP278(U_5663,U_5664,U_5665,U_5666,U_5667,U_5668)
| ~ class_Orderings_Olinorder(U_5664)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5664) ),
inference(clausify,[status(thm)],[f_1270_4]) ).
cnf(f_1270_6,plain,
( sP277(U_5664,U_5665,U_5666,U_5667,U_5668)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5665,U_5664),U_5666),U_5667)),U_5668))
| ~ sP278(U_5663,U_5664,U_5665,U_5666,U_5667,U_5668) ),
inference(clausify,[status(thm)],[f_1270_4]) ).
cnf(f_1270_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5665,U_5664),U_5666),U_5667)),U_5668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(U_5667,U_5663)),U_5668))
| ~ hBOOL(hAPP(hAPP(c_member(U_5665),U_5663),U_5666))
| ~ sP278(U_5663,U_5664,U_5665,U_5666,U_5667,U_5668) ),
inference(clausify,[status(thm)],[f_1270_4]) ).
cnf(f_1270_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_5665),sK114(U_5668,U_5667,U_5666,U_5665,U_5664)),U_5666))
| ~ sP277(U_5664,U_5665,U_5666,U_5667,U_5668) ),
inference(clausify,[status(thm)],[f_1270_4]) ).
cnf(f_1270_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5664),hAPP(U_5667,sK114(U_5668,U_5667,U_5666,U_5665,U_5664))),U_5668))
| ~ sP277(U_5664,U_5665,U_5666,U_5667,U_5668) ),
inference(clausify,[status(thm)],[f_1270_4]) ).
fof(f_1271_1,plain,
! [V_B_2,V_a_2,T_d,V_A_2,V_u_2,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_d),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_u_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_INT__insert__distrib]) ).
fof(f_1271_2,plain,
! [U_5674,U_5673,U_5672,U_5671,U_5670,U_5669] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5669,tc_fun(U_5672,tc_HOL_Obool)),U_5671),hAPP(hAPP(c_COMBB(tc_fun(U_5672,tc_HOL_Obool),tc_fun(U_5672,tc_HOL_Obool),U_5669),hAPP(c_Set_Oinsert(U_5672),U_5673)),U_5674)) = hAPP(hAPP(c_Set_Oinsert(U_5672),U_5673),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5669,tc_fun(U_5672,tc_HOL_Obool)),U_5671),U_5674))
| ~ hBOOL(hAPP(hAPP(c_member(U_5669),U_5670),U_5671)) ),
inference(variable_rename,[status(thm)],[f_1271_1]) ).
fof(f_1271_3,plain,
! [U_5674,U_5672,U_5670,U_5669,U_5671,U_5673] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5669,tc_fun(U_5672,tc_HOL_Obool)),U_5671),hAPP(hAPP(c_COMBB(tc_fun(U_5672,tc_HOL_Obool),tc_fun(U_5672,tc_HOL_Obool),U_5669),hAPP(c_Set_Oinsert(U_5672),U_5673)),U_5674)) = hAPP(hAPP(c_Set_Oinsert(U_5672),U_5673),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5669,tc_fun(U_5672,tc_HOL_Obool)),U_5671),U_5674))
| ~ hBOOL(hAPP(hAPP(c_member(U_5669),U_5670),U_5671)) ),
inference(definitional_conversion,[status(esa)],[f_1271_2]) ).
cnf(f_1271_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5669,tc_fun(U_5672,tc_HOL_Obool)),U_5671),hAPP(hAPP(c_COMBB(tc_fun(U_5672,tc_HOL_Obool),tc_fun(U_5672,tc_HOL_Obool),U_5669),hAPP(c_Set_Oinsert(U_5672),U_5673)),U_5674)) = hAPP(hAPP(c_Set_Oinsert(U_5672),U_5673),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5669,tc_fun(U_5672,tc_HOL_Obool)),U_5671),U_5674))
| ~ hBOOL(hAPP(hAPP(c_member(U_5669),U_5670),U_5671)) ),
inference(clausify,[status(thm)],[f_1271_3]) ).
fof(f_1272_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_1272_2,plain,
! [U_5676,U_5675] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5675),U_5676)),hAPP(c_Nat_OSuc,U_5675))),
inference(variable_rename,[status(thm)],[f_1272_1]) ).
fof(f_1272_3,plain,
! [U_5675,U_5676] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5675),U_5676)),hAPP(c_Nat_OSuc,U_5675))),
inference(definitional_conversion,[status(esa)],[f_1272_2]) ).
cnf(f_1272_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5675),U_5676)),hAPP(c_Nat_OSuc,U_5675))),
inference(clausify,[status(thm)],[f_1272_3]) ).
fof(f_1273_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_1273_2,plain,
! [U_5679,U_5678,U_5677] :
( ( 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_5677)),U_5678)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5677)),U_5679)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5678),U_5679)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5678),U_5679))
| ~ 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_5677)),U_5678)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5677)),U_5679))) ) ),
inference(variable_rename,[status(thm)],[f_1273_1]) ).
fof(f_1273_3,plain,
( ! [U_5685,U_5683] :
( ! [U_5681] : 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_5681)),U_5683)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5681)),U_5685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5683),U_5685)) )
& ! [U_5684,U_5682] :
( ! [U_5680] : ~ 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_5680)),U_5682)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5680)),U_5684)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5682),U_5684)) ) ),
inference(miniscope,[status(thm)],[f_1273_2]) ).
fof(f_1273_4,plain,
( ! [U_5685,U_5681,U_5683] :
( 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_5681)),U_5683)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5681)),U_5685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5683),U_5685)) )
& ! [U_5680,U_5682,U_5684] :
( ~ 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_5680)),U_5682)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5680)),U_5684)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5682),U_5684)) ) ),
inference(definitional_conversion,[status(esa)],[f_1273_3]) ).
cnf(f_1273_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_5680)),U_5682)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5680)),U_5684)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5682),U_5684)) ),
inference(clausify,[status(thm)],[f_1273_4]) ).
cnf(f_1273_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_5681)),U_5683)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5681)),U_5685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5683),U_5685)) ),
inference(clausify,[status(thm)],[f_1273_4]) ).
fof(f_1274_1,plain,
! [V_B_2,T_d,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_INT__lower]) ).
fof(f_1274_2,plain,
! [U_5690,U_5689,U_5688,U_5687,U_5686] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5689,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5686,tc_fun(U_5689,tc_HOL_Obool)),U_5688),U_5690)),hAPP(U_5690,U_5687)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5686),U_5687),U_5688)) ),
inference(variable_rename,[status(thm)],[f_1274_1]) ).
fof(f_1274_3,plain,
! [U_5687,U_5686,U_5688,U_5689,U_5690] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5689,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5686,tc_fun(U_5689,tc_HOL_Obool)),U_5688),U_5690)),hAPP(U_5690,U_5687)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5686),U_5687),U_5688)) ),
inference(definitional_conversion,[status(esa)],[f_1274_2]) ).
cnf(f_1274_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5689,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5686,tc_fun(U_5689,tc_HOL_Obool)),U_5688),U_5690)),hAPP(U_5690,U_5687)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5686),U_5687),U_5688)) ),
inference(clausify,[status(thm)],[f_1274_3]) ).
fof(f_1275_1,plain,
! [V_x_2,V_r_2,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d))),V_r_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_d),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d))),V_r_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF__INT__eq]) ).
fof(f_1275_2,plain,
! [U_5694,U_5693,U_5692,U_5691] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5691,tc_fun(U_5692,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5691,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5692,tc_HOL_Obool),tc_fun(U_5692,tc_HOL_Obool),U_5691),hAPP(c_COMBC(U_5692,tc_fun(U_5692,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5692))),U_5693)),U_5694))
| ~ hBOOL(hAPP(hAPP(c_member(U_5692),U_5694),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5691,tc_fun(U_5692,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5691,tc_HOL_Obool))),U_5693))) )
& ( hBOOL(hAPP(hAPP(c_member(U_5692),U_5694),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5691,tc_fun(U_5692,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5691,tc_HOL_Obool))),U_5693)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5691,tc_fun(U_5692,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5691,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5692,tc_HOL_Obool),tc_fun(U_5692,tc_HOL_Obool),U_5691),hAPP(c_COMBC(U_5692,tc_fun(U_5692,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5692))),U_5693)),U_5694)) ) ),
inference(variable_rename,[status(thm)],[f_1275_1]) ).
fof(f_1275_3,plain,
( ! [U_5702,U_5700,U_5698,U_5696] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5696,tc_fun(U_5698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5696,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5698,tc_HOL_Obool),tc_fun(U_5698,tc_HOL_Obool),U_5696),hAPP(c_COMBC(U_5698,tc_fun(U_5698,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5698))),U_5700)),U_5702))
| ~ hBOOL(hAPP(hAPP(c_member(U_5698),U_5702),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5696,tc_fun(U_5698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5696,tc_HOL_Obool))),U_5700))) )
& ! [U_5701,U_5699,U_5697,U_5695] :
( hBOOL(hAPP(hAPP(c_member(U_5697),U_5701),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5695,tc_fun(U_5697,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5695,tc_HOL_Obool))),U_5699)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5695,tc_fun(U_5697,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5695,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5697,tc_HOL_Obool),tc_fun(U_5697,tc_HOL_Obool),U_5695),hAPP(c_COMBC(U_5697,tc_fun(U_5697,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5697))),U_5699)),U_5701)) ) ),
inference(miniscope,[status(thm)],[f_1275_2]) ).
fof(f_1275_4,plain,
( ! [U_5696,U_5698,U_5700,U_5702] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5696,tc_fun(U_5698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5696,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5698,tc_HOL_Obool),tc_fun(U_5698,tc_HOL_Obool),U_5696),hAPP(c_COMBC(U_5698,tc_fun(U_5698,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5698))),U_5700)),U_5702))
| ~ hBOOL(hAPP(hAPP(c_member(U_5698),U_5702),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5696,tc_fun(U_5698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5696,tc_HOL_Obool))),U_5700))) )
& ! [U_5697,U_5701,U_5695,U_5699] :
( hBOOL(hAPP(hAPP(c_member(U_5697),U_5701),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5695,tc_fun(U_5697,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5695,tc_HOL_Obool))),U_5699)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5695,tc_fun(U_5697,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5695,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5697,tc_HOL_Obool),tc_fun(U_5697,tc_HOL_Obool),U_5695),hAPP(c_COMBC(U_5697,tc_fun(U_5697,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5697))),U_5699)),U_5701)) ) ),
inference(definitional_conversion,[status(esa)],[f_1275_3]) ).
cnf(f_1275_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_5697),U_5701),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5695,tc_fun(U_5697,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5695,tc_HOL_Obool))),U_5699)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5695,tc_fun(U_5697,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5695,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5697,tc_HOL_Obool),tc_fun(U_5697,tc_HOL_Obool),U_5695),hAPP(c_COMBC(U_5697,tc_fun(U_5697,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5697))),U_5699)),U_5701)) ),
inference(clausify,[status(thm)],[f_1275_4]) ).
cnf(f_1275_6,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5696,tc_fun(U_5698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5696,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_5698,tc_HOL_Obool),tc_fun(U_5698,tc_HOL_Obool),U_5696),hAPP(c_COMBC(U_5698,tc_fun(U_5698,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5698))),U_5700)),U_5702))
| ~ hBOOL(hAPP(hAPP(c_member(U_5698),U_5702),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5696,tc_fun(U_5698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5696,tc_HOL_Obool))),U_5700))) ),
inference(clausify,[status(thm)],[f_1275_4]) ).
fof(f_1276_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_1276_2,plain,
! [U_5704,U_5703] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5703)),U_5704) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5703),U_5704)),
inference(variable_rename,[status(thm)],[f_1276_1]) ).
fof(f_1276_3,plain,
! [U_5703,U_5704] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5703)),U_5704) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5703),U_5704)),
inference(definitional_conversion,[status(esa)],[f_1276_2]) ).
cnf(f_1276_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5703)),U_5704) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5703),U_5704)),
inference(clausify,[status(thm)],[f_1276_3]) ).
fof(f_1277_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_1277_2,plain,
! [U_5706,U_5705] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5705),hAPP(c_Nat_OSuc,U_5706)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5705),U_5706)),
inference(variable_rename,[status(thm)],[f_1277_1]) ).
fof(f_1277_3,plain,
! [U_5705,U_5706] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5705),hAPP(c_Nat_OSuc,U_5706)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5705),U_5706)),
inference(definitional_conversion,[status(esa)],[f_1277_2]) ).
cnf(f_1277_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5705),hAPP(c_Nat_OSuc,U_5706)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5705),U_5706)),
inference(clausify,[status(thm)],[f_1277_3]) ).
fof(f_1278_1,plain,
! [V_A_2,T_d,V_I_2,V_k_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_k_2),V_I_2)) ),
inference(fof_nnf,[status(thm)],[fact_INT__absorb]) ).
fof(f_1278_2,plain,
! [U_5711,U_5710,U_5709,U_5708,U_5707] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5710,tc_HOL_Obool)),hAPP(U_5711,U_5708)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5707,tc_fun(U_5710,tc_HOL_Obool)),U_5709),U_5711)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5707,tc_fun(U_5710,tc_HOL_Obool)),U_5709),U_5711)
| ~ hBOOL(hAPP(hAPP(c_member(U_5707),U_5708),U_5709)) ),
inference(variable_rename,[status(thm)],[f_1278_1]) ).
fof(f_1278_3,plain,
! [U_5707,U_5708,U_5709,U_5710,U_5711] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5710,tc_HOL_Obool)),hAPP(U_5711,U_5708)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5707,tc_fun(U_5710,tc_HOL_Obool)),U_5709),U_5711)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5707,tc_fun(U_5710,tc_HOL_Obool)),U_5709),U_5711)
| ~ hBOOL(hAPP(hAPP(c_member(U_5707),U_5708),U_5709)) ),
inference(definitional_conversion,[status(esa)],[f_1278_2]) ).
cnf(f_1278_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5710,tc_HOL_Obool)),hAPP(U_5711,U_5708)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5707,tc_fun(U_5710,tc_HOL_Obool)),U_5709),U_5711)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5707,tc_fun(U_5710,tc_HOL_Obool)),U_5709),U_5711)
| ~ hBOOL(hAPP(hAPP(c_member(U_5707),U_5708),U_5709)) ),
inference(clausify,[status(thm)],[f_1278_3]) ).
fof(f_1279_1,plain,
! [V_M_2,T_c,V_A_2,T_d] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),hAPP(c_COMBK(T_d,T_c),V_M_2)) = V_M_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_d) ),
inference(fof_nnf,[status(thm)],[fact_INF__const]) ).
fof(f_1279_2,plain,
! [U_5715,U_5714,U_5713,U_5712] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5714,U_5712),U_5713),hAPP(c_COMBK(U_5712,U_5714),U_5715)) = U_5715
| U_5713 = c_Orderings_Obot__class_Obot(tc_fun(U_5714,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5712) ),
inference(variable_rename,[status(thm)],[f_1279_1]) ).
fof(f_1279_3,plain,
! [U_5713,U_5712,U_5714,U_5715] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5714,U_5712),U_5713),hAPP(c_COMBK(U_5712,U_5714),U_5715)) = U_5715
| U_5713 = c_Orderings_Obot__class_Obot(tc_fun(U_5714,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5712) ),
inference(definitional_conversion,[status(esa)],[f_1279_2]) ).
cnf(f_1279_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5714,U_5712),U_5713),hAPP(c_COMBK(U_5712,U_5714),U_5715)) = U_5715
| U_5713 = c_Orderings_Obot__class_Obot(tc_fun(U_5714,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5712) ),
inference(clausify,[status(thm)],[f_1279_3]) ).
fof(f_1280_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_1280_2,plain,
! [U_5717,U_5716] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5717)),U_5716) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5717),U_5716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5716),U_5717)) ),
inference(variable_rename,[status(thm)],[f_1280_1]) ).
fof(f_1280_3,plain,
! [U_5717,U_5716] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5717)),U_5716) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5717),U_5716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5716),U_5717)) ),
inference(definitional_conversion,[status(esa)],[f_1280_2]) ).
cnf(f_1280_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5717)),U_5716) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5717),U_5716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5716),U_5717)) ),
inference(clausify,[status(thm)],[f_1280_3]) ).
fof(f_1281_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_1281_2,plain,
! [U_5720,U_5719,U_5718] :
( ( 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_5718)),U_5719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5718)),U_5720)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5719),U_5720)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5719),U_5720))
| ~ 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_5718)),U_5719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5718)),U_5720))) ) ),
inference(variable_rename,[status(thm)],[f_1281_1]) ).
fof(f_1281_3,plain,
( ! [U_5726,U_5724] :
( ! [U_5722] : 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_5722)),U_5724)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5722)),U_5726)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5724),U_5726)) )
& ! [U_5725,U_5723] :
( ! [U_5721] : ~ 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_5721)),U_5723)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5721)),U_5725)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5723),U_5725)) ) ),
inference(miniscope,[status(thm)],[f_1281_2]) ).
fof(f_1281_4,plain,
( ! [U_5726,U_5722,U_5724] :
( 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_5722)),U_5724)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5722)),U_5726)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5724),U_5726)) )
& ! [U_5723,U_5721,U_5725] :
( ~ 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_5721)),U_5723)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5721)),U_5725)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5723),U_5725)) ) ),
inference(definitional_conversion,[status(esa)],[f_1281_3]) ).
cnf(f_1281_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_5721)),U_5723)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5721)),U_5725)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5723),U_5725)) ),
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),hAPP(c_Nat_OSuc,U_5722)),U_5724)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5722)),U_5726)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5724),U_5726)) ),
inference(clausify,[status(thm)],[f_1281_4]) ).
fof(f_1282_1,plain,
! [V_c_2,T_d,T_c,V_A_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_c_2)) = V_c_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__constant]) ).
fof(f_1282_2,plain,
! [U_5730,U_5729,U_5728,U_5727] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5728,tc_fun(U_5729,tc_HOL_Obool)),U_5727),hAPP(c_COMBK(tc_fun(U_5729,tc_HOL_Obool),U_5728),U_5730)) = U_5730
| U_5727 = c_Orderings_Obot__class_Obot(tc_fun(U_5728,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5728,tc_fun(U_5729,tc_HOL_Obool)),U_5727),hAPP(c_COMBK(tc_fun(U_5729,tc_HOL_Obool),U_5728),U_5730)) = c_Orderings_Otop__class_Otop(tc_fun(U_5729,tc_HOL_Obool))
| U_5727 != c_Orderings_Obot__class_Obot(tc_fun(U_5728,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1282_1]) ).
fof(f_1282_3,plain,
( ! [U_5738,U_5736,U_5734,U_5732] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5734,tc_fun(U_5736,tc_HOL_Obool)),U_5732),hAPP(c_COMBK(tc_fun(U_5736,tc_HOL_Obool),U_5734),U_5738)) = U_5738
| U_5732 = c_Orderings_Obot__class_Obot(tc_fun(U_5734,tc_HOL_Obool)) )
& ! [U_5737,U_5735,U_5733,U_5731] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5733,tc_fun(U_5735,tc_HOL_Obool)),U_5731),hAPP(c_COMBK(tc_fun(U_5735,tc_HOL_Obool),U_5733),U_5737)) = c_Orderings_Otop__class_Otop(tc_fun(U_5735,tc_HOL_Obool))
| U_5731 != c_Orderings_Obot__class_Obot(tc_fun(U_5733,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1282_2]) ).
fof(f_1282_4,plain,
( ! [U_5732,U_5734,U_5736,U_5738] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5734,tc_fun(U_5736,tc_HOL_Obool)),U_5732),hAPP(c_COMBK(tc_fun(U_5736,tc_HOL_Obool),U_5734),U_5738)) = U_5738
| U_5732 = c_Orderings_Obot__class_Obot(tc_fun(U_5734,tc_HOL_Obool)) )
& ! [U_5733,U_5735,U_5737,U_5731] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5733,tc_fun(U_5735,tc_HOL_Obool)),U_5731),hAPP(c_COMBK(tc_fun(U_5735,tc_HOL_Obool),U_5733),U_5737)) = c_Orderings_Otop__class_Otop(tc_fun(U_5735,tc_HOL_Obool))
| U_5731 != c_Orderings_Obot__class_Obot(tc_fun(U_5733,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1282_3]) ).
cnf(f_1282_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5733,tc_fun(U_5735,tc_HOL_Obool)),U_5731),hAPP(c_COMBK(tc_fun(U_5735,tc_HOL_Obool),U_5733),U_5737)) = c_Orderings_Otop__class_Otop(tc_fun(U_5735,tc_HOL_Obool))
| U_5731 != c_Orderings_Obot__class_Obot(tc_fun(U_5733,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1282_4]) ).
cnf(f_1282_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5734,tc_fun(U_5736,tc_HOL_Obool)),U_5732),hAPP(c_COMBK(tc_fun(U_5736,tc_HOL_Obool),U_5734),U_5738)) = U_5738
| U_5732 = c_Orderings_Obot__class_Obot(tc_fun(U_5734,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1282_4]) ).
fof(f_1283_1,plain,
! [V_B_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_INT__empty]) ).
fof(f_1283_2,plain,
! [U_5741,U_5740,U_5739] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5739,tc_fun(U_5740,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_5739,tc_HOL_Obool))),U_5741) = c_Orderings_Otop__class_Otop(tc_fun(U_5740,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1283_1]) ).
fof(f_1283_3,plain,
! [U_5739,U_5740,U_5741] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5739,tc_fun(U_5740,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_5739,tc_HOL_Obool))),U_5741) = c_Orderings_Otop__class_Otop(tc_fun(U_5740,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1283_2]) ).
cnf(f_1283_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5739,tc_fun(U_5740,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_5739,tc_HOL_Obool))),U_5741) = c_Orderings_Otop__class_Otop(tc_fun(U_5740,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1283_3]) ).
fof(f_1284_1,plain,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,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_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,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_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J]) ).
fof(f_1284_2,plain,
! [U_5746,U_5745,U_5744,U_5743,U_5742] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5744,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5743,tc_fun(U_5744,tc_HOL_Obool)),U_5742),U_5745)),U_5746) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5743,tc_fun(U_5744,tc_HOL_Obool)),U_5742),hAPP(hAPP(c_COMBC(U_5743,tc_fun(U_5744,tc_HOL_Obool),tc_fun(U_5744,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5744,tc_HOL_Obool),tc_fun(tc_fun(U_5744,tc_HOL_Obool),tc_fun(U_5744,tc_HOL_Obool)),U_5743),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5744,tc_HOL_Obool))),U_5745)),U_5746))
| U_5742 = c_Orderings_Obot__class_Obot(tc_fun(U_5743,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5744,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5743,tc_fun(U_5744,tc_HOL_Obool)),U_5742),U_5745)),U_5746) = U_5746
| U_5742 != c_Orderings_Obot__class_Obot(tc_fun(U_5743,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1284_1]) ).
fof(f_1284_3,plain,
( ! [U_5756,U_5754,U_5752,U_5750,U_5748] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5752,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5750,tc_fun(U_5752,tc_HOL_Obool)),U_5748),U_5754)),U_5756) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5750,tc_fun(U_5752,tc_HOL_Obool)),U_5748),hAPP(hAPP(c_COMBC(U_5750,tc_fun(U_5752,tc_HOL_Obool),tc_fun(U_5752,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5752,tc_HOL_Obool),tc_fun(tc_fun(U_5752,tc_HOL_Obool),tc_fun(U_5752,tc_HOL_Obool)),U_5750),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5752,tc_HOL_Obool))),U_5754)),U_5756))
| U_5748 = c_Orderings_Obot__class_Obot(tc_fun(U_5750,tc_HOL_Obool)) )
& ! [U_5755,U_5753,U_5751,U_5749,U_5747] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5751,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5749,tc_fun(U_5751,tc_HOL_Obool)),U_5747),U_5753)),U_5755) = U_5755
| U_5747 != c_Orderings_Obot__class_Obot(tc_fun(U_5749,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1284_2]) ).
fof(f_1284_4,plain,
( ! [U_5756,U_5748,U_5750,U_5752,U_5754] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5752,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5750,tc_fun(U_5752,tc_HOL_Obool)),U_5748),U_5754)),U_5756) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5750,tc_fun(U_5752,tc_HOL_Obool)),U_5748),hAPP(hAPP(c_COMBC(U_5750,tc_fun(U_5752,tc_HOL_Obool),tc_fun(U_5752,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5752,tc_HOL_Obool),tc_fun(tc_fun(U_5752,tc_HOL_Obool),tc_fun(U_5752,tc_HOL_Obool)),U_5750),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5752,tc_HOL_Obool))),U_5754)),U_5756))
| U_5748 = c_Orderings_Obot__class_Obot(tc_fun(U_5750,tc_HOL_Obool)) )
& ! [U_5751,U_5753,U_5749,U_5747,U_5755] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5751,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5749,tc_fun(U_5751,tc_HOL_Obool)),U_5747),U_5753)),U_5755) = U_5755
| U_5747 != c_Orderings_Obot__class_Obot(tc_fun(U_5749,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1284_3]) ).
cnf(f_1284_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5751,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5749,tc_fun(U_5751,tc_HOL_Obool)),U_5747),U_5753)),U_5755) = U_5755
| U_5747 != c_Orderings_Obot__class_Obot(tc_fun(U_5749,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1284_4]) ).
cnf(f_1284_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5752,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5750,tc_fun(U_5752,tc_HOL_Obool)),U_5748),U_5754)),U_5756) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5750,tc_fun(U_5752,tc_HOL_Obool)),U_5748),hAPP(hAPP(c_COMBC(U_5750,tc_fun(U_5752,tc_HOL_Obool),tc_fun(U_5752,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5752,tc_HOL_Obool),tc_fun(tc_fun(U_5752,tc_HOL_Obool),tc_fun(U_5752,tc_HOL_Obool)),U_5750),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5752,tc_HOL_Obool))),U_5754)),U_5756))
| U_5748 = c_Orderings_Obot__class_Obot(tc_fun(U_5750,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1284_4]) ).
fof(f_1285_1,plain,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I2_J]) ).
fof(f_1285_2,plain,
! [U_5761,U_5760,U_5759,U_5758,U_5757] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5759,tc_HOL_Obool)),U_5760),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5758,tc_fun(U_5759,tc_HOL_Obool)),U_5757),U_5761)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5758,tc_fun(U_5759,tc_HOL_Obool)),U_5757),hAPP(hAPP(c_COMBB(tc_fun(U_5759,tc_HOL_Obool),tc_fun(U_5759,tc_HOL_Obool),U_5758),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5759,tc_HOL_Obool)),U_5760)),U_5761))
| U_5757 = c_Orderings_Obot__class_Obot(tc_fun(U_5758,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5759,tc_HOL_Obool)),U_5760),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5758,tc_fun(U_5759,tc_HOL_Obool)),U_5757),U_5761)) = U_5760
| U_5757 != c_Orderings_Obot__class_Obot(tc_fun(U_5758,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1285_1]) ).
fof(f_1285_3,plain,
( ! [U_5771,U_5769,U_5767,U_5765,U_5763] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5767,tc_HOL_Obool)),U_5769),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5765,tc_fun(U_5767,tc_HOL_Obool)),U_5763),U_5771)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5765,tc_fun(U_5767,tc_HOL_Obool)),U_5763),hAPP(hAPP(c_COMBB(tc_fun(U_5767,tc_HOL_Obool),tc_fun(U_5767,tc_HOL_Obool),U_5765),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5767,tc_HOL_Obool)),U_5769)),U_5771))
| U_5763 = c_Orderings_Obot__class_Obot(tc_fun(U_5765,tc_HOL_Obool)) )
& ! [U_5770,U_5768,U_5766,U_5764,U_5762] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5766,tc_HOL_Obool)),U_5768),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5764,tc_fun(U_5766,tc_HOL_Obool)),U_5762),U_5770)) = U_5768
| U_5762 != c_Orderings_Obot__class_Obot(tc_fun(U_5764,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1285_2]) ).
fof(f_1285_4,plain,
( ! [U_5763,U_5765,U_5767,U_5769,U_5771] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5767,tc_HOL_Obool)),U_5769),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5765,tc_fun(U_5767,tc_HOL_Obool)),U_5763),U_5771)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5765,tc_fun(U_5767,tc_HOL_Obool)),U_5763),hAPP(hAPP(c_COMBB(tc_fun(U_5767,tc_HOL_Obool),tc_fun(U_5767,tc_HOL_Obool),U_5765),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5767,tc_HOL_Obool)),U_5769)),U_5771))
| U_5763 = c_Orderings_Obot__class_Obot(tc_fun(U_5765,tc_HOL_Obool)) )
& ! [U_5766,U_5768,U_5764,U_5762,U_5770] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5766,tc_HOL_Obool)),U_5768),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5764,tc_fun(U_5766,tc_HOL_Obool)),U_5762),U_5770)) = U_5768
| U_5762 != c_Orderings_Obot__class_Obot(tc_fun(U_5764,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1285_3]) ).
cnf(f_1285_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5766,tc_HOL_Obool)),U_5768),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5764,tc_fun(U_5766,tc_HOL_Obool)),U_5762),U_5770)) = U_5768
| U_5762 != c_Orderings_Obot__class_Obot(tc_fun(U_5764,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1285_4]) ).
cnf(f_1285_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5767,tc_HOL_Obool)),U_5769),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5765,tc_fun(U_5767,tc_HOL_Obool)),U_5763),U_5771)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5765,tc_fun(U_5767,tc_HOL_Obool)),U_5763),hAPP(hAPP(c_COMBB(tc_fun(U_5767,tc_HOL_Obool),tc_fun(U_5767,tc_HOL_Obool),U_5765),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5767,tc_HOL_Obool)),U_5769)),U_5771))
| U_5763 = c_Orderings_Obot__class_Obot(tc_fun(U_5765,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1285_4]) ).
fof(f_1286_1,plain,
! [V_B_2,V_A_2,V_a_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_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)),
inference(fof_nnf,[status(thm)],[fact_INT__insert]) ).
fof(f_1286_2,plain,
! [U_5776,U_5775,U_5774,U_5773,U_5772] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5772,tc_fun(U_5773,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5772),U_5774),U_5775)),U_5776) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5773,tc_HOL_Obool)),hAPP(U_5776,U_5774)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5772,tc_fun(U_5773,tc_HOL_Obool)),U_5775),U_5776)),
inference(variable_rename,[status(thm)],[f_1286_1]) ).
fof(f_1286_3,plain,
! [U_5773,U_5772,U_5774,U_5775,U_5776] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5772,tc_fun(U_5773,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5772),U_5774),U_5775)),U_5776) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5773,tc_HOL_Obool)),hAPP(U_5776,U_5774)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5772,tc_fun(U_5773,tc_HOL_Obool)),U_5775),U_5776)),
inference(definitional_conversion,[status(esa)],[f_1286_2]) ).
cnf(f_1286_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5772,tc_fun(U_5773,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_5772),U_5774),U_5775)),U_5776) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5773,tc_HOL_Obool)),hAPP(U_5776,U_5774)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5772,tc_fun(U_5773,tc_HOL_Obool)),U_5775),U_5776)),
inference(clausify,[status(thm)],[f_1286_3]) ).
fof(f_1287_1,plain,
! [V_M_2,V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_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_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_M_2)),
inference(fof_nnf,[status(thm)],[fact_INT__Un]) ).
fof(f_1287_2,plain,
! [U_5781,U_5780,U_5779,U_5778,U_5777] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5777,tc_fun(U_5778,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5777,tc_HOL_Obool)),U_5779),U_5780)),U_5781) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5778,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5777,tc_fun(U_5778,tc_HOL_Obool)),U_5779),U_5781)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5777,tc_fun(U_5778,tc_HOL_Obool)),U_5780),U_5781)),
inference(variable_rename,[status(thm)],[f_1287_1]) ).
fof(f_1287_3,plain,
! [U_5777,U_5778,U_5779,U_5780,U_5781] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5777,tc_fun(U_5778,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5777,tc_HOL_Obool)),U_5779),U_5780)),U_5781) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5778,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5777,tc_fun(U_5778,tc_HOL_Obool)),U_5779),U_5781)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5777,tc_fun(U_5778,tc_HOL_Obool)),U_5780),U_5781)),
inference(definitional_conversion,[status(esa)],[f_1287_2]) ).
cnf(f_1287_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5777,tc_fun(U_5778,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5777,tc_HOL_Obool)),U_5779),U_5780)),U_5781) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5778,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5777,tc_fun(U_5778,tc_HOL_Obool)),U_5779),U_5781)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5777,tc_fun(U_5778,tc_HOL_Obool)),U_5780),U_5781)),
inference(clausify,[status(thm)],[f_1287_3]) ).
fof(f_1288_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_1288_2,plain,
! [U_5782] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5782)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_5782,
inference(variable_rename,[status(thm)],[f_1288_1]) ).
fof(f_1288_3,plain,
! [U_5782] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5782)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_5782,
inference(definitional_conversion,[status(esa)],[f_1288_2]) ).
cnf(f_1288_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5782)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_5782,
inference(clausify,[status(thm)],[f_1288_3]) ).
fof(f_1289_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d),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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I7_J]) ).
fof(f_1289_2,plain,
! [U_5787,U_5786,U_5785,U_5784,U_5783] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5783,tc_fun(U_5784,tc_HOL_Obool)),U_5785),hAPP(hAPP(c_COMBB(tc_fun(U_5784,tc_HOL_Obool),tc_fun(U_5784,tc_HOL_Obool),U_5783),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5784,tc_HOL_Obool)),U_5786)),U_5787)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5784,tc_HOL_Obool)),U_5786),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5783,tc_fun(U_5784,tc_HOL_Obool)),U_5785),U_5787)),
inference(variable_rename,[status(thm)],[f_1289_1]) ).
fof(f_1289_3,plain,
! [U_5783,U_5784,U_5785,U_5786,U_5787] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5783,tc_fun(U_5784,tc_HOL_Obool)),U_5785),hAPP(hAPP(c_COMBB(tc_fun(U_5784,tc_HOL_Obool),tc_fun(U_5784,tc_HOL_Obool),U_5783),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5784,tc_HOL_Obool)),U_5786)),U_5787)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5784,tc_HOL_Obool)),U_5786),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5783,tc_fun(U_5784,tc_HOL_Obool)),U_5785),U_5787)),
inference(definitional_conversion,[status(esa)],[f_1289_2]) ).
cnf(f_1289_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5783,tc_fun(U_5784,tc_HOL_Obool)),U_5785),hAPP(hAPP(c_COMBB(tc_fun(U_5784,tc_HOL_Obool),tc_fun(U_5784,tc_HOL_Obool),U_5783),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5784,tc_HOL_Obool)),U_5786)),U_5787)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5784,tc_HOL_Obool)),U_5786),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5783,tc_fun(U_5784,tc_HOL_Obool)),U_5785),U_5787)),
inference(clausify,[status(thm)],[f_1289_3]) ).
fof(f_1290_1,plain,
! [V_B_2,V_C_2,T_d,V_A_2,T_c] : 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_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,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_d),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_UN__extend__simps_I7_J]) ).
fof(f_1290_2,plain,
! [U_5792,U_5791,U_5790,U_5789,U_5788] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5788,tc_HOL_Obool)),U_5789),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5790,tc_fun(U_5788,tc_HOL_Obool)),U_5791),U_5792)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5790,tc_fun(U_5788,tc_HOL_Obool)),U_5791),hAPP(hAPP(c_COMBB(tc_fun(U_5788,tc_HOL_Obool),tc_fun(U_5788,tc_HOL_Obool),U_5790),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5788,tc_HOL_Obool)),U_5789)),U_5792)),
inference(variable_rename,[status(thm)],[f_1290_1]) ).
fof(f_1290_3,plain,
! [U_5788,U_5789,U_5790,U_5791,U_5792] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5788,tc_HOL_Obool)),U_5789),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5790,tc_fun(U_5788,tc_HOL_Obool)),U_5791),U_5792)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5790,tc_fun(U_5788,tc_HOL_Obool)),U_5791),hAPP(hAPP(c_COMBB(tc_fun(U_5788,tc_HOL_Obool),tc_fun(U_5788,tc_HOL_Obool),U_5790),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5788,tc_HOL_Obool)),U_5789)),U_5792)),
inference(definitional_conversion,[status(esa)],[f_1290_2]) ).
cnf(f_1290_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5788,tc_HOL_Obool)),U_5789),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5790,tc_fun(U_5788,tc_HOL_Obool)),U_5791),U_5792)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5790,tc_fun(U_5788,tc_HOL_Obool)),U_5791),hAPP(hAPP(c_COMBB(tc_fun(U_5788,tc_HOL_Obool),tc_fun(U_5788,tc_HOL_Obool),U_5790),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5788,tc_HOL_Obool)),U_5789)),U_5792)),
inference(clausify,[status(thm)],[f_1290_3]) ).
fof(f_1291_1,plain,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Inter__Un__subset]) ).
fof(f_1291_2,plain,
! [U_5795,U_5794,U_5793] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5793,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5793,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5793,tc_HOL_Obool),U_5794)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5793,tc_HOL_Obool),U_5795))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5793,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_5793,tc_HOL_Obool),tc_HOL_Obool)),U_5794),U_5795)))),
inference(variable_rename,[status(thm)],[f_1291_1]) ).
fof(f_1291_3,plain,
! [U_5793,U_5794,U_5795] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5793,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5793,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5793,tc_HOL_Obool),U_5794)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5793,tc_HOL_Obool),U_5795))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5793,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_5793,tc_HOL_Obool),tc_HOL_Obool)),U_5794),U_5795)))),
inference(definitional_conversion,[status(esa)],[f_1291_2]) ).
cnf(f_1291_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5793,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5793,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5793,tc_HOL_Obool),U_5794)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5793,tc_HOL_Obool),U_5795))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_5793,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_5793,tc_HOL_Obool),tc_HOL_Obool)),U_5794),U_5795)))),
inference(clausify,[status(thm)],[f_1291_3]) ).
fof(f_1292_1,plain,
! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,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)) = 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_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool))),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Compl__UN]) ).
fof(f_1292_2,plain,
! [U_5799,U_5798,U_5797,U_5796] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5796,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5797,tc_fun(U_5796,tc_HOL_Obool)),U_5798),U_5799)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5797,tc_fun(U_5796,tc_HOL_Obool)),U_5798),hAPP(hAPP(c_COMBB(tc_fun(U_5796,tc_HOL_Obool),tc_fun(U_5796,tc_HOL_Obool),U_5797),c_Groups_Ouminus__class_Ouminus(tc_fun(U_5796,tc_HOL_Obool))),U_5799)),
inference(variable_rename,[status(thm)],[f_1292_1]) ).
fof(f_1292_3,plain,
! [U_5796,U_5797,U_5798,U_5799] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5796,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5797,tc_fun(U_5796,tc_HOL_Obool)),U_5798),U_5799)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5797,tc_fun(U_5796,tc_HOL_Obool)),U_5798),hAPP(hAPP(c_COMBB(tc_fun(U_5796,tc_HOL_Obool),tc_fun(U_5796,tc_HOL_Obool),U_5797),c_Groups_Ouminus__class_Ouminus(tc_fun(U_5796,tc_HOL_Obool))),U_5799)),
inference(definitional_conversion,[status(esa)],[f_1292_2]) ).
cnf(f_1292_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5796,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5797,tc_fun(U_5796,tc_HOL_Obool)),U_5798),U_5799)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5797,tc_fun(U_5796,tc_HOL_Obool)),U_5798),hAPP(hAPP(c_COMBB(tc_fun(U_5796,tc_HOL_Obool),tc_fun(U_5796,tc_HOL_Obool),U_5797),c_Groups_Ouminus__class_Ouminus(tc_fun(U_5796,tc_HOL_Obool))),U_5799)),
inference(clausify,[status(thm)],[f_1292_3]) ).
fof(f_1293_1,plain,
! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),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_OSUPR(T_d,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_d),c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool))),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Compl__INT]) ).
fof(f_1293_2,plain,
! [U_5803,U_5802,U_5801,U_5800] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5800,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5801,tc_fun(U_5800,tc_HOL_Obool)),U_5802),U_5803)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5801,tc_fun(U_5800,tc_HOL_Obool)),U_5802),hAPP(hAPP(c_COMBB(tc_fun(U_5800,tc_HOL_Obool),tc_fun(U_5800,tc_HOL_Obool),U_5801),c_Groups_Ouminus__class_Ouminus(tc_fun(U_5800,tc_HOL_Obool))),U_5803)),
inference(variable_rename,[status(thm)],[f_1293_1]) ).
fof(f_1293_3,plain,
! [U_5800,U_5801,U_5802,U_5803] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5800,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5801,tc_fun(U_5800,tc_HOL_Obool)),U_5802),U_5803)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5801,tc_fun(U_5800,tc_HOL_Obool)),U_5802),hAPP(hAPP(c_COMBB(tc_fun(U_5800,tc_HOL_Obool),tc_fun(U_5800,tc_HOL_Obool),U_5801),c_Groups_Ouminus__class_Ouminus(tc_fun(U_5800,tc_HOL_Obool))),U_5803)),
inference(definitional_conversion,[status(esa)],[f_1293_2]) ).
cnf(f_1293_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5800,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5801,tc_fun(U_5800,tc_HOL_Obool)),U_5802),U_5803)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5801,tc_fun(U_5800,tc_HOL_Obool)),U_5802),hAPP(hAPP(c_COMBB(tc_fun(U_5800,tc_HOL_Obool),tc_fun(U_5800,tc_HOL_Obool),U_5801),c_Groups_Ouminus__class_Ouminus(tc_fun(U_5800,tc_HOL_Obool))),U_5803)),
inference(clausify,[status(thm)],[f_1293_3]) ).
fof(f_1294_1,plain,
! [V_x_2,T_c] :
( c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_x_2
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton]) ).
fof(f_1294_2,plain,
! [U_5805,U_5804] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5804,hAPP(hAPP(c_Set_Oinsert(U_5804),U_5805),c_Orderings_Obot__class_Obot(tc_fun(U_5804,tc_HOL_Obool)))) = U_5805
| ~ class_Lattices_Olattice(U_5804) ),
inference(variable_rename,[status(thm)],[f_1294_1]) ).
fof(f_1294_3,plain,
! [U_5804,U_5805] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5804,hAPP(hAPP(c_Set_Oinsert(U_5804),U_5805),c_Orderings_Obot__class_Obot(tc_fun(U_5804,tc_HOL_Obool)))) = U_5805
| ~ class_Lattices_Olattice(U_5804) ),
inference(definitional_conversion,[status(esa)],[f_1294_2]) ).
cnf(f_1294_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5804,hAPP(hAPP(c_Set_Oinsert(U_5804),U_5805),c_Orderings_Obot__class_Obot(tc_fun(U_5804,tc_HOL_Obool)))) = U_5805
| ~ class_Lattices_Olattice(U_5804) ),
inference(clausify,[status(thm)],[f_1294_3]) ).
fof(f_1295_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_1295_2,plain,
! [U_5806] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5806) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5806)),
inference(variable_rename,[status(thm)],[f_1295_1]) ).
fof(f_1295_3,plain,
! [U_5806] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5806) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5806)),
inference(definitional_conversion,[status(esa)],[f_1295_2]) ).
cnf(f_1295_4,plain,
hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5806) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5806)),
inference(clausify,[status(thm)],[f_1295_3]) ).
fof(f_1296_1,plain,
! [V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__lower]) ).
fof(f_1296_2,plain,
! [U_5809,U_5808,U_5807] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5807),c_Complete__Lattice_OInf__class_OInf(U_5807,U_5809)),U_5808))
| ~ hBOOL(hAPP(hAPP(c_member(U_5807),U_5808),U_5809))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5807) ),
inference(variable_rename,[status(thm)],[f_1296_1]) ).
fof(f_1296_3,plain,
! [U_5807,U_5808,U_5809] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5807),c_Complete__Lattice_OInf__class_OInf(U_5807,U_5809)),U_5808))
| ~ hBOOL(hAPP(hAPP(c_member(U_5807),U_5808),U_5809))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5807) ),
inference(definitional_conversion,[status(esa)],[f_1296_2]) ).
cnf(f_1296_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5807),c_Complete__Lattice_OInf__class_OInf(U_5807,U_5809)),U_5808))
| ~ hBOOL(hAPP(hAPP(c_member(U_5807),U_5808),U_5809))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5807) ),
inference(clausify,[status(thm)],[f_1296_3]) ).
fof(f_1297_1,plain,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_d) ),
inference(fof_nnf,[status(thm)],[fact_INF__subset]) ).
fof(f_1297_2,plain,
! [U_5814,U_5813,U_5812,U_5811,U_5810] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5810),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5811,U_5810),U_5813),U_5814)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5811,U_5810),U_5812),U_5814)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5811,tc_HOL_Obool)),U_5812),U_5813))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5810) ),
inference(variable_rename,[status(thm)],[f_1297_1]) ).
fof(f_1297_3,plain,
! [U_5810,U_5811,U_5812,U_5813,U_5814] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5810),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5811,U_5810),U_5813),U_5814)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5811,U_5810),U_5812),U_5814)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5811,tc_HOL_Obool)),U_5812),U_5813))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5810) ),
inference(definitional_conversion,[status(esa)],[f_1297_2]) ).
cnf(f_1297_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5810),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5811,U_5810),U_5813),U_5814)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5811,U_5810),U_5812),U_5814)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5811,tc_HOL_Obool)),U_5812),U_5813))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5810) ),
inference(clausify,[status(thm)],[f_1297_3]) ).
fof(f_1298_1,plain,
! [V_a_2,T_c] :
( c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_a_2
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__singleton]) ).
fof(f_1298_2,plain,
! [U_5816,U_5815] :
( c_Complete__Lattice_OInf__class_OInf(U_5815,hAPP(hAPP(c_Set_Oinsert(U_5815),U_5816),c_Orderings_Obot__class_Obot(tc_fun(U_5815,tc_HOL_Obool)))) = U_5816
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5815) ),
inference(variable_rename,[status(thm)],[f_1298_1]) ).
fof(f_1298_3,plain,
! [U_5816,U_5815] :
( c_Complete__Lattice_OInf__class_OInf(U_5815,hAPP(hAPP(c_Set_Oinsert(U_5815),U_5816),c_Orderings_Obot__class_Obot(tc_fun(U_5815,tc_HOL_Obool)))) = U_5816
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5815) ),
inference(definitional_conversion,[status(esa)],[f_1298_2]) ).
cnf(f_1298_4,plain,
( c_Complete__Lattice_OInf__class_OInf(U_5815,hAPP(hAPP(c_Set_Oinsert(U_5815),U_5816),c_Orderings_Obot__class_Obot(tc_fun(U_5815,tc_HOL_Obool)))) = U_5816
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5815) ),
inference(clausify,[status(thm)],[f_1298_3]) ).
fof(f_1299_1,plain,
! [T_c] :
( c_Complete__Lattice_OInf__class_OInf(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_c)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__empty]) ).
fof(f_1299_2,plain,
! [U_5817] :
( c_Complete__Lattice_OInf__class_OInf(U_5817,c_Orderings_Obot__class_Obot(tc_fun(U_5817,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_5817)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5817) ),
inference(variable_rename,[status(thm)],[f_1299_1]) ).
fof(f_1299_3,plain,
! [U_5817] :
( c_Complete__Lattice_OInf__class_OInf(U_5817,c_Orderings_Obot__class_Obot(tc_fun(U_5817,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_5817)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5817) ),
inference(definitional_conversion,[status(esa)],[f_1299_2]) ).
cnf(f_1299_4,plain,
( c_Complete__Lattice_OInf__class_OInf(U_5817,c_Orderings_Obot__class_Obot(tc_fun(U_5817,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_5817)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5817) ),
inference(clausify,[status(thm)],[f_1299_3]) ).
fof(f_1300_1,plain,
! [T_c] :
( c_Complete__Lattice_OInf__class_OInf(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_c)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__UNIV]) ).
fof(f_1300_2,plain,
! [U_5818] :
( c_Complete__Lattice_OInf__class_OInf(U_5818,c_Orderings_Otop__class_Otop(tc_fun(U_5818,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_5818)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5818) ),
inference(variable_rename,[status(thm)],[f_1300_1]) ).
fof(f_1300_3,plain,
! [U_5818] :
( c_Complete__Lattice_OInf__class_OInf(U_5818,c_Orderings_Otop__class_Otop(tc_fun(U_5818,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_5818)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5818) ),
inference(definitional_conversion,[status(esa)],[f_1300_2]) ).
cnf(f_1300_4,plain,
( c_Complete__Lattice_OInf__class_OInf(U_5818,c_Orderings_Otop__class_Otop(tc_fun(U_5818,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_5818)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5818) ),
inference(clausify,[status(thm)],[f_1300_3]) ).
fof(f_1301_1,plain,
! [V_A_2,V_a_2,T_c] :
( c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__insert]) ).
fof(f_1301_2,plain,
! [U_5821,U_5820,U_5819] :
( c_Complete__Lattice_OInf__class_OInf(U_5819,hAPP(hAPP(c_Set_Oinsert(U_5819),U_5820),U_5821)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5819),U_5820),c_Complete__Lattice_OInf__class_OInf(U_5819,U_5821))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5819) ),
inference(variable_rename,[status(thm)],[f_1301_1]) ).
fof(f_1301_3,plain,
! [U_5819,U_5820,U_5821] :
( c_Complete__Lattice_OInf__class_OInf(U_5819,hAPP(hAPP(c_Set_Oinsert(U_5819),U_5820),U_5821)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5819),U_5820),c_Complete__Lattice_OInf__class_OInf(U_5819,U_5821))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5819) ),
inference(definitional_conversion,[status(esa)],[f_1301_2]) ).
cnf(f_1301_4,plain,
( c_Complete__Lattice_OInf__class_OInf(U_5819,hAPP(hAPP(c_Set_Oinsert(U_5819),U_5820),U_5821)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5819),U_5820),c_Complete__Lattice_OInf__class_OInf(U_5819,U_5821))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5819) ),
inference(clausify,[status(thm)],[f_1301_3]) ).
fof(f_1302_1,plain,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J]) ).
fof(f_1302_2,plain,
! [U_5826,U_5825,U_5824,U_5823,U_5822] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5823,tc_fun(U_5824,tc_HOL_Obool)),U_5822),hAPP(hAPP(c_COMBC(U_5823,tc_fun(U_5824,tc_HOL_Obool),tc_fun(U_5824,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5824,tc_HOL_Obool),tc_fun(tc_fun(U_5824,tc_HOL_Obool),tc_fun(U_5824,tc_HOL_Obool)),U_5823),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5824,tc_HOL_Obool))),U_5825)),U_5826)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5824,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5823,tc_fun(U_5824,tc_HOL_Obool)),U_5822),U_5825)),U_5826)
| U_5822 = c_Orderings_Obot__class_Obot(tc_fun(U_5823,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5823,tc_fun(U_5824,tc_HOL_Obool)),U_5822),hAPP(hAPP(c_COMBC(U_5823,tc_fun(U_5824,tc_HOL_Obool),tc_fun(U_5824,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5824,tc_HOL_Obool),tc_fun(tc_fun(U_5824,tc_HOL_Obool),tc_fun(U_5824,tc_HOL_Obool)),U_5823),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5824,tc_HOL_Obool))),U_5825)),U_5826)) = c_Orderings_Otop__class_Otop(tc_fun(U_5824,tc_HOL_Obool))
| U_5822 != c_Orderings_Obot__class_Obot(tc_fun(U_5823,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1302_1]) ).
fof(f_1302_3,plain,
( ! [U_5836,U_5834,U_5832,U_5830,U_5828] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5830,tc_fun(U_5832,tc_HOL_Obool)),U_5828),hAPP(hAPP(c_COMBC(U_5830,tc_fun(U_5832,tc_HOL_Obool),tc_fun(U_5832,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5832,tc_HOL_Obool),tc_fun(tc_fun(U_5832,tc_HOL_Obool),tc_fun(U_5832,tc_HOL_Obool)),U_5830),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5832,tc_HOL_Obool))),U_5834)),U_5836)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5832,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5830,tc_fun(U_5832,tc_HOL_Obool)),U_5828),U_5834)),U_5836)
| U_5828 = c_Orderings_Obot__class_Obot(tc_fun(U_5830,tc_HOL_Obool)) )
& ! [U_5835,U_5833,U_5831,U_5829,U_5827] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5829,tc_fun(U_5831,tc_HOL_Obool)),U_5827),hAPP(hAPP(c_COMBC(U_5829,tc_fun(U_5831,tc_HOL_Obool),tc_fun(U_5831,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5831,tc_HOL_Obool),tc_fun(tc_fun(U_5831,tc_HOL_Obool),tc_fun(U_5831,tc_HOL_Obool)),U_5829),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5831,tc_HOL_Obool))),U_5833)),U_5835)) = c_Orderings_Otop__class_Otop(tc_fun(U_5831,tc_HOL_Obool))
| U_5827 != c_Orderings_Obot__class_Obot(tc_fun(U_5829,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1302_2]) ).
fof(f_1302_4,plain,
( ! [U_5828,U_5830,U_5832,U_5834,U_5836] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5830,tc_fun(U_5832,tc_HOL_Obool)),U_5828),hAPP(hAPP(c_COMBC(U_5830,tc_fun(U_5832,tc_HOL_Obool),tc_fun(U_5832,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5832,tc_HOL_Obool),tc_fun(tc_fun(U_5832,tc_HOL_Obool),tc_fun(U_5832,tc_HOL_Obool)),U_5830),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5832,tc_HOL_Obool))),U_5834)),U_5836)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5832,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5830,tc_fun(U_5832,tc_HOL_Obool)),U_5828),U_5834)),U_5836)
| U_5828 = c_Orderings_Obot__class_Obot(tc_fun(U_5830,tc_HOL_Obool)) )
& ! [U_5829,U_5833,U_5831,U_5827,U_5835] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5829,tc_fun(U_5831,tc_HOL_Obool)),U_5827),hAPP(hAPP(c_COMBC(U_5829,tc_fun(U_5831,tc_HOL_Obool),tc_fun(U_5831,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5831,tc_HOL_Obool),tc_fun(tc_fun(U_5831,tc_HOL_Obool),tc_fun(U_5831,tc_HOL_Obool)),U_5829),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5831,tc_HOL_Obool))),U_5833)),U_5835)) = c_Orderings_Otop__class_Otop(tc_fun(U_5831,tc_HOL_Obool))
| U_5827 != c_Orderings_Obot__class_Obot(tc_fun(U_5829,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1302_3]) ).
cnf(f_1302_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5829,tc_fun(U_5831,tc_HOL_Obool)),U_5827),hAPP(hAPP(c_COMBC(U_5829,tc_fun(U_5831,tc_HOL_Obool),tc_fun(U_5831,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5831,tc_HOL_Obool),tc_fun(tc_fun(U_5831,tc_HOL_Obool),tc_fun(U_5831,tc_HOL_Obool)),U_5829),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5831,tc_HOL_Obool))),U_5833)),U_5835)) = c_Orderings_Otop__class_Otop(tc_fun(U_5831,tc_HOL_Obool))
| U_5827 != c_Orderings_Obot__class_Obot(tc_fun(U_5829,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1302_4]) ).
cnf(f_1302_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5830,tc_fun(U_5832,tc_HOL_Obool)),U_5828),hAPP(hAPP(c_COMBC(U_5830,tc_fun(U_5832,tc_HOL_Obool),tc_fun(U_5832,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5832,tc_HOL_Obool),tc_fun(tc_fun(U_5832,tc_HOL_Obool),tc_fun(U_5832,tc_HOL_Obool)),U_5830),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5832,tc_HOL_Obool))),U_5834)),U_5836)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5832,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5830,tc_fun(U_5832,tc_HOL_Obool)),U_5828),U_5834)),U_5836)
| U_5828 = c_Orderings_Obot__class_Obot(tc_fun(U_5830,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1302_4]) ).
fof(f_1303_1,plain,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I2_J]) ).
fof(f_1303_2,plain,
! [U_5841,U_5840,U_5839,U_5838,U_5837] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5838,tc_fun(U_5839,tc_HOL_Obool)),U_5837),hAPP(hAPP(c_COMBB(tc_fun(U_5839,tc_HOL_Obool),tc_fun(U_5839,tc_HOL_Obool),U_5838),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5839,tc_HOL_Obool)),U_5840)),U_5841)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5839,tc_HOL_Obool)),U_5840),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5838,tc_fun(U_5839,tc_HOL_Obool)),U_5837),U_5841))
| U_5837 = c_Orderings_Obot__class_Obot(tc_fun(U_5838,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5838,tc_fun(U_5839,tc_HOL_Obool)),U_5837),hAPP(hAPP(c_COMBB(tc_fun(U_5839,tc_HOL_Obool),tc_fun(U_5839,tc_HOL_Obool),U_5838),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5839,tc_HOL_Obool)),U_5840)),U_5841)) = c_Orderings_Otop__class_Otop(tc_fun(U_5839,tc_HOL_Obool))
| U_5837 != c_Orderings_Obot__class_Obot(tc_fun(U_5838,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1303_1]) ).
fof(f_1303_3,plain,
( ! [U_5851,U_5849,U_5847,U_5845,U_5843] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5845,tc_fun(U_5847,tc_HOL_Obool)),U_5843),hAPP(hAPP(c_COMBB(tc_fun(U_5847,tc_HOL_Obool),tc_fun(U_5847,tc_HOL_Obool),U_5845),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5847,tc_HOL_Obool)),U_5849)),U_5851)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5847,tc_HOL_Obool)),U_5849),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5845,tc_fun(U_5847,tc_HOL_Obool)),U_5843),U_5851))
| U_5843 = c_Orderings_Obot__class_Obot(tc_fun(U_5845,tc_HOL_Obool)) )
& ! [U_5850,U_5848,U_5846,U_5844,U_5842] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5844,tc_fun(U_5846,tc_HOL_Obool)),U_5842),hAPP(hAPP(c_COMBB(tc_fun(U_5846,tc_HOL_Obool),tc_fun(U_5846,tc_HOL_Obool),U_5844),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5846,tc_HOL_Obool)),U_5848)),U_5850)) = c_Orderings_Otop__class_Otop(tc_fun(U_5846,tc_HOL_Obool))
| U_5842 != c_Orderings_Obot__class_Obot(tc_fun(U_5844,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1303_2]) ).
fof(f_1303_4,plain,
( ! [U_5843,U_5845,U_5847,U_5849,U_5851] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5845,tc_fun(U_5847,tc_HOL_Obool)),U_5843),hAPP(hAPP(c_COMBB(tc_fun(U_5847,tc_HOL_Obool),tc_fun(U_5847,tc_HOL_Obool),U_5845),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5847,tc_HOL_Obool)),U_5849)),U_5851)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5847,tc_HOL_Obool)),U_5849),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5845,tc_fun(U_5847,tc_HOL_Obool)),U_5843),U_5851))
| U_5843 = c_Orderings_Obot__class_Obot(tc_fun(U_5845,tc_HOL_Obool)) )
& ! [U_5844,U_5848,U_5842,U_5846,U_5850] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5844,tc_fun(U_5846,tc_HOL_Obool)),U_5842),hAPP(hAPP(c_COMBB(tc_fun(U_5846,tc_HOL_Obool),tc_fun(U_5846,tc_HOL_Obool),U_5844),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5846,tc_HOL_Obool)),U_5848)),U_5850)) = c_Orderings_Otop__class_Otop(tc_fun(U_5846,tc_HOL_Obool))
| U_5842 != c_Orderings_Obot__class_Obot(tc_fun(U_5844,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1303_3]) ).
cnf(f_1303_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5844,tc_fun(U_5846,tc_HOL_Obool)),U_5842),hAPP(hAPP(c_COMBB(tc_fun(U_5846,tc_HOL_Obool),tc_fun(U_5846,tc_HOL_Obool),U_5844),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5846,tc_HOL_Obool)),U_5848)),U_5850)) = c_Orderings_Otop__class_Otop(tc_fun(U_5846,tc_HOL_Obool))
| U_5842 != c_Orderings_Obot__class_Obot(tc_fun(U_5844,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1303_4]) ).
cnf(f_1303_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5845,tc_fun(U_5847,tc_HOL_Obool)),U_5843),hAPP(hAPP(c_COMBB(tc_fun(U_5847,tc_HOL_Obool),tc_fun(U_5847,tc_HOL_Obool),U_5845),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5847,tc_HOL_Obool)),U_5849)),U_5851)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5847,tc_HOL_Obool)),U_5849),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5845,tc_fun(U_5847,tc_HOL_Obool)),U_5843),U_5851))
| U_5843 = c_Orderings_Obot__class_Obot(tc_fun(U_5845,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1303_4]) ).
fof(f_1304_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_1304_2,plain,
! [U_5854,U_5853,U_5852] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5852),c_Groups_Oone__class_Oone(U_5852)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5852),U_5853),hAPP(c_Nat_OSuc,U_5854))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5852),c_Groups_Oone__class_Oone(U_5852)),U_5853))
| ~ class_Rings_Olinordered__semidom(U_5852) ),
inference(variable_rename,[status(thm)],[f_1304_1]) ).
fof(f_1304_3,plain,
! [U_5852,U_5854,U_5853] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5852),c_Groups_Oone__class_Oone(U_5852)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5852),U_5853),hAPP(c_Nat_OSuc,U_5854))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5852),c_Groups_Oone__class_Oone(U_5852)),U_5853))
| ~ class_Rings_Olinordered__semidom(U_5852) ),
inference(definitional_conversion,[status(esa)],[f_1304_2]) ).
cnf(f_1304_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5852),c_Groups_Oone__class_Oone(U_5852)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5852),U_5853),hAPP(c_Nat_OSuc,U_5854))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5852),c_Groups_Oone__class_Oone(U_5852)),U_5853))
| ~ class_Rings_Olinordered__semidom(U_5852) ),
inference(clausify,[status(thm)],[f_1304_3]) ).
fof(f_1305_1,plain,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,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_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))),V_B_2)
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I3_J]) ).
fof(f_1305_2,plain,
! [U_5859,U_5858,U_5857,U_5856,U_5855] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5857,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5856,tc_fun(U_5857,tc_HOL_Obool)),U_5855),U_5858)),U_5859) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5856,tc_fun(U_5857,tc_HOL_Obool)),U_5855),hAPP(hAPP(c_COMBC(U_5856,tc_fun(U_5857,tc_HOL_Obool),tc_fun(U_5857,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5857,tc_HOL_Obool),tc_fun(tc_fun(U_5857,tc_HOL_Obool),tc_fun(U_5857,tc_HOL_Obool)),U_5856),c_Groups_Ominus__class_Ominus(tc_fun(U_5857,tc_HOL_Obool))),U_5858)),U_5859))
| U_5855 = c_Orderings_Obot__class_Obot(tc_fun(U_5856,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5857,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5856,tc_fun(U_5857,tc_HOL_Obool)),U_5855),U_5858)),U_5859) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5857,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5857,tc_HOL_Obool))),U_5859)
| U_5855 != c_Orderings_Obot__class_Obot(tc_fun(U_5856,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1305_1]) ).
fof(f_1305_3,plain,
( ! [U_5869,U_5867,U_5865,U_5863,U_5861] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5865,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5863,tc_fun(U_5865,tc_HOL_Obool)),U_5861),U_5867)),U_5869) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5863,tc_fun(U_5865,tc_HOL_Obool)),U_5861),hAPP(hAPP(c_COMBC(U_5863,tc_fun(U_5865,tc_HOL_Obool),tc_fun(U_5865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5865,tc_HOL_Obool),tc_fun(tc_fun(U_5865,tc_HOL_Obool),tc_fun(U_5865,tc_HOL_Obool)),U_5863),c_Groups_Ominus__class_Ominus(tc_fun(U_5865,tc_HOL_Obool))),U_5867)),U_5869))
| U_5861 = c_Orderings_Obot__class_Obot(tc_fun(U_5863,tc_HOL_Obool)) )
& ! [U_5868,U_5866,U_5864,U_5862,U_5860] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5864,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5862,tc_fun(U_5864,tc_HOL_Obool)),U_5860),U_5866)),U_5868) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5864,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5864,tc_HOL_Obool))),U_5868)
| U_5860 != c_Orderings_Obot__class_Obot(tc_fun(U_5862,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1305_2]) ).
fof(f_1305_4,plain,
( ! [U_5861,U_5863,U_5865,U_5867,U_5869] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5865,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5863,tc_fun(U_5865,tc_HOL_Obool)),U_5861),U_5867)),U_5869) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5863,tc_fun(U_5865,tc_HOL_Obool)),U_5861),hAPP(hAPP(c_COMBC(U_5863,tc_fun(U_5865,tc_HOL_Obool),tc_fun(U_5865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5865,tc_HOL_Obool),tc_fun(tc_fun(U_5865,tc_HOL_Obool),tc_fun(U_5865,tc_HOL_Obool)),U_5863),c_Groups_Ominus__class_Ominus(tc_fun(U_5865,tc_HOL_Obool))),U_5867)),U_5869))
| U_5861 = c_Orderings_Obot__class_Obot(tc_fun(U_5863,tc_HOL_Obool)) )
& ! [U_5864,U_5862,U_5866,U_5860,U_5868] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5864,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5862,tc_fun(U_5864,tc_HOL_Obool)),U_5860),U_5866)),U_5868) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5864,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5864,tc_HOL_Obool))),U_5868)
| U_5860 != c_Orderings_Obot__class_Obot(tc_fun(U_5862,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1305_3]) ).
cnf(f_1305_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5864,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5862,tc_fun(U_5864,tc_HOL_Obool)),U_5860),U_5866)),U_5868) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5864,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5864,tc_HOL_Obool))),U_5868)
| U_5860 != c_Orderings_Obot__class_Obot(tc_fun(U_5862,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1305_4]) ).
cnf(f_1305_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5865,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5863,tc_fun(U_5865,tc_HOL_Obool)),U_5861),U_5867)),U_5869) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5863,tc_fun(U_5865,tc_HOL_Obool)),U_5861),hAPP(hAPP(c_COMBC(U_5863,tc_fun(U_5865,tc_HOL_Obool),tc_fun(U_5865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5865,tc_HOL_Obool),tc_fun(tc_fun(U_5865,tc_HOL_Obool),tc_fun(U_5865,tc_HOL_Obool)),U_5863),c_Groups_Ominus__class_Ominus(tc_fun(U_5865,tc_HOL_Obool))),U_5867)),U_5869))
| U_5861 = c_Orderings_Obot__class_Obot(tc_fun(U_5863,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1305_4]) ).
fof(f_1306_1,plain,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J]) ).
fof(f_1306_2,plain,
! [U_5874,U_5873,U_5872,U_5871,U_5870] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5871,tc_fun(U_5872,tc_HOL_Obool)),U_5870),hAPP(hAPP(c_COMBC(U_5871,tc_fun(U_5872,tc_HOL_Obool),tc_fun(U_5872,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5872,tc_HOL_Obool),tc_fun(tc_fun(U_5872,tc_HOL_Obool),tc_fun(U_5872,tc_HOL_Obool)),U_5871),c_Groups_Ominus__class_Ominus(tc_fun(U_5872,tc_HOL_Obool))),U_5873)),U_5874)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5872,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5871,tc_fun(U_5872,tc_HOL_Obool)),U_5870),U_5873)),U_5874)
| U_5870 = c_Orderings_Obot__class_Obot(tc_fun(U_5871,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5871,tc_fun(U_5872,tc_HOL_Obool)),U_5870),hAPP(hAPP(c_COMBC(U_5871,tc_fun(U_5872,tc_HOL_Obool),tc_fun(U_5872,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5872,tc_HOL_Obool),tc_fun(tc_fun(U_5872,tc_HOL_Obool),tc_fun(U_5872,tc_HOL_Obool)),U_5871),c_Groups_Ominus__class_Ominus(tc_fun(U_5872,tc_HOL_Obool))),U_5873)),U_5874)) = c_Orderings_Otop__class_Otop(tc_fun(U_5872,tc_HOL_Obool))
| U_5870 != c_Orderings_Obot__class_Obot(tc_fun(U_5871,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1306_1]) ).
fof(f_1306_3,plain,
( ! [U_5884,U_5882,U_5880,U_5878,U_5876] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5878,tc_fun(U_5880,tc_HOL_Obool)),U_5876),hAPP(hAPP(c_COMBC(U_5878,tc_fun(U_5880,tc_HOL_Obool),tc_fun(U_5880,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5880,tc_HOL_Obool),tc_fun(tc_fun(U_5880,tc_HOL_Obool),tc_fun(U_5880,tc_HOL_Obool)),U_5878),c_Groups_Ominus__class_Ominus(tc_fun(U_5880,tc_HOL_Obool))),U_5882)),U_5884)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5880,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5878,tc_fun(U_5880,tc_HOL_Obool)),U_5876),U_5882)),U_5884)
| U_5876 = c_Orderings_Obot__class_Obot(tc_fun(U_5878,tc_HOL_Obool)) )
& ! [U_5883,U_5881,U_5879,U_5877,U_5875] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5877,tc_fun(U_5879,tc_HOL_Obool)),U_5875),hAPP(hAPP(c_COMBC(U_5877,tc_fun(U_5879,tc_HOL_Obool),tc_fun(U_5879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5879,tc_HOL_Obool),tc_fun(tc_fun(U_5879,tc_HOL_Obool),tc_fun(U_5879,tc_HOL_Obool)),U_5877),c_Groups_Ominus__class_Ominus(tc_fun(U_5879,tc_HOL_Obool))),U_5881)),U_5883)) = c_Orderings_Otop__class_Otop(tc_fun(U_5879,tc_HOL_Obool))
| U_5875 != c_Orderings_Obot__class_Obot(tc_fun(U_5877,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1306_2]) ).
fof(f_1306_4,plain,
( ! [U_5876,U_5878,U_5880,U_5882,U_5884] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5878,tc_fun(U_5880,tc_HOL_Obool)),U_5876),hAPP(hAPP(c_COMBC(U_5878,tc_fun(U_5880,tc_HOL_Obool),tc_fun(U_5880,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5880,tc_HOL_Obool),tc_fun(tc_fun(U_5880,tc_HOL_Obool),tc_fun(U_5880,tc_HOL_Obool)),U_5878),c_Groups_Ominus__class_Ominus(tc_fun(U_5880,tc_HOL_Obool))),U_5882)),U_5884)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5880,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5878,tc_fun(U_5880,tc_HOL_Obool)),U_5876),U_5882)),U_5884)
| U_5876 = c_Orderings_Obot__class_Obot(tc_fun(U_5878,tc_HOL_Obool)) )
& ! [U_5877,U_5881,U_5875,U_5883,U_5879] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5877,tc_fun(U_5879,tc_HOL_Obool)),U_5875),hAPP(hAPP(c_COMBC(U_5877,tc_fun(U_5879,tc_HOL_Obool),tc_fun(U_5879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5879,tc_HOL_Obool),tc_fun(tc_fun(U_5879,tc_HOL_Obool),tc_fun(U_5879,tc_HOL_Obool)),U_5877),c_Groups_Ominus__class_Ominus(tc_fun(U_5879,tc_HOL_Obool))),U_5881)),U_5883)) = c_Orderings_Otop__class_Otop(tc_fun(U_5879,tc_HOL_Obool))
| U_5875 != c_Orderings_Obot__class_Obot(tc_fun(U_5877,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1306_3]) ).
cnf(f_1306_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5877,tc_fun(U_5879,tc_HOL_Obool)),U_5875),hAPP(hAPP(c_COMBC(U_5877,tc_fun(U_5879,tc_HOL_Obool),tc_fun(U_5879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5879,tc_HOL_Obool),tc_fun(tc_fun(U_5879,tc_HOL_Obool),tc_fun(U_5879,tc_HOL_Obool)),U_5877),c_Groups_Ominus__class_Ominus(tc_fun(U_5879,tc_HOL_Obool))),U_5881)),U_5883)) = c_Orderings_Otop__class_Otop(tc_fun(U_5879,tc_HOL_Obool))
| U_5875 != c_Orderings_Obot__class_Obot(tc_fun(U_5877,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1306_4]) ).
cnf(f_1306_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5878,tc_fun(U_5880,tc_HOL_Obool)),U_5876),hAPP(hAPP(c_COMBC(U_5878,tc_fun(U_5880,tc_HOL_Obool),tc_fun(U_5880,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5880,tc_HOL_Obool),tc_fun(tc_fun(U_5880,tc_HOL_Obool),tc_fun(U_5880,tc_HOL_Obool)),U_5878),c_Groups_Ominus__class_Ominus(tc_fun(U_5880,tc_HOL_Obool))),U_5882)),U_5884)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5880,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5878,tc_fun(U_5880,tc_HOL_Obool)),U_5876),U_5882)),U_5884)
| U_5876 = c_Orderings_Obot__class_Obot(tc_fun(U_5878,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1306_4]) ).
fof(f_1307_1,plain,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I4_J]) ).
fof(f_1307_2,plain,
! [U_5889,U_5888,U_5887,U_5886,U_5885] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5887,tc_HOL_Obool)),U_5888),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5886,tc_fun(U_5887,tc_HOL_Obool)),U_5885),U_5889)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5886,tc_fun(U_5887,tc_HOL_Obool)),U_5885),hAPP(hAPP(c_COMBB(tc_fun(U_5887,tc_HOL_Obool),tc_fun(U_5887,tc_HOL_Obool),U_5886),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5887,tc_HOL_Obool)),U_5888)),U_5889))
| U_5885 = c_Orderings_Obot__class_Obot(tc_fun(U_5886,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5887,tc_HOL_Obool)),U_5888),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5886,tc_fun(U_5887,tc_HOL_Obool)),U_5885),U_5889)) = U_5888
| U_5885 != c_Orderings_Obot__class_Obot(tc_fun(U_5886,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1307_1]) ).
fof(f_1307_3,plain,
( ! [U_5899,U_5897,U_5895,U_5893,U_5891] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5895,tc_HOL_Obool)),U_5897),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5893,tc_fun(U_5895,tc_HOL_Obool)),U_5891),U_5899)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5893,tc_fun(U_5895,tc_HOL_Obool)),U_5891),hAPP(hAPP(c_COMBB(tc_fun(U_5895,tc_HOL_Obool),tc_fun(U_5895,tc_HOL_Obool),U_5893),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5895,tc_HOL_Obool)),U_5897)),U_5899))
| U_5891 = c_Orderings_Obot__class_Obot(tc_fun(U_5893,tc_HOL_Obool)) )
& ! [U_5898,U_5896,U_5894,U_5892,U_5890] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5894,tc_HOL_Obool)),U_5896),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5892,tc_fun(U_5894,tc_HOL_Obool)),U_5890),U_5898)) = U_5896
| U_5890 != c_Orderings_Obot__class_Obot(tc_fun(U_5892,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1307_2]) ).
fof(f_1307_4,plain,
( ! [U_5891,U_5893,U_5895,U_5897,U_5899] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5895,tc_HOL_Obool)),U_5897),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5893,tc_fun(U_5895,tc_HOL_Obool)),U_5891),U_5899)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5893,tc_fun(U_5895,tc_HOL_Obool)),U_5891),hAPP(hAPP(c_COMBB(tc_fun(U_5895,tc_HOL_Obool),tc_fun(U_5895,tc_HOL_Obool),U_5893),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5895,tc_HOL_Obool)),U_5897)),U_5899))
| U_5891 = c_Orderings_Obot__class_Obot(tc_fun(U_5893,tc_HOL_Obool)) )
& ! [U_5892,U_5896,U_5890,U_5894,U_5898] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5894,tc_HOL_Obool)),U_5896),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5892,tc_fun(U_5894,tc_HOL_Obool)),U_5890),U_5898)) = U_5896
| U_5890 != c_Orderings_Obot__class_Obot(tc_fun(U_5892,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1307_3]) ).
cnf(f_1307_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5894,tc_HOL_Obool)),U_5896),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5892,tc_fun(U_5894,tc_HOL_Obool)),U_5890),U_5898)) = U_5896
| U_5890 != c_Orderings_Obot__class_Obot(tc_fun(U_5892,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1307_4]) ).
cnf(f_1307_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5895,tc_HOL_Obool)),U_5897),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5893,tc_fun(U_5895,tc_HOL_Obool)),U_5891),U_5899)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5893,tc_fun(U_5895,tc_HOL_Obool)),U_5891),hAPP(hAPP(c_COMBB(tc_fun(U_5895,tc_HOL_Obool),tc_fun(U_5895,tc_HOL_Obool),U_5893),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5895,tc_HOL_Obool)),U_5897)),U_5899))
| U_5891 = c_Orderings_Obot__class_Obot(tc_fun(U_5893,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1307_4]) ).
fof(f_1308_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_1308_2,plain,
! [U_5902,U_5901,U_5900] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5902),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5901),U_5900))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5902),U_5900)),hAPP(c_Nat_OSuc,U_5901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5900),U_5901)) ),
inference(variable_rename,[status(thm)],[f_1308_1]) ).
fof(f_1308_3,plain,
! [U_5901,U_5900,U_5902] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5902),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5901),U_5900))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5902),U_5900)),hAPP(c_Nat_OSuc,U_5901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5900),U_5901)) ),
inference(definitional_conversion,[status(esa)],[f_1308_2]) ).
cnf(f_1308_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5902),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5901),U_5900))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5902),U_5900)),hAPP(c_Nat_OSuc,U_5901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5900),U_5901)) ),
inference(clausify,[status(thm)],[f_1308_3]) ).
fof(f_1309_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_1309_2,plain,
! [U_5905,U_5904,U_5903] :
( 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_5904),U_5903))),U_5905) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5904)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5903),U_5905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5903),U_5904)) ),
inference(variable_rename,[status(thm)],[f_1309_1]) ).
fof(f_1309_3,plain,
! [U_5903,U_5904,U_5905] :
( 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_5904),U_5903))),U_5905) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5904)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5903),U_5905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5903),U_5904)) ),
inference(definitional_conversion,[status(esa)],[f_1309_2]) ).
cnf(f_1309_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_5904),U_5903))),U_5905) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5904)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5903),U_5905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5903),U_5904)) ),
inference(clausify,[status(thm)],[f_1309_3]) ).
fof(f_1310_1,plain,
! [V_M_2,V_A_2,V_i_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_d) ),
inference(fof_nnf,[status(thm)],[fact_INF__leI]) ).
fof(f_1310_2,plain,
! [U_5910,U_5909,U_5908,U_5907,U_5906] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5907,U_5906),U_5909),U_5910)),hAPP(U_5910,U_5908)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5907),U_5908),U_5909))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5906) ),
inference(variable_rename,[status(thm)],[f_1310_1]) ).
fof(f_1310_3,plain,
! [U_5906,U_5907,U_5908,U_5909,U_5910] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5907,U_5906),U_5909),U_5910)),hAPP(U_5910,U_5908)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5907),U_5908),U_5909))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5906) ),
inference(definitional_conversion,[status(esa)],[f_1310_2]) ).
cnf(f_1310_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5906),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5907,U_5906),U_5909),U_5910)),hAPP(U_5910,U_5908)))
| ~ hBOOL(hAPP(hAPP(c_member(U_5907),U_5908),U_5909))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5906) ),
inference(clausify,[status(thm)],[f_1310_3]) ).
fof(f_1311_1,plain,
! [V_a_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) = V_a_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sup__Inf__absorb]) ).
fof(f_1311_2,plain,
! [U_5913,U_5912,U_5911] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5911),U_5913),c_Big__Operators_Olattice__class_OInf__fin(U_5911,U_5912)) = U_5913
| ~ hBOOL(hAPP(hAPP(c_member(U_5911),U_5913),U_5912))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5911),U_5912))
| ~ class_Lattices_Olattice(U_5911) ),
inference(variable_rename,[status(thm)],[f_1311_1]) ).
fof(f_1311_3,plain,
! [U_5911,U_5912,U_5913] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5911),U_5913),c_Big__Operators_Olattice__class_OInf__fin(U_5911,U_5912)) = U_5913
| ~ hBOOL(hAPP(hAPP(c_member(U_5911),U_5913),U_5912))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5911),U_5912))
| ~ class_Lattices_Olattice(U_5911) ),
inference(definitional_conversion,[status(esa)],[f_1311_2]) ).
cnf(f_1311_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_5911),U_5913),c_Big__Operators_Olattice__class_OInf__fin(U_5911,U_5912)) = U_5913
| ~ hBOOL(hAPP(hAPP(c_member(U_5911),U_5913),U_5912))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5911),U_5912))
| ~ class_Lattices_Olattice(U_5911) ),
inference(clausify,[status(thm)],[f_1311_3]) ).
fof(f_1312_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,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))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem]) ).
fof(f_1312_2,plain,
! [U_5916,U_5915,U_5914] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5914),U_5916),c_Big__Operators_Olattice__class_OInf__fin(U_5914,U_5915)) = c_Big__Operators_Olattice__class_OInf__fin(U_5914,U_5915)
| ~ hBOOL(hAPP(hAPP(c_member(U_5914),U_5916),U_5915))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5914),U_5915))
| ~ class_Lattices_Olattice(U_5914) ),
inference(variable_rename,[status(thm)],[f_1312_1]) ).
fof(f_1312_3,plain,
! [U_5914,U_5915,U_5916] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5914),U_5916),c_Big__Operators_Olattice__class_OInf__fin(U_5914,U_5915)) = c_Big__Operators_Olattice__class_OInf__fin(U_5914,U_5915)
| ~ hBOOL(hAPP(hAPP(c_member(U_5914),U_5916),U_5915))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5914),U_5915))
| ~ class_Lattices_Olattice(U_5914) ),
inference(definitional_conversion,[status(esa)],[f_1312_2]) ).
cnf(f_1312_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5914),U_5916),c_Big__Operators_Olattice__class_OInf__fin(U_5914,U_5915)) = c_Big__Operators_Olattice__class_OInf__fin(U_5914,U_5915)
| ~ hBOOL(hAPP(hAPP(c_member(U_5914),U_5916),U_5915))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5914),U_5915))
| ~ class_Lattices_Olattice(U_5914) ),
inference(clausify,[status(thm)],[f_1312_3]) ).
fof(f_1313_1,plain,
! [V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_OF__eq]) ).
fof(f_1313_2,plain,
! [U_5918,U_5917] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5917,U_5918) = hAPP(c_Finite__Set_Ofold1(U_5917,c_Lattices_Osemilattice__inf__class_Oinf(U_5917)),U_5918)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5917),U_5918))
| ~ class_Lattices_Olattice(U_5917) ),
inference(variable_rename,[status(thm)],[f_1313_1]) ).
fof(f_1313_3,plain,
! [U_5918,U_5917] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5917,U_5918) = hAPP(c_Finite__Set_Ofold1(U_5917,c_Lattices_Osemilattice__inf__class_Oinf(U_5917)),U_5918)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5917),U_5918))
| ~ class_Lattices_Olattice(U_5917) ),
inference(definitional_conversion,[status(esa)],[f_1313_2]) ).
cnf(f_1313_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5917,U_5918) = hAPP(c_Finite__Set_Ofold1(U_5917,c_Lattices_Osemilattice__inf__class_Oinf(U_5917)),U_5918)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5917),U_5918))
| ~ class_Lattices_Olattice(U_5917) ),
inference(clausify,[status(thm)],[f_1313_3]) ).
fof(f_1314_1,plain,
! [V_B_2,V_A_2,T_d,T_c,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_d,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I4_J]) ).
fof(f_1314_2,plain,
! [U_5923,U_5922,U_5921,U_5920,U_5919] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5920,tc_fun(U_5921,tc_HOL_Obool)),U_5919),hAPP(hAPP(c_COMBB(tc_fun(U_5921,tc_HOL_Obool),tc_fun(U_5921,tc_HOL_Obool),U_5920),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5921,tc_HOL_Obool)),U_5922)),U_5923)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5921,tc_HOL_Obool)),U_5922),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5920,tc_fun(U_5921,tc_HOL_Obool)),U_5919),U_5923))
| U_5919 = c_Orderings_Obot__class_Obot(tc_fun(U_5920,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5920,tc_fun(U_5921,tc_HOL_Obool)),U_5919),hAPP(hAPP(c_COMBB(tc_fun(U_5921,tc_HOL_Obool),tc_fun(U_5921,tc_HOL_Obool),U_5920),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5921,tc_HOL_Obool)),U_5922)),U_5923)) = c_Orderings_Otop__class_Otop(tc_fun(U_5921,tc_HOL_Obool))
| U_5919 != c_Orderings_Obot__class_Obot(tc_fun(U_5920,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1314_1]) ).
fof(f_1314_3,plain,
( ! [U_5933,U_5931,U_5929,U_5927,U_5925] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5927,tc_fun(U_5929,tc_HOL_Obool)),U_5925),hAPP(hAPP(c_COMBB(tc_fun(U_5929,tc_HOL_Obool),tc_fun(U_5929,tc_HOL_Obool),U_5927),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5929,tc_HOL_Obool)),U_5931)),U_5933)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5929,tc_HOL_Obool)),U_5931),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5927,tc_fun(U_5929,tc_HOL_Obool)),U_5925),U_5933))
| U_5925 = c_Orderings_Obot__class_Obot(tc_fun(U_5927,tc_HOL_Obool)) )
& ! [U_5932,U_5930,U_5928,U_5926,U_5924] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5926,tc_fun(U_5928,tc_HOL_Obool)),U_5924),hAPP(hAPP(c_COMBB(tc_fun(U_5928,tc_HOL_Obool),tc_fun(U_5928,tc_HOL_Obool),U_5926),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5928,tc_HOL_Obool)),U_5930)),U_5932)) = c_Orderings_Otop__class_Otop(tc_fun(U_5928,tc_HOL_Obool))
| U_5924 != c_Orderings_Obot__class_Obot(tc_fun(U_5926,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1314_2]) ).
fof(f_1314_4,plain,
( ! [U_5925,U_5927,U_5929,U_5931,U_5933] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5927,tc_fun(U_5929,tc_HOL_Obool)),U_5925),hAPP(hAPP(c_COMBB(tc_fun(U_5929,tc_HOL_Obool),tc_fun(U_5929,tc_HOL_Obool),U_5927),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5929,tc_HOL_Obool)),U_5931)),U_5933)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5929,tc_HOL_Obool)),U_5931),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5927,tc_fun(U_5929,tc_HOL_Obool)),U_5925),U_5933))
| U_5925 = c_Orderings_Obot__class_Obot(tc_fun(U_5927,tc_HOL_Obool)) )
& ! [U_5928,U_5926,U_5930,U_5924,U_5932] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5926,tc_fun(U_5928,tc_HOL_Obool)),U_5924),hAPP(hAPP(c_COMBB(tc_fun(U_5928,tc_HOL_Obool),tc_fun(U_5928,tc_HOL_Obool),U_5926),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5928,tc_HOL_Obool)),U_5930)),U_5932)) = c_Orderings_Otop__class_Otop(tc_fun(U_5928,tc_HOL_Obool))
| U_5924 != c_Orderings_Obot__class_Obot(tc_fun(U_5926,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_1314_3]) ).
cnf(f_1314_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5926,tc_fun(U_5928,tc_HOL_Obool)),U_5924),hAPP(hAPP(c_COMBB(tc_fun(U_5928,tc_HOL_Obool),tc_fun(U_5928,tc_HOL_Obool),U_5926),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5928,tc_HOL_Obool)),U_5930)),U_5932)) = c_Orderings_Otop__class_Otop(tc_fun(U_5928,tc_HOL_Obool))
| U_5924 != c_Orderings_Obot__class_Obot(tc_fun(U_5926,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1314_4]) ).
cnf(f_1314_6,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5927,tc_fun(U_5929,tc_HOL_Obool)),U_5925),hAPP(hAPP(c_COMBB(tc_fun(U_5929,tc_HOL_Obool),tc_fun(U_5929,tc_HOL_Obool),U_5927),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5929,tc_HOL_Obool)),U_5931)),U_5933)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5929,tc_HOL_Obool)),U_5931),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_5927,tc_fun(U_5929,tc_HOL_Obool)),U_5925),U_5933))
| U_5925 = c_Orderings_Obot__class_Obot(tc_fun(U_5927,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1314_4]) ).
fof(f_1315_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_c),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) )
& ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_c),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)) ),
inference(fof_nnf,[status(thm)],[fact_card__insert__if]) ).
fof(f_1315_2,plain,
! [U_5936,U_5935,U_5934] :
( ( ( hAPP(c_Finite__Set_Ocard(U_5934),hAPP(hAPP(c_Set_Oinsert(U_5934),U_5936),U_5935)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5934),U_5935))
| hBOOL(hAPP(hAPP(c_member(U_5934),U_5936),U_5935)) )
& ( hAPP(c_Finite__Set_Ocard(U_5934),hAPP(hAPP(c_Set_Oinsert(U_5934),U_5936),U_5935)) = hAPP(c_Finite__Set_Ocard(U_5934),U_5935)
| ~ hBOOL(hAPP(hAPP(c_member(U_5934),U_5936),U_5935)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5934),U_5935)) ),
inference(variable_rename,[status(thm)],[f_1315_1]) ).
fof(f_1315_3,plain,
( ! [U_5934,U_5935,U_5936] :
( hAPP(c_Finite__Set_Ocard(U_5934),hAPP(hAPP(c_Set_Oinsert(U_5934),U_5936),U_5935)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5934),U_5935))
| hBOOL(hAPP(hAPP(c_member(U_5934),U_5936),U_5935))
| ~ sP279(U_5934,U_5935,U_5936) )
& ! [U_5934,U_5935,U_5936] :
( hAPP(c_Finite__Set_Ocard(U_5934),hAPP(hAPP(c_Set_Oinsert(U_5934),U_5936),U_5935)) = hAPP(c_Finite__Set_Ocard(U_5934),U_5935)
| ~ hBOOL(hAPP(hAPP(c_member(U_5934),U_5936),U_5935))
| ~ sP279(U_5934,U_5935,U_5936) )
& ! [U_5934,U_5935,U_5936] :
( sP279(U_5934,U_5935,U_5936)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5934),U_5935)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP279])],[f_1315_2]) ).
cnf(f_1315_4,plain,
( sP279(U_5934,U_5935,U_5936)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5934),U_5935)) ),
inference(clausify,[status(thm)],[f_1315_3]) ).
cnf(f_1315_5,plain,
( hAPP(c_Finite__Set_Ocard(U_5934),hAPP(hAPP(c_Set_Oinsert(U_5934),U_5936),U_5935)) = hAPP(c_Finite__Set_Ocard(U_5934),U_5935)
| ~ hBOOL(hAPP(hAPP(c_member(U_5934),U_5936),U_5935))
| ~ sP279(U_5934,U_5935,U_5936) ),
inference(clausify,[status(thm)],[f_1315_3]) ).
cnf(f_1315_6,plain,
( hAPP(c_Finite__Set_Ocard(U_5934),hAPP(hAPP(c_Set_Oinsert(U_5934),U_5936),U_5935)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5934),U_5935))
| hBOOL(hAPP(hAPP(c_member(U_5934),U_5936),U_5935))
| ~ sP279(U_5934,U_5935,U_5936) ),
inference(clausify,[status(thm)],[f_1315_3]) ).
fof(f_1316_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_c),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)) ),
inference(fof_nnf,[status(thm)],[fact_card__insert__disjoint]) ).
fof(f_1316_2,plain,
! [U_5939,U_5938,U_5937] :
( hAPP(c_Finite__Set_Ocard(U_5937),hAPP(hAPP(c_Set_Oinsert(U_5937),U_5939),U_5938)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5937),U_5938))
| hBOOL(hAPP(hAPP(c_member(U_5937),U_5939),U_5938))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5937),U_5938)) ),
inference(variable_rename,[status(thm)],[f_1316_1]) ).
fof(f_1316_3,plain,
! [U_5938,U_5937,U_5939] :
( hAPP(c_Finite__Set_Ocard(U_5937),hAPP(hAPP(c_Set_Oinsert(U_5937),U_5939),U_5938)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5937),U_5938))
| hBOOL(hAPP(hAPP(c_member(U_5937),U_5939),U_5938))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5937),U_5938)) ),
inference(definitional_conversion,[status(esa)],[f_1316_2]) ).
cnf(f_1316_4,plain,
( hAPP(c_Finite__Set_Ocard(U_5937),hAPP(hAPP(c_Set_Oinsert(U_5937),U_5939),U_5938)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5937),U_5938))
| hBOOL(hAPP(hAPP(c_member(U_5937),U_5939),U_5938))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5937),U_5938)) ),
inference(clausify,[status(thm)],[f_1316_3]) ).
fof(f_1317_1,plain,
! [V_b_2,V_a_2,T_c] :
( c_Complete__Lattice_OInf__class_OInf(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_a_2),V_b_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__binary]) ).
fof(f_1317_2,plain,
! [U_5942,U_5941,U_5940] :
( c_Complete__Lattice_OInf__class_OInf(U_5940,hAPP(hAPP(c_Set_Oinsert(U_5940),U_5941),hAPP(hAPP(c_Set_Oinsert(U_5940),U_5942),c_Orderings_Obot__class_Obot(tc_fun(U_5940,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5940),U_5941),U_5942)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5940) ),
inference(variable_rename,[status(thm)],[f_1317_1]) ).
fof(f_1317_3,plain,
! [U_5940,U_5941,U_5942] :
( c_Complete__Lattice_OInf__class_OInf(U_5940,hAPP(hAPP(c_Set_Oinsert(U_5940),U_5941),hAPP(hAPP(c_Set_Oinsert(U_5940),U_5942),c_Orderings_Obot__class_Obot(tc_fun(U_5940,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5940),U_5941),U_5942)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5940) ),
inference(definitional_conversion,[status(esa)],[f_1317_2]) ).
cnf(f_1317_4,plain,
( c_Complete__Lattice_OInf__class_OInf(U_5940,hAPP(hAPP(c_Set_Oinsert(U_5940),U_5941),hAPP(hAPP(c_Set_Oinsert(U_5940),U_5942),c_Orderings_Obot__class_Obot(tc_fun(U_5940,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5940),U_5941),U_5942)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5940) ),
inference(clausify,[status(thm)],[f_1317_3]) ).
fof(f_1318_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_c,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inf__Inf__fold__inf]) ).
fof(f_1318_2,plain,
! [U_5945,U_5944,U_5943] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5943),U_5945),c_Complete__Lattice_OInf__class_OInf(U_5943,U_5944)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5943,U_5943,c_Lattices_Osemilattice__inf__class_Oinf(U_5943)),U_5945),U_5944)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5943),U_5944))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5943) ),
inference(variable_rename,[status(thm)],[f_1318_1]) ).
fof(f_1318_3,plain,
! [U_5943,U_5944,U_5945] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5943),U_5945),c_Complete__Lattice_OInf__class_OInf(U_5943,U_5944)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5943,U_5943,c_Lattices_Osemilattice__inf__class_Oinf(U_5943)),U_5945),U_5944)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5943),U_5944))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5943) ),
inference(definitional_conversion,[status(esa)],[f_1318_2]) ).
cnf(f_1318_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5943),U_5945),c_Complete__Lattice_OInf__class_OInf(U_5943,U_5944)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5943,U_5943,c_Lattices_Osemilattice__inf__class_Oinf(U_5943)),U_5945),U_5944)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5943),U_5944))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5943) ),
inference(clausify,[status(thm)],[f_1318_3]) ).
fof(f_1319_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem]) ).
fof(f_1319_2,plain,
! [U_5948,U_5947,U_5946] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5946,hAPP(hAPP(c_Set_Oinsert(U_5946),U_5948),U_5947)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5946),U_5948),c_Big__Operators_Olattice__class_OInf__fin(U_5946,U_5947))
| U_5947 = c_Orderings_Obot__class_Obot(tc_fun(U_5946,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5946),U_5947))
| ~ class_Lattices_Olattice(U_5946) ),
inference(variable_rename,[status(thm)],[f_1319_1]) ).
fof(f_1319_3,plain,
! [U_5946,U_5947,U_5948] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5946,hAPP(hAPP(c_Set_Oinsert(U_5946),U_5948),U_5947)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5946),U_5948),c_Big__Operators_Olattice__class_OInf__fin(U_5946,U_5947))
| U_5947 = c_Orderings_Obot__class_Obot(tc_fun(U_5946,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5946),U_5947))
| ~ class_Lattices_Olattice(U_5946) ),
inference(definitional_conversion,[status(esa)],[f_1319_2]) ).
cnf(f_1319_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5946,hAPP(hAPP(c_Set_Oinsert(U_5946),U_5948),U_5947)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5946),U_5948),c_Big__Operators_Olattice__class_OInf__fin(U_5946,U_5947))
| U_5947 = c_Orderings_Obot__class_Obot(tc_fun(U_5946,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5946),U_5947))
| ~ class_Lattices_Olattice(U_5946) ),
inference(clausify,[status(thm)],[f_1319_3]) ).
fof(f_1320_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(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))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osubset__idem]) ).
fof(f_1320_2,plain,
! [U_5951,U_5950,U_5949] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5949),c_Big__Operators_Olattice__class_OInf__fin(U_5949,U_5951)),c_Big__Operators_Olattice__class_OInf__fin(U_5949,U_5950)) = c_Big__Operators_Olattice__class_OInf__fin(U_5949,U_5950)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5949,tc_HOL_Obool)),U_5951),U_5950))
| U_5951 = c_Orderings_Obot__class_Obot(tc_fun(U_5949,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5949),U_5950))
| ~ class_Lattices_Olattice(U_5949) ),
inference(variable_rename,[status(thm)],[f_1320_1]) ).
fof(f_1320_3,plain,
! [U_5949,U_5950,U_5951] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5949),c_Big__Operators_Olattice__class_OInf__fin(U_5949,U_5951)),c_Big__Operators_Olattice__class_OInf__fin(U_5949,U_5950)) = c_Big__Operators_Olattice__class_OInf__fin(U_5949,U_5950)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5949,tc_HOL_Obool)),U_5951),U_5950))
| U_5951 = c_Orderings_Obot__class_Obot(tc_fun(U_5949,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5949),U_5950))
| ~ class_Lattices_Olattice(U_5949) ),
inference(definitional_conversion,[status(esa)],[f_1320_2]) ).
cnf(f_1320_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5949),c_Big__Operators_Olattice__class_OInf__fin(U_5949,U_5951)),c_Big__Operators_Olattice__class_OInf__fin(U_5949,U_5950)) = c_Big__Operators_Olattice__class_OInf__fin(U_5949,U_5950)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5949,tc_HOL_Obool)),U_5951),U_5950))
| U_5951 = c_Orderings_Obot__class_Obot(tc_fun(U_5949,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5949),U_5950))
| ~ class_Lattices_Olattice(U_5949) ),
inference(clausify,[status(thm)],[f_1320_3]) ).
fof(f_1321_1,plain,
! [V_B_2,V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OInf__fin(T_c,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__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,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_c),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__idem]) ).
fof(f_1321_2,plain,
! [U_5954,U_5953,U_5952] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5952,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5952,tc_HOL_Obool)),U_5953),U_5954)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5952),c_Big__Operators_Olattice__class_OInf__fin(U_5952,U_5953)),c_Big__Operators_Olattice__class_OInf__fin(U_5952,U_5954))
| U_5954 = c_Orderings_Obot__class_Obot(tc_fun(U_5952,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5952),U_5954))
| U_5953 = c_Orderings_Obot__class_Obot(tc_fun(U_5952,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5952),U_5953))
| ~ class_Lattices_Olattice(U_5952) ),
inference(variable_rename,[status(thm)],[f_1321_1]) ).
fof(f_1321_3,plain,
! [U_5952,U_5953,U_5954] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5952,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5952,tc_HOL_Obool)),U_5953),U_5954)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5952),c_Big__Operators_Olattice__class_OInf__fin(U_5952,U_5953)),c_Big__Operators_Olattice__class_OInf__fin(U_5952,U_5954))
| U_5954 = c_Orderings_Obot__class_Obot(tc_fun(U_5952,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5952),U_5954))
| U_5953 = c_Orderings_Obot__class_Obot(tc_fun(U_5952,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5952),U_5953))
| ~ class_Lattices_Olattice(U_5952) ),
inference(definitional_conversion,[status(esa)],[f_1321_2]) ).
cnf(f_1321_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5952,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5952,tc_HOL_Obool)),U_5953),U_5954)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5952),c_Big__Operators_Olattice__class_OInf__fin(U_5952,U_5953)),c_Big__Operators_Olattice__class_OInf__fin(U_5952,U_5954))
| U_5954 = c_Orderings_Obot__class_Obot(tc_fun(U_5952,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5952),U_5954))
| U_5953 = c_Orderings_Obot__class_Obot(tc_fun(U_5952,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5952),U_5953))
| ~ class_Lattices_Olattice(U_5952) ),
inference(clausify,[status(thm)],[f_1321_3]) ).
fof(f_1322_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__le__Sup]) ).
fof(f_1322_2,plain,
! [U_5956,U_5955] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5955),c_Big__Operators_Olattice__class_OInf__fin(U_5955,U_5956)),c_Big__Operators_Olattice__class_OSup__fin(U_5955,U_5956)))
| U_5956 = c_Orderings_Obot__class_Obot(tc_fun(U_5955,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5955),U_5956))
| ~ class_Lattices_Olattice(U_5955) ),
inference(variable_rename,[status(thm)],[f_1322_1]) ).
fof(f_1322_3,plain,
! [U_5956,U_5955] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5955),c_Big__Operators_Olattice__class_OInf__fin(U_5955,U_5956)),c_Big__Operators_Olattice__class_OSup__fin(U_5955,U_5956)))
| U_5956 = c_Orderings_Obot__class_Obot(tc_fun(U_5955,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5955),U_5956))
| ~ class_Lattices_Olattice(U_5955) ),
inference(definitional_conversion,[status(esa)],[f_1322_2]) ).
cnf(f_1322_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5955),c_Big__Operators_Olattice__class_OInf__fin(U_5955,U_5956)),c_Big__Operators_Olattice__class_OSup__fin(U_5955,U_5956)))
| U_5956 = c_Orderings_Obot__class_Obot(tc_fun(U_5955,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5955),U_5956))
| ~ class_Lattices_Olattice(U_5955) ),
inference(clausify,[status(thm)],[f_1322_3]) ).
fof(f_1323_1,plain,
! [V_a_2,V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H]) ).
fof(f_1323_2,plain,
! [U_5959,U_5958,U_5957] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5957,hAPP(hAPP(c_Set_Oinsert(U_5957),U_5959),U_5958)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5957,U_5957,c_Lattices_Osemilattice__inf__class_Oinf(U_5957)),U_5959),U_5958)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5957),U_5958))
| ~ class_Lattices_Olattice(U_5957) ),
inference(variable_rename,[status(thm)],[f_1323_1]) ).
fof(f_1323_3,plain,
! [U_5957,U_5958,U_5959] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5957,hAPP(hAPP(c_Set_Oinsert(U_5957),U_5959),U_5958)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5957,U_5957,c_Lattices_Osemilattice__inf__class_Oinf(U_5957)),U_5959),U_5958)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5957),U_5958))
| ~ class_Lattices_Olattice(U_5957) ),
inference(definitional_conversion,[status(esa)],[f_1323_2]) ).
cnf(f_1323_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5957,hAPP(hAPP(c_Set_Oinsert(U_5957),U_5959),U_5958)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5957,U_5957,c_Lattices_Osemilattice__inf__class_Oinf(U_5957)),U_5959),U_5958)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5957),U_5958))
| ~ class_Lattices_Olattice(U_5957) ),
inference(clausify,[status(thm)],[f_1323_3]) ).
fof(f_1324_1,plain,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_d),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_d),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_d,hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_d)),V_f_2)),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_d) ),
inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf]) ).
fof(f_1324_2,plain,
! [U_5964,U_5963,U_5962,U_5961,U_5960] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5960),U_5963),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5961,U_5960),U_5962),U_5964)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5961,U_5960,hAPP(hAPP(c_COMBB(U_5960,tc_fun(U_5960,U_5960),U_5961),c_Lattices_Osemilattice__inf__class_Oinf(U_5960)),U_5964)),U_5963),U_5962)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5961),U_5962))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5960) ),
inference(variable_rename,[status(thm)],[f_1324_1]) ).
fof(f_1324_3,plain,
! [U_5960,U_5961,U_5962,U_5963,U_5964] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5960),U_5963),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5961,U_5960),U_5962),U_5964)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5961,U_5960,hAPP(hAPP(c_COMBB(U_5960,tc_fun(U_5960,U_5960),U_5961),c_Lattices_Osemilattice__inf__class_Oinf(U_5960)),U_5964)),U_5963),U_5962)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5961),U_5962))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5960) ),
inference(definitional_conversion,[status(esa)],[f_1324_2]) ).
cnf(f_1324_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5960),U_5963),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5961,U_5960),U_5962),U_5964)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5961,U_5960,hAPP(hAPP(c_COMBB(U_5960,tc_fun(U_5960,U_5960),U_5961),c_Lattices_Osemilattice__inf__class_Oinf(U_5960)),U_5964)),U_5963),U_5962)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5961),U_5962))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_5960) ),
inference(clausify,[status(thm)],[f_1324_3]) ).
fof(f_1325_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_c),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)) ),
inference(fof_nnf,[status(thm)],[fact_card__insert]) ).
fof(f_1325_2,plain,
! [U_5967,U_5966,U_5965] :
( hAPP(c_Finite__Set_Ocard(U_5965),hAPP(hAPP(c_Set_Oinsert(U_5965),U_5967),U_5966)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5965),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5965,tc_HOL_Obool)),U_5966),hAPP(hAPP(c_Set_Oinsert(U_5965),U_5967),c_Orderings_Obot__class_Obot(tc_fun(U_5965,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5965),U_5966)) ),
inference(variable_rename,[status(thm)],[f_1325_1]) ).
fof(f_1325_3,plain,
! [U_5965,U_5966,U_5967] :
( hAPP(c_Finite__Set_Ocard(U_5965),hAPP(hAPP(c_Set_Oinsert(U_5965),U_5967),U_5966)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5965),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5965,tc_HOL_Obool)),U_5966),hAPP(hAPP(c_Set_Oinsert(U_5965),U_5967),c_Orderings_Obot__class_Obot(tc_fun(U_5965,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5965),U_5966)) ),
inference(definitional_conversion,[status(esa)],[f_1325_2]) ).
cnf(f_1325_4,plain,
( hAPP(c_Finite__Set_Ocard(U_5965),hAPP(hAPP(c_Set_Oinsert(U_5965),U_5967),U_5966)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_5965),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5965,tc_HOL_Obool)),U_5966),hAPP(hAPP(c_Set_Oinsert(U_5965),U_5967),c_Orderings_Obot__class_Obot(tc_fun(U_5965,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5965),U_5966)) ),
inference(clausify,[status(thm)],[f_1325_3]) ).
fof(f_1326_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2))
| V_A_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))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert]) ).
fof(f_1326_2,plain,
! [U_5970,U_5969,U_5968] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5968,hAPP(hAPP(c_Set_Oinsert(U_5968),U_5970),U_5969)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5968),U_5970),c_Big__Operators_Olattice__class_OInf__fin(U_5968,U_5969))
| U_5969 = c_Orderings_Obot__class_Obot(tc_fun(U_5968,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_5968),U_5970),U_5969))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5968),U_5969))
| ~ class_Lattices_Olattice(U_5968) ),
inference(variable_rename,[status(thm)],[f_1326_1]) ).
fof(f_1326_3,plain,
! [U_5968,U_5969,U_5970] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5968,hAPP(hAPP(c_Set_Oinsert(U_5968),U_5970),U_5969)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5968),U_5970),c_Big__Operators_Olattice__class_OInf__fin(U_5968,U_5969))
| U_5969 = c_Orderings_Obot__class_Obot(tc_fun(U_5968,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_5968),U_5970),U_5969))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5968),U_5969))
| ~ class_Lattices_Olattice(U_5968) ),
inference(definitional_conversion,[status(esa)],[f_1326_2]) ).
cnf(f_1326_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5968,hAPP(hAPP(c_Set_Oinsert(U_5968),U_5970),U_5969)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5968),U_5970),c_Big__Operators_Olattice__class_OInf__fin(U_5968,U_5969))
| U_5969 = c_Orderings_Obot__class_Obot(tc_fun(U_5968,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_5968),U_5970),U_5969))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5968),U_5969))
| ~ class_Lattices_Olattice(U_5968) ),
inference(clausify,[status(thm)],[f_1326_3]) ).
fof(f_1327_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( ( c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,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))))))
| 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = V_x_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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__remove]) ).
fof(f_1327_2,plain,
! [U_5973,U_5972,U_5971] :
( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_5971,hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),U_5972)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5971),U_5973),c_Big__Operators_Olattice__class_OInf__fin(U_5971,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5971,tc_HOL_Obool)),U_5972),hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5971,tc_HOL_Obool)),U_5972),hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(U_5971,hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),U_5972)) = U_5973
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5971,tc_HOL_Obool)),U_5972),hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5971),U_5972))
| ~ class_Lattices_Olattice(U_5971) ),
inference(variable_rename,[status(thm)],[f_1327_1]) ).
fof(f_1327_3,plain,
( ! [U_5971,U_5972,U_5973] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5971,hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),U_5972)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5971),U_5973),c_Big__Operators_Olattice__class_OInf__fin(U_5971,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5971,tc_HOL_Obool)),U_5972),hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5971,tc_HOL_Obool)),U_5972),hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool))
| ~ sP280(U_5971,U_5972,U_5973) )
& ! [U_5971,U_5972,U_5973] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5971,hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),U_5972)) = U_5973
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5971,tc_HOL_Obool)),U_5972),hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool))
| ~ sP280(U_5971,U_5972,U_5973) )
& ! [U_5971,U_5972,U_5973] :
( sP280(U_5971,U_5972,U_5973)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5971),U_5972))
| ~ class_Lattices_Olattice(U_5971) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP280])],[f_1327_2]) ).
cnf(f_1327_4,plain,
( sP280(U_5971,U_5972,U_5973)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5971),U_5972))
| ~ class_Lattices_Olattice(U_5971) ),
inference(clausify,[status(thm)],[f_1327_3]) ).
cnf(f_1327_5,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5971,hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),U_5972)) = U_5973
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5971,tc_HOL_Obool)),U_5972),hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool))
| ~ sP280(U_5971,U_5972,U_5973) ),
inference(clausify,[status(thm)],[f_1327_3]) ).
cnf(f_1327_6,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5971,hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),U_5972)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5971),U_5973),c_Big__Operators_Olattice__class_OInf__fin(U_5971,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5971,tc_HOL_Obool)),U_5972),hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5971,tc_HOL_Obool)),U_5972),hAPP(hAPP(c_Set_Oinsert(U_5971),U_5973),c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_5971,tc_HOL_Obool))
| ~ sP280(U_5971,U_5972,U_5973) ),
inference(clausify,[status(thm)],[f_1327_3]) ).
fof(f_1328_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_c,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(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__inter]) ).
fof(f_1328_2,plain,
! [U_5976,U_5975,U_5974] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5974),c_Big__Operators_Olattice__class_OInf__fin(U_5974,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5974,tc_HOL_Obool)),U_5975),U_5976))),c_Big__Operators_Olattice__class_OInf__fin(U_5974,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5974,tc_HOL_Obool)),U_5975),U_5976))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5974),c_Big__Operators_Olattice__class_OInf__fin(U_5974,U_5975)),c_Big__Operators_Olattice__class_OInf__fin(U_5974,U_5976))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5974,tc_HOL_Obool)),U_5975),U_5976) = c_Orderings_Obot__class_Obot(tc_fun(U_5974,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5974),U_5976))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5974),U_5975))
| ~ class_Lattices_Olattice(U_5974) ),
inference(variable_rename,[status(thm)],[f_1328_1]) ).
fof(f_1328_3,plain,
! [U_5976,U_5974,U_5975] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5974),c_Big__Operators_Olattice__class_OInf__fin(U_5974,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5974,tc_HOL_Obool)),U_5975),U_5976))),c_Big__Operators_Olattice__class_OInf__fin(U_5974,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5974,tc_HOL_Obool)),U_5975),U_5976))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5974),c_Big__Operators_Olattice__class_OInf__fin(U_5974,U_5975)),c_Big__Operators_Olattice__class_OInf__fin(U_5974,U_5976))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5974,tc_HOL_Obool)),U_5975),U_5976) = c_Orderings_Obot__class_Obot(tc_fun(U_5974,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5974),U_5976))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5974),U_5975))
| ~ class_Lattices_Olattice(U_5974) ),
inference(definitional_conversion,[status(esa)],[f_1328_2]) ).
cnf(f_1328_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5974),c_Big__Operators_Olattice__class_OInf__fin(U_5974,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5974,tc_HOL_Obool)),U_5975),U_5976))),c_Big__Operators_Olattice__class_OInf__fin(U_5974,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5974,tc_HOL_Obool)),U_5975),U_5976))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5974),c_Big__Operators_Olattice__class_OInf__fin(U_5974,U_5975)),c_Big__Operators_Olattice__class_OInf__fin(U_5974,U_5976))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5974,tc_HOL_Obool)),U_5975),U_5976) = c_Orderings_Obot__class_Obot(tc_fun(U_5974,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5974),U_5976))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5974),U_5975))
| ~ class_Lattices_Olattice(U_5974) ),
inference(clausify,[status(thm)],[f_1328_3]) ).
fof(f_1329_1,plain,
! [V_B_2,V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OInf__fin(T_c,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__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(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))
| 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))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__disjoint]) ).
fof(f_1329_2,plain,
! [U_5979,U_5978,U_5977] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5977,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5977,tc_HOL_Obool)),U_5978),U_5979)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5977),c_Big__Operators_Olattice__class_OInf__fin(U_5977,U_5978)),c_Big__Operators_Olattice__class_OInf__fin(U_5977,U_5979))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5977,tc_HOL_Obool)),U_5978),U_5979) != c_Orderings_Obot__class_Obot(tc_fun(U_5977,tc_HOL_Obool))
| U_5979 = c_Orderings_Obot__class_Obot(tc_fun(U_5977,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5977),U_5979))
| U_5978 = c_Orderings_Obot__class_Obot(tc_fun(U_5977,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5977),U_5978))
| ~ class_Lattices_Olattice(U_5977) ),
inference(variable_rename,[status(thm)],[f_1329_1]) ).
fof(f_1329_3,plain,
! [U_5978,U_5977,U_5979] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5977,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5977,tc_HOL_Obool)),U_5978),U_5979)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5977),c_Big__Operators_Olattice__class_OInf__fin(U_5977,U_5978)),c_Big__Operators_Olattice__class_OInf__fin(U_5977,U_5979))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5977,tc_HOL_Obool)),U_5978),U_5979) != c_Orderings_Obot__class_Obot(tc_fun(U_5977,tc_HOL_Obool))
| U_5979 = c_Orderings_Obot__class_Obot(tc_fun(U_5977,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5977),U_5979))
| U_5978 = c_Orderings_Obot__class_Obot(tc_fun(U_5977,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5977),U_5978))
| ~ class_Lattices_Olattice(U_5977) ),
inference(definitional_conversion,[status(esa)],[f_1329_2]) ).
cnf(f_1329_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5977,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5977,tc_HOL_Obool)),U_5978),U_5979)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5977),c_Big__Operators_Olattice__class_OInf__fin(U_5977,U_5978)),c_Big__Operators_Olattice__class_OInf__fin(U_5977,U_5979))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5977,tc_HOL_Obool)),U_5978),U_5979) != c_Orderings_Obot__class_Obot(tc_fun(U_5977,tc_HOL_Obool))
| U_5979 = c_Orderings_Obot__class_Obot(tc_fun(U_5977,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5977),U_5979))
| U_5978 = c_Orderings_Obot__class_Obot(tc_fun(U_5977,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5977),U_5978))
| ~ class_Lattices_Olattice(U_5977) ),
inference(clausify,[status(thm)],[f_1329_3]) ).
fof(f_1330_1,plain,
! [V_x_2,V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_x_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))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold_H]) ).
fof(f_1330_2,plain,
! [U_5982,U_5981,U_5980] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5980,hAPP(hAPP(c_Set_Oinsert(U_5980),U_5982),U_5981)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5980,U_5980,c_Lattices_Osemilattice__inf__class_Oinf(U_5980)),U_5982),U_5981)
| hBOOL(hAPP(hAPP(c_member(U_5980),U_5982),U_5981))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5980),U_5981))
| ~ class_Lattices_Olattice(U_5980) ),
inference(variable_rename,[status(thm)],[f_1330_1]) ).
fof(f_1330_3,plain,
! [U_5981,U_5980,U_5982] :
( c_Big__Operators_Olattice__class_OInf__fin(U_5980,hAPP(hAPP(c_Set_Oinsert(U_5980),U_5982),U_5981)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5980,U_5980,c_Lattices_Osemilattice__inf__class_Oinf(U_5980)),U_5982),U_5981)
| hBOOL(hAPP(hAPP(c_member(U_5980),U_5982),U_5981))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5980),U_5981))
| ~ class_Lattices_Olattice(U_5980) ),
inference(definitional_conversion,[status(esa)],[f_1330_2]) ).
cnf(f_1330_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_5980,hAPP(hAPP(c_Set_Oinsert(U_5980),U_5982),U_5981)) = hAPP(hAPP(c_Finite__Set_Ofold(U_5980,U_5980,c_Lattices_Osemilattice__inf__class_Oinf(U_5980)),U_5982),U_5981)
| hBOOL(hAPP(hAPP(c_member(U_5980),U_5982),U_5981))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5980),U_5981))
| ~ class_Lattices_Olattice(U_5980) ),
inference(clausify,[status(thm)],[f_1330_3]) ).
fof(f_1331_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_1331_2,plain,
! [U_5984,U_5983] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5983),hAPP(c_Nat_OSuc,U_5984)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5983),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5984),
inference(variable_rename,[status(thm)],[f_1331_1]) ).
fof(f_1331_3,plain,
! [U_5983,U_5984] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5983),hAPP(c_Nat_OSuc,U_5984)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5983),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5984),
inference(definitional_conversion,[status(esa)],[f_1331_2]) ).
cnf(f_1331_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5983),hAPP(c_Nat_OSuc,U_5984)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5983),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5984),
inference(clausify,[status(thm)],[f_1331_3]) ).
fof(f_1332_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_1332_2,plain,
! [U_5985] : hAPP(c_Nat_OSuc,U_5985) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5985),
inference(variable_rename,[status(thm)],[f_1332_1]) ).
fof(f_1332_3,plain,
! [U_5985] : hAPP(c_Nat_OSuc,U_5985) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5985),
inference(definitional_conversion,[status(esa)],[f_1332_2]) ).
cnf(f_1332_4,plain,
hAPP(c_Nat_OSuc,U_5985) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5985),
inference(clausify,[status(thm)],[f_1332_3]) ).
fof(f_1333_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_1333_2,plain,
! [U_5986] : hAPP(c_Nat_OSuc,U_5986) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5986),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_1333_1]) ).
fof(f_1333_3,plain,
! [U_5986] : hAPP(c_Nat_OSuc,U_5986) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5986),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_1333_2]) ).
cnf(f_1333_4,plain,
hAPP(c_Nat_OSuc,U_5986) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5986),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_1333_3]) ).
fof(f_1334_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),hAPP(hAPP(c_Set_Oinsert(T_c),B_y),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))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oclosed]) ).
fof(f_1334_2,plain,
! [U_5990,U_5989] :
( hBOOL(hAPP(hAPP(c_member(U_5989),c_Big__Operators_Olattice__class_OInf__fin(U_5989,U_5990)),U_5990))
| ? [U_5988,U_5987] : ~ hBOOL(hAPP(hAPP(c_member(U_5989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5989),U_5988),U_5987)),hAPP(hAPP(c_Set_Oinsert(U_5989),U_5988),hAPP(hAPP(c_Set_Oinsert(U_5989),U_5987),c_Orderings_Obot__class_Obot(tc_fun(U_5989,tc_HOL_Obool))))))
| U_5990 = c_Orderings_Obot__class_Obot(tc_fun(U_5989,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5989),U_5990))
| ~ class_Lattices_Olattice(U_5989) ),
inference(variable_rename,[status(thm)],[f_1334_1]) ).
fof(f_1334_3,plain,
! [U_5990,U_5989] :
( hBOOL(hAPP(hAPP(c_member(U_5989),c_Big__Operators_Olattice__class_OInf__fin(U_5989,U_5990)),U_5990))
| ? [U_5987] : ~ hBOOL(hAPP(hAPP(c_member(U_5989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5989),sK115(U_5990,U_5989)),U_5987)),hAPP(hAPP(c_Set_Oinsert(U_5989),sK115(U_5990,U_5989)),hAPP(hAPP(c_Set_Oinsert(U_5989),U_5987),c_Orderings_Obot__class_Obot(tc_fun(U_5989,tc_HOL_Obool))))))
| U_5990 = c_Orderings_Obot__class_Obot(tc_fun(U_5989,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5989),U_5990))
| ~ class_Lattices_Olattice(U_5989) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_5988,sK115(U_5990,U_5989))],[f_1334_2]) ).
fof(f_1334_4,plain,
! [U_5990,U_5989] :
( hBOOL(hAPP(hAPP(c_member(U_5989),c_Big__Operators_Olattice__class_OInf__fin(U_5989,U_5990)),U_5990))
| ~ hBOOL(hAPP(hAPP(c_member(U_5989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5989),sK115(U_5990,U_5989)),sK116(U_5990,U_5989))),hAPP(hAPP(c_Set_Oinsert(U_5989),sK115(U_5990,U_5989)),hAPP(hAPP(c_Set_Oinsert(U_5989),sK116(U_5990,U_5989)),c_Orderings_Obot__class_Obot(tc_fun(U_5989,tc_HOL_Obool))))))
| U_5990 = c_Orderings_Obot__class_Obot(tc_fun(U_5989,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5989),U_5990))
| ~ class_Lattices_Olattice(U_5989) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_5987,sK116(U_5990,U_5989))],[f_1334_3]) ).
fof(f_1334_5,plain,
! [U_5989,U_5990] :
( hBOOL(hAPP(hAPP(c_member(U_5989),c_Big__Operators_Olattice__class_OInf__fin(U_5989,U_5990)),U_5990))
| ~ hBOOL(hAPP(hAPP(c_member(U_5989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5989),sK115(U_5990,U_5989)),sK116(U_5990,U_5989))),hAPP(hAPP(c_Set_Oinsert(U_5989),sK115(U_5990,U_5989)),hAPP(hAPP(c_Set_Oinsert(U_5989),sK116(U_5990,U_5989)),c_Orderings_Obot__class_Obot(tc_fun(U_5989,tc_HOL_Obool))))))
| U_5990 = c_Orderings_Obot__class_Obot(tc_fun(U_5989,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5989),U_5990))
| ~ class_Lattices_Olattice(U_5989) ),
inference(definitional_conversion,[status(esa)],[f_1334_4]) ).
cnf(f_1334_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5989),c_Big__Operators_Olattice__class_OInf__fin(U_5989,U_5990)),U_5990))
| ~ hBOOL(hAPP(hAPP(c_member(U_5989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5989),sK115(U_5990,U_5989)),sK116(U_5990,U_5989))),hAPP(hAPP(c_Set_Oinsert(U_5989),sK115(U_5990,U_5989)),hAPP(hAPP(c_Set_Oinsert(U_5989),sK116(U_5990,U_5989)),c_Orderings_Obot__class_Obot(tc_fun(U_5989,tc_HOL_Obool))))))
| U_5990 = c_Orderings_Obot__class_Obot(tc_fun(U_5989,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5989),U_5990))
| ~ class_Lattices_Olattice(U_5989) ),
inference(clausify,[status(thm)],[f_1334_5]) ).
fof(f_1335_1,plain,
! [T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(T_d),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,T_d)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,T_d),tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1]) ).
fof(f_1335_2,plain,
! [U_5992,U_5991] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5991),c_Orderings_Otop__class_Otop(tc_fun(U_5991,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(U_5992),c_Orderings_Otop__class_Otop(tc_fun(U_5992,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_5991,U_5992)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_5991,U_5992),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_1335_1]) ).
fof(f_1335_3,plain,
! [U_5992,U_5991] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5991),c_Orderings_Otop__class_Otop(tc_fun(U_5991,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(U_5992),c_Orderings_Otop__class_Otop(tc_fun(U_5992,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_5991,U_5992)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_5991,U_5992),tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_1335_2]) ).
cnf(f_1335_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5991),c_Orderings_Otop__class_Otop(tc_fun(U_5991,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(U_5992),c_Orderings_Otop__class_Otop(tc_fun(U_5992,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_5991,U_5992)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_5991,U_5992),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_1335_3]) ).
fof(f_1336_1,plain,
! [V_N_2,V_h_2,T_c] :
( hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_c,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),B_x),B_y)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Lattices_Olattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute]) ).
fof(f_1336_2,plain,
! [U_5997,U_5996,U_5995] :
( hAPP(U_5996,c_Big__Operators_Olattice__class_OInf__fin(U_5995,U_5997)) = c_Big__Operators_Olattice__class_OInf__fin(U_5995,hAPP(c_Set_Oimage(U_5995,U_5995,U_5996),U_5997))
| U_5997 = c_Orderings_Obot__class_Obot(tc_fun(U_5995,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5995),U_5997))
| ? [U_5994,U_5993] : hAPP(U_5996,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5995),U_5994),U_5993)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5995),hAPP(U_5996,U_5994)),hAPP(U_5996,U_5993))
| ~ class_Lattices_Olattice(U_5995) ),
inference(variable_rename,[status(thm)],[f_1336_1]) ).
fof(f_1336_3,plain,
! [U_5997,U_5996,U_5995] :
( hAPP(U_5996,c_Big__Operators_Olattice__class_OInf__fin(U_5995,U_5997)) = c_Big__Operators_Olattice__class_OInf__fin(U_5995,hAPP(c_Set_Oimage(U_5995,U_5995,U_5996),U_5997))
| U_5997 = c_Orderings_Obot__class_Obot(tc_fun(U_5995,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5995),U_5997))
| ? [U_5993] : hAPP(U_5996,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5995),sK117(U_5997,U_5996,U_5995)),U_5993)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5995),hAPP(U_5996,sK117(U_5997,U_5996,U_5995))),hAPP(U_5996,U_5993))
| ~ class_Lattices_Olattice(U_5995) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_5994,sK117(U_5997,U_5996,U_5995))],[f_1336_2]) ).
fof(f_1336_4,plain,
! [U_5997,U_5996,U_5995] :
( hAPP(U_5996,c_Big__Operators_Olattice__class_OInf__fin(U_5995,U_5997)) = c_Big__Operators_Olattice__class_OInf__fin(U_5995,hAPP(c_Set_Oimage(U_5995,U_5995,U_5996),U_5997))
| U_5997 = c_Orderings_Obot__class_Obot(tc_fun(U_5995,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5995),U_5997))
| hAPP(U_5996,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5995),sK117(U_5997,U_5996,U_5995)),sK118(U_5997,U_5996,U_5995))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5995),hAPP(U_5996,sK117(U_5997,U_5996,U_5995))),hAPP(U_5996,sK118(U_5997,U_5996,U_5995)))
| ~ class_Lattices_Olattice(U_5995) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_5993,sK118(U_5997,U_5996,U_5995))],[f_1336_3]) ).
fof(f_1336_5,plain,
! [U_5995,U_5996,U_5997] :
( hAPP(U_5996,c_Big__Operators_Olattice__class_OInf__fin(U_5995,U_5997)) = c_Big__Operators_Olattice__class_OInf__fin(U_5995,hAPP(c_Set_Oimage(U_5995,U_5995,U_5996),U_5997))
| U_5997 = c_Orderings_Obot__class_Obot(tc_fun(U_5995,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5995),U_5997))
| hAPP(U_5996,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5995),sK117(U_5997,U_5996,U_5995)),sK118(U_5997,U_5996,U_5995))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5995),hAPP(U_5996,sK117(U_5997,U_5996,U_5995))),hAPP(U_5996,sK118(U_5997,U_5996,U_5995)))
| ~ class_Lattices_Olattice(U_5995) ),
inference(definitional_conversion,[status(esa)],[f_1336_4]) ).
cnf(f_1336_6,plain,
( hAPP(U_5996,c_Big__Operators_Olattice__class_OInf__fin(U_5995,U_5997)) = c_Big__Operators_Olattice__class_OInf__fin(U_5995,hAPP(c_Set_Oimage(U_5995,U_5995,U_5996),U_5997))
| U_5997 = c_Orderings_Obot__class_Obot(tc_fun(U_5995,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5995),U_5997))
| hAPP(U_5996,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5995),sK117(U_5997,U_5996,U_5995)),sK118(U_5997,U_5996,U_5995))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_5995),hAPP(U_5996,sK117(U_5997,U_5996,U_5995))),hAPP(U_5996,sK118(U_5997,U_5996,U_5995)))
| ~ class_Lattices_Olattice(U_5995) ),
inference(clausify,[status(thm)],[f_1336_5]) ).
fof(f_1337_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_1337_2,plain,
! [U_5998] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5998),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1337_1]) ).
fof(f_1337_3,plain,
! [U_5998] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5998),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_1337_2]) ).
cnf(f_1337_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5998),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1337_3]) ).
fof(f_1338_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_1338_2,plain,
! [U_5999] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5999)),
inference(variable_rename,[status(thm)],[f_1338_1]) ).
fof(f_1338_3,plain,
! [U_5999] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5999)),
inference(definitional_conversion,[status(esa)],[f_1338_2]) ).
cnf(f_1338_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5999)),
inference(clausify,[status(thm)],[f_1338_3]) ).
fof(f_1339_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_1339_2,plain,
! [U_6000] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_6000))),
inference(variable_rename,[status(thm)],[f_1339_1]) ).
fof(f_1339_3,plain,
! [U_6000] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_6000))),
inference(definitional_conversion,[status(esa)],[f_1339_2]) ).
cnf(f_1339_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_6000))),
inference(clausify,[status(thm)],[f_1339_3]) ).
fof(f_1340_1,plain,
! [V_S_2,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_c,tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_Inter__def]) ).
fof(f_1340_2,plain,
! [U_6002,U_6001] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_6001,tc_HOL_Obool),U_6002) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_6001,tc_HOL_Obool),tc_fun(U_6001,tc_HOL_Obool)),U_6002),c_COMBI(tc_fun(U_6001,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_1340_1]) ).
fof(f_1340_3,plain,
! [U_6001,U_6002] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_6001,tc_HOL_Obool),U_6002) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_6001,tc_HOL_Obool),tc_fun(U_6001,tc_HOL_Obool)),U_6002),c_COMBI(tc_fun(U_6001,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_1340_2]) ).
cnf(f_1340_4,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_6001,tc_HOL_Obool),U_6002) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_6001,tc_HOL_Obool),tc_fun(U_6001,tc_HOL_Obool)),U_6002),c_COMBI(tc_fun(U_6001,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_1340_3]) ).
fof(f_1341_1,plain,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_INTER__eq__Inter__image]) ).
fof(f_1341_2,plain,
! [U_6006,U_6005,U_6004,U_6003] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6003,tc_fun(U_6004,tc_HOL_Obool)),U_6005),U_6006) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_6004,tc_HOL_Obool),hAPP(c_Set_Oimage(U_6003,tc_fun(U_6004,tc_HOL_Obool),U_6006),U_6005)),
inference(variable_rename,[status(thm)],[f_1341_1]) ).
fof(f_1341_3,plain,
! [U_6003,U_6004,U_6005,U_6006] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6003,tc_fun(U_6004,tc_HOL_Obool)),U_6005),U_6006) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_6004,tc_HOL_Obool),hAPP(c_Set_Oimage(U_6003,tc_fun(U_6004,tc_HOL_Obool),U_6006),U_6005)),
inference(definitional_conversion,[status(esa)],[f_1341_2]) ).
cnf(f_1341_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6003,tc_fun(U_6004,tc_HOL_Obool)),U_6005),U_6006) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_6004,tc_HOL_Obool),hAPP(c_Set_Oimage(U_6003,tc_fun(U_6004,tc_HOL_Obool),U_6006),U_6005)),
inference(clausify,[status(thm)],[f_1341_3]) ).
fof(f_1342_1,plain,
! [V_A_2,V_B_2,T_d,T_c] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_A_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),
inference(fof_nnf,[status(thm)],[fact_Inter__image__eq]) ).
fof(f_1342_2,plain,
! [U_6010,U_6009,U_6008,U_6007] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_6007,tc_HOL_Obool),hAPP(c_Set_Oimage(U_6008,tc_fun(U_6007,tc_HOL_Obool),U_6009),U_6010)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6008,tc_fun(U_6007,tc_HOL_Obool)),U_6010),U_6009),
inference(variable_rename,[status(thm)],[f_1342_1]) ).
fof(f_1342_3,plain,
! [U_6007,U_6008,U_6009,U_6010] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_6007,tc_HOL_Obool),hAPP(c_Set_Oimage(U_6008,tc_fun(U_6007,tc_HOL_Obool),U_6009),U_6010)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6008,tc_fun(U_6007,tc_HOL_Obool)),U_6010),U_6009),
inference(definitional_conversion,[status(esa)],[f_1342_2]) ).
cnf(f_1342_4,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_6007,tc_HOL_Obool),hAPP(c_Set_Oimage(U_6008,tc_fun(U_6007,tc_HOL_Obool),U_6009),U_6010)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6008,tc_fun(U_6007,tc_HOL_Obool)),U_6010),U_6009),
inference(clausify,[status(thm)],[f_1342_3]) ).
fof(f_1343_1,plain,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_e,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF2__iff]) ).
fof(f_1343_2,plain,
! [U_6019,U_6018,U_6017,U_6016,U_6015,U_6014,U_6013] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6013,tc_fun(U_6014,tc_fun(U_6015,tc_HOL_Obool))),U_6016),U_6017),U_6018),U_6019))
| ? [U_6012] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_6017,U_6012),U_6018),U_6019))
& hBOOL(hAPP(hAPP(c_member(U_6013),U_6012),U_6016)) ) )
& ( ! [U_6011] :
( hBOOL(hAPP(hAPP(hAPP(U_6017,U_6011),U_6018),U_6019))
| ~ hBOOL(hAPP(hAPP(c_member(U_6013),U_6011),U_6016)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6013,tc_fun(U_6014,tc_fun(U_6015,tc_HOL_Obool))),U_6016),U_6017),U_6018),U_6019)) ) ),
inference(variable_rename,[status(thm)],[f_1343_1]) ).
fof(f_1343_3,plain,
( ! [U_6033,U_6031,U_6029,U_6027,U_6025,U_6023,U_6021] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6021,tc_fun(U_6023,tc_fun(U_6025,tc_HOL_Obool))),U_6027),U_6029),U_6031),U_6033))
| ? [U_6012] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_6029,U_6012),U_6031),U_6033))
& hBOOL(hAPP(hAPP(c_member(U_6021),U_6012),U_6027)) ) )
& ! [U_6032,U_6030,U_6028,U_6026,U_6024,U_6022,U_6020] :
( ! [U_6011] :
( hBOOL(hAPP(hAPP(hAPP(U_6028,U_6011),U_6030),U_6032))
| ~ hBOOL(hAPP(hAPP(c_member(U_6020),U_6011),U_6026)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6020,tc_fun(U_6022,tc_fun(U_6024,tc_HOL_Obool))),U_6026),U_6028),U_6030),U_6032)) ) ),
inference(miniscope,[status(thm)],[f_1343_2]) ).
fof(f_1343_4,plain,
( ! [U_6033,U_6031,U_6029,U_6027,U_6025,U_6023,U_6021] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6021,tc_fun(U_6023,tc_fun(U_6025,tc_HOL_Obool))),U_6027),U_6029),U_6031),U_6033))
| ( ~ hBOOL(hAPP(hAPP(hAPP(U_6029,sK119(U_6033,U_6031,U_6029,U_6027,U_6025,U_6023,U_6021)),U_6031),U_6033))
& hBOOL(hAPP(hAPP(c_member(U_6021),sK119(U_6033,U_6031,U_6029,U_6027,U_6025,U_6023,U_6021)),U_6027)) ) )
& ! [U_6032,U_6030,U_6028,U_6026,U_6024,U_6022,U_6020] :
( ! [U_6011] :
( hBOOL(hAPP(hAPP(hAPP(U_6028,U_6011),U_6030),U_6032))
| ~ hBOOL(hAPP(hAPP(c_member(U_6020),U_6011),U_6026)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6020,tc_fun(U_6022,tc_fun(U_6024,tc_HOL_Obool))),U_6026),U_6028),U_6030),U_6032)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_6012,sK119(U_6033,U_6031,U_6029,U_6027,U_6025,U_6023,U_6021))],[f_1343_3]) ).
fof(f_1343_5,plain,
( ! [U_6021,U_6023,U_6025,U_6027,U_6031,U_6029,U_6033] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_6029,sK119(U_6033,U_6031,U_6029,U_6027,U_6025,U_6023,U_6021)),U_6031),U_6033))
| ~ sP281(U_6021,U_6023,U_6025,U_6027,U_6031,U_6029,U_6033) )
& ! [U_6021,U_6023,U_6025,U_6027,U_6031,U_6029,U_6033] :
( hBOOL(hAPP(hAPP(c_member(U_6021),sK119(U_6033,U_6031,U_6029,U_6027,U_6025,U_6023,U_6021)),U_6027))
| ~ sP281(U_6021,U_6023,U_6025,U_6027,U_6031,U_6029,U_6033) )
& ! [U_6021,U_6023,U_6025,U_6027,U_6031,U_6029,U_6033] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6021,tc_fun(U_6023,tc_fun(U_6025,tc_HOL_Obool))),U_6027),U_6029),U_6031),U_6033))
| sP281(U_6021,U_6023,U_6025,U_6027,U_6031,U_6029,U_6033) )
& ! [U_6022,U_6011,U_6020,U_6024,U_6028,U_6032,U_6026,U_6030] :
( hBOOL(hAPP(hAPP(hAPP(U_6028,U_6011),U_6030),U_6032))
| ~ hBOOL(hAPP(hAPP(c_member(U_6020),U_6011),U_6026))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6020,tc_fun(U_6022,tc_fun(U_6024,tc_HOL_Obool))),U_6026),U_6028),U_6030),U_6032)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP281])],[f_1343_4]) ).
cnf(f_1343_6,plain,
( hBOOL(hAPP(hAPP(hAPP(U_6028,U_6011),U_6030),U_6032))
| ~ hBOOL(hAPP(hAPP(c_member(U_6020),U_6011),U_6026))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6020,tc_fun(U_6022,tc_fun(U_6024,tc_HOL_Obool))),U_6026),U_6028),U_6030),U_6032)) ),
inference(clausify,[status(thm)],[f_1343_5]) ).
cnf(f_1343_7,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6021,tc_fun(U_6023,tc_fun(U_6025,tc_HOL_Obool))),U_6027),U_6029),U_6031),U_6033))
| sP281(U_6021,U_6023,U_6025,U_6027,U_6031,U_6029,U_6033) ),
inference(clausify,[status(thm)],[f_1343_5]) ).
cnf(f_1343_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_6021),sK119(U_6033,U_6031,U_6029,U_6027,U_6025,U_6023,U_6021)),U_6027))
| ~ sP281(U_6021,U_6023,U_6025,U_6027,U_6031,U_6029,U_6033) ),
inference(clausify,[status(thm)],[f_1343_5]) ).
cnf(f_1343_9,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(U_6029,sK119(U_6033,U_6031,U_6029,U_6027,U_6025,U_6023,U_6021)),U_6031),U_6033))
| ~ sP281(U_6021,U_6023,U_6025,U_6027,U_6031,U_6029,U_6033) ),
inference(clausify,[status(thm)],[f_1343_5]) ).
fof(f_1344_1,plain,
! [V_b_2,V_B_2,V_A_2,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,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_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF1__iff]) ).
fof(f_1344_2,plain,
! [U_6040,U_6039,U_6038,U_6037,U_6036] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6036,tc_fun(U_6037,tc_HOL_Obool)),U_6038),U_6039),U_6040))
| ? [U_6035] :
( ~ hBOOL(hAPP(hAPP(U_6039,U_6035),U_6040))
& hBOOL(hAPP(hAPP(c_member(U_6036),U_6035),U_6038)) ) )
& ( ! [U_6034] :
( hBOOL(hAPP(hAPP(U_6039,U_6034),U_6040))
| ~ hBOOL(hAPP(hAPP(c_member(U_6036),U_6034),U_6038)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6036,tc_fun(U_6037,tc_HOL_Obool)),U_6038),U_6039),U_6040)) ) ),
inference(variable_rename,[status(thm)],[f_1344_1]) ).
fof(f_1344_3,plain,
( ! [U_6050,U_6048,U_6046,U_6044,U_6042] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6042,tc_fun(U_6044,tc_HOL_Obool)),U_6046),U_6048),U_6050))
| ? [U_6035] :
( ~ hBOOL(hAPP(hAPP(U_6048,U_6035),U_6050))
& hBOOL(hAPP(hAPP(c_member(U_6042),U_6035),U_6046)) ) )
& ! [U_6049,U_6047,U_6045,U_6043,U_6041] :
( ! [U_6034] :
( hBOOL(hAPP(hAPP(U_6047,U_6034),U_6049))
| ~ hBOOL(hAPP(hAPP(c_member(U_6041),U_6034),U_6045)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6041,tc_fun(U_6043,tc_HOL_Obool)),U_6045),U_6047),U_6049)) ) ),
inference(miniscope,[status(thm)],[f_1344_2]) ).
fof(f_1344_4,plain,
( ! [U_6050,U_6048,U_6046,U_6044,U_6042] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6042,tc_fun(U_6044,tc_HOL_Obool)),U_6046),U_6048),U_6050))
| ( ~ hBOOL(hAPP(hAPP(U_6048,sK120(U_6050,U_6048,U_6046,U_6044,U_6042)),U_6050))
& hBOOL(hAPP(hAPP(c_member(U_6042),sK120(U_6050,U_6048,U_6046,U_6044,U_6042)),U_6046)) ) )
& ! [U_6049,U_6047,U_6045,U_6043,U_6041] :
( ! [U_6034] :
( hBOOL(hAPP(hAPP(U_6047,U_6034),U_6049))
| ~ hBOOL(hAPP(hAPP(c_member(U_6041),U_6034),U_6045)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6041,tc_fun(U_6043,tc_HOL_Obool)),U_6045),U_6047),U_6049)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_6035,sK120(U_6050,U_6048,U_6046,U_6044,U_6042))],[f_1344_3]) ).
fof(f_1344_5,plain,
( ! [U_6046,U_6042,U_6044,U_6048,U_6050] :
( ~ hBOOL(hAPP(hAPP(U_6048,sK120(U_6050,U_6048,U_6046,U_6044,U_6042)),U_6050))
| ~ sP282(U_6046,U_6042,U_6044,U_6048,U_6050) )
& ! [U_6046,U_6042,U_6044,U_6048,U_6050] :
( hBOOL(hAPP(hAPP(c_member(U_6042),sK120(U_6050,U_6048,U_6046,U_6044,U_6042)),U_6046))
| ~ sP282(U_6046,U_6042,U_6044,U_6048,U_6050) )
& ! [U_6046,U_6042,U_6044,U_6048,U_6050] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6042,tc_fun(U_6044,tc_HOL_Obool)),U_6046),U_6048),U_6050))
| sP282(U_6046,U_6042,U_6044,U_6048,U_6050) )
& ! [U_6034,U_6043,U_6047,U_6041,U_6045,U_6049] :
( hBOOL(hAPP(hAPP(U_6047,U_6034),U_6049))
| ~ hBOOL(hAPP(hAPP(c_member(U_6041),U_6034),U_6045))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6041,tc_fun(U_6043,tc_HOL_Obool)),U_6045),U_6047),U_6049)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP282])],[f_1344_4]) ).
cnf(f_1344_6,plain,
( hBOOL(hAPP(hAPP(U_6047,U_6034),U_6049))
| ~ hBOOL(hAPP(hAPP(c_member(U_6041),U_6034),U_6045))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6041,tc_fun(U_6043,tc_HOL_Obool)),U_6045),U_6047),U_6049)) ),
inference(clausify,[status(thm)],[f_1344_5]) ).
cnf(f_1344_7,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6042,tc_fun(U_6044,tc_HOL_Obool)),U_6046),U_6048),U_6050))
| sP282(U_6046,U_6042,U_6044,U_6048,U_6050) ),
inference(clausify,[status(thm)],[f_1344_5]) ).
cnf(f_1344_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_6042),sK120(U_6050,U_6048,U_6046,U_6044,U_6042)),U_6046))
| ~ sP282(U_6046,U_6042,U_6044,U_6048,U_6050) ),
inference(clausify,[status(thm)],[f_1344_5]) ).
cnf(f_1344_9,plain,
( ~ hBOOL(hAPP(hAPP(U_6048,sK120(U_6050,U_6048,U_6046,U_6044,U_6042)),U_6050))
| ~ sP282(U_6046,U_6042,U_6044,U_6048,U_6050) ),
inference(clausify,[status(thm)],[f_1344_5]) ).
fof(f_1345_1,plain,
! [V_x_2,T_c] :
( ( ( c_Groups_Ozero__class_Ozero(T_c) = V_x_2
| V_x_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_c)
| c_Groups_Ozero__class_Ozero(T_c) != V_x_2 ) )
| ~ class_Groups_Ozero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_zero__reorient]) ).
fof(f_1345_2,plain,
! [U_6052,U_6051] :
( ( ( c_Groups_Ozero__class_Ozero(U_6051) = U_6052
| U_6052 != c_Groups_Ozero__class_Ozero(U_6051) )
& ( U_6052 = c_Groups_Ozero__class_Ozero(U_6051)
| c_Groups_Ozero__class_Ozero(U_6051) != U_6052 ) )
| ~ class_Groups_Ozero(U_6051) ),
inference(variable_rename,[status(thm)],[f_1345_1]) ).
fof(f_1345_3,plain,
( ! [U_6051,U_6052] :
( c_Groups_Ozero__class_Ozero(U_6051) = U_6052
| U_6052 != c_Groups_Ozero__class_Ozero(U_6051)
| ~ sP283(U_6051,U_6052) )
& ! [U_6051,U_6052] :
( U_6052 = c_Groups_Ozero__class_Ozero(U_6051)
| c_Groups_Ozero__class_Ozero(U_6051) != U_6052
| ~ sP283(U_6051,U_6052) )
& ! [U_6051,U_6052] :
( sP283(U_6051,U_6052)
| ~ class_Groups_Ozero(U_6051) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP283])],[f_1345_2]) ).
cnf(f_1345_4,plain,
( sP283(U_6051,U_6052)
| ~ class_Groups_Ozero(U_6051) ),
inference(clausify,[status(thm)],[f_1345_3]) ).
cnf(f_1345_5,plain,
( U_6052 = c_Groups_Ozero__class_Ozero(U_6051)
| c_Groups_Ozero__class_Ozero(U_6051) != U_6052
| ~ sP283(U_6051,U_6052) ),
inference(clausify,[status(thm)],[f_1345_3]) ).
cnf(f_1345_6,plain,
( c_Groups_Ozero__class_Ozero(U_6051) = U_6052
| U_6052 != c_Groups_Ozero__class_Ozero(U_6051)
| ~ sP283(U_6051,U_6052) ),
inference(clausify,[status(thm)],[f_1345_3]) ).
fof(f_1346_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_1346_2,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1346_1]) ).
cnf(f_1346_3,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1346_2]) ).
fof(f_1347_1,plain,
! [V_n_2,V_a_2,T_c] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_c) )
| hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_n_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ class_Rings_Ozero__neq__one(T_c)
| ~ class_Rings_Ono__zero__divisors(T_c)
| ~ class_Rings_Omult__zero(T_c)
| ~ class_Power_Opower(T_c) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff]) ).
fof(f_1347_2,plain,
! [U_6055,U_6054,U_6053] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6053),U_6054),U_6055) = c_Groups_Ozero__class_Ozero(U_6053)
| U_6055 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6054 != c_Groups_Ozero__class_Ozero(U_6053) )
& ( ( U_6055 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6054 = c_Groups_Ozero__class_Ozero(U_6053) )
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6053),U_6054),U_6055) != c_Groups_Ozero__class_Ozero(U_6053) ) )
| ~ class_Rings_Ozero__neq__one(U_6053)
| ~ class_Rings_Ono__zero__divisors(U_6053)
| ~ class_Rings_Omult__zero(U_6053)
| ~ class_Power_Opower(U_6053) ),
inference(variable_rename,[status(thm)],[f_1347_1]) ).
fof(f_1347_3,plain,
( ! [U_6053,U_6054,U_6055] :
( U_6055 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP284(U_6053,U_6054,U_6055) )
& ! [U_6053,U_6054,U_6055] :
( U_6054 = c_Groups_Ozero__class_Ozero(U_6053)
| ~ sP284(U_6053,U_6054,U_6055) )
& ! [U_6053,U_6054,U_6055] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6053),U_6054),U_6055) = c_Groups_Ozero__class_Ozero(U_6053)
| U_6055 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6054 != c_Groups_Ozero__class_Ozero(U_6053)
| ~ sP285(U_6053,U_6054,U_6055) )
& ! [U_6053,U_6054,U_6055] :
( sP284(U_6053,U_6054,U_6055)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6053),U_6054),U_6055) != c_Groups_Ozero__class_Ozero(U_6053)
| ~ sP285(U_6053,U_6054,U_6055) )
& ! [U_6053,U_6054,U_6055] :
( sP285(U_6053,U_6054,U_6055)
| ~ class_Rings_Ozero__neq__one(U_6053)
| ~ class_Rings_Ono__zero__divisors(U_6053)
| ~ class_Rings_Omult__zero(U_6053)
| ~ class_Power_Opower(U_6053) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP284,sP285])],[f_1347_2]) ).
cnf(f_1347_4,plain,
( sP285(U_6053,U_6054,U_6055)
| ~ class_Rings_Ozero__neq__one(U_6053)
| ~ class_Rings_Ono__zero__divisors(U_6053)
| ~ class_Rings_Omult__zero(U_6053)
| ~ class_Power_Opower(U_6053) ),
inference(clausify,[status(thm)],[f_1347_3]) ).
cnf(f_1347_5,plain,
( sP284(U_6053,U_6054,U_6055)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6053),U_6054),U_6055) != c_Groups_Ozero__class_Ozero(U_6053)
| ~ sP285(U_6053,U_6054,U_6055) ),
inference(clausify,[status(thm)],[f_1347_3]) ).
cnf(f_1347_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6053),U_6054),U_6055) = c_Groups_Ozero__class_Ozero(U_6053)
| U_6055 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6054 != c_Groups_Ozero__class_Ozero(U_6053)
| ~ sP285(U_6053,U_6054,U_6055) ),
inference(clausify,[status(thm)],[f_1347_3]) ).
cnf(f_1347_7,plain,
( U_6054 = c_Groups_Ozero__class_Ozero(U_6053)
| ~ sP284(U_6053,U_6054,U_6055) ),
inference(clausify,[status(thm)],[f_1347_3]) ).
cnf(f_1347_8,plain,
( U_6055 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP284(U_6053,U_6054,U_6055) ),
inference(clausify,[status(thm)],[f_1347_3]) ).
fof(f_1348_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_1348_2,plain,
! [U_6057,U_6056] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6056),c_Groups_Ozero__class_Ozero(U_6056)),U_6057) = c_Groups_Ozero__class_Ozero(U_6056)
| U_6057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6056),c_Groups_Ozero__class_Ozero(U_6056)),U_6057) = c_Groups_Oone__class_Oone(U_6056)
| U_6057 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_6056)
| ~ class_Power_Opower(U_6056) ),
inference(variable_rename,[status(thm)],[f_1348_1]) ).
fof(f_1348_3,plain,
( ! [U_6057,U_6056] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6056),c_Groups_Ozero__class_Ozero(U_6056)),U_6057) = c_Groups_Ozero__class_Ozero(U_6056)
| U_6057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP286(U_6057,U_6056) )
& ! [U_6057,U_6056] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6056),c_Groups_Ozero__class_Ozero(U_6056)),U_6057) = c_Groups_Oone__class_Oone(U_6056)
| U_6057 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP286(U_6057,U_6056) )
& ! [U_6057,U_6056] :
( sP286(U_6057,U_6056)
| ~ class_Rings_Osemiring__0(U_6056)
| ~ class_Power_Opower(U_6056) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP286])],[f_1348_2]) ).
cnf(f_1348_4,plain,
( sP286(U_6057,U_6056)
| ~ class_Rings_Osemiring__0(U_6056)
| ~ class_Power_Opower(U_6056) ),
inference(clausify,[status(thm)],[f_1348_3]) ).
cnf(f_1348_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6056),c_Groups_Ozero__class_Ozero(U_6056)),U_6057) = c_Groups_Oone__class_Oone(U_6056)
| U_6057 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP286(U_6057,U_6056) ),
inference(clausify,[status(thm)],[f_1348_3]) ).
cnf(f_1348_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6056),c_Groups_Ozero__class_Ozero(U_6056)),U_6057) = c_Groups_Ozero__class_Ozero(U_6056)
| U_6057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP286(U_6057,U_6056) ),
inference(clausify,[status(thm)],[f_1348_3]) ).
fof(f_1349_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_1349_2,plain,
! [U_6059,U_6058] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6058),c_Groups_Ozero__class_Ozero(U_6058)),U_6059) = U_6059
| ~ class_Groups_Omonoid__add(U_6058) ),
inference(variable_rename,[status(thm)],[f_1349_1]) ).
fof(f_1349_3,plain,
! [U_6059,U_6058] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6058),c_Groups_Ozero__class_Ozero(U_6058)),U_6059) = U_6059
| ~ class_Groups_Omonoid__add(U_6058) ),
inference(definitional_conversion,[status(esa)],[f_1349_2]) ).
cnf(f_1349_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6058),c_Groups_Ozero__class_Ozero(U_6058)),U_6059) = U_6059
| ~ class_Groups_Omonoid__add(U_6058) ),
inference(clausify,[status(thm)],[f_1349_3]) ).
fof(f_1350_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_1350_2,plain,
! [U_6061,U_6060] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6060),c_Groups_Ozero__class_Ozero(U_6060)),U_6061) = U_6061
| ~ class_Groups_Ocomm__monoid__add(U_6060) ),
inference(variable_rename,[status(thm)],[f_1350_1]) ).
fof(f_1350_3,plain,
! [U_6061,U_6060] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6060),c_Groups_Ozero__class_Ozero(U_6060)),U_6061) = U_6061
| ~ class_Groups_Ocomm__monoid__add(U_6060) ),
inference(definitional_conversion,[status(esa)],[f_1350_2]) ).
cnf(f_1350_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6060),c_Groups_Ozero__class_Ozero(U_6060)),U_6061) = U_6061
| ~ class_Groups_Ocomm__monoid__add(U_6060) ),
inference(clausify,[status(thm)],[f_1350_3]) ).
fof(f_1351_1,plain,
! [V_a_2,T_c] :
( ( ( c_Groups_Ozero__class_Ozero(T_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| c_Groups_Ozero__class_Ozero(T_c) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_double__zero__sym]) ).
fof(f_1351_2,plain,
! [U_6063,U_6062] :
( ( ( c_Groups_Ozero__class_Ozero(U_6062) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6062),U_6063),U_6063)
| U_6063 != c_Groups_Ozero__class_Ozero(U_6062) )
& ( U_6063 = c_Groups_Ozero__class_Ozero(U_6062)
| c_Groups_Ozero__class_Ozero(U_6062) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6062),U_6063),U_6063) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_6062) ),
inference(variable_rename,[status(thm)],[f_1351_1]) ).
fof(f_1351_3,plain,
( ! [U_6062,U_6063] :
( c_Groups_Ozero__class_Ozero(U_6062) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6062),U_6063),U_6063)
| U_6063 != c_Groups_Ozero__class_Ozero(U_6062)
| ~ sP287(U_6062,U_6063) )
& ! [U_6062,U_6063] :
( U_6063 = c_Groups_Ozero__class_Ozero(U_6062)
| c_Groups_Ozero__class_Ozero(U_6062) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6062),U_6063),U_6063)
| ~ sP287(U_6062,U_6063) )
& ! [U_6062,U_6063] :
( sP287(U_6062,U_6063)
| ~ class_Groups_Olinordered__ab__group__add(U_6062) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP287])],[f_1351_2]) ).
cnf(f_1351_4,plain,
( sP287(U_6062,U_6063)
| ~ class_Groups_Olinordered__ab__group__add(U_6062) ),
inference(clausify,[status(thm)],[f_1351_3]) ).
cnf(f_1351_5,plain,
( U_6063 = c_Groups_Ozero__class_Ozero(U_6062)
| c_Groups_Ozero__class_Ozero(U_6062) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6062),U_6063),U_6063)
| ~ sP287(U_6062,U_6063) ),
inference(clausify,[status(thm)],[f_1351_3]) ).
cnf(f_1351_6,plain,
( c_Groups_Ozero__class_Ozero(U_6062) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6062),U_6063),U_6063)
| U_6063 != c_Groups_Ozero__class_Ozero(U_6062)
| ~ sP287(U_6062,U_6063) ),
inference(clausify,[status(thm)],[f_1351_3]) ).
fof(f_1352_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_1352_2,plain,
! [U_6065,U_6064] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6064),U_6065),c_Groups_Ozero__class_Ozero(U_6064)) = U_6065
| ~ class_Groups_Omonoid__add(U_6064) ),
inference(variable_rename,[status(thm)],[f_1352_1]) ).
fof(f_1352_3,plain,
! [U_6065,U_6064] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6064),U_6065),c_Groups_Ozero__class_Ozero(U_6064)) = U_6065
| ~ class_Groups_Omonoid__add(U_6064) ),
inference(definitional_conversion,[status(esa)],[f_1352_2]) ).
cnf(f_1352_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6064),U_6065),c_Groups_Ozero__class_Ozero(U_6064)) = U_6065
| ~ class_Groups_Omonoid__add(U_6064) ),
inference(clausify,[status(thm)],[f_1352_3]) ).
fof(f_1353_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_1353_2,plain,
! [U_6067,U_6066] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6066),U_6067),c_Groups_Ozero__class_Ozero(U_6066)) = U_6067
| ~ class_Groups_Ocomm__monoid__add(U_6066) ),
inference(variable_rename,[status(thm)],[f_1353_1]) ).
fof(f_1353_3,plain,
! [U_6066,U_6067] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6066),U_6067),c_Groups_Ozero__class_Ozero(U_6066)) = U_6067
| ~ class_Groups_Ocomm__monoid__add(U_6066) ),
inference(definitional_conversion,[status(esa)],[f_1353_2]) ).
cnf(f_1353_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6066),U_6067),c_Groups_Ozero__class_Ozero(U_6066)) = U_6067
| ~ class_Groups_Ocomm__monoid__add(U_6066) ),
inference(clausify,[status(thm)],[f_1353_3]) ).
fof(f_1354_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_1354_2,plain,
! [U_6069,U_6068] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6068),c_Groups_Ozero__class_Ozero(U_6068)),U_6069) = U_6069
| ~ class_Rings_Ocomm__semiring__1(U_6068) ),
inference(variable_rename,[status(thm)],[f_1354_1]) ).
fof(f_1354_3,plain,
! [U_6068,U_6069] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6068),c_Groups_Ozero__class_Ozero(U_6068)),U_6069) = U_6069
| ~ class_Rings_Ocomm__semiring__1(U_6068) ),
inference(definitional_conversion,[status(esa)],[f_1354_2]) ).
cnf(f_1354_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6068),c_Groups_Ozero__class_Ozero(U_6068)),U_6069) = U_6069
| ~ class_Rings_Ocomm__semiring__1(U_6068) ),
inference(clausify,[status(thm)],[f_1354_3]) ).
fof(f_1355_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_1355_2,plain,
! [U_6071,U_6070] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6070),U_6071),c_Groups_Ozero__class_Ozero(U_6070)) = U_6071
| ~ class_Rings_Ocomm__semiring__1(U_6070) ),
inference(variable_rename,[status(thm)],[f_1355_1]) ).
fof(f_1355_3,plain,
! [U_6070,U_6071] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6070),U_6071),c_Groups_Ozero__class_Ozero(U_6070)) = U_6071
| ~ class_Rings_Ocomm__semiring__1(U_6070) ),
inference(definitional_conversion,[status(esa)],[f_1355_2]) ).
cnf(f_1355_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6070),U_6071),c_Groups_Ozero__class_Ozero(U_6070)) = U_6071
| ~ class_Rings_Ocomm__semiring__1(U_6070) ),
inference(clausify,[status(thm)],[f_1355_3]) ).
fof(f_1356_1,plain,
! [V_a_2,V_b_2,T_c] :
( ( ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| V_b_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_b_2),V_a_2) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_c) ),
inference(fof_nnf,[status(thm)],[fact_add__0__iff]) ).
fof(f_1356_2,plain,
! [U_6074,U_6073,U_6072] :
( ( ( U_6073 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6072),U_6073),U_6074)
| U_6074 != c_Groups_Ozero__class_Ozero(U_6072) )
& ( U_6074 = c_Groups_Ozero__class_Ozero(U_6072)
| U_6073 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6072),U_6073),U_6074) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_6072) ),
inference(variable_rename,[status(thm)],[f_1356_1]) ).
fof(f_1356_3,plain,
( ! [U_6072,U_6073,U_6074] :
( U_6073 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6072),U_6073),U_6074)
| U_6074 != c_Groups_Ozero__class_Ozero(U_6072)
| ~ sP288(U_6072,U_6073,U_6074) )
& ! [U_6072,U_6073,U_6074] :
( U_6074 = c_Groups_Ozero__class_Ozero(U_6072)
| U_6073 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6072),U_6073),U_6074)
| ~ sP288(U_6072,U_6073,U_6074) )
& ! [U_6072,U_6073,U_6074] :
( sP288(U_6072,U_6073,U_6074)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_6072) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP288])],[f_1356_2]) ).
cnf(f_1356_4,plain,
( sP288(U_6072,U_6073,U_6074)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_6072) ),
inference(clausify,[status(thm)],[f_1356_3]) ).
cnf(f_1356_5,plain,
( U_6074 = c_Groups_Ozero__class_Ozero(U_6072)
| U_6073 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6072),U_6073),U_6074)
| ~ sP288(U_6072,U_6073,U_6074) ),
inference(clausify,[status(thm)],[f_1356_3]) ).
cnf(f_1356_6,plain,
( U_6073 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6072),U_6073),U_6074)
| U_6074 != c_Groups_Ozero__class_Ozero(U_6072)
| ~ sP288(U_6072,U_6073,U_6074) ),
inference(clausify,[status(thm)],[f_1356_3]) ).
fof(f_1357_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_1357_2,plain,
! [U_6076,U_6075] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6075),c_Groups_Ozero__class_Ozero(U_6075)),U_6076) = c_Groups_Ozero__class_Ozero(U_6075)
| ~ class_Rings_Omult__zero(U_6075) ),
inference(variable_rename,[status(thm)],[f_1357_1]) ).
fof(f_1357_3,plain,
! [U_6076,U_6075] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6075),c_Groups_Ozero__class_Ozero(U_6075)),U_6076) = c_Groups_Ozero__class_Ozero(U_6075)
| ~ class_Rings_Omult__zero(U_6075) ),
inference(definitional_conversion,[status(esa)],[f_1357_2]) ).
cnf(f_1357_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6075),c_Groups_Ozero__class_Ozero(U_6075)),U_6076) = c_Groups_Ozero__class_Ozero(U_6075)
| ~ class_Rings_Omult__zero(U_6075) ),
inference(clausify,[status(thm)],[f_1357_3]) ).
fof(f_1358_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_1358_2,plain,
! [U_6078,U_6077] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6077),c_Groups_Ozero__class_Ozero(U_6077)),U_6078) = c_Groups_Ozero__class_Ozero(U_6077)
| ~ class_Rings_Ocomm__semiring__1(U_6077) ),
inference(variable_rename,[status(thm)],[f_1358_1]) ).
fof(f_1358_3,plain,
! [U_6077,U_6078] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6077),c_Groups_Ozero__class_Ozero(U_6077)),U_6078) = c_Groups_Ozero__class_Ozero(U_6077)
| ~ class_Rings_Ocomm__semiring__1(U_6077) ),
inference(definitional_conversion,[status(esa)],[f_1358_2]) ).
cnf(f_1358_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6077),c_Groups_Ozero__class_Ozero(U_6077)),U_6078) = c_Groups_Ozero__class_Ozero(U_6077)
| ~ class_Rings_Ocomm__semiring__1(U_6077) ),
inference(clausify,[status(thm)],[f_1358_3]) ).
fof(f_1359_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_1359_2,plain,
! [U_6080,U_6079] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6079),U_6080),c_Groups_Ozero__class_Ozero(U_6079)) = c_Groups_Ozero__class_Ozero(U_6079)
| ~ class_Rings_Omult__zero(U_6079) ),
inference(variable_rename,[status(thm)],[f_1359_1]) ).
fof(f_1359_3,plain,
! [U_6079,U_6080] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6079),U_6080),c_Groups_Ozero__class_Ozero(U_6079)) = c_Groups_Ozero__class_Ozero(U_6079)
| ~ class_Rings_Omult__zero(U_6079) ),
inference(definitional_conversion,[status(esa)],[f_1359_2]) ).
cnf(f_1359_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6079),U_6080),c_Groups_Ozero__class_Ozero(U_6079)) = c_Groups_Ozero__class_Ozero(U_6079)
| ~ class_Rings_Omult__zero(U_6079) ),
inference(clausify,[status(thm)],[f_1359_3]) ).
fof(f_1360_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_1360_2,plain,
! [U_6082,U_6081] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6081),U_6082),c_Groups_Ozero__class_Ozero(U_6081)) = c_Groups_Ozero__class_Ozero(U_6081)
| ~ class_Rings_Ocomm__semiring__1(U_6081) ),
inference(variable_rename,[status(thm)],[f_1360_1]) ).
fof(f_1360_3,plain,
! [U_6081,U_6082] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6081),U_6082),c_Groups_Ozero__class_Ozero(U_6081)) = c_Groups_Ozero__class_Ozero(U_6081)
| ~ class_Rings_Ocomm__semiring__1(U_6081) ),
inference(definitional_conversion,[status(esa)],[f_1360_2]) ).
cnf(f_1360_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6081),U_6082),c_Groups_Ozero__class_Ozero(U_6081)) = c_Groups_Ozero__class_Ozero(U_6081)
| ~ class_Rings_Ocomm__semiring__1(U_6081) ),
inference(clausify,[status(thm)],[f_1360_3]) ).
fof(f_1361_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_c)
| ( V_b_2 != c_Groups_Ozero__class_Ozero(T_c)
& V_a_2 != c_Groups_Ozero__class_Ozero(T_c) ) )
& ( V_b_2 = c_Groups_Ozero__class_Ozero(T_c)
| V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ class_Rings_Oring__no__zero__divisors(T_c) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff]) ).
fof(f_1361_2,plain,
! [U_6085,U_6084,U_6083] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6083),U_6084),U_6085) = c_Groups_Ozero__class_Ozero(U_6083)
| ( U_6085 != c_Groups_Ozero__class_Ozero(U_6083)
& U_6084 != c_Groups_Ozero__class_Ozero(U_6083) ) )
& ( U_6085 = c_Groups_Ozero__class_Ozero(U_6083)
| U_6084 = c_Groups_Ozero__class_Ozero(U_6083)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6083),U_6084),U_6085) != c_Groups_Ozero__class_Ozero(U_6083) ) )
| ~ class_Rings_Oring__no__zero__divisors(U_6083) ),
inference(variable_rename,[status(thm)],[f_1361_1]) ).
fof(f_1361_3,plain,
( ! [U_6083,U_6084,U_6085] :
( U_6085 != c_Groups_Ozero__class_Ozero(U_6083)
| ~ sP289(U_6083,U_6084,U_6085) )
& ! [U_6083,U_6084,U_6085] :
( U_6084 != c_Groups_Ozero__class_Ozero(U_6083)
| ~ sP289(U_6083,U_6084,U_6085) )
& ! [U_6083,U_6084,U_6085] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6083),U_6084),U_6085) = c_Groups_Ozero__class_Ozero(U_6083)
| sP289(U_6083,U_6084,U_6085)
| ~ sP290(U_6083,U_6084,U_6085) )
& ! [U_6083,U_6084,U_6085] :
( U_6085 = c_Groups_Ozero__class_Ozero(U_6083)
| U_6084 = c_Groups_Ozero__class_Ozero(U_6083)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6083),U_6084),U_6085) != c_Groups_Ozero__class_Ozero(U_6083)
| ~ sP290(U_6083,U_6084,U_6085) )
& ! [U_6083,U_6084,U_6085] :
( sP290(U_6083,U_6084,U_6085)
| ~ class_Rings_Oring__no__zero__divisors(U_6083) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP289,sP290])],[f_1361_2]) ).
cnf(f_1361_4,plain,
( sP290(U_6083,U_6084,U_6085)
| ~ class_Rings_Oring__no__zero__divisors(U_6083) ),
inference(clausify,[status(thm)],[f_1361_3]) ).
cnf(f_1361_5,plain,
( U_6085 = c_Groups_Ozero__class_Ozero(U_6083)
| U_6084 = c_Groups_Ozero__class_Ozero(U_6083)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6083),U_6084),U_6085) != c_Groups_Ozero__class_Ozero(U_6083)
| ~ sP290(U_6083,U_6084,U_6085) ),
inference(clausify,[status(thm)],[f_1361_3]) ).
cnf(f_1361_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6083),U_6084),U_6085) = c_Groups_Ozero__class_Ozero(U_6083)
| sP289(U_6083,U_6084,U_6085)
| ~ sP290(U_6083,U_6084,U_6085) ),
inference(clausify,[status(thm)],[f_1361_3]) ).
cnf(f_1361_7,plain,
( U_6084 != c_Groups_Ozero__class_Ozero(U_6083)
| ~ sP289(U_6083,U_6084,U_6085) ),
inference(clausify,[status(thm)],[f_1361_3]) ).
cnf(f_1361_8,plain,
( U_6085 != c_Groups_Ozero__class_Ozero(U_6083)
| ~ sP289(U_6083,U_6084,U_6085) ),
inference(clausify,[status(thm)],[f_1361_3]) ).
fof(f_1362_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_1362_2,plain,
! [U_6088,U_6087,U_6086] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6086),U_6087),U_6088) != c_Groups_Ozero__class_Ozero(U_6086)
| U_6088 = c_Groups_Ozero__class_Ozero(U_6086)
| U_6087 = c_Groups_Ozero__class_Ozero(U_6086)
| ~ class_Rings_Ono__zero__divisors(U_6086) ),
inference(variable_rename,[status(thm)],[f_1362_1]) ).
fof(f_1362_3,plain,
! [U_6086,U_6087,U_6088] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6086),U_6087),U_6088) != c_Groups_Ozero__class_Ozero(U_6086)
| U_6088 = c_Groups_Ozero__class_Ozero(U_6086)
| U_6087 = c_Groups_Ozero__class_Ozero(U_6086)
| ~ class_Rings_Ono__zero__divisors(U_6086) ),
inference(definitional_conversion,[status(esa)],[f_1362_2]) ).
cnf(f_1362_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6086),U_6087),U_6088) != c_Groups_Ozero__class_Ozero(U_6086)
| U_6088 = c_Groups_Ozero__class_Ozero(U_6086)
| U_6087 = c_Groups_Ozero__class_Ozero(U_6086)
| ~ class_Rings_Ono__zero__divisors(U_6086) ),
inference(clausify,[status(thm)],[f_1362_3]) ).
fof(f_1363_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_1363_2,plain,
! [U_6091,U_6090,U_6089] :
( U_6091 = c_Groups_Ozero__class_Ozero(U_6089)
| U_6090 = c_Groups_Ozero__class_Ozero(U_6089)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6089),U_6090),U_6091) != c_Groups_Ozero__class_Ozero(U_6089)
| ~ class_Rings_Ono__zero__divisors(U_6089) ),
inference(variable_rename,[status(thm)],[f_1363_1]) ).
fof(f_1363_3,plain,
! [U_6089,U_6090,U_6091] :
( U_6091 = c_Groups_Ozero__class_Ozero(U_6089)
| U_6090 = c_Groups_Ozero__class_Ozero(U_6089)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6089),U_6090),U_6091) != c_Groups_Ozero__class_Ozero(U_6089)
| ~ class_Rings_Ono__zero__divisors(U_6089) ),
inference(definitional_conversion,[status(esa)],[f_1363_2]) ).
cnf(f_1363_4,plain,
( U_6091 = c_Groups_Ozero__class_Ozero(U_6089)
| U_6090 = c_Groups_Ozero__class_Ozero(U_6089)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6089),U_6090),U_6091) != c_Groups_Ozero__class_Ozero(U_6089)
| ~ class_Rings_Ono__zero__divisors(U_6089) ),
inference(clausify,[status(thm)],[f_1363_3]) ).
fof(f_1364_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_1364_2,plain,
! [U_6093,U_6092] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6092),U_6093),c_Groups_Ozero__class_Ozero(U_6092)) = U_6093
| ~ class_Groups_Ogroup__add(U_6092) ),
inference(variable_rename,[status(thm)],[f_1364_1]) ).
fof(f_1364_3,plain,
! [U_6092,U_6093] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6092),U_6093),c_Groups_Ozero__class_Ozero(U_6092)) = U_6093
| ~ class_Groups_Ogroup__add(U_6092) ),
inference(definitional_conversion,[status(esa)],[f_1364_2]) ).
cnf(f_1364_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6092),U_6093),c_Groups_Ozero__class_Ozero(U_6092)) = U_6093
| ~ class_Groups_Ogroup__add(U_6092) ),
inference(clausify,[status(thm)],[f_1364_3]) ).
fof(f_1365_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_1365_2,plain,
! [U_6095,U_6094] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6094),U_6095),U_6095) = c_Groups_Ozero__class_Ozero(U_6094)
| ~ class_Groups_Ogroup__add(U_6094) ),
inference(variable_rename,[status(thm)],[f_1365_1]) ).
fof(f_1365_3,plain,
! [U_6094,U_6095] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6094),U_6095),U_6095) = c_Groups_Ozero__class_Ozero(U_6094)
| ~ class_Groups_Ogroup__add(U_6094) ),
inference(definitional_conversion,[status(esa)],[f_1365_2]) ).
cnf(f_1365_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6094),U_6095),U_6095) = c_Groups_Ozero__class_Ozero(U_6094)
| ~ class_Groups_Ogroup__add(U_6094) ),
inference(clausify,[status(thm)],[f_1365_3]) ).
fof(f_1366_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( V_a_2 = V_b_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_c) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_a_2 != V_b_2 ) )
| ~ class_Groups_Oab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0]) ).
fof(f_1366_2,plain,
! [U_6098,U_6097,U_6096] :
( ( ( U_6097 = U_6098
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6096),U_6097),U_6098) != c_Groups_Ozero__class_Ozero(U_6096) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6096),U_6097),U_6098) = c_Groups_Ozero__class_Ozero(U_6096)
| U_6097 != U_6098 ) )
| ~ class_Groups_Oab__group__add(U_6096) ),
inference(variable_rename,[status(thm)],[f_1366_1]) ).
fof(f_1366_3,plain,
( ! [U_6096,U_6097,U_6098] :
( U_6097 = U_6098
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6096),U_6097),U_6098) != c_Groups_Ozero__class_Ozero(U_6096)
| ~ sP291(U_6096,U_6097,U_6098) )
& ! [U_6096,U_6097,U_6098] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6096),U_6097),U_6098) = c_Groups_Ozero__class_Ozero(U_6096)
| U_6097 != U_6098
| ~ sP291(U_6096,U_6097,U_6098) )
& ! [U_6096,U_6097,U_6098] :
( sP291(U_6096,U_6097,U_6098)
| ~ class_Groups_Oab__group__add(U_6096) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP291])],[f_1366_2]) ).
cnf(f_1366_4,plain,
( sP291(U_6096,U_6097,U_6098)
| ~ class_Groups_Oab__group__add(U_6096) ),
inference(clausify,[status(thm)],[f_1366_3]) ).
cnf(f_1366_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6096),U_6097),U_6098) = c_Groups_Ozero__class_Ozero(U_6096)
| U_6097 != U_6098
| ~ sP291(U_6096,U_6097,U_6098) ),
inference(clausify,[status(thm)],[f_1366_3]) ).
cnf(f_1366_6,plain,
( U_6097 = U_6098
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6096),U_6097),U_6098) != c_Groups_Ozero__class_Ozero(U_6096)
| ~ sP291(U_6096,U_6097,U_6098) ),
inference(clausify,[status(thm)],[f_1366_3]) ).
fof(f_1367_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ class_Groups_Ogroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_right__minus__eq]) ).
fof(f_1367_2,plain,
! [U_6101,U_6100,U_6099] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6099),U_6100),U_6101) = c_Groups_Ozero__class_Ozero(U_6099)
| U_6100 != U_6101 )
& ( U_6100 = U_6101
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6099),U_6100),U_6101) != c_Groups_Ozero__class_Ozero(U_6099) ) )
| ~ class_Groups_Ogroup__add(U_6099) ),
inference(variable_rename,[status(thm)],[f_1367_1]) ).
fof(f_1367_3,plain,
( ! [U_6101,U_6100,U_6099] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6099),U_6100),U_6101) = c_Groups_Ozero__class_Ozero(U_6099)
| U_6100 != U_6101
| ~ sP292(U_6101,U_6100,U_6099) )
& ! [U_6101,U_6100,U_6099] :
( U_6100 = U_6101
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6099),U_6100),U_6101) != c_Groups_Ozero__class_Ozero(U_6099)
| ~ sP292(U_6101,U_6100,U_6099) )
& ! [U_6101,U_6100,U_6099] :
( sP292(U_6101,U_6100,U_6099)
| ~ class_Groups_Ogroup__add(U_6099) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP292])],[f_1367_2]) ).
cnf(f_1367_4,plain,
( sP292(U_6101,U_6100,U_6099)
| ~ class_Groups_Ogroup__add(U_6099) ),
inference(clausify,[status(thm)],[f_1367_3]) ).
cnf(f_1367_5,plain,
( U_6100 = U_6101
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6099),U_6100),U_6101) != c_Groups_Ozero__class_Ozero(U_6099)
| ~ sP292(U_6101,U_6100,U_6099) ),
inference(clausify,[status(thm)],[f_1367_3]) ).
cnf(f_1367_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6099),U_6100),U_6101) = c_Groups_Ozero__class_Ozero(U_6099)
| U_6100 != U_6101
| ~ sP292(U_6101,U_6100,U_6099) ),
inference(clausify,[status(thm)],[f_1367_3]) ).
fof(f_1368_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_1368_2,plain,
! [U_6102] :
( c_Groups_Ozero__class_Ozero(U_6102) != c_Groups_Oone__class_Oone(U_6102)
| ~ class_Rings_Ozero__neq__one(U_6102) ),
inference(variable_rename,[status(thm)],[f_1368_1]) ).
fof(f_1368_3,plain,
! [U_6102] :
( c_Groups_Ozero__class_Ozero(U_6102) != c_Groups_Oone__class_Oone(U_6102)
| ~ class_Rings_Ozero__neq__one(U_6102) ),
inference(definitional_conversion,[status(esa)],[f_1368_2]) ).
cnf(f_1368_4,plain,
( c_Groups_Ozero__class_Ozero(U_6102) != c_Groups_Oone__class_Oone(U_6102)
| ~ class_Rings_Ozero__neq__one(U_6102) ),
inference(clausify,[status(thm)],[f_1368_3]) ).
fof(f_1369_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_1369_2,plain,
! [U_6103] :
( c_Groups_Oone__class_Oone(U_6103) != c_Groups_Ozero__class_Ozero(U_6103)
| ~ class_Rings_Ozero__neq__one(U_6103) ),
inference(variable_rename,[status(thm)],[f_1369_1]) ).
fof(f_1369_3,plain,
! [U_6103] :
( c_Groups_Oone__class_Oone(U_6103) != c_Groups_Ozero__class_Ozero(U_6103)
| ~ class_Rings_Ozero__neq__one(U_6103) ),
inference(definitional_conversion,[status(esa)],[f_1369_2]) ).
cnf(f_1369_4,plain,
( c_Groups_Oone__class_Oone(U_6103) != c_Groups_Ozero__class_Ozero(U_6103)
| ~ class_Rings_Ozero__neq__one(U_6103) ),
inference(clausify,[status(thm)],[f_1369_3]) ).
fof(f_1370_1,plain,
! [V_a_2,T_c] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) = V_a_2
| V_a_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) != V_a_2 ) )
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__zero]) ).
fof(f_1370_2,plain,
! [U_6105,U_6104] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6104),U_6105) = U_6105
| U_6105 != c_Groups_Ozero__class_Ozero(U_6104) )
& ( U_6105 = c_Groups_Ozero__class_Ozero(U_6104)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_6104),U_6105) != U_6105 ) )
| ~ class_Groups_Olinordered__ab__group__add(U_6104) ),
inference(variable_rename,[status(thm)],[f_1370_1]) ).
fof(f_1370_3,plain,
( ! [U_6104,U_6105] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6104),U_6105) = U_6105
| U_6105 != c_Groups_Ozero__class_Ozero(U_6104)
| ~ sP293(U_6104,U_6105) )
& ! [U_6104,U_6105] :
( U_6105 = c_Groups_Ozero__class_Ozero(U_6104)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_6104),U_6105) != U_6105
| ~ sP293(U_6104,U_6105) )
& ! [U_6104,U_6105] :
( sP293(U_6104,U_6105)
| ~ class_Groups_Olinordered__ab__group__add(U_6104) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP293])],[f_1370_2]) ).
cnf(f_1370_4,plain,
( sP293(U_6104,U_6105)
| ~ class_Groups_Olinordered__ab__group__add(U_6104) ),
inference(clausify,[status(thm)],[f_1370_3]) ).
cnf(f_1370_5,plain,
( U_6105 = c_Groups_Ozero__class_Ozero(U_6104)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_6104),U_6105) != U_6105
| ~ sP293(U_6104,U_6105) ),
inference(clausify,[status(thm)],[f_1370_3]) ).
cnf(f_1370_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6104),U_6105) = U_6105
| U_6105 != c_Groups_Ozero__class_Ozero(U_6104)
| ~ sP293(U_6104,U_6105) ),
inference(clausify,[status(thm)],[f_1370_3]) ).
fof(f_1371_1,plain,
! [V_a_2,T_c] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ class_Groups_Ogroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal]) ).
fof(f_1371_2,plain,
! [U_6107,U_6106] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6106),U_6107) = c_Groups_Ozero__class_Ozero(U_6106)
| U_6107 != c_Groups_Ozero__class_Ozero(U_6106) )
& ( U_6107 = c_Groups_Ozero__class_Ozero(U_6106)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_6106),U_6107) != c_Groups_Ozero__class_Ozero(U_6106) ) )
| ~ class_Groups_Ogroup__add(U_6106) ),
inference(variable_rename,[status(thm)],[f_1371_1]) ).
fof(f_1371_3,plain,
( ! [U_6107,U_6106] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6106),U_6107) = c_Groups_Ozero__class_Ozero(U_6106)
| U_6107 != c_Groups_Ozero__class_Ozero(U_6106)
| ~ sP294(U_6107,U_6106) )
& ! [U_6107,U_6106] :
( U_6107 = c_Groups_Ozero__class_Ozero(U_6106)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_6106),U_6107) != c_Groups_Ozero__class_Ozero(U_6106)
| ~ sP294(U_6107,U_6106) )
& ! [U_6107,U_6106] :
( sP294(U_6107,U_6106)
| ~ class_Groups_Ogroup__add(U_6106) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP294])],[f_1371_2]) ).
cnf(f_1371_4,plain,
( sP294(U_6107,U_6106)
| ~ class_Groups_Ogroup__add(U_6106) ),
inference(clausify,[status(thm)],[f_1371_3]) ).
cnf(f_1371_5,plain,
( U_6107 = c_Groups_Ozero__class_Ozero(U_6106)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_6106),U_6107) != c_Groups_Ozero__class_Ozero(U_6106)
| ~ sP294(U_6107,U_6106) ),
inference(clausify,[status(thm)],[f_1371_3]) ).
cnf(f_1371_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6106),U_6107) = c_Groups_Ozero__class_Ozero(U_6106)
| U_6107 != c_Groups_Ozero__class_Ozero(U_6106)
| ~ sP294(U_6107,U_6106) ),
inference(clausify,[status(thm)],[f_1371_3]) ).
fof(f_1372_1,plain,
! [V_a_2,T_c] :
( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_equal__neg__zero]) ).
fof(f_1372_2,plain,
! [U_6109,U_6108] :
( ( ( U_6109 = hAPP(c_Groups_Ouminus__class_Ouminus(U_6108),U_6109)
| U_6109 != c_Groups_Ozero__class_Ozero(U_6108) )
& ( U_6109 = c_Groups_Ozero__class_Ozero(U_6108)
| U_6109 != hAPP(c_Groups_Ouminus__class_Ouminus(U_6108),U_6109) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_6108) ),
inference(variable_rename,[status(thm)],[f_1372_1]) ).
fof(f_1372_3,plain,
( ! [U_6109,U_6108] :
( U_6109 = hAPP(c_Groups_Ouminus__class_Ouminus(U_6108),U_6109)
| U_6109 != c_Groups_Ozero__class_Ozero(U_6108)
| ~ sP295(U_6109,U_6108) )
& ! [U_6109,U_6108] :
( U_6109 = c_Groups_Ozero__class_Ozero(U_6108)
| U_6109 != hAPP(c_Groups_Ouminus__class_Ouminus(U_6108),U_6109)
| ~ sP295(U_6109,U_6108) )
& ! [U_6109,U_6108] :
( sP295(U_6109,U_6108)
| ~ class_Groups_Olinordered__ab__group__add(U_6108) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP295])],[f_1372_2]) ).
cnf(f_1372_4,plain,
( sP295(U_6109,U_6108)
| ~ class_Groups_Olinordered__ab__group__add(U_6108) ),
inference(clausify,[status(thm)],[f_1372_3]) ).
cnf(f_1372_5,plain,
( U_6109 = c_Groups_Ozero__class_Ozero(U_6108)
| U_6109 != hAPP(c_Groups_Ouminus__class_Ouminus(U_6108),U_6109)
| ~ sP295(U_6109,U_6108) ),
inference(clausify,[status(thm)],[f_1372_3]) ).
cnf(f_1372_6,plain,
( U_6109 = hAPP(c_Groups_Ouminus__class_Ouminus(U_6108),U_6109)
| U_6109 != c_Groups_Ozero__class_Ozero(U_6108)
| ~ sP295(U_6109,U_6108) ),
inference(clausify,[status(thm)],[f_1372_3]) ).
fof(f_1373_1,plain,
! [V_a_2,T_c] :
( ( ( c_Groups_Ozero__class_Ozero(T_c) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)
| c_Groups_Ozero__class_Ozero(T_c) != V_a_2 )
& ( c_Groups_Ozero__class_Ozero(T_c) = V_a_2
| c_Groups_Ozero__class_Ozero(T_c) != hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2) ) )
| ~ class_Groups_Ogroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal]) ).
fof(f_1373_2,plain,
! [U_6111,U_6110] :
( ( ( c_Groups_Ozero__class_Ozero(U_6110) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6110),U_6111)
| c_Groups_Ozero__class_Ozero(U_6110) != U_6111 )
& ( c_Groups_Ozero__class_Ozero(U_6110) = U_6111
| c_Groups_Ozero__class_Ozero(U_6110) != hAPP(c_Groups_Ouminus__class_Ouminus(U_6110),U_6111) ) )
| ~ class_Groups_Ogroup__add(U_6110) ),
inference(variable_rename,[status(thm)],[f_1373_1]) ).
fof(f_1373_3,plain,
( ! [U_6111,U_6110] :
( c_Groups_Ozero__class_Ozero(U_6110) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6110),U_6111)
| c_Groups_Ozero__class_Ozero(U_6110) != U_6111
| ~ sP296(U_6111,U_6110) )
& ! [U_6111,U_6110] :
( c_Groups_Ozero__class_Ozero(U_6110) = U_6111
| c_Groups_Ozero__class_Ozero(U_6110) != hAPP(c_Groups_Ouminus__class_Ouminus(U_6110),U_6111)
| ~ sP296(U_6111,U_6110) )
& ! [U_6111,U_6110] :
( sP296(U_6111,U_6110)
| ~ class_Groups_Ogroup__add(U_6110) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP296])],[f_1373_2]) ).
cnf(f_1373_4,plain,
( sP296(U_6111,U_6110)
| ~ class_Groups_Ogroup__add(U_6110) ),
inference(clausify,[status(thm)],[f_1373_3]) ).
cnf(f_1373_5,plain,
( c_Groups_Ozero__class_Ozero(U_6110) = U_6111
| c_Groups_Ozero__class_Ozero(U_6110) != hAPP(c_Groups_Ouminus__class_Ouminus(U_6110),U_6111)
| ~ sP296(U_6111,U_6110) ),
inference(clausify,[status(thm)],[f_1373_3]) ).
cnf(f_1373_6,plain,
( c_Groups_Ozero__class_Ozero(U_6110) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6110),U_6111)
| c_Groups_Ozero__class_Ozero(U_6110) != U_6111
| ~ sP296(U_6111,U_6110) ),
inference(clausify,[status(thm)],[f_1373_3]) ).
fof(f_1374_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_1374_2,plain,
! [U_6112] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6112),c_Groups_Ozero__class_Ozero(U_6112)) = c_Groups_Ozero__class_Ozero(U_6112)
| ~ class_Groups_Ogroup__add(U_6112) ),
inference(variable_rename,[status(thm)],[f_1374_1]) ).
fof(f_1374_3,plain,
! [U_6112] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6112),c_Groups_Ozero__class_Ozero(U_6112)) = c_Groups_Ozero__class_Ozero(U_6112)
| ~ class_Groups_Ogroup__add(U_6112) ),
inference(definitional_conversion,[status(esa)],[f_1374_2]) ).
cnf(f_1374_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6112),c_Groups_Ozero__class_Ozero(U_6112)) = c_Groups_Ozero__class_Ozero(U_6112)
| ~ class_Groups_Ogroup__add(U_6112) ),
inference(clausify,[status(thm)],[f_1374_3]) ).
fof(f_1375_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_1375_2,plain,
! [U_6113] : hAPP(c_Nat_OSuc,U_6113) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1375_1]) ).
fof(f_1375_3,plain,
! [U_6113] : hAPP(c_Nat_OSuc,U_6113) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1375_2]) ).
cnf(f_1375_4,plain,
hAPP(c_Nat_OSuc,U_6113) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1375_3]) ).
fof(f_1376_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_1376_2,plain,
! [U_6114] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_6114),
inference(variable_rename,[status(thm)],[f_1376_1]) ).
fof(f_1376_3,plain,
! [U_6114] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_6114),
inference(definitional_conversion,[status(esa)],[f_1376_2]) ).
cnf(f_1376_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_6114),
inference(clausify,[status(thm)],[f_1376_3]) ).
fof(f_1377_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_1377_2,plain,
! [U_6115] : hAPP(c_Nat_OSuc,U_6115) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1377_1]) ).
fof(f_1377_3,plain,
! [U_6115] : hAPP(c_Nat_OSuc,U_6115) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1377_2]) ).
cnf(f_1377_4,plain,
hAPP(c_Nat_OSuc,U_6115) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1377_3]) ).
fof(f_1378_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_1378_2,plain,
! [U_6116] : hAPP(c_Nat_OSuc,U_6116) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1378_1]) ).
fof(f_1378_3,plain,
! [U_6116] : hAPP(c_Nat_OSuc,U_6116) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1378_2]) ).
cnf(f_1378_4,plain,
hAPP(c_Nat_OSuc,U_6116) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1378_3]) ).
fof(f_1379_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_1379_2,plain,
! [U_6117] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_6117),
inference(variable_rename,[status(thm)],[f_1379_1]) ).
fof(f_1379_3,plain,
! [U_6117] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_6117),
inference(definitional_conversion,[status(esa)],[f_1379_2]) ).
cnf(f_1379_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_6117),
inference(clausify,[status(thm)],[f_1379_3]) ).
fof(f_1380_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_1380_2,plain,
! [U_6118] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_6118),
inference(variable_rename,[status(thm)],[f_1380_1]) ).
fof(f_1380_3,plain,
! [U_6118] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_6118),
inference(definitional_conversion,[status(esa)],[f_1380_2]) ).
cnf(f_1380_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_6118),
inference(clausify,[status(thm)],[f_1380_3]) ).
fof(f_1381_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_1381_2,plain,
! [U_6119] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6119) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_1381_1]) ).
fof(f_1381_3,plain,
! [U_6119] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6119) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_1381_2]) ).
cnf(f_1381_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_6119) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_1381_3]) ).
fof(f_1382_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_1382_2,plain,
! [U_6121,U_6120] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6120),U_6121) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_6120 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_6121 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_6120 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6121 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6120),U_6121) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_1382_1]) ).
fof(f_1382_3,plain,
( ! [U_6125,U_6123] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6123),U_6125) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_6123 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_6125 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_6124,U_6122] :
( U_6122 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6122),U_6124) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_1382_2]) ).
fof(f_1382_4,plain,
( ! [U_6125,U_6123] :
( U_6123 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP297(U_6125,U_6123) )
& ! [U_6125,U_6123] :
( U_6125 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP297(U_6125,U_6123) )
& ! [U_6125,U_6123] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6123),U_6125) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP297(U_6125,U_6123) )
& ! [U_6124,U_6122] :
( U_6122 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6122),U_6124) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP297])],[f_1382_3]) ).
cnf(f_1382_5,plain,
( U_6122 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6122),U_6124) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1382_4]) ).
cnf(f_1382_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6123),U_6125) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP297(U_6125,U_6123) ),
inference(clausify,[status(thm)],[f_1382_4]) ).
cnf(f_1382_7,plain,
( U_6125 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP297(U_6125,U_6123) ),
inference(clausify,[status(thm)],[f_1382_4]) ).
cnf(f_1382_8,plain,
( U_6123 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP297(U_6125,U_6123) ),
inference(clausify,[status(thm)],[f_1382_4]) ).
fof(f_1383_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_1383_2,plain,
! [U_6128,U_6127,U_6126] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6126),U_6127),U_6128) != c_Groups_Ozero__class_Ozero(U_6126)
| U_6127 = c_Groups_Ozero__class_Ozero(U_6126)
| ~ class_Rings_Oring__1__no__zero__divisors(U_6126) ),
inference(variable_rename,[status(thm)],[f_1383_1]) ).
fof(f_1383_3,plain,
! [U_6128,U_6127,U_6126] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6126),U_6127),U_6128) != c_Groups_Ozero__class_Ozero(U_6126)
| U_6127 = c_Groups_Ozero__class_Ozero(U_6126)
| ~ class_Rings_Oring__1__no__zero__divisors(U_6126) ),
inference(definitional_conversion,[status(esa)],[f_1383_2]) ).
cnf(f_1383_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6126),U_6127),U_6128) != c_Groups_Ozero__class_Ozero(U_6126)
| U_6127 = c_Groups_Ozero__class_Ozero(U_6126)
| ~ class_Rings_Oring__1__no__zero__divisors(U_6126) ),
inference(clausify,[status(thm)],[f_1383_3]) ).
fof(f_1384_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_1384_2,plain,
! [U_6130,U_6129] :
( ( 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_6129),U_6130)))
| ( U_6130 != 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_6129)) ) )
& ( U_6130 = 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_6129))
| ~ 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_6129),U_6130))) ) ),
inference(variable_rename,[status(thm)],[f_1384_1]) ).
fof(f_1384_3,plain,
( ! [U_6134,U_6132] :
( 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_6132),U_6134)))
| ( U_6134 != 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_6132)) ) )
& ! [U_6133,U_6131] :
( U_6133 = 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_6131))
| ~ 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_6131),U_6133))) ) ),
inference(miniscope,[status(thm)],[f_1384_2]) ).
fof(f_1384_4,plain,
( ! [U_6132,U_6134] :
( U_6134 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP298(U_6132,U_6134) )
& ! [U_6132,U_6134] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6132))
| ~ sP298(U_6132,U_6134) )
& ! [U_6132,U_6134] :
( 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_6132),U_6134)))
| sP298(U_6132,U_6134) )
& ! [U_6133,U_6131] :
( U_6133 = 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_6131))
| ~ 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_6131),U_6133))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP298])],[f_1384_3]) ).
cnf(f_1384_5,plain,
( U_6133 = 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_6131))
| ~ 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_6131),U_6133))) ),
inference(clausify,[status(thm)],[f_1384_4]) ).
cnf(f_1384_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_6132),U_6134)))
| sP298(U_6132,U_6134) ),
inference(clausify,[status(thm)],[f_1384_4]) ).
cnf(f_1384_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6132))
| ~ sP298(U_6132,U_6134) ),
inference(clausify,[status(thm)],[f_1384_4]) ).
cnf(f_1384_8,plain,
( U_6134 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP298(U_6132,U_6134) ),
inference(clausify,[status(thm)],[f_1384_4]) ).
fof(f_1385_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_1385_2,plain,
! [U_6137,U_6136,U_6135] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6136),U_6137))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6135),U_6136)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6135),U_6137)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6135)) ),
inference(variable_rename,[status(thm)],[f_1385_1]) ).
fof(f_1385_3,plain,
! [U_6136,U_6135,U_6137] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6136),U_6137))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6135),U_6136)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6135),U_6137)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6135)) ),
inference(definitional_conversion,[status(esa)],[f_1385_2]) ).
cnf(f_1385_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6136),U_6137))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6135),U_6136)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6135),U_6137)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6135)) ),
inference(clausify,[status(thm)],[f_1385_3]) ).
fof(f_1386_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_1386_2,plain,
! [U_6138] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6138),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1386_1]) ).
fof(f_1386_3,plain,
! [U_6138] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6138),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_1386_2]) ).
cnf(f_1386_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6138),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1386_3]) ).
fof(f_1387_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_1387_2,plain,
! [U_6139] :
( ( U_6139 != 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_6139)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6139))
| U_6139 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1387_1]) ).
fof(f_1387_3,plain,
( ! [U_6141] :
( U_6141 != 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_6141)) )
& ! [U_6140] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6140))
| U_6140 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1387_2]) ).
fof(f_1387_4,plain,
( ! [U_6141] :
( U_6141 != 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_6141)) )
& ! [U_6140] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6140))
| U_6140 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1387_3]) ).
cnf(f_1387_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6140))
| U_6140 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1387_4]) ).
cnf(f_1387_6,plain,
( U_6141 != 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_6141)) ),
inference(clausify,[status(thm)],[f_1387_4]) ).
fof(f_1388_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_1388_2,plain,
! [U_6142] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6142),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1388_1]) ).
fof(f_1388_3,plain,
! [U_6142] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6142),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_1388_2]) ).
cnf(f_1388_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6142),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1388_3]) ).
fof(f_1389_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_1389_2,plain,
! [U_6144,U_6143] :
( U_6144 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6143),U_6144)) ),
inference(variable_rename,[status(thm)],[f_1389_1]) ).
fof(f_1389_3,plain,
! [U_6144] :
( ! [U_6143] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6143),U_6144))
| U_6144 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_1389_2]) ).
fof(f_1389_4,plain,
! [U_6143,U_6144] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6143),U_6144))
| U_6144 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_1389_3]) ).
cnf(f_1389_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6143),U_6144))
| U_6144 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1389_4]) ).
fof(f_1390_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_1390_2,plain,
! [U_6145] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6145))
| U_6145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_1390_1]) ).
fof(f_1390_3,plain,
! [U_6145] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6145))
| U_6145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_1390_2]) ).
cnf(f_1390_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6145))
| U_6145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1390_3]) ).
fof(f_1391_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_1391_2,plain,
! [U_6147,U_6146] :
( U_6147 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6146),U_6147) != U_6146 ),
inference(variable_rename,[status(thm)],[f_1391_1]) ).
fof(f_1391_3,plain,
! [U_6147] :
( ! [U_6146] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6146),U_6147) != U_6146
| U_6147 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_1391_2]) ).
fof(f_1391_4,plain,
! [U_6146,U_6147] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6146),U_6147) != U_6146
| U_6147 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_1391_3]) ).
cnf(f_1391_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6146),U_6147) != U_6146
| U_6147 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1391_4]) ).
fof(f_1392_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_1392_2,plain,
! [U_6149,U_6148] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6148),U_6149) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6149 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6148 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_6149 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6148 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6148),U_6149) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1392_1]) ).
fof(f_1392_3,plain,
( ! [U_6153,U_6151] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6151),U_6153) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6153 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6151 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6152,U_6150] :
( ( U_6152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6150),U_6152) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1392_2]) ).
fof(f_1392_4,plain,
( ! [U_6152,U_6150] :
( U_6152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP299(U_6152,U_6150) )
& ! [U_6152,U_6150] :
( U_6150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP299(U_6152,U_6150) )
& ! [U_6153,U_6151] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6151),U_6153) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6153 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6151 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6152,U_6150] :
( sP299(U_6152,U_6150)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6150),U_6152) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP299])],[f_1392_3]) ).
cnf(f_1392_5,plain,
( sP299(U_6152,U_6150)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6150),U_6152) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1392_4]) ).
cnf(f_1392_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6151),U_6153) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6153 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6151 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1392_4]) ).
cnf(f_1392_7,plain,
( U_6150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP299(U_6152,U_6150) ),
inference(clausify,[status(thm)],[f_1392_4]) ).
cnf(f_1392_8,plain,
( U_6152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP299(U_6152,U_6150) ),
inference(clausify,[status(thm)],[f_1392_4]) ).
fof(f_1393_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_1393_2,plain,
! [U_6154] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6154),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6154,
inference(variable_rename,[status(thm)],[f_1393_1]) ).
fof(f_1393_3,plain,
! [U_6154] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6154),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6154,
inference(definitional_conversion,[status(esa)],[f_1393_2]) ).
cnf(f_1393_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6154),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6154,
inference(clausify,[status(thm)],[f_1393_3]) ).
fof(f_1394_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_1394_2,plain,
! [U_6155] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6155) = U_6155,
inference(variable_rename,[status(thm)],[f_1394_1]) ).
fof(f_1394_3,plain,
! [U_6155] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6155) = U_6155,
inference(definitional_conversion,[status(esa)],[f_1394_2]) ).
cnf(f_1394_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6155) = U_6155,
inference(clausify,[status(thm)],[f_1394_3]) ).
fof(f_1395_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_1395_2,plain,
! [U_6156] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6156)),
inference(variable_rename,[status(thm)],[f_1395_1]) ).
fof(f_1395_3,plain,
! [U_6156] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6156)),
inference(definitional_conversion,[status(esa)],[f_1395_2]) ).
cnf(f_1395_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6156)),
inference(clausify,[status(thm)],[f_1395_3]) ).
fof(f_1396_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_1396_2,plain,
! [U_6157] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6157),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6157 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_6157 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6157),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_1396_1]) ).
fof(f_1396_3,plain,
( ! [U_6159] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6159),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6159 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6158] :
( U_6158 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6158),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_1396_2]) ).
fof(f_1396_4,plain,
( ! [U_6159] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6159),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6159 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6158] :
( U_6158 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6158),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(definitional_conversion,[status(esa)],[f_1396_3]) ).
cnf(f_1396_5,plain,
( U_6158 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6158),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_1396_4]) ).
cnf(f_1396_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6159),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_6159 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1396_4]) ).
fof(f_1397_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_1397_2,plain,
! [U_6160] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6160) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1397_1]) ).
fof(f_1397_3,plain,
! [U_6160] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6160) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1397_2]) ).
cnf(f_1397_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6160) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1397_3]) ).
fof(f_1398_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_1398_2,plain,
! [U_6161] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6161),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6161,
inference(variable_rename,[status(thm)],[f_1398_1]) ).
fof(f_1398_3,plain,
! [U_6161] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6161),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6161,
inference(definitional_conversion,[status(esa)],[f_1398_2]) ).
cnf(f_1398_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6161),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6161,
inference(clausify,[status(thm)],[f_1398_3]) ).
fof(f_1399_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_1399_2,plain,
! [U_6162] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6162),U_6162) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1399_1]) ).
fof(f_1399_3,plain,
! [U_6162] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6162),U_6162) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1399_2]) ).
cnf(f_1399_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6162),U_6162) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1399_3]) ).
fof(f_1400_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_1400_2,plain,
! [U_6164,U_6163] :
( U_6163 = U_6164
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6164),U_6163) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6163),U_6164) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_1400_1]) ).
fof(f_1400_3,plain,
! [U_6163,U_6164] :
( U_6163 = U_6164
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6164),U_6163) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6163),U_6164) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_1400_2]) ).
cnf(f_1400_4,plain,
( U_6163 = U_6164
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6164),U_6163) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6163),U_6164) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1400_3]) ).
fof(f_1401_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_1401_2,plain,
! [U_6167,U_6166,U_6165] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6165),U_6166) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6165),U_6167)
| ( U_6166 != U_6167
& U_6165 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_6166 = U_6167
| U_6165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6165),U_6166) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6165),U_6167) ) ),
inference(variable_rename,[status(thm)],[f_1401_1]) ).
fof(f_1401_3,plain,
( ! [U_6173,U_6171,U_6169] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6169),U_6171) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6169),U_6173)
| ( U_6171 != U_6173
& U_6169 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_6172,U_6170,U_6168] :
( U_6170 = U_6172
| U_6168 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6168),U_6170) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6168),U_6172) ) ),
inference(miniscope,[status(thm)],[f_1401_2]) ).
fof(f_1401_4,plain,
( ! [U_6173,U_6171,U_6169] :
( U_6171 != U_6173
| ~ sP300(U_6173,U_6171,U_6169) )
& ! [U_6173,U_6171,U_6169] :
( U_6169 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP300(U_6173,U_6171,U_6169) )
& ! [U_6173,U_6171,U_6169] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6169),U_6171) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6169),U_6173)
| sP300(U_6173,U_6171,U_6169) )
& ! [U_6170,U_6168,U_6172] :
( U_6170 = U_6172
| U_6168 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6168),U_6170) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6168),U_6172) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP300])],[f_1401_3]) ).
cnf(f_1401_5,plain,
( U_6170 = U_6172
| U_6168 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6168),U_6170) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6168),U_6172) ),
inference(clausify,[status(thm)],[f_1401_4]) ).
cnf(f_1401_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6169),U_6171) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6169),U_6173)
| sP300(U_6173,U_6171,U_6169) ),
inference(clausify,[status(thm)],[f_1401_4]) ).
cnf(f_1401_7,plain,
( U_6169 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP300(U_6173,U_6171,U_6169) ),
inference(clausify,[status(thm)],[f_1401_4]) ).
cnf(f_1401_8,plain,
( U_6171 != U_6173
| ~ sP300(U_6173,U_6171,U_6169) ),
inference(clausify,[status(thm)],[f_1401_4]) ).
fof(f_1402_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_1402_2,plain,
! [U_6174] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6174) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1402_1]) ).
fof(f_1402_3,plain,
! [U_6174] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6174) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1402_2]) ).
cnf(f_1402_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6174) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1402_3]) ).
fof(f_1403_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_1403_2,plain,
! [U_6175] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6175),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1403_1]) ).
fof(f_1403_3,plain,
! [U_6175] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6175),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1403_2]) ).
cnf(f_1403_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6175),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1403_3]) ).
fof(f_1404_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_1404_2,plain,
! [U_6177,U_6176] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6176),U_6177) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_6177 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6176 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_6177 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6176 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6176),U_6177) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1404_1]) ).
fof(f_1404_3,plain,
( ! [U_6181,U_6179] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6179),U_6181) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_6181 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6179 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_6180,U_6178] :
( U_6180 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6178),U_6180) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1404_2]) ).
fof(f_1404_4,plain,
( ! [U_6179,U_6181] :
( U_6181 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP301(U_6179,U_6181) )
& ! [U_6179,U_6181] :
( U_6179 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP301(U_6179,U_6181) )
& ! [U_6179,U_6181] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6179),U_6181) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP301(U_6179,U_6181) )
& ! [U_6180,U_6178] :
( U_6180 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6178),U_6180) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP301])],[f_1404_3]) ).
cnf(f_1404_5,plain,
( U_6180 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6178),U_6180) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1404_4]) ).
cnf(f_1404_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6179),U_6181) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP301(U_6179,U_6181) ),
inference(clausify,[status(thm)],[f_1404_4]) ).
cnf(f_1404_7,plain,
( U_6179 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP301(U_6179,U_6181) ),
inference(clausify,[status(thm)],[f_1404_4]) ).
cnf(f_1404_8,plain,
( U_6181 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP301(U_6179,U_6181) ),
inference(clausify,[status(thm)],[f_1404_4]) ).
fof(f_1405_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_1405_2,plain,
! [U_6184,U_6183,U_6182] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6182),U_6183) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6182),U_6184)
| ( U_6182 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6183 != U_6184 ) )
& ( U_6182 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6183 = U_6184
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6182),U_6183) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6182),U_6184) ) ),
inference(variable_rename,[status(thm)],[f_1405_1]) ).
fof(f_1405_3,plain,
( ! [U_6190,U_6188,U_6186] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6186),U_6188) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6186),U_6190)
| ( U_6186 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6188 != U_6190 ) )
& ! [U_6189,U_6187,U_6185] :
( U_6185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6187 = U_6189
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6185),U_6187) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6185),U_6189) ) ),
inference(miniscope,[status(thm)],[f_1405_2]) ).
fof(f_1405_4,plain,
( ! [U_6190,U_6188,U_6186] :
( U_6186 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP302(U_6190,U_6188,U_6186) )
& ! [U_6190,U_6188,U_6186] :
( U_6188 != U_6190
| ~ sP302(U_6190,U_6188,U_6186) )
& ! [U_6190,U_6188,U_6186] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6186),U_6188) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6186),U_6190)
| sP302(U_6190,U_6188,U_6186) )
& ! [U_6187,U_6185,U_6189] :
( U_6185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6187 = U_6189
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6185),U_6187) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6185),U_6189) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP302])],[f_1405_3]) ).
cnf(f_1405_5,plain,
( U_6185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6187 = U_6189
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6185),U_6187) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6185),U_6189) ),
inference(clausify,[status(thm)],[f_1405_4]) ).
cnf(f_1405_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6186),U_6188) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6186),U_6190)
| sP302(U_6190,U_6188,U_6186) ),
inference(clausify,[status(thm)],[f_1405_4]) ).
cnf(f_1405_7,plain,
( U_6188 != U_6190
| ~ sP302(U_6190,U_6188,U_6186) ),
inference(clausify,[status(thm)],[f_1405_4]) ).
cnf(f_1405_8,plain,
( U_6186 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP302(U_6190,U_6188,U_6186) ),
inference(clausify,[status(thm)],[f_1405_4]) ).
fof(f_1406_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_1406_2,plain,
! [U_6193,U_6192,U_6191] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6191),U_6192) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6193),U_6192)
| ( U_6192 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6191 != U_6193 ) )
& ( U_6192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6191 = U_6193
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6191),U_6192) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6193),U_6192) ) ),
inference(variable_rename,[status(thm)],[f_1406_1]) ).
fof(f_1406_3,plain,
( ! [U_6199,U_6197,U_6195] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6195),U_6197) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6199),U_6197)
| ( U_6197 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6195 != U_6199 ) )
& ! [U_6198,U_6196,U_6194] :
( U_6196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6194 = U_6198
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6194),U_6196) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6198),U_6196) ) ),
inference(miniscope,[status(thm)],[f_1406_2]) ).
fof(f_1406_4,plain,
( ! [U_6195,U_6197,U_6199] :
( U_6197 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP303(U_6195,U_6197,U_6199) )
& ! [U_6195,U_6197,U_6199] :
( U_6195 != U_6199
| ~ sP303(U_6195,U_6197,U_6199) )
& ! [U_6195,U_6197,U_6199] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6195),U_6197) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6199),U_6197)
| sP303(U_6195,U_6197,U_6199) )
& ! [U_6196,U_6194,U_6198] :
( U_6196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6194 = U_6198
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6194),U_6196) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6198),U_6196) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP303])],[f_1406_3]) ).
cnf(f_1406_5,plain,
( U_6196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6194 = U_6198
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6194),U_6196) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6198),U_6196) ),
inference(clausify,[status(thm)],[f_1406_4]) ).
cnf(f_1406_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6195),U_6197) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6199),U_6197)
| sP303(U_6195,U_6197,U_6199) ),
inference(clausify,[status(thm)],[f_1406_4]) ).
cnf(f_1406_7,plain,
( U_6195 != U_6199
| ~ sP303(U_6195,U_6197,U_6199) ),
inference(clausify,[status(thm)],[f_1406_4]) ).
cnf(f_1406_8,plain,
( U_6197 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP303(U_6195,U_6197,U_6199) ),
inference(clausify,[status(thm)],[f_1406_4]) ).
fof(f_1407_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_c)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_c)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_c)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_c) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_y_2),V_y_2)) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ class_Rings_Olinordered__ring__strict(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff]) ).
fof(f_1407_2,plain,
! [U_6202,U_6201,U_6200] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6200),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6201),U_6201)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6202),U_6202)) = c_Groups_Ozero__class_Ozero(U_6200)
| U_6202 != c_Groups_Ozero__class_Ozero(U_6200)
| U_6201 != c_Groups_Ozero__class_Ozero(U_6200) )
& ( ( U_6202 = c_Groups_Ozero__class_Ozero(U_6200)
& U_6201 = c_Groups_Ozero__class_Ozero(U_6200) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6200),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6201),U_6201)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6202),U_6202)) != c_Groups_Ozero__class_Ozero(U_6200) ) )
| ~ class_Rings_Olinordered__ring__strict(U_6200) ),
inference(variable_rename,[status(thm)],[f_1407_1]) ).
fof(f_1407_3,plain,
( ! [U_6201,U_6200,U_6202] :
( U_6202 = c_Groups_Ozero__class_Ozero(U_6200)
| ~ sP304(U_6201,U_6200,U_6202) )
& ! [U_6201,U_6200,U_6202] :
( U_6201 = c_Groups_Ozero__class_Ozero(U_6200)
| ~ sP304(U_6201,U_6200,U_6202) )
& ! [U_6201,U_6200,U_6202] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6200),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6201),U_6201)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6202),U_6202)) = c_Groups_Ozero__class_Ozero(U_6200)
| U_6202 != c_Groups_Ozero__class_Ozero(U_6200)
| U_6201 != c_Groups_Ozero__class_Ozero(U_6200)
| ~ sP305(U_6201,U_6200,U_6202) )
& ! [U_6201,U_6200,U_6202] :
( sP304(U_6201,U_6200,U_6202)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6200),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6201),U_6201)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6202),U_6202)) != c_Groups_Ozero__class_Ozero(U_6200)
| ~ sP305(U_6201,U_6200,U_6202) )
& ! [U_6201,U_6200,U_6202] :
( sP305(U_6201,U_6200,U_6202)
| ~ class_Rings_Olinordered__ring__strict(U_6200) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP304,sP305])],[f_1407_2]) ).
cnf(f_1407_4,plain,
( sP305(U_6201,U_6200,U_6202)
| ~ class_Rings_Olinordered__ring__strict(U_6200) ),
inference(clausify,[status(thm)],[f_1407_3]) ).
cnf(f_1407_5,plain,
( sP304(U_6201,U_6200,U_6202)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6200),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6201),U_6201)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6202),U_6202)) != c_Groups_Ozero__class_Ozero(U_6200)
| ~ sP305(U_6201,U_6200,U_6202) ),
inference(clausify,[status(thm)],[f_1407_3]) ).
cnf(f_1407_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6200),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6201),U_6201)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6200),U_6202),U_6202)) = c_Groups_Ozero__class_Ozero(U_6200)
| U_6202 != c_Groups_Ozero__class_Ozero(U_6200)
| U_6201 != c_Groups_Ozero__class_Ozero(U_6200)
| ~ sP305(U_6201,U_6200,U_6202) ),
inference(clausify,[status(thm)],[f_1407_3]) ).
cnf(f_1407_7,plain,
( U_6201 = c_Groups_Ozero__class_Ozero(U_6200)
| ~ sP304(U_6201,U_6200,U_6202) ),
inference(clausify,[status(thm)],[f_1407_3]) ).
cnf(f_1407_8,plain,
( U_6202 = c_Groups_Ozero__class_Ozero(U_6200)
| ~ sP304(U_6201,U_6200,U_6202) ),
inference(clausify,[status(thm)],[f_1407_3]) ).
fof(f_1408_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_1408_2,plain,
! [U_6203] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6203) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1408_1]) ).
fof(f_1408_3,plain,
! [U_6203] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6203) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1408_2]) ).
cnf(f_1408_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6203) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1408_3]) ).
fof(f_1409_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_1409_2,plain,
! [U_6204] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6204),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1409_1]) ).
fof(f_1409_3,plain,
! [U_6204] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6204),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1409_2]) ).
cnf(f_1409_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6204),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1409_3]) ).
fof(f_1410_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_1410_2,plain,
! [U_6205] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6205) = U_6205,
inference(variable_rename,[status(thm)],[f_1410_1]) ).
fof(f_1410_3,plain,
! [U_6205] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6205) = U_6205,
inference(definitional_conversion,[status(esa)],[f_1410_2]) ).
cnf(f_1410_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6205) = U_6205,
inference(clausify,[status(thm)],[f_1410_3]) ).
fof(f_1411_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_1411_2,plain,
! [U_6206] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6206),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6206,
inference(variable_rename,[status(thm)],[f_1411_1]) ).
fof(f_1411_3,plain,
! [U_6206] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6206),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6206,
inference(definitional_conversion,[status(esa)],[f_1411_2]) ).
cnf(f_1411_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6206),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6206,
inference(clausify,[status(thm)],[f_1411_3]) ).
fof(f_1412_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_1412_2,plain,
! [U_6210,U_6209,U_6208,U_6207] :
( U_6208 = U_6210
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6207),c_Groups_Ozero__class_Ozero(U_6207)),U_6210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6207),c_Groups_Ozero__class_Ozero(U_6207)),U_6208))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6207),U_6208),U_6209) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6207),U_6210),U_6209)
| ~ class_Rings_Olinordered__semidom(U_6207) ),
inference(variable_rename,[status(thm)],[f_1412_1]) ).
fof(f_1412_3,plain,
! [U_6207,U_6208,U_6209,U_6210] :
( U_6208 = U_6210
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6207),c_Groups_Ozero__class_Ozero(U_6207)),U_6210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6207),c_Groups_Ozero__class_Ozero(U_6207)),U_6208))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6207),U_6208),U_6209) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6207),U_6210),U_6209)
| ~ class_Rings_Olinordered__semidom(U_6207) ),
inference(definitional_conversion,[status(esa)],[f_1412_2]) ).
cnf(f_1412_4,plain,
( U_6208 = U_6210
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6207),c_Groups_Ozero__class_Ozero(U_6207)),U_6210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6207),c_Groups_Ozero__class_Ozero(U_6207)),U_6208))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6207),U_6208),U_6209) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6207),U_6210),U_6209)
| ~ class_Rings_Olinordered__semidom(U_6207) ),
inference(clausify,[status(thm)],[f_1412_3]) ).
fof(f_1413_1,plain,
! [V_A_2,T_d,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(c_COMBK(T_c,T_d),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__0]) ).
fof(f_1413_2,plain,
! [U_6213,U_6212,U_6211] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6212,U_6211),hAPP(c_COMBK(U_6211,U_6212),c_Groups_Ozero__class_Ozero(U_6211))),U_6213) = c_Groups_Ozero__class_Ozero(U_6211)
| ~ class_Groups_Ocomm__monoid__add(U_6211) ),
inference(variable_rename,[status(thm)],[f_1413_1]) ).
fof(f_1413_3,plain,
! [U_6212,U_6213,U_6211] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6212,U_6211),hAPP(c_COMBK(U_6211,U_6212),c_Groups_Ozero__class_Ozero(U_6211))),U_6213) = c_Groups_Ozero__class_Ozero(U_6211)
| ~ class_Groups_Ocomm__monoid__add(U_6211) ),
inference(definitional_conversion,[status(esa)],[f_1413_2]) ).
cnf(f_1413_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6212,U_6211),hAPP(c_COMBK(U_6211,U_6212),c_Groups_Ozero__class_Ozero(U_6211))),U_6213) = c_Groups_Ozero__class_Ozero(U_6211)
| ~ class_Groups_Ocomm__monoid__add(U_6211) ),
inference(clausify,[status(thm)],[f_1413_3]) ).
fof(f_1414_1,plain,
! [V_a_2,V_times_2,V_one_2,T_c] : hAPP(hAPP(c_Power_Opower_Opower(T_c,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_1414_2,plain,
! [U_6217,U_6216,U_6215,U_6214] : hAPP(hAPP(c_Power_Opower_Opower(U_6214,U_6215,U_6216),U_6217),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6215,
inference(variable_rename,[status(thm)],[f_1414_1]) ).
fof(f_1414_3,plain,
! [U_6215,U_6216,U_6217,U_6214] : hAPP(hAPP(c_Power_Opower_Opower(U_6214,U_6215,U_6216),U_6217),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6215,
inference(definitional_conversion,[status(esa)],[f_1414_2]) ).
cnf(f_1414_4,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_6214,U_6215,U_6216),U_6217),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6215,
inference(clausify,[status(thm)],[f_1414_3]) ).
fof(f_1415_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_1415_2,plain,
! [U_6221,U_6220,U_6219,U_6218] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6218),hAPP(hAPP(c_Power_Opower__class_Opower(U_6218),U_6219),U_6221)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6218),U_6220),U_6221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6218),c_Groups_Ozero__class_Ozero(U_6218)),U_6219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6218),U_6219),U_6220))
| ~ class_Rings_Olinordered__semidom(U_6218) ),
inference(variable_rename,[status(thm)],[f_1415_1]) ).
fof(f_1415_3,plain,
! [U_6218,U_6219,U_6220,U_6221] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6218),hAPP(hAPP(c_Power_Opower__class_Opower(U_6218),U_6219),U_6221)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6218),U_6220),U_6221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6218),c_Groups_Ozero__class_Ozero(U_6218)),U_6219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6218),U_6219),U_6220))
| ~ class_Rings_Olinordered__semidom(U_6218) ),
inference(definitional_conversion,[status(esa)],[f_1415_2]) ).
cnf(f_1415_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6218),hAPP(hAPP(c_Power_Opower__class_Opower(U_6218),U_6219),U_6221)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6218),U_6220),U_6221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6218),c_Groups_Ozero__class_Ozero(U_6218)),U_6219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6218),U_6219),U_6220))
| ~ class_Rings_Olinordered__semidom(U_6218) ),
inference(clausify,[status(thm)],[f_1415_3]) ).
fof(f_1416_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_c)))
| V_y_2 != c_Groups_Ozero__class_Ozero(T_c)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_c)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_c) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff]) ).
fof(f_1416_2,plain,
! [U_6224,U_6223,U_6222] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6222),U_6223),U_6223)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6222),U_6224),U_6224))),c_Groups_Ozero__class_Ozero(U_6222)))
| U_6224 != c_Groups_Ozero__class_Ozero(U_6222)
| U_6223 != c_Groups_Ozero__class_Ozero(U_6222) )
& ( ( U_6224 = c_Groups_Ozero__class_Ozero(U_6222)
& U_6223 = c_Groups_Ozero__class_Ozero(U_6222) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6222),U_6223),U_6223)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6222),U_6224),U_6224))),c_Groups_Ozero__class_Ozero(U_6222))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_6222) ),
inference(variable_rename,[status(thm)],[f_1416_1]) ).
fof(f_1416_3,plain,
( ! [U_6223,U_6222,U_6224] :
( U_6224 = c_Groups_Ozero__class_Ozero(U_6222)
| ~ sP306(U_6223,U_6222,U_6224) )
& ! [U_6223,U_6222,U_6224] :
( U_6223 = c_Groups_Ozero__class_Ozero(U_6222)
| ~ sP306(U_6223,U_6222,U_6224) )
& ! [U_6223,U_6222,U_6224] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6222),U_6223),U_6223)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6222),U_6224),U_6224))),c_Groups_Ozero__class_Ozero(U_6222)))
| U_6224 != c_Groups_Ozero__class_Ozero(U_6222)
| U_6223 != c_Groups_Ozero__class_Ozero(U_6222)
| ~ sP307(U_6223,U_6222,U_6224) )
& ! [U_6223,U_6222,U_6224] :
( sP306(U_6223,U_6222,U_6224)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6222),U_6223),U_6223)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6222),U_6224),U_6224))),c_Groups_Ozero__class_Ozero(U_6222)))
| ~ sP307(U_6223,U_6222,U_6224) )
& ! [U_6223,U_6222,U_6224] :
( sP307(U_6223,U_6222,U_6224)
| ~ class_Rings_Olinordered__ring__strict(U_6222) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP306,sP307])],[f_1416_2]) ).
cnf(f_1416_4,plain,
( sP307(U_6223,U_6222,U_6224)
| ~ class_Rings_Olinordered__ring__strict(U_6222) ),
inference(clausify,[status(thm)],[f_1416_3]) ).
cnf(f_1416_5,plain,
( sP306(U_6223,U_6222,U_6224)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6222),U_6223),U_6223)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6222),U_6224),U_6224))),c_Groups_Ozero__class_Ozero(U_6222)))
| ~ sP307(U_6223,U_6222,U_6224) ),
inference(clausify,[status(thm)],[f_1416_3]) ).
cnf(f_1416_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6222),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6222),U_6223),U_6223)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6222),U_6224),U_6224))),c_Groups_Ozero__class_Ozero(U_6222)))
| U_6224 != c_Groups_Ozero__class_Ozero(U_6222)
| U_6223 != c_Groups_Ozero__class_Ozero(U_6222)
| ~ sP307(U_6223,U_6222,U_6224) ),
inference(clausify,[status(thm)],[f_1416_3]) ).
cnf(f_1416_7,plain,
( U_6223 = c_Groups_Ozero__class_Ozero(U_6222)
| ~ sP306(U_6223,U_6222,U_6224) ),
inference(clausify,[status(thm)],[f_1416_3]) ).
cnf(f_1416_8,plain,
( U_6224 = c_Groups_Ozero__class_Ozero(U_6222)
| ~ sP306(U_6223,U_6222,U_6224) ),
inference(clausify,[status(thm)],[f_1416_3]) ).
fof(f_1417_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_1417_2,plain,
! [U_6227,U_6226,U_6225] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6225),c_Groups_Ozero__class_Ozero(U_6225)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6225),U_6226),U_6226)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6225),U_6227),U_6227))))
| ~ class_Rings_Olinordered__ring(U_6225) ),
inference(variable_rename,[status(thm)],[f_1417_1]) ).
fof(f_1417_3,plain,
! [U_6226,U_6227,U_6225] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6225),c_Groups_Ozero__class_Ozero(U_6225)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6225),U_6226),U_6226)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6225),U_6227),U_6227))))
| ~ class_Rings_Olinordered__ring(U_6225) ),
inference(definitional_conversion,[status(esa)],[f_1417_2]) ).
cnf(f_1417_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6225),c_Groups_Ozero__class_Ozero(U_6225)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6225),U_6226),U_6226)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6225),U_6227),U_6227))))
| ~ class_Rings_Olinordered__ring(U_6225) ),
inference(clausify,[status(thm)],[f_1417_3]) ).
fof(f_1418_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_y_2),V_y_2))))
| ( V_y_2 = c_Groups_Ozero__class_Ozero(T_c)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_c) ) )
& ( V_y_2 != c_Groups_Ozero__class_Ozero(T_c)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_y_2),V_y_2)))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff]) ).
fof(f_1418_2,plain,
! [U_6230,U_6229,U_6228] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6228),c_Groups_Ozero__class_Ozero(U_6228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6228),U_6229),U_6229)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6228),U_6230),U_6230))))
| ( U_6230 = c_Groups_Ozero__class_Ozero(U_6228)
& U_6229 = c_Groups_Ozero__class_Ozero(U_6228) ) )
& ( U_6230 != c_Groups_Ozero__class_Ozero(U_6228)
| U_6229 != c_Groups_Ozero__class_Ozero(U_6228)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6228),c_Groups_Ozero__class_Ozero(U_6228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6228),U_6229),U_6229)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6228),U_6230),U_6230)))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_6228) ),
inference(variable_rename,[status(thm)],[f_1418_1]) ).
fof(f_1418_3,plain,
( ! [U_6228,U_6229,U_6230] :
( U_6230 = c_Groups_Ozero__class_Ozero(U_6228)
| ~ sP308(U_6228,U_6229,U_6230) )
& ! [U_6228,U_6229,U_6230] :
( U_6229 = c_Groups_Ozero__class_Ozero(U_6228)
| ~ sP308(U_6228,U_6229,U_6230) )
& ! [U_6228,U_6229,U_6230] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6228),c_Groups_Ozero__class_Ozero(U_6228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6228),U_6229),U_6229)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6228),U_6230),U_6230))))
| sP308(U_6228,U_6229,U_6230)
| ~ sP309(U_6228,U_6229,U_6230) )
& ! [U_6228,U_6229,U_6230] :
( U_6230 != c_Groups_Ozero__class_Ozero(U_6228)
| U_6229 != c_Groups_Ozero__class_Ozero(U_6228)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6228),c_Groups_Ozero__class_Ozero(U_6228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6228),U_6229),U_6229)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6228),U_6230),U_6230))))
| ~ sP309(U_6228,U_6229,U_6230) )
& ! [U_6228,U_6229,U_6230] :
( sP309(U_6228,U_6229,U_6230)
| ~ class_Rings_Olinordered__ring__strict(U_6228) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP308,sP309])],[f_1418_2]) ).
cnf(f_1418_4,plain,
( sP309(U_6228,U_6229,U_6230)
| ~ class_Rings_Olinordered__ring__strict(U_6228) ),
inference(clausify,[status(thm)],[f_1418_3]) ).
cnf(f_1418_5,plain,
( U_6230 != c_Groups_Ozero__class_Ozero(U_6228)
| U_6229 != c_Groups_Ozero__class_Ozero(U_6228)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6228),c_Groups_Ozero__class_Ozero(U_6228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6228),U_6229),U_6229)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6228),U_6230),U_6230))))
| ~ sP309(U_6228,U_6229,U_6230) ),
inference(clausify,[status(thm)],[f_1418_3]) ).
cnf(f_1418_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6228),c_Groups_Ozero__class_Ozero(U_6228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6228),U_6229),U_6229)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6228),U_6230),U_6230))))
| sP308(U_6228,U_6229,U_6230)
| ~ sP309(U_6228,U_6229,U_6230) ),
inference(clausify,[status(thm)],[f_1418_3]) ).
cnf(f_1418_7,plain,
( U_6229 = c_Groups_Ozero__class_Ozero(U_6228)
| ~ sP308(U_6228,U_6229,U_6230) ),
inference(clausify,[status(thm)],[f_1418_3]) ).
cnf(f_1418_8,plain,
( U_6230 = c_Groups_Ozero__class_Ozero(U_6228)
| ~ sP308(U_6228,U_6229,U_6230) ),
inference(clausify,[status(thm)],[f_1418_3]) ).
fof(f_1419_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_1419_2,plain,
! [U_6233,U_6232,U_6231] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6231),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6231),U_6232),U_6232)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6231),U_6233),U_6233))),c_Groups_Ozero__class_Ozero(U_6231)))
| ~ class_Rings_Olinordered__ring(U_6231) ),
inference(variable_rename,[status(thm)],[f_1419_1]) ).
fof(f_1419_3,plain,
! [U_6232,U_6233,U_6231] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6231),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6231),U_6232),U_6232)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6231),U_6233),U_6233))),c_Groups_Ozero__class_Ozero(U_6231)))
| ~ class_Rings_Olinordered__ring(U_6231) ),
inference(definitional_conversion,[status(esa)],[f_1419_2]) ).
cnf(f_1419_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6231),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6231),U_6232),U_6232)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6231),U_6233),U_6233))),c_Groups_Ozero__class_Ozero(U_6231)))
| ~ class_Rings_Olinordered__ring(U_6231) ),
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__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_1420_2,plain,
! [U_6236,U_6235,U_6234] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6234),U_6235),U_6236)),c_Groups_Ozero__class_Ozero(U_6234)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6234),U_6236),c_Groups_Ozero__class_Ozero(U_6234)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6234),U_6235),c_Groups_Ozero__class_Ozero(U_6234)))
| ~ class_Groups_Oordered__comm__monoid__add(U_6234) ),
inference(variable_rename,[status(thm)],[f_1420_1]) ).
fof(f_1420_3,plain,
! [U_6234,U_6235,U_6236] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6234),U_6235),U_6236)),c_Groups_Ozero__class_Ozero(U_6234)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6234),U_6236),c_Groups_Ozero__class_Ozero(U_6234)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6234),U_6235),c_Groups_Ozero__class_Ozero(U_6234)))
| ~ class_Groups_Oordered__comm__monoid__add(U_6234) ),
inference(definitional_conversion,[status(esa)],[f_1420_2]) ).
cnf(f_1420_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6234),U_6235),U_6236)),c_Groups_Ozero__class_Ozero(U_6234)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6234),U_6236),c_Groups_Ozero__class_Ozero(U_6234)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6234),U_6235),c_Groups_Ozero__class_Ozero(U_6234)))
| ~ class_Groups_Oordered__comm__monoid__add(U_6234) ),
inference(clausify,[status(thm)],[f_1420_3]) ).
fof(f_1421_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_1421_2,plain,
! [U_6240,U_6239,U_6238,U_6237] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6237),U_6239),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6237),U_6240),U_6238)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6237),U_6239),U_6240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6237),c_Groups_Ozero__class_Ozero(U_6237)),U_6238))
| ~ class_Groups_Oordered__comm__monoid__add(U_6237) ),
inference(variable_rename,[status(thm)],[f_1421_1]) ).
fof(f_1421_3,plain,
! [U_6237,U_6238,U_6239,U_6240] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6237),U_6239),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6237),U_6240),U_6238)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6237),U_6239),U_6240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6237),c_Groups_Ozero__class_Ozero(U_6237)),U_6238))
| ~ class_Groups_Oordered__comm__monoid__add(U_6237) ),
inference(definitional_conversion,[status(esa)],[f_1421_2]) ).
cnf(f_1421_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6237),U_6239),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6237),U_6240),U_6238)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6237),U_6239),U_6240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6237),c_Groups_Ozero__class_Ozero(U_6237)),U_6238))
| ~ class_Groups_Oordered__comm__monoid__add(U_6237) ),
inference(clausify,[status(thm)],[f_1421_3]) ).
fof(f_1422_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_1422_2,plain,
! [U_6244,U_6243,U_6242,U_6241] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6241),U_6243),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6241),U_6242),U_6244)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6241),U_6243),U_6244))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6241),c_Groups_Ozero__class_Ozero(U_6241)),U_6242))
| ~ class_Groups_Oordered__comm__monoid__add(U_6241) ),
inference(variable_rename,[status(thm)],[f_1422_1]) ).
fof(f_1422_3,plain,
! [U_6242,U_6241,U_6243,U_6244] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6241),U_6243),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6241),U_6242),U_6244)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6241),U_6243),U_6244))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6241),c_Groups_Ozero__class_Ozero(U_6241)),U_6242))
| ~ class_Groups_Oordered__comm__monoid__add(U_6241) ),
inference(definitional_conversion,[status(esa)],[f_1422_2]) ).
cnf(f_1422_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6241),U_6243),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6241),U_6242),U_6244)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6241),U_6243),U_6244))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6241),c_Groups_Ozero__class_Ozero(U_6241)),U_6242))
| ~ class_Groups_Oordered__comm__monoid__add(U_6241) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
fof(f_1423_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_c)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_c)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_c) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_x_2),V_y_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_x_2))
| ~ class_Groups_Oordered__comm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff]) ).
fof(f_1423_2,plain,
! [U_6247,U_6246,U_6245] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6245),U_6246),U_6247) = c_Groups_Ozero__class_Ozero(U_6245)
| U_6247 != c_Groups_Ozero__class_Ozero(U_6245)
| U_6246 != c_Groups_Ozero__class_Ozero(U_6245) )
& ( ( U_6247 = c_Groups_Ozero__class_Ozero(U_6245)
& U_6246 = c_Groups_Ozero__class_Ozero(U_6245) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6245),U_6246),U_6247) != c_Groups_Ozero__class_Ozero(U_6245) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6245),c_Groups_Ozero__class_Ozero(U_6245)),U_6247))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6245),c_Groups_Ozero__class_Ozero(U_6245)),U_6246))
| ~ class_Groups_Oordered__comm__monoid__add(U_6245) ),
inference(variable_rename,[status(thm)],[f_1423_1]) ).
fof(f_1423_3,plain,
( ! [U_6245,U_6246,U_6247] :
( U_6247 = c_Groups_Ozero__class_Ozero(U_6245)
| ~ sP310(U_6245,U_6246,U_6247) )
& ! [U_6245,U_6246,U_6247] :
( U_6246 = c_Groups_Ozero__class_Ozero(U_6245)
| ~ sP310(U_6245,U_6246,U_6247) )
& ! [U_6245,U_6246,U_6247] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6245),U_6246),U_6247) = c_Groups_Ozero__class_Ozero(U_6245)
| U_6247 != c_Groups_Ozero__class_Ozero(U_6245)
| U_6246 != c_Groups_Ozero__class_Ozero(U_6245)
| ~ sP311(U_6245,U_6246,U_6247) )
& ! [U_6245,U_6246,U_6247] :
( sP310(U_6245,U_6246,U_6247)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6245),U_6246),U_6247) != c_Groups_Ozero__class_Ozero(U_6245)
| ~ sP311(U_6245,U_6246,U_6247) )
& ! [U_6245,U_6246,U_6247] :
( sP311(U_6245,U_6246,U_6247)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6245),c_Groups_Ozero__class_Ozero(U_6245)),U_6247))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6245),c_Groups_Ozero__class_Ozero(U_6245)),U_6246))
| ~ class_Groups_Oordered__comm__monoid__add(U_6245) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP310,sP311])],[f_1423_2]) ).
cnf(f_1423_4,plain,
( sP311(U_6245,U_6246,U_6247)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6245),c_Groups_Ozero__class_Ozero(U_6245)),U_6247))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6245),c_Groups_Ozero__class_Ozero(U_6245)),U_6246))
| ~ class_Groups_Oordered__comm__monoid__add(U_6245) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_5,plain,
( sP310(U_6245,U_6246,U_6247)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6245),U_6246),U_6247) != c_Groups_Ozero__class_Ozero(U_6245)
| ~ sP311(U_6245,U_6246,U_6247) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6245),U_6246),U_6247) = c_Groups_Ozero__class_Ozero(U_6245)
| U_6247 != c_Groups_Ozero__class_Ozero(U_6245)
| U_6246 != c_Groups_Ozero__class_Ozero(U_6245)
| ~ sP311(U_6245,U_6246,U_6247) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_7,plain,
( U_6246 = c_Groups_Ozero__class_Ozero(U_6245)
| ~ sP310(U_6245,U_6246,U_6247) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
cnf(f_1423_8,plain,
( U_6247 = c_Groups_Ozero__class_Ozero(U_6245)
| ~ sP310(U_6245,U_6246,U_6247) ),
inference(clausify,[status(thm)],[f_1423_3]) ).
fof(f_1424_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_1424_2,plain,
! [U_6250,U_6249,U_6248] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6248),c_Groups_Ozero__class_Ozero(U_6248)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6248),U_6249),U_6250)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6248),c_Groups_Ozero__class_Ozero(U_6248)),U_6250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6248),c_Groups_Ozero__class_Ozero(U_6248)),U_6249))
| ~ class_Groups_Oordered__comm__monoid__add(U_6248) ),
inference(variable_rename,[status(thm)],[f_1424_1]) ).
fof(f_1424_3,plain,
! [U_6249,U_6250,U_6248] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6248),c_Groups_Ozero__class_Ozero(U_6248)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6248),U_6249),U_6250)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6248),c_Groups_Ozero__class_Ozero(U_6248)),U_6250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6248),c_Groups_Ozero__class_Ozero(U_6248)),U_6249))
| ~ class_Groups_Oordered__comm__monoid__add(U_6248) ),
inference(definitional_conversion,[status(esa)],[f_1424_2]) ).
cnf(f_1424_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6248),c_Groups_Ozero__class_Ozero(U_6248)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6248),U_6249),U_6250)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6248),c_Groups_Ozero__class_Ozero(U_6248)),U_6250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6248),c_Groups_Ozero__class_Ozero(U_6248)),U_6249))
| ~ class_Groups_Oordered__comm__monoid__add(U_6248) ),
inference(clausify,[status(thm)],[f_1424_3]) ).
fof(f_1425_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero]) ).
fof(f_1425_2,plain,
! [U_6252,U_6251] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6251),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6251),U_6252),U_6252)),c_Groups_Ozero__class_Ozero(U_6251)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6251),U_6252),c_Groups_Ozero__class_Ozero(U_6251))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6251),U_6252),c_Groups_Ozero__class_Ozero(U_6251)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6251),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6251),U_6252),U_6252)),c_Groups_Ozero__class_Ozero(U_6251))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_6251) ),
inference(variable_rename,[status(thm)],[f_1425_1]) ).
fof(f_1425_3,plain,
( ! [U_6251,U_6252] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6251),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6251),U_6252),U_6252)),c_Groups_Ozero__class_Ozero(U_6251)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6251),U_6252),c_Groups_Ozero__class_Ozero(U_6251)))
| ~ sP312(U_6251,U_6252) )
& ! [U_6251,U_6252] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6251),U_6252),c_Groups_Ozero__class_Ozero(U_6251)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6251),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6251),U_6252),U_6252)),c_Groups_Ozero__class_Ozero(U_6251)))
| ~ sP312(U_6251,U_6252) )
& ! [U_6251,U_6252] :
( sP312(U_6251,U_6252)
| ~ class_Groups_Olinordered__ab__group__add(U_6251) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP312])],[f_1425_2]) ).
cnf(f_1425_4,plain,
( sP312(U_6251,U_6252)
| ~ class_Groups_Olinordered__ab__group__add(U_6251) ),
inference(clausify,[status(thm)],[f_1425_3]) ).
cnf(f_1425_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6251),U_6252),c_Groups_Ozero__class_Ozero(U_6251)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6251),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6251),U_6252),U_6252)),c_Groups_Ozero__class_Ozero(U_6251)))
| ~ sP312(U_6251,U_6252) ),
inference(clausify,[status(thm)],[f_1425_3]) ).
cnf(f_1425_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6251),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6251),U_6252),U_6252)),c_Groups_Ozero__class_Ozero(U_6251)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6251),U_6252),c_Groups_Ozero__class_Ozero(U_6251)))
| ~ sP312(U_6251,U_6252) ),
inference(clausify,[status(thm)],[f_1425_3]) ).
fof(f_1426_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add]) ).
fof(f_1426_2,plain,
! [U_6254,U_6253] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),c_Groups_Ozero__class_Ozero(U_6253)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6253),U_6254),U_6254)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),c_Groups_Ozero__class_Ozero(U_6253)),U_6254)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),c_Groups_Ozero__class_Ozero(U_6253)),U_6254))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),c_Groups_Ozero__class_Ozero(U_6253)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6253),U_6254),U_6254))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_6253) ),
inference(variable_rename,[status(thm)],[f_1426_1]) ).
fof(f_1426_3,plain,
( ! [U_6254,U_6253] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),c_Groups_Ozero__class_Ozero(U_6253)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6253),U_6254),U_6254)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),c_Groups_Ozero__class_Ozero(U_6253)),U_6254))
| ~ sP313(U_6254,U_6253) )
& ! [U_6254,U_6253] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),c_Groups_Ozero__class_Ozero(U_6253)),U_6254))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),c_Groups_Ozero__class_Ozero(U_6253)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6253),U_6254),U_6254)))
| ~ sP313(U_6254,U_6253) )
& ! [U_6254,U_6253] :
( sP313(U_6254,U_6253)
| ~ class_Groups_Olinordered__ab__group__add(U_6253) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP313])],[f_1426_2]) ).
cnf(f_1426_4,plain,
( sP313(U_6254,U_6253)
| ~ class_Groups_Olinordered__ab__group__add(U_6253) ),
inference(clausify,[status(thm)],[f_1426_3]) ).
cnf(f_1426_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),c_Groups_Ozero__class_Ozero(U_6253)),U_6254))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),c_Groups_Ozero__class_Ozero(U_6253)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6253),U_6254),U_6254)))
| ~ sP313(U_6254,U_6253) ),
inference(clausify,[status(thm)],[f_1426_3]) ).
cnf(f_1426_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),c_Groups_Ozero__class_Ozero(U_6253)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6253),U_6254),U_6254)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),c_Groups_Ozero__class_Ozero(U_6253)),U_6254))
| ~ sP313(U_6254,U_6253) ),
inference(clausify,[status(thm)],[f_1426_3]) ).
fof(f_1427_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_1427_2,plain,
! [U_6256,U_6255] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6255),c_Groups_Ozero__class_Ozero(U_6255)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6255),U_6256),U_6256)))
| ~ class_Rings_Olinordered__ring(U_6255) ),
inference(variable_rename,[status(thm)],[f_1427_1]) ).
fof(f_1427_3,plain,
! [U_6256,U_6255] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6255),c_Groups_Ozero__class_Ozero(U_6255)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6255),U_6256),U_6256)))
| ~ class_Rings_Olinordered__ring(U_6255) ),
inference(definitional_conversion,[status(esa)],[f_1427_2]) ).
cnf(f_1427_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6255),c_Groups_Ozero__class_Ozero(U_6255)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6255),U_6256),U_6256)))
| ~ class_Rings_Olinordered__ring(U_6255) ),
inference(clausify,[status(thm)],[f_1427_3]) ).
fof(f_1428_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_c) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff]) ).
fof(f_1428_2,plain,
! [U_6259,U_6258,U_6257] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6257),U_6258),U_6259)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6259),c_Groups_Ozero__class_Ozero(U_6257)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),c_Groups_Ozero__class_Ozero(U_6257))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),U_6259))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),U_6258)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6259),c_Groups_Ozero__class_Ozero(U_6257)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),c_Groups_Ozero__class_Ozero(U_6257))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),U_6259))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),U_6258)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6257),U_6258),U_6259))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_6257) ),
inference(variable_rename,[status(thm)],[f_1428_1]) ).
fof(f_1428_3,plain,
( ! [U_6257,U_6258,U_6259] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6259),c_Groups_Ozero__class_Ozero(U_6257)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),c_Groups_Ozero__class_Ozero(U_6257)))
| ~ sP316(U_6257,U_6258,U_6259) )
& ! [U_6257,U_6258,U_6259] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),U_6259))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),U_6258))
| ~ sP316(U_6257,U_6258,U_6259) )
& ! [U_6257,U_6258,U_6259] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6259),c_Groups_Ozero__class_Ozero(U_6257)))
| ~ sP315(U_6257,U_6258,U_6259) )
& ! [U_6257,U_6258,U_6259] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),c_Groups_Ozero__class_Ozero(U_6257)))
| ~ sP315(U_6257,U_6258,U_6259) )
& ! [U_6257,U_6258,U_6259] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),U_6259))
| ~ sP314(U_6257,U_6258,U_6259) )
& ! [U_6257,U_6258,U_6259] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),U_6258))
| ~ sP314(U_6257,U_6258,U_6259) )
& ! [U_6257,U_6258,U_6259] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6257),U_6258),U_6259)))
| sP316(U_6257,U_6258,U_6259)
| ~ sP317(U_6257,U_6258,U_6259) )
& ! [U_6257,U_6258,U_6259] :
( sP315(U_6257,U_6258,U_6259)
| sP314(U_6257,U_6258,U_6259)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6257),U_6258),U_6259)))
| ~ sP317(U_6257,U_6258,U_6259) )
& ! [U_6257,U_6258,U_6259] :
( sP317(U_6257,U_6258,U_6259)
| ~ class_Rings_Olinordered__ring__strict(U_6257) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP314,sP315,sP316,sP317])],[f_1428_2]) ).
cnf(f_1428_4,plain,
( sP317(U_6257,U_6258,U_6259)
| ~ class_Rings_Olinordered__ring__strict(U_6257) ),
inference(clausify,[status(thm)],[f_1428_3]) ).
cnf(f_1428_5,plain,
( sP315(U_6257,U_6258,U_6259)
| sP314(U_6257,U_6258,U_6259)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6257),U_6258),U_6259)))
| ~ sP317(U_6257,U_6258,U_6259) ),
inference(clausify,[status(thm)],[f_1428_3]) ).
cnf(f_1428_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6257),U_6258),U_6259)))
| sP316(U_6257,U_6258,U_6259)
| ~ sP317(U_6257,U_6258,U_6259) ),
inference(clausify,[status(thm)],[f_1428_3]) ).
cnf(f_1428_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),U_6258))
| ~ sP314(U_6257,U_6258,U_6259) ),
inference(clausify,[status(thm)],[f_1428_3]) ).
cnf(f_1428_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),U_6259))
| ~ sP314(U_6257,U_6258,U_6259) ),
inference(clausify,[status(thm)],[f_1428_3]) ).
cnf(f_1428_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),c_Groups_Ozero__class_Ozero(U_6257)))
| ~ sP315(U_6257,U_6258,U_6259) ),
inference(clausify,[status(thm)],[f_1428_3]) ).
cnf(f_1428_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6259),c_Groups_Ozero__class_Ozero(U_6257)))
| ~ sP315(U_6257,U_6258,U_6259) ),
inference(clausify,[status(thm)],[f_1428_3]) ).
cnf(f_1428_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),U_6259))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),c_Groups_Ozero__class_Ozero(U_6257)),U_6258))
| ~ sP316(U_6257,U_6258,U_6259) ),
inference(clausify,[status(thm)],[f_1428_3]) ).
cnf(f_1428_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6259),c_Groups_Ozero__class_Ozero(U_6257)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),c_Groups_Ozero__class_Ozero(U_6257)))
| ~ sP316(U_6257,U_6258,U_6259) ),
inference(clausify,[status(thm)],[f_1428_3]) ).
fof(f_1429_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_c) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff]) ).
fof(f_1429_2,plain,
! [U_6262,U_6261,U_6260] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6260),U_6261),U_6262)),c_Groups_Ozero__class_Ozero(U_6260)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),c_Groups_Ozero__class_Ozero(U_6260)),U_6262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),U_6261),c_Groups_Ozero__class_Ozero(U_6260))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),U_6262),c_Groups_Ozero__class_Ozero(U_6260)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),c_Groups_Ozero__class_Ozero(U_6260)),U_6261)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),c_Groups_Ozero__class_Ozero(U_6260)),U_6262))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),U_6261),c_Groups_Ozero__class_Ozero(U_6260))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),U_6262),c_Groups_Ozero__class_Ozero(U_6260)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),c_Groups_Ozero__class_Ozero(U_6260)),U_6261)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6260),U_6261),U_6262)),c_Groups_Ozero__class_Ozero(U_6260))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_6260) ),
inference(variable_rename,[status(thm)],[f_1429_1]) ).
fof(f_1429_3,plain,
( ! [U_6261,U_6262,U_6260] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),c_Groups_Ozero__class_Ozero(U_6260)),U_6262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),U_6261),c_Groups_Ozero__class_Ozero(U_6260)))
| ~ sP320(U_6261,U_6262,U_6260) )
& ! [U_6261,U_6262,U_6260] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),U_6262),c_Groups_Ozero__class_Ozero(U_6260)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),c_Groups_Ozero__class_Ozero(U_6260)),U_6261))
| ~ sP320(U_6261,U_6262,U_6260) )
& ! [U_6261,U_6262,U_6260] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),c_Groups_Ozero__class_Ozero(U_6260)),U_6262))
| ~ sP319(U_6261,U_6262,U_6260) )
& ! [U_6261,U_6262,U_6260] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),U_6261),c_Groups_Ozero__class_Ozero(U_6260)))
| ~ sP319(U_6261,U_6262,U_6260) )
& ! [U_6261,U_6262,U_6260] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),U_6262),c_Groups_Ozero__class_Ozero(U_6260)))
| ~ sP318(U_6261,U_6262,U_6260) )
& ! [U_6261,U_6262,U_6260] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),c_Groups_Ozero__class_Ozero(U_6260)),U_6261))
| ~ sP318(U_6261,U_6262,U_6260) )
& ! [U_6261,U_6262,U_6260] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6260),U_6261),U_6262)),c_Groups_Ozero__class_Ozero(U_6260)))
| sP320(U_6261,U_6262,U_6260)
| ~ sP321(U_6261,U_6262,U_6260) )
& ! [U_6261,U_6262,U_6260] :
( sP319(U_6261,U_6262,U_6260)
| sP318(U_6261,U_6262,U_6260)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6260),U_6261),U_6262)),c_Groups_Ozero__class_Ozero(U_6260)))
| ~ sP321(U_6261,U_6262,U_6260) )
& ! [U_6261,U_6262,U_6260] :
( sP321(U_6261,U_6262,U_6260)
| ~ class_Rings_Olinordered__ring__strict(U_6260) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP318,sP319,sP320,sP321])],[f_1429_2]) ).
cnf(f_1429_4,plain,
( sP321(U_6261,U_6262,U_6260)
| ~ class_Rings_Olinordered__ring__strict(U_6260) ),
inference(clausify,[status(thm)],[f_1429_3]) ).
cnf(f_1429_5,plain,
( sP319(U_6261,U_6262,U_6260)
| sP318(U_6261,U_6262,U_6260)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6260),U_6261),U_6262)),c_Groups_Ozero__class_Ozero(U_6260)))
| ~ sP321(U_6261,U_6262,U_6260) ),
inference(clausify,[status(thm)],[f_1429_3]) ).
cnf(f_1429_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6260),U_6261),U_6262)),c_Groups_Ozero__class_Ozero(U_6260)))
| sP320(U_6261,U_6262,U_6260)
| ~ sP321(U_6261,U_6262,U_6260) ),
inference(clausify,[status(thm)],[f_1429_3]) ).
cnf(f_1429_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),c_Groups_Ozero__class_Ozero(U_6260)),U_6261))
| ~ sP318(U_6261,U_6262,U_6260) ),
inference(clausify,[status(thm)],[f_1429_3]) ).
cnf(f_1429_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),U_6262),c_Groups_Ozero__class_Ozero(U_6260)))
| ~ sP318(U_6261,U_6262,U_6260) ),
inference(clausify,[status(thm)],[f_1429_3]) ).
cnf(f_1429_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),U_6261),c_Groups_Ozero__class_Ozero(U_6260)))
| ~ sP319(U_6261,U_6262,U_6260) ),
inference(clausify,[status(thm)],[f_1429_3]) ).
cnf(f_1429_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),c_Groups_Ozero__class_Ozero(U_6260)),U_6262))
| ~ sP319(U_6261,U_6262,U_6260) ),
inference(clausify,[status(thm)],[f_1429_3]) ).
cnf(f_1429_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),U_6262),c_Groups_Ozero__class_Ozero(U_6260)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),c_Groups_Ozero__class_Ozero(U_6260)),U_6261))
| ~ sP320(U_6261,U_6262,U_6260) ),
inference(clausify,[status(thm)],[f_1429_3]) ).
cnf(f_1429_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),c_Groups_Ozero__class_Ozero(U_6260)),U_6262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6260),U_6261),c_Groups_Ozero__class_Ozero(U_6260)))
| ~ sP320(U_6261,U_6262,U_6260) ),
inference(clausify,[status(thm)],[f_1429_3]) ).
fof(f_1430_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_1430_2,plain,
! [U_6265,U_6264,U_6263] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6263),c_Groups_Ozero__class_Ozero(U_6263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6263),U_6264),U_6265)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6263),c_Groups_Ozero__class_Ozero(U_6263)),U_6265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6263),c_Groups_Ozero__class_Ozero(U_6263)),U_6264))
| ~ class_Rings_Oordered__cancel__semiring(U_6263) ),
inference(variable_rename,[status(thm)],[f_1430_1]) ).
fof(f_1430_3,plain,
! [U_6264,U_6263,U_6265] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6263),c_Groups_Ozero__class_Ozero(U_6263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6263),U_6264),U_6265)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6263),c_Groups_Ozero__class_Ozero(U_6263)),U_6265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6263),c_Groups_Ozero__class_Ozero(U_6263)),U_6264))
| ~ class_Rings_Oordered__cancel__semiring(U_6263) ),
inference(definitional_conversion,[status(esa)],[f_1430_2]) ).
cnf(f_1430_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6263),c_Groups_Ozero__class_Ozero(U_6263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6263),U_6264),U_6265)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6263),c_Groups_Ozero__class_Ozero(U_6263)),U_6265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6263),c_Groups_Ozero__class_Ozero(U_6263)),U_6264))
| ~ class_Rings_Oordered__cancel__semiring(U_6263) ),
inference(clausify,[status(thm)],[f_1430_3]) ).
fof(f_1431_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_1431_2,plain,
! [U_6268,U_6267,U_6266] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6266),U_6267),U_6268)),c_Groups_Ozero__class_Ozero(U_6266)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),U_6268),c_Groups_Ozero__class_Ozero(U_6266)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),c_Groups_Ozero__class_Ozero(U_6266)),U_6267))
| ~ class_Rings_Oordered__cancel__semiring(U_6266) ),
inference(variable_rename,[status(thm)],[f_1431_1]) ).
fof(f_1431_3,plain,
! [U_6267,U_6266,U_6268] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6266),U_6267),U_6268)),c_Groups_Ozero__class_Ozero(U_6266)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),U_6268),c_Groups_Ozero__class_Ozero(U_6266)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),c_Groups_Ozero__class_Ozero(U_6266)),U_6267))
| ~ class_Rings_Oordered__cancel__semiring(U_6266) ),
inference(definitional_conversion,[status(esa)],[f_1431_2]) ).
cnf(f_1431_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6266),U_6267),U_6268)),c_Groups_Ozero__class_Ozero(U_6266)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),U_6268),c_Groups_Ozero__class_Ozero(U_6266)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),c_Groups_Ozero__class_Ozero(U_6266)),U_6267))
| ~ class_Rings_Oordered__cancel__semiring(U_6266) ),
inference(clausify,[status(thm)],[f_1431_3]) ).
fof(f_1432_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_1432_2,plain,
! [U_6271,U_6270,U_6269] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6269),U_6271),U_6270)),c_Groups_Ozero__class_Ozero(U_6269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6269),U_6271),c_Groups_Ozero__class_Ozero(U_6269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6269),c_Groups_Ozero__class_Ozero(U_6269)),U_6270))
| ~ class_Rings_Oordered__cancel__semiring(U_6269) ),
inference(variable_rename,[status(thm)],[f_1432_1]) ).
fof(f_1432_3,plain,
! [U_6269,U_6270,U_6271] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6269),U_6271),U_6270)),c_Groups_Ozero__class_Ozero(U_6269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6269),U_6271),c_Groups_Ozero__class_Ozero(U_6269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6269),c_Groups_Ozero__class_Ozero(U_6269)),U_6270))
| ~ class_Rings_Oordered__cancel__semiring(U_6269) ),
inference(definitional_conversion,[status(esa)],[f_1432_2]) ).
cnf(f_1432_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6269),U_6271),U_6270)),c_Groups_Ozero__class_Ozero(U_6269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6269),U_6271),c_Groups_Ozero__class_Ozero(U_6269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6269),c_Groups_Ozero__class_Ozero(U_6269)),U_6270))
| ~ class_Rings_Oordered__cancel__semiring(U_6269) ),
inference(clausify,[status(thm)],[f_1432_3]) ).
fof(f_1433_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_1433_2,plain,
! [U_6274,U_6273,U_6272] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6272),U_6273),U_6274)),c_Groups_Ozero__class_Ozero(U_6272)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6272),c_Groups_Ozero__class_Ozero(U_6272)),U_6274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6272),U_6273),c_Groups_Ozero__class_Ozero(U_6272)))
| ~ class_Rings_Oordered__cancel__semiring(U_6272) ),
inference(variable_rename,[status(thm)],[f_1433_1]) ).
fof(f_1433_3,plain,
! [U_6272,U_6273,U_6274] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6272),U_6273),U_6274)),c_Groups_Ozero__class_Ozero(U_6272)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6272),c_Groups_Ozero__class_Ozero(U_6272)),U_6274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6272),U_6273),c_Groups_Ozero__class_Ozero(U_6272)))
| ~ class_Rings_Oordered__cancel__semiring(U_6272) ),
inference(definitional_conversion,[status(esa)],[f_1433_2]) ).
cnf(f_1433_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6272),U_6273),U_6274)),c_Groups_Ozero__class_Ozero(U_6272)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6272),c_Groups_Ozero__class_Ozero(U_6272)),U_6274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6272),U_6273),c_Groups_Ozero__class_Ozero(U_6272)))
| ~ class_Rings_Oordered__cancel__semiring(U_6272) ),
inference(clausify,[status(thm)],[f_1433_3]) ).
fof(f_1434_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_1434_2,plain,
! [U_6277,U_6276,U_6275] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6275),c_Groups_Ozero__class_Ozero(U_6275)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6275),U_6276),U_6277)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6275),U_6277),c_Groups_Ozero__class_Ozero(U_6275)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6275),U_6276),c_Groups_Ozero__class_Ozero(U_6275)))
| ~ class_Rings_Oordered__ring(U_6275) ),
inference(variable_rename,[status(thm)],[f_1434_1]) ).
fof(f_1434_3,plain,
! [U_6275,U_6276,U_6277] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6275),c_Groups_Ozero__class_Ozero(U_6275)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6275),U_6276),U_6277)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6275),U_6277),c_Groups_Ozero__class_Ozero(U_6275)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6275),U_6276),c_Groups_Ozero__class_Ozero(U_6275)))
| ~ class_Rings_Oordered__ring(U_6275) ),
inference(definitional_conversion,[status(esa)],[f_1434_2]) ).
cnf(f_1434_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6275),c_Groups_Ozero__class_Ozero(U_6275)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6275),U_6276),U_6277)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6275),U_6277),c_Groups_Ozero__class_Ozero(U_6275)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6275),U_6276),c_Groups_Ozero__class_Ozero(U_6275)))
| ~ class_Rings_Oordered__ring(U_6275) ),
inference(clausify,[status(thm)],[f_1434_3]) ).
fof(f_1435_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_1435_2,plain,
! [U_6281,U_6280,U_6279,U_6278] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6278),U_6279),U_6281)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6278),U_6280),U_6281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),c_Groups_Ozero__class_Ozero(U_6278)),U_6281))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),U_6279),U_6280))
| ~ class_Rings_Oordered__semiring(U_6278) ),
inference(variable_rename,[status(thm)],[f_1435_1]) ).
fof(f_1435_3,plain,
! [U_6278,U_6279,U_6280,U_6281] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6278),U_6279),U_6281)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6278),U_6280),U_6281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),c_Groups_Ozero__class_Ozero(U_6278)),U_6281))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),U_6279),U_6280))
| ~ class_Rings_Oordered__semiring(U_6278) ),
inference(definitional_conversion,[status(esa)],[f_1435_2]) ).
cnf(f_1435_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6278),U_6279),U_6281)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6278),U_6280),U_6281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),c_Groups_Ozero__class_Ozero(U_6278)),U_6281))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6278),U_6279),U_6280))
| ~ class_Rings_Oordered__semiring(U_6278) ),
inference(clausify,[status(thm)],[f_1435_3]) ).
fof(f_1436_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_1436_2,plain,
! [U_6285,U_6284,U_6283,U_6282] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6282),U_6285),U_6283)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6282),U_6285),U_6284)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6282),c_Groups_Ozero__class_Ozero(U_6282)),U_6285))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6282),U_6283),U_6284))
| ~ class_Rings_Oordered__semiring(U_6282) ),
inference(variable_rename,[status(thm)],[f_1436_1]) ).
fof(f_1436_3,plain,
! [U_6282,U_6283,U_6284,U_6285] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6282),U_6285),U_6283)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6282),U_6285),U_6284)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6282),c_Groups_Ozero__class_Ozero(U_6282)),U_6285))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6282),U_6283),U_6284))
| ~ class_Rings_Oordered__semiring(U_6282) ),
inference(definitional_conversion,[status(esa)],[f_1436_2]) ).
cnf(f_1436_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6282),U_6285),U_6283)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6282),U_6285),U_6284)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6282),c_Groups_Ozero__class_Ozero(U_6282)),U_6285))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6282),U_6283),U_6284))
| ~ class_Rings_Oordered__semiring(U_6282) ),
inference(clausify,[status(thm)],[f_1436_3]) ).
fof(f_1437_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_1437_2,plain,
! [U_6289,U_6288,U_6287,U_6286] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6286),U_6289),U_6287)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6286),U_6289),U_6288)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6286),c_Groups_Ozero__class_Ozero(U_6286)),U_6289))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6286),U_6287),U_6288))
| ~ class_Rings_Oordered__comm__semiring(U_6286) ),
inference(variable_rename,[status(thm)],[f_1437_1]) ).
fof(f_1437_3,plain,
! [U_6286,U_6287,U_6288,U_6289] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6286),U_6289),U_6287)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6286),U_6289),U_6288)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6286),c_Groups_Ozero__class_Ozero(U_6286)),U_6289))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6286),U_6287),U_6288))
| ~ class_Rings_Oordered__comm__semiring(U_6286) ),
inference(definitional_conversion,[status(esa)],[f_1437_2]) ).
cnf(f_1437_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6286),U_6289),U_6287)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6286),U_6289),U_6288)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6286),c_Groups_Ozero__class_Ozero(U_6286)),U_6289))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6286),U_6287),U_6288))
| ~ class_Rings_Oordered__comm__semiring(U_6286) ),
inference(clausify,[status(thm)],[f_1437_3]) ).
fof(f_1438_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_1438_2,plain,
! [U_6293,U_6292,U_6291,U_6290] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6290),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6290),U_6292),U_6293)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6290),U_6291),U_6293)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6290),U_6293),c_Groups_Ozero__class_Ozero(U_6290)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6290),U_6291),U_6292))
| ~ class_Rings_Oordered__ring(U_6290) ),
inference(variable_rename,[status(thm)],[f_1438_1]) ).
fof(f_1438_3,plain,
! [U_6290,U_6291,U_6292,U_6293] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6290),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6290),U_6292),U_6293)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6290),U_6291),U_6293)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6290),U_6293),c_Groups_Ozero__class_Ozero(U_6290)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6290),U_6291),U_6292))
| ~ class_Rings_Oordered__ring(U_6290) ),
inference(definitional_conversion,[status(esa)],[f_1438_2]) ).
cnf(f_1438_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6290),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6290),U_6292),U_6293)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6290),U_6291),U_6293)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6290),U_6293),c_Groups_Ozero__class_Ozero(U_6290)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6290),U_6291),U_6292))
| ~ class_Rings_Oordered__ring(U_6290) ),
inference(clausify,[status(thm)],[f_1438_3]) ).
fof(f_1439_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_1439_2,plain,
! [U_6297,U_6296,U_6295,U_6294] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6294),U_6297),U_6296)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6294),U_6297),U_6295)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6294),U_6297),c_Groups_Ozero__class_Ozero(U_6294)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6294),U_6295),U_6296))
| ~ class_Rings_Oordered__ring(U_6294) ),
inference(variable_rename,[status(thm)],[f_1439_1]) ).
fof(f_1439_3,plain,
! [U_6294,U_6295,U_6296,U_6297] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6294),U_6297),U_6296)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6294),U_6297),U_6295)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6294),U_6297),c_Groups_Ozero__class_Ozero(U_6294)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6294),U_6295),U_6296))
| ~ class_Rings_Oordered__ring(U_6294) ),
inference(definitional_conversion,[status(esa)],[f_1439_2]) ).
cnf(f_1439_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6294),U_6297),U_6296)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6294),U_6297),U_6295)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6294),U_6297),c_Groups_Ozero__class_Ozero(U_6294)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6294),U_6295),U_6296))
| ~ class_Rings_Oordered__ring(U_6294) ),
inference(clausify,[status(thm)],[f_1439_3]) ).
fof(f_1440_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_1440_2,plain,
! [U_6302,U_6301,U_6300,U_6299,U_6298] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6298),U_6299),U_6301)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6298),U_6300),U_6302)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),c_Groups_Ozero__class_Ozero(U_6298)),U_6301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),c_Groups_Ozero__class_Ozero(U_6298)),U_6299))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),U_6301),U_6302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),U_6299),U_6300))
| ~ class_Rings_Oordered__semiring(U_6298) ),
inference(variable_rename,[status(thm)],[f_1440_1]) ).
fof(f_1440_3,plain,
! [U_6298,U_6299,U_6300,U_6301,U_6302] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6298),U_6299),U_6301)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6298),U_6300),U_6302)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),c_Groups_Ozero__class_Ozero(U_6298)),U_6301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),c_Groups_Ozero__class_Ozero(U_6298)),U_6299))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),U_6301),U_6302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),U_6299),U_6300))
| ~ class_Rings_Oordered__semiring(U_6298) ),
inference(definitional_conversion,[status(esa)],[f_1440_2]) ).
cnf(f_1440_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6298),U_6299),U_6301)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6298),U_6300),U_6302)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),c_Groups_Ozero__class_Ozero(U_6298)),U_6301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),c_Groups_Ozero__class_Ozero(U_6298)),U_6299))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),U_6301),U_6302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6298),U_6299),U_6300))
| ~ class_Rings_Oordered__semiring(U_6298) ),
inference(clausify,[status(thm)],[f_1440_3]) ).
fof(f_1441_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_1441_2,plain,
! [U_6307,U_6306,U_6305,U_6304,U_6303] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6303),U_6304),U_6306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6303),U_6305),U_6307)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),c_Groups_Ozero__class_Ozero(U_6303)),U_6306))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),c_Groups_Ozero__class_Ozero(U_6303)),U_6305))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),U_6306),U_6307))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),U_6304),U_6305))
| ~ class_Rings_Oordered__semiring(U_6303) ),
inference(variable_rename,[status(thm)],[f_1441_1]) ).
fof(f_1441_3,plain,
! [U_6304,U_6303,U_6306,U_6305,U_6307] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6303),U_6304),U_6306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6303),U_6305),U_6307)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),c_Groups_Ozero__class_Ozero(U_6303)),U_6306))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),c_Groups_Ozero__class_Ozero(U_6303)),U_6305))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),U_6306),U_6307))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),U_6304),U_6305))
| ~ class_Rings_Oordered__semiring(U_6303) ),
inference(definitional_conversion,[status(esa)],[f_1441_2]) ).
cnf(f_1441_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6303),U_6304),U_6306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6303),U_6305),U_6307)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),c_Groups_Ozero__class_Ozero(U_6303)),U_6306))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),c_Groups_Ozero__class_Ozero(U_6303)),U_6305))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),U_6306),U_6307))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6303),U_6304),U_6305))
| ~ class_Rings_Oordered__semiring(U_6303) ),
inference(clausify,[status(thm)],[f_1441_3]) ).
fof(f_1442_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_1442_2,plain,
! [U_6310,U_6309,U_6308] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),c_Groups_Ozero__class_Ozero(U_6308)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6308),U_6309),U_6310)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),U_6310),c_Groups_Ozero__class_Ozero(U_6308)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),U_6309),c_Groups_Ozero__class_Ozero(U_6308))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),c_Groups_Ozero__class_Ozero(U_6308)),U_6310))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),c_Groups_Ozero__class_Ozero(U_6308)),U_6309)) ) )
| ~ class_Rings_Oordered__ring(U_6308) ),
inference(variable_rename,[status(thm)],[f_1442_1]) ).
fof(f_1442_3,plain,
( ! [U_6308,U_6310,U_6309] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),U_6310),c_Groups_Ozero__class_Ozero(U_6308)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),U_6309),c_Groups_Ozero__class_Ozero(U_6308)))
| ~ sP322(U_6308,U_6310,U_6309) )
& ! [U_6308,U_6310,U_6309] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),c_Groups_Ozero__class_Ozero(U_6308)),U_6310))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),c_Groups_Ozero__class_Ozero(U_6308)),U_6309))
| ~ sP322(U_6308,U_6310,U_6309) )
& ! [U_6308,U_6310,U_6309] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),c_Groups_Ozero__class_Ozero(U_6308)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6308),U_6309),U_6310)))
| sP322(U_6308,U_6310,U_6309)
| ~ class_Rings_Oordered__ring(U_6308) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP322])],[f_1442_2]) ).
cnf(f_1442_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),c_Groups_Ozero__class_Ozero(U_6308)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6308),U_6309),U_6310)))
| sP322(U_6308,U_6310,U_6309)
| ~ class_Rings_Oordered__ring(U_6308) ),
inference(clausify,[status(thm)],[f_1442_3]) ).
cnf(f_1442_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),c_Groups_Ozero__class_Ozero(U_6308)),U_6310))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),c_Groups_Ozero__class_Ozero(U_6308)),U_6309))
| ~ sP322(U_6308,U_6310,U_6309) ),
inference(clausify,[status(thm)],[f_1442_3]) ).
cnf(f_1442_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),U_6310),c_Groups_Ozero__class_Ozero(U_6308)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6308),U_6309),c_Groups_Ozero__class_Ozero(U_6308)))
| ~ sP322(U_6308,U_6310,U_6309) ),
inference(clausify,[status(thm)],[f_1442_3]) ).
fof(f_1443_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_1443_2,plain,
! [U_6313,U_6312,U_6311] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6311),U_6312),U_6313)),c_Groups_Ozero__class_Ozero(U_6311)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),c_Groups_Ozero__class_Ozero(U_6311)),U_6313))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),U_6312),c_Groups_Ozero__class_Ozero(U_6311))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),U_6313),c_Groups_Ozero__class_Ozero(U_6311)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),c_Groups_Ozero__class_Ozero(U_6311)),U_6312)) ) )
| ~ class_Rings_Oordered__cancel__semiring(U_6311) ),
inference(variable_rename,[status(thm)],[f_1443_1]) ).
fof(f_1443_3,plain,
( ! [U_6311,U_6313,U_6312] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),c_Groups_Ozero__class_Ozero(U_6311)),U_6313))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),U_6312),c_Groups_Ozero__class_Ozero(U_6311)))
| ~ sP323(U_6311,U_6313,U_6312) )
& ! [U_6311,U_6313,U_6312] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),U_6313),c_Groups_Ozero__class_Ozero(U_6311)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),c_Groups_Ozero__class_Ozero(U_6311)),U_6312))
| ~ sP323(U_6311,U_6313,U_6312) )
& ! [U_6311,U_6313,U_6312] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6311),U_6312),U_6313)),c_Groups_Ozero__class_Ozero(U_6311)))
| sP323(U_6311,U_6313,U_6312)
| ~ class_Rings_Oordered__cancel__semiring(U_6311) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP323])],[f_1443_2]) ).
cnf(f_1443_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6311),U_6312),U_6313)),c_Groups_Ozero__class_Ozero(U_6311)))
| sP323(U_6311,U_6313,U_6312)
| ~ class_Rings_Oordered__cancel__semiring(U_6311) ),
inference(clausify,[status(thm)],[f_1443_3]) ).
cnf(f_1443_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),U_6313),c_Groups_Ozero__class_Ozero(U_6311)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),c_Groups_Ozero__class_Ozero(U_6311)),U_6312))
| ~ sP323(U_6311,U_6313,U_6312) ),
inference(clausify,[status(thm)],[f_1443_3]) ).
cnf(f_1443_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),c_Groups_Ozero__class_Ozero(U_6311)),U_6313))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6311),U_6312),c_Groups_Ozero__class_Ozero(U_6311)))
| ~ sP323(U_6311,U_6313,U_6312) ),
inference(clausify,[status(thm)],[f_1443_3]) ).
fof(f_1444_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add]) ).
fof(f_1444_2,plain,
! [U_6315,U_6314] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6314),c_Groups_Ozero__class_Ozero(U_6314)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6314),U_6315),U_6315)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6314),c_Groups_Ozero__class_Ozero(U_6314)),U_6315)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6314),c_Groups_Ozero__class_Ozero(U_6314)),U_6315))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6314),c_Groups_Ozero__class_Ozero(U_6314)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6314),U_6315),U_6315))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_6314) ),
inference(variable_rename,[status(thm)],[f_1444_1]) ).
fof(f_1444_3,plain,
( ! [U_6315,U_6314] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6314),c_Groups_Ozero__class_Ozero(U_6314)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6314),U_6315),U_6315)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6314),c_Groups_Ozero__class_Ozero(U_6314)),U_6315))
| ~ sP324(U_6315,U_6314) )
& ! [U_6315,U_6314] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6314),c_Groups_Ozero__class_Ozero(U_6314)),U_6315))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6314),c_Groups_Ozero__class_Ozero(U_6314)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6314),U_6315),U_6315)))
| ~ sP324(U_6315,U_6314) )
& ! [U_6315,U_6314] :
( sP324(U_6315,U_6314)
| ~ class_Groups_Olinordered__ab__group__add(U_6314) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP324])],[f_1444_2]) ).
cnf(f_1444_4,plain,
( sP324(U_6315,U_6314)
| ~ class_Groups_Olinordered__ab__group__add(U_6314) ),
inference(clausify,[status(thm)],[f_1444_3]) ).
cnf(f_1444_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6314),c_Groups_Ozero__class_Ozero(U_6314)),U_6315))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6314),c_Groups_Ozero__class_Ozero(U_6314)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6314),U_6315),U_6315)))
| ~ sP324(U_6315,U_6314) ),
inference(clausify,[status(thm)],[f_1444_3]) ).
cnf(f_1444_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6314),c_Groups_Ozero__class_Ozero(U_6314)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6314),U_6315),U_6315)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6314),c_Groups_Ozero__class_Ozero(U_6314)),U_6315))
| ~ sP324(U_6315,U_6314) ),
inference(clausify,[status(thm)],[f_1444_3]) ).
fof(f_1445_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero]) ).
fof(f_1445_2,plain,
! [U_6317,U_6316] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6316),U_6317),U_6317)),c_Groups_Ozero__class_Ozero(U_6316)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6316),U_6317),c_Groups_Ozero__class_Ozero(U_6316))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6316),U_6317),c_Groups_Ozero__class_Ozero(U_6316)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6316),U_6317),U_6317)),c_Groups_Ozero__class_Ozero(U_6316))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_6316) ),
inference(variable_rename,[status(thm)],[f_1445_1]) ).
fof(f_1445_3,plain,
( ! [U_6316,U_6317] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6316),U_6317),U_6317)),c_Groups_Ozero__class_Ozero(U_6316)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6316),U_6317),c_Groups_Ozero__class_Ozero(U_6316)))
| ~ sP325(U_6316,U_6317) )
& ! [U_6316,U_6317] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6316),U_6317),c_Groups_Ozero__class_Ozero(U_6316)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6316),U_6317),U_6317)),c_Groups_Ozero__class_Ozero(U_6316)))
| ~ sP325(U_6316,U_6317) )
& ! [U_6316,U_6317] :
( sP325(U_6316,U_6317)
| ~ class_Groups_Olinordered__ab__group__add(U_6316) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP325])],[f_1445_2]) ).
cnf(f_1445_4,plain,
( sP325(U_6316,U_6317)
| ~ class_Groups_Olinordered__ab__group__add(U_6316) ),
inference(clausify,[status(thm)],[f_1445_3]) ).
cnf(f_1445_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6316),U_6317),c_Groups_Ozero__class_Ozero(U_6316)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6316),U_6317),U_6317)),c_Groups_Ozero__class_Ozero(U_6316)))
| ~ sP325(U_6316,U_6317) ),
inference(clausify,[status(thm)],[f_1445_3]) ).
cnf(f_1445_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6316),U_6317),U_6317)),c_Groups_Ozero__class_Ozero(U_6316)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6316),U_6317),c_Groups_Ozero__class_Ozero(U_6316)))
| ~ sP325(U_6316,U_6317) ),
inference(clausify,[status(thm)],[f_1445_3]) ).
fof(f_1446_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_1446_2,plain,
! [U_6320,U_6319,U_6318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6318),c_Groups_Ozero__class_Ozero(U_6318)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6318),U_6319),U_6320)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6318),c_Groups_Ozero__class_Ozero(U_6318)),U_6320))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6318),c_Groups_Ozero__class_Ozero(U_6318)),U_6319))
| ~ class_Groups_Oordered__comm__monoid__add(U_6318) ),
inference(variable_rename,[status(thm)],[f_1446_1]) ).
fof(f_1446_3,plain,
! [U_6320,U_6319,U_6318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6318),c_Groups_Ozero__class_Ozero(U_6318)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6318),U_6319),U_6320)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6318),c_Groups_Ozero__class_Ozero(U_6318)),U_6320))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6318),c_Groups_Ozero__class_Ozero(U_6318)),U_6319))
| ~ class_Groups_Oordered__comm__monoid__add(U_6318) ),
inference(definitional_conversion,[status(esa)],[f_1446_2]) ).
cnf(f_1446_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6318),c_Groups_Ozero__class_Ozero(U_6318)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6318),U_6319),U_6320)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6318),c_Groups_Ozero__class_Ozero(U_6318)),U_6320))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6318),c_Groups_Ozero__class_Ozero(U_6318)),U_6319))
| ~ class_Groups_Oordered__comm__monoid__add(U_6318) ),
inference(clausify,[status(thm)],[f_1446_3]) ).
fof(f_1447_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_1447_2,plain,
! [U_6323,U_6322,U_6321] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6321),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6321),U_6322),U_6323)),c_Groups_Ozero__class_Ozero(U_6321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6321),U_6323),c_Groups_Ozero__class_Ozero(U_6321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6321),U_6322),c_Groups_Ozero__class_Ozero(U_6321)))
| ~ class_Groups_Oordered__comm__monoid__add(U_6321) ),
inference(variable_rename,[status(thm)],[f_1447_1]) ).
fof(f_1447_3,plain,
! [U_6321,U_6322,U_6323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6321),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6321),U_6322),U_6323)),c_Groups_Ozero__class_Ozero(U_6321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6321),U_6323),c_Groups_Ozero__class_Ozero(U_6321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6321),U_6322),c_Groups_Ozero__class_Ozero(U_6321)))
| ~ class_Groups_Oordered__comm__monoid__add(U_6321) ),
inference(definitional_conversion,[status(esa)],[f_1447_2]) ).
cnf(f_1447_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6321),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6321),U_6322),U_6323)),c_Groups_Ozero__class_Ozero(U_6321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6321),U_6323),c_Groups_Ozero__class_Ozero(U_6321)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6321),U_6322),c_Groups_Ozero__class_Ozero(U_6321)))
| ~ class_Groups_Oordered__comm__monoid__add(U_6321) ),
inference(clausify,[status(thm)],[f_1447_3]) ).
fof(f_1448_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_1448_2,plain,
! [U_6327,U_6326,U_6325,U_6324] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6324),U_6326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6324),U_6325),U_6327)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6324),U_6326),U_6327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6324),c_Groups_Ozero__class_Ozero(U_6324)),U_6325))
| ~ class_Rings_Olinordered__semidom(U_6324) ),
inference(variable_rename,[status(thm)],[f_1448_1]) ).
fof(f_1448_3,plain,
! [U_6324,U_6325,U_6326,U_6327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6324),U_6326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6324),U_6325),U_6327)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6324),U_6326),U_6327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6324),c_Groups_Ozero__class_Ozero(U_6324)),U_6325))
| ~ class_Rings_Olinordered__semidom(U_6324) ),
inference(definitional_conversion,[status(esa)],[f_1448_2]) ).
cnf(f_1448_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6324),U_6326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6324),U_6325),U_6327)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6324),U_6326),U_6327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6324),c_Groups_Ozero__class_Ozero(U_6324)),U_6325))
| ~ class_Rings_Olinordered__semidom(U_6324) ),
inference(clausify,[status(thm)],[f_1448_3]) ).
fof(f_1449_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_1449_2,plain,
! [U_6329,U_6328] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6328),U_6329),U_6329)),c_Groups_Ozero__class_Ozero(U_6328)))
| ~ class_Rings_Olinordered__ring(U_6328) ),
inference(variable_rename,[status(thm)],[f_1449_1]) ).
fof(f_1449_3,plain,
! [U_6328,U_6329] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6328),U_6329),U_6329)),c_Groups_Ozero__class_Ozero(U_6328)))
| ~ class_Rings_Olinordered__ring(U_6328) ),
inference(definitional_conversion,[status(esa)],[f_1449_2]) ).
cnf(f_1449_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6328),U_6329),U_6329)),c_Groups_Ozero__class_Ozero(U_6328)))
| ~ class_Rings_Olinordered__ring(U_6328) ),
inference(clausify,[status(thm)],[f_1449_3]) ).
fof(f_1450_1,plain,
! [V_b_2,V_c_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_c_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_b_2),V_c_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_c) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).
fof(f_1450_2,plain,
! [U_6333,U_6332,U_6331,U_6330] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6330),U_6331),U_6332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6330),U_6333),U_6332)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6333),U_6331))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6332),c_Groups_Ozero__class_Ozero(U_6330))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6331),U_6333))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),c_Groups_Ozero__class_Ozero(U_6330)),U_6332)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6333),U_6331))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6332),c_Groups_Ozero__class_Ozero(U_6330))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6331),U_6333))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),c_Groups_Ozero__class_Ozero(U_6330)),U_6332)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6330),U_6331),U_6332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6330),U_6333),U_6332))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_6330) ),
inference(variable_rename,[status(thm)],[f_1450_1]) ).
fof(f_1450_3,plain,
( ! [U_6330,U_6331,U_6332,U_6333] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6333),U_6331))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6332),c_Groups_Ozero__class_Ozero(U_6330)))
| ~ sP328(U_6330,U_6331,U_6332,U_6333) )
& ! [U_6330,U_6331,U_6332,U_6333] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6331),U_6333))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),c_Groups_Ozero__class_Ozero(U_6330)),U_6332))
| ~ sP328(U_6330,U_6331,U_6332,U_6333) )
& ! [U_6330,U_6331,U_6332,U_6333] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6333),U_6331))
| ~ sP327(U_6330,U_6331,U_6332,U_6333) )
& ! [U_6330,U_6331,U_6332,U_6333] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6332),c_Groups_Ozero__class_Ozero(U_6330)))
| ~ sP327(U_6330,U_6331,U_6332,U_6333) )
& ! [U_6330,U_6331,U_6332,U_6333] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6331),U_6333))
| ~ sP326(U_6330,U_6331,U_6332,U_6333) )
& ! [U_6330,U_6331,U_6332,U_6333] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),c_Groups_Ozero__class_Ozero(U_6330)),U_6332))
| ~ sP326(U_6330,U_6331,U_6332,U_6333) )
& ! [U_6330,U_6331,U_6332,U_6333] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6330),U_6331),U_6332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6330),U_6333),U_6332)))
| sP328(U_6330,U_6331,U_6332,U_6333)
| ~ sP329(U_6330,U_6331,U_6332,U_6333) )
& ! [U_6330,U_6331,U_6332,U_6333] :
( sP327(U_6330,U_6331,U_6332,U_6333)
| sP326(U_6330,U_6331,U_6332,U_6333)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6330),U_6331),U_6332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6330),U_6333),U_6332)))
| ~ sP329(U_6330,U_6331,U_6332,U_6333) )
& ! [U_6330,U_6331,U_6332,U_6333] :
( sP329(U_6330,U_6331,U_6332,U_6333)
| ~ class_Rings_Olinordered__ring__strict(U_6330) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP326,sP327,sP328,sP329])],[f_1450_2]) ).
cnf(f_1450_4,plain,
( sP329(U_6330,U_6331,U_6332,U_6333)
| ~ class_Rings_Olinordered__ring__strict(U_6330) ),
inference(clausify,[status(thm)],[f_1450_3]) ).
cnf(f_1450_5,plain,
( sP327(U_6330,U_6331,U_6332,U_6333)
| sP326(U_6330,U_6331,U_6332,U_6333)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6330),U_6331),U_6332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6330),U_6333),U_6332)))
| ~ sP329(U_6330,U_6331,U_6332,U_6333) ),
inference(clausify,[status(thm)],[f_1450_3]) ).
cnf(f_1450_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6330),U_6331),U_6332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6330),U_6333),U_6332)))
| sP328(U_6330,U_6331,U_6332,U_6333)
| ~ sP329(U_6330,U_6331,U_6332,U_6333) ),
inference(clausify,[status(thm)],[f_1450_3]) ).
cnf(f_1450_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),c_Groups_Ozero__class_Ozero(U_6330)),U_6332))
| ~ sP326(U_6330,U_6331,U_6332,U_6333) ),
inference(clausify,[status(thm)],[f_1450_3]) ).
cnf(f_1450_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6331),U_6333))
| ~ sP326(U_6330,U_6331,U_6332,U_6333) ),
inference(clausify,[status(thm)],[f_1450_3]) ).
cnf(f_1450_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6332),c_Groups_Ozero__class_Ozero(U_6330)))
| ~ sP327(U_6330,U_6331,U_6332,U_6333) ),
inference(clausify,[status(thm)],[f_1450_3]) ).
cnf(f_1450_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6333),U_6331))
| ~ sP327(U_6330,U_6331,U_6332,U_6333) ),
inference(clausify,[status(thm)],[f_1450_3]) ).
cnf(f_1450_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6331),U_6333))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),c_Groups_Ozero__class_Ozero(U_6330)),U_6332))
| ~ sP328(U_6330,U_6331,U_6332,U_6333) ),
inference(clausify,[status(thm)],[f_1450_3]) ).
cnf(f_1450_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6333),U_6331))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6330),U_6332),c_Groups_Ozero__class_Ozero(U_6330)))
| ~ sP328(U_6330,U_6331,U_6332,U_6333) ),
inference(clausify,[status(thm)],[f_1450_3]) ).
fof(f_1451_1,plain,
! [V_b_2,V_a_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_c) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).
fof(f_1451_2,plain,
! [U_6337,U_6336,U_6335,U_6334] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6334),U_6335),U_6336)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6334),U_6335),U_6337)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6337),U_6336))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6335),c_Groups_Ozero__class_Ozero(U_6334))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6336),U_6337))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),U_6335)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6337),U_6336))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6335),c_Groups_Ozero__class_Ozero(U_6334))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6336),U_6337))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),U_6335)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6334),U_6335),U_6336)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6334),U_6335),U_6337))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_6334) ),
inference(variable_rename,[status(thm)],[f_1451_1]) ).
fof(f_1451_3,plain,
( ! [U_6335,U_6336,U_6337,U_6334] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6337),U_6336))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6335),c_Groups_Ozero__class_Ozero(U_6334)))
| ~ sP332(U_6335,U_6336,U_6337,U_6334) )
& ! [U_6335,U_6336,U_6337,U_6334] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6336),U_6337))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),U_6335))
| ~ sP332(U_6335,U_6336,U_6337,U_6334) )
& ! [U_6335,U_6336,U_6337,U_6334] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6337),U_6336))
| ~ sP331(U_6335,U_6336,U_6337,U_6334) )
& ! [U_6335,U_6336,U_6337,U_6334] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6335),c_Groups_Ozero__class_Ozero(U_6334)))
| ~ sP331(U_6335,U_6336,U_6337,U_6334) )
& ! [U_6335,U_6336,U_6337,U_6334] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6336),U_6337))
| ~ sP330(U_6335,U_6336,U_6337,U_6334) )
& ! [U_6335,U_6336,U_6337,U_6334] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),U_6335))
| ~ sP330(U_6335,U_6336,U_6337,U_6334) )
& ! [U_6335,U_6336,U_6337,U_6334] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6334),U_6335),U_6336)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6334),U_6335),U_6337)))
| sP332(U_6335,U_6336,U_6337,U_6334)
| ~ sP333(U_6335,U_6336,U_6337,U_6334) )
& ! [U_6335,U_6336,U_6337,U_6334] :
( sP331(U_6335,U_6336,U_6337,U_6334)
| sP330(U_6335,U_6336,U_6337,U_6334)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6334),U_6335),U_6336)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6334),U_6335),U_6337)))
| ~ sP333(U_6335,U_6336,U_6337,U_6334) )
& ! [U_6335,U_6336,U_6337,U_6334] :
( sP333(U_6335,U_6336,U_6337,U_6334)
| ~ class_Rings_Olinordered__ring__strict(U_6334) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP330,sP331,sP332,sP333])],[f_1451_2]) ).
cnf(f_1451_4,plain,
( sP333(U_6335,U_6336,U_6337,U_6334)
| ~ class_Rings_Olinordered__ring__strict(U_6334) ),
inference(clausify,[status(thm)],[f_1451_3]) ).
cnf(f_1451_5,plain,
( sP331(U_6335,U_6336,U_6337,U_6334)
| sP330(U_6335,U_6336,U_6337,U_6334)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6334),U_6335),U_6336)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6334),U_6335),U_6337)))
| ~ sP333(U_6335,U_6336,U_6337,U_6334) ),
inference(clausify,[status(thm)],[f_1451_3]) ).
cnf(f_1451_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6334),U_6335),U_6336)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6334),U_6335),U_6337)))
| sP332(U_6335,U_6336,U_6337,U_6334)
| ~ sP333(U_6335,U_6336,U_6337,U_6334) ),
inference(clausify,[status(thm)],[f_1451_3]) ).
cnf(f_1451_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),U_6335))
| ~ sP330(U_6335,U_6336,U_6337,U_6334) ),
inference(clausify,[status(thm)],[f_1451_3]) ).
cnf(f_1451_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6336),U_6337))
| ~ sP330(U_6335,U_6336,U_6337,U_6334) ),
inference(clausify,[status(thm)],[f_1451_3]) ).
cnf(f_1451_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6335),c_Groups_Ozero__class_Ozero(U_6334)))
| ~ sP331(U_6335,U_6336,U_6337,U_6334) ),
inference(clausify,[status(thm)],[f_1451_3]) ).
cnf(f_1451_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6337),U_6336))
| ~ sP331(U_6335,U_6336,U_6337,U_6334) ),
inference(clausify,[status(thm)],[f_1451_3]) ).
cnf(f_1451_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6336),U_6337))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),U_6335))
| ~ sP332(U_6335,U_6336,U_6337,U_6334) ),
inference(clausify,[status(thm)],[f_1451_3]) ).
cnf(f_1451_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6337),U_6336))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),U_6335),c_Groups_Ozero__class_Ozero(U_6334)))
| ~ sP332(U_6335,U_6336,U_6337,U_6334) ),
inference(clausify,[status(thm)],[f_1451_3]) ).
fof(f_1452_1,plain,
! [V_b_2,V_a_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
| ~ class_Rings_Olinordered__ring__strict(T_c) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).
fof(f_1452_2,plain,
! [U_6341,U_6340,U_6339,U_6338] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6338),U_6339),U_6340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6338),U_6339),U_6341)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),U_6340),U_6341)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),U_6340),U_6341))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6338),U_6339),U_6340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6338),U_6339),U_6341))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),c_Groups_Ozero__class_Ozero(U_6338)),U_6339))
| ~ class_Rings_Olinordered__ring__strict(U_6338) ),
inference(variable_rename,[status(thm)],[f_1452_1]) ).
fof(f_1452_3,plain,
( ! [U_6338,U_6339,U_6341,U_6340] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6338),U_6339),U_6340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6338),U_6339),U_6341)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),U_6340),U_6341))
| ~ sP334(U_6338,U_6339,U_6341,U_6340) )
& ! [U_6338,U_6339,U_6341,U_6340] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),U_6340),U_6341))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6338),U_6339),U_6340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6338),U_6339),U_6341)))
| ~ sP334(U_6338,U_6339,U_6341,U_6340) )
& ! [U_6338,U_6339,U_6341,U_6340] :
( sP334(U_6338,U_6339,U_6341,U_6340)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),c_Groups_Ozero__class_Ozero(U_6338)),U_6339))
| ~ class_Rings_Olinordered__ring__strict(U_6338) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP334])],[f_1452_2]) ).
cnf(f_1452_4,plain,
( sP334(U_6338,U_6339,U_6341,U_6340)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),c_Groups_Ozero__class_Ozero(U_6338)),U_6339))
| ~ class_Rings_Olinordered__ring__strict(U_6338) ),
inference(clausify,[status(thm)],[f_1452_3]) ).
cnf(f_1452_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),U_6340),U_6341))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6338),U_6339),U_6340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6338),U_6339),U_6341)))
| ~ sP334(U_6338,U_6339,U_6341,U_6340) ),
inference(clausify,[status(thm)],[f_1452_3]) ).
cnf(f_1452_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6338),U_6339),U_6340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6338),U_6339),U_6341)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6338),U_6340),U_6341))
| ~ sP334(U_6338,U_6339,U_6341,U_6340) ),
inference(clausify,[status(thm)],[f_1452_3]) ).
fof(f_1453_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_1453_2,plain,
! [U_6344,U_6343,U_6342] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6342),c_Groups_Ozero__class_Ozero(U_6342)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6342),U_6343),U_6344)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6342),c_Groups_Ozero__class_Ozero(U_6342)),U_6344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6342),c_Groups_Ozero__class_Ozero(U_6342)),U_6343))
| ~ class_Rings_Olinordered__semiring__strict(U_6342) ),
inference(variable_rename,[status(thm)],[f_1453_1]) ).
fof(f_1453_3,plain,
! [U_6342,U_6344,U_6343] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6342),c_Groups_Ozero__class_Ozero(U_6342)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6342),U_6343),U_6344)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6342),c_Groups_Ozero__class_Ozero(U_6342)),U_6344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6342),c_Groups_Ozero__class_Ozero(U_6342)),U_6343))
| ~ class_Rings_Olinordered__semiring__strict(U_6342) ),
inference(definitional_conversion,[status(esa)],[f_1453_2]) ).
cnf(f_1453_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6342),c_Groups_Ozero__class_Ozero(U_6342)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6342),U_6343),U_6344)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6342),c_Groups_Ozero__class_Ozero(U_6342)),U_6344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6342),c_Groups_Ozero__class_Ozero(U_6342)),U_6343))
| ~ class_Rings_Olinordered__semiring__strict(U_6342) ),
inference(clausify,[status(thm)],[f_1453_3]) ).
fof(f_1454_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_1454_2,plain,
! [U_6347,U_6346,U_6345] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6345),U_6346),U_6347)),c_Groups_Ozero__class_Ozero(U_6345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6345),U_6347),c_Groups_Ozero__class_Ozero(U_6345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6345),c_Groups_Ozero__class_Ozero(U_6345)),U_6346))
| ~ class_Rings_Olinordered__semiring__strict(U_6345) ),
inference(variable_rename,[status(thm)],[f_1454_1]) ).
fof(f_1454_3,plain,
! [U_6345,U_6346,U_6347] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6345),U_6346),U_6347)),c_Groups_Ozero__class_Ozero(U_6345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6345),U_6347),c_Groups_Ozero__class_Ozero(U_6345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6345),c_Groups_Ozero__class_Ozero(U_6345)),U_6346))
| ~ class_Rings_Olinordered__semiring__strict(U_6345) ),
inference(definitional_conversion,[status(esa)],[f_1454_2]) ).
cnf(f_1454_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6345),U_6346),U_6347)),c_Groups_Ozero__class_Ozero(U_6345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6345),U_6347),c_Groups_Ozero__class_Ozero(U_6345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6345),c_Groups_Ozero__class_Ozero(U_6345)),U_6346))
| ~ class_Rings_Olinordered__semiring__strict(U_6345) ),
inference(clausify,[status(thm)],[f_1454_3]) ).
fof(f_1455_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_1455_2,plain,
! [U_6350,U_6349,U_6348] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6348),U_6350),U_6349)),c_Groups_Ozero__class_Ozero(U_6348)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6348),U_6350),c_Groups_Ozero__class_Ozero(U_6348)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6348),c_Groups_Ozero__class_Ozero(U_6348)),U_6349))
| ~ class_Rings_Olinordered__semiring__strict(U_6348) ),
inference(variable_rename,[status(thm)],[f_1455_1]) ).
fof(f_1455_3,plain,
! [U_6348,U_6349,U_6350] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6348),U_6350),U_6349)),c_Groups_Ozero__class_Ozero(U_6348)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6348),U_6350),c_Groups_Ozero__class_Ozero(U_6348)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6348),c_Groups_Ozero__class_Ozero(U_6348)),U_6349))
| ~ class_Rings_Olinordered__semiring__strict(U_6348) ),
inference(definitional_conversion,[status(esa)],[f_1455_2]) ).
cnf(f_1455_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6348),U_6350),U_6349)),c_Groups_Ozero__class_Ozero(U_6348)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6348),U_6350),c_Groups_Ozero__class_Ozero(U_6348)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6348),c_Groups_Ozero__class_Ozero(U_6348)),U_6349))
| ~ class_Rings_Olinordered__semiring__strict(U_6348) ),
inference(clausify,[status(thm)],[f_1455_3]) ).
fof(f_1456_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_1456_2,plain,
! [U_6353,U_6352,U_6351] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6351),c_Groups_Ozero__class_Ozero(U_6351)),U_6353))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6351),c_Groups_Ozero__class_Ozero(U_6351)),U_6352))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6351),c_Groups_Ozero__class_Ozero(U_6351)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6351),U_6352),U_6353)))
| ~ class_Rings_Olinordered__semiring__strict(U_6351) ),
inference(variable_rename,[status(thm)],[f_1456_1]) ).
fof(f_1456_3,plain,
! [U_6352,U_6351,U_6353] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6351),c_Groups_Ozero__class_Ozero(U_6351)),U_6353))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6351),c_Groups_Ozero__class_Ozero(U_6351)),U_6352))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6351),c_Groups_Ozero__class_Ozero(U_6351)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6351),U_6352),U_6353)))
| ~ class_Rings_Olinordered__semiring__strict(U_6351) ),
inference(definitional_conversion,[status(esa)],[f_1456_2]) ).
cnf(f_1456_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6351),c_Groups_Ozero__class_Ozero(U_6351)),U_6353))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6351),c_Groups_Ozero__class_Ozero(U_6351)),U_6352))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6351),c_Groups_Ozero__class_Ozero(U_6351)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6351),U_6352),U_6353)))
| ~ class_Rings_Olinordered__semiring__strict(U_6351) ),
inference(clausify,[status(thm)],[f_1456_3]) ).
fof(f_1457_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_1457_2,plain,
! [U_6356,U_6355,U_6354] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6354),c_Groups_Ozero__class_Ozero(U_6354)),U_6355))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6354),c_Groups_Ozero__class_Ozero(U_6354)),U_6356))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6354),c_Groups_Ozero__class_Ozero(U_6354)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6354),U_6355),U_6356)))
| ~ class_Rings_Olinordered__semiring__strict(U_6354) ),
inference(variable_rename,[status(thm)],[f_1457_1]) ).
fof(f_1457_3,plain,
! [U_6355,U_6354,U_6356] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6354),c_Groups_Ozero__class_Ozero(U_6354)),U_6355))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6354),c_Groups_Ozero__class_Ozero(U_6354)),U_6356))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6354),c_Groups_Ozero__class_Ozero(U_6354)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6354),U_6355),U_6356)))
| ~ class_Rings_Olinordered__semiring__strict(U_6354) ),
inference(definitional_conversion,[status(esa)],[f_1457_2]) ).
cnf(f_1457_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6354),c_Groups_Ozero__class_Ozero(U_6354)),U_6355))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6354),c_Groups_Ozero__class_Ozero(U_6354)),U_6356))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6354),c_Groups_Ozero__class_Ozero(U_6354)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6354),U_6355),U_6356)))
| ~ class_Rings_Olinordered__semiring__strict(U_6354) ),
inference(clausify,[status(thm)],[f_1457_3]) ).
fof(f_1458_1,plain,
! [V_b_2,V_a_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ class_Rings_Olinordered__ring__strict(T_c) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg]) ).
fof(f_1458_2,plain,
! [U_6360,U_6359,U_6358,U_6357] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),U_6358),U_6359)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),U_6358),U_6360)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),U_6360),U_6359)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),U_6360),U_6359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),U_6358),U_6359)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),U_6358),U_6360))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),U_6358),c_Groups_Ozero__class_Ozero(U_6357)))
| ~ class_Rings_Olinordered__ring__strict(U_6357) ),
inference(variable_rename,[status(thm)],[f_1458_1]) ).
fof(f_1458_3,plain,
( ! [U_6357,U_6359,U_6358,U_6360] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),U_6358),U_6359)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),U_6358),U_6360)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),U_6360),U_6359))
| ~ sP335(U_6357,U_6359,U_6358,U_6360) )
& ! [U_6357,U_6359,U_6358,U_6360] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),U_6360),U_6359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),U_6358),U_6359)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),U_6358),U_6360)))
| ~ sP335(U_6357,U_6359,U_6358,U_6360) )
& ! [U_6357,U_6359,U_6358,U_6360] :
( sP335(U_6357,U_6359,U_6358,U_6360)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),U_6358),c_Groups_Ozero__class_Ozero(U_6357)))
| ~ class_Rings_Olinordered__ring__strict(U_6357) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP335])],[f_1458_2]) ).
cnf(f_1458_4,plain,
( sP335(U_6357,U_6359,U_6358,U_6360)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),U_6358),c_Groups_Ozero__class_Ozero(U_6357)))
| ~ class_Rings_Olinordered__ring__strict(U_6357) ),
inference(clausify,[status(thm)],[f_1458_3]) ).
cnf(f_1458_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),U_6360),U_6359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),U_6358),U_6359)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),U_6358),U_6360)))
| ~ sP335(U_6357,U_6359,U_6358,U_6360) ),
inference(clausify,[status(thm)],[f_1458_3]) ).
cnf(f_1458_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),U_6358),U_6359)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),U_6358),U_6360)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6357),U_6360),U_6359))
| ~ sP335(U_6357,U_6359,U_6358,U_6360) ),
inference(clausify,[status(thm)],[f_1458_3]) ).
fof(f_1459_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_1459_2,plain,
! [U_6363,U_6362,U_6361] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6361),U_6362),U_6363)),c_Groups_Ozero__class_Ozero(U_6361)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),c_Groups_Ozero__class_Ozero(U_6361)),U_6363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),U_6362),c_Groups_Ozero__class_Ozero(U_6361)))
| ~ class_Rings_Olinordered__semiring__strict(U_6361) ),
inference(variable_rename,[status(thm)],[f_1459_1]) ).
fof(f_1459_3,plain,
! [U_6361,U_6363,U_6362] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6361),U_6362),U_6363)),c_Groups_Ozero__class_Ozero(U_6361)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),c_Groups_Ozero__class_Ozero(U_6361)),U_6363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),U_6362),c_Groups_Ozero__class_Ozero(U_6361)))
| ~ class_Rings_Olinordered__semiring__strict(U_6361) ),
inference(definitional_conversion,[status(esa)],[f_1459_2]) ).
cnf(f_1459_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6361),U_6362),U_6363)),c_Groups_Ozero__class_Ozero(U_6361)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),c_Groups_Ozero__class_Ozero(U_6361)),U_6363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6361),U_6362),c_Groups_Ozero__class_Ozero(U_6361)))
| ~ class_Rings_Olinordered__semiring__strict(U_6361) ),
inference(clausify,[status(thm)],[f_1459_3]) ).
fof(f_1460_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_1460_2,plain,
! [U_6366,U_6365,U_6364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6364),c_Groups_Ozero__class_Ozero(U_6364)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6364),U_6365),U_6366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6364),U_6366),c_Groups_Ozero__class_Ozero(U_6364)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6364),U_6365),c_Groups_Ozero__class_Ozero(U_6364)))
| ~ class_Rings_Olinordered__ring__strict(U_6364) ),
inference(variable_rename,[status(thm)],[f_1460_1]) ).
fof(f_1460_3,plain,
! [U_6364,U_6365,U_6366] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6364),c_Groups_Ozero__class_Ozero(U_6364)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6364),U_6365),U_6366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6364),U_6366),c_Groups_Ozero__class_Ozero(U_6364)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6364),U_6365),c_Groups_Ozero__class_Ozero(U_6364)))
| ~ class_Rings_Olinordered__ring__strict(U_6364) ),
inference(definitional_conversion,[status(esa)],[f_1460_2]) ).
cnf(f_1460_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6364),c_Groups_Ozero__class_Ozero(U_6364)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6364),U_6365),U_6366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6364),U_6366),c_Groups_Ozero__class_Ozero(U_6364)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6364),U_6365),c_Groups_Ozero__class_Ozero(U_6364)))
| ~ class_Rings_Olinordered__ring__strict(U_6364) ),
inference(clausify,[status(thm)],[f_1460_3]) ).
fof(f_1461_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_1461_2,plain,
! [U_6370,U_6369,U_6368,U_6367] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6367),U_6368),U_6370)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6367),U_6369),U_6370)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6367),c_Groups_Ozero__class_Ozero(U_6367)),U_6370))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6367),U_6368),U_6369))
| ~ class_Rings_Olinordered__semiring__strict(U_6367) ),
inference(variable_rename,[status(thm)],[f_1461_1]) ).
fof(f_1461_3,plain,
! [U_6367,U_6368,U_6369,U_6370] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6367),U_6368),U_6370)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6367),U_6369),U_6370)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6367),c_Groups_Ozero__class_Ozero(U_6367)),U_6370))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6367),U_6368),U_6369))
| ~ class_Rings_Olinordered__semiring__strict(U_6367) ),
inference(definitional_conversion,[status(esa)],[f_1461_2]) ).
cnf(f_1461_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6367),U_6368),U_6370)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6367),U_6369),U_6370)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6367),c_Groups_Ozero__class_Ozero(U_6367)),U_6370))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6367),U_6368),U_6369))
| ~ class_Rings_Olinordered__semiring__strict(U_6367) ),
inference(clausify,[status(thm)],[f_1461_3]) ).
fof(f_1462_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_1462_2,plain,
! [U_6374,U_6373,U_6372,U_6371] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6371),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6371),U_6374),U_6372)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6371),U_6374),U_6373)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6371),c_Groups_Ozero__class_Ozero(U_6371)),U_6374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6371),U_6372),U_6373))
| ~ class_Rings_Olinordered__semiring__strict(U_6371) ),
inference(variable_rename,[status(thm)],[f_1462_1]) ).
fof(f_1462_3,plain,
! [U_6371,U_6372,U_6373,U_6374] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6371),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6371),U_6374),U_6372)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6371),U_6374),U_6373)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6371),c_Groups_Ozero__class_Ozero(U_6371)),U_6374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6371),U_6372),U_6373))
| ~ class_Rings_Olinordered__semiring__strict(U_6371) ),
inference(definitional_conversion,[status(esa)],[f_1462_2]) ).
cnf(f_1462_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6371),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6371),U_6374),U_6372)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6371),U_6374),U_6373)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6371),c_Groups_Ozero__class_Ozero(U_6371)),U_6374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6371),U_6372),U_6373))
| ~ class_Rings_Olinordered__semiring__strict(U_6371) ),
inference(clausify,[status(thm)],[f_1462_3]) ).
fof(f_1463_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_1463_2,plain,
! [U_6378,U_6377,U_6376,U_6375] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6375),U_6378),U_6376)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6375),U_6378),U_6377)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6375),c_Groups_Ozero__class_Ozero(U_6375)),U_6378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6375),U_6376),U_6377))
| ~ class_Rings_Olinordered__comm__semiring__strict(U_6375) ),
inference(variable_rename,[status(thm)],[f_1463_1]) ).
fof(f_1463_3,plain,
! [U_6375,U_6376,U_6377,U_6378] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6375),U_6378),U_6376)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6375),U_6378),U_6377)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6375),c_Groups_Ozero__class_Ozero(U_6375)),U_6378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6375),U_6376),U_6377))
| ~ class_Rings_Olinordered__comm__semiring__strict(U_6375) ),
inference(definitional_conversion,[status(esa)],[f_1463_2]) ).
cnf(f_1463_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6375),U_6378),U_6376)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6375),U_6378),U_6377)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6375),c_Groups_Ozero__class_Ozero(U_6375)),U_6378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6375),U_6376),U_6377))
| ~ class_Rings_Olinordered__comm__semiring__strict(U_6375) ),
inference(clausify,[status(thm)],[f_1463_3]) ).
fof(f_1464_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_1464_2,plain,
! [U_6382,U_6381,U_6380,U_6379] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6379),U_6381),U_6382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6379),U_6380),U_6382)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6379),U_6382),c_Groups_Ozero__class_Ozero(U_6379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6379),U_6380),U_6381))
| ~ class_Rings_Olinordered__ring__strict(U_6379) ),
inference(variable_rename,[status(thm)],[f_1464_1]) ).
fof(f_1464_3,plain,
! [U_6379,U_6380,U_6381,U_6382] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6379),U_6381),U_6382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6379),U_6380),U_6382)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6379),U_6382),c_Groups_Ozero__class_Ozero(U_6379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6379),U_6380),U_6381))
| ~ class_Rings_Olinordered__ring__strict(U_6379) ),
inference(definitional_conversion,[status(esa)],[f_1464_2]) ).
cnf(f_1464_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6379),U_6381),U_6382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6379),U_6380),U_6382)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6379),U_6382),c_Groups_Ozero__class_Ozero(U_6379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6379),U_6380),U_6381))
| ~ class_Rings_Olinordered__ring__strict(U_6379) ),
inference(clausify,[status(thm)],[f_1464_3]) ).
fof(f_1465_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_1465_2,plain,
! [U_6386,U_6385,U_6384,U_6383] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6383),U_6386),U_6385)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6383),U_6386),U_6384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6383),U_6386),c_Groups_Ozero__class_Ozero(U_6383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6383),U_6384),U_6385))
| ~ class_Rings_Olinordered__ring__strict(U_6383) ),
inference(variable_rename,[status(thm)],[f_1465_1]) ).
fof(f_1465_3,plain,
! [U_6383,U_6384,U_6385,U_6386] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6383),U_6386),U_6385)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6383),U_6386),U_6384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6383),U_6386),c_Groups_Ozero__class_Ozero(U_6383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6383),U_6384),U_6385))
| ~ class_Rings_Olinordered__ring__strict(U_6383) ),
inference(definitional_conversion,[status(esa)],[f_1465_2]) ).
cnf(f_1465_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6383),U_6386),U_6385)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6383),U_6386),U_6384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6383),U_6386),c_Groups_Ozero__class_Ozero(U_6383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6383),U_6384),U_6385))
| ~ class_Rings_Olinordered__ring__strict(U_6383) ),
inference(clausify,[status(thm)],[f_1465_3]) ).
fof(f_1466_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0]) ).
fof(f_1466_2,plain,
! [U_6389,U_6388,U_6387] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6387),U_6388),U_6389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6387),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6387),U_6388),U_6389)),c_Groups_Ozero__class_Ozero(U_6387))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6387),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6387),U_6388),U_6389)),c_Groups_Ozero__class_Ozero(U_6387)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6387),U_6388),U_6389)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_6387) ),
inference(variable_rename,[status(thm)],[f_1466_1]) ).
fof(f_1466_3,plain,
( ! [U_6388,U_6389,U_6387] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6387),U_6388),U_6389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6387),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6387),U_6388),U_6389)),c_Groups_Ozero__class_Ozero(U_6387)))
| ~ sP336(U_6388,U_6389,U_6387) )
& ! [U_6388,U_6389,U_6387] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6387),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6387),U_6388),U_6389)),c_Groups_Ozero__class_Ozero(U_6387)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6387),U_6388),U_6389))
| ~ sP336(U_6388,U_6389,U_6387) )
& ! [U_6388,U_6389,U_6387] :
( sP336(U_6388,U_6389,U_6387)
| ~ class_Groups_Oordered__ab__group__add(U_6387) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP336])],[f_1466_2]) ).
cnf(f_1466_4,plain,
( sP336(U_6388,U_6389,U_6387)
| ~ class_Groups_Oordered__ab__group__add(U_6387) ),
inference(clausify,[status(thm)],[f_1466_3]) ).
cnf(f_1466_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6387),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6387),U_6388),U_6389)),c_Groups_Ozero__class_Ozero(U_6387)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6387),U_6388),U_6389))
| ~ sP336(U_6388,U_6389,U_6387) ),
inference(clausify,[status(thm)],[f_1466_3]) ).
cnf(f_1466_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6387),U_6388),U_6389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6387),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6387),U_6388),U_6389)),c_Groups_Ozero__class_Ozero(U_6387)))
| ~ sP336(U_6388,U_6389,U_6387) ),
inference(clausify,[status(thm)],[f_1466_3]) ).
fof(f_1467_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0]) ).
fof(f_1467_2,plain,
! [U_6392,U_6391,U_6390] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6390),U_6391),U_6392))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6390),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6390),U_6391),U_6392)),c_Groups_Ozero__class_Ozero(U_6390))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6390),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6390),U_6391),U_6392)),c_Groups_Ozero__class_Ozero(U_6390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6390),U_6391),U_6392)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_6390) ),
inference(variable_rename,[status(thm)],[f_1467_1]) ).
fof(f_1467_3,plain,
( ! [U_6390,U_6391,U_6392] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6390),U_6391),U_6392))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6390),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6390),U_6391),U_6392)),c_Groups_Ozero__class_Ozero(U_6390)))
| ~ sP337(U_6390,U_6391,U_6392) )
& ! [U_6390,U_6391,U_6392] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6390),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6390),U_6391),U_6392)),c_Groups_Ozero__class_Ozero(U_6390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6390),U_6391),U_6392))
| ~ sP337(U_6390,U_6391,U_6392) )
& ! [U_6390,U_6391,U_6392] :
( sP337(U_6390,U_6391,U_6392)
| ~ class_Groups_Oordered__ab__group__add(U_6390) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP337])],[f_1467_2]) ).
cnf(f_1467_4,plain,
( sP337(U_6390,U_6391,U_6392)
| ~ class_Groups_Oordered__ab__group__add(U_6390) ),
inference(clausify,[status(thm)],[f_1467_3]) ).
cnf(f_1467_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6390),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6390),U_6391),U_6392)),c_Groups_Ozero__class_Ozero(U_6390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6390),U_6391),U_6392))
| ~ sP337(U_6390,U_6391,U_6392) ),
inference(clausify,[status(thm)],[f_1467_3]) ).
cnf(f_1467_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6390),U_6391),U_6392))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6390),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6390),U_6391),U_6392)),c_Groups_Ozero__class_Ozero(U_6390)))
| ~ sP337(U_6390,U_6391,U_6392) ),
inference(clausify,[status(thm)],[f_1467_3]) ).
fof(f_1468_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_1468_2,plain,
! [U_6398,U_6397,U_6396,U_6395,U_6394,U_6393] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6393),U_6395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6393),U_6394),U_6397)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6393),U_6396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6393),U_6394),U_6398))
| U_6397 = U_6398
| U_6395 != U_6396
| U_6394 = c_Groups_Ozero__class_Ozero(U_6393)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_6393) ),
inference(variable_rename,[status(thm)],[f_1468_1]) ).
fof(f_1468_3,plain,
! [U_6393,U_6394,U_6395,U_6396,U_6397,U_6398] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6393),U_6395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6393),U_6394),U_6397)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6393),U_6396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6393),U_6394),U_6398))
| U_6397 = U_6398
| U_6395 != U_6396
| U_6394 = c_Groups_Ozero__class_Ozero(U_6393)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_6393) ),
inference(definitional_conversion,[status(esa)],[f_1468_2]) ).
cnf(f_1468_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6393),U_6395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6393),U_6394),U_6397)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6393),U_6396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6393),U_6394),U_6398))
| U_6397 = U_6398
| U_6395 != U_6396
| U_6394 = c_Groups_Ozero__class_Ozero(U_6393)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_6393) ),
inference(clausify,[status(thm)],[f_1468_3]) ).
fof(f_1469_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_1469_2,plain,
! [U_6399] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6399),c_Groups_Ozero__class_Ozero(U_6399)),c_Groups_Oone__class_Oone(U_6399)))
| ~ class_Rings_Olinordered__semidom(U_6399) ),
inference(variable_rename,[status(thm)],[f_1469_1]) ).
fof(f_1469_3,plain,
! [U_6399] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6399),c_Groups_Ozero__class_Ozero(U_6399)),c_Groups_Oone__class_Oone(U_6399)))
| ~ class_Rings_Olinordered__semidom(U_6399) ),
inference(definitional_conversion,[status(esa)],[f_1469_2]) ).
cnf(f_1469_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6399),c_Groups_Ozero__class_Ozero(U_6399)),c_Groups_Oone__class_Oone(U_6399)))
| ~ class_Rings_Olinordered__semidom(U_6399) ),
inference(clausify,[status(thm)],[f_1469_3]) ).
fof(f_1470_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_1470_2,plain,
! [U_6400] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6400),c_Groups_Oone__class_Oone(U_6400)),c_Groups_Ozero__class_Ozero(U_6400)))
| ~ class_Rings_Olinordered__semidom(U_6400) ),
inference(variable_rename,[status(thm)],[f_1470_1]) ).
fof(f_1470_3,plain,
! [U_6400] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6400),c_Groups_Oone__class_Oone(U_6400)),c_Groups_Ozero__class_Ozero(U_6400)))
| ~ class_Rings_Olinordered__semidom(U_6400) ),
inference(definitional_conversion,[status(esa)],[f_1470_2]) ).
cnf(f_1470_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6400),c_Groups_Oone__class_Oone(U_6400)),c_Groups_Ozero__class_Ozero(U_6400)))
| ~ class_Rings_Olinordered__semidom(U_6400) ),
inference(clausify,[status(thm)],[f_1470_3]) ).
fof(f_1471_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_1471_2,plain,
! [U_6401] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6401),c_Groups_Ozero__class_Ozero(U_6401)),c_Groups_Oone__class_Oone(U_6401)))
| ~ class_Rings_Olinordered__semidom(U_6401) ),
inference(variable_rename,[status(thm)],[f_1471_1]) ).
fof(f_1471_3,plain,
! [U_6401] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6401),c_Groups_Ozero__class_Ozero(U_6401)),c_Groups_Oone__class_Oone(U_6401)))
| ~ class_Rings_Olinordered__semidom(U_6401) ),
inference(definitional_conversion,[status(esa)],[f_1471_2]) ).
cnf(f_1471_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6401),c_Groups_Ozero__class_Ozero(U_6401)),c_Groups_Oone__class_Oone(U_6401)))
| ~ class_Rings_Olinordered__semidom(U_6401) ),
inference(clausify,[status(thm)],[f_1471_3]) ).
fof(f_1472_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_1472_2,plain,
! [U_6402] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6402),c_Groups_Oone__class_Oone(U_6402)),c_Groups_Ozero__class_Ozero(U_6402)))
| ~ class_Rings_Olinordered__semidom(U_6402) ),
inference(variable_rename,[status(thm)],[f_1472_1]) ).
fof(f_1472_3,plain,
! [U_6402] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6402),c_Groups_Oone__class_Oone(U_6402)),c_Groups_Ozero__class_Ozero(U_6402)))
| ~ class_Rings_Olinordered__semidom(U_6402) ),
inference(definitional_conversion,[status(esa)],[f_1472_2]) ).
cnf(f_1472_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6402),c_Groups_Oone__class_Oone(U_6402)),c_Groups_Ozero__class_Ozero(U_6402)))
| ~ class_Rings_Olinordered__semidom(U_6402) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
fof(f_1473_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le]) ).
fof(f_1473_2,plain,
! [U_6404,U_6403] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6403),c_Groups_Ozero__class_Ozero(U_6403)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6403),U_6404)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6403),U_6404),c_Groups_Ozero__class_Ozero(U_6403))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6403),U_6404),c_Groups_Ozero__class_Ozero(U_6403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6403),c_Groups_Ozero__class_Ozero(U_6403)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6403),U_6404))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_6403) ),
inference(variable_rename,[status(thm)],[f_1473_1]) ).
fof(f_1473_3,plain,
( ! [U_6403,U_6404] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6403),c_Groups_Ozero__class_Ozero(U_6403)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6403),U_6404)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6403),U_6404),c_Groups_Ozero__class_Ozero(U_6403)))
| ~ sP338(U_6403,U_6404) )
& ! [U_6403,U_6404] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6403),U_6404),c_Groups_Ozero__class_Ozero(U_6403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6403),c_Groups_Ozero__class_Ozero(U_6403)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6403),U_6404)))
| ~ sP338(U_6403,U_6404) )
& ! [U_6403,U_6404] :
( sP338(U_6403,U_6404)
| ~ class_Groups_Oordered__ab__group__add(U_6403) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP338])],[f_1473_2]) ).
cnf(f_1473_4,plain,
( sP338(U_6403,U_6404)
| ~ class_Groups_Oordered__ab__group__add(U_6403) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
cnf(f_1473_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6403),U_6404),c_Groups_Ozero__class_Ozero(U_6403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6403),c_Groups_Ozero__class_Ozero(U_6403)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6403),U_6404)))
| ~ sP338(U_6403,U_6404) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
cnf(f_1473_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6403),c_Groups_Ozero__class_Ozero(U_6403)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6403),U_6404)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6403),U_6404),c_Groups_Ozero__class_Ozero(U_6403)))
| ~ sP338(U_6403,U_6404) ),
inference(clausify,[status(thm)],[f_1473_3]) ).
fof(f_1474_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff]) ).
fof(f_1474_2,plain,
! [U_6406,U_6405] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6405),U_6406),hAPP(c_Groups_Ouminus__class_Ouminus(U_6405),U_6406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6405),U_6406),c_Groups_Ozero__class_Ozero(U_6405))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6405),U_6406),c_Groups_Ozero__class_Ozero(U_6405)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6405),U_6406),hAPP(c_Groups_Ouminus__class_Ouminus(U_6405),U_6406))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_6405) ),
inference(variable_rename,[status(thm)],[f_1474_1]) ).
fof(f_1474_3,plain,
( ! [U_6406,U_6405] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6405),U_6406),hAPP(c_Groups_Ouminus__class_Ouminus(U_6405),U_6406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6405),U_6406),c_Groups_Ozero__class_Ozero(U_6405)))
| ~ sP339(U_6406,U_6405) )
& ! [U_6406,U_6405] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6405),U_6406),c_Groups_Ozero__class_Ozero(U_6405)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6405),U_6406),hAPP(c_Groups_Ouminus__class_Ouminus(U_6405),U_6406)))
| ~ sP339(U_6406,U_6405) )
& ! [U_6406,U_6405] :
( sP339(U_6406,U_6405)
| ~ class_Groups_Olinordered__ab__group__add(U_6405) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP339])],[f_1474_2]) ).
cnf(f_1474_4,plain,
( sP339(U_6406,U_6405)
| ~ class_Groups_Olinordered__ab__group__add(U_6405) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6405),U_6406),c_Groups_Ozero__class_Ozero(U_6405)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6405),U_6406),hAPP(c_Groups_Ouminus__class_Ouminus(U_6405),U_6406)))
| ~ sP339(U_6406,U_6405) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6405),U_6406),hAPP(c_Groups_Ouminus__class_Ouminus(U_6405),U_6406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6405),U_6406),c_Groups_Ozero__class_Ozero(U_6405)))
| ~ sP339(U_6406,U_6405) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
fof(f_1475_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le]) ).
fof(f_1475_2,plain,
! [U_6408,U_6407] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6407),hAPP(c_Groups_Ouminus__class_Ouminus(U_6407),U_6408)),c_Groups_Ozero__class_Ozero(U_6407)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6407),c_Groups_Ozero__class_Ozero(U_6407)),U_6408)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6407),c_Groups_Ozero__class_Ozero(U_6407)),U_6408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6407),hAPP(c_Groups_Ouminus__class_Ouminus(U_6407),U_6408)),c_Groups_Ozero__class_Ozero(U_6407))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_6407) ),
inference(variable_rename,[status(thm)],[f_1475_1]) ).
fof(f_1475_3,plain,
( ! [U_6407,U_6408] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6407),hAPP(c_Groups_Ouminus__class_Ouminus(U_6407),U_6408)),c_Groups_Ozero__class_Ozero(U_6407)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6407),c_Groups_Ozero__class_Ozero(U_6407)),U_6408))
| ~ sP340(U_6407,U_6408) )
& ! [U_6407,U_6408] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6407),c_Groups_Ozero__class_Ozero(U_6407)),U_6408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6407),hAPP(c_Groups_Ouminus__class_Ouminus(U_6407),U_6408)),c_Groups_Ozero__class_Ozero(U_6407)))
| ~ sP340(U_6407,U_6408) )
& ! [U_6407,U_6408] :
( sP340(U_6407,U_6408)
| ~ class_Groups_Oordered__ab__group__add(U_6407) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP340])],[f_1475_2]) ).
cnf(f_1475_4,plain,
( sP340(U_6407,U_6408)
| ~ class_Groups_Oordered__ab__group__add(U_6407) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6407),c_Groups_Ozero__class_Ozero(U_6407)),U_6408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6407),hAPP(c_Groups_Ouminus__class_Ouminus(U_6407),U_6408)),c_Groups_Ozero__class_Ozero(U_6407)))
| ~ sP340(U_6407,U_6408) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
cnf(f_1475_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6407),hAPP(c_Groups_Ouminus__class_Ouminus(U_6407),U_6408)),c_Groups_Ozero__class_Ozero(U_6407)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6407),c_Groups_Ozero__class_Ozero(U_6407)),U_6408))
| ~ sP340(U_6407,U_6408) ),
inference(clausify,[status(thm)],[f_1475_3]) ).
fof(f_1476_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_a_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff]) ).
fof(f_1476_2,plain,
! [U_6410,U_6409] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6409),hAPP(c_Groups_Ouminus__class_Ouminus(U_6409),U_6410)),U_6410))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6409),c_Groups_Ozero__class_Ozero(U_6409)),U_6410)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6409),c_Groups_Ozero__class_Ozero(U_6409)),U_6410))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6409),hAPP(c_Groups_Ouminus__class_Ouminus(U_6409),U_6410)),U_6410)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_6409) ),
inference(variable_rename,[status(thm)],[f_1476_1]) ).
fof(f_1476_3,plain,
( ! [U_6410,U_6409] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6409),hAPP(c_Groups_Ouminus__class_Ouminus(U_6409),U_6410)),U_6410))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6409),c_Groups_Ozero__class_Ozero(U_6409)),U_6410))
| ~ sP341(U_6410,U_6409) )
& ! [U_6410,U_6409] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6409),c_Groups_Ozero__class_Ozero(U_6409)),U_6410))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6409),hAPP(c_Groups_Ouminus__class_Ouminus(U_6409),U_6410)),U_6410))
| ~ sP341(U_6410,U_6409) )
& ! [U_6410,U_6409] :
( sP341(U_6410,U_6409)
| ~ class_Groups_Olinordered__ab__group__add(U_6409) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP341])],[f_1476_2]) ).
cnf(f_1476_4,plain,
( sP341(U_6410,U_6409)
| ~ class_Groups_Olinordered__ab__group__add(U_6409) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6409),c_Groups_Ozero__class_Ozero(U_6409)),U_6410))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6409),hAPP(c_Groups_Ouminus__class_Ouminus(U_6409),U_6410)),U_6410))
| ~ sP341(U_6410,U_6409) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6409),hAPP(c_Groups_Ouminus__class_Ouminus(U_6409),U_6410)),U_6410))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6409),c_Groups_Ozero__class_Ozero(U_6409)),U_6410))
| ~ sP341(U_6410,U_6409) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
fof(f_1477_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff]) ).
fof(f_1477_2,plain,
! [U_6412,U_6411] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),U_6412),hAPP(c_Groups_Ouminus__class_Ouminus(U_6411),U_6412)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),U_6412),c_Groups_Ozero__class_Ozero(U_6411))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),U_6412),c_Groups_Ozero__class_Ozero(U_6411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),U_6412),hAPP(c_Groups_Ouminus__class_Ouminus(U_6411),U_6412))) ) )
| ~ class_Rings_Olinordered__idom(U_6411) ),
inference(variable_rename,[status(thm)],[f_1477_1]) ).
fof(f_1477_3,plain,
( ! [U_6412,U_6411] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),U_6412),hAPP(c_Groups_Ouminus__class_Ouminus(U_6411),U_6412)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),U_6412),c_Groups_Ozero__class_Ozero(U_6411)))
| ~ sP342(U_6412,U_6411) )
& ! [U_6412,U_6411] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),U_6412),c_Groups_Ozero__class_Ozero(U_6411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),U_6412),hAPP(c_Groups_Ouminus__class_Ouminus(U_6411),U_6412)))
| ~ sP342(U_6412,U_6411) )
& ! [U_6412,U_6411] :
( sP342(U_6412,U_6411)
| ~ class_Rings_Olinordered__idom(U_6411) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP342])],[f_1477_2]) ).
cnf(f_1477_4,plain,
( sP342(U_6412,U_6411)
| ~ class_Rings_Olinordered__idom(U_6411) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),U_6412),c_Groups_Ozero__class_Ozero(U_6411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),U_6412),hAPP(c_Groups_Ouminus__class_Ouminus(U_6411),U_6412)))
| ~ sP342(U_6412,U_6411) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
cnf(f_1477_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),U_6412),hAPP(c_Groups_Ouminus__class_Ouminus(U_6411),U_6412)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),U_6412),c_Groups_Ozero__class_Ozero(U_6411)))
| ~ sP342(U_6412,U_6411) ),
inference(clausify,[status(thm)],[f_1477_3]) ).
fof(f_1478_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less]) ).
fof(f_1478_2,plain,
! [U_6414,U_6413] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),c_Groups_Ozero__class_Ozero(U_6413)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6413),U_6414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),U_6414),c_Groups_Ozero__class_Ozero(U_6413))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),U_6414),c_Groups_Ozero__class_Ozero(U_6413)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),c_Groups_Ozero__class_Ozero(U_6413)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6413),U_6414))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_6413) ),
inference(variable_rename,[status(thm)],[f_1478_1]) ).
fof(f_1478_3,plain,
( ! [U_6414,U_6413] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),c_Groups_Ozero__class_Ozero(U_6413)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6413),U_6414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),U_6414),c_Groups_Ozero__class_Ozero(U_6413)))
| ~ sP343(U_6414,U_6413) )
& ! [U_6414,U_6413] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),U_6414),c_Groups_Ozero__class_Ozero(U_6413)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),c_Groups_Ozero__class_Ozero(U_6413)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6413),U_6414)))
| ~ sP343(U_6414,U_6413) )
& ! [U_6414,U_6413] :
( sP343(U_6414,U_6413)
| ~ class_Groups_Oordered__ab__group__add(U_6413) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP343])],[f_1478_2]) ).
cnf(f_1478_4,plain,
( sP343(U_6414,U_6413)
| ~ class_Groups_Oordered__ab__group__add(U_6413) ),
inference(clausify,[status(thm)],[f_1478_3]) ).
cnf(f_1478_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),U_6414),c_Groups_Ozero__class_Ozero(U_6413)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),c_Groups_Ozero__class_Ozero(U_6413)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6413),U_6414)))
| ~ sP343(U_6414,U_6413) ),
inference(clausify,[status(thm)],[f_1478_3]) ).
cnf(f_1478_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),c_Groups_Ozero__class_Ozero(U_6413)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6413),U_6414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6413),U_6414),c_Groups_Ozero__class_Ozero(U_6413)))
| ~ sP343(U_6414,U_6413) ),
inference(clausify,[status(thm)],[f_1478_3]) ).
fof(f_1479_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less]) ).
fof(f_1479_2,plain,
! [U_6416,U_6415] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),hAPP(c_Groups_Ouminus__class_Ouminus(U_6415),U_6416)),c_Groups_Ozero__class_Ozero(U_6415)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),c_Groups_Ozero__class_Ozero(U_6415)),U_6416)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),c_Groups_Ozero__class_Ozero(U_6415)),U_6416))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),hAPP(c_Groups_Ouminus__class_Ouminus(U_6415),U_6416)),c_Groups_Ozero__class_Ozero(U_6415))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_6415) ),
inference(variable_rename,[status(thm)],[f_1479_1]) ).
fof(f_1479_3,plain,
( ! [U_6415,U_6416] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),hAPP(c_Groups_Ouminus__class_Ouminus(U_6415),U_6416)),c_Groups_Ozero__class_Ozero(U_6415)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),c_Groups_Ozero__class_Ozero(U_6415)),U_6416))
| ~ sP344(U_6415,U_6416) )
& ! [U_6415,U_6416] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),c_Groups_Ozero__class_Ozero(U_6415)),U_6416))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),hAPP(c_Groups_Ouminus__class_Ouminus(U_6415),U_6416)),c_Groups_Ozero__class_Ozero(U_6415)))
| ~ sP344(U_6415,U_6416) )
& ! [U_6415,U_6416] :
( sP344(U_6415,U_6416)
| ~ class_Groups_Oordered__ab__group__add(U_6415) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP344])],[f_1479_2]) ).
cnf(f_1479_4,plain,
( sP344(U_6415,U_6416)
| ~ class_Groups_Oordered__ab__group__add(U_6415) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),c_Groups_Ozero__class_Ozero(U_6415)),U_6416))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),hAPP(c_Groups_Ouminus__class_Ouminus(U_6415),U_6416)),c_Groups_Ozero__class_Ozero(U_6415)))
| ~ sP344(U_6415,U_6416) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
cnf(f_1479_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),hAPP(c_Groups_Ouminus__class_Ouminus(U_6415),U_6416)),c_Groups_Ozero__class_Ozero(U_6415)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),c_Groups_Ozero__class_Ozero(U_6415)),U_6416))
| ~ sP344(U_6415,U_6416) ),
inference(clausify,[status(thm)],[f_1479_3]) ).
fof(f_1480_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_a_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg]) ).
fof(f_1480_2,plain,
! [U_6418,U_6417] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6417),hAPP(c_Groups_Ouminus__class_Ouminus(U_6417),U_6418)),U_6418))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6417),c_Groups_Ozero__class_Ozero(U_6417)),U_6418)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6417),c_Groups_Ozero__class_Ozero(U_6417)),U_6418))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6417),hAPP(c_Groups_Ouminus__class_Ouminus(U_6417),U_6418)),U_6418)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_6417) ),
inference(variable_rename,[status(thm)],[f_1480_1]) ).
fof(f_1480_3,plain,
( ! [U_6418,U_6417] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6417),hAPP(c_Groups_Ouminus__class_Ouminus(U_6417),U_6418)),U_6418))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6417),c_Groups_Ozero__class_Ozero(U_6417)),U_6418))
| ~ sP345(U_6418,U_6417) )
& ! [U_6418,U_6417] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6417),c_Groups_Ozero__class_Ozero(U_6417)),U_6418))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6417),hAPP(c_Groups_Ouminus__class_Ouminus(U_6417),U_6418)),U_6418))
| ~ sP345(U_6418,U_6417) )
& ! [U_6418,U_6417] :
( sP345(U_6418,U_6417)
| ~ class_Groups_Olinordered__ab__group__add(U_6417) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP345])],[f_1480_2]) ).
cnf(f_1480_4,plain,
( sP345(U_6418,U_6417)
| ~ class_Groups_Olinordered__ab__group__add(U_6417) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6417),c_Groups_Ozero__class_Ozero(U_6417)),U_6418))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6417),hAPP(c_Groups_Ouminus__class_Ouminus(U_6417),U_6418)),U_6418))
| ~ sP345(U_6418,U_6417) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
cnf(f_1480_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6417),hAPP(c_Groups_Ouminus__class_Ouminus(U_6417),U_6418)),U_6418))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6417),c_Groups_Ozero__class_Ozero(U_6417)),U_6418))
| ~ sP345(U_6418,U_6417) ),
inference(clausify,[status(thm)],[f_1480_3]) ).
fof(f_1481_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_1481_2,plain,
! [U_6421,U_6420,U_6419] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6419),U_6420) = U_6421
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6419),U_6420),U_6421) != c_Groups_Ozero__class_Ozero(U_6419)
| ~ class_Groups_Ogroup__add(U_6419) ),
inference(variable_rename,[status(thm)],[f_1481_1]) ).
fof(f_1481_3,plain,
! [U_6419,U_6421,U_6420] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6419),U_6420) = U_6421
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6419),U_6420),U_6421) != c_Groups_Ozero__class_Ozero(U_6419)
| ~ class_Groups_Ogroup__add(U_6419) ),
inference(definitional_conversion,[status(esa)],[f_1481_2]) ).
cnf(f_1481_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_6419),U_6420) = U_6421
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6419),U_6420),U_6421) != c_Groups_Ozero__class_Ozero(U_6419)
| ~ class_Groups_Ogroup__add(U_6419) ),
inference(clausify,[status(thm)],[f_1481_3]) ).
fof(f_1482_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_1482_2,plain,
! [U_6423,U_6422] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6422),hAPP(c_Groups_Ouminus__class_Ouminus(U_6422),U_6423)),U_6423) = c_Groups_Ozero__class_Ozero(U_6422)
| ~ class_Groups_Oab__group__add(U_6422) ),
inference(variable_rename,[status(thm)],[f_1482_1]) ).
fof(f_1482_3,plain,
! [U_6422,U_6423] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6422),hAPP(c_Groups_Ouminus__class_Ouminus(U_6422),U_6423)),U_6423) = c_Groups_Ozero__class_Ozero(U_6422)
| ~ class_Groups_Oab__group__add(U_6422) ),
inference(definitional_conversion,[status(esa)],[f_1482_2]) ).
cnf(f_1482_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6422),hAPP(c_Groups_Ouminus__class_Ouminus(U_6422),U_6423)),U_6423) = c_Groups_Ozero__class_Ozero(U_6422)
| ~ class_Groups_Oab__group__add(U_6422) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
fof(f_1483_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_1483_2,plain,
! [U_6425,U_6424] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6424),hAPP(c_Groups_Ouminus__class_Ouminus(U_6424),U_6425)),U_6425) = c_Groups_Ozero__class_Ozero(U_6424)
| ~ class_Groups_Ogroup__add(U_6424) ),
inference(variable_rename,[status(thm)],[f_1483_1]) ).
fof(f_1483_3,plain,
! [U_6424,U_6425] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6424),hAPP(c_Groups_Ouminus__class_Ouminus(U_6424),U_6425)),U_6425) = c_Groups_Ozero__class_Ozero(U_6424)
| ~ class_Groups_Ogroup__add(U_6424) ),
inference(definitional_conversion,[status(esa)],[f_1483_2]) ).
cnf(f_1483_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6424),hAPP(c_Groups_Ouminus__class_Ouminus(U_6424),U_6425)),U_6425) = c_Groups_Ozero__class_Ozero(U_6424)
| ~ class_Groups_Ogroup__add(U_6424) ),
inference(clausify,[status(thm)],[f_1483_3]) ).
fof(f_1484_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_c) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0]) ).
fof(f_1484_2,plain,
! [U_6428,U_6427,U_6426] :
( ( ( U_6427 = hAPP(c_Groups_Ouminus__class_Ouminus(U_6426),U_6428)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6426),U_6427),U_6428) != c_Groups_Ozero__class_Ozero(U_6426) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6426),U_6427),U_6428) = c_Groups_Ozero__class_Ozero(U_6426)
| U_6427 != hAPP(c_Groups_Ouminus__class_Ouminus(U_6426),U_6428) ) )
| ~ class_Groups_Ogroup__add(U_6426) ),
inference(variable_rename,[status(thm)],[f_1484_1]) ).
fof(f_1484_3,plain,
( ! [U_6426,U_6427,U_6428] :
( U_6427 = hAPP(c_Groups_Ouminus__class_Ouminus(U_6426),U_6428)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6426),U_6427),U_6428) != c_Groups_Ozero__class_Ozero(U_6426)
| ~ sP346(U_6426,U_6427,U_6428) )
& ! [U_6426,U_6427,U_6428] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6426),U_6427),U_6428) = c_Groups_Ozero__class_Ozero(U_6426)
| U_6427 != hAPP(c_Groups_Ouminus__class_Ouminus(U_6426),U_6428)
| ~ sP346(U_6426,U_6427,U_6428) )
& ! [U_6426,U_6427,U_6428] :
( sP346(U_6426,U_6427,U_6428)
| ~ class_Groups_Ogroup__add(U_6426) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP346])],[f_1484_2]) ).
cnf(f_1484_4,plain,
( sP346(U_6426,U_6427,U_6428)
| ~ class_Groups_Ogroup__add(U_6426) ),
inference(clausify,[status(thm)],[f_1484_3]) ).
cnf(f_1484_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6426),U_6427),U_6428) = c_Groups_Ozero__class_Ozero(U_6426)
| U_6427 != hAPP(c_Groups_Ouminus__class_Ouminus(U_6426),U_6428)
| ~ sP346(U_6426,U_6427,U_6428) ),
inference(clausify,[status(thm)],[f_1484_3]) ).
cnf(f_1484_6,plain,
( U_6427 = hAPP(c_Groups_Ouminus__class_Ouminus(U_6426),U_6428)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6426),U_6427),U_6428) != c_Groups_Ozero__class_Ozero(U_6426)
| ~ sP346(U_6426,U_6427,U_6428) ),
inference(clausify,[status(thm)],[f_1484_3]) ).
fof(f_1485_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_1485_2,plain,
! [U_6430,U_6429] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6429),U_6430),hAPP(c_Groups_Ouminus__class_Ouminus(U_6429),U_6430)) = c_Groups_Ozero__class_Ozero(U_6429)
| ~ class_Groups_Ogroup__add(U_6429) ),
inference(variable_rename,[status(thm)],[f_1485_1]) ).
fof(f_1485_3,plain,
! [U_6430,U_6429] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6429),U_6430),hAPP(c_Groups_Ouminus__class_Ouminus(U_6429),U_6430)) = c_Groups_Ozero__class_Ozero(U_6429)
| ~ class_Groups_Ogroup__add(U_6429) ),
inference(definitional_conversion,[status(esa)],[f_1485_2]) ).
cnf(f_1485_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6429),U_6430),hAPP(c_Groups_Ouminus__class_Ouminus(U_6429),U_6430)) = c_Groups_Ozero__class_Ozero(U_6429)
| ~ class_Groups_Ogroup__add(U_6429) ),
inference(clausify,[status(thm)],[f_1485_3]) ).
fof(f_1486_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_1486_2,plain,
! [U_6434,U_6433,U_6432,U_6431] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),hAPP(hAPP(c_Power_Opower__class_Opower(U_6431),U_6432),U_6434)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6431),U_6433),U_6434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),c_Groups_Ozero__class_Ozero(U_6431)),U_6432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),U_6432),U_6433))
| ~ class_Rings_Olinordered__semidom(U_6431) ),
inference(variable_rename,[status(thm)],[f_1486_1]) ).
fof(f_1486_3,plain,
! [U_6431,U_6432,U_6433,U_6434] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),hAPP(hAPP(c_Power_Opower__class_Opower(U_6431),U_6432),U_6434)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6431),U_6433),U_6434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),c_Groups_Ozero__class_Ozero(U_6431)),U_6432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),U_6432),U_6433))
| ~ class_Rings_Olinordered__semidom(U_6431) ),
inference(definitional_conversion,[status(esa)],[f_1486_2]) ).
cnf(f_1486_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),hAPP(hAPP(c_Power_Opower__class_Opower(U_6431),U_6432),U_6434)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6431),U_6433),U_6434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),c_Groups_Ozero__class_Ozero(U_6431)),U_6432))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),U_6432),U_6433))
| ~ class_Rings_Olinordered__semidom(U_6431) ),
inference(clausify,[status(thm)],[f_1486_3]) ).
fof(f_1487_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_1487_2,plain,
! [U_6437,U_6436,U_6435] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6435),c_Groups_Ozero__class_Ozero(U_6435)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6435),U_6436),U_6437)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6435),c_Groups_Ozero__class_Ozero(U_6435)),U_6436))
| ~ class_Rings_Olinordered__semidom(U_6435) ),
inference(variable_rename,[status(thm)],[f_1487_1]) ).
fof(f_1487_3,plain,
! [U_6435,U_6436,U_6437] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6435),c_Groups_Ozero__class_Ozero(U_6435)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6435),U_6436),U_6437)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6435),c_Groups_Ozero__class_Ozero(U_6435)),U_6436))
| ~ class_Rings_Olinordered__semidom(U_6435) ),
inference(definitional_conversion,[status(esa)],[f_1487_2]) ).
cnf(f_1487_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6435),c_Groups_Ozero__class_Ozero(U_6435)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6435),U_6436),U_6437)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6435),c_Groups_Ozero__class_Ozero(U_6435)),U_6436))
| ~ class_Rings_Olinordered__semidom(U_6435) ),
inference(clausify,[status(thm)],[f_1487_3]) ).
fof(f_1488_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_1488_2,plain,
! [U_6440,U_6439,U_6438] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6438),c_Groups_Ozero__class_Ozero(U_6438)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6438),U_6439),U_6440)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6438),c_Groups_Ozero__class_Ozero(U_6438)),U_6439))
| ~ class_Rings_Olinordered__semidom(U_6438) ),
inference(variable_rename,[status(thm)],[f_1488_1]) ).
fof(f_1488_3,plain,
! [U_6438,U_6439,U_6440] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6438),c_Groups_Ozero__class_Ozero(U_6438)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6438),U_6439),U_6440)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6438),c_Groups_Ozero__class_Ozero(U_6438)),U_6439))
| ~ class_Rings_Olinordered__semidom(U_6438) ),
inference(definitional_conversion,[status(esa)],[f_1488_2]) ).
cnf(f_1488_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6438),c_Groups_Ozero__class_Ozero(U_6438)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6438),U_6439),U_6440)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6438),c_Groups_Ozero__class_Ozero(U_6438)),U_6439))
| ~ class_Rings_Olinordered__semidom(U_6438) ),
inference(clausify,[status(thm)],[f_1488_3]) ).
fof(f_1489_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_1489_2,plain,
! [U_6442,U_6441] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6441),c_Groups_Ozero__class_Ozero(U_6441)),U_6442) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6441),U_6442)
| ~ class_Groups_Ogroup__add(U_6441) ),
inference(variable_rename,[status(thm)],[f_1489_1]) ).
fof(f_1489_3,plain,
! [U_6441,U_6442] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6441),c_Groups_Ozero__class_Ozero(U_6441)),U_6442) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6441),U_6442)
| ~ class_Groups_Ogroup__add(U_6441) ),
inference(definitional_conversion,[status(esa)],[f_1489_2]) ).
cnf(f_1489_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6441),c_Groups_Ozero__class_Ozero(U_6441)),U_6442) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6441),U_6442)
| ~ class_Groups_Ogroup__add(U_6441) ),
inference(clausify,[status(thm)],[f_1489_3]) ).
fof(f_1490_1,plain,
! [V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__empty]) ).
fof(f_1490_2,plain,
! [U_6445,U_6444,U_6443] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6444,U_6443),U_6445),c_Orderings_Obot__class_Obot(tc_fun(U_6444,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_6443)
| ~ class_Groups_Ocomm__monoid__add(U_6443) ),
inference(variable_rename,[status(thm)],[f_1490_1]) ).
fof(f_1490_3,plain,
! [U_6443,U_6444,U_6445] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6444,U_6443),U_6445),c_Orderings_Obot__class_Obot(tc_fun(U_6444,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_6443)
| ~ class_Groups_Ocomm__monoid__add(U_6443) ),
inference(definitional_conversion,[status(esa)],[f_1490_2]) ).
cnf(f_1490_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6444,U_6443),U_6445),c_Orderings_Obot__class_Obot(tc_fun(U_6444,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_6443)
| ~ class_Groups_Ocomm__monoid__add(U_6443) ),
inference(clausify,[status(thm)],[f_1490_3]) ).
fof(f_1491_1,plain,
! [V_g_2,T_d,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oempty]) ).
fof(f_1491_2,plain,
! [U_6448,U_6447,U_6446] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6447,U_6446),U_6448),c_Orderings_Obot__class_Obot(tc_fun(U_6447,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_6446)
| ~ class_Groups_Ocomm__monoid__add(U_6446) ),
inference(variable_rename,[status(thm)],[f_1491_1]) ).
fof(f_1491_3,plain,
! [U_6446,U_6447,U_6448] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6447,U_6446),U_6448),c_Orderings_Obot__class_Obot(tc_fun(U_6447,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_6446)
| ~ class_Groups_Ocomm__monoid__add(U_6446) ),
inference(definitional_conversion,[status(esa)],[f_1491_2]) ).
cnf(f_1491_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6447,U_6446),U_6448),c_Orderings_Obot__class_Obot(tc_fun(U_6447,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_6446)
| ~ class_Groups_Ocomm__monoid__add(U_6446) ),
inference(clausify,[status(thm)],[f_1491_3]) ).
fof(f_1492_1,plain,
! [V_g_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oinfinite]) ).
fof(f_1492_2,plain,
! [U_6452,U_6451,U_6450,U_6449] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6450,U_6449),U_6452),U_6451) = c_Groups_Ozero__class_Ozero(U_6449)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6450),U_6451))
| ~ class_Groups_Ocomm__monoid__add(U_6449) ),
inference(variable_rename,[status(thm)],[f_1492_1]) ).
fof(f_1492_3,plain,
! [U_6449,U_6450,U_6451,U_6452] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6450,U_6449),U_6452),U_6451) = c_Groups_Ozero__class_Ozero(U_6449)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6450),U_6451))
| ~ class_Groups_Ocomm__monoid__add(U_6449) ),
inference(definitional_conversion,[status(esa)],[f_1492_2]) ).
cnf(f_1492_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6450,U_6449),U_6452),U_6451) = c_Groups_Ozero__class_Ozero(U_6449)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6450),U_6451))
| ~ class_Groups_Ocomm__monoid__add(U_6449) ),
inference(clausify,[status(thm)],[f_1492_3]) ).
fof(f_1493_1,plain,
! [V_f_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__infinite]) ).
fof(f_1493_2,plain,
! [U_6456,U_6455,U_6454,U_6453] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6454,U_6453),U_6456),U_6455) = c_Groups_Ozero__class_Ozero(U_6453)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6454),U_6455))
| ~ class_Groups_Ocomm__monoid__add(U_6453) ),
inference(variable_rename,[status(thm)],[f_1493_1]) ).
fof(f_1493_3,plain,
! [U_6454,U_6453,U_6455,U_6456] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6454,U_6453),U_6456),U_6455) = c_Groups_Ozero__class_Ozero(U_6453)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6454),U_6455))
| ~ class_Groups_Ocomm__monoid__add(U_6453) ),
inference(definitional_conversion,[status(esa)],[f_1493_2]) ).
cnf(f_1493_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6454,U_6453),U_6456),U_6455) = c_Groups_Ozero__class_Ozero(U_6453)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6454),U_6455))
| ~ class_Groups_Ocomm__monoid__add(U_6453) ),
inference(clausify,[status(thm)],[f_1493_3]) ).
fof(f_1494_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_1494_2,plain,
! [U_6458,U_6457] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6457),c_Groups_Ozero__class_Ozero(U_6457)),hAPP(c_Nat_OSuc,U_6458)) = c_Groups_Ozero__class_Ozero(U_6457)
| ~ class_Rings_Osemiring__0(U_6457)
| ~ class_Power_Opower(U_6457) ),
inference(variable_rename,[status(thm)],[f_1494_1]) ).
fof(f_1494_3,plain,
! [U_6458,U_6457] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6457),c_Groups_Ozero__class_Ozero(U_6457)),hAPP(c_Nat_OSuc,U_6458)) = c_Groups_Ozero__class_Ozero(U_6457)
| ~ class_Rings_Osemiring__0(U_6457)
| ~ class_Power_Opower(U_6457) ),
inference(definitional_conversion,[status(esa)],[f_1494_2]) ).
cnf(f_1494_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6457),c_Groups_Ozero__class_Ozero(U_6457)),hAPP(c_Nat_OSuc,U_6458)) = c_Groups_Ozero__class_Ozero(U_6457)
| ~ class_Rings_Osemiring__0(U_6457)
| ~ class_Power_Opower(U_6457) ),
inference(clausify,[status(thm)],[f_1494_3]) ).
fof(f_1495_1,plain,
! [V_f_2,V_A_2,T_c,T_d] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d)
| ! [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_d)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_d)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2) != c_Groups_Ozero__class_Ozero(T_d) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Rings_Ono__zero__divisors(T_d)
| ~ class_Rings_Ocomm__semiring__1(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__zero__iff]) ).
fof(f_1495_2,plain,
! [U_6464,U_6463,U_6462,U_6461] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6462,U_6461),U_6464),U_6463) = c_Groups_Ozero__class_Ozero(U_6461)
| ! [U_6460] :
( hAPP(U_6464,U_6460) != c_Groups_Ozero__class_Ozero(U_6461)
| ~ hBOOL(hAPP(hAPP(c_member(U_6462),U_6460),U_6463)) ) )
& ( ? [U_6459] :
( hAPP(U_6464,U_6459) = c_Groups_Ozero__class_Ozero(U_6461)
& hBOOL(hAPP(hAPP(c_member(U_6462),U_6459),U_6463)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6462,U_6461),U_6464),U_6463) != c_Groups_Ozero__class_Ozero(U_6461) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6462),U_6463))
| ~ class_Rings_Ono__zero__divisors(U_6461)
| ~ class_Rings_Ocomm__semiring__1(U_6461) ),
inference(variable_rename,[status(thm)],[f_1495_1]) ).
fof(f_1495_3,plain,
! [U_6464,U_6463,U_6462,U_6461] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6462,U_6461),U_6464),U_6463) = c_Groups_Ozero__class_Ozero(U_6461)
| ! [U_6460] :
( hAPP(U_6464,U_6460) != c_Groups_Ozero__class_Ozero(U_6461)
| ~ hBOOL(hAPP(hAPP(c_member(U_6462),U_6460),U_6463)) ) )
& ( ( hAPP(U_6464,sK121(U_6464,U_6463,U_6462,U_6461)) = c_Groups_Ozero__class_Ozero(U_6461)
& hBOOL(hAPP(hAPP(c_member(U_6462),sK121(U_6464,U_6463,U_6462,U_6461)),U_6463)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6462,U_6461),U_6464),U_6463) != c_Groups_Ozero__class_Ozero(U_6461) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6462),U_6463))
| ~ class_Rings_Ono__zero__divisors(U_6461)
| ~ class_Rings_Ocomm__semiring__1(U_6461) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_6459,sK121(U_6464,U_6463,U_6462,U_6461))],[f_1495_2]) ).
fof(f_1495_4,plain,
( ! [U_6461,U_6462,U_6463,U_6464] :
( hAPP(U_6464,sK121(U_6464,U_6463,U_6462,U_6461)) = c_Groups_Ozero__class_Ozero(U_6461)
| ~ sP347(U_6461,U_6462,U_6463,U_6464) )
& ! [U_6461,U_6462,U_6463,U_6464] :
( hBOOL(hAPP(hAPP(c_member(U_6462),sK121(U_6464,U_6463,U_6462,U_6461)),U_6463))
| ~ sP347(U_6461,U_6462,U_6463,U_6464) )
& ! [U_6460,U_6461,U_6462,U_6463,U_6464] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6462,U_6461),U_6464),U_6463) = c_Groups_Ozero__class_Ozero(U_6461)
| hAPP(U_6464,U_6460) != c_Groups_Ozero__class_Ozero(U_6461)
| ~ hBOOL(hAPP(hAPP(c_member(U_6462),U_6460),U_6463))
| ~ sP348(U_6460,U_6461,U_6462,U_6463,U_6464) )
& ! [U_6460,U_6461,U_6462,U_6463,U_6464] :
( sP347(U_6461,U_6462,U_6463,U_6464)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6462,U_6461),U_6464),U_6463) != c_Groups_Ozero__class_Ozero(U_6461)
| ~ sP348(U_6460,U_6461,U_6462,U_6463,U_6464) )
& ! [U_6460,U_6461,U_6462,U_6463,U_6464] :
( sP348(U_6460,U_6461,U_6462,U_6463,U_6464)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6462),U_6463))
| ~ class_Rings_Ono__zero__divisors(U_6461)
| ~ class_Rings_Ocomm__semiring__1(U_6461) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP347,sP348])],[f_1495_3]) ).
cnf(f_1495_5,plain,
( sP348(U_6460,U_6461,U_6462,U_6463,U_6464)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6462),U_6463))
| ~ class_Rings_Ono__zero__divisors(U_6461)
| ~ class_Rings_Ocomm__semiring__1(U_6461) ),
inference(clausify,[status(thm)],[f_1495_4]) ).
cnf(f_1495_6,plain,
( sP347(U_6461,U_6462,U_6463,U_6464)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6462,U_6461),U_6464),U_6463) != c_Groups_Ozero__class_Ozero(U_6461)
| ~ sP348(U_6460,U_6461,U_6462,U_6463,U_6464) ),
inference(clausify,[status(thm)],[f_1495_4]) ).
cnf(f_1495_7,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6462,U_6461),U_6464),U_6463) = c_Groups_Ozero__class_Ozero(U_6461)
| hAPP(U_6464,U_6460) != c_Groups_Ozero__class_Ozero(U_6461)
| ~ hBOOL(hAPP(hAPP(c_member(U_6462),U_6460),U_6463))
| ~ sP348(U_6460,U_6461,U_6462,U_6463,U_6464) ),
inference(clausify,[status(thm)],[f_1495_4]) ).
cnf(f_1495_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_6462),sK121(U_6464,U_6463,U_6462,U_6461)),U_6463))
| ~ sP347(U_6461,U_6462,U_6463,U_6464) ),
inference(clausify,[status(thm)],[f_1495_4]) ).
cnf(f_1495_9,plain,
( hAPP(U_6464,sK121(U_6464,U_6463,U_6462,U_6461)) = c_Groups_Ozero__class_Ozero(U_6461)
| ~ sP347(U_6461,U_6462,U_6463,U_6464) ),
inference(clausify,[status(thm)],[f_1495_4]) ).
fof(f_1496_1,plain,
! [V_f_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d)
| ! [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_d)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Rings_Ocomm__semiring__1(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__zero]) ).
fof(f_1496_2,plain,
! [U_6469,U_6468,U_6467,U_6466] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6467,U_6466),U_6469),U_6468) = c_Groups_Ozero__class_Ozero(U_6466)
| ! [U_6465] :
( hAPP(U_6469,U_6465) != c_Groups_Ozero__class_Ozero(U_6466)
| ~ hBOOL(hAPP(hAPP(c_member(U_6467),U_6465),U_6468)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6467),U_6468))
| ~ class_Rings_Ocomm__semiring__1(U_6466) ),
inference(variable_rename,[status(thm)],[f_1496_1]) ).
fof(f_1496_3,plain,
! [U_6468,U_6465,U_6466,U_6469,U_6467] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6467,U_6466),U_6469),U_6468) = c_Groups_Ozero__class_Ozero(U_6466)
| hAPP(U_6469,U_6465) != c_Groups_Ozero__class_Ozero(U_6466)
| ~ hBOOL(hAPP(hAPP(c_member(U_6467),U_6465),U_6468))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6467),U_6468))
| ~ class_Rings_Ocomm__semiring__1(U_6466) ),
inference(definitional_conversion,[status(esa)],[f_1496_2]) ).
cnf(f_1496_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6467,U_6466),U_6469),U_6468) = c_Groups_Ozero__class_Ozero(U_6466)
| hAPP(U_6469,U_6465) != c_Groups_Ozero__class_Ozero(U_6466)
| ~ hBOOL(hAPP(hAPP(c_member(U_6467),U_6465),U_6468))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6467),U_6468))
| ~ class_Rings_Ocomm__semiring__1(U_6466) ),
inference(clausify,[status(thm)],[f_1496_3]) ).
fof(f_1497_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_1497_2,plain,
! [U_6472] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6472))
| ! [U_6471] : U_6472 != hAPP(c_Nat_OSuc,U_6471) )
& ( ? [U_6470] : U_6472 = hAPP(c_Nat_OSuc,U_6470)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6472)) ) ),
inference(variable_rename,[status(thm)],[f_1497_1]) ).
fof(f_1497_3,plain,
( ! [U_6474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6474))
| ! [U_6471] : U_6474 != hAPP(c_Nat_OSuc,U_6471) )
& ! [U_6473] :
( ? [U_6470] : U_6473 = hAPP(c_Nat_OSuc,U_6470)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6473)) ) ),
inference(miniscope,[status(thm)],[f_1497_2]) ).
fof(f_1497_4,plain,
( ! [U_6474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6474))
| ! [U_6471] : U_6474 != hAPP(c_Nat_OSuc,U_6471) )
& ! [U_6473] :
( U_6473 = hAPP(c_Nat_OSuc,sK122(U_6473))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6473)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_6470,sK122(U_6473))],[f_1497_3]) ).
fof(f_1497_5,plain,
( ! [U_6471,U_6474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6474))
| U_6474 != hAPP(c_Nat_OSuc,U_6471) )
& ! [U_6473] :
( U_6473 = hAPP(c_Nat_OSuc,sK122(U_6473))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6473)) ) ),
inference(definitional_conversion,[status(esa)],[f_1497_4]) ).
cnf(f_1497_6,plain,
( U_6473 = hAPP(c_Nat_OSuc,sK122(U_6473))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6473)) ),
inference(clausify,[status(thm)],[f_1497_5]) ).
cnf(f_1497_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6474))
| U_6474 != hAPP(c_Nat_OSuc,U_6471) ),
inference(clausify,[status(thm)],[f_1497_5]) ).
fof(f_1498_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_1498_2,plain,
! [U_6475] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6475),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_6475 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_6475 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6475),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[f_1498_1]) ).
fof(f_1498_3,plain,
( ! [U_6477] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6477),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_6477 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6476] :
( U_6476 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6476),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(miniscope,[status(thm)],[f_1498_2]) ).
fof(f_1498_4,plain,
( ! [U_6477] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6477),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_6477 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6476] :
( U_6476 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6476),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(definitional_conversion,[status(esa)],[f_1498_3]) ).
cnf(f_1498_5,plain,
( U_6476 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6476),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(clausify,[status(thm)],[f_1498_4]) ).
cnf(f_1498_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6477),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_6477 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1498_4]) ).
fof(f_1499_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_1499_2,plain,
! [U_6481,U_6480] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6480),hAPP(c_Nat_OSuc,U_6481)))
| ( ! [U_6479] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6479),U_6481))
| U_6480 != hAPP(c_Nat_OSuc,U_6479) )
& U_6480 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [U_6478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6478),U_6481))
& U_6480 = hAPP(c_Nat_OSuc,U_6478) )
| U_6480 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6480),hAPP(c_Nat_OSuc,U_6481))) ) ),
inference(variable_rename,[status(thm)],[f_1499_1]) ).
fof(f_1499_3,plain,
( ! [U_6485,U_6483] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6483),hAPP(c_Nat_OSuc,U_6485)))
| ( ! [U_6479] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6479),U_6485))
| U_6483 != hAPP(c_Nat_OSuc,U_6479) )
& U_6483 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_6484,U_6482] :
( ? [U_6478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6478),U_6484))
& U_6482 = hAPP(c_Nat_OSuc,U_6478) )
| U_6482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6482),hAPP(c_Nat_OSuc,U_6484))) ) ),
inference(miniscope,[status(thm)],[f_1499_2]) ).
fof(f_1499_4,plain,
( ! [U_6485,U_6483] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6483),hAPP(c_Nat_OSuc,U_6485)))
| ( ! [U_6479] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6479),U_6485))
| U_6483 != hAPP(c_Nat_OSuc,U_6479) )
& U_6483 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_6484,U_6482] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK123(U_6484,U_6482)),U_6484))
& U_6482 = hAPP(c_Nat_OSuc,sK123(U_6484,U_6482)) )
| U_6482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6482),hAPP(c_Nat_OSuc,U_6484))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_6478,sK123(U_6484,U_6482))],[f_1499_3]) ).
fof(f_1499_5,plain,
( ! [U_6479,U_6485,U_6483] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6479),U_6485))
| U_6483 != hAPP(c_Nat_OSuc,U_6479)
| ~ sP350(U_6479,U_6485,U_6483) )
& ! [U_6479,U_6485,U_6483] :
( U_6483 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP350(U_6479,U_6485,U_6483) )
& ! [U_6482,U_6484] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK123(U_6484,U_6482)),U_6484))
| ~ sP349(U_6482,U_6484) )
& ! [U_6482,U_6484] :
( U_6482 = hAPP(c_Nat_OSuc,sK123(U_6484,U_6482))
| ~ sP349(U_6482,U_6484) )
& ! [U_6479,U_6485,U_6483] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6483),hAPP(c_Nat_OSuc,U_6485)))
| sP350(U_6479,U_6485,U_6483) )
& ! [U_6482,U_6484] :
( sP349(U_6482,U_6484)
| U_6482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6482),hAPP(c_Nat_OSuc,U_6484))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP349,sP350])],[f_1499_4]) ).
cnf(f_1499_6,plain,
( sP349(U_6482,U_6484)
| U_6482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6482),hAPP(c_Nat_OSuc,U_6484))) ),
inference(clausify,[status(thm)],[f_1499_5]) ).
cnf(f_1499_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6483),hAPP(c_Nat_OSuc,U_6485)))
| sP350(U_6479,U_6485,U_6483) ),
inference(clausify,[status(thm)],[f_1499_5]) ).
cnf(f_1499_8,plain,
( U_6482 = hAPP(c_Nat_OSuc,sK123(U_6484,U_6482))
| ~ sP349(U_6482,U_6484) ),
inference(clausify,[status(thm)],[f_1499_5]) ).
cnf(f_1499_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK123(U_6484,U_6482)),U_6484))
| ~ sP349(U_6482,U_6484) ),
inference(clausify,[status(thm)],[f_1499_5]) ).
cnf(f_1499_10,plain,
( U_6483 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP350(U_6479,U_6485,U_6483) ),
inference(clausify,[status(thm)],[f_1499_5]) ).
cnf(f_1499_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6479),U_6485))
| U_6483 != hAPP(c_Nat_OSuc,U_6479)
| ~ sP350(U_6479,U_6485,U_6483) ),
inference(clausify,[status(thm)],[f_1499_5]) ).
fof(f_1500_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_1500_2,plain,
! [U_6487,U_6486] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6486),U_6487)
| ( ( U_6487 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6486 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_6487 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6486 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_6487 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_6486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_6487 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6486 = 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_6486),U_6487) ) ),
inference(variable_rename,[status(thm)],[f_1500_1]) ).
fof(f_1500_3,plain,
( ! [U_6491,U_6489] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6489),U_6491)
| ( ( U_6491 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6489 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_6491 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6489 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_6490,U_6488] :
( ( U_6490 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_6488 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_6490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6488 = 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_6488),U_6490) ) ),
inference(miniscope,[status(thm)],[f_1500_2]) ).
fof(f_1500_4,plain,
( ! [U_6491,U_6489] :
( U_6491 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6489 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP353(U_6491,U_6489) )
& ! [U_6491,U_6489] :
( U_6491 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6489 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP353(U_6491,U_6489) )
& ! [U_6488,U_6490] :
( U_6490 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP352(U_6488,U_6490) )
& ! [U_6488,U_6490] :
( U_6488 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP352(U_6488,U_6490) )
& ! [U_6488,U_6490] :
( U_6490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP351(U_6488,U_6490) )
& ! [U_6488,U_6490] :
( U_6488 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP351(U_6488,U_6490) )
& ! [U_6491,U_6489] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6489),U_6491)
| sP353(U_6491,U_6489) )
& ! [U_6488,U_6490] :
( sP352(U_6488,U_6490)
| sP351(U_6488,U_6490)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6488),U_6490) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP351,sP352,sP353])],[f_1500_3]) ).
cnf(f_1500_5,plain,
( sP352(U_6488,U_6490)
| sP351(U_6488,U_6490)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6488),U_6490) ),
inference(clausify,[status(thm)],[f_1500_4]) ).
cnf(f_1500_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_6489),U_6491)
| sP353(U_6491,U_6489) ),
inference(clausify,[status(thm)],[f_1500_4]) ).
cnf(f_1500_7,plain,
( U_6488 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP351(U_6488,U_6490) ),
inference(clausify,[status(thm)],[f_1500_4]) ).
cnf(f_1500_8,plain,
( U_6490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP351(U_6488,U_6490) ),
inference(clausify,[status(thm)],[f_1500_4]) ).
cnf(f_1500_9,plain,
( U_6488 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP352(U_6488,U_6490) ),
inference(clausify,[status(thm)],[f_1500_4]) ).
cnf(f_1500_10,plain,
( U_6490 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP352(U_6488,U_6490) ),
inference(clausify,[status(thm)],[f_1500_4]) ).
cnf(f_1500_11,plain,
( U_6491 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6489 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP353(U_6491,U_6489) ),
inference(clausify,[status(thm)],[f_1500_4]) ).
cnf(f_1500_12,plain,
( U_6491 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6489 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP353(U_6491,U_6489) ),
inference(clausify,[status(thm)],[f_1500_4]) ).
fof(f_1501_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_1501_2,plain,
! [U_6493,U_6492] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6492),U_6493) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_6493 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6492 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_6493 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6492 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_6493 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_6492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_6493 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6492 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6492),U_6493) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_1501_1]) ).
fof(f_1501_3,plain,
( ! [U_6497,U_6495] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6495),U_6497) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_6497 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6495 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_6497 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6495 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_6496,U_6494] :
( ( U_6496 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_6494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_6496 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6494 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6494),U_6496) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_1501_2]) ).
fof(f_1501_4,plain,
( ! [U_6497,U_6495] :
( U_6497 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6495 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP356(U_6497,U_6495) )
& ! [U_6497,U_6495] :
( U_6497 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6495 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP356(U_6497,U_6495) )
& ! [U_6496,U_6494] :
( U_6496 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP355(U_6496,U_6494) )
& ! [U_6496,U_6494] :
( U_6494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP355(U_6496,U_6494) )
& ! [U_6496,U_6494] :
( U_6496 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP354(U_6496,U_6494) )
& ! [U_6496,U_6494] :
( U_6494 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP354(U_6496,U_6494) )
& ! [U_6497,U_6495] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6495),U_6497) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP356(U_6497,U_6495) )
& ! [U_6496,U_6494] :
( sP355(U_6496,U_6494)
| sP354(U_6496,U_6494)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6494),U_6496) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP354,sP355,sP356])],[f_1501_3]) ).
cnf(f_1501_5,plain,
( sP355(U_6496,U_6494)
| sP354(U_6496,U_6494)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6494),U_6496) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1501_4]) ).
cnf(f_1501_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6495),U_6497) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP356(U_6497,U_6495) ),
inference(clausify,[status(thm)],[f_1501_4]) ).
cnf(f_1501_7,plain,
( U_6494 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP354(U_6496,U_6494) ),
inference(clausify,[status(thm)],[f_1501_4]) ).
cnf(f_1501_8,plain,
( U_6496 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP354(U_6496,U_6494) ),
inference(clausify,[status(thm)],[f_1501_4]) ).
cnf(f_1501_9,plain,
( U_6494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP355(U_6496,U_6494) ),
inference(clausify,[status(thm)],[f_1501_4]) ).
cnf(f_1501_10,plain,
( U_6496 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP355(U_6496,U_6494) ),
inference(clausify,[status(thm)],[f_1501_4]) ).
cnf(f_1501_11,plain,
( U_6497 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6495 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP356(U_6497,U_6495) ),
inference(clausify,[status(thm)],[f_1501_4]) ).
cnf(f_1501_12,plain,
( U_6497 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6495 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP356(U_6497,U_6495) ),
inference(clausify,[status(thm)],[f_1501_4]) ).
fof(f_1502_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_1502_2,plain,
! [U_6499,U_6498] :
( ( 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_6498),U_6499)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6499))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6498)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6499))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6498))
| ~ 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_6498),U_6499))) ) ),
inference(variable_rename,[status(thm)],[f_1502_1]) ).
fof(f_1502_3,plain,
( ! [U_6503,U_6501] :
( 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_6501),U_6503)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6503))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6501)) ) )
& ! [U_6502,U_6500] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6502))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6500))
| ~ 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_6500),U_6502))) ) ),
inference(miniscope,[status(thm)],[f_1502_2]) ).
fof(f_1502_4,plain,
( ! [U_6501,U_6503] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6503))
| ~ sP357(U_6501,U_6503) )
& ! [U_6501,U_6503] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6501))
| ~ sP357(U_6501,U_6503) )
& ! [U_6501,U_6503] :
( 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_6501),U_6503)))
| sP357(U_6501,U_6503) )
& ! [U_6500,U_6502] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6502))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6500))
| ~ 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_6500),U_6502))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP357])],[f_1502_3]) ).
cnf(f_1502_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6502))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6500))
| ~ 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_6500),U_6502))) ),
inference(clausify,[status(thm)],[f_1502_4]) ).
cnf(f_1502_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_6501),U_6503)))
| sP357(U_6501,U_6503) ),
inference(clausify,[status(thm)],[f_1502_4]) ).
cnf(f_1502_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6501))
| ~ sP357(U_6501,U_6503) ),
inference(clausify,[status(thm)],[f_1502_4]) ).
cnf(f_1502_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6503))
| ~ sP357(U_6501,U_6503) ),
inference(clausify,[status(thm)],[f_1502_4]) ).
fof(f_1503_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_1503_2,plain,
! [U_6505,U_6504] :
( 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_6504),U_6505)))
| ~ 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_6504)) ),
inference(variable_rename,[status(thm)],[f_1503_1]) ).
fof(f_1503_3,plain,
! [U_6504,U_6505] :
( 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_6504),U_6505)))
| ~ 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_6504)) ),
inference(definitional_conversion,[status(esa)],[f_1503_2]) ).
cnf(f_1503_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_6504),U_6505)))
| ~ 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_6504)) ),
inference(clausify,[status(thm)],[f_1503_3]) ).
fof(f_1504_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_1504_2,plain,
! [U_6507,U_6506] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6506),U_6507),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6506)
| ~ class_Power_Opower(U_6506) ),
inference(variable_rename,[status(thm)],[f_1504_1]) ).
fof(f_1504_3,plain,
! [U_6506,U_6507] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6506),U_6507),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6506)
| ~ class_Power_Opower(U_6506) ),
inference(definitional_conversion,[status(esa)],[f_1504_2]) ).
cnf(f_1504_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6506),U_6507),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6506)
| ~ class_Power_Opower(U_6506) ),
inference(clausify,[status(thm)],[f_1504_3]) ).
fof(f_1505_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_1505_2,plain,
! [U_6509,U_6508] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6508),U_6509),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6508)
| ~ class_Rings_Ocomm__semiring__1(U_6508) ),
inference(variable_rename,[status(thm)],[f_1505_1]) ).
fof(f_1505_3,plain,
! [U_6508,U_6509] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6508),U_6509),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6508)
| ~ class_Rings_Ocomm__semiring__1(U_6508) ),
inference(definitional_conversion,[status(esa)],[f_1505_2]) ).
cnf(f_1505_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6508),U_6509),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6508)
| ~ class_Rings_Ocomm__semiring__1(U_6508) ),
inference(clausify,[status(thm)],[f_1505_3]) ).
fof(f_1506_1,plain,
! [T_c] : hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_card_Oempty]) ).
fof(f_1506_2,plain,
! [U_6510] : hAPP(c_Finite__Set_Ocard(U_6510),c_Orderings_Obot__class_Obot(tc_fun(U_6510,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1506_1]) ).
fof(f_1506_3,plain,
! [U_6510] : hAPP(c_Finite__Set_Ocard(U_6510),c_Orderings_Obot__class_Obot(tc_fun(U_6510,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1506_2]) ).
cnf(f_1506_4,plain,
hAPP(c_Finite__Set_Ocard(U_6510),c_Orderings_Obot__class_Obot(tc_fun(U_6510,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1506_3]) ).
fof(f_1507_1,plain,
! [V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__infinite]) ).
fof(f_1507_2,plain,
! [U_6512,U_6511] :
( hAPP(c_Finite__Set_Ocard(U_6511),U_6512) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6511),U_6512)) ),
inference(variable_rename,[status(thm)],[f_1507_1]) ).
fof(f_1507_3,plain,
! [U_6511,U_6512] :
( hAPP(c_Finite__Set_Ocard(U_6511),U_6512) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6511),U_6512)) ),
inference(definitional_conversion,[status(esa)],[f_1507_2]) ).
cnf(f_1507_4,plain,
( hAPP(c_Finite__Set_Ocard(U_6511),U_6512) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6511),U_6512)) ),
inference(clausify,[status(thm)],[f_1507_3]) ).
fof(f_1508_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_1508_2,plain,
! [U_6514,U_6513] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6513),U_6514) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6514 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6513 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ( U_6514 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_6513 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6513),U_6514) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_1508_1]) ).
fof(f_1508_3,plain,
( ! [U_6518,U_6516] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6516),U_6518) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6518 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6516 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_6517,U_6515] :
( ( U_6517 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_6515 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6515),U_6517) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_1508_2]) ).
fof(f_1508_4,plain,
( ! [U_6517,U_6515] :
( U_6517 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP358(U_6517,U_6515) )
& ! [U_6517,U_6515] :
( U_6515 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP358(U_6517,U_6515) )
& ! [U_6518,U_6516] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6516),U_6518) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6518 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6516 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_6517,U_6515] :
( sP358(U_6517,U_6515)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6515),U_6517) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP358])],[f_1508_3]) ).
cnf(f_1508_5,plain,
( sP358(U_6517,U_6515)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6515),U_6517) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1508_4]) ).
cnf(f_1508_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6516),U_6518) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6518 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_6516 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1508_4]) ).
cnf(f_1508_7,plain,
( U_6515 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP358(U_6517,U_6515) ),
inference(clausify,[status(thm)],[f_1508_4]) ).
cnf(f_1508_8,plain,
( U_6517 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP358(U_6517,U_6515) ),
inference(clausify,[status(thm)],[f_1508_4]) ).
fof(f_1509_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_1509_2,plain,
! [U_6520,U_6519] :
( ( 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_6519),U_6520)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6520),U_6519)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6520),U_6519))
| ~ 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_6519),U_6520))) ) ),
inference(variable_rename,[status(thm)],[f_1509_1]) ).
fof(f_1509_3,plain,
( ! [U_6524,U_6522] :
( 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_6522),U_6524)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6524),U_6522)) )
& ! [U_6523,U_6521] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6523),U_6521))
| ~ 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_6521),U_6523))) ) ),
inference(miniscope,[status(thm)],[f_1509_2]) ).
fof(f_1509_4,plain,
( ! [U_6522,U_6524] :
( 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_6522),U_6524)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6524),U_6522)) )
& ! [U_6523,U_6521] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6523),U_6521))
| ~ 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_6521),U_6523))) ) ),
inference(definitional_conversion,[status(esa)],[f_1509_3]) ).
cnf(f_1509_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6523),U_6521))
| ~ 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_6521),U_6523))) ),
inference(clausify,[status(thm)],[f_1509_4]) ).
cnf(f_1509_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_6522),U_6524)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6524),U_6522)) ),
inference(clausify,[status(thm)],[f_1509_4]) ).
fof(f_1510_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_1510_2,plain,
! [U_6526,U_6525] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6526),U_6525)),U_6526))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6526))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6525)) ),
inference(variable_rename,[status(thm)],[f_1510_1]) ).
fof(f_1510_3,plain,
! [U_6525,U_6526] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6526),U_6525)),U_6526))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6526))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6525)) ),
inference(definitional_conversion,[status(esa)],[f_1510_2]) ).
cnf(f_1510_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6526),U_6525)),U_6526))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6526))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6525)) ),
inference(clausify,[status(thm)],[f_1510_3]) ).
fof(f_1511_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_1511_2,plain,
! [U_6528,U_6527] :
( ( 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_6527),U_6528)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6528))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6527)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6528))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6527)) )
| ~ 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_6527),U_6528))) ) ),
inference(variable_rename,[status(thm)],[f_1511_1]) ).
fof(f_1511_3,plain,
( ! [U_6532,U_6530] :
( 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_6530),U_6532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6530)) )
& ! [U_6531,U_6529] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6531))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6529)) )
| ~ 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_6529),U_6531))) ) ),
inference(miniscope,[status(thm)],[f_1511_2]) ).
fof(f_1511_4,plain,
( ! [U_6531,U_6529] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6531))
| ~ sP359(U_6531,U_6529) )
& ! [U_6531,U_6529] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6529))
| ~ sP359(U_6531,U_6529) )
& ! [U_6532,U_6530] :
( 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_6530),U_6532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6530)) )
& ! [U_6531,U_6529] :
( sP359(U_6531,U_6529)
| ~ 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_6529),U_6531))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP359])],[f_1511_3]) ).
cnf(f_1511_5,plain,
( sP359(U_6531,U_6529)
| ~ 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_6529),U_6531))) ),
inference(clausify,[status(thm)],[f_1511_4]) ).
cnf(f_1511_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_6530),U_6532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6530)) ),
inference(clausify,[status(thm)],[f_1511_4]) ).
cnf(f_1511_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6529))
| ~ sP359(U_6531,U_6529) ),
inference(clausify,[status(thm)],[f_1511_4]) ).
cnf(f_1511_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6531))
| ~ sP359(U_6531,U_6529) ),
inference(clausify,[status(thm)],[f_1511_4]) ).
fof(f_1512_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_1512_2,plain,
! [U_6535,U_6534,U_6533] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6533),U_6534)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6533),U_6535)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6534),U_6535))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6533)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6534),U_6535))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6533)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6533),U_6534)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6533),U_6535))) ) ),
inference(variable_rename,[status(thm)],[f_1512_1]) ).
fof(f_1512_3,plain,
( ! [U_6541,U_6539,U_6537] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6537),U_6539)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6537),U_6541)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6539),U_6541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6537)) )
& ! [U_6540,U_6538,U_6536] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6538),U_6540))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6536)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6536),U_6538)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6536),U_6540))) ) ),
inference(miniscope,[status(thm)],[f_1512_2]) ).
fof(f_1512_4,plain,
( ! [U_6536,U_6538,U_6540] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6538),U_6540))
| ~ sP360(U_6536,U_6538,U_6540) )
& ! [U_6536,U_6538,U_6540] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6536))
| ~ sP360(U_6536,U_6538,U_6540) )
& ! [U_6541,U_6539,U_6537] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6537),U_6539)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6537),U_6541)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6539),U_6541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6537)) )
& ! [U_6536,U_6538,U_6540] :
( sP360(U_6536,U_6538,U_6540)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6536),U_6538)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6536),U_6540))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP360])],[f_1512_3]) ).
cnf(f_1512_5,plain,
( sP360(U_6536,U_6538,U_6540)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6536),U_6538)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6536),U_6540))) ),
inference(clausify,[status(thm)],[f_1512_4]) ).
cnf(f_1512_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6537),U_6539)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6537),U_6541)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6539),U_6541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6537)) ),
inference(clausify,[status(thm)],[f_1512_4]) ).
cnf(f_1512_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6536))
| ~ sP360(U_6536,U_6538,U_6540) ),
inference(clausify,[status(thm)],[f_1512_4]) ).
cnf(f_1512_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6538),U_6540))
| ~ sP360(U_6536,U_6538,U_6540) ),
inference(clausify,[status(thm)],[f_1512_4]) ).
fof(f_1513_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_1513_2,plain,
! [U_6544,U_6543,U_6542] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6542),U_6543)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6544),U_6543)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6542),U_6544))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6543)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6542),U_6544))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6543)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6542),U_6543)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6544),U_6543))) ) ),
inference(variable_rename,[status(thm)],[f_1513_1]) ).
fof(f_1513_3,plain,
( ! [U_6550,U_6548,U_6546] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6546),U_6548)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6550),U_6548)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6546),U_6550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6548)) )
& ! [U_6549,U_6547,U_6545] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6545),U_6549))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6547)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6545),U_6547)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6549),U_6547))) ) ),
inference(miniscope,[status(thm)],[f_1513_2]) ).
fof(f_1513_4,plain,
( ! [U_6545,U_6547,U_6549] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6545),U_6549))
| ~ sP361(U_6545,U_6547,U_6549) )
& ! [U_6545,U_6547,U_6549] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6547))
| ~ sP361(U_6545,U_6547,U_6549) )
& ! [U_6548,U_6546,U_6550] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6546),U_6548)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6550),U_6548)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6546),U_6550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6548)) )
& ! [U_6545,U_6547,U_6549] :
( sP361(U_6545,U_6547,U_6549)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6545),U_6547)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6549),U_6547))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP361])],[f_1513_3]) ).
cnf(f_1513_5,plain,
( sP361(U_6545,U_6547,U_6549)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6545),U_6547)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6549),U_6547))) ),
inference(clausify,[status(thm)],[f_1513_4]) ).
cnf(f_1513_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6546),U_6548)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6550),U_6548)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6546),U_6550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6548)) ),
inference(clausify,[status(thm)],[f_1513_4]) ).
cnf(f_1513_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6547))
| ~ sP361(U_6545,U_6547,U_6549) ),
inference(clausify,[status(thm)],[f_1513_4]) ).
cnf(f_1513_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6545),U_6549))
| ~ sP361(U_6545,U_6547,U_6549) ),
inference(clausify,[status(thm)],[f_1513_4]) ).
fof(f_1514_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_1514_2,plain,
! [U_6553,U_6552,U_6551] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6551),U_6553)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6552),U_6553)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6553))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6551),U_6552)) ),
inference(variable_rename,[status(thm)],[f_1514_1]) ).
fof(f_1514_3,plain,
! [U_6552,U_6553,U_6551] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6551),U_6553)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6552),U_6553)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6553))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6551),U_6552)) ),
inference(definitional_conversion,[status(esa)],[f_1514_2]) ).
cnf(f_1514_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6551),U_6553)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6552),U_6553)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6553))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6551),U_6552)) ),
inference(clausify,[status(thm)],[f_1514_3]) ).
fof(f_1515_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_1515_2,plain,
! [U_6556,U_6555,U_6554] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6556),U_6554)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6556),U_6555)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6554),U_6555)) ),
inference(variable_rename,[status(thm)],[f_1515_1]) ).
fof(f_1515_3,plain,
! [U_6555,U_6554,U_6556] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6556),U_6554)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6556),U_6555)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6554),U_6555)) ),
inference(definitional_conversion,[status(esa)],[f_1515_2]) ).
cnf(f_1515_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6556),U_6554)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6556),U_6555)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6554),U_6555)) ),
inference(clausify,[status(thm)],[f_1515_3]) ).
fof(f_1516_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_1516_2,plain,
! [U_6559,U_6558,U_6557] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6557),U_6558)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6557),U_6559)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6558),U_6559)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6558),U_6559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6557),U_6558)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6557),U_6559))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6557)) ),
inference(variable_rename,[status(thm)],[f_1516_1]) ).
fof(f_1516_3,plain,
( ! [U_6558,U_6557,U_6559] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6557),U_6558)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6557),U_6559)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6558),U_6559))
| ~ sP362(U_6558,U_6557,U_6559) )
& ! [U_6558,U_6557,U_6559] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6558),U_6559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6557),U_6558)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6557),U_6559)))
| ~ sP362(U_6558,U_6557,U_6559) )
& ! [U_6558,U_6557,U_6559] :
( sP362(U_6558,U_6557,U_6559)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6557)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP362])],[f_1516_2]) ).
cnf(f_1516_4,plain,
( sP362(U_6558,U_6557,U_6559)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6557)) ),
inference(clausify,[status(thm)],[f_1516_3]) ).
cnf(f_1516_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6558),U_6559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6557),U_6558)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6557),U_6559)))
| ~ sP362(U_6558,U_6557,U_6559) ),
inference(clausify,[status(thm)],[f_1516_3]) ).
cnf(f_1516_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6557),U_6558)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6557),U_6559)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6558),U_6559))
| ~ sP362(U_6558,U_6557,U_6559) ),
inference(clausify,[status(thm)],[f_1516_3]) ).
fof(f_1517_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_1517_2,plain,
! [U_6562,U_6561,U_6560] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6560),U_6561) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6560),U_6562)
| U_6561 != U_6562 )
& ( U_6561 = U_6562
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6560),U_6561) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6560),U_6562) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6560)) ),
inference(variable_rename,[status(thm)],[f_1517_1]) ).
fof(f_1517_3,plain,
( ! [U_6560,U_6561,U_6562] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6560),U_6561) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6560),U_6562)
| U_6561 != U_6562
| ~ sP363(U_6560,U_6561,U_6562) )
& ! [U_6560,U_6561,U_6562] :
( U_6561 = U_6562
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6560),U_6561) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6560),U_6562)
| ~ sP363(U_6560,U_6561,U_6562) )
& ! [U_6560,U_6561,U_6562] :
( sP363(U_6560,U_6561,U_6562)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6560)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP363])],[f_1517_2]) ).
cnf(f_1517_4,plain,
( sP363(U_6560,U_6561,U_6562)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6560)) ),
inference(clausify,[status(thm)],[f_1517_3]) ).
cnf(f_1517_5,plain,
( U_6561 = U_6562
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6560),U_6561) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6560),U_6562)
| ~ sP363(U_6560,U_6561,U_6562) ),
inference(clausify,[status(thm)],[f_1517_3]) ).
cnf(f_1517_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6560),U_6561) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6560),U_6562)
| U_6561 != U_6562
| ~ sP363(U_6560,U_6561,U_6562) ),
inference(clausify,[status(thm)],[f_1517_3]) ).
fof(f_1518_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_1518_2,plain,
! [U_6564,U_6563] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6563),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6563),U_6564)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1518_1]) ).
fof(f_1518_3,plain,
! [U_6564,U_6563] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6563),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6563),U_6564)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1518_2]) ).
cnf(f_1518_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6563),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6563),U_6564)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1518_3]) ).
fof(f_1519_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_1519_2,plain,
! [U_6566,U_6565] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6566),U_6565) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6566),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6566),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6565),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_6565 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6566),U_6565) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_6565 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1519_1]) ).
fof(f_1519_3,plain,
( ! [U_6570,U_6568] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6570),U_6568) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6570),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6570),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6568),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_6568 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6569,U_6567] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6569),U_6567) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_6567 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1519_2]) ).
fof(f_1519_4,plain,
( ! [U_6568,U_6570] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6570),U_6568) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6570),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6570),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6568),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_6568 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6569,U_6567] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6569),U_6567) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_6567 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1519_3]) ).
cnf(f_1519_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6569),U_6567) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_6567 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1519_4]) ).
cnf(f_1519_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6570),U_6568) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6570),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6570),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6568),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_6568 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1519_4]) ).
fof(f_1520_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_1520_2,plain,
! [U_6572,U_6571] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6571),U_6572) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6571),U_6572)) ),
inference(variable_rename,[status(thm)],[f_1520_1]) ).
fof(f_1520_3,plain,
! [U_6571,U_6572] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6571),U_6572) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6571),U_6572)) ),
inference(definitional_conversion,[status(esa)],[f_1520_2]) ).
cnf(f_1520_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6571),U_6572) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6571),U_6572)) ),
inference(clausify,[status(thm)],[f_1520_3]) ).
fof(f_1521_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_1521_2,plain,
! [U_6574,U_6573] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6573),U_6574) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6573),U_6574)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6573),U_6574))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6573),U_6574) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1521_1]) ).
fof(f_1521_3,plain,
( ! [U_6578,U_6576] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6576),U_6578) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6576),U_6578)) )
& ! [U_6577,U_6575] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6575),U_6577))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6575),U_6577) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1521_2]) ).
fof(f_1521_4,plain,
( ! [U_6576,U_6578] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6576),U_6578) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6576),U_6578)) )
& ! [U_6577,U_6575] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6575),U_6577))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6575),U_6577) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1521_3]) ).
cnf(f_1521_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6575),U_6577))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6575),U_6577) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1521_4]) ).
cnf(f_1521_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6576),U_6578) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6576),U_6578)) ),
inference(clausify,[status(thm)],[f_1521_4]) ).
fof(f_1522_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_1522_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_1522_1]) ).
cnf(f_1522_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_1522_2]) ).
fof(f_1523_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_1523_2,plain,
! [U_6580,U_6579] :
( U_6579 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6580 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_6579 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6579),U_6580) ),
inference(variable_rename,[status(thm)],[f_1523_1]) ).
fof(f_1523_3,plain,
! [U_6579,U_6580] :
( U_6579 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6580 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_6579 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6579),U_6580) ),
inference(definitional_conversion,[status(esa)],[f_1523_2]) ).
cnf(f_1523_4,plain,
( U_6579 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6580 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_6579 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6579),U_6580) ),
inference(clausify,[status(thm)],[f_1523_3]) ).
fof(f_1524_1,plain,
! [V_f_2,V_F_2,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_c),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_c),B_x),V_F_2)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_F_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__eq__0__iff]) ).
fof(f_1524_2,plain,
! [U_6585,U_6584,U_6583] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6583,tc_Nat_Onat),U_6585),U_6584) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [U_6582] :
( hAPP(U_6585,U_6582) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_6583),U_6582),U_6584)) ) )
& ( ! [U_6581] :
( hAPP(U_6585,U_6581) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_6583),U_6581),U_6584)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6583,tc_Nat_Onat),U_6585),U_6584) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6583),U_6584)) ),
inference(variable_rename,[status(thm)],[f_1524_1]) ).
fof(f_1524_3,plain,
! [U_6585,U_6584,U_6583] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6583,tc_Nat_Onat),U_6585),U_6584) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hAPP(U_6585,sK124(U_6585,U_6584,U_6583)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_6583),sK124(U_6585,U_6584,U_6583)),U_6584)) ) )
& ( ! [U_6581] :
( hAPP(U_6585,U_6581) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_6583),U_6581),U_6584)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6583,tc_Nat_Onat),U_6585),U_6584) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6583),U_6584)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_6582,sK124(U_6585,U_6584,U_6583))],[f_1524_2]) ).
fof(f_1524_4,plain,
( ! [U_6583,U_6584,U_6585] :
( hAPP(U_6585,sK124(U_6585,U_6584,U_6583)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP364(U_6583,U_6584,U_6585) )
& ! [U_6583,U_6584,U_6585] :
( hBOOL(hAPP(hAPP(c_member(U_6583),sK124(U_6585,U_6584,U_6583)),U_6584))
| ~ sP364(U_6583,U_6584,U_6585) )
& ! [U_6581,U_6583,U_6584,U_6585] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6583,tc_Nat_Onat),U_6585),U_6584) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP364(U_6583,U_6584,U_6585)
| ~ sP365(U_6581,U_6583,U_6584,U_6585) )
& ! [U_6581,U_6583,U_6584,U_6585] :
( hAPP(U_6585,U_6581) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_6583),U_6581),U_6584))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6583,tc_Nat_Onat),U_6585),U_6584) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP365(U_6581,U_6583,U_6584,U_6585) )
& ! [U_6581,U_6583,U_6584,U_6585] :
( sP365(U_6581,U_6583,U_6584,U_6585)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6583),U_6584)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP364,sP365])],[f_1524_3]) ).
cnf(f_1524_5,plain,
( sP365(U_6581,U_6583,U_6584,U_6585)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6583),U_6584)) ),
inference(clausify,[status(thm)],[f_1524_4]) ).
cnf(f_1524_6,plain,
( hAPP(U_6585,U_6581) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_6583),U_6581),U_6584))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6583,tc_Nat_Onat),U_6585),U_6584) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP365(U_6581,U_6583,U_6584,U_6585) ),
inference(clausify,[status(thm)],[f_1524_4]) ).
cnf(f_1524_7,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6583,tc_Nat_Onat),U_6585),U_6584) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP364(U_6583,U_6584,U_6585)
| ~ sP365(U_6581,U_6583,U_6584,U_6585) ),
inference(clausify,[status(thm)],[f_1524_4]) ).
cnf(f_1524_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_6583),sK124(U_6585,U_6584,U_6583)),U_6584))
| ~ sP364(U_6583,U_6584,U_6585) ),
inference(clausify,[status(thm)],[f_1524_4]) ).
cnf(f_1524_9,plain,
( hAPP(U_6585,sK124(U_6585,U_6584,U_6583)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP364(U_6583,U_6584,U_6585) ),
inference(clausify,[status(thm)],[f_1524_4]) ).
fof(f_1525_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_1525_2,plain,
! [U_6586] :
( U_6586 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6586),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_6586)) ),
inference(variable_rename,[status(thm)],[f_1525_1]) ).
fof(f_1525_3,plain,
! [U_6586] :
( U_6586 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6586),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_6586)) ),
inference(definitional_conversion,[status(esa)],[f_1525_2]) ).
cnf(f_1525_4,plain,
( U_6586 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6586),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_6586)) ),
inference(clausify,[status(thm)],[f_1525_3]) ).
fof(f_1526_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_1526_2,plain,
! [U_6588,U_6587] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6587),U_6588) = 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_6587),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6588))
| U_6587 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6587),U_6588) = U_6588
| U_6587 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1526_1]) ).
fof(f_1526_3,plain,
( ! [U_6592,U_6590] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6590),U_6592) = 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_6590),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6592))
| U_6590 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6591,U_6589] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6589),U_6591) = U_6591
| U_6589 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1526_2]) ).
fof(f_1526_4,plain,
( ! [U_6590,U_6592] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6590),U_6592) = 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_6590),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6592))
| U_6590 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6591,U_6589] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6589),U_6591) = U_6591
| U_6589 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1526_3]) ).
cnf(f_1526_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6589),U_6591) = U_6591
| U_6589 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1526_4]) ).
cnf(f_1526_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6590),U_6592) = 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_6590),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6592))
| U_6590 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1526_4]) ).
fof(f_1527_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_1527_2,plain,
! [U_6595,U_6594,U_6593] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6593),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6593),U_6594),U_6595)),c_Groups_Ozero__class_Ozero(U_6593)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6593),U_6595),c_Groups_Ozero__class_Ozero(U_6593)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6593),U_6594),c_Groups_Ozero__class_Ozero(U_6593)))
| ~ class_Groups_Oordered__comm__monoid__add(U_6593) ),
inference(variable_rename,[status(thm)],[f_1527_1]) ).
fof(f_1527_3,plain,
! [U_6593,U_6594,U_6595] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6593),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6593),U_6594),U_6595)),c_Groups_Ozero__class_Ozero(U_6593)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6593),U_6595),c_Groups_Ozero__class_Ozero(U_6593)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6593),U_6594),c_Groups_Ozero__class_Ozero(U_6593)))
| ~ class_Groups_Oordered__comm__monoid__add(U_6593) ),
inference(definitional_conversion,[status(esa)],[f_1527_2]) ).
cnf(f_1527_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6593),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6593),U_6594),U_6595)),c_Groups_Ozero__class_Ozero(U_6593)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6593),U_6595),c_Groups_Ozero__class_Ozero(U_6593)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6593),U_6594),c_Groups_Ozero__class_Ozero(U_6593)))
| ~ class_Groups_Oordered__comm__monoid__add(U_6593) ),
inference(clausify,[status(thm)],[f_1527_3]) ).
fof(f_1528_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_1528_2,plain,
! [U_6598,U_6597,U_6596] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6596),U_6597),U_6598)),c_Groups_Ozero__class_Ozero(U_6596)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6596),U_6598),c_Groups_Ozero__class_Ozero(U_6596)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6596),U_6597),c_Groups_Ozero__class_Ozero(U_6596)))
| ~ class_Groups_Oordered__comm__monoid__add(U_6596) ),
inference(variable_rename,[status(thm)],[f_1528_1]) ).
fof(f_1528_3,plain,
! [U_6596,U_6597,U_6598] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6596),U_6597),U_6598)),c_Groups_Ozero__class_Ozero(U_6596)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6596),U_6598),c_Groups_Ozero__class_Ozero(U_6596)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6596),U_6597),c_Groups_Ozero__class_Ozero(U_6596)))
| ~ class_Groups_Oordered__comm__monoid__add(U_6596) ),
inference(definitional_conversion,[status(esa)],[f_1528_2]) ).
cnf(f_1528_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6596),U_6597),U_6598)),c_Groups_Ozero__class_Ozero(U_6596)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6596),U_6598),c_Groups_Ozero__class_Ozero(U_6596)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6596),U_6597),c_Groups_Ozero__class_Ozero(U_6596)))
| ~ class_Groups_Oordered__comm__monoid__add(U_6596) ),
inference(clausify,[status(thm)],[f_1528_3]) ).
fof(f_1529_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_1529_2,plain,
! [U_6602,U_6601,U_6600,U_6599] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6599),U_6601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6599),U_6600),U_6602)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6599),U_6601),U_6602))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6599),c_Groups_Ozero__class_Ozero(U_6599)),U_6600))
| ~ class_Groups_Oordered__comm__monoid__add(U_6599) ),
inference(variable_rename,[status(thm)],[f_1529_1]) ).
fof(f_1529_3,plain,
! [U_6599,U_6600,U_6601,U_6602] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6599),U_6601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6599),U_6600),U_6602)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6599),U_6601),U_6602))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6599),c_Groups_Ozero__class_Ozero(U_6599)),U_6600))
| ~ class_Groups_Oordered__comm__monoid__add(U_6599) ),
inference(definitional_conversion,[status(esa)],[f_1529_2]) ).
cnf(f_1529_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6599),U_6601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6599),U_6600),U_6602)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6599),U_6601),U_6602))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6599),c_Groups_Ozero__class_Ozero(U_6599)),U_6600))
| ~ class_Groups_Oordered__comm__monoid__add(U_6599) ),
inference(clausify,[status(thm)],[f_1529_3]) ).
fof(f_1530_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_1530_2,plain,
! [U_6606,U_6605,U_6604,U_6603] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6603),U_6605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6603),U_6604),U_6606)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6603),U_6605),U_6606))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6603),c_Groups_Ozero__class_Ozero(U_6603)),U_6604))
| ~ class_Groups_Oordered__comm__monoid__add(U_6603) ),
inference(variable_rename,[status(thm)],[f_1530_1]) ).
fof(f_1530_3,plain,
! [U_6603,U_6604,U_6605,U_6606] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6603),U_6605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6603),U_6604),U_6606)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6603),U_6605),U_6606))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6603),c_Groups_Ozero__class_Ozero(U_6603)),U_6604))
| ~ class_Groups_Oordered__comm__monoid__add(U_6603) ),
inference(definitional_conversion,[status(esa)],[f_1530_2]) ).
cnf(f_1530_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6603),U_6605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6603),U_6604),U_6606)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6603),U_6605),U_6606))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6603),c_Groups_Ozero__class_Ozero(U_6603)),U_6604))
| ~ class_Groups_Oordered__comm__monoid__add(U_6603) ),
inference(clausify,[status(thm)],[f_1530_3]) ).
fof(f_1531_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_1531_2,plain,
! [U_6609,U_6608,U_6607] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6607),c_Groups_Ozero__class_Ozero(U_6607)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6607),U_6608),U_6609)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6607),c_Groups_Ozero__class_Ozero(U_6607)),U_6609))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6607),c_Groups_Ozero__class_Ozero(U_6607)),U_6608))
| ~ class_Groups_Oordered__comm__monoid__add(U_6607) ),
inference(variable_rename,[status(thm)],[f_1531_1]) ).
fof(f_1531_3,plain,
! [U_6608,U_6607,U_6609] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6607),c_Groups_Ozero__class_Ozero(U_6607)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6607),U_6608),U_6609)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6607),c_Groups_Ozero__class_Ozero(U_6607)),U_6609))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6607),c_Groups_Ozero__class_Ozero(U_6607)),U_6608))
| ~ class_Groups_Oordered__comm__monoid__add(U_6607) ),
inference(definitional_conversion,[status(esa)],[f_1531_2]) ).
cnf(f_1531_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6607),c_Groups_Ozero__class_Ozero(U_6607)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6607),U_6608),U_6609)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6607),c_Groups_Ozero__class_Ozero(U_6607)),U_6609))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6607),c_Groups_Ozero__class_Ozero(U_6607)),U_6608))
| ~ class_Groups_Oordered__comm__monoid__add(U_6607) ),
inference(clausify,[status(thm)],[f_1531_3]) ).
fof(f_1532_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_1532_2,plain,
! [U_6612,U_6611,U_6610] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6610),c_Groups_Ozero__class_Ozero(U_6610)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6610),U_6611),U_6612)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6610),c_Groups_Ozero__class_Ozero(U_6610)),U_6612))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6610),c_Groups_Ozero__class_Ozero(U_6610)),U_6611))
| ~ class_Groups_Oordered__comm__monoid__add(U_6610) ),
inference(variable_rename,[status(thm)],[f_1532_1]) ).
fof(f_1532_3,plain,
! [U_6610,U_6611,U_6612] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6610),c_Groups_Ozero__class_Ozero(U_6610)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6610),U_6611),U_6612)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6610),c_Groups_Ozero__class_Ozero(U_6610)),U_6612))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6610),c_Groups_Ozero__class_Ozero(U_6610)),U_6611))
| ~ class_Groups_Oordered__comm__monoid__add(U_6610) ),
inference(definitional_conversion,[status(esa)],[f_1532_2]) ).
cnf(f_1532_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6610),c_Groups_Ozero__class_Ozero(U_6610)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6610),U_6611),U_6612)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6610),c_Groups_Ozero__class_Ozero(U_6610)),U_6612))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6610),c_Groups_Ozero__class_Ozero(U_6610)),U_6611))
| ~ class_Groups_Oordered__comm__monoid__add(U_6610) ),
inference(clausify,[status(thm)],[f_1532_3]) ).
fof(f_1533_1,plain,
! [V_b_2,V_a_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
| ~ class_Rings_Olinordered__ring__strict(T_c) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).
fof(f_1533_2,plain,
! [U_6616,U_6615,U_6614,U_6613] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6613),U_6614),U_6615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6613),U_6614),U_6616)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6613),U_6615),U_6616)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6613),U_6615),U_6616))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6613),U_6614),U_6615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6613),U_6614),U_6616))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6613),c_Groups_Ozero__class_Ozero(U_6613)),U_6614))
| ~ class_Rings_Olinordered__ring__strict(U_6613) ),
inference(variable_rename,[status(thm)],[f_1533_1]) ).
fof(f_1533_3,plain,
( ! [U_6614,U_6613,U_6615,U_6616] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6613),U_6614),U_6615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6613),U_6614),U_6616)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6613),U_6615),U_6616))
| ~ sP366(U_6614,U_6613,U_6615,U_6616) )
& ! [U_6614,U_6613,U_6615,U_6616] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6613),U_6615),U_6616))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6613),U_6614),U_6615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6613),U_6614),U_6616)))
| ~ sP366(U_6614,U_6613,U_6615,U_6616) )
& ! [U_6614,U_6613,U_6615,U_6616] :
( sP366(U_6614,U_6613,U_6615,U_6616)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6613),c_Groups_Ozero__class_Ozero(U_6613)),U_6614))
| ~ class_Rings_Olinordered__ring__strict(U_6613) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP366])],[f_1533_2]) ).
cnf(f_1533_4,plain,
( sP366(U_6614,U_6613,U_6615,U_6616)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6613),c_Groups_Ozero__class_Ozero(U_6613)),U_6614))
| ~ class_Rings_Olinordered__ring__strict(U_6613) ),
inference(clausify,[status(thm)],[f_1533_3]) ).
cnf(f_1533_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6613),U_6615),U_6616))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6613),U_6614),U_6615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6613),U_6614),U_6616)))
| ~ sP366(U_6614,U_6613,U_6615,U_6616) ),
inference(clausify,[status(thm)],[f_1533_3]) ).
cnf(f_1533_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6613),U_6614),U_6615)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6613),U_6614),U_6616)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6613),U_6615),U_6616))
| ~ sP366(U_6614,U_6613,U_6615,U_6616) ),
inference(clausify,[status(thm)],[f_1533_3]) ).
fof(f_1534_1,plain,
! [V_b_2,V_a_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ class_Rings_Olinordered__ring__strict(T_c) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg]) ).
fof(f_1534_2,plain,
! [U_6620,U_6619,U_6618,U_6617] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6617),U_6618),U_6619)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6617),U_6618),U_6620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6617),U_6620),U_6619)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6617),U_6620),U_6619))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6617),U_6618),U_6619)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6617),U_6618),U_6620))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6617),U_6618),c_Groups_Ozero__class_Ozero(U_6617)))
| ~ class_Rings_Olinordered__ring__strict(U_6617) ),
inference(variable_rename,[status(thm)],[f_1534_1]) ).
fof(f_1534_3,plain,
( ! [U_6618,U_6617,U_6619,U_6620] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6617),U_6618),U_6619)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6617),U_6618),U_6620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6617),U_6620),U_6619))
| ~ sP367(U_6618,U_6617,U_6619,U_6620) )
& ! [U_6618,U_6617,U_6619,U_6620] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6617),U_6620),U_6619))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6617),U_6618),U_6619)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6617),U_6618),U_6620)))
| ~ sP367(U_6618,U_6617,U_6619,U_6620) )
& ! [U_6618,U_6617,U_6619,U_6620] :
( sP367(U_6618,U_6617,U_6619,U_6620)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6617),U_6618),c_Groups_Ozero__class_Ozero(U_6617)))
| ~ class_Rings_Olinordered__ring__strict(U_6617) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP367])],[f_1534_2]) ).
cnf(f_1534_4,plain,
( sP367(U_6618,U_6617,U_6619,U_6620)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6617),U_6618),c_Groups_Ozero__class_Ozero(U_6617)))
| ~ class_Rings_Olinordered__ring__strict(U_6617) ),
inference(clausify,[status(thm)],[f_1534_3]) ).
cnf(f_1534_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6617),U_6620),U_6619))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6617),U_6618),U_6619)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6617),U_6618),U_6620)))
| ~ sP367(U_6618,U_6617,U_6619,U_6620) ),
inference(clausify,[status(thm)],[f_1534_3]) ).
cnf(f_1534_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6617),U_6618),U_6619)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6617),U_6618),U_6620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6617),U_6620),U_6619))
| ~ sP367(U_6618,U_6617,U_6619,U_6620) ),
inference(clausify,[status(thm)],[f_1534_3]) ).
fof(f_1535_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_1535_2,plain,
! [U_6625,U_6624,U_6623,U_6622,U_6621] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6621),U_6622),U_6624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6621),U_6623),U_6625)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6621),c_Groups_Ozero__class_Ozero(U_6621)),U_6624))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6621),c_Groups_Ozero__class_Ozero(U_6621)),U_6623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6621),U_6624),U_6625))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6621),U_6622),U_6623))
| ~ class_Rings_Olinordered__semiring__strict(U_6621) ),
inference(variable_rename,[status(thm)],[f_1535_1]) ).
fof(f_1535_3,plain,
! [U_6621,U_6622,U_6623,U_6624,U_6625] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6621),U_6622),U_6624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6621),U_6623),U_6625)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6621),c_Groups_Ozero__class_Ozero(U_6621)),U_6624))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6621),c_Groups_Ozero__class_Ozero(U_6621)),U_6623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6621),U_6624),U_6625))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6621),U_6622),U_6623))
| ~ class_Rings_Olinordered__semiring__strict(U_6621) ),
inference(definitional_conversion,[status(esa)],[f_1535_2]) ).
cnf(f_1535_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6621),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6621),U_6622),U_6624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6621),U_6623),U_6625)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6621),c_Groups_Ozero__class_Ozero(U_6621)),U_6624))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6621),c_Groups_Ozero__class_Ozero(U_6621)),U_6623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6621),U_6624),U_6625))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6621),U_6622),U_6623))
| ~ class_Rings_Olinordered__semiring__strict(U_6621) ),
inference(clausify,[status(thm)],[f_1535_3]) ).
fof(f_1536_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_1536_2,plain,
! [U_6630,U_6629,U_6628,U_6627,U_6626] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6626),U_6627),U_6629)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6626),U_6628),U_6630)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6626),c_Groups_Ozero__class_Ozero(U_6626)),U_6629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6626),c_Groups_Ozero__class_Ozero(U_6626)),U_6627))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6626),U_6629),U_6630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6626),U_6627),U_6628))
| ~ class_Rings_Olinordered__semiring__strict(U_6626) ),
inference(variable_rename,[status(thm)],[f_1536_1]) ).
fof(f_1536_3,plain,
! [U_6628,U_6627,U_6626,U_6629,U_6630] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6626),U_6627),U_6629)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6626),U_6628),U_6630)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6626),c_Groups_Ozero__class_Ozero(U_6626)),U_6629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6626),c_Groups_Ozero__class_Ozero(U_6626)),U_6627))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6626),U_6629),U_6630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6626),U_6627),U_6628))
| ~ class_Rings_Olinordered__semiring__strict(U_6626) ),
inference(definitional_conversion,[status(esa)],[f_1536_2]) ).
cnf(f_1536_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6626),U_6627),U_6629)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6626),U_6628),U_6630)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6626),c_Groups_Ozero__class_Ozero(U_6626)),U_6629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6626),c_Groups_Ozero__class_Ozero(U_6626)),U_6627))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6626),U_6629),U_6630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6626),U_6627),U_6628))
| ~ class_Rings_Olinordered__semiring__strict(U_6626) ),
inference(clausify,[status(thm)],[f_1536_3]) ).
fof(f_1537_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_1537_2,plain,
! [U_6635,U_6634,U_6633,U_6632,U_6631] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6631),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6631),U_6632),U_6634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6631),U_6633),U_6635)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6631),c_Groups_Ozero__class_Ozero(U_6631)),U_6634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6631),c_Groups_Ozero__class_Ozero(U_6631)),U_6632))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6631),U_6634),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6631),U_6632),U_6633))
| ~ class_Rings_Olinordered__semiring__strict(U_6631) ),
inference(variable_rename,[status(thm)],[f_1537_1]) ).
fof(f_1537_3,plain,
! [U_6633,U_6632,U_6634,U_6631,U_6635] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6631),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6631),U_6632),U_6634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6631),U_6633),U_6635)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6631),c_Groups_Ozero__class_Ozero(U_6631)),U_6634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6631),c_Groups_Ozero__class_Ozero(U_6631)),U_6632))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6631),U_6634),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6631),U_6632),U_6633))
| ~ class_Rings_Olinordered__semiring__strict(U_6631) ),
inference(definitional_conversion,[status(esa)],[f_1537_2]) ).
cnf(f_1537_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6631),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6631),U_6632),U_6634)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6631),U_6633),U_6635)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6631),c_Groups_Ozero__class_Ozero(U_6631)),U_6634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6631),c_Groups_Ozero__class_Ozero(U_6631)),U_6632))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6631),U_6634),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6631),U_6632),U_6633))
| ~ class_Rings_Olinordered__semiring__strict(U_6631) ),
inference(clausify,[status(thm)],[f_1537_3]) ).
fof(f_1538_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_1538_2,plain,
! [U_6640,U_6639,U_6638,U_6637,U_6636] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6636),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6636),U_6637),U_6639)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6636),U_6638),U_6640)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6636),c_Groups_Ozero__class_Ozero(U_6636)),U_6639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6636),c_Groups_Ozero__class_Ozero(U_6636)),U_6637))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6636),U_6639),U_6640))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6636),U_6637),U_6638))
| ~ class_Rings_Olinordered__semiring__strict(U_6636) ),
inference(variable_rename,[status(thm)],[f_1538_1]) ).
fof(f_1538_3,plain,
! [U_6636,U_6639,U_6637,U_6638,U_6640] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6636),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6636),U_6637),U_6639)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6636),U_6638),U_6640)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6636),c_Groups_Ozero__class_Ozero(U_6636)),U_6639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6636),c_Groups_Ozero__class_Ozero(U_6636)),U_6637))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6636),U_6639),U_6640))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6636),U_6637),U_6638))
| ~ class_Rings_Olinordered__semiring__strict(U_6636) ),
inference(definitional_conversion,[status(esa)],[f_1538_2]) ).
cnf(f_1538_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6636),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6636),U_6637),U_6639)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6636),U_6638),U_6640)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6636),c_Groups_Ozero__class_Ozero(U_6636)),U_6639))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6636),c_Groups_Ozero__class_Ozero(U_6636)),U_6637))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6636),U_6639),U_6640))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6636),U_6637),U_6638))
| ~ class_Rings_Olinordered__semiring__strict(U_6636) ),
inference(clausify,[status(thm)],[f_1538_3]) ).
fof(f_1539_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_1539_2,plain,
! [U_6644,U_6643,U_6642,U_6641] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6641),U_6642),U_6644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6641),c_Groups_Ozero__class_Ozero(U_6641)),U_6643))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6641),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6641),U_6642),U_6643)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6641),U_6644),U_6643)))
| ~ class_Rings_Olinordered__semiring(U_6641) ),
inference(variable_rename,[status(thm)],[f_1539_1]) ).
fof(f_1539_3,plain,
! [U_6643,U_6644,U_6641,U_6642] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6641),U_6642),U_6644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6641),c_Groups_Ozero__class_Ozero(U_6641)),U_6643))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6641),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6641),U_6642),U_6643)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6641),U_6644),U_6643)))
| ~ class_Rings_Olinordered__semiring(U_6641) ),
inference(definitional_conversion,[status(esa)],[f_1539_2]) ).
cnf(f_1539_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6641),U_6642),U_6644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6641),c_Groups_Ozero__class_Ozero(U_6641)),U_6643))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6641),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6641),U_6642),U_6643)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6641),U_6644),U_6643)))
| ~ class_Rings_Olinordered__semiring(U_6641) ),
inference(clausify,[status(thm)],[f_1539_3]) ).
fof(f_1540_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_1540_2,plain,
! [U_6648,U_6647,U_6646,U_6645] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6645),U_6646),U_6648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6645),c_Groups_Ozero__class_Ozero(U_6645)),U_6647))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6645),U_6646),U_6647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6645),U_6648),U_6647)))
| ~ class_Rings_Olinordered__semiring__strict(U_6645) ),
inference(variable_rename,[status(thm)],[f_1540_1]) ).
fof(f_1540_3,plain,
! [U_6645,U_6646,U_6647,U_6648] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6645),U_6646),U_6648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6645),c_Groups_Ozero__class_Ozero(U_6645)),U_6647))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6645),U_6646),U_6647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6645),U_6648),U_6647)))
| ~ class_Rings_Olinordered__semiring__strict(U_6645) ),
inference(definitional_conversion,[status(esa)],[f_1540_2]) ).
cnf(f_1540_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6645),U_6646),U_6648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6645),c_Groups_Ozero__class_Ozero(U_6645)),U_6647))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6645),U_6646),U_6647)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6645),U_6648),U_6647)))
| ~ class_Rings_Olinordered__semiring__strict(U_6645) ),
inference(clausify,[status(thm)],[f_1540_3]) ).
fof(f_1541_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_1541_2,plain,
! [U_6652,U_6651,U_6650,U_6649] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6649),U_6651),U_6652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6649),c_Groups_Ozero__class_Ozero(U_6649)),U_6650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6649),U_6650),U_6651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6649),U_6650),U_6652)))
| ~ class_Rings_Olinordered__semiring(U_6649) ),
inference(variable_rename,[status(thm)],[f_1541_1]) ).
fof(f_1541_3,plain,
! [U_6649,U_6650,U_6651,U_6652] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6649),U_6651),U_6652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6649),c_Groups_Ozero__class_Ozero(U_6649)),U_6650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6649),U_6650),U_6651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6649),U_6650),U_6652)))
| ~ class_Rings_Olinordered__semiring(U_6649) ),
inference(definitional_conversion,[status(esa)],[f_1541_2]) ).
cnf(f_1541_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6649),U_6651),U_6652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6649),c_Groups_Ozero__class_Ozero(U_6649)),U_6650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6649),U_6650),U_6651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6649),U_6650),U_6652)))
| ~ class_Rings_Olinordered__semiring(U_6649) ),
inference(clausify,[status(thm)],[f_1541_3]) ).
fof(f_1542_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_1542_2,plain,
! [U_6656,U_6655,U_6654,U_6653] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6653),U_6655),U_6656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6653),c_Groups_Ozero__class_Ozero(U_6653)),U_6654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6653),U_6654),U_6655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6653),U_6654),U_6656)))
| ~ class_Rings_Olinordered__semiring__strict(U_6653) ),
inference(variable_rename,[status(thm)],[f_1542_1]) ).
fof(f_1542_3,plain,
! [U_6653,U_6654,U_6655,U_6656] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6653),U_6655),U_6656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6653),c_Groups_Ozero__class_Ozero(U_6653)),U_6654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6653),U_6654),U_6655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6653),U_6654),U_6656)))
| ~ class_Rings_Olinordered__semiring__strict(U_6653) ),
inference(definitional_conversion,[status(esa)],[f_1542_2]) ).
cnf(f_1542_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6653),U_6655),U_6656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6653),c_Groups_Ozero__class_Ozero(U_6653)),U_6654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6653),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6653),U_6654),U_6655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6653),U_6654),U_6656)))
| ~ class_Rings_Olinordered__semiring__strict(U_6653) ),
inference(clausify,[status(thm)],[f_1542_3]) ).
fof(f_1543_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_1543_2,plain,
! [U_6660,U_6659,U_6658,U_6657] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6657),U_6658),U_6660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6657),c_Groups_Ozero__class_Ozero(U_6657)),U_6659))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6657),U_6658),U_6659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6657),U_6660),U_6659)))
| ~ class_Rings_Olinordered__semiring__strict(U_6657) ),
inference(variable_rename,[status(thm)],[f_1543_1]) ).
fof(f_1543_3,plain,
! [U_6657,U_6658,U_6659,U_6660] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6657),U_6658),U_6660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6657),c_Groups_Ozero__class_Ozero(U_6657)),U_6659))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6657),U_6658),U_6659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6657),U_6660),U_6659)))
| ~ class_Rings_Olinordered__semiring__strict(U_6657) ),
inference(definitional_conversion,[status(esa)],[f_1543_2]) ).
cnf(f_1543_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6657),U_6658),U_6660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6657),c_Groups_Ozero__class_Ozero(U_6657)),U_6659))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6657),U_6658),U_6659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6657),U_6660),U_6659)))
| ~ class_Rings_Olinordered__semiring__strict(U_6657) ),
inference(clausify,[status(thm)],[f_1543_3]) ).
fof(f_1544_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_1544_2,plain,
! [U_6664,U_6663,U_6662,U_6661] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6661),U_6663),U_6664))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6661),c_Groups_Ozero__class_Ozero(U_6661)),U_6662))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6661),U_6662),U_6663)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6661),U_6662),U_6664)))
| ~ class_Rings_Olinordered__semiring__strict(U_6661) ),
inference(variable_rename,[status(thm)],[f_1544_1]) ).
fof(f_1544_3,plain,
! [U_6661,U_6662,U_6663,U_6664] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6661),U_6663),U_6664))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6661),c_Groups_Ozero__class_Ozero(U_6661)),U_6662))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6661),U_6662),U_6663)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6661),U_6662),U_6664)))
| ~ class_Rings_Olinordered__semiring__strict(U_6661) ),
inference(definitional_conversion,[status(esa)],[f_1544_2]) ).
cnf(f_1544_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6661),U_6663),U_6664))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6661),c_Groups_Ozero__class_Ozero(U_6661)),U_6662))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6661),U_6662),U_6663)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6661),U_6662),U_6664)))
| ~ class_Rings_Olinordered__semiring__strict(U_6661) ),
inference(clausify,[status(thm)],[f_1544_3]) ).
fof(f_1545_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_1545_2,plain,
! [U_6666,U_6665] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6665),U_6666) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6665),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6666))
| U_6665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6665),U_6666) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6665 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1545_1]) ).
fof(f_1545_3,plain,
( ! [U_6670,U_6668] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6668),U_6670) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6668),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6670))
| U_6668 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6669,U_6667] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6667),U_6669) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6667 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1545_2]) ).
fof(f_1545_4,plain,
( ! [U_6670,U_6668] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6668),U_6670) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6668),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6670))
| U_6668 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6669,U_6667] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6667),U_6669) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6667 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1545_3]) ).
cnf(f_1545_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6667),U_6669) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6667 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1545_4]) ).
cnf(f_1545_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6668),U_6670) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6668),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6670))
| U_6668 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1545_4]) ).
fof(f_1546_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_1546_2,plain,
! [U_6673,U_6672,U_6671] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6671),U_6672),U_6673)),U_6672))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6671),U_6673),c_Groups_Oone__class_Oone(U_6671)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6671),c_Groups_Ozero__class_Ozero(U_6671)),U_6673))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6671),c_Groups_Ozero__class_Ozero(U_6671)),U_6672))
| ~ class_Rings_Olinordered__idom(U_6671) ),
inference(variable_rename,[status(thm)],[f_1546_1]) ).
fof(f_1546_3,plain,
! [U_6671,U_6672,U_6673] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6671),U_6672),U_6673)),U_6672))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6671),U_6673),c_Groups_Oone__class_Oone(U_6671)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6671),c_Groups_Ozero__class_Ozero(U_6671)),U_6673))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6671),c_Groups_Ozero__class_Ozero(U_6671)),U_6672))
| ~ class_Rings_Olinordered__idom(U_6671) ),
inference(definitional_conversion,[status(esa)],[f_1546_2]) ).
cnf(f_1546_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6671),U_6672),U_6673)),U_6672))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6671),U_6673),c_Groups_Oone__class_Oone(U_6671)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6671),c_Groups_Ozero__class_Ozero(U_6671)),U_6673))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6671),c_Groups_Ozero__class_Ozero(U_6671)),U_6672))
| ~ class_Rings_Olinordered__idom(U_6671) ),
inference(clausify,[status(thm)],[f_1546_3]) ).
fof(f_1547_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_1547_2,plain,
! [U_6676,U_6675,U_6674] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6674),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6674),U_6676),U_6675)),U_6675))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6674),U_6676),c_Groups_Oone__class_Oone(U_6674)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6674),c_Groups_Ozero__class_Ozero(U_6674)),U_6676))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6674),c_Groups_Ozero__class_Ozero(U_6674)),U_6675))
| ~ class_Rings_Olinordered__idom(U_6674) ),
inference(variable_rename,[status(thm)],[f_1547_1]) ).
fof(f_1547_3,plain,
! [U_6675,U_6676,U_6674] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6674),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6674),U_6676),U_6675)),U_6675))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6674),U_6676),c_Groups_Oone__class_Oone(U_6674)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6674),c_Groups_Ozero__class_Ozero(U_6674)),U_6676))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6674),c_Groups_Ozero__class_Ozero(U_6674)),U_6675))
| ~ class_Rings_Olinordered__idom(U_6674) ),
inference(definitional_conversion,[status(esa)],[f_1547_2]) ).
cnf(f_1547_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6674),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6674),U_6676),U_6675)),U_6675))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6674),U_6676),c_Groups_Oone__class_Oone(U_6674)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6674),c_Groups_Ozero__class_Ozero(U_6674)),U_6676))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6674),c_Groups_Ozero__class_Ozero(U_6674)),U_6675))
| ~ class_Rings_Olinordered__idom(U_6674) ),
inference(clausify,[status(thm)],[f_1547_3]) ).
fof(f_1548_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_1548_2,plain,
! [U_6677] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6677),c_Groups_Ozero__class_Ozero(U_6677)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6677),c_Groups_Oone__class_Oone(U_6677)),c_Groups_Oone__class_Oone(U_6677))))
| ~ class_Rings_Olinordered__semidom(U_6677) ),
inference(variable_rename,[status(thm)],[f_1548_1]) ).
fof(f_1548_3,plain,
! [U_6677] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6677),c_Groups_Ozero__class_Ozero(U_6677)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6677),c_Groups_Oone__class_Oone(U_6677)),c_Groups_Oone__class_Oone(U_6677))))
| ~ class_Rings_Olinordered__semidom(U_6677) ),
inference(definitional_conversion,[status(esa)],[f_1548_2]) ).
cnf(f_1548_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6677),c_Groups_Ozero__class_Ozero(U_6677)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6677),c_Groups_Oone__class_Oone(U_6677)),c_Groups_Oone__class_Oone(U_6677))))
| ~ class_Rings_Olinordered__semidom(U_6677) ),
inference(clausify,[status(thm)],[f_1548_3]) ).
fof(f_1549_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_1549_2,plain,
! [U_6681,U_6680,U_6679,U_6678] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6678),U_6679),U_6681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6678),c_Groups_Ozero__class_Ozero(U_6678)),U_6681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6678),hAPP(hAPP(c_Power_Opower__class_Opower(U_6678),U_6679),U_6680)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6678),U_6681),U_6680)))
| ~ class_Rings_Olinordered__semidom(U_6678) ),
inference(variable_rename,[status(thm)],[f_1549_1]) ).
fof(f_1549_3,plain,
! [U_6678,U_6679,U_6680,U_6681] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6678),U_6679),U_6681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6678),c_Groups_Ozero__class_Ozero(U_6678)),U_6681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6678),hAPP(hAPP(c_Power_Opower__class_Opower(U_6678),U_6679),U_6680)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6678),U_6681),U_6680)))
| ~ class_Rings_Olinordered__semidom(U_6678) ),
inference(definitional_conversion,[status(esa)],[f_1549_2]) ).
cnf(f_1549_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6678),U_6679),U_6681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6678),c_Groups_Ozero__class_Ozero(U_6678)),U_6681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6678),hAPP(hAPP(c_Power_Opower__class_Opower(U_6678),U_6679),U_6680)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6678),U_6681),U_6680)))
| ~ class_Rings_Olinordered__semidom(U_6678) ),
inference(clausify,[status(thm)],[f_1549_3]) ).
fof(f_1550_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_1550_2,plain,
! [U_6685,U_6684,U_6683,U_6682] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6682),U_6683),U_6685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6682),c_Groups_Ozero__class_Ozero(U_6682)),U_6685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6682),hAPP(hAPP(c_Power_Opower__class_Opower(U_6682),U_6683),hAPP(c_Nat_OSuc,U_6684))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6682),U_6685),hAPP(c_Nat_OSuc,U_6684))))
| ~ class_Rings_Olinordered__semidom(U_6682) ),
inference(variable_rename,[status(thm)],[f_1550_1]) ).
fof(f_1550_3,plain,
! [U_6682,U_6683,U_6684,U_6685] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6682),U_6683),U_6685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6682),c_Groups_Ozero__class_Ozero(U_6682)),U_6685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6682),hAPP(hAPP(c_Power_Opower__class_Opower(U_6682),U_6683),hAPP(c_Nat_OSuc,U_6684))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6682),U_6685),hAPP(c_Nat_OSuc,U_6684))))
| ~ class_Rings_Olinordered__semidom(U_6682) ),
inference(definitional_conversion,[status(esa)],[f_1550_2]) ).
cnf(f_1550_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6682),U_6683),U_6685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6682),c_Groups_Ozero__class_Ozero(U_6682)),U_6685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6682),hAPP(hAPP(c_Power_Opower__class_Opower(U_6682),U_6683),hAPP(c_Nat_OSuc,U_6684))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6682),U_6685),hAPP(c_Nat_OSuc,U_6684))))
| ~ class_Rings_Olinordered__semidom(U_6682) ),
inference(clausify,[status(thm)],[f_1550_3]) ).
fof(f_1551_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_1551_2,plain,
! [U_6689,U_6688,U_6687,U_6686] :
( U_6687 = U_6689
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6686),c_Groups_Ozero__class_Ozero(U_6686)),U_6689))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6686),c_Groups_Ozero__class_Ozero(U_6686)),U_6687))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6686),U_6687),hAPP(c_Nat_OSuc,U_6688)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6686),U_6689),hAPP(c_Nat_OSuc,U_6688))
| ~ class_Rings_Olinordered__semidom(U_6686) ),
inference(variable_rename,[status(thm)],[f_1551_1]) ).
fof(f_1551_3,plain,
! [U_6686,U_6687,U_6688,U_6689] :
( U_6687 = U_6689
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6686),c_Groups_Ozero__class_Ozero(U_6686)),U_6689))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6686),c_Groups_Ozero__class_Ozero(U_6686)),U_6687))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6686),U_6687),hAPP(c_Nat_OSuc,U_6688)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6686),U_6689),hAPP(c_Nat_OSuc,U_6688))
| ~ class_Rings_Olinordered__semidom(U_6686) ),
inference(definitional_conversion,[status(esa)],[f_1551_2]) ).
cnf(f_1551_4,plain,
( U_6687 = U_6689
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6686),c_Groups_Ozero__class_Ozero(U_6686)),U_6689))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6686),c_Groups_Ozero__class_Ozero(U_6686)),U_6687))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_6686),U_6687),hAPP(c_Nat_OSuc,U_6688)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6686),U_6689),hAPP(c_Nat_OSuc,U_6688))
| ~ class_Rings_Olinordered__semidom(U_6686) ),
inference(clausify,[status(thm)],[f_1551_3]) ).
fof(f_1552_1,plain,
! [V_A_2,T_c] :
( ( hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
& V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(T_c),V_A_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_card__eq__0__iff]) ).
fof(f_1552_2,plain,
! [U_6691,U_6690] :
( ( hAPP(c_Finite__Set_Ocard(U_6690),U_6691) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_6690),U_6691))
& U_6691 != c_Orderings_Obot__class_Obot(tc_fun(U_6690,tc_HOL_Obool)) ) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6690),U_6691))
| U_6691 = c_Orderings_Obot__class_Obot(tc_fun(U_6690,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_6690),U_6691) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1552_1]) ).
fof(f_1552_3,plain,
( ! [U_6695,U_6693] :
( hAPP(c_Finite__Set_Ocard(U_6693),U_6695) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_6693),U_6695))
& U_6695 != c_Orderings_Obot__class_Obot(tc_fun(U_6693,tc_HOL_Obool)) ) )
& ! [U_6694,U_6692] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6692),U_6694))
| U_6694 = c_Orderings_Obot__class_Obot(tc_fun(U_6692,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_6692),U_6694) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1552_2]) ).
fof(f_1552_4,plain,
( ! [U_6695,U_6693] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_6693),U_6695))
| ~ sP368(U_6695,U_6693) )
& ! [U_6695,U_6693] :
( U_6695 != c_Orderings_Obot__class_Obot(tc_fun(U_6693,tc_HOL_Obool))
| ~ sP368(U_6695,U_6693) )
& ! [U_6695,U_6693] :
( hAPP(c_Finite__Set_Ocard(U_6693),U_6695) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP368(U_6695,U_6693) )
& ! [U_6692,U_6694] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6692),U_6694))
| U_6694 = c_Orderings_Obot__class_Obot(tc_fun(U_6692,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_6692),U_6694) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP368])],[f_1552_3]) ).
cnf(f_1552_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6692),U_6694))
| U_6694 = c_Orderings_Obot__class_Obot(tc_fun(U_6692,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_6692),U_6694) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1552_4]) ).
cnf(f_1552_6,plain,
( hAPP(c_Finite__Set_Ocard(U_6693),U_6695) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP368(U_6695,U_6693) ),
inference(clausify,[status(thm)],[f_1552_4]) ).
cnf(f_1552_7,plain,
( U_6695 != c_Orderings_Obot__class_Obot(tc_fun(U_6693,tc_HOL_Obool))
| ~ sP368(U_6695,U_6693) ),
inference(clausify,[status(thm)],[f_1552_4]) ).
cnf(f_1552_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_6693),U_6695))
| ~ sP368(U_6695,U_6693) ),
inference(clausify,[status(thm)],[f_1552_4]) ).
fof(f_1553_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),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_c),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite]) ).
fof(f_1553_2,plain,
! [U_6697,U_6696] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_6696),U_6697))
| ~ 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_6696),U_6697))) ),
inference(variable_rename,[status(thm)],[f_1553_1]) ).
fof(f_1553_3,plain,
! [U_6696,U_6697] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_6696),U_6697))
| ~ 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_6696),U_6697))) ),
inference(definitional_conversion,[status(esa)],[f_1553_2]) ).
cnf(f_1553_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_6696),U_6697))
| ~ 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_6696),U_6697))) ),
inference(clausify,[status(thm)],[f_1553_3]) ).
fof(f_1554_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_1554_2,plain,
! [U_6699,U_6698] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6698),hAPP(c_Nat_OSuc,U_6699))),U_6698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6698)) ),
inference(variable_rename,[status(thm)],[f_1554_1]) ).
fof(f_1554_3,plain,
! [U_6698,U_6699] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6698),hAPP(c_Nat_OSuc,U_6699))),U_6698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6698)) ),
inference(definitional_conversion,[status(esa)],[f_1554_2]) ).
cnf(f_1554_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6698),hAPP(c_Nat_OSuc,U_6699))),U_6698))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6698)) ),
inference(clausify,[status(thm)],[f_1554_3]) ).
fof(f_1555_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_1555_2,plain,
! [U_6700] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6700),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_6700
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6700)) ),
inference(variable_rename,[status(thm)],[f_1555_1]) ).
fof(f_1555_3,plain,
! [U_6700] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6700),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_6700
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6700)) ),
inference(definitional_conversion,[status(esa)],[f_1555_2]) ).
cnf(f_1555_4,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6700),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_6700
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6700)) ),
inference(clausify,[status(thm)],[f_1555_3]) ).
fof(f_1556_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_1556_2,plain,
! [U_6702,U_6701] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6701),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6702),U_6701)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6702))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6701)) ),
inference(variable_rename,[status(thm)],[f_1556_1]) ).
fof(f_1556_3,plain,
! [U_6701,U_6702] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6701),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6702),U_6701)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6702))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6701)) ),
inference(definitional_conversion,[status(esa)],[f_1556_2]) ).
cnf(f_1556_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6701),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6702),U_6701)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6702))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6701)) ),
inference(clausify,[status(thm)],[f_1556_3]) ).
fof(f_1557_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_1557_2,plain,
! [U_6704,U_6703] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6703),U_6704)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6704))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6703)) ),
inference(variable_rename,[status(thm)],[f_1557_1]) ).
fof(f_1557_3,plain,
! [U_6703,U_6704] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6703),U_6704)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6704))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6703)) ),
inference(definitional_conversion,[status(esa)],[f_1557_2]) ).
cnf(f_1557_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6703),U_6704)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6704))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6703)) ),
inference(clausify,[status(thm)],[f_1557_3]) ).
fof(f_1558_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_1558_2,plain,
! [U_6706,U_6705] :
( 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_6706),U_6705)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6706))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6705)) ),
inference(variable_rename,[status(thm)],[f_1558_1]) ).
fof(f_1558_3,plain,
! [U_6706,U_6705] :
( 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_6706),U_6705)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6706))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6705)) ),
inference(definitional_conversion,[status(esa)],[f_1558_2]) ).
cnf(f_1558_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_6706),U_6705)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6706))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6705)) ),
inference(clausify,[status(thm)],[f_1558_3]) ).
fof(f_1559_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_1559_2,plain,
! [U_6711,U_6710,U_6709] :
( ( hBOOL(hAPP(U_6709,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6710),U_6711)))
| ? [U_6708] :
( ~ hBOOL(hAPP(U_6709,U_6708))
& U_6710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6711),U_6708) )
| ( ~ hBOOL(hAPP(U_6709,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6710),U_6711)) ) )
& ( ( ! [U_6707] :
( hBOOL(hAPP(U_6709,U_6707))
| U_6710 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6711),U_6707) )
& ( hBOOL(hAPP(U_6709,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6710),U_6711)) ) )
| ~ hBOOL(hAPP(U_6709,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6710),U_6711))) ) ),
inference(variable_rename,[status(thm)],[f_1559_1]) ).
fof(f_1559_3,plain,
( ! [U_6717,U_6715,U_6713] :
( hBOOL(hAPP(U_6713,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6715),U_6717)))
| ? [U_6708] :
( ~ hBOOL(hAPP(U_6713,U_6708))
& U_6715 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6717),U_6708) )
| ( ~ hBOOL(hAPP(U_6713,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6715),U_6717)) ) )
& ! [U_6716,U_6714,U_6712] :
( ( ! [U_6707] :
( hBOOL(hAPP(U_6712,U_6707))
| U_6714 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6716),U_6707) )
& ( hBOOL(hAPP(U_6712,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6714),U_6716)) ) )
| ~ hBOOL(hAPP(U_6712,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6714),U_6716))) ) ),
inference(miniscope,[status(thm)],[f_1559_2]) ).
fof(f_1559_4,plain,
( ! [U_6717,U_6715,U_6713] :
( hBOOL(hAPP(U_6713,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6715),U_6717)))
| ( ~ hBOOL(hAPP(U_6713,sK125(U_6717,U_6715,U_6713)))
& U_6715 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6717),sK125(U_6717,U_6715,U_6713)) )
| ( ~ hBOOL(hAPP(U_6713,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6715),U_6717)) ) )
& ! [U_6716,U_6714,U_6712] :
( ( ! [U_6707] :
( hBOOL(hAPP(U_6712,U_6707))
| U_6714 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6716),U_6707) )
& ( hBOOL(hAPP(U_6712,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6714),U_6716)) ) )
| ~ hBOOL(hAPP(U_6712,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6714),U_6716))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_6708,sK125(U_6717,U_6715,U_6713))],[f_1559_3]) ).
fof(f_1559_5,plain,
( ! [U_6713,U_6717,U_6715] :
( ~ hBOOL(hAPP(U_6713,sK125(U_6717,U_6715,U_6713)))
| ~ sP371(U_6713,U_6717,U_6715) )
& ! [U_6713,U_6717,U_6715] :
( U_6715 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6717),sK125(U_6717,U_6715,U_6713))
| ~ sP371(U_6713,U_6717,U_6715) )
& ! [U_6713,U_6717,U_6715] :
( ~ hBOOL(hAPP(U_6713,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP370(U_6713,U_6717,U_6715) )
& ! [U_6713,U_6717,U_6715] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6715),U_6717))
| ~ sP370(U_6713,U_6717,U_6715) )
& ! [U_6707,U_6712,U_6716,U_6714] :
( hBOOL(hAPP(U_6712,U_6707))
| U_6714 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6716),U_6707)
| ~ sP369(U_6707,U_6712,U_6716,U_6714) )
& ! [U_6707,U_6712,U_6716,U_6714] :
( hBOOL(hAPP(U_6712,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6714),U_6716))
| ~ sP369(U_6707,U_6712,U_6716,U_6714) )
& ! [U_6713,U_6717,U_6715] :
( hBOOL(hAPP(U_6713,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6715),U_6717)))
| sP371(U_6713,U_6717,U_6715)
| sP370(U_6713,U_6717,U_6715) )
& ! [U_6707,U_6712,U_6716,U_6714] :
( sP369(U_6707,U_6712,U_6716,U_6714)
| ~ hBOOL(hAPP(U_6712,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6714),U_6716))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP369,sP370,sP371])],[f_1559_4]) ).
cnf(f_1559_6,plain,
( sP369(U_6707,U_6712,U_6716,U_6714)
| ~ hBOOL(hAPP(U_6712,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6714),U_6716))) ),
inference(clausify,[status(thm)],[f_1559_5]) ).
cnf(f_1559_7,plain,
( hBOOL(hAPP(U_6713,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6715),U_6717)))
| sP371(U_6713,U_6717,U_6715)
| sP370(U_6713,U_6717,U_6715) ),
inference(clausify,[status(thm)],[f_1559_5]) ).
cnf(f_1559_8,plain,
( hBOOL(hAPP(U_6712,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6714),U_6716))
| ~ sP369(U_6707,U_6712,U_6716,U_6714) ),
inference(clausify,[status(thm)],[f_1559_5]) ).
cnf(f_1559_9,plain,
( hBOOL(hAPP(U_6712,U_6707))
| U_6714 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6716),U_6707)
| ~ sP369(U_6707,U_6712,U_6716,U_6714) ),
inference(clausify,[status(thm)],[f_1559_5]) ).
cnf(f_1559_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6715),U_6717))
| ~ sP370(U_6713,U_6717,U_6715) ),
inference(clausify,[status(thm)],[f_1559_5]) ).
cnf(f_1559_11,plain,
( ~ hBOOL(hAPP(U_6713,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP370(U_6713,U_6717,U_6715) ),
inference(clausify,[status(thm)],[f_1559_5]) ).
cnf(f_1559_12,plain,
( U_6715 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6717),sK125(U_6717,U_6715,U_6713))
| ~ sP371(U_6713,U_6717,U_6715) ),
inference(clausify,[status(thm)],[f_1559_5]) ).
cnf(f_1559_13,plain,
( ~ hBOOL(hAPP(U_6713,sK125(U_6717,U_6715,U_6713)))
| ~ sP371(U_6713,U_6717,U_6715) ),
inference(clausify,[status(thm)],[f_1559_5]) ).
fof(f_1560_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_1560_2,plain,
! [U_6722,U_6721,U_6720] :
( ( hBOOL(hAPP(U_6720,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6721),U_6722)))
| ? [U_6719] :
( ~ hBOOL(hAPP(U_6720,U_6719))
& U_6721 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6722),U_6719) )
| ( ~ hBOOL(hAPP(U_6720,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6721),U_6722)) ) )
& ( ( ! [U_6718] :
( hBOOL(hAPP(U_6720,U_6718))
| U_6721 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6722),U_6718) )
& ( hBOOL(hAPP(U_6720,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6721),U_6722)) ) )
| ~ hBOOL(hAPP(U_6720,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6721),U_6722))) ) ),
inference(variable_rename,[status(thm)],[f_1560_1]) ).
fof(f_1560_3,plain,
( ! [U_6728,U_6726,U_6724] :
( hBOOL(hAPP(U_6724,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6726),U_6728)))
| ? [U_6719] :
( ~ hBOOL(hAPP(U_6724,U_6719))
& U_6726 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6728),U_6719) )
| ( ~ hBOOL(hAPP(U_6724,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6726),U_6728)) ) )
& ! [U_6727,U_6725,U_6723] :
( ( ! [U_6718] :
( hBOOL(hAPP(U_6723,U_6718))
| U_6725 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6727),U_6718) )
& ( hBOOL(hAPP(U_6723,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6725),U_6727)) ) )
| ~ hBOOL(hAPP(U_6723,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6725),U_6727))) ) ),
inference(miniscope,[status(thm)],[f_1560_2]) ).
fof(f_1560_4,plain,
( ! [U_6728,U_6726,U_6724] :
( hBOOL(hAPP(U_6724,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6726),U_6728)))
| ( ~ hBOOL(hAPP(U_6724,sK126(U_6728,U_6726,U_6724)))
& U_6726 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6728),sK126(U_6728,U_6726,U_6724)) )
| ( ~ hBOOL(hAPP(U_6724,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6726),U_6728)) ) )
& ! [U_6727,U_6725,U_6723] :
( ( ! [U_6718] :
( hBOOL(hAPP(U_6723,U_6718))
| U_6725 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6727),U_6718) )
& ( hBOOL(hAPP(U_6723,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6725),U_6727)) ) )
| ~ hBOOL(hAPP(U_6723,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6725),U_6727))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_6719,sK126(U_6728,U_6726,U_6724))],[f_1560_3]) ).
fof(f_1560_5,plain,
( ! [U_6726,U_6728,U_6724] :
( ~ hBOOL(hAPP(U_6724,sK126(U_6728,U_6726,U_6724)))
| ~ sP374(U_6726,U_6728,U_6724) )
& ! [U_6726,U_6728,U_6724] :
( U_6726 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6728),sK126(U_6728,U_6726,U_6724))
| ~ sP374(U_6726,U_6728,U_6724) )
& ! [U_6726,U_6728,U_6724] :
( ~ hBOOL(hAPP(U_6724,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP373(U_6726,U_6728,U_6724) )
& ! [U_6726,U_6728,U_6724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6726),U_6728))
| ~ sP373(U_6726,U_6728,U_6724) )
& ! [U_6725,U_6718,U_6723,U_6727] :
( hBOOL(hAPP(U_6723,U_6718))
| U_6725 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6727),U_6718)
| ~ sP372(U_6725,U_6718,U_6723,U_6727) )
& ! [U_6725,U_6718,U_6723,U_6727] :
( hBOOL(hAPP(U_6723,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6725),U_6727))
| ~ sP372(U_6725,U_6718,U_6723,U_6727) )
& ! [U_6726,U_6728,U_6724] :
( hBOOL(hAPP(U_6724,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6726),U_6728)))
| sP374(U_6726,U_6728,U_6724)
| sP373(U_6726,U_6728,U_6724) )
& ! [U_6725,U_6718,U_6723,U_6727] :
( sP372(U_6725,U_6718,U_6723,U_6727)
| ~ hBOOL(hAPP(U_6723,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6725),U_6727))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP372,sP373,sP374])],[f_1560_4]) ).
cnf(f_1560_6,plain,
( sP372(U_6725,U_6718,U_6723,U_6727)
| ~ hBOOL(hAPP(U_6723,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6725),U_6727))) ),
inference(clausify,[status(thm)],[f_1560_5]) ).
cnf(f_1560_7,plain,
( hBOOL(hAPP(U_6724,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6726),U_6728)))
| sP374(U_6726,U_6728,U_6724)
| sP373(U_6726,U_6728,U_6724) ),
inference(clausify,[status(thm)],[f_1560_5]) ).
cnf(f_1560_8,plain,
( hBOOL(hAPP(U_6723,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6725),U_6727))
| ~ sP372(U_6725,U_6718,U_6723,U_6727) ),
inference(clausify,[status(thm)],[f_1560_5]) ).
cnf(f_1560_9,plain,
( hBOOL(hAPP(U_6723,U_6718))
| U_6725 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6727),U_6718)
| ~ sP372(U_6725,U_6718,U_6723,U_6727) ),
inference(clausify,[status(thm)],[f_1560_5]) ).
cnf(f_1560_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6726),U_6728))
| ~ sP373(U_6726,U_6728,U_6724) ),
inference(clausify,[status(thm)],[f_1560_5]) ).
cnf(f_1560_11,plain,
( ~ hBOOL(hAPP(U_6724,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP373(U_6726,U_6728,U_6724) ),
inference(clausify,[status(thm)],[f_1560_5]) ).
cnf(f_1560_12,plain,
( U_6726 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6728),sK126(U_6728,U_6726,U_6724))
| ~ sP374(U_6726,U_6728,U_6724) ),
inference(clausify,[status(thm)],[f_1560_5]) ).
cnf(f_1560_13,plain,
( ~ hBOOL(hAPP(U_6724,sK126(U_6728,U_6726,U_6724)))
| ~ sP374(U_6726,U_6728,U_6724) ),
inference(clausify,[status(thm)],[f_1560_5]) ).
fof(f_1561_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_1561_2,plain,
! [U_6730,U_6729] :
( ( 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_6729),U_6730)))
| ~ 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_6730))
| ~ 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_6729)) )
& ( ( 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_6730))
& 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_6729)) )
| ~ 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_6729),U_6730))) ) ),
inference(variable_rename,[status(thm)],[f_1561_1]) ).
fof(f_1561_3,plain,
( ! [U_6734,U_6732] :
( 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_6732),U_6734)))
| ~ 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_6734))
| ~ 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_6732)) )
& ! [U_6733,U_6731] :
( ( 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_6733))
& 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_6731)) )
| ~ 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_6731),U_6733))) ) ),
inference(miniscope,[status(thm)],[f_1561_2]) ).
fof(f_1561_4,plain,
( ! [U_6733,U_6731] :
( 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_6733))
| ~ sP375(U_6733,U_6731) )
& ! [U_6733,U_6731] :
( 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_6731))
| ~ sP375(U_6733,U_6731) )
& ! [U_6732,U_6734] :
( 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_6732),U_6734)))
| ~ 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_6734))
| ~ 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_6732)) )
& ! [U_6733,U_6731] :
( sP375(U_6733,U_6731)
| ~ 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_6731),U_6733))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP375])],[f_1561_3]) ).
cnf(f_1561_5,plain,
( sP375(U_6733,U_6731)
| ~ 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_6731),U_6733))) ),
inference(clausify,[status(thm)],[f_1561_4]) ).
cnf(f_1561_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_6732),U_6734)))
| ~ 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_6734))
| ~ 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_6732)) ),
inference(clausify,[status(thm)],[f_1561_4]) ).
cnf(f_1561_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_6731))
| ~ sP375(U_6733,U_6731) ),
inference(clausify,[status(thm)],[f_1561_4]) ).
cnf(f_1561_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_6733))
| ~ sP375(U_6733,U_6731) ),
inference(clausify,[status(thm)],[f_1561_4]) ).
fof(f_1562_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_1562_2,plain,
! [U_6737,U_6736,U_6735] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6735),U_6736)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6735),U_6737)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6736),U_6737))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6735)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6736),U_6737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6735))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6735),U_6736)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6735),U_6737))) ) ),
inference(variable_rename,[status(thm)],[f_1562_1]) ).
fof(f_1562_3,plain,
( ! [U_6743,U_6741,U_6739] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6739),U_6741)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6739),U_6743)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6741),U_6743))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6739)) ) )
& ! [U_6742,U_6740,U_6738] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6740),U_6742))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6738))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6738),U_6740)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6738),U_6742))) ) ),
inference(miniscope,[status(thm)],[f_1562_2]) ).
fof(f_1562_4,plain,
( ! [U_6739,U_6743,U_6741] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6741),U_6743))
| ~ sP376(U_6739,U_6743,U_6741) )
& ! [U_6739,U_6743,U_6741] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6739))
| ~ sP376(U_6739,U_6743,U_6741) )
& ! [U_6739,U_6743,U_6741] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6739),U_6741)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6739),U_6743)))
| sP376(U_6739,U_6743,U_6741) )
& ! [U_6742,U_6738,U_6740] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6740),U_6742))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6738))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6738),U_6740)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6738),U_6742))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP376])],[f_1562_3]) ).
cnf(f_1562_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6740),U_6742))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6738))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6738),U_6740)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6738),U_6742))) ),
inference(clausify,[status(thm)],[f_1562_4]) ).
cnf(f_1562_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_6739),U_6741)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6739),U_6743)))
| sP376(U_6739,U_6743,U_6741) ),
inference(clausify,[status(thm)],[f_1562_4]) ).
cnf(f_1562_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6739))
| ~ sP376(U_6739,U_6743,U_6741) ),
inference(clausify,[status(thm)],[f_1562_4]) ).
cnf(f_1562_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6741),U_6743))
| ~ sP376(U_6739,U_6743,U_6741) ),
inference(clausify,[status(thm)],[f_1562_4]) ).
fof(f_1563_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_1563_2,plain,
! [U_6746,U_6745,U_6744] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6744),U_6745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6746),U_6745)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6744),U_6746))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6745)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6744),U_6746))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6745))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6744),U_6745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6746),U_6745))) ) ),
inference(variable_rename,[status(thm)],[f_1563_1]) ).
fof(f_1563_3,plain,
( ! [U_6752,U_6750,U_6748] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6748),U_6750)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6752),U_6750)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6748),U_6752))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6750)) ) )
& ! [U_6751,U_6749,U_6747] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6747),U_6751))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6747),U_6749)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6751),U_6749))) ) ),
inference(miniscope,[status(thm)],[f_1563_2]) ).
fof(f_1563_4,plain,
( ! [U_6750,U_6752,U_6748] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6748),U_6752))
| ~ sP377(U_6750,U_6752,U_6748) )
& ! [U_6750,U_6752,U_6748] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6750))
| ~ sP377(U_6750,U_6752,U_6748) )
& ! [U_6750,U_6752,U_6748] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6748),U_6750)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6752),U_6750)))
| sP377(U_6750,U_6752,U_6748) )
& ! [U_6749,U_6747,U_6751] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6747),U_6751))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6747),U_6749)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6751),U_6749))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP377])],[f_1563_3]) ).
cnf(f_1563_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6747),U_6751))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6747),U_6749)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6751),U_6749))) ),
inference(clausify,[status(thm)],[f_1563_4]) ).
cnf(f_1563_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_6748),U_6750)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6752),U_6750)))
| sP377(U_6750,U_6752,U_6748) ),
inference(clausify,[status(thm)],[f_1563_4]) ).
cnf(f_1563_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6750))
| ~ sP377(U_6750,U_6752,U_6748) ),
inference(clausify,[status(thm)],[f_1563_4]) ).
cnf(f_1563_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6748),U_6752))
| ~ sP377(U_6750,U_6752,U_6748) ),
inference(clausify,[status(thm)],[f_1563_4]) ).
fof(f_1564_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_1564_2,plain,
! [U_6755,U_6754,U_6753] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6753),U_6754)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6753),U_6755)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6754),U_6755)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6754),U_6755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6753),U_6754)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6753),U_6755))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6753)) ),
inference(variable_rename,[status(thm)],[f_1564_1]) ).
fof(f_1564_3,plain,
( ! [U_6754,U_6755,U_6753] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6753),U_6754)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6753),U_6755)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6754),U_6755))
| ~ sP378(U_6754,U_6755,U_6753) )
& ! [U_6754,U_6755,U_6753] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6754),U_6755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6753),U_6754)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6753),U_6755)))
| ~ sP378(U_6754,U_6755,U_6753) )
& ! [U_6754,U_6755,U_6753] :
( sP378(U_6754,U_6755,U_6753)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6753)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP378])],[f_1564_2]) ).
cnf(f_1564_4,plain,
( sP378(U_6754,U_6755,U_6753)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6753)) ),
inference(clausify,[status(thm)],[f_1564_3]) ).
cnf(f_1564_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6754),U_6755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6753),U_6754)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6753),U_6755)))
| ~ sP378(U_6754,U_6755,U_6753) ),
inference(clausify,[status(thm)],[f_1564_3]) ).
cnf(f_1564_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_6753),U_6754)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6753),U_6755)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6754),U_6755))
| ~ sP378(U_6754,U_6755,U_6753) ),
inference(clausify,[status(thm)],[f_1564_3]) ).
fof(f_1565_1,plain,
! [V_f_2,V_A_2,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_c),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_c),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_c),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_c),B_x),V_A_2)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__eq__Suc0__iff]) ).
fof(f_1565_2,plain,
! [U_6762,U_6761,U_6760] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6760,tc_Nat_Onat),U_6762),U_6761) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [U_6759] :
( ? [U_6758] :
( hAPP(U_6762,U_6758) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6759 != U_6758
& hBOOL(hAPP(hAPP(c_member(U_6760),U_6758),U_6761)) )
| hAPP(U_6762,U_6759) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_6760),U_6759),U_6761)) ) )
& ( ? [U_6757] :
( ! [U_6756] :
( hAPP(U_6762,U_6756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6757 = U_6756
| ~ hBOOL(hAPP(hAPP(c_member(U_6760),U_6756),U_6761)) )
& hAPP(U_6762,U_6757) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(U_6760),U_6757),U_6761)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6760,tc_Nat_Onat),U_6762),U_6761) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6760),U_6761)) ),
inference(variable_rename,[status(thm)],[f_1565_1]) ).
fof(f_1565_3,plain,
! [U_6762,U_6761,U_6760] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6760,tc_Nat_Onat),U_6762),U_6761) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [U_6759] :
( ? [U_6758] :
( hAPP(U_6762,U_6758) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6759 != U_6758
& hBOOL(hAPP(hAPP(c_member(U_6760),U_6758),U_6761)) )
| hAPP(U_6762,U_6759) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_6760),U_6759),U_6761)) ) )
& ( ( ! [U_6756] :
( hAPP(U_6762,U_6756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK127(U_6762,U_6761,U_6760) = U_6756
| ~ hBOOL(hAPP(hAPP(c_member(U_6760),U_6756),U_6761)) )
& hAPP(U_6762,sK127(U_6762,U_6761,U_6760)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(U_6760),sK127(U_6762,U_6761,U_6760)),U_6761)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6760,tc_Nat_Onat),U_6762),U_6761) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6760),U_6761)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_6757,sK127(U_6762,U_6761,U_6760))],[f_1565_2]) ).
fof(f_1565_4,plain,
! [U_6762,U_6761,U_6760] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6760,tc_Nat_Onat),U_6762),U_6761) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [U_6759] :
( ( hAPP(U_6762,sK128(U_6762,U_6761,U_6760,U_6759)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6759 != sK128(U_6762,U_6761,U_6760,U_6759)
& hBOOL(hAPP(hAPP(c_member(U_6760),sK128(U_6762,U_6761,U_6760,U_6759)),U_6761)) )
| hAPP(U_6762,U_6759) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_6760),U_6759),U_6761)) ) )
& ( ( ! [U_6756] :
( hAPP(U_6762,U_6756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK127(U_6762,U_6761,U_6760) = U_6756
| ~ hBOOL(hAPP(hAPP(c_member(U_6760),U_6756),U_6761)) )
& hAPP(U_6762,sK127(U_6762,U_6761,U_6760)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(U_6760),sK127(U_6762,U_6761,U_6760)),U_6761)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6760,tc_Nat_Onat),U_6762),U_6761) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6760),U_6761)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_6758,sK128(U_6762,U_6761,U_6760,U_6759))],[f_1565_3]) ).
fof(f_1565_5,plain,
( ! [U_6759,U_6760,U_6761,U_6762] :
( hAPP(U_6762,sK128(U_6762,U_6761,U_6760,U_6759)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP380(U_6759,U_6760,U_6761,U_6762) )
& ! [U_6759,U_6760,U_6761,U_6762] :
( U_6759 != sK128(U_6762,U_6761,U_6760,U_6759)
| ~ sP380(U_6759,U_6760,U_6761,U_6762) )
& ! [U_6759,U_6760,U_6761,U_6762] :
( hBOOL(hAPP(hAPP(c_member(U_6760),sK128(U_6762,U_6761,U_6760,U_6759)),U_6761))
| ~ sP380(U_6759,U_6760,U_6761,U_6762) )
& ! [U_6756,U_6760,U_6761,U_6762] :
( hAPP(U_6762,U_6756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK127(U_6762,U_6761,U_6760) = U_6756
| ~ hBOOL(hAPP(hAPP(c_member(U_6760),U_6756),U_6761))
| ~ sP379(U_6756,U_6760,U_6761,U_6762) )
& ! [U_6756,U_6760,U_6761,U_6762] :
( hAPP(U_6762,sK127(U_6762,U_6761,U_6760)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP379(U_6756,U_6760,U_6761,U_6762) )
& ! [U_6756,U_6760,U_6761,U_6762] :
( hBOOL(hAPP(hAPP(c_member(U_6760),sK127(U_6762,U_6761,U_6760)),U_6761))
| ~ sP379(U_6756,U_6760,U_6761,U_6762) )
& ! [U_6756,U_6759,U_6760,U_6761,U_6762] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6760,tc_Nat_Onat),U_6762),U_6761) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP380(U_6759,U_6760,U_6761,U_6762)
| hAPP(U_6762,U_6759) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_6760),U_6759),U_6761))
| ~ sP381(U_6756,U_6759,U_6760,U_6761,U_6762) )
& ! [U_6756,U_6759,U_6760,U_6761,U_6762] :
( sP379(U_6756,U_6760,U_6761,U_6762)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6760,tc_Nat_Onat),U_6762),U_6761) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP381(U_6756,U_6759,U_6760,U_6761,U_6762) )
& ! [U_6756,U_6759,U_6760,U_6761,U_6762] :
( sP381(U_6756,U_6759,U_6760,U_6761,U_6762)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6760),U_6761)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP379,sP380,sP381])],[f_1565_4]) ).
cnf(f_1565_6,plain,
( sP381(U_6756,U_6759,U_6760,U_6761,U_6762)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6760),U_6761)) ),
inference(clausify,[status(thm)],[f_1565_5]) ).
cnf(f_1565_7,plain,
( sP379(U_6756,U_6760,U_6761,U_6762)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6760,tc_Nat_Onat),U_6762),U_6761) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP381(U_6756,U_6759,U_6760,U_6761,U_6762) ),
inference(clausify,[status(thm)],[f_1565_5]) ).
cnf(f_1565_8,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6760,tc_Nat_Onat),U_6762),U_6761) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP380(U_6759,U_6760,U_6761,U_6762)
| hAPP(U_6762,U_6759) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_6760),U_6759),U_6761))
| ~ sP381(U_6756,U_6759,U_6760,U_6761,U_6762) ),
inference(clausify,[status(thm)],[f_1565_5]) ).
cnf(f_1565_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_6760),sK127(U_6762,U_6761,U_6760)),U_6761))
| ~ sP379(U_6756,U_6760,U_6761,U_6762) ),
inference(clausify,[status(thm)],[f_1565_5]) ).
cnf(f_1565_10,plain,
( hAPP(U_6762,sK127(U_6762,U_6761,U_6760)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP379(U_6756,U_6760,U_6761,U_6762) ),
inference(clausify,[status(thm)],[f_1565_5]) ).
cnf(f_1565_11,plain,
( hAPP(U_6762,U_6756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK127(U_6762,U_6761,U_6760) = U_6756
| ~ hBOOL(hAPP(hAPP(c_member(U_6760),U_6756),U_6761))
| ~ sP379(U_6756,U_6760,U_6761,U_6762) ),
inference(clausify,[status(thm)],[f_1565_5]) ).
cnf(f_1565_12,plain,
( hBOOL(hAPP(hAPP(c_member(U_6760),sK128(U_6762,U_6761,U_6760,U_6759)),U_6761))
| ~ sP380(U_6759,U_6760,U_6761,U_6762) ),
inference(clausify,[status(thm)],[f_1565_5]) ).
cnf(f_1565_13,plain,
( U_6759 != sK128(U_6762,U_6761,U_6760,U_6759)
| ~ sP380(U_6759,U_6760,U_6761,U_6762) ),
inference(clausify,[status(thm)],[f_1565_5]) ).
cnf(f_1565_14,plain,
( hAPP(U_6762,sK128(U_6762,U_6761,U_6760,U_6759)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP380(U_6759,U_6760,U_6761,U_6762) ),
inference(clausify,[status(thm)],[f_1565_5]) ).
fof(f_1566_1,plain,
! [V_f_2,V_A_2,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_c),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_c),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_c),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_c),B_x),V_A_2)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__eq__1__iff]) ).
fof(f_1566_2,plain,
! [U_6769,U_6768,U_6767] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6767,tc_Nat_Onat),U_6769),U_6768) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [U_6766] :
( ? [U_6765] :
( hAPP(U_6769,U_6765) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6766 != U_6765
& hBOOL(hAPP(hAPP(c_member(U_6767),U_6765),U_6768)) )
| hAPP(U_6769,U_6766) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_6767),U_6766),U_6768)) ) )
& ( ? [U_6764] :
( ! [U_6763] :
( hAPP(U_6769,U_6763) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6764 = U_6763
| ~ hBOOL(hAPP(hAPP(c_member(U_6767),U_6763),U_6768)) )
& hAPP(U_6769,U_6764) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_6767),U_6764),U_6768)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6767,tc_Nat_Onat),U_6769),U_6768) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6767),U_6768)) ),
inference(variable_rename,[status(thm)],[f_1566_1]) ).
fof(f_1566_3,plain,
! [U_6769,U_6768,U_6767] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6767,tc_Nat_Onat),U_6769),U_6768) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [U_6766] :
( ? [U_6765] :
( hAPP(U_6769,U_6765) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6766 != U_6765
& hBOOL(hAPP(hAPP(c_member(U_6767),U_6765),U_6768)) )
| hAPP(U_6769,U_6766) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_6767),U_6766),U_6768)) ) )
& ( ( ! [U_6763] :
( hAPP(U_6769,U_6763) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK129(U_6769,U_6768,U_6767) = U_6763
| ~ hBOOL(hAPP(hAPP(c_member(U_6767),U_6763),U_6768)) )
& hAPP(U_6769,sK129(U_6769,U_6768,U_6767)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_6767),sK129(U_6769,U_6768,U_6767)),U_6768)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6767,tc_Nat_Onat),U_6769),U_6768) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6767),U_6768)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_6764,sK129(U_6769,U_6768,U_6767))],[f_1566_2]) ).
fof(f_1566_4,plain,
! [U_6769,U_6768,U_6767] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6767,tc_Nat_Onat),U_6769),U_6768) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [U_6766] :
( ( hAPP(U_6769,sK130(U_6769,U_6768,U_6767,U_6766)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6766 != sK130(U_6769,U_6768,U_6767,U_6766)
& hBOOL(hAPP(hAPP(c_member(U_6767),sK130(U_6769,U_6768,U_6767,U_6766)),U_6768)) )
| hAPP(U_6769,U_6766) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_6767),U_6766),U_6768)) ) )
& ( ( ! [U_6763] :
( hAPP(U_6769,U_6763) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK129(U_6769,U_6768,U_6767) = U_6763
| ~ hBOOL(hAPP(hAPP(c_member(U_6767),U_6763),U_6768)) )
& hAPP(U_6769,sK129(U_6769,U_6768,U_6767)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_6767),sK129(U_6769,U_6768,U_6767)),U_6768)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6767,tc_Nat_Onat),U_6769),U_6768) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6767),U_6768)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_6765,sK130(U_6769,U_6768,U_6767,U_6766))],[f_1566_3]) ).
fof(f_1566_5,plain,
( ! [U_6769,U_6766,U_6768,U_6767] :
( hAPP(U_6769,sK130(U_6769,U_6768,U_6767,U_6766)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP383(U_6769,U_6766,U_6768,U_6767) )
& ! [U_6769,U_6766,U_6768,U_6767] :
( U_6766 != sK130(U_6769,U_6768,U_6767,U_6766)
| ~ sP383(U_6769,U_6766,U_6768,U_6767) )
& ! [U_6769,U_6766,U_6768,U_6767] :
( hBOOL(hAPP(hAPP(c_member(U_6767),sK130(U_6769,U_6768,U_6767,U_6766)),U_6768))
| ~ sP383(U_6769,U_6766,U_6768,U_6767) )
& ! [U_6769,U_6768,U_6767,U_6763] :
( hAPP(U_6769,U_6763) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK129(U_6769,U_6768,U_6767) = U_6763
| ~ hBOOL(hAPP(hAPP(c_member(U_6767),U_6763),U_6768))
| ~ sP382(U_6769,U_6768,U_6767,U_6763) )
& ! [U_6769,U_6768,U_6767,U_6763] :
( hAPP(U_6769,sK129(U_6769,U_6768,U_6767)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP382(U_6769,U_6768,U_6767,U_6763) )
& ! [U_6769,U_6768,U_6767,U_6763] :
( hBOOL(hAPP(hAPP(c_member(U_6767),sK129(U_6769,U_6768,U_6767)),U_6768))
| ~ sP382(U_6769,U_6768,U_6767,U_6763) )
& ! [U_6769,U_6766,U_6768,U_6767,U_6763] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6767,tc_Nat_Onat),U_6769),U_6768) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| sP383(U_6769,U_6766,U_6768,U_6767)
| hAPP(U_6769,U_6766) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_6767),U_6766),U_6768))
| ~ sP384(U_6769,U_6766,U_6768,U_6767,U_6763) )
& ! [U_6769,U_6766,U_6768,U_6767,U_6763] :
( sP382(U_6769,U_6768,U_6767,U_6763)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6767,tc_Nat_Onat),U_6769),U_6768) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP384(U_6769,U_6766,U_6768,U_6767,U_6763) )
& ! [U_6769,U_6766,U_6768,U_6767,U_6763] :
( sP384(U_6769,U_6766,U_6768,U_6767,U_6763)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6767),U_6768)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP382,sP383,sP384])],[f_1566_4]) ).
cnf(f_1566_6,plain,
( sP384(U_6769,U_6766,U_6768,U_6767,U_6763)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6767),U_6768)) ),
inference(clausify,[status(thm)],[f_1566_5]) ).
cnf(f_1566_7,plain,
( sP382(U_6769,U_6768,U_6767,U_6763)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6767,tc_Nat_Onat),U_6769),U_6768) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP384(U_6769,U_6766,U_6768,U_6767,U_6763) ),
inference(clausify,[status(thm)],[f_1566_5]) ).
cnf(f_1566_8,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6767,tc_Nat_Onat),U_6769),U_6768) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| sP383(U_6769,U_6766,U_6768,U_6767)
| hAPP(U_6769,U_6766) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_6767),U_6766),U_6768))
| ~ sP384(U_6769,U_6766,U_6768,U_6767,U_6763) ),
inference(clausify,[status(thm)],[f_1566_5]) ).
cnf(f_1566_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_6767),sK129(U_6769,U_6768,U_6767)),U_6768))
| ~ sP382(U_6769,U_6768,U_6767,U_6763) ),
inference(clausify,[status(thm)],[f_1566_5]) ).
cnf(f_1566_10,plain,
( hAPP(U_6769,sK129(U_6769,U_6768,U_6767)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP382(U_6769,U_6768,U_6767,U_6763) ),
inference(clausify,[status(thm)],[f_1566_5]) ).
cnf(f_1566_11,plain,
( hAPP(U_6769,U_6763) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK129(U_6769,U_6768,U_6767) = U_6763
| ~ hBOOL(hAPP(hAPP(c_member(U_6767),U_6763),U_6768))
| ~ sP382(U_6769,U_6768,U_6767,U_6763) ),
inference(clausify,[status(thm)],[f_1566_5]) ).
cnf(f_1566_12,plain,
( hBOOL(hAPP(hAPP(c_member(U_6767),sK130(U_6769,U_6768,U_6767,U_6766)),U_6768))
| ~ sP383(U_6769,U_6766,U_6768,U_6767) ),
inference(clausify,[status(thm)],[f_1566_5]) ).
cnf(f_1566_13,plain,
( U_6766 != sK130(U_6769,U_6768,U_6767,U_6766)
| ~ sP383(U_6769,U_6766,U_6768,U_6767) ),
inference(clausify,[status(thm)],[f_1566_5]) ).
cnf(f_1566_14,plain,
( hAPP(U_6769,sK130(U_6769,U_6768,U_6767,U_6766)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP383(U_6769,U_6766,U_6768,U_6767) ),
inference(clausify,[status(thm)],[f_1566_5]) ).
fof(f_1567_1,plain,
! [V_b_2,V_a_2,V_S_2,T_c,T_d] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_d))),V_S_2) = c_Groups_Ozero__class_Ozero(T_d)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_d))),V_S_2) = hAPP(V_b_2,V_a_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__delta]) ).
fof(f_1567_2,plain,
! [U_6774,U_6773,U_6772,U_6771,U_6770] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),hAPP(hAPP(c_COMBC(U_6771,U_6770,U_6770),hAPP(hAPP(c_COMBS(U_6771,U_6770,tc_fun(U_6770,U_6770)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6770,tc_fun(U_6770,U_6770)),U_6771),c_If(U_6770)),hAPP(hAPP(c_COMBC(U_6771,U_6771,tc_HOL_Obool),c_fequal),U_6773))),U_6774)),c_Groups_Ozero__class_Ozero(U_6770))),U_6772) = c_Groups_Ozero__class_Ozero(U_6770)
| hBOOL(hAPP(hAPP(c_member(U_6771),U_6773),U_6772)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),hAPP(hAPP(c_COMBC(U_6771,U_6770,U_6770),hAPP(hAPP(c_COMBS(U_6771,U_6770,tc_fun(U_6770,U_6770)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6770,tc_fun(U_6770,U_6770)),U_6771),c_If(U_6770)),hAPP(hAPP(c_COMBC(U_6771,U_6771,tc_HOL_Obool),c_fequal),U_6773))),U_6774)),c_Groups_Ozero__class_Ozero(U_6770))),U_6772) = hAPP(U_6774,U_6773)
| ~ hBOOL(hAPP(hAPP(c_member(U_6771),U_6773),U_6772)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6771),U_6772))
| ~ class_Groups_Ocomm__monoid__add(U_6770) ),
inference(variable_rename,[status(thm)],[f_1567_1]) ).
fof(f_1567_3,plain,
( ! [U_6772,U_6773,U_6774,U_6771,U_6770] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),hAPP(hAPP(c_COMBC(U_6771,U_6770,U_6770),hAPP(hAPP(c_COMBS(U_6771,U_6770,tc_fun(U_6770,U_6770)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6770,tc_fun(U_6770,U_6770)),U_6771),c_If(U_6770)),hAPP(hAPP(c_COMBC(U_6771,U_6771,tc_HOL_Obool),c_fequal),U_6773))),U_6774)),c_Groups_Ozero__class_Ozero(U_6770))),U_6772) = c_Groups_Ozero__class_Ozero(U_6770)
| hBOOL(hAPP(hAPP(c_member(U_6771),U_6773),U_6772))
| ~ sP385(U_6772,U_6773,U_6774,U_6771,U_6770) )
& ! [U_6772,U_6773,U_6774,U_6771,U_6770] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),hAPP(hAPP(c_COMBC(U_6771,U_6770,U_6770),hAPP(hAPP(c_COMBS(U_6771,U_6770,tc_fun(U_6770,U_6770)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6770,tc_fun(U_6770,U_6770)),U_6771),c_If(U_6770)),hAPP(hAPP(c_COMBC(U_6771,U_6771,tc_HOL_Obool),c_fequal),U_6773))),U_6774)),c_Groups_Ozero__class_Ozero(U_6770))),U_6772) = hAPP(U_6774,U_6773)
| ~ hBOOL(hAPP(hAPP(c_member(U_6771),U_6773),U_6772))
| ~ sP385(U_6772,U_6773,U_6774,U_6771,U_6770) )
& ! [U_6772,U_6773,U_6774,U_6771,U_6770] :
( sP385(U_6772,U_6773,U_6774,U_6771,U_6770)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6771),U_6772))
| ~ class_Groups_Ocomm__monoid__add(U_6770) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP385])],[f_1567_2]) ).
cnf(f_1567_4,plain,
( sP385(U_6772,U_6773,U_6774,U_6771,U_6770)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6771),U_6772))
| ~ class_Groups_Ocomm__monoid__add(U_6770) ),
inference(clausify,[status(thm)],[f_1567_3]) ).
cnf(f_1567_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),hAPP(hAPP(c_COMBC(U_6771,U_6770,U_6770),hAPP(hAPP(c_COMBS(U_6771,U_6770,tc_fun(U_6770,U_6770)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6770,tc_fun(U_6770,U_6770)),U_6771),c_If(U_6770)),hAPP(hAPP(c_COMBC(U_6771,U_6771,tc_HOL_Obool),c_fequal),U_6773))),U_6774)),c_Groups_Ozero__class_Ozero(U_6770))),U_6772) = hAPP(U_6774,U_6773)
| ~ hBOOL(hAPP(hAPP(c_member(U_6771),U_6773),U_6772))
| ~ sP385(U_6772,U_6773,U_6774,U_6771,U_6770) ),
inference(clausify,[status(thm)],[f_1567_3]) ).
cnf(f_1567_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),hAPP(hAPP(c_COMBC(U_6771,U_6770,U_6770),hAPP(hAPP(c_COMBS(U_6771,U_6770,tc_fun(U_6770,U_6770)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6770,tc_fun(U_6770,U_6770)),U_6771),c_If(U_6770)),hAPP(hAPP(c_COMBC(U_6771,U_6771,tc_HOL_Obool),c_fequal),U_6773))),U_6774)),c_Groups_Ozero__class_Ozero(U_6770))),U_6772) = c_Groups_Ozero__class_Ozero(U_6770)
| hBOOL(hAPP(hAPP(c_member(U_6771),U_6773),U_6772))
| ~ sP385(U_6772,U_6773,U_6774,U_6771,U_6770) ),
inference(clausify,[status(thm)],[f_1567_3]) ).
fof(f_1568_1,plain,
! [V_b_2,V_a_2,V_S_2,T_c,T_d] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_d))),V_S_2) = c_Groups_Ozero__class_Ozero(T_d)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_d))),V_S_2) = hAPP(V_b_2,V_a_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__delta_H]) ).
fof(f_1568_2,plain,
! [U_6779,U_6778,U_6777,U_6776,U_6775] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6776,U_6775),hAPP(hAPP(c_COMBC(U_6776,U_6775,U_6775),hAPP(hAPP(c_COMBS(U_6776,U_6775,tc_fun(U_6775,U_6775)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6775,tc_fun(U_6775,U_6775)),U_6776),c_If(U_6775)),hAPP(c_fequal,U_6778))),U_6779)),c_Groups_Ozero__class_Ozero(U_6775))),U_6777) = c_Groups_Ozero__class_Ozero(U_6775)
| hBOOL(hAPP(hAPP(c_member(U_6776),U_6778),U_6777)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6776,U_6775),hAPP(hAPP(c_COMBC(U_6776,U_6775,U_6775),hAPP(hAPP(c_COMBS(U_6776,U_6775,tc_fun(U_6775,U_6775)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6775,tc_fun(U_6775,U_6775)),U_6776),c_If(U_6775)),hAPP(c_fequal,U_6778))),U_6779)),c_Groups_Ozero__class_Ozero(U_6775))),U_6777) = hAPP(U_6779,U_6778)
| ~ hBOOL(hAPP(hAPP(c_member(U_6776),U_6778),U_6777)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6776),U_6777))
| ~ class_Groups_Ocomm__monoid__add(U_6775) ),
inference(variable_rename,[status(thm)],[f_1568_1]) ).
fof(f_1568_3,plain,
( ! [U_6776,U_6777,U_6779,U_6778,U_6775] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6776,U_6775),hAPP(hAPP(c_COMBC(U_6776,U_6775,U_6775),hAPP(hAPP(c_COMBS(U_6776,U_6775,tc_fun(U_6775,U_6775)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6775,tc_fun(U_6775,U_6775)),U_6776),c_If(U_6775)),hAPP(c_fequal,U_6778))),U_6779)),c_Groups_Ozero__class_Ozero(U_6775))),U_6777) = c_Groups_Ozero__class_Ozero(U_6775)
| hBOOL(hAPP(hAPP(c_member(U_6776),U_6778),U_6777))
| ~ sP386(U_6776,U_6777,U_6779,U_6778,U_6775) )
& ! [U_6776,U_6777,U_6779,U_6778,U_6775] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6776,U_6775),hAPP(hAPP(c_COMBC(U_6776,U_6775,U_6775),hAPP(hAPP(c_COMBS(U_6776,U_6775,tc_fun(U_6775,U_6775)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6775,tc_fun(U_6775,U_6775)),U_6776),c_If(U_6775)),hAPP(c_fequal,U_6778))),U_6779)),c_Groups_Ozero__class_Ozero(U_6775))),U_6777) = hAPP(U_6779,U_6778)
| ~ hBOOL(hAPP(hAPP(c_member(U_6776),U_6778),U_6777))
| ~ sP386(U_6776,U_6777,U_6779,U_6778,U_6775) )
& ! [U_6776,U_6777,U_6779,U_6778,U_6775] :
( sP386(U_6776,U_6777,U_6779,U_6778,U_6775)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6776),U_6777))
| ~ class_Groups_Ocomm__monoid__add(U_6775) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP386])],[f_1568_2]) ).
cnf(f_1568_4,plain,
( sP386(U_6776,U_6777,U_6779,U_6778,U_6775)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6776),U_6777))
| ~ class_Groups_Ocomm__monoid__add(U_6775) ),
inference(clausify,[status(thm)],[f_1568_3]) ).
cnf(f_1568_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6776,U_6775),hAPP(hAPP(c_COMBC(U_6776,U_6775,U_6775),hAPP(hAPP(c_COMBS(U_6776,U_6775,tc_fun(U_6775,U_6775)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6775,tc_fun(U_6775,U_6775)),U_6776),c_If(U_6775)),hAPP(c_fequal,U_6778))),U_6779)),c_Groups_Ozero__class_Ozero(U_6775))),U_6777) = hAPP(U_6779,U_6778)
| ~ hBOOL(hAPP(hAPP(c_member(U_6776),U_6778),U_6777))
| ~ sP386(U_6776,U_6777,U_6779,U_6778,U_6775) ),
inference(clausify,[status(thm)],[f_1568_3]) ).
cnf(f_1568_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6776,U_6775),hAPP(hAPP(c_COMBC(U_6776,U_6775,U_6775),hAPP(hAPP(c_COMBS(U_6776,U_6775,tc_fun(U_6775,U_6775)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6775,tc_fun(U_6775,U_6775)),U_6776),c_If(U_6775)),hAPP(c_fequal,U_6778))),U_6779)),c_Groups_Ozero__class_Ozero(U_6775))),U_6777) = c_Groups_Ozero__class_Ozero(U_6775)
| hBOOL(hAPP(hAPP(c_member(U_6776),U_6778),U_6777))
| ~ sP386(U_6776,U_6777,U_6779,U_6778,U_6775) ),
inference(clausify,[status(thm)],[f_1568_3]) ).
fof(f_1569_1,plain,
! [V_f_2,V_S_2,T_c] :
( ( ( 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_c,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_c),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_c),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_c,tc_Nat_Onat),V_f_2),V_S_2))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) ),
inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat__iff]) ).
fof(f_1569_2,plain,
! [U_6784,U_6783,U_6782] :
( ( ( 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_6782,tc_Nat_Onat),U_6784),U_6783)))
| ? [U_6781] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6784,U_6781)))
& hBOOL(hAPP(hAPP(c_member(U_6782),U_6781),U_6783)) ) )
& ( ! [U_6780] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6784,U_6780)))
| ~ hBOOL(hAPP(hAPP(c_member(U_6782),U_6780),U_6783)) )
| ~ 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_6782,tc_Nat_Onat),U_6784),U_6783))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6782),U_6783)) ),
inference(variable_rename,[status(thm)],[f_1569_1]) ).
fof(f_1569_3,plain,
! [U_6784,U_6783,U_6782] :
( ( ( 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_6782,tc_Nat_Onat),U_6784),U_6783)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6784,sK131(U_6784,U_6783,U_6782))))
& hBOOL(hAPP(hAPP(c_member(U_6782),sK131(U_6784,U_6783,U_6782)),U_6783)) ) )
& ( ! [U_6780] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6784,U_6780)))
| ~ hBOOL(hAPP(hAPP(c_member(U_6782),U_6780),U_6783)) )
| ~ 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_6782,tc_Nat_Onat),U_6784),U_6783))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6782),U_6783)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_6781,sK131(U_6784,U_6783,U_6782))],[f_1569_2]) ).
fof(f_1569_4,plain,
( ! [U_6784,U_6783,U_6782] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6784,sK131(U_6784,U_6783,U_6782))))
| ~ sP387(U_6784,U_6783,U_6782) )
& ! [U_6784,U_6783,U_6782] :
( hBOOL(hAPP(hAPP(c_member(U_6782),sK131(U_6784,U_6783,U_6782)),U_6783))
| ~ sP387(U_6784,U_6783,U_6782) )
& ! [U_6784,U_6783,U_6780,U_6782] :
( 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_6782,tc_Nat_Onat),U_6784),U_6783)))
| sP387(U_6784,U_6783,U_6782)
| ~ sP388(U_6784,U_6783,U_6780,U_6782) )
& ! [U_6784,U_6783,U_6780,U_6782] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6784,U_6780)))
| ~ hBOOL(hAPP(hAPP(c_member(U_6782),U_6780),U_6783))
| ~ 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_6782,tc_Nat_Onat),U_6784),U_6783)))
| ~ sP388(U_6784,U_6783,U_6780,U_6782) )
& ! [U_6784,U_6783,U_6780,U_6782] :
( sP388(U_6784,U_6783,U_6780,U_6782)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6782),U_6783)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP387,sP388])],[f_1569_3]) ).
cnf(f_1569_5,plain,
( sP388(U_6784,U_6783,U_6780,U_6782)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6782),U_6783)) ),
inference(clausify,[status(thm)],[f_1569_4]) ).
cnf(f_1569_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6784,U_6780)))
| ~ hBOOL(hAPP(hAPP(c_member(U_6782),U_6780),U_6783))
| ~ 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_6782,tc_Nat_Onat),U_6784),U_6783)))
| ~ sP388(U_6784,U_6783,U_6780,U_6782) ),
inference(clausify,[status(thm)],[f_1569_4]) ).
cnf(f_1569_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_6782,tc_Nat_Onat),U_6784),U_6783)))
| sP387(U_6784,U_6783,U_6782)
| ~ sP388(U_6784,U_6783,U_6780,U_6782) ),
inference(clausify,[status(thm)],[f_1569_4]) ).
cnf(f_1569_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_6782),sK131(U_6784,U_6783,U_6782)),U_6783))
| ~ sP387(U_6784,U_6783,U_6782) ),
inference(clausify,[status(thm)],[f_1569_4]) ).
cnf(f_1569_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6784,sK131(U_6784,U_6783,U_6782))))
| ~ sP387(U_6784,U_6783,U_6782) ),
inference(clausify,[status(thm)],[f_1569_4]) ).
fof(f_1570_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_1570_2,plain,
! [U_6790,U_6789,U_6788,U_6787,U_6786,U_6785] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6785),U_6789),U_6786)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6785),U_6790),U_6788))),U_6787))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6785),U_6789),U_6790) != c_Groups_Oone__class_Oone(U_6785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),c_Groups_Ozero__class_Ozero(U_6785)),U_6790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),c_Groups_Ozero__class_Ozero(U_6785)),U_6789))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),U_6788),U_6787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),U_6786),U_6787))
| ~ class_Rings_Olinordered__semiring__1(U_6785) ),
inference(variable_rename,[status(thm)],[f_1570_1]) ).
fof(f_1570_3,plain,
! [U_6787,U_6789,U_6788,U_6790,U_6785,U_6786] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6785),U_6789),U_6786)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6785),U_6790),U_6788))),U_6787))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6785),U_6789),U_6790) != c_Groups_Oone__class_Oone(U_6785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),c_Groups_Ozero__class_Ozero(U_6785)),U_6790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),c_Groups_Ozero__class_Ozero(U_6785)),U_6789))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),U_6788),U_6787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),U_6786),U_6787))
| ~ class_Rings_Olinordered__semiring__1(U_6785) ),
inference(definitional_conversion,[status(esa)],[f_1570_2]) ).
cnf(f_1570_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6785),U_6789),U_6786)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6785),U_6790),U_6788))),U_6787))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6785),U_6789),U_6790) != c_Groups_Oone__class_Oone(U_6785)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),c_Groups_Ozero__class_Ozero(U_6785)),U_6790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),c_Groups_Ozero__class_Ozero(U_6785)),U_6789))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),U_6788),U_6787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6785),U_6786),U_6787))
| ~ class_Rings_Olinordered__semiring__1(U_6785) ),
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_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_1571_2,plain,
! [U_6793,U_6792,U_6791] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6791),U_6792),hAPP(hAPP(c_Power_Opower__class_Opower(U_6791),U_6792),U_6793))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6791),U_6792),U_6793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6791),U_6792),c_Groups_Oone__class_Oone(U_6791)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6791),c_Groups_Ozero__class_Ozero(U_6791)),U_6792))
| ~ class_Rings_Olinordered__semidom(U_6791) ),
inference(variable_rename,[status(thm)],[f_1571_1]) ).
fof(f_1571_3,plain,
! [U_6792,U_6793,U_6791] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6791),U_6792),hAPP(hAPP(c_Power_Opower__class_Opower(U_6791),U_6792),U_6793))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6791),U_6792),U_6793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6791),U_6792),c_Groups_Oone__class_Oone(U_6791)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6791),c_Groups_Ozero__class_Ozero(U_6791)),U_6792))
| ~ class_Rings_Olinordered__semidom(U_6791) ),
inference(definitional_conversion,[status(esa)],[f_1571_2]) ).
cnf(f_1571_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6791),U_6792),hAPP(hAPP(c_Power_Opower__class_Opower(U_6791),U_6792),U_6793))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6791),U_6792),U_6793)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6791),U_6792),c_Groups_Oone__class_Oone(U_6791)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6791),c_Groups_Ozero__class_Ozero(U_6791)),U_6792))
| ~ class_Rings_Olinordered__semidom(U_6791) ),
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),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_1572_2,plain,
! [U_6796,U_6795,U_6794] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6794),hAPP(hAPP(c_Power_Opower__class_Opower(U_6794),U_6795),hAPP(c_Nat_OSuc,U_6796))),c_Groups_Oone__class_Oone(U_6794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6794),U_6795),c_Groups_Oone__class_Oone(U_6794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6794),c_Groups_Ozero__class_Ozero(U_6794)),U_6795))
| ~ class_Rings_Olinordered__semidom(U_6794) ),
inference(variable_rename,[status(thm)],[f_1572_1]) ).
fof(f_1572_3,plain,
! [U_6794,U_6795,U_6796] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6794),hAPP(hAPP(c_Power_Opower__class_Opower(U_6794),U_6795),hAPP(c_Nat_OSuc,U_6796))),c_Groups_Oone__class_Oone(U_6794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6794),U_6795),c_Groups_Oone__class_Oone(U_6794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6794),c_Groups_Ozero__class_Ozero(U_6794)),U_6795))
| ~ class_Rings_Olinordered__semidom(U_6794) ),
inference(definitional_conversion,[status(esa)],[f_1572_2]) ).
cnf(f_1572_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6794),hAPP(hAPP(c_Power_Opower__class_Opower(U_6794),U_6795),hAPP(c_Nat_OSuc,U_6796))),c_Groups_Oone__class_Oone(U_6794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6794),U_6795),c_Groups_Oone__class_Oone(U_6794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6794),c_Groups_Ozero__class_Ozero(U_6794)),U_6795))
| ~ class_Rings_Olinordered__semidom(U_6794) ),
inference(clausify,[status(thm)],[f_1572_3]) ).
fof(f_1573_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_1573_2,plain,
! [U_6800,U_6799,U_6798,U_6797] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6797),hAPP(hAPP(c_Power_Opower__class_Opower(U_6797),U_6800),U_6799)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6797),U_6800),U_6798)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6797),U_6800),c_Groups_Oone__class_Oone(U_6797)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6797),c_Groups_Ozero__class_Ozero(U_6797)),U_6800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6798),U_6799))
| ~ class_Rings_Olinordered__semidom(U_6797) ),
inference(variable_rename,[status(thm)],[f_1573_1]) ).
fof(f_1573_3,plain,
! [U_6797,U_6798,U_6799,U_6800] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6797),hAPP(hAPP(c_Power_Opower__class_Opower(U_6797),U_6800),U_6799)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6797),U_6800),U_6798)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6797),U_6800),c_Groups_Oone__class_Oone(U_6797)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6797),c_Groups_Ozero__class_Ozero(U_6797)),U_6800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6798),U_6799))
| ~ class_Rings_Olinordered__semidom(U_6797) ),
inference(definitional_conversion,[status(esa)],[f_1573_2]) ).
cnf(f_1573_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6797),hAPP(hAPP(c_Power_Opower__class_Opower(U_6797),U_6800),U_6799)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6797),U_6800),U_6798)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6797),U_6800),c_Groups_Oone__class_Oone(U_6797)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6797),c_Groups_Ozero__class_Ozero(U_6797)),U_6800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6798),U_6799))
| ~ class_Rings_Olinordered__semidom(U_6797) ),
inference(clausify,[status(thm)],[f_1573_3]) ).
fof(f_1574_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_1574_2,plain,
! [U_6804,U_6803,U_6802,U_6801] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6801),hAPP(hAPP(c_Power_Opower__class_Opower(U_6801),U_6804),U_6803)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6801),U_6804),U_6802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6801),U_6804),c_Groups_Oone__class_Oone(U_6801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6801),c_Groups_Ozero__class_Ozero(U_6801)),U_6804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6802),U_6803))
| ~ class_Rings_Olinordered__semidom(U_6801) ),
inference(variable_rename,[status(thm)],[f_1574_1]) ).
fof(f_1574_3,plain,
! [U_6802,U_6803,U_6801,U_6804] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6801),hAPP(hAPP(c_Power_Opower__class_Opower(U_6801),U_6804),U_6803)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6801),U_6804),U_6802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6801),U_6804),c_Groups_Oone__class_Oone(U_6801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6801),c_Groups_Ozero__class_Ozero(U_6801)),U_6804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6802),U_6803))
| ~ class_Rings_Olinordered__semidom(U_6801) ),
inference(definitional_conversion,[status(esa)],[f_1574_2]) ).
cnf(f_1574_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6801),hAPP(hAPP(c_Power_Opower__class_Opower(U_6801),U_6804),U_6803)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6801),U_6804),U_6802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6801),U_6804),c_Groups_Oone__class_Oone(U_6801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6801),c_Groups_Ozero__class_Ozero(U_6801)),U_6804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6802),U_6803))
| ~ class_Rings_Olinordered__semidom(U_6801) ),
inference(clausify,[status(thm)],[f_1574_3]) ).
fof(f_1575_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_1575_2,plain,
! [U_6807,U_6806,U_6805] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6805),c_Groups_Oone__class_Oone(U_6805)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6805),U_6806),U_6807)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6805),c_Groups_Oone__class_Oone(U_6805)),U_6806))
| ~ class_Rings_Olinordered__semidom(U_6805) ),
inference(variable_rename,[status(thm)],[f_1575_1]) ).
fof(f_1575_3,plain,
! [U_6805,U_6807,U_6806] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6805),c_Groups_Oone__class_Oone(U_6805)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6805),U_6806),U_6807)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6805),c_Groups_Oone__class_Oone(U_6805)),U_6806))
| ~ class_Rings_Olinordered__semidom(U_6805) ),
inference(definitional_conversion,[status(esa)],[f_1575_2]) ).
cnf(f_1575_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6805),c_Groups_Oone__class_Oone(U_6805)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6805),U_6806),U_6807)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6807))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6805),c_Groups_Oone__class_Oone(U_6805)),U_6806))
| ~ class_Rings_Olinordered__semidom(U_6805) ),
inference(clausify,[status(thm)],[f_1575_3]) ).
fof(f_1576_1,plain,
! [V_A_2,T_c] :
( ( 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_c),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
& V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff]) ).
fof(f_1576_2,plain,
! [U_6809,U_6808] :
( ( 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_6808),U_6809)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6808),U_6809))
| U_6809 = c_Orderings_Obot__class_Obot(tc_fun(U_6808,tc_HOL_Obool)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_6808),U_6809))
& U_6809 != c_Orderings_Obot__class_Obot(tc_fun(U_6808,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_6808),U_6809))) ) ),
inference(variable_rename,[status(thm)],[f_1576_1]) ).
fof(f_1576_3,plain,
( ! [U_6813,U_6811] :
( 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_6811),U_6813)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6811),U_6813))
| U_6813 = c_Orderings_Obot__class_Obot(tc_fun(U_6811,tc_HOL_Obool)) )
& ! [U_6812,U_6810] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_6810),U_6812))
& U_6812 != c_Orderings_Obot__class_Obot(tc_fun(U_6810,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_6810),U_6812))) ) ),
inference(miniscope,[status(thm)],[f_1576_2]) ).
fof(f_1576_4,plain,
( ! [U_6812,U_6810] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_6810),U_6812))
| ~ sP389(U_6812,U_6810) )
& ! [U_6812,U_6810] :
( U_6812 != c_Orderings_Obot__class_Obot(tc_fun(U_6810,tc_HOL_Obool))
| ~ sP389(U_6812,U_6810) )
& ! [U_6813,U_6811] :
( 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_6811),U_6813)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6811),U_6813))
| U_6813 = c_Orderings_Obot__class_Obot(tc_fun(U_6811,tc_HOL_Obool)) )
& ! [U_6812,U_6810] :
( sP389(U_6812,U_6810)
| ~ 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_6810),U_6812))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP389])],[f_1576_3]) ).
cnf(f_1576_5,plain,
( sP389(U_6812,U_6810)
| ~ 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_6810),U_6812))) ),
inference(clausify,[status(thm)],[f_1576_4]) ).
cnf(f_1576_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_6811),U_6813)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6811),U_6813))
| U_6813 = c_Orderings_Obot__class_Obot(tc_fun(U_6811,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1576_4]) ).
cnf(f_1576_7,plain,
( U_6812 != c_Orderings_Obot__class_Obot(tc_fun(U_6810,tc_HOL_Obool))
| ~ sP389(U_6812,U_6810) ),
inference(clausify,[status(thm)],[f_1576_4]) ).
cnf(f_1576_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_6810),U_6812))
| ~ sP389(U_6812,U_6810) ),
inference(clausify,[status(thm)],[f_1576_4]) ).
fof(f_1577_1,plain,
! [T_c] :
( 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_c),c_Orderings_Otop__class_Otop(tc_fun(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)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0]) ).
fof(f_1577_2,plain,
! [U_6814] :
( 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_6814),c_Orderings_Otop__class_Otop(tc_fun(U_6814,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6814),c_Orderings_Otop__class_Otop(tc_fun(U_6814,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_1577_1]) ).
fof(f_1577_3,plain,
! [U_6814] :
( 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_6814),c_Orderings_Otop__class_Otop(tc_fun(U_6814,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6814),c_Orderings_Otop__class_Otop(tc_fun(U_6814,tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_1577_2]) ).
cnf(f_1577_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_6814),c_Orderings_Otop__class_Otop(tc_fun(U_6814,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6814),c_Orderings_Otop__class_Otop(tc_fun(U_6814,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_1577_3]) ).
fof(f_1578_1,plain,
! [V_g_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Oplus__class_Oplus(T_d)),V_g_2),c_Groups_Ozero__class_Ozero(T_d)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oeq__fold]) ).
fof(f_1578_2,plain,
! [U_6818,U_6817,U_6816,U_6815] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6816,U_6815),U_6818),U_6817) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6815,U_6816,c_Groups_Oplus__class_Oplus(U_6815)),U_6818),c_Groups_Ozero__class_Ozero(U_6815)),U_6817)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6816),U_6817))
| ~ class_Groups_Ocomm__monoid__add(U_6815) ),
inference(variable_rename,[status(thm)],[f_1578_1]) ).
fof(f_1578_3,plain,
! [U_6815,U_6816,U_6817,U_6818] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6816,U_6815),U_6818),U_6817) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6815,U_6816,c_Groups_Oplus__class_Oplus(U_6815)),U_6818),c_Groups_Ozero__class_Ozero(U_6815)),U_6817)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6816),U_6817))
| ~ class_Groups_Ocomm__monoid__add(U_6815) ),
inference(definitional_conversion,[status(esa)],[f_1578_2]) ).
cnf(f_1578_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6816,U_6815),U_6818),U_6817) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6815,U_6816,c_Groups_Oplus__class_Oplus(U_6815)),U_6818),c_Groups_Ozero__class_Ozero(U_6815)),U_6817)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6816),U_6817))
| ~ class_Groups_Ocomm__monoid__add(U_6815) ),
inference(clausify,[status(thm)],[f_1578_3]) ).
fof(f_1579_1,plain,
! [V_g_2,V_A_2,T_c,T_d] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_d)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Oplus__class_Oplus(T_d)),V_g_2),c_Groups_Ozero__class_Ozero(T_d)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) )
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum_OF__eq]) ).
fof(f_1579_2,plain,
! [U_6822,U_6821,U_6820,U_6819] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6820,U_6819),U_6822),U_6821) = c_Groups_Ozero__class_Ozero(U_6819)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6820),U_6821)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6820,U_6819),U_6822),U_6821) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6819,U_6820,c_Groups_Oplus__class_Oplus(U_6819)),U_6822),c_Groups_Ozero__class_Ozero(U_6819)),U_6821)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6820),U_6821)) ) )
| ~ class_Groups_Ocomm__monoid__add(U_6819) ),
inference(variable_rename,[status(thm)],[f_1579_1]) ).
fof(f_1579_3,plain,
( ! [U_6819,U_6820,U_6821,U_6822] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6820,U_6819),U_6822),U_6821) = c_Groups_Ozero__class_Ozero(U_6819)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6820),U_6821))
| ~ sP390(U_6819,U_6820,U_6821,U_6822) )
& ! [U_6819,U_6820,U_6821,U_6822] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6820,U_6819),U_6822),U_6821) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6819,U_6820,c_Groups_Oplus__class_Oplus(U_6819)),U_6822),c_Groups_Ozero__class_Ozero(U_6819)),U_6821)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6820),U_6821))
| ~ sP390(U_6819,U_6820,U_6821,U_6822) )
& ! [U_6819,U_6820,U_6821,U_6822] :
( sP390(U_6819,U_6820,U_6821,U_6822)
| ~ class_Groups_Ocomm__monoid__add(U_6819) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP390])],[f_1579_2]) ).
cnf(f_1579_4,plain,
( sP390(U_6819,U_6820,U_6821,U_6822)
| ~ class_Groups_Ocomm__monoid__add(U_6819) ),
inference(clausify,[status(thm)],[f_1579_3]) ).
cnf(f_1579_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6820,U_6819),U_6822),U_6821) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6819,U_6820,c_Groups_Oplus__class_Oplus(U_6819)),U_6822),c_Groups_Ozero__class_Ozero(U_6819)),U_6821)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6820),U_6821))
| ~ sP390(U_6819,U_6820,U_6821,U_6822) ),
inference(clausify,[status(thm)],[f_1579_3]) ).
cnf(f_1579_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6820,U_6819),U_6822),U_6821) = c_Groups_Ozero__class_Ozero(U_6819)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6820),U_6821))
| ~ sP390(U_6819,U_6820,U_6821,U_6822) ),
inference(clausify,[status(thm)],[f_1579_3]) ).
fof(f_1580_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_1580_2,plain,
! [U_6823] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6823),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_6823
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6823)) ),
inference(variable_rename,[status(thm)],[f_1580_1]) ).
fof(f_1580_3,plain,
! [U_6823] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6823),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_6823
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6823)) ),
inference(definitional_conversion,[status(esa)],[f_1580_2]) ).
cnf(f_1580_4,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6823),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_6823
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6823)) ),
inference(clausify,[status(thm)],[f_1580_3]) ).
fof(f_1581_1,plain,
! [V_B_2,V_f_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_d))),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set]) ).
fof(f_1581_2,plain,
! [U_6828,U_6827,U_6826,U_6825,U_6824] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6825,U_6824),U_6827),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6825,tc_HOL_Obool)),U_6826),U_6828)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6825,U_6824),hAPP(hAPP(c_COMBC(U_6825,U_6824,U_6824),hAPP(hAPP(c_COMBS(U_6825,U_6824,tc_fun(U_6824,U_6824)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6824,tc_fun(U_6824,U_6824)),U_6825),c_If(U_6824)),hAPP(hAPP(c_COMBC(U_6825,tc_fun(U_6825,tc_HOL_Obool),tc_HOL_Obool),c_member(U_6825)),U_6828))),U_6827)),c_Groups_Ozero__class_Ozero(U_6824))),U_6826)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6825),U_6826))
| ~ class_Groups_Ocomm__monoid__add(U_6824) ),
inference(variable_rename,[status(thm)],[f_1581_1]) ).
fof(f_1581_3,plain,
! [U_6824,U_6825,U_6826,U_6827,U_6828] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6825,U_6824),U_6827),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6825,tc_HOL_Obool)),U_6826),U_6828)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6825,U_6824),hAPP(hAPP(c_COMBC(U_6825,U_6824,U_6824),hAPP(hAPP(c_COMBS(U_6825,U_6824,tc_fun(U_6824,U_6824)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6824,tc_fun(U_6824,U_6824)),U_6825),c_If(U_6824)),hAPP(hAPP(c_COMBC(U_6825,tc_fun(U_6825,tc_HOL_Obool),tc_HOL_Obool),c_member(U_6825)),U_6828))),U_6827)),c_Groups_Ozero__class_Ozero(U_6824))),U_6826)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6825),U_6826))
| ~ class_Groups_Ocomm__monoid__add(U_6824) ),
inference(definitional_conversion,[status(esa)],[f_1581_2]) ).
cnf(f_1581_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6825,U_6824),U_6827),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6825,tc_HOL_Obool)),U_6826),U_6828)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6825,U_6824),hAPP(hAPP(c_COMBC(U_6825,U_6824,U_6824),hAPP(hAPP(c_COMBS(U_6825,U_6824,tc_fun(U_6824,U_6824)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6824,tc_fun(U_6824,U_6824)),U_6825),c_If(U_6824)),hAPP(hAPP(c_COMBC(U_6825,tc_fun(U_6825,tc_HOL_Obool),tc_HOL_Obool),c_member(U_6825)),U_6828))),U_6827)),c_Groups_Ozero__class_Ozero(U_6824))),U_6826)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6825),U_6826))
| ~ class_Groups_Ocomm__monoid__add(U_6824) ),
inference(clausify,[status(thm)],[f_1581_3]) ).
fof(f_1582_1,plain,
! [V_A_2,T_c] :
( ( hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
& ( hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_c,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_c),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_c),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_card__def]) ).
fof(f_1582_2,plain,
! [U_6830,U_6829] :
( ( hAPP(c_Finite__Set_Ocard(U_6829),U_6830) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6829),U_6830)) )
& ( hAPP(c_Finite__Set_Ocard(U_6829),U_6830) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_6829,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_6829),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6830)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6829),U_6830)) ) ),
inference(variable_rename,[status(thm)],[f_1582_1]) ).
fof(f_1582_3,plain,
( ! [U_6834,U_6832] :
( hAPP(c_Finite__Set_Ocard(U_6832),U_6834) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6832),U_6834)) )
& ! [U_6833,U_6831] :
( hAPP(c_Finite__Set_Ocard(U_6831),U_6833) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_6831,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_6831),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6833)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6831),U_6833)) ) ),
inference(miniscope,[status(thm)],[f_1582_2]) ).
fof(f_1582_4,plain,
( ! [U_6832,U_6834] :
( hAPP(c_Finite__Set_Ocard(U_6832),U_6834) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6832),U_6834)) )
& ! [U_6833,U_6831] :
( hAPP(c_Finite__Set_Ocard(U_6831),U_6833) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_6831,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_6831),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6833)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6831),U_6833)) ) ),
inference(definitional_conversion,[status(esa)],[f_1582_3]) ).
cnf(f_1582_5,plain,
( hAPP(c_Finite__Set_Ocard(U_6831),U_6833) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_6831,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_6831),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6833)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6831),U_6833)) ),
inference(clausify,[status(thm)],[f_1582_4]) ).
cnf(f_1582_6,plain,
( hAPP(c_Finite__Set_Ocard(U_6832),U_6834) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_6832),U_6834)) ),
inference(clausify,[status(thm)],[f_1582_4]) ).
fof(f_1583_1,plain,
! [V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_c,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_c),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_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g]) ).
fof(f_1583_2,plain,
! [U_6836,U_6835] :
( hAPP(c_Finite__Set_Ocard(U_6835),U_6836) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_6835,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_6835),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6836)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6835),U_6836)) ),
inference(variable_rename,[status(thm)],[f_1583_1]) ).
fof(f_1583_3,plain,
! [U_6835,U_6836] :
( hAPP(c_Finite__Set_Ocard(U_6835),U_6836) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_6835,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_6835),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6836)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6835),U_6836)) ),
inference(definitional_conversion,[status(esa)],[f_1583_2]) ).
cnf(f_1583_4,plain,
( hAPP(c_Finite__Set_Ocard(U_6835),U_6836) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_6835,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_6835),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6836)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6835),U_6836)) ),
inference(clausify,[status(thm)],[f_1583_3]) ).
fof(f_1584_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_1584_2,plain,
! [U_6842,U_6841,U_6840,U_6839,U_6838,U_6837] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6837),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6837),U_6841),U_6838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6837),U_6842),U_6840))),U_6839))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6837),U_6841),U_6842) != c_Groups_Oone__class_Oone(U_6837)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6837),c_Groups_Ozero__class_Ozero(U_6837)),U_6842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6837),c_Groups_Ozero__class_Ozero(U_6837)),U_6841))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6837),U_6840),U_6839))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6837),U_6838),U_6839))
| ~ class_Rings_Olinordered__semiring__1__strict(U_6837) ),
inference(variable_rename,[status(thm)],[f_1584_1]) ).
fof(f_1584_3,plain,
! [U_6837,U_6838,U_6839,U_6840,U_6841,U_6842] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6837),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6837),U_6841),U_6838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6837),U_6842),U_6840))),U_6839))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6837),U_6841),U_6842) != c_Groups_Oone__class_Oone(U_6837)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6837),c_Groups_Ozero__class_Ozero(U_6837)),U_6842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6837),c_Groups_Ozero__class_Ozero(U_6837)),U_6841))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6837),U_6840),U_6839))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6837),U_6838),U_6839))
| ~ class_Rings_Olinordered__semiring__1__strict(U_6837) ),
inference(definitional_conversion,[status(esa)],[f_1584_2]) ).
cnf(f_1584_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6837),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6837),U_6841),U_6838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6837),U_6842),U_6840))),U_6839))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6837),U_6841),U_6842) != c_Groups_Oone__class_Oone(U_6837)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6837),c_Groups_Ozero__class_Ozero(U_6837)),U_6842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6837),c_Groups_Ozero__class_Ozero(U_6837)),U_6841))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6837),U_6840),U_6839))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6837),U_6838),U_6839))
| ~ class_Rings_Olinordered__semiring__1__strict(U_6837) ),
inference(clausify,[status(thm)],[f_1584_3]) ).
fof(f_1585_1,plain,
! [V_fun2_2,V_com_2,V_fun1_2,V_fa_2,T_c] : c_Hoare__Mirabelle_Otriple_Otriple__size(T_c,V_fa_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_triple_Osize_I1_J]) ).
fof(f_1585_2,plain,
! [U_6847,U_6846,U_6845,U_6844,U_6843] : c_Hoare__Mirabelle_Otriple_Otriple__size(U_6843,U_6844,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_6843),U_6845),U_6846),U_6847)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1585_1]) ).
fof(f_1585_3,plain,
! [U_6844,U_6847,U_6845,U_6843,U_6846] : c_Hoare__Mirabelle_Otriple_Otriple__size(U_6843,U_6844,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_6843),U_6845),U_6846),U_6847)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1585_2]) ).
cnf(f_1585_4,plain,
c_Hoare__Mirabelle_Otriple_Otriple__size(U_6843,U_6844,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_6843),U_6845),U_6846),U_6847)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1585_3]) ).
fof(f_1586_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_even__less__0__iff]) ).
fof(f_1586_2,plain,
! [U_6849,U_6848] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6848),U_6849),U_6849)),c_Groups_Ozero__class_Ozero(U_6848)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6848),U_6849),c_Groups_Ozero__class_Ozero(U_6848))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6848),U_6849),c_Groups_Ozero__class_Ozero(U_6848)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6848),U_6849),U_6849)),c_Groups_Ozero__class_Ozero(U_6848))) ) )
| ~ class_Rings_Olinordered__idom(U_6848) ),
inference(variable_rename,[status(thm)],[f_1586_1]) ).
fof(f_1586_3,plain,
( ! [U_6848,U_6849] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6848),U_6849),U_6849)),c_Groups_Ozero__class_Ozero(U_6848)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6848),U_6849),c_Groups_Ozero__class_Ozero(U_6848)))
| ~ sP391(U_6848,U_6849) )
& ! [U_6848,U_6849] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6848),U_6849),c_Groups_Ozero__class_Ozero(U_6848)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6848),U_6849),U_6849)),c_Groups_Ozero__class_Ozero(U_6848)))
| ~ sP391(U_6848,U_6849) )
& ! [U_6848,U_6849] :
( sP391(U_6848,U_6849)
| ~ class_Rings_Olinordered__idom(U_6848) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP391])],[f_1586_2]) ).
cnf(f_1586_4,plain,
( sP391(U_6848,U_6849)
| ~ class_Rings_Olinordered__idom(U_6848) ),
inference(clausify,[status(thm)],[f_1586_3]) ).
cnf(f_1586_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6848),U_6849),c_Groups_Ozero__class_Ozero(U_6848)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6848),U_6849),U_6849)),c_Groups_Ozero__class_Ozero(U_6848)))
| ~ sP391(U_6848,U_6849) ),
inference(clausify,[status(thm)],[f_1586_3]) ).
cnf(f_1586_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6848),U_6849),U_6849)),c_Groups_Ozero__class_Ozero(U_6848)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6848),U_6849),c_Groups_Ozero__class_Ozero(U_6848)))
| ~ sP391(U_6848,U_6849) ),
inference(clausify,[status(thm)],[f_1586_3]) ).
fof(f_1587_1,plain,
! [V_fun2_2,V_com_2,V_fun1_2,T_c] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),V_fun1_2),V_com_2),V_fun2_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_triple_Osize_I2_J]) ).
fof(f_1587_2,plain,
! [U_6853,U_6852,U_6851,U_6850] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_6850)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_6850),U_6851),U_6852),U_6853)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1587_1]) ).
fof(f_1587_3,plain,
! [U_6851,U_6850,U_6852,U_6853] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_6850)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_6850),U_6851),U_6852),U_6853)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1587_2]) ).
cnf(f_1587_4,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_6850)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_6850),U_6851),U_6852),U_6853)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1587_3]) ).
fof(f_1588_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),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_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)) ),
inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter__neutral]) ).
fof(f_1588_2,plain,
! [U_6857,U_6856,U_6855] :
( hAPP(c_Finite__Set_Ocard(U_6855),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6855,tc_HOL_Obool)),U_6856),U_6857)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6855),U_6856)),hAPP(c_Finite__Set_Ocard(U_6855),U_6857))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [U_6854] : hBOOL(hAPP(hAPP(c_member(U_6855),U_6854),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6855,tc_HOL_Obool)),U_6856),U_6857))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6855),U_6857))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6855),U_6856)) ),
inference(variable_rename,[status(thm)],[f_1588_1]) ).
fof(f_1588_3,plain,
! [U_6857,U_6856,U_6855] :
( hAPP(c_Finite__Set_Ocard(U_6855),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6855,tc_HOL_Obool)),U_6856),U_6857)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6855),U_6856)),hAPP(c_Finite__Set_Ocard(U_6855),U_6857))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_6855),sK132(U_6857,U_6856,U_6855)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6855,tc_HOL_Obool)),U_6856),U_6857))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6855),U_6857))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6855),U_6856)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_6854,sK132(U_6857,U_6856,U_6855))],[f_1588_2]) ).
fof(f_1588_4,plain,
( ! [U_6855,U_6856,U_6857] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP392(U_6855,U_6856,U_6857) )
& ! [U_6855,U_6856,U_6857] :
( hBOOL(hAPP(hAPP(c_member(U_6855),sK132(U_6857,U_6856,U_6855)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6855,tc_HOL_Obool)),U_6856),U_6857)))
| ~ sP392(U_6855,U_6856,U_6857) )
& ! [U_6855,U_6856,U_6857] :
( hAPP(c_Finite__Set_Ocard(U_6855),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6855,tc_HOL_Obool)),U_6856),U_6857)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6855),U_6856)),hAPP(c_Finite__Set_Ocard(U_6855),U_6857))
| sP392(U_6855,U_6856,U_6857)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6855),U_6857))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6855),U_6856)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP392])],[f_1588_3]) ).
cnf(f_1588_5,plain,
( hAPP(c_Finite__Set_Ocard(U_6855),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6855,tc_HOL_Obool)),U_6856),U_6857)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_6855),U_6856)),hAPP(c_Finite__Set_Ocard(U_6855),U_6857))
| sP392(U_6855,U_6856,U_6857)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6855),U_6857))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6855),U_6856)) ),
inference(clausify,[status(thm)],[f_1588_4]) ).
cnf(f_1588_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_6855),sK132(U_6857,U_6856,U_6855)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6855,tc_HOL_Obool)),U_6856),U_6857)))
| ~ sP392(U_6855,U_6856,U_6857) ),
inference(clausify,[status(thm)],[f_1588_4]) ).
cnf(f_1588_7,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP392(U_6855,U_6856,U_6857) ),
inference(clausify,[status(thm)],[f_1588_4]) ).
fof(f_1589_1,plain,
! [V_f_2,V_A_2,V_B_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_B_2)))
| ? [B_b] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_b)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ class_Groups_Oordered__comm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono2]) ).
fof(f_1589_2,plain,
! [U_6863,U_6862,U_6861,U_6860,U_6859] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6860,U_6859),U_6863),U_6862)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6860,U_6859),U_6863),U_6861)))
| ? [U_6858] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),c_Groups_Ozero__class_Ozero(U_6859)),hAPP(U_6863,U_6858)))
& hBOOL(hAPP(hAPP(c_member(U_6860),U_6858),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6860,tc_HOL_Obool)),U_6861),U_6862))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6860,tc_HOL_Obool)),U_6862),U_6861))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6860),U_6861))
| ~ class_Groups_Oordered__comm__monoid__add(U_6859) ),
inference(variable_rename,[status(thm)],[f_1589_1]) ).
fof(f_1589_3,plain,
! [U_6863,U_6862,U_6861,U_6860,U_6859] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6860,U_6859),U_6863),U_6862)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6860,U_6859),U_6863),U_6861)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),c_Groups_Ozero__class_Ozero(U_6859)),hAPP(U_6863,sK133(U_6863,U_6862,U_6861,U_6860,U_6859))))
& hBOOL(hAPP(hAPP(c_member(U_6860),sK133(U_6863,U_6862,U_6861,U_6860,U_6859)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6860,tc_HOL_Obool)),U_6861),U_6862))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6860,tc_HOL_Obool)),U_6862),U_6861))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6860),U_6861))
| ~ class_Groups_Oordered__comm__monoid__add(U_6859) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_6858,sK133(U_6863,U_6862,U_6861,U_6860,U_6859))],[f_1589_2]) ).
fof(f_1589_4,plain,
( ! [U_6860,U_6859,U_6861,U_6862,U_6863] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),c_Groups_Ozero__class_Ozero(U_6859)),hAPP(U_6863,sK133(U_6863,U_6862,U_6861,U_6860,U_6859))))
| ~ sP393(U_6860,U_6859,U_6861,U_6862,U_6863) )
& ! [U_6860,U_6859,U_6861,U_6862,U_6863] :
( hBOOL(hAPP(hAPP(c_member(U_6860),sK133(U_6863,U_6862,U_6861,U_6860,U_6859)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6860,tc_HOL_Obool)),U_6861),U_6862)))
| ~ sP393(U_6860,U_6859,U_6861,U_6862,U_6863) )
& ! [U_6860,U_6859,U_6861,U_6862,U_6863] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6860,U_6859),U_6863),U_6862)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6860,U_6859),U_6863),U_6861)))
| sP393(U_6860,U_6859,U_6861,U_6862,U_6863)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6860,tc_HOL_Obool)),U_6862),U_6861))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6860),U_6861))
| ~ class_Groups_Oordered__comm__monoid__add(U_6859) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP393])],[f_1589_3]) ).
cnf(f_1589_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6860,U_6859),U_6863),U_6862)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6860,U_6859),U_6863),U_6861)))
| sP393(U_6860,U_6859,U_6861,U_6862,U_6863)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6860,tc_HOL_Obool)),U_6862),U_6861))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6860),U_6861))
| ~ class_Groups_Oordered__comm__monoid__add(U_6859) ),
inference(clausify,[status(thm)],[f_1589_4]) ).
cnf(f_1589_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_6860),sK133(U_6863,U_6862,U_6861,U_6860,U_6859)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6860,tc_HOL_Obool)),U_6861),U_6862)))
| ~ sP393(U_6860,U_6859,U_6861,U_6862,U_6863) ),
inference(clausify,[status(thm)],[f_1589_4]) ).
cnf(f_1589_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6859),c_Groups_Ozero__class_Ozero(U_6859)),hAPP(U_6863,sK133(U_6863,U_6862,U_6861,U_6860,U_6859))))
| ~ sP393(U_6860,U_6859,U_6861,U_6862,U_6863) ),
inference(clausify,[status(thm)],[f_1589_4]) ).
fof(f_1590_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_1590_2,plain,
! [U_6866,U_6865,U_6864] : 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_6864)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_6865))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6866))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6866),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6864),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6866),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6865)))),
inference(variable_rename,[status(thm)],[f_1590_1]) ).
fof(f_1590_3,plain,
! [U_6864,U_6866,U_6865] : 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_6864)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_6865))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6866))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6866),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6864),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6866),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6865)))),
inference(definitional_conversion,[status(esa)],[f_1590_2]) ).
cnf(f_1590_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_6864)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_6865))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6866))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6866),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6864),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6866),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6865)))),
inference(clausify,[status(thm)],[f_1590_3]) ).
fof(f_1591_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_1591_2,plain,
! [U_6867] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6867))),
inference(variable_rename,[status(thm)],[f_1591_1]) ).
fof(f_1591_3,plain,
! [U_6867] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6867))),
inference(definitional_conversion,[status(esa)],[f_1591_2]) ).
cnf(f_1591_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6867))),
inference(clausify,[status(thm)],[f_1591_3]) ).
fof(f_1592_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_x_2) != hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_y_2) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_lessThan__eq__iff]) ).
fof(f_1592_2,plain,
! [U_6870,U_6869,U_6868] :
( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(U_6868),U_6869) = hAPP(c_SetInterval_Oord__class_OlessThan(U_6868),U_6870)
| U_6869 != U_6870 )
& ( U_6869 = U_6870
| hAPP(c_SetInterval_Oord__class_OlessThan(U_6868),U_6869) != hAPP(c_SetInterval_Oord__class_OlessThan(U_6868),U_6870) ) )
| ~ class_Orderings_Olinorder(U_6868) ),
inference(variable_rename,[status(thm)],[f_1592_1]) ).
fof(f_1592_3,plain,
( ! [U_6869,U_6870,U_6868] :
( hAPP(c_SetInterval_Oord__class_OlessThan(U_6868),U_6869) = hAPP(c_SetInterval_Oord__class_OlessThan(U_6868),U_6870)
| U_6869 != U_6870
| ~ sP394(U_6869,U_6870,U_6868) )
& ! [U_6869,U_6870,U_6868] :
( U_6869 = U_6870
| hAPP(c_SetInterval_Oord__class_OlessThan(U_6868),U_6869) != hAPP(c_SetInterval_Oord__class_OlessThan(U_6868),U_6870)
| ~ sP394(U_6869,U_6870,U_6868) )
& ! [U_6869,U_6870,U_6868] :
( sP394(U_6869,U_6870,U_6868)
| ~ class_Orderings_Olinorder(U_6868) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP394])],[f_1592_2]) ).
cnf(f_1592_4,plain,
( sP394(U_6869,U_6870,U_6868)
| ~ class_Orderings_Olinorder(U_6868) ),
inference(clausify,[status(thm)],[f_1592_3]) ).
cnf(f_1592_5,plain,
( U_6869 = U_6870
| hAPP(c_SetInterval_Oord__class_OlessThan(U_6868),U_6869) != hAPP(c_SetInterval_Oord__class_OlessThan(U_6868),U_6870)
| ~ sP394(U_6869,U_6870,U_6868) ),
inference(clausify,[status(thm)],[f_1592_3]) ).
cnf(f_1592_6,plain,
( hAPP(c_SetInterval_Oord__class_OlessThan(U_6868),U_6869) = hAPP(c_SetInterval_Oord__class_OlessThan(U_6868),U_6870)
| U_6869 != U_6870
| ~ sP394(U_6869,U_6870,U_6868) ),
inference(clausify,[status(thm)],[f_1592_3]) ).
fof(f_1593_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_1593_2,plain,
! [U_6871] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6871)) = U_6871,
inference(variable_rename,[status(thm)],[f_1593_1]) ).
fof(f_1593_3,plain,
! [U_6871] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6871)) = U_6871,
inference(definitional_conversion,[status(esa)],[f_1593_2]) ).
cnf(f_1593_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6871)) = U_6871,
inference(clausify,[status(thm)],[f_1593_3]) ).
fof(f_1594_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_1594_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_1594_1]) ).
cnf(f_1594_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_1594_2]) ).
fof(f_1595_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_1595_2,plain,
! [U_6872] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6872)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_6872),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6872)),
inference(variable_rename,[status(thm)],[f_1595_1]) ).
fof(f_1595_3,plain,
! [U_6872] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6872)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_6872),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6872)),
inference(definitional_conversion,[status(esa)],[f_1595_2]) ).
cnf(f_1595_4,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6872)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_6872),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6872)),
inference(clausify,[status(thm)],[f_1595_3]) ).
fof(f_1596_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_1596_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_1596_1]) ).
cnf(f_1596_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_1596_2]) ).
fof(f_1597_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_1597_2,plain,
! [U_6873] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6873)) = 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_6873))),
inference(variable_rename,[status(thm)],[f_1597_1]) ).
fof(f_1597_3,plain,
! [U_6873] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6873)) = 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_6873))),
inference(definitional_conversion,[status(esa)],[f_1597_2]) ).
cnf(f_1597_4,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6873)) = 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_6873))),
inference(clausify,[status(thm)],[f_1597_3]) ).
fof(f_1598_1,plain,
! [V_n_2,V_f_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc]) ).
fof(f_1598_2,plain,
! [U_6876,U_6875,U_6874] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6874),U_6875),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6876))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6874),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6874),U_6875),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6876))),hAPP(U_6875,U_6876))
| ~ class_Groups_Ocomm__monoid__add(U_6874) ),
inference(variable_rename,[status(thm)],[f_1598_1]) ).
fof(f_1598_3,plain,
! [U_6874,U_6875,U_6876] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6874),U_6875),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6876))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6874),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6874),U_6875),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6876))),hAPP(U_6875,U_6876))
| ~ class_Groups_Ocomm__monoid__add(U_6874) ),
inference(definitional_conversion,[status(esa)],[f_1598_2]) ).
cnf(f_1598_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6874),U_6875),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6876))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6874),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6874),U_6875),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6876))),hAPP(U_6875,U_6876))
| ~ class_Groups_Ocomm__monoid__add(U_6874) ),
inference(clausify,[status(thm)],[f_1598_3]) ).
fof(f_1599_1,plain,
! [V_k_2,V_i_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_i_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2))) ) )
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_lessThan__iff]) ).
fof(f_1599_2,plain,
! [U_6879,U_6878,U_6877] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_6877),U_6878),hAPP(c_SetInterval_Oord__class_OlessThan(U_6877),U_6879)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6877),U_6878),U_6879)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6877),U_6878),U_6879))
| ~ hBOOL(hAPP(hAPP(c_member(U_6877),U_6878),hAPP(c_SetInterval_Oord__class_OlessThan(U_6877),U_6879))) ) )
| ~ class_Orderings_Oord(U_6877) ),
inference(variable_rename,[status(thm)],[f_1599_1]) ).
fof(f_1599_3,plain,
( ! [U_6877,U_6878,U_6879] :
( hBOOL(hAPP(hAPP(c_member(U_6877),U_6878),hAPP(c_SetInterval_Oord__class_OlessThan(U_6877),U_6879)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6877),U_6878),U_6879))
| ~ sP395(U_6877,U_6878,U_6879) )
& ! [U_6877,U_6878,U_6879] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6877),U_6878),U_6879))
| ~ hBOOL(hAPP(hAPP(c_member(U_6877),U_6878),hAPP(c_SetInterval_Oord__class_OlessThan(U_6877),U_6879)))
| ~ sP395(U_6877,U_6878,U_6879) )
& ! [U_6877,U_6878,U_6879] :
( sP395(U_6877,U_6878,U_6879)
| ~ class_Orderings_Oord(U_6877) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP395])],[f_1599_2]) ).
cnf(f_1599_4,plain,
( sP395(U_6877,U_6878,U_6879)
| ~ class_Orderings_Oord(U_6877) ),
inference(clausify,[status(thm)],[f_1599_3]) ).
cnf(f_1599_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6877),U_6878),U_6879))
| ~ hBOOL(hAPP(hAPP(c_member(U_6877),U_6878),hAPP(c_SetInterval_Oord__class_OlessThan(U_6877),U_6879)))
| ~ sP395(U_6877,U_6878,U_6879) ),
inference(clausify,[status(thm)],[f_1599_3]) ).
cnf(f_1599_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_6877),U_6878),hAPP(c_SetInterval_Oord__class_OlessThan(U_6877),U_6879)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6877),U_6878),U_6879))
| ~ sP395(U_6877,U_6878,U_6879) ),
inference(clausify,[status(thm)],[f_1599_3]) ).
fof(f_1600_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_y_2))) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff]) ).
fof(f_1600_2,plain,
! [U_6882,U_6881,U_6880] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6880,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6880),U_6881)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6880),U_6882)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6880),U_6881),U_6882)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6880),U_6881),U_6882))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6880,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6880),U_6881)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6880),U_6882))) ) )
| ~ class_Orderings_Olinorder(U_6880) ),
inference(variable_rename,[status(thm)],[f_1600_1]) ).
fof(f_1600_3,plain,
( ! [U_6881,U_6880,U_6882] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6880,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6880),U_6881)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6880),U_6882)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6880),U_6881),U_6882))
| ~ sP396(U_6881,U_6880,U_6882) )
& ! [U_6881,U_6880,U_6882] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6880),U_6881),U_6882))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6880,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6880),U_6881)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6880),U_6882)))
| ~ sP396(U_6881,U_6880,U_6882) )
& ! [U_6881,U_6880,U_6882] :
( sP396(U_6881,U_6880,U_6882)
| ~ class_Orderings_Olinorder(U_6880) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP396])],[f_1600_2]) ).
cnf(f_1600_4,plain,
( sP396(U_6881,U_6880,U_6882)
| ~ class_Orderings_Olinorder(U_6880) ),
inference(clausify,[status(thm)],[f_1600_3]) ).
cnf(f_1600_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6880),U_6881),U_6882))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6880,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6880),U_6881)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6880),U_6882)))
| ~ sP396(U_6881,U_6880,U_6882) ),
inference(clausify,[status(thm)],[f_1600_3]) ).
cnf(f_1600_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6880,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6880),U_6881)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6880),U_6882)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6880),U_6881),U_6882))
| ~ sP396(U_6881,U_6880,U_6882) ),
inference(clausify,[status(thm)],[f_1600_3]) ).
fof(f_1601_1,plain,
! [V_n_2,V_m_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_n_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_m_2),V_n_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_m_2),V_n_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_n_2))) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff]) ).
fof(f_1601_2,plain,
! [U_6885,U_6884,U_6883] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6883,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6883),U_6884)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6883),U_6885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6883),U_6884),U_6885)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6883),U_6884),U_6885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6883,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6883),U_6884)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6883),U_6885))) ) )
| ~ class_Orderings_Olinorder(U_6883) ),
inference(variable_rename,[status(thm)],[f_1601_1]) ).
fof(f_1601_3,plain,
( ! [U_6883,U_6885,U_6884] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6883,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6883),U_6884)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6883),U_6885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6883),U_6884),U_6885))
| ~ sP397(U_6883,U_6885,U_6884) )
& ! [U_6883,U_6885,U_6884] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6883),U_6884),U_6885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6883,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6883),U_6884)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6883),U_6885)))
| ~ sP397(U_6883,U_6885,U_6884) )
& ! [U_6883,U_6885,U_6884] :
( sP397(U_6883,U_6885,U_6884)
| ~ class_Orderings_Olinorder(U_6883) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP397])],[f_1601_2]) ).
cnf(f_1601_4,plain,
( sP397(U_6883,U_6885,U_6884)
| ~ class_Orderings_Olinorder(U_6883) ),
inference(clausify,[status(thm)],[f_1601_3]) ).
cnf(f_1601_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6883),U_6884),U_6885))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6883,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6883),U_6884)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6883),U_6885)))
| ~ sP397(U_6883,U_6885,U_6884) ),
inference(clausify,[status(thm)],[f_1601_3]) ).
cnf(f_1601_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6883,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6883),U_6884)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6883),U_6885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6883),U_6884),U_6885))
| ~ sP397(U_6883,U_6885,U_6884) ),
inference(clausify,[status(thm)],[f_1601_3]) ).
fof(f_1602_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_1602_2,plain,
! [U_6888,U_6887,U_6886] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6886),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6887),U_6888)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6886),U_6887)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6886),U_6888)),
inference(variable_rename,[status(thm)],[f_1602_1]) ).
fof(f_1602_3,plain,
! [U_6887,U_6886,U_6888] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6886),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6887),U_6888)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6886),U_6887)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6886),U_6888)),
inference(definitional_conversion,[status(esa)],[f_1602_2]) ).
cnf(f_1602_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6886),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6887),U_6888)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6886),U_6887)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6886),U_6888)),
inference(clausify,[status(thm)],[f_1602_3]) ).
fof(f_1603_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_1603_2,plain,
! [U_6891,U_6890,U_6889] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6889),U_6890)),U_6891) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6890),U_6891)),
inference(variable_rename,[status(thm)],[f_1603_1]) ).
fof(f_1603_3,plain,
! [U_6889,U_6890,U_6891] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6889),U_6890)),U_6891) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6890),U_6891)),
inference(definitional_conversion,[status(esa)],[f_1603_2]) ).
cnf(f_1603_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6889),U_6890)),U_6891) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6889),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6890),U_6891)),
inference(clausify,[status(thm)],[f_1603_3]) ).
fof(f_1604_1,plain,
! [V_k_2,T_c] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_single__Diff__lessThan]) ).
fof(f_1604_2,plain,
! [U_6893,U_6892] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6892,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_6892),U_6893),c_Orderings_Obot__class_Obot(tc_fun(U_6892,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_6892),U_6893)) = hAPP(hAPP(c_Set_Oinsert(U_6892),U_6893),c_Orderings_Obot__class_Obot(tc_fun(U_6892,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_6892) ),
inference(variable_rename,[status(thm)],[f_1604_1]) ).
fof(f_1604_3,plain,
! [U_6892,U_6893] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6892,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_6892),U_6893),c_Orderings_Obot__class_Obot(tc_fun(U_6892,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_6892),U_6893)) = hAPP(hAPP(c_Set_Oinsert(U_6892),U_6893),c_Orderings_Obot__class_Obot(tc_fun(U_6892,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_6892) ),
inference(definitional_conversion,[status(esa)],[f_1604_2]) ).
cnf(f_1604_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6892,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_6892),U_6893),c_Orderings_Obot__class_Obot(tc_fun(U_6892,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_6892),U_6893)) = hAPP(hAPP(c_Set_Oinsert(U_6892),U_6893),c_Orderings_Obot__class_Obot(tc_fun(U_6892,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_6892) ),
inference(clausify,[status(thm)],[f_1604_3]) ).
fof(f_1605_1,plain,
! [V_a_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff]) ).
fof(f_1605_2,plain,
! [U_6895,U_6894] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6894),U_6895),U_6895) = c_Groups_Ozero__class_Ozero(U_6894)
| U_6895 != c_Groups_Ozero__class_Ozero(U_6894) )
& ( U_6895 = c_Groups_Ozero__class_Ozero(U_6894)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6894),U_6895),U_6895) != c_Groups_Ozero__class_Ozero(U_6894) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_6894) ),
inference(variable_rename,[status(thm)],[f_1605_1]) ).
fof(f_1605_3,plain,
( ! [U_6894,U_6895] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6894),U_6895),U_6895) = c_Groups_Ozero__class_Ozero(U_6894)
| U_6895 != c_Groups_Ozero__class_Ozero(U_6894)
| ~ sP398(U_6894,U_6895) )
& ! [U_6894,U_6895] :
( U_6895 = c_Groups_Ozero__class_Ozero(U_6894)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6894),U_6895),U_6895) != c_Groups_Ozero__class_Ozero(U_6894)
| ~ sP398(U_6894,U_6895) )
& ! [U_6894,U_6895] :
( sP398(U_6894,U_6895)
| ~ class_Groups_Olinordered__ab__group__add(U_6894) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP398])],[f_1605_2]) ).
cnf(f_1605_4,plain,
( sP398(U_6894,U_6895)
| ~ class_Groups_Olinordered__ab__group__add(U_6894) ),
inference(clausify,[status(thm)],[f_1605_3]) ).
cnf(f_1605_5,plain,
( U_6895 = c_Groups_Ozero__class_Ozero(U_6894)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6894),U_6895),U_6895) != c_Groups_Ozero__class_Ozero(U_6894)
| ~ sP398(U_6894,U_6895) ),
inference(clausify,[status(thm)],[f_1605_3]) ).
cnf(f_1605_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6894),U_6895),U_6895) = c_Groups_Ozero__class_Ozero(U_6894)
| U_6895 != c_Groups_Ozero__class_Ozero(U_6894)
| ~ sP398(U_6894,U_6895) ),
inference(clausify,[status(thm)],[f_1605_3]) ).
fof(f_1606_1,plain,
! [V_n_2,V_d_2,V_a_2,T_c] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),c_Groups_Oone__class_Oone(T_c))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_c)),c_Nat_Osemiring__1__class_Oof__nat(T_c))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),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_c) ),
inference(fof_nnf,[status(thm)],[fact_arith__series__general]) ).
fof(f_1606_2,plain,
! [U_6899,U_6898,U_6897,U_6896] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6896),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6896),c_Groups_Oone__class_Oone(U_6896)),c_Groups_Oone__class_Oone(U_6896))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6896),hAPP(hAPP(c_COMBB(U_6896,U_6896,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_6896),U_6897)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_6896,U_6896),hAPP(hAPP(c_COMBB(U_6896,tc_fun(U_6896,U_6896),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_6896)),c_Nat_Osemiring__1__class_Oof__nat(U_6896))),U_6898))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6899))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6896),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6896),U_6899)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6896),U_6897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6896),U_6897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6896),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6896),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6899),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_6898))))
| ~ class_Rings_Ocomm__semiring__1(U_6896) ),
inference(variable_rename,[status(thm)],[f_1606_1]) ).
fof(f_1606_3,plain,
! [U_6896,U_6897,U_6898,U_6899] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6896),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6896),c_Groups_Oone__class_Oone(U_6896)),c_Groups_Oone__class_Oone(U_6896))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6896),hAPP(hAPP(c_COMBB(U_6896,U_6896,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_6896),U_6897)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_6896,U_6896),hAPP(hAPP(c_COMBB(U_6896,tc_fun(U_6896,U_6896),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_6896)),c_Nat_Osemiring__1__class_Oof__nat(U_6896))),U_6898))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6899))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6896),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6896),U_6899)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6896),U_6897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6896),U_6897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6896),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6896),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6899),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_6898))))
| ~ class_Rings_Ocomm__semiring__1(U_6896) ),
inference(definitional_conversion,[status(esa)],[f_1606_2]) ).
cnf(f_1606_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6896),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6896),c_Groups_Oone__class_Oone(U_6896)),c_Groups_Oone__class_Oone(U_6896))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6896),hAPP(hAPP(c_COMBB(U_6896,U_6896,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_6896),U_6897)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_6896,U_6896),hAPP(hAPP(c_COMBB(U_6896,tc_fun(U_6896,U_6896),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_6896)),c_Nat_Osemiring__1__class_Oof__nat(U_6896))),U_6898))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6899))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6896),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6896),U_6899)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6896),U_6897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6896),U_6897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6896),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6896),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6899),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_6898))))
| ~ class_Rings_Ocomm__semiring__1(U_6896) ),
inference(clausify,[status(thm)],[f_1606_3]) ).
fof(f_1607_1,plain,
! [V_f_2,V_T_2,V_S_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_T_2))
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_d)
& 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_S_2),V_T_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un__zero]) ).
fof(f_1607_2,plain,
! [U_6905,U_6904,U_6903,U_6902,U_6901] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6902,U_6901),U_6905),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6902,tc_HOL_Obool)),U_6903),U_6904)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6901),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6902,U_6901),U_6905),U_6903)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6902,U_6901),U_6905),U_6904))
| ? [U_6900] :
( hAPP(U_6905,U_6900) != c_Groups_Ozero__class_Ozero(U_6901)
& hBOOL(hAPP(hAPP(c_member(U_6902),U_6900),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6902,tc_HOL_Obool)),U_6903),U_6904))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6902),U_6904))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6902),U_6903))
| ~ class_Groups_Ocomm__monoid__add(U_6901) ),
inference(variable_rename,[status(thm)],[f_1607_1]) ).
fof(f_1607_3,plain,
! [U_6905,U_6904,U_6903,U_6902,U_6901] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6902,U_6901),U_6905),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6902,tc_HOL_Obool)),U_6903),U_6904)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6901),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6902,U_6901),U_6905),U_6903)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6902,U_6901),U_6905),U_6904))
| ( hAPP(U_6905,sK134(U_6905,U_6904,U_6903,U_6902,U_6901)) != c_Groups_Ozero__class_Ozero(U_6901)
& hBOOL(hAPP(hAPP(c_member(U_6902),sK134(U_6905,U_6904,U_6903,U_6902,U_6901)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6902,tc_HOL_Obool)),U_6903),U_6904))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6902),U_6904))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6902),U_6903))
| ~ class_Groups_Ocomm__monoid__add(U_6901) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_6900,sK134(U_6905,U_6904,U_6903,U_6902,U_6901))],[f_1607_2]) ).
fof(f_1607_4,plain,
( ! [U_6901,U_6902,U_6903,U_6904,U_6905] :
( hAPP(U_6905,sK134(U_6905,U_6904,U_6903,U_6902,U_6901)) != c_Groups_Ozero__class_Ozero(U_6901)
| ~ sP399(U_6901,U_6902,U_6903,U_6904,U_6905) )
& ! [U_6901,U_6902,U_6903,U_6904,U_6905] :
( hBOOL(hAPP(hAPP(c_member(U_6902),sK134(U_6905,U_6904,U_6903,U_6902,U_6901)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6902,tc_HOL_Obool)),U_6903),U_6904)))
| ~ sP399(U_6901,U_6902,U_6903,U_6904,U_6905) )
& ! [U_6901,U_6902,U_6903,U_6904,U_6905] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6902,U_6901),U_6905),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6902,tc_HOL_Obool)),U_6903),U_6904)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6901),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6902,U_6901),U_6905),U_6903)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6902,U_6901),U_6905),U_6904))
| sP399(U_6901,U_6902,U_6903,U_6904,U_6905)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6902),U_6904))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6902),U_6903))
| ~ class_Groups_Ocomm__monoid__add(U_6901) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP399])],[f_1607_3]) ).
cnf(f_1607_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6902,U_6901),U_6905),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6902,tc_HOL_Obool)),U_6903),U_6904)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6901),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6902,U_6901),U_6905),U_6903)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6902,U_6901),U_6905),U_6904))
| sP399(U_6901,U_6902,U_6903,U_6904,U_6905)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6902),U_6904))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6902),U_6903))
| ~ class_Groups_Ocomm__monoid__add(U_6901) ),
inference(clausify,[status(thm)],[f_1607_4]) ).
cnf(f_1607_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_6902),sK134(U_6905,U_6904,U_6903,U_6902,U_6901)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6902,tc_HOL_Obool)),U_6903),U_6904)))
| ~ sP399(U_6901,U_6902,U_6903,U_6904,U_6905) ),
inference(clausify,[status(thm)],[f_1607_4]) ).
cnf(f_1607_7,plain,
( hAPP(U_6905,sK134(U_6905,U_6904,U_6903,U_6902,U_6901)) != c_Groups_Ozero__class_Ozero(U_6901)
| ~ sP399(U_6901,U_6902,U_6903,U_6904,U_6905) ),
inference(clausify,[status(thm)],[f_1607_4]) ).
fof(f_1608_1,plain,
! [V_g_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_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_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2))
| ? [B_x] :
( hAPP(V_g_2,B_x) != c_Groups_Ozero__class_Ozero(T_d)
& 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))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Ounion__inter__neutral]) ).
fof(f_1608_2,plain,
! [U_6911,U_6910,U_6909,U_6908,U_6907] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6908,U_6907),U_6911),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6908,tc_HOL_Obool)),U_6909),U_6910)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6907),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6908,U_6907),U_6911),U_6909)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6908,U_6907),U_6911),U_6910))
| ? [U_6906] :
( hAPP(U_6911,U_6906) != c_Groups_Ozero__class_Ozero(U_6907)
& hBOOL(hAPP(hAPP(c_member(U_6908),U_6906),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6908,tc_HOL_Obool)),U_6909),U_6910))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6908),U_6910))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6908),U_6909))
| ~ class_Groups_Ocomm__monoid__add(U_6907) ),
inference(variable_rename,[status(thm)],[f_1608_1]) ).
fof(f_1608_3,plain,
! [U_6911,U_6910,U_6909,U_6908,U_6907] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6908,U_6907),U_6911),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6908,tc_HOL_Obool)),U_6909),U_6910)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6907),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6908,U_6907),U_6911),U_6909)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6908,U_6907),U_6911),U_6910))
| ( hAPP(U_6911,sK135(U_6911,U_6910,U_6909,U_6908,U_6907)) != c_Groups_Ozero__class_Ozero(U_6907)
& hBOOL(hAPP(hAPP(c_member(U_6908),sK135(U_6911,U_6910,U_6909,U_6908,U_6907)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6908,tc_HOL_Obool)),U_6909),U_6910))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6908),U_6910))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6908),U_6909))
| ~ class_Groups_Ocomm__monoid__add(U_6907) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_6906,sK135(U_6911,U_6910,U_6909,U_6908,U_6907))],[f_1608_2]) ).
fof(f_1608_4,plain,
( ! [U_6907,U_6909,U_6908,U_6910,U_6911] :
( hAPP(U_6911,sK135(U_6911,U_6910,U_6909,U_6908,U_6907)) != c_Groups_Ozero__class_Ozero(U_6907)
| ~ sP400(U_6907,U_6909,U_6908,U_6910,U_6911) )
& ! [U_6907,U_6909,U_6908,U_6910,U_6911] :
( hBOOL(hAPP(hAPP(c_member(U_6908),sK135(U_6911,U_6910,U_6909,U_6908,U_6907)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6908,tc_HOL_Obool)),U_6909),U_6910)))
| ~ sP400(U_6907,U_6909,U_6908,U_6910,U_6911) )
& ! [U_6907,U_6909,U_6908,U_6910,U_6911] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6908,U_6907),U_6911),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6908,tc_HOL_Obool)),U_6909),U_6910)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6907),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6908,U_6907),U_6911),U_6909)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6908,U_6907),U_6911),U_6910))
| sP400(U_6907,U_6909,U_6908,U_6910,U_6911)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6908),U_6910))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6908),U_6909))
| ~ class_Groups_Ocomm__monoid__add(U_6907) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP400])],[f_1608_3]) ).
cnf(f_1608_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6908,U_6907),U_6911),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6908,tc_HOL_Obool)),U_6909),U_6910)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6907),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6908,U_6907),U_6911),U_6909)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6908,U_6907),U_6911),U_6910))
| sP400(U_6907,U_6909,U_6908,U_6910,U_6911)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6908),U_6910))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6908),U_6909))
| ~ class_Groups_Ocomm__monoid__add(U_6907) ),
inference(clausify,[status(thm)],[f_1608_4]) ).
cnf(f_1608_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_6908),sK135(U_6911,U_6910,U_6909,U_6908,U_6907)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6908,tc_HOL_Obool)),U_6909),U_6910)))
| ~ sP400(U_6907,U_6909,U_6908,U_6910,U_6911) ),
inference(clausify,[status(thm)],[f_1608_4]) ).
cnf(f_1608_7,plain,
( hAPP(U_6911,sK135(U_6911,U_6910,U_6909,U_6908,U_6907)) != c_Groups_Ozero__class_Ozero(U_6907)
| ~ sP400(U_6907,U_6909,U_6908,U_6910,U_6911) ),
inference(clausify,[status(thm)],[f_1608_4]) ).
fof(f_1609_1,plain,
! [V_k_2,V_A_2,T_c] :
( ( hAPP(c_Finite__Set_Ocard(T_c),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
| ! [B_b,B_B] :
( ( B_B != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(T_c),B_B) != V_k_2
| hBOOL(hAPP(hAPP(c_member(T_c),B_b),B_B))
| V_A_2 != hAPP(hAPP(c_Set_Oinsert(T_c),B_b),B_B) ) )
& ( ? [B_b,B_B] :
( ( B_B = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(T_c),B_B) = V_k_2
& ~ hBOOL(hAPP(hAPP(c_member(T_c),B_b),B_B))
& V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_c),B_b),B_B) )
| hAPP(c_Finite__Set_Ocard(T_c),V_A_2) != hAPP(c_Nat_OSuc,V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_card__Suc__eq]) ).
fof(f_1609_2,plain,
! [U_6918,U_6917,U_6916] :
( ( hAPP(c_Finite__Set_Ocard(U_6916),U_6917) = hAPP(c_Nat_OSuc,U_6918)
| ! [U_6915,U_6914] :
( ( U_6914 != c_Orderings_Obot__class_Obot(tc_fun(U_6916,tc_HOL_Obool))
& U_6918 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_6916),U_6914) != U_6918
| hBOOL(hAPP(hAPP(c_member(U_6916),U_6915),U_6914))
| U_6917 != hAPP(hAPP(c_Set_Oinsert(U_6916),U_6915),U_6914) ) )
& ( ? [U_6913,U_6912] :
( ( U_6912 = c_Orderings_Obot__class_Obot(tc_fun(U_6916,tc_HOL_Obool))
| U_6918 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_6916),U_6912) = U_6918
& ~ hBOOL(hAPP(hAPP(c_member(U_6916),U_6913),U_6912))
& U_6917 = hAPP(hAPP(c_Set_Oinsert(U_6916),U_6913),U_6912) )
| hAPP(c_Finite__Set_Ocard(U_6916),U_6917) != hAPP(c_Nat_OSuc,U_6918) ) ),
inference(variable_rename,[status(thm)],[f_1609_1]) ).
fof(f_1609_3,plain,
( ! [U_6924,U_6922,U_6920] :
( hAPP(c_Finite__Set_Ocard(U_6920),U_6922) = hAPP(c_Nat_OSuc,U_6924)
| ! [U_6915,U_6914] :
( ( U_6914 != c_Orderings_Obot__class_Obot(tc_fun(U_6920,tc_HOL_Obool))
& U_6924 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_6920),U_6914) != U_6924
| hBOOL(hAPP(hAPP(c_member(U_6920),U_6915),U_6914))
| U_6922 != hAPP(hAPP(c_Set_Oinsert(U_6920),U_6915),U_6914) ) )
& ! [U_6923,U_6921,U_6919] :
( ? [U_6913,U_6912] :
( ( U_6912 = c_Orderings_Obot__class_Obot(tc_fun(U_6919,tc_HOL_Obool))
| U_6923 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_6919),U_6912) = U_6923
& ~ hBOOL(hAPP(hAPP(c_member(U_6919),U_6913),U_6912))
& U_6921 = hAPP(hAPP(c_Set_Oinsert(U_6919),U_6913),U_6912) )
| hAPP(c_Finite__Set_Ocard(U_6919),U_6921) != hAPP(c_Nat_OSuc,U_6923) ) ),
inference(miniscope,[status(thm)],[f_1609_2]) ).
fof(f_1609_4,plain,
( ! [U_6924,U_6922,U_6920] :
( hAPP(c_Finite__Set_Ocard(U_6920),U_6922) = hAPP(c_Nat_OSuc,U_6924)
| ! [U_6915,U_6914] :
( ( U_6914 != c_Orderings_Obot__class_Obot(tc_fun(U_6920,tc_HOL_Obool))
& U_6924 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_6920),U_6914) != U_6924
| hBOOL(hAPP(hAPP(c_member(U_6920),U_6915),U_6914))
| U_6922 != hAPP(hAPP(c_Set_Oinsert(U_6920),U_6915),U_6914) ) )
& ! [U_6923,U_6921,U_6919] :
( ? [U_6912] :
( ( U_6912 = c_Orderings_Obot__class_Obot(tc_fun(U_6919,tc_HOL_Obool))
| U_6923 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_6919),U_6912) = U_6923
& ~ hBOOL(hAPP(hAPP(c_member(U_6919),sK136(U_6923,U_6921,U_6919)),U_6912))
& U_6921 = hAPP(hAPP(c_Set_Oinsert(U_6919),sK136(U_6923,U_6921,U_6919)),U_6912) )
| hAPP(c_Finite__Set_Ocard(U_6919),U_6921) != hAPP(c_Nat_OSuc,U_6923) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_6913,sK136(U_6923,U_6921,U_6919))],[f_1609_3]) ).
fof(f_1609_5,plain,
( ! [U_6924,U_6922,U_6920] :
( hAPP(c_Finite__Set_Ocard(U_6920),U_6922) = hAPP(c_Nat_OSuc,U_6924)
| ! [U_6915,U_6914] :
( ( U_6914 != c_Orderings_Obot__class_Obot(tc_fun(U_6920,tc_HOL_Obool))
& U_6924 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_6920),U_6914) != U_6924
| hBOOL(hAPP(hAPP(c_member(U_6920),U_6915),U_6914))
| U_6922 != hAPP(hAPP(c_Set_Oinsert(U_6920),U_6915),U_6914) ) )
& ! [U_6923,U_6921,U_6919] :
( ( ( sK137(U_6923,U_6921,U_6919) = c_Orderings_Obot__class_Obot(tc_fun(U_6919,tc_HOL_Obool))
| U_6923 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_6919),sK137(U_6923,U_6921,U_6919)) = U_6923
& ~ hBOOL(hAPP(hAPP(c_member(U_6919),sK136(U_6923,U_6921,U_6919)),sK137(U_6923,U_6921,U_6919)))
& U_6921 = hAPP(hAPP(c_Set_Oinsert(U_6919),sK136(U_6923,U_6921,U_6919)),sK137(U_6923,U_6921,U_6919)) )
| hAPP(c_Finite__Set_Ocard(U_6919),U_6921) != hAPP(c_Nat_OSuc,U_6923) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_6912,sK137(U_6923,U_6921,U_6919))],[f_1609_4]) ).
fof(f_1609_6,plain,
( ! [U_6914,U_6924,U_6920] :
( U_6914 != c_Orderings_Obot__class_Obot(tc_fun(U_6920,tc_HOL_Obool))
| ~ sP402(U_6914,U_6924,U_6920) )
& ! [U_6914,U_6924,U_6920] :
( U_6924 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP402(U_6914,U_6924,U_6920) )
& ! [U_6921,U_6923,U_6919] :
( sK137(U_6923,U_6921,U_6919) = c_Orderings_Obot__class_Obot(tc_fun(U_6919,tc_HOL_Obool))
| U_6923 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP401(U_6921,U_6923,U_6919) )
& ! [U_6921,U_6923,U_6919] :
( hAPP(c_Finite__Set_Ocard(U_6919),sK137(U_6923,U_6921,U_6919)) = U_6923
| ~ sP401(U_6921,U_6923,U_6919) )
& ! [U_6921,U_6923,U_6919] :
( ~ hBOOL(hAPP(hAPP(c_member(U_6919),sK136(U_6923,U_6921,U_6919)),sK137(U_6923,U_6921,U_6919)))
| ~ sP401(U_6921,U_6923,U_6919) )
& ! [U_6921,U_6923,U_6919] :
( U_6921 = hAPP(hAPP(c_Set_Oinsert(U_6919),sK136(U_6923,U_6921,U_6919)),sK137(U_6923,U_6921,U_6919))
| ~ sP401(U_6921,U_6923,U_6919) )
& ! [U_6914,U_6922,U_6915,U_6924,U_6920] :
( hAPP(c_Finite__Set_Ocard(U_6920),U_6922) = hAPP(c_Nat_OSuc,U_6924)
| sP402(U_6914,U_6924,U_6920)
| hAPP(c_Finite__Set_Ocard(U_6920),U_6914) != U_6924
| hBOOL(hAPP(hAPP(c_member(U_6920),U_6915),U_6914))
| U_6922 != hAPP(hAPP(c_Set_Oinsert(U_6920),U_6915),U_6914) )
& ! [U_6921,U_6923,U_6919] :
( sP401(U_6921,U_6923,U_6919)
| hAPP(c_Finite__Set_Ocard(U_6919),U_6921) != hAPP(c_Nat_OSuc,U_6923) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP401,sP402])],[f_1609_5]) ).
cnf(f_1609_7,plain,
( sP401(U_6921,U_6923,U_6919)
| hAPP(c_Finite__Set_Ocard(U_6919),U_6921) != hAPP(c_Nat_OSuc,U_6923) ),
inference(clausify,[status(thm)],[f_1609_6]) ).
cnf(f_1609_8,plain,
( hAPP(c_Finite__Set_Ocard(U_6920),U_6922) = hAPP(c_Nat_OSuc,U_6924)
| sP402(U_6914,U_6924,U_6920)
| hAPP(c_Finite__Set_Ocard(U_6920),U_6914) != U_6924
| hBOOL(hAPP(hAPP(c_member(U_6920),U_6915),U_6914))
| U_6922 != hAPP(hAPP(c_Set_Oinsert(U_6920),U_6915),U_6914) ),
inference(clausify,[status(thm)],[f_1609_6]) ).
cnf(f_1609_9,plain,
( U_6921 = hAPP(hAPP(c_Set_Oinsert(U_6919),sK136(U_6923,U_6921,U_6919)),sK137(U_6923,U_6921,U_6919))
| ~ sP401(U_6921,U_6923,U_6919) ),
inference(clausify,[status(thm)],[f_1609_6]) ).
cnf(f_1609_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_6919),sK136(U_6923,U_6921,U_6919)),sK137(U_6923,U_6921,U_6919)))
| ~ sP401(U_6921,U_6923,U_6919) ),
inference(clausify,[status(thm)],[f_1609_6]) ).
cnf(f_1609_11,plain,
( hAPP(c_Finite__Set_Ocard(U_6919),sK137(U_6923,U_6921,U_6919)) = U_6923
| ~ sP401(U_6921,U_6923,U_6919) ),
inference(clausify,[status(thm)],[f_1609_6]) ).
cnf(f_1609_12,plain,
( sK137(U_6923,U_6921,U_6919) = c_Orderings_Obot__class_Obot(tc_fun(U_6919,tc_HOL_Obool))
| U_6923 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP401(U_6921,U_6923,U_6919) ),
inference(clausify,[status(thm)],[f_1609_6]) ).
cnf(f_1609_13,plain,
( U_6924 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP402(U_6914,U_6924,U_6920) ),
inference(clausify,[status(thm)],[f_1609_6]) ).
cnf(f_1609_14,plain,
( U_6914 != c_Orderings_Obot__class_Obot(tc_fun(U_6920,tc_HOL_Obool))
| ~ sP402(U_6914,U_6924,U_6920) ),
inference(clausify,[status(thm)],[f_1609_6]) ).
fof(f_1610_1,plain,
! [V_f_2,V_A_2,V_B_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_B_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ class_Groups_Oordered__ab__semigroup__add(T_d)
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono3]) ).
fof(f_1610_2,plain,
! [U_6930,U_6929,U_6928,U_6927,U_6926] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6926),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6927,U_6926),U_6930),U_6929)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6927,U_6926),U_6930),U_6928)))
| ? [U_6925] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6926),c_Groups_Ozero__class_Ozero(U_6926)),hAPP(U_6930,U_6925)))
& hBOOL(hAPP(hAPP(c_member(U_6927),U_6925),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6927,tc_HOL_Obool)),U_6928),U_6929))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6927,tc_HOL_Obool)),U_6929),U_6928))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6927),U_6928))
| ~ class_Groups_Oordered__ab__semigroup__add(U_6926)
| ~ class_Groups_Ocomm__monoid__add(U_6926) ),
inference(variable_rename,[status(thm)],[f_1610_1]) ).
fof(f_1610_3,plain,
! [U_6930,U_6929,U_6928,U_6927,U_6926] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6926),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6927,U_6926),U_6930),U_6929)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6927,U_6926),U_6930),U_6928)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6926),c_Groups_Ozero__class_Ozero(U_6926)),hAPP(U_6930,sK138(U_6930,U_6929,U_6928,U_6927,U_6926))))
& hBOOL(hAPP(hAPP(c_member(U_6927),sK138(U_6930,U_6929,U_6928,U_6927,U_6926)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6927,tc_HOL_Obool)),U_6928),U_6929))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6927,tc_HOL_Obool)),U_6929),U_6928))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6927),U_6928))
| ~ class_Groups_Oordered__ab__semigroup__add(U_6926)
| ~ class_Groups_Ocomm__monoid__add(U_6926) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_6925,sK138(U_6930,U_6929,U_6928,U_6927,U_6926))],[f_1610_2]) ).
fof(f_1610_4,plain,
( ! [U_6926,U_6927,U_6928,U_6929,U_6930] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6926),c_Groups_Ozero__class_Ozero(U_6926)),hAPP(U_6930,sK138(U_6930,U_6929,U_6928,U_6927,U_6926))))
| ~ sP403(U_6926,U_6927,U_6928,U_6929,U_6930) )
& ! [U_6926,U_6927,U_6928,U_6929,U_6930] :
( hBOOL(hAPP(hAPP(c_member(U_6927),sK138(U_6930,U_6929,U_6928,U_6927,U_6926)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6927,tc_HOL_Obool)),U_6928),U_6929)))
| ~ sP403(U_6926,U_6927,U_6928,U_6929,U_6930) )
& ! [U_6926,U_6927,U_6928,U_6929,U_6930] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6926),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6927,U_6926),U_6930),U_6929)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6927,U_6926),U_6930),U_6928)))
| sP403(U_6926,U_6927,U_6928,U_6929,U_6930)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6927,tc_HOL_Obool)),U_6929),U_6928))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6927),U_6928))
| ~ class_Groups_Oordered__ab__semigroup__add(U_6926)
| ~ class_Groups_Ocomm__monoid__add(U_6926) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP403])],[f_1610_3]) ).
cnf(f_1610_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6926),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6927,U_6926),U_6930),U_6929)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6927,U_6926),U_6930),U_6928)))
| sP403(U_6926,U_6927,U_6928,U_6929,U_6930)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6927,tc_HOL_Obool)),U_6929),U_6928))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6927),U_6928))
| ~ class_Groups_Oordered__ab__semigroup__add(U_6926)
| ~ class_Groups_Ocomm__monoid__add(U_6926) ),
inference(clausify,[status(thm)],[f_1610_4]) ).
cnf(f_1610_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_6927),sK138(U_6930,U_6929,U_6928,U_6927,U_6926)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6927,tc_HOL_Obool)),U_6928),U_6929)))
| ~ sP403(U_6926,U_6927,U_6928,U_6929,U_6930) ),
inference(clausify,[status(thm)],[f_1610_4]) ).
cnf(f_1610_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6926),c_Groups_Ozero__class_Ozero(U_6926)),hAPP(U_6930,sK138(U_6930,U_6929,U_6928,U_6927,U_6926))))
| ~ sP403(U_6926,U_6927,U_6928,U_6929,U_6930) ),
inference(clausify,[status(thm)],[f_1610_4]) ).
fof(f_1611_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0]) ).
fof(f_1611_2,plain,
! [U_6932,U_6931] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6931),c_Groups_Oone__class_Oone(U_6931)),U_6932)),U_6932)),c_Groups_Ozero__class_Ozero(U_6931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6931),U_6932),c_Groups_Ozero__class_Ozero(U_6931))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6931),U_6932),c_Groups_Ozero__class_Ozero(U_6931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6931),c_Groups_Oone__class_Oone(U_6931)),U_6932)),U_6932)),c_Groups_Ozero__class_Ozero(U_6931))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_6931),U_6932),c_Int_Oring__1__class_OInts(U_6931)))
| ~ class_Rings_Olinordered__idom(U_6931) ),
inference(variable_rename,[status(thm)],[f_1611_1]) ).
fof(f_1611_3,plain,
( ! [U_6932,U_6931] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6931),c_Groups_Oone__class_Oone(U_6931)),U_6932)),U_6932)),c_Groups_Ozero__class_Ozero(U_6931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6931),U_6932),c_Groups_Ozero__class_Ozero(U_6931)))
| ~ sP404(U_6932,U_6931) )
& ! [U_6932,U_6931] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6931),U_6932),c_Groups_Ozero__class_Ozero(U_6931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6931),c_Groups_Oone__class_Oone(U_6931)),U_6932)),U_6932)),c_Groups_Ozero__class_Ozero(U_6931)))
| ~ sP404(U_6932,U_6931) )
& ! [U_6932,U_6931] :
( sP404(U_6932,U_6931)
| ~ hBOOL(hAPP(hAPP(c_member(U_6931),U_6932),c_Int_Oring__1__class_OInts(U_6931)))
| ~ class_Rings_Olinordered__idom(U_6931) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP404])],[f_1611_2]) ).
cnf(f_1611_4,plain,
( sP404(U_6932,U_6931)
| ~ hBOOL(hAPP(hAPP(c_member(U_6931),U_6932),c_Int_Oring__1__class_OInts(U_6931)))
| ~ class_Rings_Olinordered__idom(U_6931) ),
inference(clausify,[status(thm)],[f_1611_3]) ).
cnf(f_1611_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6931),U_6932),c_Groups_Ozero__class_Ozero(U_6931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6931),c_Groups_Oone__class_Oone(U_6931)),U_6932)),U_6932)),c_Groups_Ozero__class_Ozero(U_6931)))
| ~ sP404(U_6932,U_6931) ),
inference(clausify,[status(thm)],[f_1611_3]) ).
cnf(f_1611_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6931),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6931),c_Groups_Oone__class_Oone(U_6931)),U_6932)),U_6932)),c_Groups_Ozero__class_Ozero(U_6931)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6931),U_6932),c_Groups_Ozero__class_Ozero(U_6931)))
| ~ sP404(U_6932,U_6931) ),
inference(clausify,[status(thm)],[f_1611_3]) ).
fof(f_1612_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_1612_2,plain,
! [U_6934,U_6933] : 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_6933)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6934))),
inference(variable_rename,[status(thm)],[f_1612_1]) ).
fof(f_1612_3,plain,
! [U_6933,U_6934] : 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_6933)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6934))),
inference(definitional_conversion,[status(esa)],[f_1612_2]) ).
cnf(f_1612_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_6933)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6934))),
inference(clausify,[status(thm)],[f_1612_3]) ).
fof(f_1613_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_1613_2,plain,
! [U_6936,U_6935] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6935),U_6936) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6936 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6935 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( U_6936 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_6935 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6935),U_6936) != 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_6935)) ),
inference(variable_rename,[status(thm)],[f_1613_1]) ).
fof(f_1613_3,plain,
( ! [U_6935,U_6936] :
( U_6936 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP405(U_6935,U_6936) )
& ! [U_6935,U_6936] :
( U_6935 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP405(U_6935,U_6936) )
& ! [U_6935,U_6936] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6935),U_6936) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6936 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6935 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP406(U_6935,U_6936) )
& ! [U_6935,U_6936] :
( sP405(U_6935,U_6936)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6935),U_6936) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP406(U_6935,U_6936) )
& ! [U_6935,U_6936] :
( sP406(U_6935,U_6936)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6935)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP405,sP406])],[f_1613_2]) ).
cnf(f_1613_4,plain,
( sP406(U_6935,U_6936)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6935)) ),
inference(clausify,[status(thm)],[f_1613_3]) ).
cnf(f_1613_5,plain,
( sP405(U_6935,U_6936)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6935),U_6936) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP406(U_6935,U_6936) ),
inference(clausify,[status(thm)],[f_1613_3]) ).
cnf(f_1613_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6935),U_6936) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6936 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6935 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP406(U_6935,U_6936) ),
inference(clausify,[status(thm)],[f_1613_3]) ).
cnf(f_1613_7,plain,
( U_6935 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP405(U_6935,U_6936) ),
inference(clausify,[status(thm)],[f_1613_3]) ).
cnf(f_1613_8,plain,
( U_6936 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP405(U_6935,U_6936) ),
inference(clausify,[status(thm)],[f_1613_3]) ).
fof(f_1614_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_1614_2,plain,
! [U_6939,U_6938,U_6937] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6939),U_6937)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6939),U_6938)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6939))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6937),U_6938)) ),
inference(variable_rename,[status(thm)],[f_1614_1]) ).
fof(f_1614_3,plain,
! [U_6937,U_6938,U_6939] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6939),U_6937)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6939),U_6938)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6939))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6937),U_6938)) ),
inference(definitional_conversion,[status(esa)],[f_1614_2]) ).
cnf(f_1614_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6939),U_6937)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6939),U_6938)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6939))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6937),U_6938)) ),
inference(clausify,[status(thm)],[f_1614_3]) ).
fof(f_1615_1,plain,
! [V_n_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Rings_Oring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__of__nat]) ).
fof(f_1615_2,plain,
! [U_6941,U_6940] :
( hBOOL(hAPP(hAPP(c_member(U_6940),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6940),U_6941)),c_Int_Oring__1__class_OInts(U_6940)))
| ~ class_Rings_Oring__1(U_6940) ),
inference(variable_rename,[status(thm)],[f_1615_1]) ).
fof(f_1615_3,plain,
! [U_6940,U_6941] :
( hBOOL(hAPP(hAPP(c_member(U_6940),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6940),U_6941)),c_Int_Oring__1__class_OInts(U_6940)))
| ~ class_Rings_Oring__1(U_6940) ),
inference(definitional_conversion,[status(esa)],[f_1615_2]) ).
cnf(f_1615_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_6940),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6940),U_6941)),c_Int_Oring__1__class_OInts(U_6940)))
| ~ class_Rings_Oring__1(U_6940) ),
inference(clausify,[status(thm)],[f_1615_3]) ).
fof(f_1616_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_1616_2,plain,
! [U_6943,U_6942] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6942)),U_6943) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6942),U_6943)),
inference(variable_rename,[status(thm)],[f_1616_1]) ).
fof(f_1616_3,plain,
! [U_6942,U_6943] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6942)),U_6943) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6942),U_6943)),
inference(definitional_conversion,[status(esa)],[f_1616_2]) ).
cnf(f_1616_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6942)),U_6943) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6942),U_6943)),
inference(clausify,[status(thm)],[f_1616_3]) ).
fof(f_1617_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_1617_2,plain,
! [U_6946,U_6945,U_6944] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),U_6945)),U_6946) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6945),U_6946)),
inference(variable_rename,[status(thm)],[f_1617_1]) ).
fof(f_1617_3,plain,
! [U_6944,U_6945,U_6946] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),U_6945)),U_6946) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6945),U_6946)),
inference(definitional_conversion,[status(esa)],[f_1617_2]) ).
cnf(f_1617_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),U_6945)),U_6946) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6945),U_6946)),
inference(clausify,[status(thm)],[f_1617_3]) ).
fof(f_1618_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_1618_2,plain,
! [U_6948,U_6947] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6947),U_6948) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6948),U_6947),
inference(variable_rename,[status(thm)],[f_1618_1]) ).
fof(f_1618_3,plain,
! [U_6947,U_6948] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6947),U_6948) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6948),U_6947),
inference(definitional_conversion,[status(esa)],[f_1618_2]) ).
cnf(f_1618_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6947),U_6948) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6948),U_6947),
inference(clausify,[status(thm)],[f_1618_3]) ).
fof(f_1619_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_1619_2,plain,
! [U_6951,U_6950,U_6949] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6949),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6950),U_6951)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6949),U_6950)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6949),U_6951)),
inference(variable_rename,[status(thm)],[f_1619_1]) ).
fof(f_1619_3,plain,
! [U_6949,U_6950,U_6951] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6949),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6950),U_6951)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6949),U_6950)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6949),U_6951)),
inference(definitional_conversion,[status(esa)],[f_1619_2]) ).
cnf(f_1619_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6949),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6950),U_6951)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6949),U_6950)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6949),U_6951)),
inference(clausify,[status(thm)],[f_1619_3]) ).
fof(f_1620_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_1620_2,plain,
! [U_6954,U_6953,U_6952] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6952),U_6953)),U_6954) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6952),U_6954)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6953),U_6954)),
inference(variable_rename,[status(thm)],[f_1620_1]) ).
fof(f_1620_3,plain,
! [U_6952,U_6953,U_6954] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6952),U_6953)),U_6954) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6952),U_6954)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6953),U_6954)),
inference(definitional_conversion,[status(esa)],[f_1620_2]) ).
cnf(f_1620_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6952),U_6953)),U_6954) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6952),U_6954)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6953),U_6954)),
inference(clausify,[status(thm)],[f_1620_3]) ).
fof(f_1621_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_1621_2,plain,
! [U_6957,U_6956,U_6955] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6955),U_6956)),U_6957) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6955),U_6957)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6956),U_6957)),
inference(variable_rename,[status(thm)],[f_1621_1]) ).
fof(f_1621_3,plain,
! [U_6955,U_6956,U_6957] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6955),U_6956)),U_6957) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6955),U_6957)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6956),U_6957)),
inference(definitional_conversion,[status(esa)],[f_1621_2]) ).
cnf(f_1621_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6955),U_6956)),U_6957) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6955),U_6957)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6956),U_6957)),
inference(clausify,[status(thm)],[f_1621_3]) ).
fof(f_1622_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_1622_2,plain,
! [U_6960,U_6959,U_6958] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6958),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6959),U_6960)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6958),U_6959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6958),U_6960)),
inference(variable_rename,[status(thm)],[f_1622_1]) ).
fof(f_1622_3,plain,
! [U_6958,U_6959,U_6960] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6958),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6959),U_6960)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6958),U_6959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6958),U_6960)),
inference(definitional_conversion,[status(esa)],[f_1622_2]) ).
cnf(f_1622_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6958),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6959),U_6960)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6958),U_6959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6958),U_6960)),
inference(clausify,[status(thm)],[f_1622_3]) ).
fof(f_1623_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_1623_2,plain,
! [U_6961] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6961) = U_6961,
inference(variable_rename,[status(thm)],[f_1623_1]) ).
fof(f_1623_3,plain,
! [U_6961] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6961) = U_6961,
inference(definitional_conversion,[status(esa)],[f_1623_2]) ).
cnf(f_1623_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6961) = U_6961,
inference(clausify,[status(thm)],[f_1623_3]) ).
fof(f_1624_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_1624_2,plain,
! [U_6962] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6962),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_6962,
inference(variable_rename,[status(thm)],[f_1624_1]) ).
fof(f_1624_3,plain,
! [U_6962] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6962),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_6962,
inference(definitional_conversion,[status(esa)],[f_1624_2]) ).
cnf(f_1624_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6962),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_6962,
inference(clausify,[status(thm)],[f_1624_3]) ).
fof(f_1625_1,plain,
! [V_n_2,V_m_2,T_c] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_m_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2) ) )
| ~ class_Nat_Osemiring__char__0(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff]) ).
fof(f_1625_2,plain,
! [U_6965,U_6964,U_6963] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6963),U_6964) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6963),U_6965)
| U_6964 != U_6965 )
& ( U_6964 = U_6965
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6963),U_6964) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6963),U_6965) ) )
| ~ class_Nat_Osemiring__char__0(U_6963) ),
inference(variable_rename,[status(thm)],[f_1625_1]) ).
fof(f_1625_3,plain,
( ! [U_6963,U_6964,U_6965] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6963),U_6964) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6963),U_6965)
| U_6964 != U_6965
| ~ sP407(U_6963,U_6964,U_6965) )
& ! [U_6963,U_6964,U_6965] :
( U_6964 = U_6965
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6963),U_6964) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6963),U_6965)
| ~ sP407(U_6963,U_6964,U_6965) )
& ! [U_6963,U_6964,U_6965] :
( sP407(U_6963,U_6964,U_6965)
| ~ class_Nat_Osemiring__char__0(U_6963) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP407])],[f_1625_2]) ).
cnf(f_1625_4,plain,
( sP407(U_6963,U_6964,U_6965)
| ~ class_Nat_Osemiring__char__0(U_6963) ),
inference(clausify,[status(thm)],[f_1625_3]) ).
cnf(f_1625_5,plain,
( U_6964 = U_6965
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6963),U_6964) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6963),U_6965)
| ~ sP407(U_6963,U_6964,U_6965) ),
inference(clausify,[status(thm)],[f_1625_3]) ).
cnf(f_1625_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6963),U_6964) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6963),U_6965)
| U_6964 != U_6965
| ~ sP407(U_6963,U_6964,U_6965) ),
inference(clausify,[status(thm)],[f_1625_3]) ).
fof(f_1626_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_1626_2,plain,
! [U_6967,U_6966] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6966)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6967))))
| U_6967 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6966 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_6967 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6966 = 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_6966)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6967)))) ) ),
inference(variable_rename,[status(thm)],[f_1626_1]) ).
fof(f_1626_3,plain,
( ! [U_6971,U_6969] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6969)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6971))))
| U_6971 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6969 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6970,U_6968] :
( ( U_6970 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6968 = 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_6968)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6970)))) ) ),
inference(miniscope,[status(thm)],[f_1626_2]) ).
fof(f_1626_4,plain,
( ! [U_6968,U_6970] :
( U_6970 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP408(U_6968,U_6970) )
& ! [U_6968,U_6970] :
( U_6968 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP408(U_6968,U_6970) )
& ! [U_6969,U_6971] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6969)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6971))))
| U_6971 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6969 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6968,U_6970] :
( sP408(U_6968,U_6970)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6968)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6970)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP408])],[f_1626_3]) ).
cnf(f_1626_5,plain,
( sP408(U_6968,U_6970)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6968)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6970)))) ),
inference(clausify,[status(thm)],[f_1626_4]) ).
cnf(f_1626_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_6969)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6971))))
| U_6971 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6969 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1626_4]) ).
cnf(f_1626_7,plain,
( U_6968 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP408(U_6968,U_6970) ),
inference(clausify,[status(thm)],[f_1626_4]) ).
cnf(f_1626_8,plain,
( U_6970 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP408(U_6968,U_6970) ),
inference(clausify,[status(thm)],[f_1626_4]) ).
fof(f_1627_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_1627_2,plain,
! [U_6972] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6972)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6972 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_6972 = 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_6972)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1627_1]) ).
fof(f_1627_3,plain,
( ! [U_6974] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6974)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6974 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6973] :
( U_6973 = 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_6973)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1627_2]) ).
fof(f_1627_4,plain,
( ! [U_6974] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6974)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6974 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6973] :
( U_6973 = 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_6973)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_1627_3]) ).
cnf(f_1627_5,plain,
( U_6973 = 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_6973)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1627_4]) ).
cnf(f_1627_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_6974)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_6974 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1627_4]) ).
fof(f_1628_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_1628_2,plain,
! [U_6975] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6975) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6975 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_6975 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6975) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1628_1]) ).
fof(f_1628_3,plain,
( ! [U_6977] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6977) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6977 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6976] :
( U_6976 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6976) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1628_2]) ).
fof(f_1628_4,plain,
( ! [U_6977] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6977) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6977 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6976] :
( U_6976 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6976) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa)],[f_1628_3]) ).
cnf(f_1628_5,plain,
( U_6976 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6976) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1628_4]) ).
cnf(f_1628_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6977) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_6977 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1628_4]) ).
fof(f_1629_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_1629_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_1629_1]) ).
cnf(f_1629_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_1629_2]) ).
fof(f_1630_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_1630_2,plain,
! [U_6979,U_6978] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6978)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6979)
| U_6979 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6978 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_6979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6978 = 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_6978)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6979) ) ),
inference(variable_rename,[status(thm)],[f_1630_1]) ).
fof(f_1630_3,plain,
( ! [U_6983,U_6981] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6981)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6983)
| U_6983 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6981 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6982,U_6980] :
( ( U_6982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_6980 = 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_6980)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6982) ) ),
inference(miniscope,[status(thm)],[f_1630_2]) ).
fof(f_1630_4,plain,
( ! [U_6980,U_6982] :
( U_6982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP409(U_6980,U_6982) )
& ! [U_6980,U_6982] :
( U_6980 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP409(U_6980,U_6982) )
& ! [U_6983,U_6981] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6981)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6983)
| U_6983 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6981 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_6980,U_6982] :
( sP409(U_6980,U_6982)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6980)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6982) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP409])],[f_1630_3]) ).
cnf(f_1630_5,plain,
( sP409(U_6980,U_6982)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6980)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6982) ),
inference(clausify,[status(thm)],[f_1630_4]) ).
cnf(f_1630_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6981)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6983)
| U_6983 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_6981 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1630_4]) ).
cnf(f_1630_7,plain,
( U_6980 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP409(U_6980,U_6982) ),
inference(clausify,[status(thm)],[f_1630_4]) ).
cnf(f_1630_8,plain,
( U_6982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP409(U_6980,U_6982) ),
inference(clausify,[status(thm)],[f_1630_4]) ).
fof(f_1631_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_1631_2,plain,
! [U_6987,U_6986] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6986),U_6987))
| ! [U_6985] : U_6987 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6986),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6985))) )
& ( ? [U_6984] : U_6987 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6986),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6984)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6986),U_6987)) ) ),
inference(variable_rename,[status(thm)],[f_1631_1]) ).
fof(f_1631_3,plain,
( ! [U_6991,U_6989] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6989),U_6991))
| ! [U_6985] : U_6991 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6989),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6985))) )
& ! [U_6990,U_6988] :
( ? [U_6984] : U_6990 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6988),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6984)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6988),U_6990)) ) ),
inference(miniscope,[status(thm)],[f_1631_2]) ).
fof(f_1631_4,plain,
( ! [U_6991,U_6989] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6989),U_6991))
| ! [U_6985] : U_6991 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6989),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6985))) )
& ! [U_6990,U_6988] :
( U_6990 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6988),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK139(U_6990,U_6988))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6988),U_6990)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_6984,sK139(U_6990,U_6988))],[f_1631_3]) ).
fof(f_1631_5,plain,
( ! [U_6991,U_6985,U_6989] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6989),U_6991))
| U_6991 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6989),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6985))) )
& ! [U_6990,U_6988] :
( U_6990 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6988),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK139(U_6990,U_6988))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6988),U_6990)) ) ),
inference(definitional_conversion,[status(esa)],[f_1631_4]) ).
cnf(f_1631_6,plain,
( U_6990 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6988),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK139(U_6990,U_6988))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6988),U_6990)) ),
inference(clausify,[status(thm)],[f_1631_5]) ).
cnf(f_1631_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6989),U_6991))
| U_6991 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6989),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6985))) ),
inference(clausify,[status(thm)],[f_1631_5]) ).
fof(f_1632_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_1632_2,plain,
! [U_6992] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6992)) = 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_6992)),
inference(variable_rename,[status(thm)],[f_1632_1]) ).
fof(f_1632_3,plain,
! [U_6992] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6992)) = 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_6992)),
inference(definitional_conversion,[status(esa)],[f_1632_2]) ).
cnf(f_1632_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_6992)) = 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_6992)),
inference(clausify,[status(thm)],[f_1632_3]) ).
fof(f_1633_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_1633_2,plain,
! [U_6993] : 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_6993)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1633_1]) ).
fof(f_1633_3,plain,
! [U_6993] : 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_6993)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_1633_2]) ).
cnf(f_1633_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_6993)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1633_3]) ).
fof(f_1634_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_1634_2,plain,
! [U_6994] : ~ 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_6994))))),
inference(variable_rename,[status(thm)],[f_1634_1]) ).
fof(f_1634_3,plain,
! [U_6994] : ~ 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_6994))))),
inference(definitional_conversion,[status(esa)],[f_1634_2]) ).
cnf(f_1634_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_6994))))),
inference(clausify,[status(thm)],[f_1634_3]) ).
fof(f_1635_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_1635_2,plain,
! [U_6996,U_6995] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6995)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6996)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6995),U_6996)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6995),U_6996))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6995)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6996))) ) ),
inference(variable_rename,[status(thm)],[f_1635_1]) ).
fof(f_1635_3,plain,
( ! [U_7000,U_6998] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6998)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7000)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6998),U_7000)) )
& ! [U_6999,U_6997] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6997),U_6999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6997)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6999))) ) ),
inference(miniscope,[status(thm)],[f_1635_2]) ).
fof(f_1635_4,plain,
( ! [U_6998,U_7000] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6998)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7000)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6998),U_7000)) )
& ! [U_6999,U_6997] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6997),U_6999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6997)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6999))) ) ),
inference(definitional_conversion,[status(esa)],[f_1635_3]) ).
cnf(f_1635_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6997),U_6999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6997)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6999))) ),
inference(clausify,[status(thm)],[f_1635_4]) ).
cnf(f_1635_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_6998)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7000)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6998),U_7000)) ),
inference(clausify,[status(thm)],[f_1635_4]) ).
fof(f_1636_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_1636_2,plain,
! [U_7002,U_7001] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7001)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7002)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7001),U_7002)),
inference(variable_rename,[status(thm)],[f_1636_1]) ).
fof(f_1636_3,plain,
! [U_7001,U_7002] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7001)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7002)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7001),U_7002)),
inference(definitional_conversion,[status(esa)],[f_1636_2]) ).
cnf(f_1636_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7001)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7002)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7001),U_7002)),
inference(clausify,[status(thm)],[f_1636_3]) ).
fof(f_1637_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_1637_2,plain,
! [U_7005,U_7004,U_7003] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7003)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7004)),U_7005)) = 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_7003),U_7004))),U_7005),
inference(variable_rename,[status(thm)],[f_1637_1]) ).
fof(f_1637_3,plain,
! [U_7003,U_7004,U_7005] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7003)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7004)),U_7005)) = 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_7003),U_7004))),U_7005),
inference(definitional_conversion,[status(esa)],[f_1637_2]) ).
cnf(f_1637_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7003)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7004)),U_7005)) = 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_7003),U_7004))),U_7005),
inference(clausify,[status(thm)],[f_1637_3]) ).
fof(f_1638_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_1638_2,plain,
! [U_7007,U_7006] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7006)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7007)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7006),U_7007)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7006),U_7007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7006)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7007))) ) ),
inference(variable_rename,[status(thm)],[f_1638_1]) ).
fof(f_1638_3,plain,
( ! [U_7011,U_7009] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7009)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7011)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7009),U_7011)) )
& ! [U_7010,U_7008] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7008),U_7010))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7008)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7010))) ) ),
inference(miniscope,[status(thm)],[f_1638_2]) ).
fof(f_1638_4,plain,
( ! [U_7009,U_7011] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7009)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7011)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7009),U_7011)) )
& ! [U_7010,U_7008] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7008),U_7010))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7008)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7010))) ) ),
inference(definitional_conversion,[status(esa)],[f_1638_3]) ).
cnf(f_1638_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7008),U_7010))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7008)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7010))) ),
inference(clausify,[status(thm)],[f_1638_4]) ).
cnf(f_1638_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_7009)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7011)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7009),U_7011)) ),
inference(clausify,[status(thm)],[f_1638_4]) ).
fof(f_1639_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_1639_2,plain,
! [U_7013,U_7012] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7012),U_7013)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7012)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7013)),
inference(variable_rename,[status(thm)],[f_1639_1]) ).
fof(f_1639_3,plain,
! [U_7013,U_7012] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7012),U_7013)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7012)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7013)),
inference(definitional_conversion,[status(esa)],[f_1639_2]) ).
cnf(f_1639_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7012),U_7013)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7012)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7013)),
inference(clausify,[status(thm)],[f_1639_3]) ).
fof(f_1640_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_1640_2,plain,
! [U_7015,U_7014] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7014)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7015)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7014),U_7015)),
inference(variable_rename,[status(thm)],[f_1640_1]) ).
fof(f_1640_3,plain,
! [U_7014,U_7015] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7014)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7015)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7014),U_7015)),
inference(definitional_conversion,[status(esa)],[f_1640_2]) ).
cnf(f_1640_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7014)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7015)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7014),U_7015)),
inference(clausify,[status(thm)],[f_1640_3]) ).
fof(f_1641_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_1641_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_1641_1]) ).
cnf(f_1641_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_1641_2]) ).
fof(f_1642_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_inj__int]) ).
fof(f_1642_2,plain,
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))),
inference(definitional_conversion,[status(esa)],[f_1642_1]) ).
cnf(f_1642_3,plain,
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))),
inference(clausify,[status(thm)],[f_1642_2]) ).
fof(f_1643_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_1643_2,plain,
! [U_7017,U_7016] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7016)),U_7017) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7016),U_7017)),
inference(variable_rename,[status(thm)],[f_1643_1]) ).
fof(f_1643_3,plain,
! [U_7016,U_7017] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7016)),U_7017) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7016),U_7017)),
inference(definitional_conversion,[status(esa)],[f_1643_2]) ).
cnf(f_1643_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7016)),U_7017) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7016),U_7017)),
inference(clausify,[status(thm)],[f_1643_3]) ).
fof(f_1644_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_1644_2,plain,
! [U_7019,U_7018] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7018),U_7019)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7018)),U_7019),
inference(variable_rename,[status(thm)],[f_1644_1]) ).
fof(f_1644_3,plain,
! [U_7018,U_7019] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7018),U_7019)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7018)),U_7019),
inference(definitional_conversion,[status(esa)],[f_1644_2]) ).
cnf(f_1644_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7018),U_7019)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7018)),U_7019),
inference(clausify,[status(thm)],[f_1644_3]) ).
fof(f_1645_1,plain,
! [V_A_2,V_f_2,T_c] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_c),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_1645_2,plain,
! [U_7022,U_7021,U_7020] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7020,tc_Nat_Onat),U_7021),U_7022)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7020,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7020),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7021)),U_7022),
inference(variable_rename,[status(thm)],[f_1645_1]) ).
fof(f_1645_3,plain,
! [U_7020,U_7021,U_7022] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7020,tc_Nat_Onat),U_7021),U_7022)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7020,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7020),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7021)),U_7022),
inference(definitional_conversion,[status(esa)],[f_1645_2]) ).
cnf(f_1645_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7020,tc_Nat_Onat),U_7021),U_7022)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7020,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7020),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7021)),U_7022),
inference(clausify,[status(thm)],[f_1645_3]) ).
fof(f_1646_1,plain,
! [V_A_2,V_f_2,T_c] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_c),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_1646_2,plain,
! [U_7025,U_7024,U_7023] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7023,tc_Nat_Onat),U_7024),U_7025)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7023,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7023),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7024)),U_7025),
inference(variable_rename,[status(thm)],[f_1646_1]) ).
fof(f_1646_3,plain,
! [U_7023,U_7024,U_7025] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7023,tc_Nat_Onat),U_7024),U_7025)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7023,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7023),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7024)),U_7025),
inference(definitional_conversion,[status(esa)],[f_1646_2]) ).
cnf(f_1646_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7023,tc_Nat_Onat),U_7024),U_7025)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7023,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_7023),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7024)),U_7025),
inference(clausify,[status(thm)],[f_1646_3]) ).
fof(f_1647_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_1647_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_1647_1]) ).
cnf(f_1647_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_1647_2]) ).
fof(f_1648_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_1648_2,plain,
! [U_7028,U_7027,U_7026] :
( 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_7028)),U_7026)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7028)),U_7027)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7028))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7026),U_7027)) ),
inference(variable_rename,[status(thm)],[f_1648_1]) ).
fof(f_1648_3,plain,
! [U_7026,U_7027,U_7028] :
( 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_7028)),U_7026)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7028)),U_7027)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7028))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7026),U_7027)) ),
inference(definitional_conversion,[status(esa)],[f_1648_2]) ).
cnf(f_1648_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_7028)),U_7026)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7028)),U_7027)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7028))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7026),U_7027)) ),
inference(clausify,[status(thm)],[f_1648_3]) ).
fof(f_1649_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_1649_2,plain,
! [U_7029] :
( ( 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_7029)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7029)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7029))
| ~ 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_7029))) ) ),
inference(variable_rename,[status(thm)],[f_1649_1]) ).
fof(f_1649_3,plain,
( ! [U_7031] :
( 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_7031)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7031)) )
& ! [U_7030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7030))
| ~ 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_7030))) ) ),
inference(miniscope,[status(thm)],[f_1649_2]) ).
fof(f_1649_4,plain,
( ! [U_7031] :
( 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_7031)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7031)) )
& ! [U_7030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7030))
| ~ 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_7030))) ) ),
inference(definitional_conversion,[status(esa)],[f_1649_3]) ).
cnf(f_1649_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7030))
| ~ 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_7030))) ),
inference(clausify,[status(thm)],[f_1649_4]) ).
cnf(f_1649_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_7031)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7031)) ),
inference(clausify,[status(thm)],[f_1649_4]) ).
fof(f_1650_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_1650_2,plain,
! [U_7033,U_7032] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7032),c_Groups_Ozero__class_Ozero(U_7032)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7032),U_7033)))
| ~ class_Rings_Olinordered__semidom(U_7032) ),
inference(variable_rename,[status(thm)],[f_1650_1]) ).
fof(f_1650_3,plain,
! [U_7032,U_7033] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7032),c_Groups_Ozero__class_Ozero(U_7032)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7032),U_7033)))
| ~ class_Rings_Olinordered__semidom(U_7032) ),
inference(definitional_conversion,[status(esa)],[f_1650_2]) ).
cnf(f_1650_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7032),c_Groups_Ozero__class_Ozero(U_7032)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7032),U_7033)))
| ~ class_Rings_Olinordered__semidom(U_7032) ),
inference(clausify,[status(thm)],[f_1650_3]) ).
fof(f_1651_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_1651_2,plain,
! [U_7035,U_7034] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7034),c_Groups_Ozero__class_Ozero(U_7034)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7034),U_7035)))
| ~ class_Rings_Olinordered__semidom(U_7034) ),
inference(variable_rename,[status(thm)],[f_1651_1]) ).
fof(f_1651_3,plain,
! [U_7034,U_7035] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7034),c_Groups_Ozero__class_Ozero(U_7034)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7034),U_7035)))
| ~ class_Rings_Olinordered__semidom(U_7034) ),
inference(definitional_conversion,[status(esa)],[f_1651_2]) ).
cnf(f_1651_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7034),c_Groups_Ozero__class_Ozero(U_7034)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7034),U_7035)))
| ~ class_Rings_Olinordered__semidom(U_7034) ),
inference(clausify,[status(thm)],[f_1651_3]) ).
fof(f_1652_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_1652_2,plain,
! [U_7037,U_7036] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7037)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7036)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7037),U_7036))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7036),U_7037)) ),
inference(variable_rename,[status(thm)],[f_1652_1]) ).
fof(f_1652_3,plain,
! [U_7036,U_7037] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7037)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7036)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7037),U_7036))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7036),U_7037)) ),
inference(definitional_conversion,[status(esa)],[f_1652_2]) ).
cnf(f_1652_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7037)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7036)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7037),U_7036))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7036),U_7037)) ),
inference(clausify,[status(thm)],[f_1652_3]) ).
fof(f_1653_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_1653_2,plain,
! [U_7039,U_7038] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7038),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7038),U_7039)),c_Groups_Ozero__class_Ozero(U_7038)))
| ~ class_Rings_Olinordered__semidom(U_7038) ),
inference(variable_rename,[status(thm)],[f_1653_1]) ).
fof(f_1653_3,plain,
! [U_7038,U_7039] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7038),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7038),U_7039)),c_Groups_Ozero__class_Ozero(U_7038)))
| ~ class_Rings_Olinordered__semidom(U_7038) ),
inference(definitional_conversion,[status(esa)],[f_1653_2]) ).
cnf(f_1653_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7038),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7038),U_7039)),c_Groups_Ozero__class_Ozero(U_7038)))
| ~ class_Rings_Olinordered__semidom(U_7038) ),
inference(clausify,[status(thm)],[f_1653_3]) ).
fof(f_1654_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_1654_2,plain,
! [U_7040] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7040),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_7040)
| ~ class_Rings_Osemiring__1(U_7040) ),
inference(variable_rename,[status(thm)],[f_1654_1]) ).
fof(f_1654_3,plain,
! [U_7040] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7040),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_7040)
| ~ class_Rings_Osemiring__1(U_7040) ),
inference(definitional_conversion,[status(esa)],[f_1654_2]) ).
cnf(f_1654_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7040),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_7040)
| ~ class_Rings_Osemiring__1(U_7040) ),
inference(clausify,[status(thm)],[f_1654_3]) ).
fof(f_1655_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_1655_2,plain,
! [U_7043,U_7042,U_7041] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7042),U_7043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7041),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7041),U_7042)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7041),U_7043)))
| ~ class_Rings_Olinordered__semidom(U_7041) ),
inference(variable_rename,[status(thm)],[f_1655_1]) ).
fof(f_1655_3,plain,
! [U_7041,U_7042,U_7043] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7042),U_7043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7041),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7041),U_7042)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7041),U_7043)))
| ~ class_Rings_Olinordered__semidom(U_7041) ),
inference(definitional_conversion,[status(esa)],[f_1655_2]) ).
cnf(f_1655_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7042),U_7043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7041),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7041),U_7042)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7041),U_7043)))
| ~ class_Rings_Olinordered__semidom(U_7041) ),
inference(clausify,[status(thm)],[f_1655_3]) ).
fof(f_1656_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_1656_2,plain,
! [U_7046,U_7045,U_7044] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7044),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7044),U_7045)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7044),U_7046)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7045),U_7046))
| ~ class_Rings_Olinordered__semidom(U_7044) ),
inference(variable_rename,[status(thm)],[f_1656_1]) ).
fof(f_1656_3,plain,
! [U_7044,U_7045,U_7046] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7044),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7044),U_7045)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7044),U_7046)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7045),U_7046))
| ~ class_Rings_Olinordered__semidom(U_7044) ),
inference(definitional_conversion,[status(esa)],[f_1656_2]) ).
cnf(f_1656_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7044),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7044),U_7045)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7044),U_7046)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7045),U_7046))
| ~ class_Rings_Olinordered__semidom(U_7044) ),
inference(clausify,[status(thm)],[f_1656_3]) ).
fof(f_1657_1,plain,
! [V_n_2,V_m_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),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_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2))) ) )
| ~ class_Rings_Olinordered__semidom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff]) ).
fof(f_1657_2,plain,
! [U_7049,U_7048,U_7047] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7047),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7047),U_7048)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7047),U_7049)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7048),U_7049)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7048),U_7049))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7047),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7047),U_7048)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7047),U_7049))) ) )
| ~ class_Rings_Olinordered__semidom(U_7047) ),
inference(variable_rename,[status(thm)],[f_1657_1]) ).
fof(f_1657_3,plain,
( ! [U_7047,U_7048,U_7049] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7047),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7047),U_7048)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7047),U_7049)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7048),U_7049))
| ~ sP410(U_7047,U_7048,U_7049) )
& ! [U_7047,U_7048,U_7049] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7048),U_7049))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7047),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7047),U_7048)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7047),U_7049)))
| ~ sP410(U_7047,U_7048,U_7049) )
& ! [U_7047,U_7048,U_7049] :
( sP410(U_7047,U_7048,U_7049)
| ~ class_Rings_Olinordered__semidom(U_7047) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP410])],[f_1657_2]) ).
cnf(f_1657_4,plain,
( sP410(U_7047,U_7048,U_7049)
| ~ class_Rings_Olinordered__semidom(U_7047) ),
inference(clausify,[status(thm)],[f_1657_3]) ).
cnf(f_1657_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7048),U_7049))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7047),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7047),U_7048)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7047),U_7049)))
| ~ sP410(U_7047,U_7048,U_7049) ),
inference(clausify,[status(thm)],[f_1657_3]) ).
cnf(f_1657_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7047),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7047),U_7048)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7047),U_7049)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7048),U_7049))
| ~ sP410(U_7047,U_7048,U_7049) ),
inference(clausify,[status(thm)],[f_1657_3]) ).
fof(f_1658_1,plain,
! [V_n_2,V_m_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),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_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2))) ) )
| ~ class_Rings_Olinordered__semidom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff]) ).
fof(f_1658_2,plain,
! [U_7052,U_7051,U_7050] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7050),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7050),U_7051)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7050),U_7052)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7051),U_7052)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7051),U_7052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7050),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7050),U_7051)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7050),U_7052))) ) )
| ~ class_Rings_Olinordered__semidom(U_7050) ),
inference(variable_rename,[status(thm)],[f_1658_1]) ).
fof(f_1658_3,plain,
( ! [U_7052,U_7051,U_7050] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7050),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7050),U_7051)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7050),U_7052)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7051),U_7052))
| ~ sP411(U_7052,U_7051,U_7050) )
& ! [U_7052,U_7051,U_7050] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7051),U_7052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7050),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7050),U_7051)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7050),U_7052)))
| ~ sP411(U_7052,U_7051,U_7050) )
& ! [U_7052,U_7051,U_7050] :
( sP411(U_7052,U_7051,U_7050)
| ~ class_Rings_Olinordered__semidom(U_7050) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP411])],[f_1658_2]) ).
cnf(f_1658_4,plain,
( sP411(U_7052,U_7051,U_7050)
| ~ class_Rings_Olinordered__semidom(U_7050) ),
inference(clausify,[status(thm)],[f_1658_3]) ).
cnf(f_1658_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7051),U_7052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7050),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7050),U_7051)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7050),U_7052)))
| ~ sP411(U_7052,U_7051,U_7050) ),
inference(clausify,[status(thm)],[f_1658_3]) ).
cnf(f_1658_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7050),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7050),U_7051)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7050),U_7052)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7051),U_7052))
| ~ sP411(U_7052,U_7051,U_7050) ),
inference(clausify,[status(thm)],[f_1658_3]) ).
fof(f_1659_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_1659_2,plain,
! [U_7055,U_7054,U_7053] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7053),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7054),U_7055)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7053),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7053),U_7054)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7053),U_7055))
| ~ class_Rings_Osemiring__1(U_7053) ),
inference(variable_rename,[status(thm)],[f_1659_1]) ).
fof(f_1659_3,plain,
! [U_7054,U_7053,U_7055] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7053),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7054),U_7055)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7053),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7053),U_7054)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7053),U_7055))
| ~ class_Rings_Osemiring__1(U_7053) ),
inference(definitional_conversion,[status(esa)],[f_1659_2]) ).
cnf(f_1659_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7053),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7054),U_7055)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7053),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7053),U_7054)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7053),U_7055))
| ~ class_Rings_Osemiring__1(U_7053) ),
inference(clausify,[status(thm)],[f_1659_3]) ).
fof(f_1660_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_1660_2,plain,
! [U_7058,U_7057,U_7056] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7057),U_7058)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7056),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7056),U_7057)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7056),U_7058))
| ~ class_Rings_Osemiring__1(U_7056) ),
inference(variable_rename,[status(thm)],[f_1660_1]) ).
fof(f_1660_3,plain,
! [U_7056,U_7057,U_7058] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7057),U_7058)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7056),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7056),U_7057)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7056),U_7058))
| ~ class_Rings_Osemiring__1(U_7056) ),
inference(definitional_conversion,[status(esa)],[f_1660_2]) ).
cnf(f_1660_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7057),U_7058)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7056),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7056),U_7057)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7056),U_7058))
| ~ class_Rings_Osemiring__1(U_7056) ),
inference(clausify,[status(thm)],[f_1660_3]) ).
fof(f_1661_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_1661_2,plain,
! [U_7059] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7059),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_7059)
| ~ class_Rings_Osemiring__1(U_7059) ),
inference(variable_rename,[status(thm)],[f_1661_1]) ).
fof(f_1661_3,plain,
! [U_7059] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7059),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_7059)
| ~ class_Rings_Osemiring__1(U_7059) ),
inference(definitional_conversion,[status(esa)],[f_1661_2]) ).
cnf(f_1661_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7059),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_7059)
| ~ class_Rings_Osemiring__1(U_7059) ),
inference(clausify,[status(thm)],[f_1661_3]) ).
fof(f_1662_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_1662_2,plain,
! [U_7062,U_7061,U_7060] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7060),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7061),U_7062)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7060),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7060),U_7061)),U_7062)
| ~ class_Rings_Osemiring__1(U_7060) ),
inference(variable_rename,[status(thm)],[f_1662_1]) ).
fof(f_1662_3,plain,
! [U_7060,U_7061,U_7062] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7060),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7061),U_7062)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7060),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7060),U_7061)),U_7062)
| ~ class_Rings_Osemiring__1(U_7060) ),
inference(definitional_conversion,[status(esa)],[f_1662_2]) ).
cnf(f_1662_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7060),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7061),U_7062)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7060),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7060),U_7061)),U_7062)
| ~ class_Rings_Osemiring__1(U_7060) ),
inference(clausify,[status(thm)],[f_1662_3]) ).
fof(f_1663_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,T_d),c_Nat_Osemiring__1__class_Oof__nat(T_c)),V_f_2)),V_A_2)
| ~ class_Rings_Osemiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__setsum]) ).
fof(f_1663_2,plain,
! [U_7066,U_7065,U_7064,U_7063] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7063),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7064,tc_Nat_Onat),U_7065),U_7066)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7064,U_7063),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7063,U_7064),c_Nat_Osemiring__1__class_Oof__nat(U_7063)),U_7065)),U_7066)
| ~ class_Rings_Osemiring__1(U_7063) ),
inference(variable_rename,[status(thm)],[f_1663_1]) ).
fof(f_1663_3,plain,
! [U_7063,U_7064,U_7065,U_7066] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7063),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7064,tc_Nat_Onat),U_7065),U_7066)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7064,U_7063),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7063,U_7064),c_Nat_Osemiring__1__class_Oof__nat(U_7063)),U_7065)),U_7066)
| ~ class_Rings_Osemiring__1(U_7063) ),
inference(definitional_conversion,[status(esa)],[f_1663_2]) ).
cnf(f_1663_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7063),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7064,tc_Nat_Onat),U_7065),U_7066)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7064,U_7063),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7063,U_7064),c_Nat_Osemiring__1__class_Oof__nat(U_7063)),U_7065)),U_7066)
| ~ class_Rings_Osemiring__1(U_7063) ),
inference(clausify,[status(thm)],[f_1663_3]) ).
fof(f_1664_1,plain,
! [T_c] :
( c_Fun_Oinj__on(tc_Nat_Onat,T_c,c_Nat_Osemiring__1__class_Oof__nat(T_c),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inj__of__nat]) ).
fof(f_1664_2,plain,
! [U_7067] :
( c_Fun_Oinj__on(tc_Nat_Onat,U_7067,c_Nat_Osemiring__1__class_Oof__nat(U_7067),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(U_7067) ),
inference(variable_rename,[status(thm)],[f_1664_1]) ).
fof(f_1664_3,plain,
! [U_7067] :
( c_Fun_Oinj__on(tc_Nat_Onat,U_7067,c_Nat_Osemiring__1__class_Oof__nat(U_7067),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(U_7067) ),
inference(definitional_conversion,[status(esa)],[f_1664_2]) ).
cnf(f_1664_4,plain,
( c_Fun_Oinj__on(tc_Nat_Onat,U_7067,c_Nat_Osemiring__1__class_Oof__nat(U_7067),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(U_7067) ),
inference(clausify,[status(thm)],[f_1664_3]) ).
fof(f_1665_1,plain,
! [T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),c_Groups_Ozero__class_Ozero(T_c)),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Rings_Oring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__0]) ).
fof(f_1665_2,plain,
! [U_7068] :
( hBOOL(hAPP(hAPP(c_member(U_7068),c_Groups_Ozero__class_Ozero(U_7068)),c_Int_Oring__1__class_OInts(U_7068)))
| ~ class_Rings_Oring__1(U_7068) ),
inference(variable_rename,[status(thm)],[f_1665_1]) ).
fof(f_1665_3,plain,
! [U_7068] :
( hBOOL(hAPP(hAPP(c_member(U_7068),c_Groups_Ozero__class_Ozero(U_7068)),c_Int_Oring__1__class_OInts(U_7068)))
| ~ class_Rings_Oring__1(U_7068) ),
inference(definitional_conversion,[status(esa)],[f_1665_2]) ).
cnf(f_1665_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7068),c_Groups_Ozero__class_Ozero(U_7068)),c_Int_Oring__1__class_OInts(U_7068)))
| ~ class_Rings_Oring__1(U_7068) ),
inference(clausify,[status(thm)],[f_1665_3]) ).
fof(f_1666_1,plain,
! [V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_c)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Int_Oring__1__class_OInts(T_c)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Rings_Oring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__add]) ).
fof(f_1666_2,plain,
! [U_7071,U_7070,U_7069] :
( hBOOL(hAPP(hAPP(c_member(U_7069),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7069),U_7070),U_7071)),c_Int_Oring__1__class_OInts(U_7069)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7069),U_7071),c_Int_Oring__1__class_OInts(U_7069)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7069),U_7070),c_Int_Oring__1__class_OInts(U_7069)))
| ~ class_Rings_Oring__1(U_7069) ),
inference(variable_rename,[status(thm)],[f_1666_1]) ).
fof(f_1666_3,plain,
! [U_7069,U_7070,U_7071] :
( hBOOL(hAPP(hAPP(c_member(U_7069),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7069),U_7070),U_7071)),c_Int_Oring__1__class_OInts(U_7069)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7069),U_7071),c_Int_Oring__1__class_OInts(U_7069)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7069),U_7070),c_Int_Oring__1__class_OInts(U_7069)))
| ~ class_Rings_Oring__1(U_7069) ),
inference(definitional_conversion,[status(esa)],[f_1666_2]) ).
cnf(f_1666_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7069),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7069),U_7070),U_7071)),c_Int_Oring__1__class_OInts(U_7069)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7069),U_7071),c_Int_Oring__1__class_OInts(U_7069)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7069),U_7070),c_Int_Oring__1__class_OInts(U_7069)))
| ~ class_Rings_Oring__1(U_7069) ),
inference(clausify,[status(thm)],[f_1666_3]) ).
fof(f_1667_1,plain,
! [V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_c)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Int_Oring__1__class_OInts(T_c)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Rings_Oring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__mult]) ).
fof(f_1667_2,plain,
! [U_7074,U_7073,U_7072] :
( hBOOL(hAPP(hAPP(c_member(U_7072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7072),U_7073),U_7074)),c_Int_Oring__1__class_OInts(U_7072)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7072),U_7074),c_Int_Oring__1__class_OInts(U_7072)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7072),U_7073),c_Int_Oring__1__class_OInts(U_7072)))
| ~ class_Rings_Oring__1(U_7072) ),
inference(variable_rename,[status(thm)],[f_1667_1]) ).
fof(f_1667_3,plain,
! [U_7072,U_7073,U_7074] :
( hBOOL(hAPP(hAPP(c_member(U_7072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7072),U_7073),U_7074)),c_Int_Oring__1__class_OInts(U_7072)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7072),U_7074),c_Int_Oring__1__class_OInts(U_7072)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7072),U_7073),c_Int_Oring__1__class_OInts(U_7072)))
| ~ class_Rings_Oring__1(U_7072) ),
inference(definitional_conversion,[status(esa)],[f_1667_2]) ).
cnf(f_1667_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7072),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7072),U_7073),U_7074)),c_Int_Oring__1__class_OInts(U_7072)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7072),U_7074),c_Int_Oring__1__class_OInts(U_7072)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7072),U_7073),c_Int_Oring__1__class_OInts(U_7072)))
| ~ class_Rings_Oring__1(U_7072) ),
inference(clausify,[status(thm)],[f_1667_3]) ).
fof(f_1668_1,plain,
! [V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_c)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Int_Oring__1__class_OInts(T_c)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Rings_Oring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__diff]) ).
fof(f_1668_2,plain,
! [U_7077,U_7076,U_7075] :
( hBOOL(hAPP(hAPP(c_member(U_7075),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7075),U_7076),U_7077)),c_Int_Oring__1__class_OInts(U_7075)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7075),U_7077),c_Int_Oring__1__class_OInts(U_7075)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7075),U_7076),c_Int_Oring__1__class_OInts(U_7075)))
| ~ class_Rings_Oring__1(U_7075) ),
inference(variable_rename,[status(thm)],[f_1668_1]) ).
fof(f_1668_3,plain,
! [U_7075,U_7076,U_7077] :
( hBOOL(hAPP(hAPP(c_member(U_7075),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7075),U_7076),U_7077)),c_Int_Oring__1__class_OInts(U_7075)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7075),U_7077),c_Int_Oring__1__class_OInts(U_7075)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7075),U_7076),c_Int_Oring__1__class_OInts(U_7075)))
| ~ class_Rings_Oring__1(U_7075) ),
inference(definitional_conversion,[status(esa)],[f_1668_2]) ).
cnf(f_1668_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7075),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7075),U_7076),U_7077)),c_Int_Oring__1__class_OInts(U_7075)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7075),U_7077),c_Int_Oring__1__class_OInts(U_7075)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7075),U_7076),c_Int_Oring__1__class_OInts(U_7075)))
| ~ class_Rings_Oring__1(U_7075) ),
inference(clausify,[status(thm)],[f_1668_3]) ).
fof(f_1669_1,plain,
! [T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),c_Groups_Oone__class_Oone(T_c)),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Rings_Oring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__1]) ).
fof(f_1669_2,plain,
! [U_7078] :
( hBOOL(hAPP(hAPP(c_member(U_7078),c_Groups_Oone__class_Oone(U_7078)),c_Int_Oring__1__class_OInts(U_7078)))
| ~ class_Rings_Oring__1(U_7078) ),
inference(variable_rename,[status(thm)],[f_1669_1]) ).
fof(f_1669_3,plain,
! [U_7078] :
( hBOOL(hAPP(hAPP(c_member(U_7078),c_Groups_Oone__class_Oone(U_7078)),c_Int_Oring__1__class_OInts(U_7078)))
| ~ class_Rings_Oring__1(U_7078) ),
inference(definitional_conversion,[status(esa)],[f_1669_2]) ).
cnf(f_1669_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7078),c_Groups_Oone__class_Oone(U_7078)),c_Int_Oring__1__class_OInts(U_7078)))
| ~ class_Rings_Oring__1(U_7078) ),
inference(clausify,[status(thm)],[f_1669_3]) ).
fof(f_1670_1,plain,
! [V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),c_Int_Oring__1__class_OInts(T_c)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Rings_Oring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__minus]) ).
fof(f_1670_2,plain,
! [U_7080,U_7079] :
( hBOOL(hAPP(hAPP(c_member(U_7079),hAPP(c_Groups_Ouminus__class_Ouminus(U_7079),U_7080)),c_Int_Oring__1__class_OInts(U_7079)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7079),U_7080),c_Int_Oring__1__class_OInts(U_7079)))
| ~ class_Rings_Oring__1(U_7079) ),
inference(variable_rename,[status(thm)],[f_1670_1]) ).
fof(f_1670_3,plain,
! [U_7079,U_7080] :
( hBOOL(hAPP(hAPP(c_member(U_7079),hAPP(c_Groups_Ouminus__class_Ouminus(U_7079),U_7080)),c_Int_Oring__1__class_OInts(U_7079)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7079),U_7080),c_Int_Oring__1__class_OInts(U_7079)))
| ~ class_Rings_Oring__1(U_7079) ),
inference(definitional_conversion,[status(esa)],[f_1670_2]) ).
cnf(f_1670_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7079),hAPP(c_Groups_Ouminus__class_Ouminus(U_7079),U_7080)),c_Int_Oring__1__class_OInts(U_7079)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7079),U_7080),c_Int_Oring__1__class_OInts(U_7079)))
| ~ class_Rings_Oring__1(U_7079) ),
inference(clausify,[status(thm)],[f_1670_3]) ).
fof(f_1671_1,plain,
! [V_n_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_c)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Rings_Oring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__power]) ).
fof(f_1671_2,plain,
! [U_7083,U_7082,U_7081] :
( hBOOL(hAPP(hAPP(c_member(U_7081),hAPP(hAPP(c_Power_Opower__class_Opower(U_7081),U_7082),U_7083)),c_Int_Oring__1__class_OInts(U_7081)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7081),U_7082),c_Int_Oring__1__class_OInts(U_7081)))
| ~ class_Rings_Oring__1(U_7081) ),
inference(variable_rename,[status(thm)],[f_1671_1]) ).
fof(f_1671_3,plain,
! [U_7081,U_7082,U_7083] :
( hBOOL(hAPP(hAPP(c_member(U_7081),hAPP(hAPP(c_Power_Opower__class_Opower(U_7081),U_7082),U_7083)),c_Int_Oring__1__class_OInts(U_7081)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7081),U_7082),c_Int_Oring__1__class_OInts(U_7081)))
| ~ class_Rings_Oring__1(U_7081) ),
inference(definitional_conversion,[status(esa)],[f_1671_2]) ).
cnf(f_1671_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7081),hAPP(hAPP(c_Power_Opower__class_Opower(U_7081),U_7082),U_7083)),c_Int_Oring__1__class_OInts(U_7081)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7081),U_7082),c_Int_Oring__1__class_OInts(U_7081)))
| ~ class_Rings_Oring__1(U_7081) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
fof(f_1672_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,T_d),c_Nat_Osemiring__1__class_Oof__nat(T_c)),V_f_2)),V_A_2)
| ~ class_Rings_Osemiring__1(T_c)
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__setprod]) ).
fof(f_1672_2,plain,
! [U_7087,U_7086,U_7085,U_7084] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7084),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7085,tc_Nat_Onat),U_7086),U_7087)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7085,U_7084),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7084,U_7085),c_Nat_Osemiring__1__class_Oof__nat(U_7084)),U_7086)),U_7087)
| ~ class_Rings_Osemiring__1(U_7084)
| ~ class_Groups_Ocomm__monoid__mult(U_7084) ),
inference(variable_rename,[status(thm)],[f_1672_1]) ).
fof(f_1672_3,plain,
! [U_7084,U_7085,U_7086,U_7087] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7084),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7085,tc_Nat_Onat),U_7086),U_7087)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7085,U_7084),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7084,U_7085),c_Nat_Osemiring__1__class_Oof__nat(U_7084)),U_7086)),U_7087)
| ~ class_Rings_Osemiring__1(U_7084)
| ~ class_Groups_Ocomm__monoid__mult(U_7084) ),
inference(definitional_conversion,[status(esa)],[f_1672_2]) ).
cnf(f_1672_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7084),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7085,tc_Nat_Onat),U_7086),U_7087)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7085,U_7084),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7084,U_7085),c_Nat_Osemiring__1__class_Oof__nat(U_7084)),U_7086)),U_7087)
| ~ class_Rings_Osemiring__1(U_7084)
| ~ class_Groups_Ocomm__monoid__mult(U_7084) ),
inference(clausify,[status(thm)],[f_1672_3]) ).
fof(f_1673_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_1673_2,plain,
! [U_7089,U_7088] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7088),hAPP(c_Nat_OSuc,U_7089)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7088),c_Groups_Oone__class_Oone(U_7088)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7088),U_7089))
| ~ class_Rings_Osemiring__1(U_7088) ),
inference(variable_rename,[status(thm)],[f_1673_1]) ).
fof(f_1673_3,plain,
! [U_7088,U_7089] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7088),hAPP(c_Nat_OSuc,U_7089)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7088),c_Groups_Oone__class_Oone(U_7088)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7088),U_7089))
| ~ class_Rings_Osemiring__1(U_7088) ),
inference(definitional_conversion,[status(esa)],[f_1673_2]) ).
cnf(f_1673_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7088),hAPP(c_Nat_OSuc,U_7089)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7088),c_Groups_Oone__class_Oone(U_7088)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7088),U_7089))
| ~ class_Rings_Osemiring__1(U_7088) ),
inference(clausify,[status(thm)],[f_1673_3]) ).
fof(f_1674_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_1674_2,plain,
! [U_7092,U_7091,U_7090] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7092),U_7091)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7090),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7090),U_7092)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7090),U_7091))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7091),U_7092))
| ~ class_Rings_Oring__1(U_7090) ),
inference(variable_rename,[status(thm)],[f_1674_1]) ).
fof(f_1674_3,plain,
! [U_7090,U_7091,U_7092] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7092),U_7091)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7090),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7090),U_7092)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7090),U_7091))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7091),U_7092))
| ~ class_Rings_Oring__1(U_7090) ),
inference(definitional_conversion,[status(esa)],[f_1674_2]) ).
cnf(f_1674_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7090),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7092),U_7091)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7090),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7090),U_7092)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7090),U_7091))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7091),U_7092))
| ~ class_Rings_Oring__1(U_7090) ),
inference(clausify,[status(thm)],[f_1674_3]) ).
fof(f_1675_1,plain,
! [V_A_2,V_y_2,T_d,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(c_COMBK(T_c,T_d),V_y_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_d),V_A_2))),V_y_2)
| ~ class_Rings_Osemiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__constant]) ).
fof(f_1675_2,plain,
! [U_7096,U_7095,U_7094,U_7093] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7094,U_7093),hAPP(c_COMBK(U_7093,U_7094),U_7095)),U_7096) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7093),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7093),hAPP(c_Finite__Set_Ocard(U_7094),U_7096))),U_7095)
| ~ class_Rings_Osemiring__1(U_7093) ),
inference(variable_rename,[status(thm)],[f_1675_1]) ).
fof(f_1675_3,plain,
! [U_7093,U_7094,U_7095,U_7096] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7094,U_7093),hAPP(c_COMBK(U_7093,U_7094),U_7095)),U_7096) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7093),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7093),hAPP(c_Finite__Set_Ocard(U_7094),U_7096))),U_7095)
| ~ class_Rings_Osemiring__1(U_7093) ),
inference(definitional_conversion,[status(esa)],[f_1675_2]) ).
cnf(f_1675_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7094,U_7093),hAPP(c_COMBK(U_7093,U_7094),U_7095)),U_7096) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7093),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7093),hAPP(c_Finite__Set_Ocard(U_7094),U_7096))),U_7095)
| ~ class_Rings_Osemiring__1(U_7093) ),
inference(clausify,[status(thm)],[f_1675_3]) ).
fof(f_1676_1,plain,
! [V_n_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),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_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2))) ) )
| ~ class_Rings_Olinordered__semidom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff]) ).
fof(f_1676_2,plain,
! [U_7098,U_7097] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7097),c_Groups_Ozero__class_Ozero(U_7097)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7097),U_7098)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7098)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7097),c_Groups_Ozero__class_Ozero(U_7097)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7097),U_7098))) ) )
| ~ class_Rings_Olinordered__semidom(U_7097) ),
inference(variable_rename,[status(thm)],[f_1676_1]) ).
fof(f_1676_3,plain,
( ! [U_7098,U_7097] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7097),c_Groups_Ozero__class_Ozero(U_7097)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7097),U_7098)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7098))
| ~ sP412(U_7098,U_7097) )
& ! [U_7098,U_7097] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7097),c_Groups_Ozero__class_Ozero(U_7097)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7097),U_7098)))
| ~ sP412(U_7098,U_7097) )
& ! [U_7098,U_7097] :
( sP412(U_7098,U_7097)
| ~ class_Rings_Olinordered__semidom(U_7097) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP412])],[f_1676_2]) ).
cnf(f_1676_4,plain,
( sP412(U_7098,U_7097)
| ~ class_Rings_Olinordered__semidom(U_7097) ),
inference(clausify,[status(thm)],[f_1676_3]) ).
cnf(f_1676_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7098))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7097),c_Groups_Ozero__class_Ozero(U_7097)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7097),U_7098)))
| ~ sP412(U_7098,U_7097) ),
inference(clausify,[status(thm)],[f_1676_3]) ).
cnf(f_1676_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7097),c_Groups_Ozero__class_Ozero(U_7097)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7097),U_7098)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7098))
| ~ sP412(U_7098,U_7097) ),
inference(clausify,[status(thm)],[f_1676_3]) ).
fof(f_1677_1,plain,
! [V_a_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Int_Oring__char__0(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff]) ).
fof(f_1677_2,plain,
! [U_7100,U_7099] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7099),U_7100),U_7100) = c_Groups_Ozero__class_Ozero(U_7099)
| U_7100 != c_Groups_Ozero__class_Ozero(U_7099) )
& ( U_7100 = c_Groups_Ozero__class_Ozero(U_7099)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7099),U_7100),U_7100) != c_Groups_Ozero__class_Ozero(U_7099) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_7099),U_7100),c_Int_Oring__1__class_OInts(U_7099)))
| ~ class_Int_Oring__char__0(U_7099) ),
inference(variable_rename,[status(thm)],[f_1677_1]) ).
fof(f_1677_3,plain,
( ! [U_7100,U_7099] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7099),U_7100),U_7100) = c_Groups_Ozero__class_Ozero(U_7099)
| U_7100 != c_Groups_Ozero__class_Ozero(U_7099)
| ~ sP413(U_7100,U_7099) )
& ! [U_7100,U_7099] :
( U_7100 = c_Groups_Ozero__class_Ozero(U_7099)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7099),U_7100),U_7100) != c_Groups_Ozero__class_Ozero(U_7099)
| ~ sP413(U_7100,U_7099) )
& ! [U_7100,U_7099] :
( sP413(U_7100,U_7099)
| ~ hBOOL(hAPP(hAPP(c_member(U_7099),U_7100),c_Int_Oring__1__class_OInts(U_7099)))
| ~ class_Int_Oring__char__0(U_7099) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP413])],[f_1677_2]) ).
cnf(f_1677_4,plain,
( sP413(U_7100,U_7099)
| ~ hBOOL(hAPP(hAPP(c_member(U_7099),U_7100),c_Int_Oring__1__class_OInts(U_7099)))
| ~ class_Int_Oring__char__0(U_7099) ),
inference(clausify,[status(thm)],[f_1677_3]) ).
cnf(f_1677_5,plain,
( U_7100 = c_Groups_Ozero__class_Ozero(U_7099)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7099),U_7100),U_7100) != c_Groups_Ozero__class_Ozero(U_7099)
| ~ sP413(U_7100,U_7099) ),
inference(clausify,[status(thm)],[f_1677_3]) ).
cnf(f_1677_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7099),U_7100),U_7100) = c_Groups_Ozero__class_Ozero(U_7099)
| U_7100 != c_Groups_Ozero__class_Ozero(U_7099)
| ~ sP413(U_7100,U_7099) ),
inference(clausify,[status(thm)],[f_1677_3]) ).
fof(f_1678_1,plain,
! [V_a_2,T_c] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Int_Oring__char__0(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero]) ).
fof(f_1678_2,plain,
! [U_7102,U_7101] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7101),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7101),c_Groups_Oone__class_Oone(U_7101)),U_7102)),U_7102) != c_Groups_Ozero__class_Ozero(U_7101)
| ~ hBOOL(hAPP(hAPP(c_member(U_7101),U_7102),c_Int_Oring__1__class_OInts(U_7101)))
| ~ class_Int_Oring__char__0(U_7101) ),
inference(variable_rename,[status(thm)],[f_1678_1]) ).
fof(f_1678_3,plain,
! [U_7102,U_7101] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7101),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7101),c_Groups_Oone__class_Oone(U_7101)),U_7102)),U_7102) != c_Groups_Ozero__class_Ozero(U_7101)
| ~ hBOOL(hAPP(hAPP(c_member(U_7101),U_7102),c_Int_Oring__1__class_OInts(U_7101)))
| ~ class_Int_Oring__char__0(U_7101) ),
inference(definitional_conversion,[status(esa)],[f_1678_2]) ).
cnf(f_1678_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7101),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7101),c_Groups_Oone__class_Oone(U_7101)),U_7102)),U_7102) != c_Groups_Ozero__class_Ozero(U_7101)
| ~ hBOOL(hAPP(hAPP(c_member(U_7101),U_7102),c_Int_Oring__1__class_OInts(U_7101)))
| ~ class_Int_Oring__char__0(U_7101) ),
inference(clausify,[status(thm)],[f_1678_3]) ).
fof(f_1679_1,plain,
! [V_n_2,T_c] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_c,hAPP(hAPP(c_COMBC(T_c,T_c,T_c),c_Groups_Oplus__class_Oplus(T_c)),c_Groups_Oone__class_Oone(T_c)),V_n_2,c_Groups_Ozero__class_Ozero(T_c))
| ~ class_Rings_Osemiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code]) ).
fof(f_1679_2,plain,
! [U_7104,U_7103] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7103),U_7104) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_7103,hAPP(hAPP(c_COMBC(U_7103,U_7103,U_7103),c_Groups_Oplus__class_Oplus(U_7103)),c_Groups_Oone__class_Oone(U_7103)),U_7104,c_Groups_Ozero__class_Ozero(U_7103))
| ~ class_Rings_Osemiring__1(U_7103) ),
inference(variable_rename,[status(thm)],[f_1679_1]) ).
fof(f_1679_3,plain,
! [U_7103,U_7104] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7103),U_7104) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_7103,hAPP(hAPP(c_COMBC(U_7103,U_7103,U_7103),c_Groups_Oplus__class_Oplus(U_7103)),c_Groups_Oone__class_Oone(U_7103)),U_7104,c_Groups_Ozero__class_Ozero(U_7103))
| ~ class_Rings_Osemiring__1(U_7103) ),
inference(definitional_conversion,[status(esa)],[f_1679_2]) ).
cnf(f_1679_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7103),U_7104) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_7103,hAPP(hAPP(c_COMBC(U_7103,U_7103,U_7103),c_Groups_Oplus__class_Oplus(U_7103)),c_Groups_Oone__class_Oone(U_7103)),U_7104,c_Groups_Ozero__class_Ozero(U_7103))
| ~ class_Rings_Osemiring__1(U_7103) ),
inference(clausify,[status(thm)],[f_1679_3]) ).
fof(f_1680_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_1680_2,plain,
! [U_7107,U_7106,U_7105] :
( ( hBOOL(hAPP(U_7105,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7106),U_7107))))
| ( ~ hBOOL(hAPP(U_7105,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7106),U_7107)) )
| ( ~ hBOOL(hAPP(U_7105,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7106)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7107))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7107),U_7106)) ) )
& ( ( ( hBOOL(hAPP(U_7105,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7106),U_7107)) )
& ( hBOOL(hAPP(U_7105,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7106)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7107))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7107),U_7106)) ) )
| ~ hBOOL(hAPP(U_7105,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7106),U_7107)))) ) ),
inference(variable_rename,[status(thm)],[f_1680_1]) ).
fof(f_1680_3,plain,
( ! [U_7113,U_7111,U_7109] :
( hBOOL(hAPP(U_7109,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7111),U_7113))))
| ( ~ hBOOL(hAPP(U_7109,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7111),U_7113)) )
| ( ~ hBOOL(hAPP(U_7109,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7111)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7113))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7113),U_7111)) ) )
& ! [U_7112,U_7110,U_7108] :
( ( ( hBOOL(hAPP(U_7108,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7110),U_7112)) )
& ( hBOOL(hAPP(U_7108,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7110)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7112))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7112),U_7110)) ) )
| ~ hBOOL(hAPP(U_7108,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7110),U_7112)))) ) ),
inference(miniscope,[status(thm)],[f_1680_2]) ).
fof(f_1680_4,plain,
( ! [U_7109,U_7111,U_7113] :
( ~ hBOOL(hAPP(U_7109,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP416(U_7109,U_7111,U_7113) )
& ! [U_7109,U_7111,U_7113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7111),U_7113))
| ~ sP416(U_7109,U_7111,U_7113) )
& ! [U_7109,U_7111,U_7113] :
( ~ hBOOL(hAPP(U_7109,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7111)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7113))))
| ~ sP415(U_7109,U_7111,U_7113) )
& ! [U_7109,U_7111,U_7113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7113),U_7111))
| ~ sP415(U_7109,U_7111,U_7113) )
& ! [U_7112,U_7108,U_7110] :
( hBOOL(hAPP(U_7108,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7110),U_7112))
| ~ sP414(U_7112,U_7108,U_7110) )
& ! [U_7112,U_7108,U_7110] :
( hBOOL(hAPP(U_7108,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7110)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7112))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7112),U_7110))
| ~ sP414(U_7112,U_7108,U_7110) )
& ! [U_7109,U_7111,U_7113] :
( hBOOL(hAPP(U_7109,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7111),U_7113))))
| sP416(U_7109,U_7111,U_7113)
| sP415(U_7109,U_7111,U_7113) )
& ! [U_7112,U_7108,U_7110] :
( sP414(U_7112,U_7108,U_7110)
| ~ hBOOL(hAPP(U_7108,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7110),U_7112)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP414,sP415,sP416])],[f_1680_3]) ).
cnf(f_1680_5,plain,
( sP414(U_7112,U_7108,U_7110)
| ~ hBOOL(hAPP(U_7108,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7110),U_7112)))) ),
inference(clausify,[status(thm)],[f_1680_4]) ).
cnf(f_1680_6,plain,
( hBOOL(hAPP(U_7109,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7111),U_7113))))
| sP416(U_7109,U_7111,U_7113)
| sP415(U_7109,U_7111,U_7113) ),
inference(clausify,[status(thm)],[f_1680_4]) ).
cnf(f_1680_7,plain,
( hBOOL(hAPP(U_7108,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7110)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7112))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7112),U_7110))
| ~ sP414(U_7112,U_7108,U_7110) ),
inference(clausify,[status(thm)],[f_1680_4]) ).
cnf(f_1680_8,plain,
( hBOOL(hAPP(U_7108,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7110),U_7112))
| ~ sP414(U_7112,U_7108,U_7110) ),
inference(clausify,[status(thm)],[f_1680_4]) ).
cnf(f_1680_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7113),U_7111))
| ~ sP415(U_7109,U_7111,U_7113) ),
inference(clausify,[status(thm)],[f_1680_4]) ).
cnf(f_1680_10,plain,
( ~ hBOOL(hAPP(U_7109,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7111)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7113))))
| ~ sP415(U_7109,U_7111,U_7113) ),
inference(clausify,[status(thm)],[f_1680_4]) ).
cnf(f_1680_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7111),U_7113))
| ~ sP416(U_7109,U_7111,U_7113) ),
inference(clausify,[status(thm)],[f_1680_4]) ).
cnf(f_1680_12,plain,
( ~ hBOOL(hAPP(U_7109,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP416(U_7109,U_7111,U_7113) ),
inference(clausify,[status(thm)],[f_1680_4]) ).
fof(f_1681_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_1681_2,plain,
! [U_7115,U_7114] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7114)),U_7115) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7114),U_7115)),
inference(variable_rename,[status(thm)],[f_1681_1]) ).
fof(f_1681_3,plain,
! [U_7115,U_7114] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7114)),U_7115) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7114),U_7115)),
inference(definitional_conversion,[status(esa)],[f_1681_2]) ).
cnf(f_1681_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7114)),U_7115) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7114),U_7115)),
inference(clausify,[status(thm)],[f_1681_3]) ).
fof(f_1682_1,plain,
! [V_K_2,V_f_2,V_A_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_d),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_K_2)))
| ? [B_i] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,B_i)),V_K_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_A_2)) )
| ~ class_Rings_Osemiring__1(T_d)
| ~ class_Groups_Oordered__ab__semigroup__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__bounded]) ).
fof(f_1682_2,plain,
! [U_7121,U_7120,U_7119,U_7118,U_7117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7117),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7118,U_7117),U_7120),U_7119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7117),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7117),hAPP(c_Finite__Set_Ocard(U_7118),U_7119))),U_7121)))
| ? [U_7116] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7117),hAPP(U_7120,U_7116)),U_7121))
& hBOOL(hAPP(hAPP(c_member(U_7118),U_7116),U_7119)) )
| ~ class_Rings_Osemiring__1(U_7117)
| ~ class_Groups_Oordered__ab__semigroup__add(U_7117) ),
inference(variable_rename,[status(thm)],[f_1682_1]) ).
fof(f_1682_3,plain,
! [U_7121,U_7120,U_7119,U_7118,U_7117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7117),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7118,U_7117),U_7120),U_7119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7117),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7117),hAPP(c_Finite__Set_Ocard(U_7118),U_7119))),U_7121)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7117),hAPP(U_7120,sK140(U_7121,U_7120,U_7119,U_7118,U_7117))),U_7121))
& hBOOL(hAPP(hAPP(c_member(U_7118),sK140(U_7121,U_7120,U_7119,U_7118,U_7117)),U_7119)) )
| ~ class_Rings_Osemiring__1(U_7117)
| ~ class_Groups_Oordered__ab__semigroup__add(U_7117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_7116,sK140(U_7121,U_7120,U_7119,U_7118,U_7117))],[f_1682_2]) ).
fof(f_1682_4,plain,
( ! [U_7118,U_7117,U_7119,U_7120,U_7121] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7117),hAPP(U_7120,sK140(U_7121,U_7120,U_7119,U_7118,U_7117))),U_7121))
| ~ sP417(U_7118,U_7117,U_7119,U_7120,U_7121) )
& ! [U_7118,U_7117,U_7119,U_7120,U_7121] :
( hBOOL(hAPP(hAPP(c_member(U_7118),sK140(U_7121,U_7120,U_7119,U_7118,U_7117)),U_7119))
| ~ sP417(U_7118,U_7117,U_7119,U_7120,U_7121) )
& ! [U_7118,U_7117,U_7119,U_7120,U_7121] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7117),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7118,U_7117),U_7120),U_7119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7117),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7117),hAPP(c_Finite__Set_Ocard(U_7118),U_7119))),U_7121)))
| sP417(U_7118,U_7117,U_7119,U_7120,U_7121)
| ~ class_Rings_Osemiring__1(U_7117)
| ~ class_Groups_Oordered__ab__semigroup__add(U_7117) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP417])],[f_1682_3]) ).
cnf(f_1682_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7117),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7118,U_7117),U_7120),U_7119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7117),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7117),hAPP(c_Finite__Set_Ocard(U_7118),U_7119))),U_7121)))
| sP417(U_7118,U_7117,U_7119,U_7120,U_7121)
| ~ class_Rings_Osemiring__1(U_7117)
| ~ class_Groups_Oordered__ab__semigroup__add(U_7117) ),
inference(clausify,[status(thm)],[f_1682_4]) ).
cnf(f_1682_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_7118),sK140(U_7121,U_7120,U_7119,U_7118,U_7117)),U_7119))
| ~ sP417(U_7118,U_7117,U_7119,U_7120,U_7121) ),
inference(clausify,[status(thm)],[f_1682_4]) ).
cnf(f_1682_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7117),hAPP(U_7120,sK140(U_7121,U_7120,U_7119,U_7118,U_7117))),U_7121))
| ~ sP417(U_7118,U_7117,U_7119,U_7120,U_7121) ),
inference(clausify,[status(thm)],[f_1682_4]) ).
fof(f_1683_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_1683_2,plain,
! [U_7123,U_7122] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7122)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7123)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7122),U_7123)),
inference(variable_rename,[status(thm)],[f_1683_1]) ).
fof(f_1683_3,plain,
! [U_7122,U_7123] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7122)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7123)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7122),U_7123)),
inference(definitional_conversion,[status(esa)],[f_1683_2]) ).
cnf(f_1683_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7122)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7123)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7122),U_7123)),
inference(clausify,[status(thm)],[f_1683_3]) ).
fof(f_1684_1,plain,
! [V_x_2,V_y_2,V_c_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_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| 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_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ 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_c_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_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_image__minus__const__atLeastLessThan__nat]) ).
fof(f_1684_2,plain,
! [U_7126,U_7125,U_7124] :
( ( ( ( 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_7124)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7126),U_7125)) = 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_7126),U_7125)) )
& ( 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_7124)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7126),U_7125)) = 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_7126),U_7125)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7124),U_7125)) )
& ( 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_7124)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7126),U_7125)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7126),U_7124)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7125),U_7124))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7124),U_7125)) ) ),
inference(variable_rename,[status(thm)],[f_1684_1]) ).
fof(f_1684_3,plain,
( ! [U_7132,U_7130,U_7128] :
( ( ( 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_7128)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7132),U_7130)) = 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_7132),U_7130)) )
& ( 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_7128)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7132),U_7130)) = 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_7132),U_7130)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7128),U_7130)) )
& ! [U_7131,U_7129,U_7127] :
( 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_7127)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7131),U_7129)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7131),U_7127)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7129),U_7127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7127),U_7129)) ) ),
inference(miniscope,[status(thm)],[f_1684_2]) ).
fof(f_1684_4,plain,
( ! [U_7132,U_7130,U_7128] :
( 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_7128)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7132),U_7130)) = 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_7132),U_7130))
| ~ sP418(U_7132,U_7130,U_7128) )
& ! [U_7132,U_7130,U_7128] :
( 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_7128)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7132),U_7130)) = 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_7132),U_7130))
| ~ sP418(U_7132,U_7130,U_7128) )
& ! [U_7132,U_7130,U_7128] :
( sP418(U_7132,U_7130,U_7128)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7128),U_7130)) )
& ! [U_7131,U_7127,U_7129] :
( 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_7127)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7131),U_7129)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7131),U_7127)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7129),U_7127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7127),U_7129)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP418])],[f_1684_3]) ).
cnf(f_1684_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_7127)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7131),U_7129)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7131),U_7127)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7129),U_7127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7127),U_7129)) ),
inference(clausify,[status(thm)],[f_1684_4]) ).
cnf(f_1684_6,plain,
( sP418(U_7132,U_7130,U_7128)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7128),U_7130)) ),
inference(clausify,[status(thm)],[f_1684_4]) ).
cnf(f_1684_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_7128)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7132),U_7130)) = 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_7132),U_7130))
| ~ sP418(U_7132,U_7130,U_7128) ),
inference(clausify,[status(thm)],[f_1684_4]) ).
cnf(f_1684_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_7128)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7132),U_7130)) = 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_7132),U_7130))
| ~ sP418(U_7132,U_7130,U_7128) ),
inference(clausify,[status(thm)],[f_1684_4]) ).
fof(f_1685_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_1685_2,plain,
! [U_7134,U_7133] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7133),U_7134))),
inference(variable_rename,[status(thm)],[f_1685_1]) ).
fof(f_1685_3,plain,
! [U_7134,U_7133] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7133),U_7134))),
inference(definitional_conversion,[status(esa)],[f_1685_2]) ).
cnf(f_1685_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7133),U_7134))),
inference(clausify,[status(thm)],[f_1685_3]) ).
fof(f_1686_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_1686_2,plain,
! [U_7136,U_7135] : 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_7135))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7136))),
inference(variable_rename,[status(thm)],[f_1686_1]) ).
fof(f_1686_3,plain,
! [U_7135,U_7136] : 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_7135))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7136))),
inference(definitional_conversion,[status(esa)],[f_1686_2]) ).
cnf(f_1686_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_7135))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7136))),
inference(clausify,[status(thm)],[f_1686_3]) ).
fof(f_1687_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_1687_2,plain,
! [U_7137] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7137)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1687_1]) ).
fof(f_1687_3,plain,
! [U_7137] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7137)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_1687_2]) ).
cnf(f_1687_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_7137)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1687_3]) ).
fof(f_1688_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_1688_2,plain,
! [U_7141,U_7140] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7140),U_7141))
| ! [U_7139] : U_7141 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7140),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7139)) )
& ( ? [U_7138] : U_7141 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7140),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7140),U_7141)) ) ),
inference(variable_rename,[status(thm)],[f_1688_1]) ).
fof(f_1688_3,plain,
( ! [U_7145,U_7143] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7143),U_7145))
| ! [U_7139] : U_7145 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7143),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7139)) )
& ! [U_7144,U_7142] :
( ? [U_7138] : U_7144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7142),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7142),U_7144)) ) ),
inference(miniscope,[status(thm)],[f_1688_2]) ).
fof(f_1688_4,plain,
( ! [U_7145,U_7143] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7143),U_7145))
| ! [U_7139] : U_7145 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7143),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7139)) )
& ! [U_7144,U_7142] :
( U_7144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7142),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK141(U_7144,U_7142)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7142),U_7144)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_7138,sK141(U_7144,U_7142))],[f_1688_3]) ).
fof(f_1688_5,plain,
( ! [U_7139,U_7145,U_7143] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7143),U_7145))
| U_7145 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7143),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7139)) )
& ! [U_7144,U_7142] :
( U_7144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7142),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK141(U_7144,U_7142)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7142),U_7144)) ) ),
inference(definitional_conversion,[status(esa)],[f_1688_4]) ).
cnf(f_1688_6,plain,
( U_7144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7142),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK141(U_7144,U_7142)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7142),U_7144)) ),
inference(clausify,[status(thm)],[f_1688_5]) ).
cnf(f_1688_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7143),U_7145))
| U_7145 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7143),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7139)) ),
inference(clausify,[status(thm)],[f_1688_5]) ).
fof(f_1689_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_1689_2,plain,
! [U_7150] :
( ( ! [U_7149] :
( hBOOL(hAPP(U_7150,U_7149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7149)) )
| ? [U_7148] : ~ hBOOL(hAPP(U_7150,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7148))) )
& ( ! [U_7147] : hBOOL(hAPP(U_7150,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7147)))
| ? [U_7146] :
( ~ hBOOL(hAPP(U_7150,U_7146))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7146)) ) ) ),
inference(variable_rename,[status(thm)],[f_1689_1]) ).
fof(f_1689_3,plain,
( ! [U_7152] :
( ! [U_7149] :
( hBOOL(hAPP(U_7152,U_7149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7149)) )
| ? [U_7148] : ~ hBOOL(hAPP(U_7152,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7148))) )
& ! [U_7151] :
( ! [U_7147] : hBOOL(hAPP(U_7151,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7147)))
| ? [U_7146] :
( ~ hBOOL(hAPP(U_7151,U_7146))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7146)) ) ) ),
inference(miniscope,[status(thm)],[f_1689_2]) ).
fof(f_1689_4,plain,
( ! [U_7152] :
( ! [U_7149] :
( hBOOL(hAPP(U_7152,U_7149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7149)) )
| ? [U_7148] : ~ hBOOL(hAPP(U_7152,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7148))) )
& ! [U_7151] :
( ! [U_7147] : hBOOL(hAPP(U_7151,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7147)))
| ( ~ hBOOL(hAPP(U_7151,sK142(U_7151)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_7151))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_7146,sK142(U_7151))],[f_1689_3]) ).
fof(f_1689_5,plain,
( ! [U_7152] :
( ! [U_7149] :
( hBOOL(hAPP(U_7152,U_7149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7149)) )
| ~ hBOOL(hAPP(U_7152,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK143(U_7152)))) )
& ! [U_7151] :
( ! [U_7147] : hBOOL(hAPP(U_7151,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7147)))
| ( ~ hBOOL(hAPP(U_7151,sK142(U_7151)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_7151))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_7148,sK143(U_7152))],[f_1689_4]) ).
fof(f_1689_6,plain,
( ! [U_7151] :
( ~ hBOOL(hAPP(U_7151,sK142(U_7151)))
| ~ sP419(U_7151) )
& ! [U_7151] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_7151)))
| ~ sP419(U_7151) )
& ! [U_7149,U_7152] :
( hBOOL(hAPP(U_7152,U_7149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7149))
| ~ hBOOL(hAPP(U_7152,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK143(U_7152)))) )
& ! [U_7147,U_7151] :
( hBOOL(hAPP(U_7151,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7147)))
| sP419(U_7151) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP419])],[f_1689_5]) ).
cnf(f_1689_7,plain,
( hBOOL(hAPP(U_7151,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7147)))
| sP419(U_7151) ),
inference(clausify,[status(thm)],[f_1689_6]) ).
cnf(f_1689_8,plain,
( hBOOL(hAPP(U_7152,U_7149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7149))
| ~ hBOOL(hAPP(U_7152,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK143(U_7152)))) ),
inference(clausify,[status(thm)],[f_1689_6]) ).
cnf(f_1689_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK142(U_7151)))
| ~ sP419(U_7151) ),
inference(clausify,[status(thm)],[f_1689_6]) ).
cnf(f_1689_10,plain,
( ~ hBOOL(hAPP(U_7151,sK142(U_7151)))
| ~ sP419(U_7151) ),
inference(clausify,[status(thm)],[f_1689_6]) ).
fof(f_1690_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_1690_2,plain,
! [U_7157] :
( ( ? [U_7156] :
( hBOOL(hAPP(U_7157,U_7156))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7156)) )
| ! [U_7155] : ~ hBOOL(hAPP(U_7157,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7155))) )
& ( ? [U_7154] : hBOOL(hAPP(U_7157,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7154)))
| ! [U_7153] :
( ~ hBOOL(hAPP(U_7157,U_7153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7153)) ) ) ),
inference(variable_rename,[status(thm)],[f_1690_1]) ).
fof(f_1690_3,plain,
( ! [U_7159] :
( ? [U_7156] :
( hBOOL(hAPP(U_7159,U_7156))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7156)) )
| ! [U_7155] : ~ hBOOL(hAPP(U_7159,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7155))) )
& ! [U_7158] :
( ? [U_7154] : hBOOL(hAPP(U_7158,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7154)))
| ! [U_7153] :
( ~ hBOOL(hAPP(U_7158,U_7153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7153)) ) ) ),
inference(miniscope,[status(thm)],[f_1690_2]) ).
fof(f_1690_4,plain,
( ! [U_7159] :
( ? [U_7156] :
( hBOOL(hAPP(U_7159,U_7156))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7156)) )
| ! [U_7155] : ~ hBOOL(hAPP(U_7159,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7155))) )
& ! [U_7158] :
( hBOOL(hAPP(U_7158,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK144(U_7158))))
| ! [U_7153] :
( ~ hBOOL(hAPP(U_7158,U_7153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7153)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_7154,sK144(U_7158))],[f_1690_3]) ).
fof(f_1690_5,plain,
( ! [U_7159] :
( ( hBOOL(hAPP(U_7159,sK145(U_7159)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK145(U_7159))) )
| ! [U_7155] : ~ hBOOL(hAPP(U_7159,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7155))) )
& ! [U_7158] :
( hBOOL(hAPP(U_7158,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK144(U_7158))))
| ! [U_7153] :
( ~ hBOOL(hAPP(U_7158,U_7153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7153)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_7156,sK145(U_7159))],[f_1690_4]) ).
fof(f_1690_6,plain,
( ! [U_7159] :
( hBOOL(hAPP(U_7159,sK145(U_7159)))
| ~ sP420(U_7159) )
& ! [U_7159] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK145(U_7159)))
| ~ sP420(U_7159) )
& ! [U_7155,U_7159] :
( sP420(U_7159)
| ~ hBOOL(hAPP(U_7159,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7155))) )
& ! [U_7153,U_7158] :
( hBOOL(hAPP(U_7158,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK144(U_7158))))
| ~ hBOOL(hAPP(U_7158,U_7153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7153)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP420])],[f_1690_5]) ).
cnf(f_1690_7,plain,
( hBOOL(hAPP(U_7158,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK144(U_7158))))
| ~ hBOOL(hAPP(U_7158,U_7153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7153)) ),
inference(clausify,[status(thm)],[f_1690_6]) ).
cnf(f_1690_8,plain,
( sP420(U_7159)
| ~ hBOOL(hAPP(U_7159,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7155))) ),
inference(clausify,[status(thm)],[f_1690_6]) ).
cnf(f_1690_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK145(U_7159)))
| ~ sP420(U_7159) ),
inference(clausify,[status(thm)],[f_1690_6]) ).
cnf(f_1690_10,plain,
( hBOOL(hAPP(U_7159,sK145(U_7159)))
| ~ sP420(U_7159) ),
inference(clausify,[status(thm)],[f_1690_6]) ).
fof(f_1691_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_1691_2,plain,
! [U_7160] : 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_7160))),
inference(variable_rename,[status(thm)],[f_1691_1]) ).
fof(f_1691_3,plain,
! [U_7160] : 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_7160))),
inference(definitional_conversion,[status(esa)],[f_1691_2]) ).
cnf(f_1691_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_7160))),
inference(clausify,[status(thm)],[f_1691_3]) ).
fof(f_1692_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_1692_2,plain,
! [U_7161] : 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_7161))),
inference(variable_rename,[status(thm)],[f_1692_1]) ).
fof(f_1692_3,plain,
! [U_7161] : 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_7161))),
inference(definitional_conversion,[status(esa)],[f_1692_2]) ).
cnf(f_1692_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_7161))),
inference(clausify,[status(thm)],[f_1692_3]) ).
fof(f_1693_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_1693_2,plain,
! [U_7162] : 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_7162))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1693_1]) ).
fof(f_1693_3,plain,
! [U_7162] : 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_7162))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_1693_2]) ).
cnf(f_1693_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_7162))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1693_3]) ).
fof(f_1694_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_1694_2,plain,
! [U_7164,U_7163] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7163) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7164)
| U_7163 != U_7164 )
& ( U_7163 = U_7164
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7163) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7164) ) ),
inference(variable_rename,[status(thm)],[f_1694_1]) ).
fof(f_1694_3,plain,
( ! [U_7168,U_7166] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7166) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7168)
| U_7166 != U_7168 )
& ! [U_7167,U_7165] :
( U_7165 = U_7167
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7165) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7167) ) ),
inference(miniscope,[status(thm)],[f_1694_2]) ).
fof(f_1694_4,plain,
( ! [U_7166,U_7168] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7166) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7168)
| U_7166 != U_7168 )
& ! [U_7167,U_7165] :
( U_7165 = U_7167
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7165) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7167) ) ),
inference(definitional_conversion,[status(esa)],[f_1694_3]) ).
cnf(f_1694_5,plain,
( U_7165 = U_7167
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7165) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7167) ),
inference(clausify,[status(thm)],[f_1694_4]) ).
cnf(f_1694_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7166) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7168)
| U_7166 != U_7168 ),
inference(clausify,[status(thm)],[f_1694_4]) ).
fof(f_1695_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_1695_2,plain,
! [U_7170,U_7169] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7169)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7170)))),
inference(variable_rename,[status(thm)],[f_1695_1]) ).
fof(f_1695_3,plain,
! [U_7169,U_7170] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7169)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7170)))),
inference(definitional_conversion,[status(esa)],[f_1695_2]) ).
cnf(f_1695_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_7169)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7170)))),
inference(clausify,[status(thm)],[f_1695_3]) ).
fof(f_1696_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_1696_2,plain,
! [U_7172,U_7171] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7171) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7172)
| U_7171 != U_7172 )
& ( U_7171 = U_7172
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7171) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7172) ) ),
inference(variable_rename,[status(thm)],[f_1696_1]) ).
fof(f_1696_3,plain,
( ! [U_7176,U_7174] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7174) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7176)
| U_7174 != U_7176 )
& ! [U_7175,U_7173] :
( U_7173 = U_7175
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7173) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7175) ) ),
inference(miniscope,[status(thm)],[f_1696_2]) ).
fof(f_1696_4,plain,
( ! [U_7174,U_7176] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7174) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7176)
| U_7174 != U_7176 )
& ! [U_7175,U_7173] :
( U_7173 = U_7175
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7173) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7175) ) ),
inference(definitional_conversion,[status(esa)],[f_1696_3]) ).
cnf(f_1696_5,plain,
( U_7173 = U_7175
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7173) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7175) ),
inference(clausify,[status(thm)],[f_1696_4]) ).
cnf(f_1696_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7174) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7176)
| U_7174 != U_7176 ),
inference(clausify,[status(thm)],[f_1696_4]) ).
fof(f_1697_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_1697_2,plain,
! [U_7178,U_7177] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7177),U_7178))
| ~ 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_7177)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7178))) )
& ( 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_7177)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7178)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7177),U_7178)) ) ),
inference(variable_rename,[status(thm)],[f_1697_1]) ).
fof(f_1697_3,plain,
( ! [U_7182,U_7180] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7180),U_7182))
| ~ 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_7180)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7182))) )
& ! [U_7181,U_7179] :
( 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_7179)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7181)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7179),U_7181)) ) ),
inference(miniscope,[status(thm)],[f_1697_2]) ).
fof(f_1697_4,plain,
( ! [U_7180,U_7182] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7180),U_7182))
| ~ 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_7180)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7182))) )
& ! [U_7181,U_7179] :
( 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_7179)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7181)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7179),U_7181)) ) ),
inference(definitional_conversion,[status(esa)],[f_1697_3]) ).
cnf(f_1697_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_7179)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7181)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7179),U_7181)) ),
inference(clausify,[status(thm)],[f_1697_4]) ).
cnf(f_1697_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7180),U_7182))
| ~ 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_7180)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7182))) ),
inference(clausify,[status(thm)],[f_1697_4]) ).
fof(f_1698_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_1698_2,plain,
! [U_7184,U_7183] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7183),U_7184))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7183)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7184))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7183)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7184)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7183),U_7184)) ) ),
inference(variable_rename,[status(thm)],[f_1698_1]) ).
fof(f_1698_3,plain,
( ! [U_7188,U_7186] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7186),U_7188))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7186)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7188))) )
& ! [U_7187,U_7185] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7185)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7187)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7185),U_7187)) ) ),
inference(miniscope,[status(thm)],[f_1698_2]) ).
fof(f_1698_4,plain,
( ! [U_7186,U_7188] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7186),U_7188))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7186)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7188))) )
& ! [U_7187,U_7185] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7185)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7187)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7185),U_7187)) ) ),
inference(definitional_conversion,[status(esa)],[f_1698_3]) ).
cnf(f_1698_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7185)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7187)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7185),U_7187)) ),
inference(clausify,[status(thm)],[f_1698_4]) ).
cnf(f_1698_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7186),U_7188))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7186)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7188))) ),
inference(clausify,[status(thm)],[f_1698_4]) ).
fof(f_1699_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_1699_2,plain,
! [U_7190,U_7189] :
( ( U_7189 = U_7190
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7189) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7190) )
& ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7189) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7190)
| U_7189 != U_7190 ) ),
inference(variable_rename,[status(thm)],[f_1699_1]) ).
fof(f_1699_3,plain,
( ! [U_7194,U_7192] :
( U_7192 = U_7194
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7192) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7194) )
& ! [U_7193,U_7191] :
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7191) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7193)
| U_7191 != U_7193 ) ),
inference(miniscope,[status(thm)],[f_1699_2]) ).
fof(f_1699_4,plain,
( ! [U_7192,U_7194] :
( U_7192 = U_7194
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7192) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7194) )
& ! [U_7191,U_7193] :
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7191) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7193)
| U_7191 != U_7193 ) ),
inference(definitional_conversion,[status(esa)],[f_1699_3]) ).
cnf(f_1699_5,plain,
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7191) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7193)
| U_7191 != U_7193 ),
inference(clausify,[status(thm)],[f_1699_4]) ).
cnf(f_1699_6,plain,
( U_7192 = U_7194
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7192) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7194) ),
inference(clausify,[status(thm)],[f_1699_4]) ).
fof(f_1700_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_1700_2,plain,
! [U_7196,U_7195] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7195),U_7196))
| ~ 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_7195)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7196))) )
& ( 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_7195)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7196)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7195),U_7196)) ) ),
inference(variable_rename,[status(thm)],[f_1700_1]) ).
fof(f_1700_3,plain,
( ! [U_7200,U_7198] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7198),U_7200))
| ~ 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_7198)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7200))) )
& ! [U_7199,U_7197] :
( 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_7197)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7199)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7197),U_7199)) ) ),
inference(miniscope,[status(thm)],[f_1700_2]) ).
fof(f_1700_4,plain,
( ! [U_7198,U_7200] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7198),U_7200))
| ~ 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_7198)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7200))) )
& ! [U_7199,U_7197] :
( 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_7197)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7199)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7197),U_7199)) ) ),
inference(definitional_conversion,[status(esa)],[f_1700_3]) ).
cnf(f_1700_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_7197)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7199)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7197),U_7199)) ),
inference(clausify,[status(thm)],[f_1700_4]) ).
cnf(f_1700_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7198),U_7200))
| ~ 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_7198)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7200))) ),
inference(clausify,[status(thm)],[f_1700_4]) ).
fof(f_1701_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_1701_2,plain,
! [U_7202,U_7201] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7201),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7202),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( U_7201 != U_7202
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7201),U_7202)) ) )
& ( U_7201 = U_7202
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7201),U_7202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7201),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7202),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_1701_1]) ).
fof(f_1701_3,plain,
( ! [U_7206,U_7204] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7204),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7206),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( U_7204 != U_7206
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7204),U_7206)) ) )
& ! [U_7205,U_7203] :
( U_7203 = U_7205
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7203),U_7205))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7203),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7205),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_1701_2]) ).
fof(f_1701_4,plain,
( ! [U_7206,U_7204] :
( U_7204 != U_7206
| ~ sP421(U_7206,U_7204) )
& ! [U_7206,U_7204] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7204),U_7206))
| ~ sP421(U_7206,U_7204) )
& ! [U_7206,U_7204] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7204),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7206),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| sP421(U_7206,U_7204) )
& ! [U_7203,U_7205] :
( U_7203 = U_7205
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7203),U_7205))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7203),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7205),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP421])],[f_1701_3]) ).
cnf(f_1701_5,plain,
( U_7203 = U_7205
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7203),U_7205))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7203),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7205),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_1701_4]) ).
cnf(f_1701_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7204),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7206),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| sP421(U_7206,U_7204) ),
inference(clausify,[status(thm)],[f_1701_4]) ).
cnf(f_1701_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7204),U_7206))
| ~ sP421(U_7206,U_7204) ),
inference(clausify,[status(thm)],[f_1701_4]) ).
cnf(f_1701_8,plain,
( U_7204 != U_7206
| ~ sP421(U_7206,U_7204) ),
inference(clausify,[status(thm)],[f_1701_4]) ).
fof(f_1702_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_1702_2,plain,
! [U_7208,U_7207] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7208),U_7207))
| U_7207 = U_7208
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7207),U_7208)) ),
inference(variable_rename,[status(thm)],[f_1702_1]) ).
fof(f_1702_3,plain,
! [U_7208,U_7207] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7208),U_7207))
| U_7207 = U_7208
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7207),U_7208)) ),
inference(definitional_conversion,[status(esa)],[f_1702_2]) ).
cnf(f_1702_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7208),U_7207))
| U_7207 = U_7208
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7207),U_7208)) ),
inference(clausify,[status(thm)],[f_1702_3]) ).
fof(f_1703_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_1703_2,plain,
! [U_7209] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7209)) = U_7209,
inference(variable_rename,[status(thm)],[f_1703_1]) ).
fof(f_1703_3,plain,
! [U_7209] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7209)) = U_7209,
inference(definitional_conversion,[status(esa)],[f_1703_2]) ).
cnf(f_1703_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7209)) = U_7209,
inference(clausify,[status(thm)],[f_1703_3]) ).
fof(f_1704_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_1704_2,plain,
! [U_7211,U_7210] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7210),U_7211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7211),U_7210),
inference(variable_rename,[status(thm)],[f_1704_1]) ).
fof(f_1704_3,plain,
! [U_7210,U_7211] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7210),U_7211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7211),U_7210),
inference(definitional_conversion,[status(esa)],[f_1704_2]) ).
cnf(f_1704_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7210),U_7211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7211),U_7210),
inference(clausify,[status(thm)],[f_1704_3]) ).
fof(f_1705_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_1705_2,plain,
! [U_7214,U_7213,U_7212] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7213),U_7214)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7213),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7212),U_7214)),
inference(variable_rename,[status(thm)],[f_1705_1]) ).
fof(f_1705_3,plain,
! [U_7212,U_7213,U_7214] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7213),U_7214)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7213),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7212),U_7214)),
inference(definitional_conversion,[status(esa)],[f_1705_2]) ).
cnf(f_1705_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7213),U_7214)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7213),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7212),U_7214)),
inference(clausify,[status(thm)],[f_1705_3]) ).
fof(f_1706_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_1706_2,plain,
! [U_7217,U_7216,U_7215] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7215),U_7216)),U_7217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7215),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7216),U_7217)),
inference(variable_rename,[status(thm)],[f_1706_1]) ).
fof(f_1706_3,plain,
! [U_7215,U_7216,U_7217] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7215),U_7216)),U_7217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7215),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7216),U_7217)),
inference(definitional_conversion,[status(esa)],[f_1706_2]) ).
cnf(f_1706_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7215),U_7216)),U_7217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7215),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7216),U_7217)),
inference(clausify,[status(thm)],[f_1706_3]) ).
fof(f_1707_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_1707_2,plain,
! [U_7219,U_7218] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7218),U_7219) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7218),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7219)),
inference(variable_rename,[status(thm)],[f_1707_1]) ).
fof(f_1707_3,plain,
! [U_7218,U_7219] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7218),U_7219) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7218),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7219)),
inference(definitional_conversion,[status(esa)],[f_1707_2]) ).
cnf(f_1707_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7218),U_7219) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7218),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7219)),
inference(clausify,[status(thm)],[f_1707_3]) ).
fof(f_1708_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_1708_2,plain,
! [U_7221,U_7220] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7220),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7221)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7220),U_7221),
inference(variable_rename,[status(thm)],[f_1708_1]) ).
fof(f_1708_3,plain,
! [U_7220,U_7221] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7220),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7221)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7220),U_7221),
inference(definitional_conversion,[status(esa)],[f_1708_2]) ).
cnf(f_1708_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7220),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7221)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7220),U_7221),
inference(clausify,[status(thm)],[f_1708_3]) ).
fof(f_1709_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_1709_2,plain,
! [U_7223,U_7222] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7222),U_7223)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7222)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7223)),
inference(variable_rename,[status(thm)],[f_1709_1]) ).
fof(f_1709_3,plain,
! [U_7222,U_7223] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7222),U_7223)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7222)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7223)),
inference(definitional_conversion,[status(esa)],[f_1709_2]) ).
cnf(f_1709_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7222),U_7223)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7222)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7223)),
inference(clausify,[status(thm)],[f_1709_3]) ).
fof(f_1710_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_1710_2,plain,
! [U_7226,U_7225,U_7224] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7224),U_7226)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7225),U_7226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7224),U_7225)) ),
inference(variable_rename,[status(thm)],[f_1710_1]) ).
fof(f_1710_3,plain,
! [U_7224,U_7225,U_7226] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7224),U_7226)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7225),U_7226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7224),U_7225)) ),
inference(definitional_conversion,[status(esa)],[f_1710_2]) ).
cnf(f_1710_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7224),U_7226)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7225),U_7226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7224),U_7225)) ),
inference(clausify,[status(thm)],[f_1710_3]) ).
fof(f_1711_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_1711_2,plain,
! [U_7230,U_7229,U_7228,U_7227] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7227),U_7229)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7228),U_7230)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7229),U_7230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7227),U_7228)) ),
inference(variable_rename,[status(thm)],[f_1711_1]) ).
fof(f_1711_3,plain,
! [U_7227,U_7228,U_7229,U_7230] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7227),U_7229)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7228),U_7230)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7229),U_7230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7227),U_7228)) ),
inference(definitional_conversion,[status(esa)],[f_1711_2]) ).
cnf(f_1711_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7227),U_7229)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7228),U_7230)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7229),U_7230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7227),U_7228)) ),
inference(clausify,[status(thm)],[f_1711_3]) ).
fof(f_1712_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_1712_2,plain,
! [U_7232,U_7231] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7231),U_7232))
| U_7231 = U_7232
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7231),U_7232)) )
& ( ( U_7231 != U_7232
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7231),U_7232)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7231),U_7232)) ) ),
inference(variable_rename,[status(thm)],[f_1712_1]) ).
fof(f_1712_3,plain,
( ! [U_7236,U_7234] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7234),U_7236))
| U_7234 = U_7236
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7234),U_7236)) )
& ! [U_7235,U_7233] :
( ( U_7233 != U_7235
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7233),U_7235)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7233),U_7235)) ) ),
inference(miniscope,[status(thm)],[f_1712_2]) ).
fof(f_1712_4,plain,
( ! [U_7235,U_7233] :
( U_7233 != U_7235
| ~ sP422(U_7235,U_7233) )
& ! [U_7235,U_7233] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7233),U_7235))
| ~ sP422(U_7235,U_7233) )
& ! [U_7236,U_7234] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7234),U_7236))
| U_7234 = U_7236
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7234),U_7236)) )
& ! [U_7235,U_7233] :
( sP422(U_7235,U_7233)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7233),U_7235)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP422])],[f_1712_3]) ).
cnf(f_1712_5,plain,
( sP422(U_7235,U_7233)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7233),U_7235)) ),
inference(clausify,[status(thm)],[f_1712_4]) ).
cnf(f_1712_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7234),U_7236))
| U_7234 = U_7236
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7234),U_7236)) ),
inference(clausify,[status(thm)],[f_1712_4]) ).
cnf(f_1712_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7233),U_7235))
| ~ sP422(U_7235,U_7233) ),
inference(clausify,[status(thm)],[f_1712_4]) ).
cnf(f_1712_8,plain,
( U_7233 != U_7235
| ~ sP422(U_7235,U_7233) ),
inference(clausify,[status(thm)],[f_1712_4]) ).
fof(f_1713_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_1713_2,plain,
! [U_7237] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7237)),U_7237) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1713_1]) ).
fof(f_1713_3,plain,
! [U_7237] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7237)),U_7237) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1713_2]) ).
cnf(f_1713_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7237)),U_7237) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1713_3]) ).
fof(f_1714_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_1714_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_1714_1]) ).
cnf(f_1714_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_1714_2]) ).
fof(f_1715_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_1715_2,plain,
! [U_7238] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7238),U_7238)),
inference(variable_rename,[status(thm)],[f_1715_1]) ).
fof(f_1715_3,plain,
! [U_7238] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7238),U_7238)),
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),U_7238),U_7238)),
inference(clausify,[status(thm)],[f_1715_3]) ).
fof(f_1716_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_1716_2,plain,
! [U_7240,U_7239] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7240),U_7239))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7239),U_7240)) ),
inference(variable_rename,[status(thm)],[f_1716_1]) ).
fof(f_1716_3,plain,
! [U_7240,U_7239] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7240),U_7239))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7239),U_7240)) ),
inference(definitional_conversion,[status(esa)],[f_1716_2]) ).
cnf(f_1716_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7240),U_7239))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7239),U_7240)) ),
inference(clausify,[status(thm)],[f_1716_3]) ).
fof(f_1717_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_1717_2,plain,
! [U_7242,U_7241] :
( 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_7241),U_7242)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7242))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7241)) ),
inference(variable_rename,[status(thm)],[f_1717_1]) ).
fof(f_1717_3,plain,
! [U_7241,U_7242] :
( 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_7241),U_7242)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7242))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7241)) ),
inference(definitional_conversion,[status(esa)],[f_1717_2]) ).
cnf(f_1717_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_7241),U_7242)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7242))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7241)) ),
inference(clausify,[status(thm)],[f_1717_3]) ).
fof(f_1718_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_1718_2,plain,
! [U_7245,U_7244,U_7243] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7245),U_7243)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7245),U_7244)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7243),U_7244)) ),
inference(variable_rename,[status(thm)],[f_1718_1]) ).
fof(f_1718_3,plain,
! [U_7243,U_7244,U_7245] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7245),U_7243)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7245),U_7244)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7243),U_7244)) ),
inference(definitional_conversion,[status(esa)],[f_1718_2]) ).
cnf(f_1718_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_7245),U_7243)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7245),U_7244)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7243),U_7244)) ),
inference(clausify,[status(thm)],[f_1718_3]) ).
fof(f_1719_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_1719_2,plain,
! [U_7248,U_7247,U_7246] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7246),U_7248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7247),U_7248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7246),U_7247)) ),
inference(variable_rename,[status(thm)],[f_1719_1]) ).
fof(f_1719_3,plain,
! [U_7246,U_7247,U_7248] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7246),U_7248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7247),U_7248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7246),U_7247)) ),
inference(definitional_conversion,[status(esa)],[f_1719_2]) ).
cnf(f_1719_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7246),U_7248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7247),U_7248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7246),U_7247)) ),
inference(clausify,[status(thm)],[f_1719_3]) ).
fof(f_1720_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_1720_2,plain,
! [U_7250,U_7249] :
( U_7249 = U_7250
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7250),U_7249))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7249),U_7250)) ),
inference(variable_rename,[status(thm)],[f_1720_1]) ).
fof(f_1720_3,plain,
! [U_7249,U_7250] :
( U_7249 = U_7250
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7250),U_7249))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7249),U_7250)) ),
inference(definitional_conversion,[status(esa)],[f_1720_2]) ).
cnf(f_1720_4,plain,
( U_7249 = U_7250
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7250),U_7249))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7249),U_7250)) ),
inference(clausify,[status(thm)],[f_1720_3]) ).
fof(f_1721_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_1721_2,plain,
! [U_7251] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7251),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_7251,
inference(variable_rename,[status(thm)],[f_1721_1]) ).
fof(f_1721_3,plain,
! [U_7251] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7251),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_7251,
inference(definitional_conversion,[status(esa)],[f_1721_2]) ).
cnf(f_1721_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7251),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_7251,
inference(clausify,[status(thm)],[f_1721_3]) ).
fof(f_1722_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_1722_2,plain,
! [U_7252] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7252) = U_7252,
inference(variable_rename,[status(thm)],[f_1722_1]) ).
fof(f_1722_3,plain,
! [U_7252] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7252) = U_7252,
inference(definitional_conversion,[status(esa)],[f_1722_2]) ).
cnf(f_1722_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7252) = U_7252,
inference(clausify,[status(thm)],[f_1722_3]) ).
fof(f_1723_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_1723_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_1723_1]) ).
cnf(f_1723_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_1723_2]) ).
fof(f_1724_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_1724_2,plain,
! [U_7254,U_7253] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7253),U_7254))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7253),U_7254)),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_7253),U_7254)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7253),U_7254)) ) ),
inference(variable_rename,[status(thm)],[f_1724_1]) ).
fof(f_1724_3,plain,
( ! [U_7258,U_7256] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7256),U_7258))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7256),U_7258)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7257,U_7255] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7255),U_7257)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7255),U_7257)) ) ),
inference(miniscope,[status(thm)],[f_1724_2]) ).
fof(f_1724_4,plain,
( ! [U_7256,U_7258] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7256),U_7258))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7256),U_7258)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7257,U_7255] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7255),U_7257)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7255),U_7257)) ) ),
inference(definitional_conversion,[status(esa)],[f_1724_3]) ).
cnf(f_1724_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7255),U_7257)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7255),U_7257)) ),
inference(clausify,[status(thm)],[f_1724_4]) ).
cnf(f_1724_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7256),U_7258))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7256),U_7258)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1724_4]) ).
fof(f_1725_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_1725_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1725_1]) ).
cnf(f_1725_3,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1725_2]) ).
fof(f_1726_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_1726_2,plain,
! [U_7259] : 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_7259)),U_7259) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1726_1]) ).
fof(f_1726_3,plain,
! [U_7259] : 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_7259)),U_7259) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1726_2]) ).
cnf(f_1726_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_7259)),U_7259) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1726_3]) ).
fof(f_1727_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_1727_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_1727_1]) ).
cnf(f_1727_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_1727_2]) ).
fof(f_1728_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_1728_2,plain,
! [U_7261,U_7260] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7260),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7261),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7260),U_7261)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7260),U_7261))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7260),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7261),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_1728_1]) ).
fof(f_1728_3,plain,
( ! [U_7265,U_7263] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7263),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7265),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7263),U_7265)) )
& ! [U_7264,U_7262] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7262),U_7264))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7262),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7264),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_1728_2]) ).
fof(f_1728_4,plain,
( ! [U_7263,U_7265] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7263),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7265),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7263),U_7265)) )
& ! [U_7264,U_7262] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7262),U_7264))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7262),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7264),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(definitional_conversion,[status(esa)],[f_1728_3]) ).
cnf(f_1728_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7262),U_7264))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7262),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7264),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_1728_4]) ).
cnf(f_1728_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7263),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7265),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7263),U_7265)) ),
inference(clausify,[status(thm)],[f_1728_4]) ).
fof(f_1729_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_1729_2,plain,
! [U_7266] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7266))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7266)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7266))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7266)) ) ),
inference(variable_rename,[status(thm)],[f_1729_1]) ).
fof(f_1729_3,plain,
( ! [U_7268] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7268))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7268)) )
& ! [U_7267] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7267)) ) ),
inference(miniscope,[status(thm)],[f_1729_2]) ).
fof(f_1729_4,plain,
( ! [U_7268] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7268))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7268)) )
& ! [U_7267] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7267)) ) ),
inference(definitional_conversion,[status(esa)],[f_1729_3]) ).
cnf(f_1729_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7267)) ),
inference(clausify,[status(thm)],[f_1729_4]) ).
cnf(f_1729_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7268))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7268)) ),
inference(clausify,[status(thm)],[f_1729_4]) ).
fof(f_1730_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_1730_2,plain,
! [U_7270,U_7269] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7269),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7270),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7269),U_7270)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7269),U_7270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7269),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7270),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_1730_1]) ).
fof(f_1730_3,plain,
( ! [U_7274,U_7272] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7272),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7274),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7272),U_7274)) )
& ! [U_7273,U_7271] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7271),U_7273))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7271),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7273),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_1730_2]) ).
fof(f_1730_4,plain,
( ! [U_7272,U_7274] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7272),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7274),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7272),U_7274)) )
& ! [U_7273,U_7271] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7271),U_7273))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7271),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7273),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(definitional_conversion,[status(esa)],[f_1730_3]) ).
cnf(f_1730_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7271),U_7273))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7271),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7273),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_1730_4]) ).
cnf(f_1730_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7272),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7274),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7272),U_7274)) ),
inference(clausify,[status(thm)],[f_1730_4]) ).
fof(f_1731_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_1731_2,plain,
! [U_7276,U_7275] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7275),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7276))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7275),U_7276)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7275),U_7276))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7275),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7276)) ) ),
inference(variable_rename,[status(thm)],[f_1731_1]) ).
fof(f_1731_3,plain,
( ! [U_7280,U_7278] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7278),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7278),U_7280)) )
& ! [U_7279,U_7277] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7277),U_7279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7277),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7279)) ) ),
inference(miniscope,[status(thm)],[f_1731_2]) ).
fof(f_1731_4,plain,
( ! [U_7278,U_7280] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7278),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7278),U_7280)) )
& ! [U_7279,U_7277] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7277),U_7279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7277),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7279)) ) ),
inference(definitional_conversion,[status(esa)],[f_1731_3]) ).
cnf(f_1731_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7277),U_7279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7277),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7279)) ),
inference(clausify,[status(thm)],[f_1731_4]) ).
cnf(f_1731_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_7278),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7278),U_7280)) ),
inference(clausify,[status(thm)],[f_1731_4]) ).
fof(f_1732_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_1732_2,plain,
! [U_7281] :
( 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_7281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7281)) ),
inference(variable_rename,[status(thm)],[f_1732_1]) ).
fof(f_1732_3,plain,
! [U_7281] :
( 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_7281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7281)) ),
inference(definitional_conversion,[status(esa)],[f_1732_2]) ).
cnf(f_1732_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_7281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7281)) ),
inference(clausify,[status(thm)],[f_1732_3]) ).
fof(f_1733_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_1733_2,plain,
! [U_7283,U_7282] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7282),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7283))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7282),U_7283)) ),
inference(variable_rename,[status(thm)],[f_1733_1]) ).
fof(f_1733_3,plain,
! [U_7282,U_7283] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7282),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7283))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7282),U_7283)) ),
inference(definitional_conversion,[status(esa)],[f_1733_2]) ).
cnf(f_1733_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_7282),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7283))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7282),U_7283)) ),
inference(clausify,[status(thm)],[f_1733_3]) ).
fof(f_1734_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_1734_2,plain,
! [U_7284] :
( ( 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_7284)),U_7284)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7284),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7284),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_7284)),U_7284)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1734_1]) ).
fof(f_1734_3,plain,
( ! [U_7286] :
( 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_7286)),U_7286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7286),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7285] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7285),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_7285)),U_7285)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1734_2]) ).
fof(f_1734_4,plain,
( ! [U_7286] :
( 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_7286)),U_7286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7286),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7285] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7285),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_7285)),U_7285)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_1734_3]) ).
cnf(f_1734_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7285),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_7285)),U_7285)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1734_4]) ).
cnf(f_1734_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_7286)),U_7286)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7286),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1734_4]) ).
fof(f_1735_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_1735_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_1735_1]) ).
cnf(f_1735_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_1735_2]) ).
fof(f_1736_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( V_b_2 = V_d_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J]) ).
fof(f_1736_2,plain,
! [U_7291,U_7290,U_7289,U_7288,U_7287] :
( U_7289 = U_7291
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7287),U_7290),U_7291))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7287),U_7288),U_7289))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7287,U_7288),U_7289) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7287,U_7290),U_7291)
| ~ class_Orderings_Olinorder(U_7287) ),
inference(variable_rename,[status(thm)],[f_1736_1]) ).
fof(f_1736_3,plain,
! [U_7287,U_7288,U_7289,U_7290,U_7291] :
( U_7289 = U_7291
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7287),U_7290),U_7291))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7287),U_7288),U_7289))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7287,U_7288),U_7289) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7287,U_7290),U_7291)
| ~ class_Orderings_Olinorder(U_7287) ),
inference(definitional_conversion,[status(esa)],[f_1736_2]) ).
cnf(f_1736_4,plain,
( U_7289 = U_7291
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7287),U_7290),U_7291))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7287),U_7288),U_7289))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7287,U_7288),U_7289) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7287,U_7290),U_7291)
| ~ class_Orderings_Olinorder(U_7287) ),
inference(clausify,[status(thm)],[f_1736_3]) ).
fof(f_1737_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( V_a_2 = V_c_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J]) ).
fof(f_1737_2,plain,
! [U_7296,U_7295,U_7294,U_7293,U_7292] :
( U_7293 = U_7295
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7292),U_7295),U_7296))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7292),U_7293),U_7294))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7292,U_7293),U_7294) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7292,U_7295),U_7296)
| ~ class_Orderings_Olinorder(U_7292) ),
inference(variable_rename,[status(thm)],[f_1737_1]) ).
fof(f_1737_3,plain,
! [U_7292,U_7293,U_7294,U_7295,U_7296] :
( U_7293 = U_7295
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7292),U_7295),U_7296))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7292),U_7293),U_7294))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7292,U_7293),U_7294) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7292,U_7295),U_7296)
| ~ class_Orderings_Olinorder(U_7292) ),
inference(definitional_conversion,[status(esa)],[f_1737_2]) ).
cnf(f_1737_4,plain,
( U_7293 = U_7295
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7292),U_7295),U_7296))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7292),U_7293),U_7294))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7292,U_7293),U_7294) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7292,U_7295),U_7296)
| ~ class_Orderings_Olinorder(U_7292) ),
inference(clausify,[status(thm)],[f_1737_3]) ).
fof(f_1738_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)
| V_b_2 != V_d_2
| V_a_2 != V_c_2 )
& ( ( V_b_2 = V_d_2
& V_a_2 = V_c_2 )
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff]) ).
fof(f_1738_2,plain,
! [U_7301,U_7300,U_7299,U_7298,U_7297] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7297,U_7298),U_7299) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7297,U_7300),U_7301)
| U_7299 != U_7301
| U_7298 != U_7300 )
& ( ( U_7299 = U_7301
& U_7298 = U_7300 )
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7297,U_7298),U_7299) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7297,U_7300),U_7301) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7297),U_7300),U_7301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7297),U_7298),U_7299))
| ~ class_Orderings_Olinorder(U_7297) ),
inference(variable_rename,[status(thm)],[f_1738_1]) ).
fof(f_1738_3,plain,
( ! [U_7299,U_7298,U_7300,U_7301] :
( U_7299 = U_7301
| ~ sP423(U_7299,U_7298,U_7300,U_7301) )
& ! [U_7299,U_7298,U_7300,U_7301] :
( U_7298 = U_7300
| ~ sP423(U_7299,U_7298,U_7300,U_7301) )
& ! [U_7299,U_7298,U_7300,U_7297,U_7301] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7297,U_7298),U_7299) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7297,U_7300),U_7301)
| U_7299 != U_7301
| U_7298 != U_7300
| ~ sP424(U_7299,U_7298,U_7300,U_7297,U_7301) )
& ! [U_7299,U_7298,U_7300,U_7297,U_7301] :
( sP423(U_7299,U_7298,U_7300,U_7301)
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7297,U_7298),U_7299) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7297,U_7300),U_7301)
| ~ sP424(U_7299,U_7298,U_7300,U_7297,U_7301) )
& ! [U_7299,U_7298,U_7300,U_7297,U_7301] :
( sP424(U_7299,U_7298,U_7300,U_7297,U_7301)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7297),U_7300),U_7301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7297),U_7298),U_7299))
| ~ class_Orderings_Olinorder(U_7297) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP423,sP424])],[f_1738_2]) ).
cnf(f_1738_4,plain,
( sP424(U_7299,U_7298,U_7300,U_7297,U_7301)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7297),U_7300),U_7301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7297),U_7298),U_7299))
| ~ class_Orderings_Olinorder(U_7297) ),
inference(clausify,[status(thm)],[f_1738_3]) ).
cnf(f_1738_5,plain,
( sP423(U_7299,U_7298,U_7300,U_7301)
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7297,U_7298),U_7299) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7297,U_7300),U_7301)
| ~ sP424(U_7299,U_7298,U_7300,U_7297,U_7301) ),
inference(clausify,[status(thm)],[f_1738_3]) ).
cnf(f_1738_6,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7297,U_7298),U_7299) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7297,U_7300),U_7301)
| U_7299 != U_7301
| U_7298 != U_7300
| ~ sP424(U_7299,U_7298,U_7300,U_7297,U_7301) ),
inference(clausify,[status(thm)],[f_1738_3]) ).
cnf(f_1738_7,plain,
( U_7298 = U_7300
| ~ sP423(U_7299,U_7298,U_7300,U_7301) ),
inference(clausify,[status(thm)],[f_1738_3]) ).
cnf(f_1738_8,plain,
( U_7299 = U_7301
| ~ sP423(U_7299,U_7298,U_7300,U_7301) ),
inference(clausify,[status(thm)],[f_1738_3]) ).
fof(f_1739_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_1739_2,plain,
! [U_7304,U_7303,U_7302] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7303),U_7304)) = 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_7302),U_7303)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7303),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7303),U_7304)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7302),U_7303)) ),
inference(variable_rename,[status(thm)],[f_1739_1]) ).
fof(f_1739_3,plain,
! [U_7304,U_7302,U_7303] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7303),U_7304)) = 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_7302),U_7303)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7303),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7303),U_7304)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7302),U_7303)) ),
inference(definitional_conversion,[status(esa)],[f_1739_2]) ).
cnf(f_1739_4,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7303),U_7304)) = 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_7302),U_7303)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7303),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7303),U_7304)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7302),U_7303)) ),
inference(clausify,[status(thm)],[f_1739_3]) ).
fof(f_1740_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_1740_2,plain,
! [U_7305] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7305),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_1740_1]) ).
fof(f_1740_3,plain,
! [U_7305] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7305),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_1740_2]) ).
cnf(f_1740_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7305),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_1740_3]) ).
fof(f_1741_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_1741_2,plain,
! [U_7306] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7306) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7306),
inference(variable_rename,[status(thm)],[f_1741_1]) ).
fof(f_1741_3,plain,
! [U_7306] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7306) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7306),
inference(definitional_conversion,[status(esa)],[f_1741_2]) ).
cnf(f_1741_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7306) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7306),
inference(clausify,[status(thm)],[f_1741_3]) ).
fof(f_1742_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_1742_2,plain,
! [U_7308,U_7307] :
( U_7307 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7308),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_7307)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7307),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7308),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_7307))))) ),
inference(variable_rename,[status(thm)],[f_1742_1]) ).
fof(f_1742_3,plain,
! [U_7307,U_7308] :
( U_7307 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7308),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_7307)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7307),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7308),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_7307))))) ),
inference(definitional_conversion,[status(esa)],[f_1742_2]) ).
cnf(f_1742_4,plain,
( U_7307 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7308),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_7307)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7307),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7308),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_7307))))) ),
inference(clausify,[status(thm)],[f_1742_3]) ).
fof(f_1743_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_1743_2,plain,
! [U_7310,U_7309] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7309),U_7310)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7310),U_7309),
inference(variable_rename,[status(thm)],[f_1743_1]) ).
fof(f_1743_3,plain,
! [U_7310,U_7309] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7309),U_7310)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7310),U_7309),
inference(definitional_conversion,[status(esa)],[f_1743_2]) ).
cnf(f_1743_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7309),U_7310)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7310),U_7309),
inference(clausify,[status(thm)],[f_1743_3]) ).
fof(f_1744_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_1744_2,plain,
! [U_7312,U_7311] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7311),U_7312)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7311)),hAPP(c_Nat_OSuc,U_7312)),
inference(variable_rename,[status(thm)],[f_1744_1]) ).
fof(f_1744_3,plain,
! [U_7311,U_7312] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7311),U_7312)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7311)),hAPP(c_Nat_OSuc,U_7312)),
inference(definitional_conversion,[status(esa)],[f_1744_2]) ).
cnf(f_1744_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_7311),U_7312)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7311)),hAPP(c_Nat_OSuc,U_7312)),
inference(clausify,[status(thm)],[f_1744_3]) ).
fof(f_1745_1,plain,
! [V_a_2,V_b_2,T_c] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_a_2))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty]) ).
fof(f_1745_2,plain,
! [U_7315,U_7314,U_7313] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7313,U_7315),U_7314) = c_Orderings_Obot__class_Obot(tc_fun(U_7313,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7313),U_7314),U_7315))
| ~ class_Orderings_Oorder(U_7313) ),
inference(variable_rename,[status(thm)],[f_1745_1]) ).
fof(f_1745_3,plain,
! [U_7313,U_7314,U_7315] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7313,U_7315),U_7314) = c_Orderings_Obot__class_Obot(tc_fun(U_7313,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7313),U_7314),U_7315))
| ~ class_Orderings_Oorder(U_7313) ),
inference(definitional_conversion,[status(esa)],[f_1745_2]) ).
cnf(f_1745_4,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7313,U_7315),U_7314) = c_Orderings_Obot__class_Obot(tc_fun(U_7313,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7313),U_7314),U_7315))
| ~ class_Orderings_Oorder(U_7313) ),
inference(clausify,[status(thm)],[f_1745_3]) ).
fof(f_1746_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).
fof(f_1746_2,plain,
! [U_7318,U_7317,U_7316] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7316,U_7317),U_7318) = c_Orderings_Obot__class_Obot(tc_fun(U_7316,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7316),U_7317),U_7318)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7316),U_7317),U_7318))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7316,U_7317),U_7318) != c_Orderings_Obot__class_Obot(tc_fun(U_7316,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(U_7316) ),
inference(variable_rename,[status(thm)],[f_1746_1]) ).
fof(f_1746_3,plain,
( ! [U_7316,U_7317,U_7318] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7316,U_7317),U_7318) = c_Orderings_Obot__class_Obot(tc_fun(U_7316,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7316),U_7317),U_7318))
| ~ sP425(U_7316,U_7317,U_7318) )
& ! [U_7316,U_7317,U_7318] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7316),U_7317),U_7318))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7316,U_7317),U_7318) != c_Orderings_Obot__class_Obot(tc_fun(U_7316,tc_HOL_Obool))
| ~ sP425(U_7316,U_7317,U_7318) )
& ! [U_7316,U_7317,U_7318] :
( sP425(U_7316,U_7317,U_7318)
| ~ class_Orderings_Oorder(U_7316) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP425])],[f_1746_2]) ).
cnf(f_1746_4,plain,
( sP425(U_7316,U_7317,U_7318)
| ~ class_Orderings_Oorder(U_7316) ),
inference(clausify,[status(thm)],[f_1746_3]) ).
cnf(f_1746_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7316),U_7317),U_7318))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7316,U_7317),U_7318) != c_Orderings_Obot__class_Obot(tc_fun(U_7316,tc_HOL_Obool))
| ~ sP425(U_7316,U_7317,U_7318) ),
inference(clausify,[status(thm)],[f_1746_3]) ).
cnf(f_1746_6,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7316,U_7317),U_7318) = c_Orderings_Obot__class_Obot(tc_fun(U_7316,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7316),U_7317),U_7318))
| ~ sP425(U_7316,U_7317,U_7318) ),
inference(clausify,[status(thm)],[f_1746_3]) ).
fof(f_1747_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2))
| c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).
fof(f_1747_2,plain,
! [U_7321,U_7320,U_7319] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_7319,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7319,U_7320),U_7321)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7319),U_7320),U_7321)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7319),U_7320),U_7321))
| c_Orderings_Obot__class_Obot(tc_fun(U_7319,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7319,U_7320),U_7321) ) )
| ~ class_Orderings_Oorder(U_7319) ),
inference(variable_rename,[status(thm)],[f_1747_1]) ).
fof(f_1747_3,plain,
( ! [U_7320,U_7321,U_7319] :
( c_Orderings_Obot__class_Obot(tc_fun(U_7319,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7319,U_7320),U_7321)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7319),U_7320),U_7321))
| ~ sP426(U_7320,U_7321,U_7319) )
& ! [U_7320,U_7321,U_7319] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7319),U_7320),U_7321))
| c_Orderings_Obot__class_Obot(tc_fun(U_7319,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7319,U_7320),U_7321)
| ~ sP426(U_7320,U_7321,U_7319) )
& ! [U_7320,U_7321,U_7319] :
( sP426(U_7320,U_7321,U_7319)
| ~ class_Orderings_Oorder(U_7319) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP426])],[f_1747_2]) ).
cnf(f_1747_4,plain,
( sP426(U_7320,U_7321,U_7319)
| ~ class_Orderings_Oorder(U_7319) ),
inference(clausify,[status(thm)],[f_1747_3]) ).
cnf(f_1747_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7319),U_7320),U_7321))
| c_Orderings_Obot__class_Obot(tc_fun(U_7319,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7319,U_7320),U_7321)
| ~ sP426(U_7320,U_7321,U_7319) ),
inference(clausify,[status(thm)],[f_1747_3]) ).
cnf(f_1747_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_7319,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7319,U_7320),U_7321)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7319),U_7320),U_7321))
| ~ sP426(U_7320,U_7321,U_7319) ),
inference(clausify,[status(thm)],[f_1747_3]) ).
fof(f_1748_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_a_2)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff]) ).
fof(f_1748_2,plain,
! [U_7326,U_7325,U_7324,U_7323,U_7322] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7322),U_7324),U_7326))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7322),U_7325),U_7323)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7322),U_7324),U_7323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7322,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7322,U_7323),U_7324)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7322,U_7325),U_7326)))
| ~ class_Orderings_Olinorder(U_7322) ),
inference(variable_rename,[status(thm)],[f_1748_1]) ).
fof(f_1748_3,plain,
( ! [U_7322,U_7323,U_7324,U_7325,U_7326] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7322),U_7324),U_7326))
| ~ sP427(U_7322,U_7323,U_7324,U_7325,U_7326) )
& ! [U_7322,U_7323,U_7324,U_7325,U_7326] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7322),U_7325),U_7323))
| ~ sP427(U_7322,U_7323,U_7324,U_7325,U_7326) )
& ! [U_7322,U_7323,U_7324,U_7325,U_7326] :
( sP427(U_7322,U_7323,U_7324,U_7325,U_7326)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7322),U_7324),U_7323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7322,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7322,U_7323),U_7324)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7322,U_7325),U_7326)))
| ~ class_Orderings_Olinorder(U_7322) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP427])],[f_1748_2]) ).
cnf(f_1748_4,plain,
( sP427(U_7322,U_7323,U_7324,U_7325,U_7326)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7322),U_7324),U_7323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7322,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7322,U_7323),U_7324)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7322,U_7325),U_7326)))
| ~ class_Orderings_Olinorder(U_7322) ),
inference(clausify,[status(thm)],[f_1748_3]) ).
cnf(f_1748_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7322),U_7325),U_7323))
| ~ sP427(U_7322,U_7323,U_7324,U_7325,U_7326) ),
inference(clausify,[status(thm)],[f_1748_3]) ).
cnf(f_1748_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7322),U_7324),U_7326))
| ~ sP427(U_7322,U_7323,U_7324,U_7325,U_7326) ),
inference(clausify,[status(thm)],[f_1748_3]) ).
fof(f_1749_1,plain,
! [V_n_2,V_m_2,V_f_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl]) ).
fof(f_1749_2,plain,
! [U_7330,U_7329,U_7328,U_7327] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7327),U_7328),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7329)),hAPP(c_Nat_OSuc,U_7330))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7327),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7327,tc_Nat_Onat),U_7328),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7329),U_7330))
| ~ class_Groups_Ocomm__monoid__add(U_7327) ),
inference(variable_rename,[status(thm)],[f_1749_1]) ).
fof(f_1749_3,plain,
! [U_7327,U_7328,U_7329,U_7330] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7327),U_7328),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7329)),hAPP(c_Nat_OSuc,U_7330))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7327),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7327,tc_Nat_Onat),U_7328),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7329),U_7330))
| ~ class_Groups_Ocomm__monoid__add(U_7327) ),
inference(definitional_conversion,[status(esa)],[f_1749_2]) ).
cnf(f_1749_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7327),U_7328),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7329)),hAPP(c_Nat_OSuc,U_7330))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7327),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7327,tc_Nat_Onat),U_7328),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7329),U_7330))
| ~ class_Groups_Ocomm__monoid__add(U_7327) ),
inference(clausify,[status(thm)],[f_1749_3]) ).
fof(f_1750_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I17_J]) ).
fof(f_1750_2,plain,
! [U_7334,U_7333,U_7332,U_7331] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7331,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7331,U_7332),U_7333)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7331,U_7333),U_7334)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7331,U_7332),U_7334)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7331),U_7333),U_7334))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7331),U_7332),U_7333))
| ~ class_Orderings_Olinorder(U_7331) ),
inference(variable_rename,[status(thm)],[f_1750_1]) ).
fof(f_1750_3,plain,
! [U_7331,U_7332,U_7333,U_7334] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7331,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7331,U_7332),U_7333)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7331,U_7333),U_7334)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7331,U_7332),U_7334)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7331),U_7333),U_7334))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7331),U_7332),U_7333))
| ~ class_Orderings_Olinorder(U_7331) ),
inference(definitional_conversion,[status(esa)],[f_1750_2]) ).
cnf(f_1750_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7331,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7331,U_7332),U_7333)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7331,U_7333),U_7334)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7331,U_7332),U_7334)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7331),U_7333),U_7334))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7331),U_7332),U_7333))
| ~ class_Orderings_Olinorder(U_7331) ),
inference(clausify,[status(thm)],[f_1750_3]) ).
fof(f_1751_1,plain,
! [V_n_2,V_k_2,V_m_2,V_f_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl]) ).
fof(f_1751_2,plain,
! [U_7339,U_7338,U_7337,U_7336,U_7335] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7335),U_7336),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7337),U_7338)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7339),U_7338))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7335),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7335,tc_Nat_Onat),U_7336),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_7338))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7337),U_7339))
| ~ class_Groups_Ocomm__monoid__add(U_7335) ),
inference(variable_rename,[status(thm)],[f_1751_1]) ).
fof(f_1751_3,plain,
! [U_7335,U_7337,U_7336,U_7338,U_7339] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7335),U_7336),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7337),U_7338)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7339),U_7338))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7335),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7335,tc_Nat_Onat),U_7336),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_7338))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7337),U_7339))
| ~ class_Groups_Ocomm__monoid__add(U_7335) ),
inference(definitional_conversion,[status(esa)],[f_1751_2]) ).
cnf(f_1751_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7335),U_7336),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7337),U_7338)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7339),U_7338))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7335),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7335,tc_Nat_Onat),U_7336),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_7338))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7337),U_7339))
| ~ class_Groups_Ocomm__monoid__add(U_7335) ),
inference(clausify,[status(thm)],[f_1751_3]) ).
fof(f_1752_1,plain,
! [V_m_2,V_n_2,V_i_2,T_c] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_n_2),V_m_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_i_2),V_n_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__diff]) ).
fof(f_1752_2,plain,
! [U_7343,U_7342,U_7341,U_7340] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7340,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7340,U_7341),U_7343)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7340,U_7341),U_7342)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7340,U_7342),U_7343)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7340),U_7341),U_7342))
| ~ class_Orderings_Olinorder(U_7340) ),
inference(variable_rename,[status(thm)],[f_1752_1]) ).
fof(f_1752_3,plain,
! [U_7340,U_7341,U_7342,U_7343] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7340,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7340,U_7341),U_7343)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7340,U_7341),U_7342)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7340,U_7342),U_7343)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7340),U_7341),U_7342))
| ~ class_Orderings_Olinorder(U_7340) ),
inference(definitional_conversion,[status(esa)],[f_1752_2]) ).
cnf(f_1752_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7340,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7340,U_7341),U_7343)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7340,U_7341),U_7342)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7340,U_7342),U_7343)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7340),U_7341),U_7342))
| ~ class_Orderings_Olinorder(U_7340) ),
inference(clausify,[status(thm)],[f_1752_3]) ).
fof(f_1753_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J]) ).
fof(f_1753_2,plain,
! [U_7347,U_7346,U_7345,U_7344] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7344,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7344,U_7345),U_7346)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7344,U_7346),U_7347)) = c_Orderings_Obot__class_Obot(tc_fun(U_7344,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7344) ),
inference(variable_rename,[status(thm)],[f_1753_1]) ).
fof(f_1753_3,plain,
! [U_7344,U_7345,U_7346,U_7347] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7344,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7344,U_7345),U_7346)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7344,U_7346),U_7347)) = c_Orderings_Obot__class_Obot(tc_fun(U_7344,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7344) ),
inference(definitional_conversion,[status(esa)],[f_1753_2]) ).
cnf(f_1753_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7344,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7344,U_7345),U_7346)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7344,U_7346),U_7347)) = c_Orderings_Obot__class_Obot(tc_fun(U_7344,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7344) ),
inference(clausify,[status(thm)],[f_1753_3]) ).
fof(f_1754_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_1754_2,plain,
! [U_7350,U_7349,U_7348] : 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_7348)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7349),U_7350)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7349),U_7348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7350),U_7348)),
inference(variable_rename,[status(thm)],[f_1754_1]) ).
fof(f_1754_3,plain,
! [U_7348,U_7349,U_7350] : 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_7348)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7349),U_7350)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7349),U_7348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7350),U_7348)),
inference(definitional_conversion,[status(esa)],[f_1754_2]) ).
cnf(f_1754_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_7348)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7349),U_7350)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7349),U_7348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7350),U_7348)),
inference(clausify,[status(thm)],[f_1754_3]) ).
fof(f_1755_1,plain,
! [V_f_2,V_p_2,V_n_2,V_m_2,T_c] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_c),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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl]) ).
fof(f_1755_2,plain,
! [U_7355,U_7354,U_7353,U_7352,U_7351] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7351),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7351),U_7355),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7352),U_7353))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7351),U_7355),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7353),U_7354))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7351),U_7355),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7352),U_7354))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7353),U_7354))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7352),U_7353))
| ~ class_Groups_Ocomm__monoid__add(U_7351) ),
inference(variable_rename,[status(thm)],[f_1755_1]) ).
fof(f_1755_3,plain,
! [U_7351,U_7352,U_7353,U_7354,U_7355] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7351),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7351),U_7355),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7352),U_7353))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7351),U_7355),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7353),U_7354))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7351),U_7355),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7352),U_7354))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7353),U_7354))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7352),U_7353))
| ~ class_Groups_Ocomm__monoid__add(U_7351) ),
inference(definitional_conversion,[status(esa)],[f_1755_2]) ).
cnf(f_1755_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7351),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7351),U_7355),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7352),U_7353))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7351),U_7355),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7353),U_7354))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7351),U_7355),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7352),U_7354))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7353),U_7354))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7352),U_7353))
| ~ class_Groups_Ocomm__monoid__add(U_7351) ),
inference(clausify,[status(thm)],[f_1755_3]) ).
fof(f_1756_1,plain,
! [V_f_2,V_p_2,V_n_2,V_m_2,T_c] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_c),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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl]) ).
fof(f_1756_2,plain,
! [U_7360,U_7359,U_7358,U_7357,U_7356] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7356),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7356),U_7360),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7357),U_7359))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7356),U_7360),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7357),U_7358))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7356),U_7360),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7358),U_7359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7358),U_7359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7357),U_7358))
| ~ class_Groups_Oab__group__add(U_7356) ),
inference(variable_rename,[status(thm)],[f_1756_1]) ).
fof(f_1756_3,plain,
! [U_7357,U_7356,U_7358,U_7359,U_7360] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7356),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7356),U_7360),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7357),U_7359))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7356),U_7360),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7357),U_7358))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7356),U_7360),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7358),U_7359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7358),U_7359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7357),U_7358))
| ~ class_Groups_Oab__group__add(U_7356) ),
inference(definitional_conversion,[status(esa)],[f_1756_2]) ).
cnf(f_1756_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7356),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7356),U_7360),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7357),U_7359))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7356),U_7360),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7357),U_7358))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7356),U_7360),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7358),U_7359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7358),U_7359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7357),U_7358))
| ~ class_Groups_Oab__group__add(U_7356) ),
inference(clausify,[status(thm)],[f_1756_3]) ).
fof(f_1757_1,plain,
! [V_i_2,V_inc_2,T_c] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(T_c,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2
| ~ class_Rings_Osemiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J]) ).
fof(f_1757_2,plain,
! [U_7363,U_7362,U_7361] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_7361,U_7362,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7363) = U_7363
| ~ class_Rings_Osemiring__1(U_7361) ),
inference(variable_rename,[status(thm)],[f_1757_1]) ).
fof(f_1757_3,plain,
! [U_7362,U_7361,U_7363] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_7361,U_7362,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7363) = U_7363
| ~ class_Rings_Osemiring__1(U_7361) ),
inference(definitional_conversion,[status(esa)],[f_1757_2]) ).
cnf(f_1757_4,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_7361,U_7362,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_7363) = U_7363
| ~ class_Rings_Osemiring__1(U_7361) ),
inference(clausify,[status(thm)],[f_1757_3]) ).
fof(f_1758_1,plain,
! [V_i_2,V_n_2,V_inc_2,T_c] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(T_c,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_c,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2))
| ~ class_Rings_Osemiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J]) ).
fof(f_1758_2,plain,
! [U_7367,U_7366,U_7365,U_7364] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_7364,U_7365,hAPP(c_Nat_OSuc,U_7366),U_7367) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_7364,U_7365,U_7366,hAPP(U_7365,U_7367))
| ~ class_Rings_Osemiring__1(U_7364) ),
inference(variable_rename,[status(thm)],[f_1758_1]) ).
fof(f_1758_3,plain,
! [U_7364,U_7365,U_7366,U_7367] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_7364,U_7365,hAPP(c_Nat_OSuc,U_7366),U_7367) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_7364,U_7365,U_7366,hAPP(U_7365,U_7367))
| ~ class_Rings_Osemiring__1(U_7364) ),
inference(definitional_conversion,[status(esa)],[f_1758_2]) ).
cnf(f_1758_4,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_7364,U_7365,hAPP(c_Nat_OSuc,U_7366),U_7367) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_7364,U_7365,U_7366,hAPP(U_7365,U_7367))
| ~ class_Rings_Osemiring__1(U_7364) ),
inference(clausify,[status(thm)],[f_1758_3]) ).
fof(f_1759_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_1759_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_1759_1]) ).
cnf(f_1759_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_1759_2]) ).
fof(f_1760_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_1760_2,plain,
! [U_7368] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7368),hAPP(c_Nat_OSuc,U_7368)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_7368),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_1760_1]) ).
fof(f_1760_3,plain,
! [U_7368] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7368),hAPP(c_Nat_OSuc,U_7368)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_7368),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_1760_2]) ).
cnf(f_1760_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7368),hAPP(c_Nat_OSuc,U_7368)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_7368),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_1760_3]) ).
fof(f_1761_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_1761_2,plain,
! [U_7370,U_7369] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7369)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7370)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7369),U_7370)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7369),U_7370))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7369)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7370))) ) ),
inference(variable_rename,[status(thm)],[f_1761_1]) ).
fof(f_1761_3,plain,
( ! [U_7374,U_7372] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7372)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7374)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7372),U_7374)) )
& ! [U_7373,U_7371] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7371),U_7373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7371)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7373))) ) ),
inference(miniscope,[status(thm)],[f_1761_2]) ).
fof(f_1761_4,plain,
( ! [U_7372,U_7374] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7372)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7374)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7372),U_7374)) )
& ! [U_7373,U_7371] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7371),U_7373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7371)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7373))) ) ),
inference(definitional_conversion,[status(esa)],[f_1761_3]) ).
cnf(f_1761_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7371),U_7373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7371)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7373))) ),
inference(clausify,[status(thm)],[f_1761_4]) ).
cnf(f_1761_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_7372)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7374)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7372),U_7374)) ),
inference(clausify,[status(thm)],[f_1761_4]) ).
fof(f_1762_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_1762_2,plain,
! [U_7376,U_7375] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7375)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7376)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7375),U_7376)),
inference(variable_rename,[status(thm)],[f_1762_1]) ).
fof(f_1762_3,plain,
! [U_7376,U_7375] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7375)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7376)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7375),U_7376)),
inference(definitional_conversion,[status(esa)],[f_1762_2]) ).
cnf(f_1762_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7375)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7376)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7375),U_7376)),
inference(clausify,[status(thm)],[f_1762_3]) ).
fof(f_1763_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_1763_2,plain,
! [U_7378,U_7377] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7377)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7378)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7377),U_7378)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7377),U_7378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7377)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7378))) ) ),
inference(variable_rename,[status(thm)],[f_1763_1]) ).
fof(f_1763_3,plain,
( ! [U_7382,U_7380] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7380)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7382)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7380),U_7382)) )
& ! [U_7381,U_7379] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7379),U_7381))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7379)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7381))) ) ),
inference(miniscope,[status(thm)],[f_1763_2]) ).
fof(f_1763_4,plain,
( ! [U_7380,U_7382] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7380)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7382)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7380),U_7382)) )
& ! [U_7381,U_7379] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7379),U_7381))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7379)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7381))) ) ),
inference(definitional_conversion,[status(esa)],[f_1763_3]) ).
cnf(f_1763_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7379),U_7381))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7379)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7381))) ),
inference(clausify,[status(thm)],[f_1763_4]) ).
cnf(f_1763_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_7380)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7382)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7380),U_7382)) ),
inference(clausify,[status(thm)],[f_1763_4]) ).
fof(f_1764_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_1764_2,plain,
! [U_7384,U_7383] :
( 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_7383),U_7384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7383)) ),
inference(variable_rename,[status(thm)],[f_1764_1]) ).
fof(f_1764_3,plain,
! [U_7383,U_7384] :
( 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_7383),U_7384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7383)) ),
inference(definitional_conversion,[status(esa)],[f_1764_2]) ).
cnf(f_1764_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_7383),U_7384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7383)) ),
inference(clausify,[status(thm)],[f_1764_3]) ).
fof(f_1765_1,plain,
! [V_A_2,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,tc_HOL_Obool)),tc_fun(T_c,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_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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_1765_2,plain,
! [U_7386,U_7385] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7385,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_7385,tc_HOL_Obool)),tc_fun(U_7385,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_7385,tc_HOL_Obool)),tc_fun(U_7385,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7385,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_7386)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7385,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7386),
inference(variable_rename,[status(thm)],[f_1765_1]) ).
fof(f_1765_3,plain,
! [U_7385,U_7386] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7385,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_7385,tc_HOL_Obool)),tc_fun(U_7385,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_7385,tc_HOL_Obool)),tc_fun(U_7385,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7385,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_7386)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7385,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7386),
inference(definitional_conversion,[status(esa)],[f_1765_2]) ).
cnf(f_1765_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7385,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_7385,tc_HOL_Obool)),tc_fun(U_7385,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_7385,tc_HOL_Obool)),tc_fun(U_7385,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7385,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_7386)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7385,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7386),
inference(clausify,[status(thm)],[f_1765_3]) ).
fof(f_1766_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_1766_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_1766_1]) ).
cnf(f_1766_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_1766_2]) ).
fof(f_1767_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan]) ).
fof(f_1767_2,plain,
! [U_7391,U_7390,U_7389,U_7388,U_7387] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7387,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7387,U_7388),U_7389)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7387,U_7390),U_7391)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7387,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_7387),U_7388),U_7390)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_7387),U_7389),U_7391))
| ~ class_Orderings_Olinorder(U_7387) ),
inference(variable_rename,[status(thm)],[f_1767_1]) ).
fof(f_1767_3,plain,
! [U_7387,U_7388,U_7389,U_7390,U_7391] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7387,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7387,U_7388),U_7389)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7387,U_7390),U_7391)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7387,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_7387),U_7388),U_7390)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_7387),U_7389),U_7391))
| ~ class_Orderings_Olinorder(U_7387) ),
inference(definitional_conversion,[status(esa)],[f_1767_2]) ).
cnf(f_1767_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7387,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7387,U_7388),U_7389)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7387,U_7390),U_7391)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7387,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_7387),U_7388),U_7390)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_7387),U_7389),U_7391))
| ~ class_Orderings_Olinorder(U_7387) ),
inference(clausify,[status(thm)],[f_1767_3]) ).
fof(f_1768_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J]) ).
fof(f_1768_2,plain,
! [U_7394,U_7393,U_7392] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7392,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7392),U_7393)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7392,U_7393),U_7394)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_7392),U_7394)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7392),U_7393),U_7394))
| ~ class_Orderings_Olinorder(U_7392) ),
inference(variable_rename,[status(thm)],[f_1768_1]) ).
fof(f_1768_3,plain,
! [U_7392,U_7393,U_7394] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7392,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7392),U_7393)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7392,U_7393),U_7394)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_7392),U_7394)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7392),U_7393),U_7394))
| ~ class_Orderings_Olinorder(U_7392) ),
inference(definitional_conversion,[status(esa)],[f_1768_2]) ).
cnf(f_1768_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7392,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7392),U_7393)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7392,U_7393),U_7394)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_7392),U_7394)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7392),U_7393),U_7394))
| ~ class_Orderings_Olinorder(U_7392) ),
inference(clausify,[status(thm)],[f_1768_3]) ).
fof(f_1769_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J]) ).
fof(f_1769_2,plain,
! [U_7397,U_7396,U_7395] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7395,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7395),U_7396)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7395,U_7396),U_7397)) = c_Orderings_Obot__class_Obot(tc_fun(U_7395,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7395) ),
inference(variable_rename,[status(thm)],[f_1769_1]) ).
fof(f_1769_3,plain,
! [U_7395,U_7396,U_7397] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7395,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7395),U_7396)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7395,U_7396),U_7397)) = c_Orderings_Obot__class_Obot(tc_fun(U_7395,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7395) ),
inference(definitional_conversion,[status(esa)],[f_1769_2]) ).
cnf(f_1769_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7395,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7395),U_7396)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7395,U_7396),U_7397)) = c_Orderings_Obot__class_Obot(tc_fun(U_7395,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7395) ),
inference(clausify,[status(thm)],[f_1769_3]) ).
fof(f_1770_1,plain,
! [V_k_2,V_f_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt]) ).
fof(f_1770_2,plain,
! [U_7400,U_7399,U_7398] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7398),U_7399),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_7400)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7398),U_7399),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7400))
| hAPP(U_7399,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_7398)
| ~ class_Groups_Ocomm__monoid__add(U_7398) ),
inference(variable_rename,[status(thm)],[f_1770_1]) ).
fof(f_1770_3,plain,
! [U_7398,U_7399,U_7400] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7398),U_7399),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_7400)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7398),U_7399),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7400))
| hAPP(U_7399,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_7398)
| ~ class_Groups_Ocomm__monoid__add(U_7398) ),
inference(definitional_conversion,[status(esa)],[f_1770_2]) ).
cnf(f_1770_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7398),U_7399),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_7400)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7398),U_7399),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7400))
| hAPP(U_7399,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_7398)
| ~ class_Groups_Ocomm__monoid__add(U_7398) ),
inference(clausify,[status(thm)],[f_1770_3]) ).
fof(f_1771_1,plain,
! [V_f_2,V_n_2,V_m_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc]) ).
fof(f_1771_2,plain,
! [U_7404,U_7403,U_7402,U_7401] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7401),U_7404),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7402),U_7403)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7401),hAPP(U_7404,U_7402)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7401),U_7404),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7402)),U_7403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7402),U_7403))
| ~ class_Groups_Ocomm__monoid__add(U_7401) ),
inference(variable_rename,[status(thm)],[f_1771_1]) ).
fof(f_1771_3,plain,
! [U_7402,U_7401,U_7403,U_7404] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7401),U_7404),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7402),U_7403)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7401),hAPP(U_7404,U_7402)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7401),U_7404),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7402)),U_7403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7402),U_7403))
| ~ class_Groups_Ocomm__monoid__add(U_7401) ),
inference(definitional_conversion,[status(esa)],[f_1771_2]) ).
cnf(f_1771_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7401),U_7404),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7402),U_7403)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7401),hAPP(U_7404,U_7402)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7401),U_7404),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7402)),U_7403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7402),U_7403))
| ~ class_Groups_Ocomm__monoid__add(U_7401) ),
inference(clausify,[status(thm)],[f_1771_3]) ).
fof(f_1772_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_1772_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_1772_1]) ).
cnf(f_1772_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_1772_2]) ).
fof(f_1773_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_1773_2,plain,
! [U_7406,U_7405] :
( 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_7405),U_7406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7405)) ),
inference(variable_rename,[status(thm)],[f_1773_1]) ).
fof(f_1773_3,plain,
! [U_7405,U_7406] :
( 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_7405),U_7406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7405)) ),
inference(definitional_conversion,[status(esa)],[f_1773_2]) ).
cnf(f_1773_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_7405),U_7406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7405)) ),
inference(clausify,[status(thm)],[f_1773_3]) ).
fof(f_1774_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_1774_2,plain,
! [U_7408,U_7407] :
( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7407),hAPP(c_Nat_OSuc,U_7408)) = 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_7407),U_7408)) )
& ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7407),hAPP(c_Nat_OSuc,U_7408)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_7408),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7407),U_7408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7407),U_7408)) ) ),
inference(variable_rename,[status(thm)],[f_1774_1]) ).
fof(f_1774_3,plain,
( ! [U_7412,U_7410] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7410),hAPP(c_Nat_OSuc,U_7412)) = 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_7410),U_7412)) )
& ! [U_7411,U_7409] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7409),hAPP(c_Nat_OSuc,U_7411)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_7411),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7409),U_7411))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7409),U_7411)) ) ),
inference(miniscope,[status(thm)],[f_1774_2]) ).
fof(f_1774_4,plain,
( ! [U_7410,U_7412] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7410),hAPP(c_Nat_OSuc,U_7412)) = 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_7410),U_7412)) )
& ! [U_7411,U_7409] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7409),hAPP(c_Nat_OSuc,U_7411)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_7411),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7409),U_7411))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7409),U_7411)) ) ),
inference(definitional_conversion,[status(esa)],[f_1774_3]) ).
cnf(f_1774_5,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7409),hAPP(c_Nat_OSuc,U_7411)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_7411),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7409),U_7411))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7409),U_7411)) ),
inference(clausify,[status(thm)],[f_1774_4]) ).
cnf(f_1774_6,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7410),hAPP(c_Nat_OSuc,U_7412)) = 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_7410),U_7412)) ),
inference(clausify,[status(thm)],[f_1774_4]) ).
fof(f_1775_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_1775_2,plain,
! [U_7413] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_7413) = 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_7413)),
inference(variable_rename,[status(thm)],[f_1775_1]) ).
fof(f_1775_3,plain,
! [U_7413] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_7413) = 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_7413)),
inference(definitional_conversion,[status(esa)],[f_1775_2]) ).
cnf(f_1775_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_7413) = 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_7413)),
inference(clausify,[status(thm)],[f_1775_3]) ).
fof(f_1776_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_1776_2,plain,
! [U_7414] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7414))
| ~ 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_7414))) )
& ( 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_7414)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7414)) ) ),
inference(variable_rename,[status(thm)],[f_1776_1]) ).
fof(f_1776_3,plain,
( ! [U_7416] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7416))
| ~ 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_7416))) )
& ! [U_7415] :
( 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_7415)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7415)) ) ),
inference(miniscope,[status(thm)],[f_1776_2]) ).
fof(f_1776_4,plain,
( ! [U_7416] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7416))
| ~ 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_7416))) )
& ! [U_7415] :
( 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_7415)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7415)) ) ),
inference(definitional_conversion,[status(esa)],[f_1776_3]) ).
cnf(f_1776_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_7415)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7415)) ),
inference(clausify,[status(thm)],[f_1776_4]) ).
cnf(f_1776_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7416))
| ~ 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_7416))) ),
inference(clausify,[status(thm)],[f_1776_4]) ).
fof(f_1777_1,plain,
! [V_f_2,V_m_2,V_n_2,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_c)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) )
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__op__ivl__Suc]) ).
fof(f_1777_2,plain,
! [U_7420,U_7419,U_7418,U_7417] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7417),U_7420),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7419),hAPP(c_Nat_OSuc,U_7418))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7417),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7417),U_7420),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7419),U_7418))),hAPP(U_7420,U_7418))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7418),U_7419)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7417),U_7420),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7419),hAPP(c_Nat_OSuc,U_7418))) = c_Groups_Ozero__class_Ozero(U_7417)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7418),U_7419)) ) )
| ~ class_Groups_Ocomm__monoid__add(U_7417) ),
inference(variable_rename,[status(thm)],[f_1777_1]) ).
fof(f_1777_3,plain,
( ! [U_7417,U_7418,U_7419,U_7420] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7417),U_7420),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7419),hAPP(c_Nat_OSuc,U_7418))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7417),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7417),U_7420),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7419),U_7418))),hAPP(U_7420,U_7418))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7418),U_7419))
| ~ sP428(U_7417,U_7418,U_7419,U_7420) )
& ! [U_7417,U_7418,U_7419,U_7420] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7417),U_7420),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7419),hAPP(c_Nat_OSuc,U_7418))) = c_Groups_Ozero__class_Ozero(U_7417)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7418),U_7419))
| ~ sP428(U_7417,U_7418,U_7419,U_7420) )
& ! [U_7417,U_7418,U_7419,U_7420] :
( sP428(U_7417,U_7418,U_7419,U_7420)
| ~ class_Groups_Ocomm__monoid__add(U_7417) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP428])],[f_1777_2]) ).
cnf(f_1777_4,plain,
( sP428(U_7417,U_7418,U_7419,U_7420)
| ~ class_Groups_Ocomm__monoid__add(U_7417) ),
inference(clausify,[status(thm)],[f_1777_3]) ).
cnf(f_1777_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7417),U_7420),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7419),hAPP(c_Nat_OSuc,U_7418))) = c_Groups_Ozero__class_Ozero(U_7417)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7418),U_7419))
| ~ sP428(U_7417,U_7418,U_7419,U_7420) ),
inference(clausify,[status(thm)],[f_1777_3]) ).
cnf(f_1777_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7417),U_7420),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7419),hAPP(c_Nat_OSuc,U_7418))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7417),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7417),U_7420),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7419),U_7418))),hAPP(U_7420,U_7418))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7418),U_7419))
| ~ sP428(U_7417,U_7418,U_7419,U_7420) ),
inference(clausify,[status(thm)],[f_1777_3]) ).
fof(f_1778_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_1778_2,plain,
! [U_7423,U_7422,U_7421] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7423),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_7422))
| U_7421 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7421),U_7423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7421)) ),
inference(variable_rename,[status(thm)],[f_1778_1]) ).
fof(f_1778_3,plain,
! [U_7422,U_7423,U_7421] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7423),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_7422))
| U_7421 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7421),U_7423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7421)) ),
inference(definitional_conversion,[status(esa)],[f_1778_2]) ).
cnf(f_1778_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7423),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_7422))
| U_7421 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7421),U_7423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7421)) ),
inference(clausify,[status(thm)],[f_1778_3]) ).
fof(f_1779_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_1779_2,plain,
! [U_7426,U_7425,U_7424] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7425),U_7424))
| U_7424 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7424),U_7426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7424)) ),
inference(variable_rename,[status(thm)],[f_1779_1]) ).
fof(f_1779_3,plain,
! [U_7424,U_7426,U_7425] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7425),U_7424))
| U_7424 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7424),U_7426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7424)) ),
inference(definitional_conversion,[status(esa)],[f_1779_2]) ).
cnf(f_1779_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7425),U_7424))
| U_7424 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7424),U_7426))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7424)) ),
inference(clausify,[status(thm)],[f_1779_3]) ).
fof(f_1780_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_1780_2,plain,
! [U_7429,U_7428,U_7427] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7428))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7429),U_7427))
| ~ 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_7427),U_7428)),U_7429))) ),
inference(variable_rename,[status(thm)],[f_1780_1]) ).
fof(f_1780_3,plain,
! [U_7427,U_7428,U_7429] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7428))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7429),U_7427))
| ~ 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_7427),U_7428)),U_7429))) ),
inference(definitional_conversion,[status(esa)],[f_1780_2]) ).
cnf(f_1780_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7428))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7429),U_7427))
| ~ 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_7427),U_7428)),U_7429))) ),
inference(clausify,[status(thm)],[f_1780_3]) ).
fof(f_1781_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_1781_2,plain,
! [U_7432,U_7431,U_7430] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),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_7430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7432))
| ~ 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_7430),U_7431)),U_7432)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1781_1]) ).
fof(f_1781_3,plain,
! [U_7431,U_7430,U_7432] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),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_7430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7432))
| ~ 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_7430),U_7431)),U_7432)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1781_2]) ).
cnf(f_1781_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7431),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_7430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7432))
| ~ 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_7430),U_7431)),U_7432)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1781_3]) ).
fof(f_1782_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_1782_2,plain,
! [U_7437,U_7436,U_7435,U_7434,U_7433] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7434),U_7436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7437),U_7433))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7435),U_7433))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7435))
| ~ 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_7433),U_7434)),U_7435)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7433),U_7436)),U_7437))) ),
inference(variable_rename,[status(thm)],[f_1782_1]) ).
fof(f_1782_3,plain,
! [U_7434,U_7433,U_7435,U_7436,U_7437] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7434),U_7436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7437),U_7433))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7435),U_7433))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7435))
| ~ 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_7433),U_7434)),U_7435)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7433),U_7436)),U_7437))) ),
inference(definitional_conversion,[status(esa)],[f_1782_2]) ).
cnf(f_1782_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7434),U_7436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7437),U_7433))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7435),U_7433))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7435))
| ~ 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_7433),U_7434)),U_7435)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7433),U_7436)),U_7437))) ),
inference(clausify,[status(thm)],[f_1782_3]) ).
fof(f_1783_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_1783_2,plain,
! [U_7443,U_7442,U_7441,U_7440,U_7439,U_7438] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7439),U_7442))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7441),U_7438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7441))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7440))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7443),U_7441))
| ~ 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_7441),U_7442)),U_7443)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7438),U_7439)),U_7440) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7441),U_7442)),U_7443) ),
inference(variable_rename,[status(thm)],[f_1783_1]) ).
fof(f_1783_3,plain,
! [U_7438,U_7439,U_7441,U_7440,U_7442,U_7443] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7439),U_7442))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7441),U_7438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7441))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7440))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7443),U_7441))
| ~ 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_7441),U_7442)),U_7443)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7438),U_7439)),U_7440) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7441),U_7442)),U_7443) ),
inference(definitional_conversion,[status(esa)],[f_1783_2]) ).
cnf(f_1783_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7439),U_7442))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7441),U_7438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7441))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7440))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7443),U_7441))
| ~ 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_7441),U_7442)),U_7443)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7438),U_7439)),U_7440) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7441),U_7442)),U_7443) ),
inference(clausify,[status(thm)],[f_1783_3]) ).
fof(f_1784_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_1784_2,plain,
! [U_7445,U_7444] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7444),U_7445))),
inference(variable_rename,[status(thm)],[f_1784_1]) ).
fof(f_1784_3,plain,
! [U_7444,U_7445] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7444),U_7445))),
inference(definitional_conversion,[status(esa)],[f_1784_2]) ).
cnf(f_1784_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7444),U_7445))),
inference(clausify,[status(thm)],[f_1784_3]) ).
fof(f_1785_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_1785_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_1785_1]) ).
cnf(f_1785_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_1785_2]) ).
fof(f_1786_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_1786_2,plain,
! [U_7446] : 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_7446))),
inference(variable_rename,[status(thm)],[f_1786_1]) ).
fof(f_1786_3,plain,
! [U_7446] : 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_7446))),
inference(definitional_conversion,[status(esa)],[f_1786_2]) ).
cnf(f_1786_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_7446))),
inference(clausify,[status(thm)],[f_1786_3]) ).
fof(f_1787_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_1787_2,plain,
! [U_7448,U_7447] : 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_7447)),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_7448),U_7447))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7447),U_7448),
inference(variable_rename,[status(thm)],[f_1787_1]) ).
fof(f_1787_3,plain,
! [U_7447,U_7448] : 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_7447)),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_7448),U_7447))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7447),U_7448),
inference(definitional_conversion,[status(esa)],[f_1787_2]) ).
cnf(f_1787_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_7447)),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_7448),U_7447))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7447),U_7448),
inference(clausify,[status(thm)],[f_1787_3]) ).
fof(f_1788_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_1788_2,plain,
! [U_7454,U_7453,U_7452,U_7451,U_7450,U_7449] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7453),U_7450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7452),U_7449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7452))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7454))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7451),U_7449))
| ~ 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_7452),U_7453)),U_7454)),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_7449),U_7450)),U_7451) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7452),U_7453)),U_7454) ),
inference(variable_rename,[status(thm)],[f_1788_1]) ).
fof(f_1788_3,plain,
! [U_7449,U_7450,U_7451,U_7452,U_7453,U_7454] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7453),U_7450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7452),U_7449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7452))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7454))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7451),U_7449))
| ~ 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_7452),U_7453)),U_7454)),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_7449),U_7450)),U_7451) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7452),U_7453)),U_7454) ),
inference(definitional_conversion,[status(esa)],[f_1788_2]) ).
cnf(f_1788_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7453),U_7450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7452),U_7449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7452))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7454))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7451),U_7449))
| ~ 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_7452),U_7453)),U_7454)),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_7449),U_7450)),U_7451) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7452),U_7453)),U_7454) ),
inference(clausify,[status(thm)],[f_1788_3]) ).
fof(f_1789_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_1789_2,plain,
! [U_7459,U_7458,U_7457,U_7456,U_7455] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7458),U_7456))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7455),U_7457))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7455),U_7459))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7459),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_7455),U_7456)),U_7457)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7455),U_7458)),U_7459))) ),
inference(variable_rename,[status(thm)],[f_1789_1]) ).
fof(f_1789_3,plain,
! [U_7455,U_7456,U_7457,U_7458,U_7459] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7458),U_7456))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7455),U_7457))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7455),U_7459))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7459),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_7455),U_7456)),U_7457)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7455),U_7458)),U_7459))) ),
inference(definitional_conversion,[status(esa)],[f_1789_2]) ).
cnf(f_1789_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7458),U_7456))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7455),U_7457))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7455),U_7459))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7459),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_7455),U_7456)),U_7457)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7455),U_7458)),U_7459))) ),
inference(clausify,[status(thm)],[f_1789_3]) ).
fof(f_1790_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_1790_2,plain,
! [U_7465,U_7464] :
( ( ! [U_7463] :
( hBOOL(hAPP(U_7465,U_7463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7463),U_7464)) )
| ? [U_7462] :
( ~ hBOOL(hAPP(U_7465,U_7462))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7462),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7464))) ) )
& ( ! [U_7461] :
( hBOOL(hAPP(U_7465,U_7461))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7461),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7464))) )
| ? [U_7460] :
( ~ hBOOL(hAPP(U_7465,U_7460))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7460),U_7464)) ) ) ),
inference(variable_rename,[status(thm)],[f_1790_1]) ).
fof(f_1790_3,plain,
( ! [U_7469,U_7467] :
( ! [U_7463] :
( hBOOL(hAPP(U_7469,U_7463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7463),U_7467)) )
| ? [U_7462] :
( ~ hBOOL(hAPP(U_7469,U_7462))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7462),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7467))) ) )
& ! [U_7468,U_7466] :
( ! [U_7461] :
( hBOOL(hAPP(U_7468,U_7461))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7461),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7466))) )
| ? [U_7460] :
( ~ hBOOL(hAPP(U_7468,U_7460))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7460),U_7466)) ) ) ),
inference(miniscope,[status(thm)],[f_1790_2]) ).
fof(f_1790_4,plain,
( ! [U_7469,U_7467] :
( ! [U_7463] :
( hBOOL(hAPP(U_7469,U_7463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7463),U_7467)) )
| ? [U_7462] :
( ~ hBOOL(hAPP(U_7469,U_7462))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7462),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7467))) ) )
& ! [U_7468,U_7466] :
( ! [U_7461] :
( hBOOL(hAPP(U_7468,U_7461))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7461),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7466))) )
| ( ~ hBOOL(hAPP(U_7468,sK146(U_7468,U_7466)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK146(U_7468,U_7466)),U_7466)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_7460,sK146(U_7468,U_7466))],[f_1790_3]) ).
fof(f_1790_5,plain,
( ! [U_7469,U_7467] :
( ! [U_7463] :
( hBOOL(hAPP(U_7469,U_7463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7463),U_7467)) )
| ( ~ hBOOL(hAPP(U_7469,sK147(U_7469,U_7467)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK147(U_7469,U_7467)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7467))) ) )
& ! [U_7468,U_7466] :
( ! [U_7461] :
( hBOOL(hAPP(U_7468,U_7461))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7461),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7466))) )
| ( ~ hBOOL(hAPP(U_7468,sK146(U_7468,U_7466)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK146(U_7468,U_7466)),U_7466)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_7462,sK147(U_7469,U_7467))],[f_1790_4]) ).
fof(f_1790_6,plain,
( ! [U_7469,U_7467] :
( ~ hBOOL(hAPP(U_7469,sK147(U_7469,U_7467)))
| ~ sP430(U_7469,U_7467) )
& ! [U_7469,U_7467] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK147(U_7469,U_7467)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7467)))
| ~ sP430(U_7469,U_7467) )
& ! [U_7466,U_7468] :
( ~ hBOOL(hAPP(U_7468,sK146(U_7468,U_7466)))
| ~ sP429(U_7466,U_7468) )
& ! [U_7466,U_7468] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK146(U_7468,U_7466)),U_7466))
| ~ sP429(U_7466,U_7468) )
& ! [U_7469,U_7463,U_7467] :
( hBOOL(hAPP(U_7469,U_7463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7463),U_7467))
| sP430(U_7469,U_7467) )
& ! [U_7461,U_7466,U_7468] :
( hBOOL(hAPP(U_7468,U_7461))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7461),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7466)))
| sP429(U_7466,U_7468) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP429,sP430])],[f_1790_5]) ).
cnf(f_1790_7,plain,
( hBOOL(hAPP(U_7468,U_7461))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7461),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7466)))
| sP429(U_7466,U_7468) ),
inference(clausify,[status(thm)],[f_1790_6]) ).
cnf(f_1790_8,plain,
( hBOOL(hAPP(U_7469,U_7463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7463),U_7467))
| sP430(U_7469,U_7467) ),
inference(clausify,[status(thm)],[f_1790_6]) ).
cnf(f_1790_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK146(U_7468,U_7466)),U_7466))
| ~ sP429(U_7466,U_7468) ),
inference(clausify,[status(thm)],[f_1790_6]) ).
cnf(f_1790_10,plain,
( ~ hBOOL(hAPP(U_7468,sK146(U_7468,U_7466)))
| ~ sP429(U_7466,U_7468) ),
inference(clausify,[status(thm)],[f_1790_6]) ).
cnf(f_1790_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK147(U_7469,U_7467)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7467)))
| ~ sP430(U_7469,U_7467) ),
inference(clausify,[status(thm)],[f_1790_6]) ).
cnf(f_1790_12,plain,
( ~ hBOOL(hAPP(U_7469,sK147(U_7469,U_7467)))
| ~ sP430(U_7469,U_7467) ),
inference(clausify,[status(thm)],[f_1790_6]) ).
fof(f_1791_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_1791_2,plain,
! [U_7475,U_7474] :
( ( ? [U_7473] :
( hBOOL(hAPP(U_7475,U_7473))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7473),U_7474)) )
| ! [U_7472] :
( ~ hBOOL(hAPP(U_7475,U_7472))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7472),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7474))) ) )
& ( ? [U_7471] :
( hBOOL(hAPP(U_7475,U_7471))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7471),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7474))) )
| ! [U_7470] :
( ~ hBOOL(hAPP(U_7475,U_7470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7470),U_7474)) ) ) ),
inference(variable_rename,[status(thm)],[f_1791_1]) ).
fof(f_1791_3,plain,
( ! [U_7479,U_7477] :
( ? [U_7473] :
( hBOOL(hAPP(U_7479,U_7473))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7473),U_7477)) )
| ! [U_7472] :
( ~ hBOOL(hAPP(U_7479,U_7472))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7472),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7477))) ) )
& ! [U_7478,U_7476] :
( ? [U_7471] :
( hBOOL(hAPP(U_7478,U_7471))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7471),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7476))) )
| ! [U_7470] :
( ~ hBOOL(hAPP(U_7478,U_7470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7470),U_7476)) ) ) ),
inference(miniscope,[status(thm)],[f_1791_2]) ).
fof(f_1791_4,plain,
( ! [U_7479,U_7477] :
( ? [U_7473] :
( hBOOL(hAPP(U_7479,U_7473))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7473),U_7477)) )
| ! [U_7472] :
( ~ hBOOL(hAPP(U_7479,U_7472))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7472),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7477))) ) )
& ! [U_7478,U_7476] :
( ( hBOOL(hAPP(U_7478,sK148(U_7478,U_7476)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK148(U_7478,U_7476)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7476))) )
| ! [U_7470] :
( ~ hBOOL(hAPP(U_7478,U_7470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7470),U_7476)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_7471,sK148(U_7478,U_7476))],[f_1791_3]) ).
fof(f_1791_5,plain,
( ! [U_7479,U_7477] :
( ( hBOOL(hAPP(U_7479,sK149(U_7479,U_7477)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK149(U_7479,U_7477)),U_7477)) )
| ! [U_7472] :
( ~ hBOOL(hAPP(U_7479,U_7472))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7472),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7477))) ) )
& ! [U_7478,U_7476] :
( ( hBOOL(hAPP(U_7478,sK148(U_7478,U_7476)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK148(U_7478,U_7476)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7476))) )
| ! [U_7470] :
( ~ hBOOL(hAPP(U_7478,U_7470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7470),U_7476)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_7473,sK149(U_7479,U_7477))],[f_1791_4]) ).
fof(f_1791_6,plain,
( ! [U_7479,U_7477] :
( hBOOL(hAPP(U_7479,sK149(U_7479,U_7477)))
| ~ sP432(U_7479,U_7477) )
& ! [U_7479,U_7477] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK149(U_7479,U_7477)),U_7477))
| ~ sP432(U_7479,U_7477) )
& ! [U_7476,U_7478] :
( hBOOL(hAPP(U_7478,sK148(U_7478,U_7476)))
| ~ sP431(U_7476,U_7478) )
& ! [U_7476,U_7478] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK148(U_7478,U_7476)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7476)))
| ~ sP431(U_7476,U_7478) )
& ! [U_7479,U_7472,U_7477] :
( sP432(U_7479,U_7477)
| ~ hBOOL(hAPP(U_7479,U_7472))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7472),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7477))) )
& ! [U_7470,U_7476,U_7478] :
( sP431(U_7476,U_7478)
| ~ hBOOL(hAPP(U_7478,U_7470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7470),U_7476)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP431,sP432])],[f_1791_5]) ).
cnf(f_1791_7,plain,
( sP431(U_7476,U_7478)
| ~ hBOOL(hAPP(U_7478,U_7470))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7470),U_7476)) ),
inference(clausify,[status(thm)],[f_1791_6]) ).
cnf(f_1791_8,plain,
( sP432(U_7479,U_7477)
| ~ hBOOL(hAPP(U_7479,U_7472))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7472),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7477))) ),
inference(clausify,[status(thm)],[f_1791_6]) ).
cnf(f_1791_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK148(U_7478,U_7476)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7476)))
| ~ sP431(U_7476,U_7478) ),
inference(clausify,[status(thm)],[f_1791_6]) ).
cnf(f_1791_10,plain,
( hBOOL(hAPP(U_7478,sK148(U_7478,U_7476)))
| ~ sP431(U_7476,U_7478) ),
inference(clausify,[status(thm)],[f_1791_6]) ).
cnf(f_1791_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK149(U_7479,U_7477)),U_7477))
| ~ sP432(U_7479,U_7477) ),
inference(clausify,[status(thm)],[f_1791_6]) ).
cnf(f_1791_12,plain,
( hBOOL(hAPP(U_7479,sK149(U_7479,U_7477)))
| ~ sP432(U_7479,U_7477) ),
inference(clausify,[status(thm)],[f_1791_6]) ).
fof(f_1792_1,plain,
! [V_B_2,V_k_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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_1792_2,plain,
! [U_7484,U_7483,U_7482,U_7481] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7481,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7482)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7484)))
| ? [U_7480] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7481,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7480)),U_7482)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,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_7480),U_7483))),U_7484))) ),
inference(variable_rename,[status(thm)],[f_1792_1]) ).
fof(f_1792_3,plain,
! [U_7484,U_7483,U_7482,U_7481] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7481,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7482)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7484)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7481,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK150(U_7484,U_7483,U_7482,U_7481))),U_7482)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,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),sK150(U_7484,U_7483,U_7482,U_7481)),U_7483))),U_7484))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_7480,sK150(U_7484,U_7483,U_7482,U_7481))],[f_1792_2]) ).
fof(f_1792_4,plain,
! [U_7481,U_7482,U_7483,U_7484] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7481,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7482)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7484)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7481,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK150(U_7484,U_7483,U_7482,U_7481))),U_7482)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,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),sK150(U_7484,U_7483,U_7482,U_7481)),U_7483))),U_7484))) ),
inference(definitional_conversion,[status(esa)],[f_1792_3]) ).
cnf(f_1792_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7481,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7482)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7484)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7481,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK150(U_7484,U_7483,U_7482,U_7481))),U_7482)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7481,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),sK150(U_7484,U_7483,U_7482,U_7481)),U_7483))),U_7484))) ),
inference(clausify,[status(thm)],[f_1792_4]) ).
fof(f_1793_1,plain,
! [V_B_2,V_k_2,V_A_2,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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_c,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_c,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_1793_2,plain,
! [U_7489,U_7488,U_7487,U_7486] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7487) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7489)
| ? [U_7485] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7485)),U_7487) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,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_7485),U_7488))),U_7489) ),
inference(variable_rename,[status(thm)],[f_1793_1]) ).
fof(f_1793_3,plain,
! [U_7489,U_7488,U_7487,U_7486] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7487) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7489)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK151(U_7489,U_7488,U_7487,U_7486))),U_7487) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,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),sK151(U_7489,U_7488,U_7487,U_7486)),U_7488))),U_7489) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_7485,sK151(U_7489,U_7488,U_7487,U_7486))],[f_1793_2]) ).
fof(f_1793_4,plain,
! [U_7486,U_7487,U_7488,U_7489] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7487) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7489)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK151(U_7489,U_7488,U_7487,U_7486))),U_7487) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,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),sK151(U_7489,U_7488,U_7487,U_7486)),U_7488))),U_7489) ),
inference(definitional_conversion,[status(esa)],[f_1793_3]) ).
cnf(f_1793_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7487) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7489)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK151(U_7489,U_7488,U_7487,U_7486))),U_7487) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7486,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),sK151(U_7489,U_7488,U_7487,U_7486)),U_7488))),U_7489) ),
inference(clausify,[status(thm)],[f_1793_4]) ).
fof(f_1794_1,plain,
! [V_C_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_1794_2,plain,
! [U_7493,U_7492,U_7491] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7491,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7491,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7492)),U_7493))
| ? [U_7490] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7491,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7491,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7490)),U_7492)),U_7493)) ),
inference(variable_rename,[status(thm)],[f_1794_1]) ).
fof(f_1794_3,plain,
! [U_7493,U_7492,U_7491] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7491,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7491,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7492)),U_7493))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7491,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7491,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK152(U_7493,U_7492,U_7491))),U_7492)),U_7493)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_7490,sK152(U_7493,U_7492,U_7491))],[f_1794_2]) ).
fof(f_1794_4,plain,
! [U_7491,U_7492,U_7493] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7491,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7491,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7492)),U_7493))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7491,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7491,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK152(U_7493,U_7492,U_7491))),U_7492)),U_7493)) ),
inference(definitional_conversion,[status(esa)],[f_1794_3]) ).
cnf(f_1794_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7491,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7491,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_7492)),U_7493))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7491,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7491,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK152(U_7493,U_7492,U_7491))),U_7492)),U_7493)) ),
inference(clausify,[status(thm)],[f_1794_4]) ).
fof(f_1795_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_1795_2,plain,
! [U_7495,U_7494] :
( ( c_Nat__Transfer_Otsub(U_7495,U_7494) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7494),U_7495)) )
& ( c_Nat__Transfer_Otsub(U_7495,U_7494) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7495),U_7494)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7494),U_7495)) ) ),
inference(variable_rename,[status(thm)],[f_1795_1]) ).
fof(f_1795_3,plain,
( ! [U_7499,U_7497] :
( c_Nat__Transfer_Otsub(U_7499,U_7497) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7497),U_7499)) )
& ! [U_7498,U_7496] :
( c_Nat__Transfer_Otsub(U_7498,U_7496) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7498),U_7496)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7496),U_7498)) ) ),
inference(miniscope,[status(thm)],[f_1795_2]) ).
fof(f_1795_4,plain,
( ! [U_7497,U_7499] :
( c_Nat__Transfer_Otsub(U_7499,U_7497) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7497),U_7499)) )
& ! [U_7498,U_7496] :
( c_Nat__Transfer_Otsub(U_7498,U_7496) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7498),U_7496)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7496),U_7498)) ) ),
inference(definitional_conversion,[status(esa)],[f_1795_3]) ).
cnf(f_1795_5,plain,
( c_Nat__Transfer_Otsub(U_7498,U_7496) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7498),U_7496)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7496),U_7498)) ),
inference(clausify,[status(thm)],[f_1795_4]) ).
cnf(f_1795_6,plain,
( c_Nat__Transfer_Otsub(U_7499,U_7497) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7497),U_7499)) ),
inference(clausify,[status(thm)],[f_1795_4]) ).
fof(f_1796_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J]) ).
fof(f_1796_2,plain,
! [U_7502,U_7501,U_7500] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7500,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7500),U_7501),c_Orderings_Obot__class_Obot(tc_fun(U_7500,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7500,U_7501,U_7502)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7500,U_7501),U_7502)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7500),U_7501),U_7502))
| ~ class_Orderings_Olinorder(U_7500) ),
inference(variable_rename,[status(thm)],[f_1796_1]) ).
fof(f_1796_3,plain,
! [U_7500,U_7501,U_7502] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7500,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7500),U_7501),c_Orderings_Obot__class_Obot(tc_fun(U_7500,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7500,U_7501,U_7502)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7500,U_7501),U_7502)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7500),U_7501),U_7502))
| ~ class_Orderings_Olinorder(U_7500) ),
inference(definitional_conversion,[status(esa)],[f_1796_2]) ).
cnf(f_1796_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7500,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7500),U_7501),c_Orderings_Obot__class_Obot(tc_fun(U_7500,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7500,U_7501,U_7502)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7500,U_7501),U_7502)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7500),U_7501),U_7502))
| ~ class_Orderings_Olinorder(U_7500) ),
inference(clausify,[status(thm)],[f_1796_3]) ).
fof(f_1797_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_1797_2,plain,
! [U_7504,U_7503] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7504),U_7503)),U_7504) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7504),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7503),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_7504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7503)) ),
inference(variable_rename,[status(thm)],[f_1797_1]) ).
fof(f_1797_3,plain,
! [U_7504,U_7503] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7504),U_7503)),U_7504) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7504),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7503),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_7504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7503)) ),
inference(definitional_conversion,[status(esa)],[f_1797_2]) ).
cnf(f_1797_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7504),U_7503)),U_7504) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7504),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7503),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_7504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7503)) ),
inference(clausify,[status(thm)],[f_1797_3]) ).
fof(f_1798_1,plain,
! [V_j_2,V_B_2,V_A_2,T_e,V_C_2,V_f_2,T_d,T_c] :
( hAPP(c_Set_Oimage(T_c,T_d,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_e),c_Set_Oimage(T_c,T_d,V_f_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_e),V_j_2),V_A_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2))
& hBOOL(hAPP(hAPP(c_member(T_e),B_x),V_A_2)) )
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,V_C_2) ),
inference(fof_nnf,[status(thm)],[fact_image__INT]) ).
fof(f_1798_2,plain,
! [U_7513,U_7512,U_7511,U_7510,U_7509,U_7508,U_7507,U_7506] :
( hAPP(c_Set_Oimage(U_7506,U_7507,U_7508),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7510,tc_fun(U_7506,tc_HOL_Obool)),U_7511),U_7512)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7510,tc_fun(U_7507,tc_HOL_Obool)),U_7511),hAPP(hAPP(c_COMBB(tc_fun(U_7506,tc_HOL_Obool),tc_fun(U_7507,tc_HOL_Obool),U_7510),c_Set_Oimage(U_7506,U_7507,U_7508)),U_7512))
| ~ hBOOL(hAPP(hAPP(c_member(U_7510),U_7513),U_7511))
| ? [U_7505] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7506,tc_HOL_Obool)),hAPP(U_7512,U_7505)),U_7509))
& hBOOL(hAPP(hAPP(c_member(U_7510),U_7505),U_7511)) )
| ~ c_Fun_Oinj__on(U_7506,U_7507,U_7508,U_7509) ),
inference(variable_rename,[status(thm)],[f_1798_1]) ).
fof(f_1798_3,plain,
! [U_7513,U_7512,U_7511,U_7510,U_7509,U_7508,U_7507,U_7506] :
( hAPP(c_Set_Oimage(U_7506,U_7507,U_7508),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7510,tc_fun(U_7506,tc_HOL_Obool)),U_7511),U_7512)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7510,tc_fun(U_7507,tc_HOL_Obool)),U_7511),hAPP(hAPP(c_COMBB(tc_fun(U_7506,tc_HOL_Obool),tc_fun(U_7507,tc_HOL_Obool),U_7510),c_Set_Oimage(U_7506,U_7507,U_7508)),U_7512))
| ~ hBOOL(hAPP(hAPP(c_member(U_7510),U_7513),U_7511))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7506,tc_HOL_Obool)),hAPP(U_7512,sK153(U_7513,U_7512,U_7511,U_7510,U_7509,U_7508,U_7507,U_7506))),U_7509))
& hBOOL(hAPP(hAPP(c_member(U_7510),sK153(U_7513,U_7512,U_7511,U_7510,U_7509,U_7508,U_7507,U_7506)),U_7511)) )
| ~ c_Fun_Oinj__on(U_7506,U_7507,U_7508,U_7509) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_7505,sK153(U_7513,U_7512,U_7511,U_7510,U_7509,U_7508,U_7507,U_7506))],[f_1798_2]) ).
fof(f_1798_4,plain,
( ! [U_7506,U_7507,U_7508,U_7509,U_7510,U_7511,U_7512,U_7513] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7506,tc_HOL_Obool)),hAPP(U_7512,sK153(U_7513,U_7512,U_7511,U_7510,U_7509,U_7508,U_7507,U_7506))),U_7509))
| ~ sP433(U_7506,U_7507,U_7508,U_7509,U_7510,U_7511,U_7512,U_7513) )
& ! [U_7506,U_7507,U_7508,U_7509,U_7510,U_7511,U_7512,U_7513] :
( hBOOL(hAPP(hAPP(c_member(U_7510),sK153(U_7513,U_7512,U_7511,U_7510,U_7509,U_7508,U_7507,U_7506)),U_7511))
| ~ sP433(U_7506,U_7507,U_7508,U_7509,U_7510,U_7511,U_7512,U_7513) )
& ! [U_7506,U_7507,U_7508,U_7509,U_7510,U_7511,U_7512,U_7513] :
( hAPP(c_Set_Oimage(U_7506,U_7507,U_7508),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7510,tc_fun(U_7506,tc_HOL_Obool)),U_7511),U_7512)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7510,tc_fun(U_7507,tc_HOL_Obool)),U_7511),hAPP(hAPP(c_COMBB(tc_fun(U_7506,tc_HOL_Obool),tc_fun(U_7507,tc_HOL_Obool),U_7510),c_Set_Oimage(U_7506,U_7507,U_7508)),U_7512))
| ~ hBOOL(hAPP(hAPP(c_member(U_7510),U_7513),U_7511))
| sP433(U_7506,U_7507,U_7508,U_7509,U_7510,U_7511,U_7512,U_7513)
| ~ c_Fun_Oinj__on(U_7506,U_7507,U_7508,U_7509) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP433])],[f_1798_3]) ).
cnf(f_1798_5,plain,
( hAPP(c_Set_Oimage(U_7506,U_7507,U_7508),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7510,tc_fun(U_7506,tc_HOL_Obool)),U_7511),U_7512)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7510,tc_fun(U_7507,tc_HOL_Obool)),U_7511),hAPP(hAPP(c_COMBB(tc_fun(U_7506,tc_HOL_Obool),tc_fun(U_7507,tc_HOL_Obool),U_7510),c_Set_Oimage(U_7506,U_7507,U_7508)),U_7512))
| ~ hBOOL(hAPP(hAPP(c_member(U_7510),U_7513),U_7511))
| sP433(U_7506,U_7507,U_7508,U_7509,U_7510,U_7511,U_7512,U_7513)
| ~ c_Fun_Oinj__on(U_7506,U_7507,U_7508,U_7509) ),
inference(clausify,[status(thm)],[f_1798_4]) ).
cnf(f_1798_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_7510),sK153(U_7513,U_7512,U_7511,U_7510,U_7509,U_7508,U_7507,U_7506)),U_7511))
| ~ sP433(U_7506,U_7507,U_7508,U_7509,U_7510,U_7511,U_7512,U_7513) ),
inference(clausify,[status(thm)],[f_1798_4]) ).
cnf(f_1798_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7506,tc_HOL_Obool)),hAPP(U_7512,sK153(U_7513,U_7512,U_7511,U_7510,U_7509,U_7508,U_7507,U_7506))),U_7509))
| ~ sP433(U_7506,U_7507,U_7508,U_7509,U_7510,U_7511,U_7512,U_7513) ),
inference(clausify,[status(thm)],[f_1798_4]) ).
fof(f_1799_1,plain,
! [V_com2,V_com1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1)),c_Com_Ocom_Ocom__size(V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_com_Osize_I4_J]) ).
fof(f_1799_2,plain,
! [U_7515,U_7514] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_7514,U_7515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_7514)),c_Com_Ocom_Ocom__size(U_7515))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1799_1]) ).
fof(f_1799_3,plain,
! [U_7515,U_7514] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_7514,U_7515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_7514)),c_Com_Ocom_Ocom__size(U_7515))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_1799_2]) ).
cnf(f_1799_4,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_7514,U_7515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_7514)),c_Com_Ocom_Ocom__size(U_7515))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1799_3]) ).
fof(f_1800_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_1800_2,plain,
! [U_7517,U_7516] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7516,U_7517))),
inference(variable_rename,[status(thm)],[f_1800_1]) ).
fof(f_1800_3,plain,
! [U_7516,U_7517] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7516,U_7517))),
inference(definitional_conversion,[status(esa)],[f_1800_2]) ).
cnf(f_1800_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7516,U_7517))),
inference(clausify,[status(thm)],[f_1800_3]) ).
fof(f_1801_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_1801_2,plain,
! [U_7519,U_7518] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7518,U_7519))),
inference(variable_rename,[status(thm)],[f_1801_1]) ).
fof(f_1801_3,plain,
! [U_7518,U_7519] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7518,U_7519))),
inference(definitional_conversion,[status(esa)],[f_1801_2]) ).
cnf(f_1801_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7518,U_7519))),
inference(clausify,[status(thm)],[f_1801_3]) ).
fof(f_1802_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_1802_2,plain,
! [U_7520] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7520) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_1802_1]) ).
fof(f_1802_3,plain,
! [U_7520] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7520) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1802_2]) ).
cnf(f_1802_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7520) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1802_3]) ).
fof(f_1803_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_1803_2,plain,
! [U_7522,U_7521] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7521)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7522)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7521),U_7522),
inference(variable_rename,[status(thm)],[f_1803_1]) ).
fof(f_1803_3,plain,
! [U_7521,U_7522] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7521)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7522)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7521),U_7522),
inference(definitional_conversion,[status(esa)],[f_1803_2]) ).
cnf(f_1803_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7521)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7522)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7521),U_7522),
inference(clausify,[status(thm)],[f_1803_3]) ).
fof(f_1804_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_1804_2,plain,
! [U_7524,U_7523] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7523),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7524)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7523)),U_7524),
inference(variable_rename,[status(thm)],[f_1804_1]) ).
fof(f_1804_3,plain,
! [U_7523,U_7524] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7523),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7524)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7523)),U_7524),
inference(definitional_conversion,[status(esa)],[f_1804_2]) ).
cnf(f_1804_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7523),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7524)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7523)),U_7524),
inference(clausify,[status(thm)],[f_1804_3]) ).
fof(f_1805_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_1805_2,plain,
! [U_7526,U_7525] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7525),U_7526),c_Groups_Ozero__class_Ozero(U_7525)) = c_Groups_Ozero__class_Ozero(U_7525)
| ~ class_Divides_Osemiring__div(U_7525) ),
inference(variable_rename,[status(thm)],[f_1805_1]) ).
fof(f_1805_3,plain,
! [U_7525,U_7526] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7525),U_7526),c_Groups_Ozero__class_Ozero(U_7525)) = c_Groups_Ozero__class_Ozero(U_7525)
| ~ class_Divides_Osemiring__div(U_7525) ),
inference(definitional_conversion,[status(esa)],[f_1805_2]) ).
cnf(f_1805_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7525),U_7526),c_Groups_Ozero__class_Ozero(U_7525)) = c_Groups_Ozero__class_Ozero(U_7525)
| ~ class_Divides_Osemiring__div(U_7525) ),
inference(clausify,[status(thm)],[f_1805_3]) ).
fof(f_1806_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_1806_2,plain,
! [U_7528,U_7527] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7527),c_Groups_Ozero__class_Ozero(U_7527)),U_7528) = c_Groups_Ozero__class_Ozero(U_7527)
| ~ class_Divides_Osemiring__div(U_7527) ),
inference(variable_rename,[status(thm)],[f_1806_1]) ).
fof(f_1806_3,plain,
! [U_7527,U_7528] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7527),c_Groups_Ozero__class_Ozero(U_7527)),U_7528) = c_Groups_Ozero__class_Ozero(U_7527)
| ~ class_Divides_Osemiring__div(U_7527) ),
inference(definitional_conversion,[status(esa)],[f_1806_2]) ).
cnf(f_1806_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7527),c_Groups_Ozero__class_Ozero(U_7527)),U_7528) = c_Groups_Ozero__class_Ozero(U_7527)
| ~ class_Divides_Osemiring__div(U_7527) ),
inference(clausify,[status(thm)],[f_1806_3]) ).
fof(f_1807_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_1807_2,plain,
! [U_7530,U_7529] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7529),U_7530),c_Groups_Oone__class_Oone(U_7529)) = U_7530
| ~ class_Divides_Osemiring__div(U_7529) ),
inference(variable_rename,[status(thm)],[f_1807_1]) ).
fof(f_1807_3,plain,
! [U_7529,U_7530] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7529),U_7530),c_Groups_Oone__class_Oone(U_7529)) = U_7530
| ~ class_Divides_Osemiring__div(U_7529) ),
inference(definitional_conversion,[status(esa)],[f_1807_2]) ).
cnf(f_1807_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7529),U_7530),c_Groups_Oone__class_Oone(U_7529)) = U_7530
| ~ class_Divides_Osemiring__div(U_7529) ),
inference(clausify,[status(thm)],[f_1807_3]) ).
fof(f_1808_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_1808_2,plain,
! [U_7532,U_7531] :
( 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_7531),U_7532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7531)) ),
inference(variable_rename,[status(thm)],[f_1808_1]) ).
fof(f_1808_3,plain,
! [U_7531,U_7532] :
( 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_7531),U_7532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7531)) ),
inference(definitional_conversion,[status(esa)],[f_1808_2]) ).
cnf(f_1808_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_7531),U_7532)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7531)) ),
inference(clausify,[status(thm)],[f_1808_3]) ).
fof(f_1809_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_1809_2,plain,
! [U_7534,U_7533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7533),U_7534)),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_7534))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7533),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1809_1]) ).
fof(f_1809_3,plain,
! [U_7533,U_7534] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7533),U_7534)),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_7534))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7533),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1809_2]) ).
cnf(f_1809_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7533),U_7534)),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_7534))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7533),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1809_3]) ).
fof(f_1810_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_1810_2,plain,
! [U_7536,U_7535] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7536),U_7535)),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_7536)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7536),U_7535)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7535),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1810_1]) ).
fof(f_1810_3,plain,
( ! [U_7536,U_7535] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7536),U_7535)),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_7536))
| ~ sP434(U_7536,U_7535) )
& ! [U_7536,U_7535] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7536),U_7535)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP434(U_7536,U_7535) )
& ! [U_7536,U_7535] :
( sP434(U_7536,U_7535)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7535),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP434])],[f_1810_2]) ).
cnf(f_1810_4,plain,
( sP434(U_7536,U_7535)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7535),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1810_3]) ).
cnf(f_1810_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7536),U_7535)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP434(U_7536,U_7535) ),
inference(clausify,[status(thm)],[f_1810_3]) ).
cnf(f_1810_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7536),U_7535)),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_7536))
| ~ sP434(U_7536,U_7535) ),
inference(clausify,[status(thm)],[f_1810_3]) ).
fof(f_1811_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_1811_2,plain,
! [U_7538,U_7537] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7538),U_7537)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7538),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7538),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_7538),U_7537)),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_7537)) ),
inference(variable_rename,[status(thm)],[f_1811_1]) ).
fof(f_1811_3,plain,
( ! [U_7537,U_7538] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7538),U_7537)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7538),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP435(U_7537,U_7538) )
& ! [U_7537,U_7538] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7538),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_7538),U_7537)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP435(U_7537,U_7538) )
& ! [U_7537,U_7538] :
( sP435(U_7537,U_7538)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7537)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP435])],[f_1811_2]) ).
cnf(f_1811_4,plain,
( sP435(U_7537,U_7538)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7537)) ),
inference(clausify,[status(thm)],[f_1811_3]) ).
cnf(f_1811_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7538),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_7538),U_7537)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP435(U_7537,U_7538) ),
inference(clausify,[status(thm)],[f_1811_3]) ).
cnf(f_1811_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7538),U_7537)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7538),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP435(U_7537,U_7538) ),
inference(clausify,[status(thm)],[f_1811_3]) ).
fof(f_1812_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_1812_2,plain,
! [U_7539] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7539),U_7539) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_7539 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1812_1]) ).
fof(f_1812_3,plain,
! [U_7539] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7539),U_7539) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_7539 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_1812_2]) ).
cnf(f_1812_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7539),U_7539) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_7539 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1812_3]) ).
fof(f_1813_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_1813_2,plain,
! [U_7543,U_7542,U_7541,U_7540] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7540),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7540),U_7541),U_7542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7540),U_7541),U_7543)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7540),U_7542),U_7543)
| U_7541 = c_Groups_Ozero__class_Ozero(U_7540) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7540),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7540),U_7541),U_7542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7540),U_7541),U_7543)) = c_Groups_Ozero__class_Ozero(U_7540)
| U_7541 != c_Groups_Ozero__class_Ozero(U_7540) ) )
| ~ class_Divides_Osemiring__div(U_7540) ),
inference(variable_rename,[status(thm)],[f_1813_1]) ).
fof(f_1813_3,plain,
( ! [U_7541,U_7542,U_7543,U_7540] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7540),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7540),U_7541),U_7542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7540),U_7541),U_7543)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7540),U_7542),U_7543)
| U_7541 = c_Groups_Ozero__class_Ozero(U_7540)
| ~ sP436(U_7541,U_7542,U_7543,U_7540) )
& ! [U_7541,U_7542,U_7543,U_7540] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7540),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7540),U_7541),U_7542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7540),U_7541),U_7543)) = c_Groups_Ozero__class_Ozero(U_7540)
| U_7541 != c_Groups_Ozero__class_Ozero(U_7540)
| ~ sP436(U_7541,U_7542,U_7543,U_7540) )
& ! [U_7541,U_7542,U_7543,U_7540] :
( sP436(U_7541,U_7542,U_7543,U_7540)
| ~ class_Divides_Osemiring__div(U_7540) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP436])],[f_1813_2]) ).
cnf(f_1813_4,plain,
( sP436(U_7541,U_7542,U_7543,U_7540)
| ~ class_Divides_Osemiring__div(U_7540) ),
inference(clausify,[status(thm)],[f_1813_3]) ).
cnf(f_1813_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7540),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7540),U_7541),U_7542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7540),U_7541),U_7543)) = c_Groups_Ozero__class_Ozero(U_7540)
| U_7541 != c_Groups_Ozero__class_Ozero(U_7540)
| ~ sP436(U_7541,U_7542,U_7543,U_7540) ),
inference(clausify,[status(thm)],[f_1813_3]) ).
cnf(f_1813_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7540),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7540),U_7541),U_7542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7540),U_7541),U_7543)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7540),U_7542),U_7543)
| U_7541 = c_Groups_Ozero__class_Ozero(U_7540)
| ~ sP436(U_7541,U_7542,U_7543,U_7540) ),
inference(clausify,[status(thm)],[f_1813_3]) ).
fof(f_1814_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_1814_2,plain,
! [U_7546,U_7545,U_7544] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7544),U_7546),U_7545)),U_7545) = U_7546
| U_7545 = c_Groups_Ozero__class_Ozero(U_7544)
| ~ class_Divides_Osemiring__div(U_7544) ),
inference(variable_rename,[status(thm)],[f_1814_1]) ).
fof(f_1814_3,plain,
! [U_7545,U_7544,U_7546] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7544),U_7546),U_7545)),U_7545) = U_7546
| U_7545 = c_Groups_Ozero__class_Ozero(U_7544)
| ~ class_Divides_Osemiring__div(U_7544) ),
inference(definitional_conversion,[status(esa)],[f_1814_2]) ).
cnf(f_1814_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7544),U_7546),U_7545)),U_7545) = U_7546
| U_7545 = c_Groups_Ozero__class_Ozero(U_7544)
| ~ class_Divides_Osemiring__div(U_7544) ),
inference(clausify,[status(thm)],[f_1814_3]) ).
fof(f_1815_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_1815_2,plain,
! [U_7549,U_7548,U_7547] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7547),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7547),U_7548),U_7549)),U_7548) = U_7549
| U_7548 = c_Groups_Ozero__class_Ozero(U_7547)
| ~ class_Divides_Osemiring__div(U_7547) ),
inference(variable_rename,[status(thm)],[f_1815_1]) ).
fof(f_1815_3,plain,
! [U_7547,U_7548,U_7549] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7547),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7547),U_7548),U_7549)),U_7548) = U_7549
| U_7548 = c_Groups_Ozero__class_Ozero(U_7547)
| ~ class_Divides_Osemiring__div(U_7547) ),
inference(definitional_conversion,[status(esa)],[f_1815_2]) ).
cnf(f_1815_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7547),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7547),U_7548),U_7549)),U_7548) = U_7549
| U_7548 = c_Groups_Ozero__class_Ozero(U_7547)
| ~ class_Divides_Osemiring__div(U_7547) ),
inference(clausify,[status(thm)],[f_1815_3]) ).
fof(f_1816_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_1816_2,plain,
! [U_7553,U_7552,U_7551,U_7550] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7550),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7550),U_7552),U_7551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7550),U_7553),U_7551)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7550),U_7552),U_7553)
| U_7551 = c_Groups_Ozero__class_Ozero(U_7550)
| ~ class_Divides_Osemiring__div(U_7550) ),
inference(variable_rename,[status(thm)],[f_1816_1]) ).
fof(f_1816_3,plain,
! [U_7550,U_7551,U_7552,U_7553] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7550),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7550),U_7552),U_7551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7550),U_7553),U_7551)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7550),U_7552),U_7553)
| U_7551 = c_Groups_Ozero__class_Ozero(U_7550)
| ~ class_Divides_Osemiring__div(U_7550) ),
inference(definitional_conversion,[status(esa)],[f_1816_2]) ).
cnf(f_1816_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7550),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7550),U_7552),U_7551)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7550),U_7553),U_7551)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7550),U_7552),U_7553)
| U_7551 = c_Groups_Ozero__class_Ozero(U_7550)
| ~ class_Divides_Osemiring__div(U_7550) ),
inference(clausify,[status(thm)],[f_1816_3]) ).
fof(f_1817_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_1817_2,plain,
! [U_7557,U_7556,U_7555,U_7554] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7554),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7554),U_7555),U_7556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7554),U_7555),U_7557)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7554),U_7556),U_7557)
| U_7555 = c_Groups_Ozero__class_Ozero(U_7554)
| ~ class_Divides_Osemiring__div(U_7554) ),
inference(variable_rename,[status(thm)],[f_1817_1]) ).
fof(f_1817_3,plain,
! [U_7554,U_7555,U_7556,U_7557] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7554),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7554),U_7555),U_7556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7554),U_7555),U_7557)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7554),U_7556),U_7557)
| U_7555 = c_Groups_Ozero__class_Ozero(U_7554)
| ~ class_Divides_Osemiring__div(U_7554) ),
inference(definitional_conversion,[status(esa)],[f_1817_2]) ).
cnf(f_1817_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7554),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7554),U_7555),U_7556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7554),U_7555),U_7557)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7554),U_7556),U_7557)
| U_7555 = c_Groups_Ozero__class_Ozero(U_7554)
| ~ class_Divides_Osemiring__div(U_7554) ),
inference(clausify,[status(thm)],[f_1817_3]) ).
fof(f_1818_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_1818_2,plain,
! [U_7559,U_7558] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7558),U_7559),U_7559) = c_Groups_Oone__class_Oone(U_7558)
| U_7559 = c_Groups_Ozero__class_Ozero(U_7558)
| ~ class_Divides_Osemiring__div(U_7558) ),
inference(variable_rename,[status(thm)],[f_1818_1]) ).
fof(f_1818_3,plain,
! [U_7558,U_7559] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7558),U_7559),U_7559) = c_Groups_Oone__class_Oone(U_7558)
| U_7559 = c_Groups_Ozero__class_Ozero(U_7558)
| ~ class_Divides_Osemiring__div(U_7558) ),
inference(definitional_conversion,[status(esa)],[f_1818_2]) ).
cnf(f_1818_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7558),U_7559),U_7559) = c_Groups_Oone__class_Oone(U_7558)
| U_7559 = c_Groups_Ozero__class_Ozero(U_7558)
| ~ class_Divides_Osemiring__div(U_7558) ),
inference(clausify,[status(thm)],[f_1818_3]) ).
fof(f_1819_1,plain,
! [V_k_2,V_l_2,T_c] :
( c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_k_2))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__empty]) ).
fof(f_1819_2,plain,
! [U_7562,U_7561,U_7560] :
( c_SetInterval_Oord__class_OgreaterThanLessThan(U_7560,U_7562,U_7561) = c_Orderings_Obot__class_Obot(tc_fun(U_7560,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7560),U_7561),U_7562))
| ~ class_Orderings_Oorder(U_7560) ),
inference(variable_rename,[status(thm)],[f_1819_1]) ).
fof(f_1819_3,plain,
! [U_7560,U_7561,U_7562] :
( c_SetInterval_Oord__class_OgreaterThanLessThan(U_7560,U_7562,U_7561) = c_Orderings_Obot__class_Obot(tc_fun(U_7560,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7560),U_7561),U_7562))
| ~ class_Orderings_Oorder(U_7560) ),
inference(definitional_conversion,[status(esa)],[f_1819_2]) ).
cnf(f_1819_4,plain,
( c_SetInterval_Oord__class_OgreaterThanLessThan(U_7560,U_7562,U_7561) = c_Orderings_Obot__class_Obot(tc_fun(U_7560,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7560),U_7561),U_7562))
| ~ class_Orderings_Oorder(U_7560) ),
inference(clausify,[status(thm)],[f_1819_3]) ).
fof(f_1820_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_1820_2,plain,
! [U_7564,U_7563] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7563),U_7564) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7564),U_7563))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7563),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7563),U_7564))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7563)) )
& U_7564 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7564),U_7563))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7563),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7563),U_7564))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7563)) )
| U_7564 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7563),U_7564) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1820_1]) ).
fof(f_1820_3,plain,
( ! [U_7568,U_7566] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7566),U_7568) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7568),U_7566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7566),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7566),U_7568))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7566)) )
& U_7568 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_7567,U_7565] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7567),U_7565))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7565),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7565),U_7567))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7565)) )
| U_7567 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7565),U_7567) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1820_2]) ).
fof(f_1820_4,plain,
( ! [U_7568,U_7566] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7568),U_7566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7566),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP439(U_7568,U_7566) )
& ! [U_7568,U_7566] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7566),U_7568))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7566))
| ~ sP439(U_7568,U_7566) )
& ! [U_7568,U_7566] :
( U_7568 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP439(U_7568,U_7566) )
& ! [U_7565,U_7567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7567),U_7565))
| ~ sP438(U_7565,U_7567) )
& ! [U_7565,U_7567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7565),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP438(U_7565,U_7567) )
& ! [U_7565,U_7567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7565),U_7567))
| ~ sP437(U_7565,U_7567) )
& ! [U_7565,U_7567] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7565))
| ~ sP437(U_7565,U_7567) )
& ! [U_7568,U_7566] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7566),U_7568) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP439(U_7568,U_7566) )
& ! [U_7565,U_7567] :
( sP438(U_7565,U_7567)
| sP437(U_7565,U_7567)
| U_7567 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7565),U_7567) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP437,sP438,sP439])],[f_1820_3]) ).
cnf(f_1820_5,plain,
( sP438(U_7565,U_7567)
| sP437(U_7565,U_7567)
| U_7567 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7565),U_7567) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1820_4]) ).
cnf(f_1820_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7566),U_7568) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP439(U_7568,U_7566) ),
inference(clausify,[status(thm)],[f_1820_4]) ).
cnf(f_1820_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7565))
| ~ sP437(U_7565,U_7567) ),
inference(clausify,[status(thm)],[f_1820_4]) ).
cnf(f_1820_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7565),U_7567))
| ~ sP437(U_7565,U_7567) ),
inference(clausify,[status(thm)],[f_1820_4]) ).
cnf(f_1820_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7565),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP438(U_7565,U_7567) ),
inference(clausify,[status(thm)],[f_1820_4]) ).
cnf(f_1820_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7567),U_7565))
| ~ sP438(U_7565,U_7567) ),
inference(clausify,[status(thm)],[f_1820_4]) ).
cnf(f_1820_11,plain,
( U_7568 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP439(U_7568,U_7566) ),
inference(clausify,[status(thm)],[f_1820_4]) ).
cnf(f_1820_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7566),U_7568))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7566))
| ~ sP439(U_7568,U_7566) ),
inference(clausify,[status(thm)],[f_1820_4]) ).
cnf(f_1820_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7568),U_7566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7566),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP439(U_7568,U_7566) ),
inference(clausify,[status(thm)],[f_1820_4]) ).
fof(f_1821_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_1821_2,plain,
! [U_7570,U_7569] :
( ( ( 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_7570),U_7569)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7570)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7570))
| ~ 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_7570),U_7569))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7569)) ),
inference(variable_rename,[status(thm)],[f_1821_1]) ).
fof(f_1821_3,plain,
( ! [U_7570,U_7569] :
( 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_7570),U_7569)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7570))
| ~ sP440(U_7570,U_7569) )
& ! [U_7570,U_7569] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7570))
| ~ 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_7570),U_7569)))
| ~ sP440(U_7570,U_7569) )
& ! [U_7570,U_7569] :
( sP440(U_7570,U_7569)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7569)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP440])],[f_1821_2]) ).
cnf(f_1821_4,plain,
( sP440(U_7570,U_7569)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7569)) ),
inference(clausify,[status(thm)],[f_1821_3]) ).
cnf(f_1821_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7570))
| ~ 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_7570),U_7569)))
| ~ sP440(U_7570,U_7569) ),
inference(clausify,[status(thm)],[f_1821_3]) ).
cnf(f_1821_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_7570),U_7569)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7570))
| ~ sP440(U_7570,U_7569) ),
inference(clausify,[status(thm)],[f_1821_3]) ).
fof(f_1822_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_1822_2,plain,
! [U_7572,U_7571] :
( ( ( 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_7572),U_7571)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7571),U_7572)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7571),U_7572))
| ~ 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_7572),U_7571))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7571)) ),
inference(variable_rename,[status(thm)],[f_1822_1]) ).
fof(f_1822_3,plain,
( ! [U_7571,U_7572] :
( 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_7572),U_7571)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7571),U_7572))
| ~ sP441(U_7571,U_7572) )
& ! [U_7571,U_7572] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7571),U_7572))
| ~ 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_7572),U_7571)))
| ~ sP441(U_7571,U_7572) )
& ! [U_7571,U_7572] :
( sP441(U_7571,U_7572)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7571)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP441])],[f_1822_2]) ).
cnf(f_1822_4,plain,
( sP441(U_7571,U_7572)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7571)) ),
inference(clausify,[status(thm)],[f_1822_3]) ).
cnf(f_1822_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7571),U_7572))
| ~ 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_7572),U_7571)))
| ~ sP441(U_7571,U_7572) ),
inference(clausify,[status(thm)],[f_1822_3]) ).
cnf(f_1822_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_7572),U_7571)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7571),U_7572))
| ~ sP441(U_7571,U_7572) ),
inference(clausify,[status(thm)],[f_1822_3]) ).
fof(f_1823_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_1823_2,plain,
! [U_7574,U_7573] :
( ( ( 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_7573),U_7574)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7574))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7574),U_7573)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7574))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7574),U_7573)) )
| ~ 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_7573),U_7574))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7573)) ),
inference(variable_rename,[status(thm)],[f_1823_1]) ).
fof(f_1823_3,plain,
( ! [U_7574,U_7573] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7574))
| ~ sP442(U_7574,U_7573) )
& ! [U_7574,U_7573] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7574),U_7573))
| ~ sP442(U_7574,U_7573) )
& ! [U_7574,U_7573] :
( 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_7573),U_7574)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7574))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7574),U_7573))
| ~ sP443(U_7574,U_7573) )
& ! [U_7574,U_7573] :
( sP442(U_7574,U_7573)
| ~ 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_7573),U_7574)))
| ~ sP443(U_7574,U_7573) )
& ! [U_7574,U_7573] :
( sP443(U_7574,U_7573)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7573)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP442,sP443])],[f_1823_2]) ).
cnf(f_1823_4,plain,
( sP443(U_7574,U_7573)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7573)) ),
inference(clausify,[status(thm)],[f_1823_3]) ).
cnf(f_1823_5,plain,
( sP442(U_7574,U_7573)
| ~ 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_7573),U_7574)))
| ~ sP443(U_7574,U_7573) ),
inference(clausify,[status(thm)],[f_1823_3]) ).
cnf(f_1823_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_7573),U_7574)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7574))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7574),U_7573))
| ~ sP443(U_7574,U_7573) ),
inference(clausify,[status(thm)],[f_1823_3]) ).
cnf(f_1823_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7574),U_7573))
| ~ sP442(U_7574,U_7573) ),
inference(clausify,[status(thm)],[f_1823_3]) ).
cnf(f_1823_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7574))
| ~ sP442(U_7574,U_7573) ),
inference(clausify,[status(thm)],[f_1823_3]) ).
fof(f_1824_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_1824_2,plain,
! [U_7577,U_7576,U_7575] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7575),U_7577)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7575),U_7576)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7576),U_7577))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7576))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7575)) ),
inference(variable_rename,[status(thm)],[f_1824_1]) ).
fof(f_1824_3,plain,
! [U_7576,U_7577,U_7575] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7575),U_7577)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7575),U_7576)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7576),U_7577))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7576))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7575)) ),
inference(definitional_conversion,[status(esa)],[f_1824_2]) ).
cnf(f_1824_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_7575),U_7577)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7575),U_7576)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7576),U_7577))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7576))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7575)) ),
inference(clausify,[status(thm)],[f_1824_3]) ).
fof(f_1825_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_1825_2,plain,
! [U_7579,U_7578] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7578),U_7579)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7579),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_7578)) ),
inference(variable_rename,[status(thm)],[f_1825_1]) ).
fof(f_1825_3,plain,
! [U_7578,U_7579] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7578),U_7579)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7579),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_7578)) ),
inference(definitional_conversion,[status(esa)],[f_1825_2]) ).
cnf(f_1825_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_7578),U_7579)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7579),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_7578)) ),
inference(clausify,[status(thm)],[f_1825_3]) ).
fof(f_1826_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_1826_2,plain,
! [U_7581,U_7580] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7580),U_7581) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7580),U_7581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7580)) ),
inference(variable_rename,[status(thm)],[f_1826_1]) ).
fof(f_1826_3,plain,
! [U_7581,U_7580] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7580),U_7581) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7580),U_7581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7580)) ),
inference(definitional_conversion,[status(esa)],[f_1826_2]) ).
cnf(f_1826_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7580),U_7581) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7580),U_7581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7580)) ),
inference(clausify,[status(thm)],[f_1826_3]) ).
fof(f_1827_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_1827_2,plain,
! [U_7583,U_7582] :
( ( ( 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_7583),U_7582)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7583),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7583),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_7583),U_7582))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7582),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1827_1]) ).
fof(f_1827_3,plain,
( ! [U_7582,U_7583] :
( 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_7583),U_7582)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7583),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP444(U_7582,U_7583) )
& ! [U_7582,U_7583] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7583),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_7583),U_7582)))
| ~ sP444(U_7582,U_7583) )
& ! [U_7582,U_7583] :
( sP444(U_7582,U_7583)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7582),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP444])],[f_1827_2]) ).
cnf(f_1827_4,plain,
( sP444(U_7582,U_7583)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7582),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1827_3]) ).
cnf(f_1827_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7583),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_7583),U_7582)))
| ~ sP444(U_7582,U_7583) ),
inference(clausify,[status(thm)],[f_1827_3]) ).
cnf(f_1827_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_7583),U_7582)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7583),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP444(U_7582,U_7583) ),
inference(clausify,[status(thm)],[f_1827_3]) ).
fof(f_1828_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_1828_2,plain,
! [U_7585,U_7584] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7584),U_7585)),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_7585))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7584),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1828_1]) ).
fof(f_1828_3,plain,
! [U_7584,U_7585] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7584),U_7585)),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_7585))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7584),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1828_2]) ).
cnf(f_1828_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_7584),U_7585)),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_7585))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7584),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1828_3]) ).
fof(f_1829_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_1829_2,plain,
! [U_7588,U_7587,U_7586] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7586),U_7587)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7586),U_7588)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7587),U_7588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7587))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7586),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1829_1]) ).
fof(f_1829_3,plain,
! [U_7586,U_7587,U_7588] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7586),U_7587)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7586),U_7588)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7587),U_7588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7587))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7586),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1829_2]) ).
cnf(f_1829_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_7586),U_7587)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7586),U_7588)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7587),U_7588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7587))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7586),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1829_3]) ).
fof(f_1830_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_1830_2,plain,
! [U_7590,U_7589] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7589),U_7590) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7590),U_7589))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7589),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1830_1]) ).
fof(f_1830_3,plain,
! [U_7589,U_7590] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7589),U_7590) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7590),U_7589))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7589),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1830_2]) ).
cnf(f_1830_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7589),U_7590) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7590),U_7589))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7589),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1830_3]) ).
fof(f_1831_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_1831_2,plain,
! [U_7593,U_7592,U_7591] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7591),U_7593)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7592),U_7593)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7593))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7591),U_7592)) ),
inference(variable_rename,[status(thm)],[f_1831_1]) ).
fof(f_1831_3,plain,
! [U_7591,U_7592,U_7593] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7591),U_7593)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7592),U_7593)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7593))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7591),U_7592)) ),
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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7591),U_7593)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7592),U_7593)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7593))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7591),U_7592)) ),
inference(clausify,[status(thm)],[f_1831_3]) ).
fof(f_1832_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_1832_2,plain,
! [U_7596,U_7595,U_7594] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7595),U_7596)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7594),U_7596)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7596),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7594),U_7595)) ),
inference(variable_rename,[status(thm)],[f_1832_1]) ).
fof(f_1832_3,plain,
! [U_7594,U_7595,U_7596] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7595),U_7596)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7594),U_7596)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7596),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7594),U_7595)) ),
inference(definitional_conversion,[status(esa)],[f_1832_2]) ).
cnf(f_1832_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_7595),U_7596)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7594),U_7596)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7596),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7594),U_7595)) ),
inference(clausify,[status(thm)],[f_1832_3]) ).
fof(f_1833_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_1833_2,plain,
! [U_7598,U_7597] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7597)),U_7598) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7597,U_7598),
inference(variable_rename,[status(thm)],[f_1833_1]) ).
fof(f_1833_3,plain,
! [U_7598,U_7597] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7597)),U_7598) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7597,U_7598),
inference(definitional_conversion,[status(esa)],[f_1833_2]) ).
cnf(f_1833_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7597)),U_7598) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7597,U_7598),
inference(clausify,[status(thm)],[f_1833_3]) ).
fof(f_1834_1,plain,
! [V_y_2,V_x_2,T_c] :
( hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan]) ).
fof(f_1834_2,plain,
! [U_7601,U_7600,U_7599] :
( hAPP(c_Set_Oimage(U_7599,U_7599,c_Groups_Ouminus__class_Ouminus(U_7599)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7599,U_7600,U_7601)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7599,hAPP(c_Groups_Ouminus__class_Ouminus(U_7599),U_7601),hAPP(c_Groups_Ouminus__class_Ouminus(U_7599),U_7600))
| ~ class_Groups_Oordered__ab__group__add(U_7599) ),
inference(variable_rename,[status(thm)],[f_1834_1]) ).
fof(f_1834_3,plain,
! [U_7599,U_7600,U_7601] :
( hAPP(c_Set_Oimage(U_7599,U_7599,c_Groups_Ouminus__class_Ouminus(U_7599)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7599,U_7600,U_7601)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7599,hAPP(c_Groups_Ouminus__class_Ouminus(U_7599),U_7601),hAPP(c_Groups_Ouminus__class_Ouminus(U_7599),U_7600))
| ~ class_Groups_Oordered__ab__group__add(U_7599) ),
inference(definitional_conversion,[status(esa)],[f_1834_2]) ).
cnf(f_1834_4,plain,
( hAPP(c_Set_Oimage(U_7599,U_7599,c_Groups_Ouminus__class_Ouminus(U_7599)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7599,U_7600,U_7601)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7599,hAPP(c_Groups_Ouminus__class_Ouminus(U_7599),U_7601),hAPP(c_Groups_Ouminus__class_Ouminus(U_7599),U_7600))
| ~ class_Groups_Oordered__ab__group__add(U_7599) ),
inference(clausify,[status(thm)],[f_1834_3]) ).
fof(f_1835_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_1835_2,plain,
! [U_7603,U_7602] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7602),U_7603)),U_7602))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7603))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7602)) ),
inference(variable_rename,[status(thm)],[f_1835_1]) ).
fof(f_1835_3,plain,
! [U_7602,U_7603] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7602),U_7603)),U_7602))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7603))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7602)) ),
inference(definitional_conversion,[status(esa)],[f_1835_2]) ).
cnf(f_1835_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7602),U_7603)),U_7602))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7603))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7602)) ),
inference(clausify,[status(thm)],[f_1835_3]) ).
fof(f_1836_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_1836_2,plain,
! [U_7606,U_7605,U_7604] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7606),U_7604)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7605),U_7606)),U_7604)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7604)) ),
inference(variable_rename,[status(thm)],[f_1836_1]) ).
fof(f_1836_3,plain,
! [U_7604,U_7605,U_7606] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7606),U_7604)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7605),U_7606)),U_7604)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7604)) ),
inference(definitional_conversion,[status(esa)],[f_1836_2]) ).
cnf(f_1836_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7606),U_7604)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7605),U_7606)),U_7604)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7604)) ),
inference(clausify,[status(thm)],[f_1836_3]) ).
fof(f_1837_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_1837_2,plain,
! [U_7610,U_7609,U_7608,U_7607] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7607),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7607),U_7609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7607),U_7608),U_7610))),U_7608) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7607),U_7610),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7607),U_7609),U_7608))
| U_7608 = c_Groups_Ozero__class_Ozero(U_7607)
| ~ class_Divides_Osemiring__div(U_7607) ),
inference(variable_rename,[status(thm)],[f_1837_1]) ).
fof(f_1837_3,plain,
! [U_7607,U_7608,U_7609,U_7610] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7607),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7607),U_7609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7607),U_7608),U_7610))),U_7608) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7607),U_7610),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7607),U_7609),U_7608))
| U_7608 = c_Groups_Ozero__class_Ozero(U_7607)
| ~ class_Divides_Osemiring__div(U_7607) ),
inference(definitional_conversion,[status(esa)],[f_1837_2]) ).
cnf(f_1837_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7607),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7607),U_7609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7607),U_7608),U_7610))),U_7608) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7607),U_7610),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7607),U_7609),U_7608))
| U_7608 = c_Groups_Ozero__class_Ozero(U_7607)
| ~ class_Divides_Osemiring__div(U_7607) ),
inference(clausify,[status(thm)],[f_1837_3]) ).
fof(f_1838_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_1838_2,plain,
! [U_7614,U_7613,U_7612,U_7611] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7611),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7611),U_7613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7611),U_7614),U_7612))),U_7612) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7611),U_7614),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7611),U_7613),U_7612))
| U_7612 = c_Groups_Ozero__class_Ozero(U_7611)
| ~ class_Divides_Osemiring__div(U_7611) ),
inference(variable_rename,[status(thm)],[f_1838_1]) ).
fof(f_1838_3,plain,
! [U_7611,U_7612,U_7613,U_7614] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7611),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7611),U_7613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7611),U_7614),U_7612))),U_7612) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7611),U_7614),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7611),U_7613),U_7612))
| U_7612 = c_Groups_Ozero__class_Ozero(U_7611)
| ~ class_Divides_Osemiring__div(U_7611) ),
inference(definitional_conversion,[status(esa)],[f_1838_2]) ).
cnf(f_1838_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7611),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7611),U_7613),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7611),U_7614),U_7612))),U_7612) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7611),U_7614),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7611),U_7613),U_7612))
| U_7612 = c_Groups_Ozero__class_Ozero(U_7611)
| ~ class_Divides_Osemiring__div(U_7611) ),
inference(clausify,[status(thm)],[f_1838_3]) ).
fof(f_1839_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_1839_2,plain,
! [U_7617,U_7616,U_7615] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7615),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7615),U_7617),U_7616)),U_7616) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7615),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7615),U_7617),U_7616)),c_Groups_Oone__class_Oone(U_7615))
| U_7616 = c_Groups_Ozero__class_Ozero(U_7615)
| ~ class_Divides_Osemiring__div(U_7615) ),
inference(variable_rename,[status(thm)],[f_1839_1]) ).
fof(f_1839_3,plain,
! [U_7615,U_7616,U_7617] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7615),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7615),U_7617),U_7616)),U_7616) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7615),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7615),U_7617),U_7616)),c_Groups_Oone__class_Oone(U_7615))
| U_7616 = c_Groups_Ozero__class_Ozero(U_7615)
| ~ class_Divides_Osemiring__div(U_7615) ),
inference(definitional_conversion,[status(esa)],[f_1839_2]) ).
cnf(f_1839_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7615),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7615),U_7617),U_7616)),U_7616) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7615),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7615),U_7617),U_7616)),c_Groups_Oone__class_Oone(U_7615))
| U_7616 = c_Groups_Ozero__class_Ozero(U_7615)
| ~ class_Divides_Osemiring__div(U_7615) ),
inference(clausify,[status(thm)],[f_1839_3]) ).
fof(f_1840_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_1840_2,plain,
! [U_7620,U_7619,U_7618] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7618),U_7619),U_7620)),U_7619) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7618),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7618),U_7620),U_7619)),c_Groups_Oone__class_Oone(U_7618))
| U_7619 = c_Groups_Ozero__class_Ozero(U_7618)
| ~ class_Divides_Osemiring__div(U_7618) ),
inference(variable_rename,[status(thm)],[f_1840_1]) ).
fof(f_1840_3,plain,
! [U_7618,U_7619,U_7620] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7618),U_7619),U_7620)),U_7619) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7618),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7618),U_7620),U_7619)),c_Groups_Oone__class_Oone(U_7618))
| U_7619 = c_Groups_Ozero__class_Ozero(U_7618)
| ~ class_Divides_Osemiring__div(U_7618) ),
inference(definitional_conversion,[status(esa)],[f_1840_2]) ).
cnf(f_1840_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7618),U_7619),U_7620)),U_7619) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7618),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7618),U_7620),U_7619)),c_Groups_Oone__class_Oone(U_7618))
| U_7619 = c_Groups_Ozero__class_Ozero(U_7618)
| ~ class_Divides_Osemiring__div(U_7618) ),
inference(clausify,[status(thm)],[f_1840_3]) ).
fof(f_1841_1,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_com_Osize_I1_J]) ).
fof(f_1841_2,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1841_1]) ).
cnf(f_1841_3,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1841_2]) ).
fof(f_1842_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J]) ).
fof(f_1842_2,plain,
! [U_7624,U_7623,U_7622,U_7621] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7621,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7621,U_7622,U_7623)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7621,U_7623),U_7624)) = c_Orderings_Obot__class_Obot(tc_fun(U_7621,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7621) ),
inference(variable_rename,[status(thm)],[f_1842_1]) ).
fof(f_1842_3,plain,
! [U_7621,U_7622,U_7623,U_7624] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7621,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7621,U_7622,U_7623)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7621,U_7623),U_7624)) = c_Orderings_Obot__class_Obot(tc_fun(U_7621,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7621) ),
inference(definitional_conversion,[status(esa)],[f_1842_2]) ).
cnf(f_1842_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7621,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7621,U_7622,U_7623)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7621,U_7623),U_7624)) = c_Orderings_Obot__class_Obot(tc_fun(U_7621,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7621) ),
inference(clausify,[status(thm)],[f_1842_3]) ).
fof(f_1843_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan]) ).
fof(f_1843_2,plain,
! [U_7629,U_7628,U_7627,U_7626,U_7625] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7625,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7625,U_7626,U_7627)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7625,U_7628,U_7629)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7625,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_7625),U_7626),U_7628),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_7625),U_7627),U_7629))
| ~ class_Orderings_Olinorder(U_7625) ),
inference(variable_rename,[status(thm)],[f_1843_1]) ).
fof(f_1843_3,plain,
! [U_7625,U_7626,U_7627,U_7628,U_7629] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7625,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7625,U_7626,U_7627)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7625,U_7628,U_7629)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7625,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_7625),U_7626),U_7628),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_7625),U_7627),U_7629))
| ~ class_Orderings_Olinorder(U_7625) ),
inference(definitional_conversion,[status(esa)],[f_1843_2]) ).
cnf(f_1843_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7625,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7625,U_7626,U_7627)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7625,U_7628,U_7629)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7625,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_7625),U_7626),U_7628),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_7625),U_7627),U_7629))
| ~ class_Orderings_Olinorder(U_7625) ),
inference(clausify,[status(thm)],[f_1843_3]) ).
fof(f_1844_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_1844_2,plain,
! [U_7631,U_7630] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7630,U_7631)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7631),hAPP(c_Nat_OSuc,U_7630)),
inference(variable_rename,[status(thm)],[f_1844_1]) ).
fof(f_1844_3,plain,
! [U_7630,U_7631] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7630,U_7631)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7631),hAPP(c_Nat_OSuc,U_7630)),
inference(definitional_conversion,[status(esa)],[f_1844_2]) ).
cnf(f_1844_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7630,U_7631)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7631),hAPP(c_Nat_OSuc,U_7630)),
inference(clausify,[status(thm)],[f_1844_3]) ).
fof(f_1845_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_1845_2,plain,
! [U_7633,U_7632] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7632),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7633) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7632,U_7633),
inference(variable_rename,[status(thm)],[f_1845_1]) ).
fof(f_1845_3,plain,
! [U_7632,U_7633] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7632),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7633) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7632,U_7633),
inference(definitional_conversion,[status(esa)],[f_1845_2]) ).
cnf(f_1845_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7632),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7633) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7632,U_7633),
inference(clausify,[status(thm)],[f_1845_3]) ).
fof(f_1846_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_1846_2,plain,
! [U_7644,U_7643,U_7642] :
( ( hBOOL(hAPP(U_7642,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7643),U_7644)))
| ( ? [U_7641] :
( ~ hBOOL(hAPP(U_7642,U_7641))
& ? [U_7640] :
( U_7643 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7644),U_7641)),U_7640)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7640),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7644),U_7640)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7644),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_7639] :
( ~ hBOOL(hAPP(U_7642,U_7639))
& ? [U_7638] :
( U_7643 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7644),U_7639)),U_7638)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7638),U_7644))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7638)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7644)) )
| ( ~ hBOOL(hAPP(U_7642,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_7644 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [U_7637] :
( hBOOL(hAPP(U_7642,U_7637))
| ! [U_7636] :
( U_7643 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7644),U_7637)),U_7636)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7644),U_7636)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7644),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_7635] :
( hBOOL(hAPP(U_7642,U_7635))
| ! [U_7634] :
( U_7643 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7644),U_7635)),U_7634)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7644))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7634)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7644)) )
& ( hBOOL(hAPP(U_7642,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_7644 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_7642,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7643),U_7644))) ) ),
inference(variable_rename,[status(thm)],[f_1846_1]) ).
fof(f_1846_3,plain,
( ! [U_7650,U_7648,U_7646] :
( hBOOL(hAPP(U_7646,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7648),U_7650)))
| ( ? [U_7641] :
( ~ hBOOL(hAPP(U_7646,U_7641))
& ? [U_7640] :
( U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),U_7641)),U_7640)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7640),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),U_7640)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_7639] :
( ~ hBOOL(hAPP(U_7646,U_7639))
& ? [U_7638] :
( U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),U_7639)),U_7638)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7638),U_7650))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7638)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7650)) )
| ( ~ hBOOL(hAPP(U_7646,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_7650 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_7649,U_7647,U_7645] :
( ( ( ! [U_7637] :
( hBOOL(hAPP(U_7645,U_7637))
| ! [U_7636] :
( U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7637)),U_7636)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),U_7636)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_7635] :
( hBOOL(hAPP(U_7645,U_7635))
| ! [U_7634] :
( U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7635)),U_7634)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7634)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7649)) )
& ( hBOOL(hAPP(U_7645,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_7649 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_7645,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7647),U_7649))) ) ),
inference(miniscope,[status(thm)],[f_1846_2]) ).
fof(f_1846_4,plain,
( ! [U_7650,U_7648,U_7646] :
( hBOOL(hAPP(U_7646,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7648),U_7650)))
| ( ? [U_7641] :
( ~ hBOOL(hAPP(U_7646,U_7641))
& ? [U_7640] :
( U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),U_7641)),U_7640)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7640),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),U_7640)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_7646,sK154(U_7650,U_7648,U_7646)))
& ? [U_7638] :
( U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),sK154(U_7650,U_7648,U_7646))),U_7638)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7638),U_7650))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7638)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7650)) )
| ( ~ hBOOL(hAPP(U_7646,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_7650 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_7649,U_7647,U_7645] :
( ( ( ! [U_7637] :
( hBOOL(hAPP(U_7645,U_7637))
| ! [U_7636] :
( U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7637)),U_7636)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),U_7636)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_7635] :
( hBOOL(hAPP(U_7645,U_7635))
| ! [U_7634] :
( U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7635)),U_7634)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7634)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7649)) )
& ( hBOOL(hAPP(U_7645,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_7649 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_7645,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7647),U_7649))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_7639,sK154(U_7650,U_7648,U_7646))],[f_1846_3]) ).
fof(f_1846_5,plain,
( ! [U_7650,U_7648,U_7646] :
( hBOOL(hAPP(U_7646,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7648),U_7650)))
| ( ? [U_7641] :
( ~ hBOOL(hAPP(U_7646,U_7641))
& ? [U_7640] :
( U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),U_7641)),U_7640)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7640),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),U_7640)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_7646,sK154(U_7650,U_7648,U_7646)))
& U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),sK154(U_7650,U_7648,U_7646))),sK155(U_7650,U_7648,U_7646))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK155(U_7650,U_7648,U_7646)),U_7650))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK155(U_7650,U_7648,U_7646)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7650)) )
| ( ~ hBOOL(hAPP(U_7646,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_7650 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_7649,U_7647,U_7645] :
( ( ( ! [U_7637] :
( hBOOL(hAPP(U_7645,U_7637))
| ! [U_7636] :
( U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7637)),U_7636)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),U_7636)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_7635] :
( hBOOL(hAPP(U_7645,U_7635))
| ! [U_7634] :
( U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7635)),U_7634)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7634)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7649)) )
& ( hBOOL(hAPP(U_7645,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_7649 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_7645,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7647),U_7649))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_7638,sK155(U_7650,U_7648,U_7646))],[f_1846_4]) ).
fof(f_1846_6,plain,
( ! [U_7650,U_7648,U_7646] :
( hBOOL(hAPP(U_7646,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7648),U_7650)))
| ( ~ hBOOL(hAPP(U_7646,sK156(U_7650,U_7648,U_7646)))
& ? [U_7640] :
( U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),sK156(U_7650,U_7648,U_7646))),U_7640)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7640),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),U_7640)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_7646,sK154(U_7650,U_7648,U_7646)))
& U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),sK154(U_7650,U_7648,U_7646))),sK155(U_7650,U_7648,U_7646))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK155(U_7650,U_7648,U_7646)),U_7650))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK155(U_7650,U_7648,U_7646)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7650)) )
| ( ~ hBOOL(hAPP(U_7646,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_7650 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_7649,U_7647,U_7645] :
( ( ( ! [U_7637] :
( hBOOL(hAPP(U_7645,U_7637))
| ! [U_7636] :
( U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7637)),U_7636)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),U_7636)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_7635] :
( hBOOL(hAPP(U_7645,U_7635))
| ! [U_7634] :
( U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7635)),U_7634)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7634)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7649)) )
& ( hBOOL(hAPP(U_7645,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_7649 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_7645,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7647),U_7649))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_7641,sK156(U_7650,U_7648,U_7646))],[f_1846_5]) ).
fof(f_1846_7,plain,
( ! [U_7650,U_7648,U_7646] :
( hBOOL(hAPP(U_7646,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7648),U_7650)))
| ( ~ hBOOL(hAPP(U_7646,sK156(U_7650,U_7648,U_7646)))
& U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),sK156(U_7650,U_7648,U_7646))),sK157(U_7650,U_7648,U_7646))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK157(U_7650,U_7648,U_7646)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),sK157(U_7650,U_7648,U_7646)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_7646,sK154(U_7650,U_7648,U_7646)))
& U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),sK154(U_7650,U_7648,U_7646))),sK155(U_7650,U_7648,U_7646))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK155(U_7650,U_7648,U_7646)),U_7650))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK155(U_7650,U_7648,U_7646)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7650)) )
| ( ~ hBOOL(hAPP(U_7646,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_7650 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_7649,U_7647,U_7645] :
( ( ( ! [U_7637] :
( hBOOL(hAPP(U_7645,U_7637))
| ! [U_7636] :
( U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7637)),U_7636)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),U_7636)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_7635] :
( hBOOL(hAPP(U_7645,U_7635))
| ! [U_7634] :
( U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7635)),U_7634)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7634)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7649)) )
& ( hBOOL(hAPP(U_7645,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_7649 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_7645,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7647),U_7649))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_7640,sK157(U_7650,U_7648,U_7646))],[f_1846_6]) ).
fof(f_1846_8,plain,
( ! [U_7650,U_7646,U_7648] :
( ~ hBOOL(hAPP(U_7646,sK156(U_7650,U_7648,U_7646)))
| ~ sP448(U_7650,U_7646,U_7648) )
& ! [U_7650,U_7646,U_7648] :
( U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),sK156(U_7650,U_7648,U_7646))),sK157(U_7650,U_7648,U_7646))
| ~ sP448(U_7650,U_7646,U_7648) )
& ! [U_7650,U_7646,U_7648] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK157(U_7650,U_7648,U_7646)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP448(U_7650,U_7646,U_7648) )
& ! [U_7650,U_7646,U_7648] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),sK157(U_7650,U_7648,U_7646)))
| ~ sP448(U_7650,U_7646,U_7648) )
& ! [U_7650,U_7646,U_7648] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP448(U_7650,U_7646,U_7648) )
& ! [U_7650,U_7646,U_7648] :
( ~ hBOOL(hAPP(U_7646,sK154(U_7650,U_7648,U_7646)))
| ~ sP447(U_7650,U_7646,U_7648) )
& ! [U_7650,U_7646,U_7648] :
( U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),sK154(U_7650,U_7648,U_7646))),sK155(U_7650,U_7648,U_7646))
| ~ sP447(U_7650,U_7646,U_7648) )
& ! [U_7650,U_7646,U_7648] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK155(U_7650,U_7648,U_7646)),U_7650))
| ~ sP447(U_7650,U_7646,U_7648) )
& ! [U_7650,U_7646,U_7648] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK155(U_7650,U_7648,U_7646)))
| ~ sP447(U_7650,U_7646,U_7648) )
& ! [U_7650,U_7646,U_7648] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7650))
| ~ sP447(U_7650,U_7646,U_7648) )
& ! [U_7650,U_7646] :
( ~ hBOOL(hAPP(U_7646,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP446(U_7650,U_7646) )
& ! [U_7650,U_7646] :
( U_7650 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP446(U_7650,U_7646) )
& ! [U_7635,U_7634,U_7636,U_7649,U_7637,U_7645,U_7647] :
( hBOOL(hAPP(U_7645,U_7637))
| U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7637)),U_7636)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),U_7636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP445(U_7635,U_7634,U_7636,U_7649,U_7637,U_7645,U_7647) )
& ! [U_7635,U_7634,U_7636,U_7649,U_7637,U_7645,U_7647] :
( hBOOL(hAPP(U_7645,U_7635))
| U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7635)),U_7634)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7649))
| ~ sP445(U_7635,U_7634,U_7636,U_7649,U_7637,U_7645,U_7647) )
& ! [U_7635,U_7634,U_7636,U_7649,U_7637,U_7645,U_7647] :
( hBOOL(hAPP(U_7645,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_7649 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP445(U_7635,U_7634,U_7636,U_7649,U_7637,U_7645,U_7647) )
& ! [U_7650,U_7646,U_7648] :
( hBOOL(hAPP(U_7646,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7648),U_7650)))
| sP448(U_7650,U_7646,U_7648)
| sP447(U_7650,U_7646,U_7648)
| sP446(U_7650,U_7646) )
& ! [U_7635,U_7634,U_7636,U_7649,U_7637,U_7645,U_7647] :
( sP445(U_7635,U_7634,U_7636,U_7649,U_7637,U_7645,U_7647)
| ~ hBOOL(hAPP(U_7645,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7647),U_7649))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP445,sP446,sP447,sP448])],[f_1846_7]) ).
cnf(f_1846_9,plain,
( sP445(U_7635,U_7634,U_7636,U_7649,U_7637,U_7645,U_7647)
| ~ hBOOL(hAPP(U_7645,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7647),U_7649))) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_10,plain,
( hBOOL(hAPP(U_7646,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7648),U_7650)))
| sP448(U_7650,U_7646,U_7648)
| sP447(U_7650,U_7646,U_7648)
| sP446(U_7650,U_7646) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_11,plain,
( hBOOL(hAPP(U_7645,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_7649 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP445(U_7635,U_7634,U_7636,U_7649,U_7637,U_7645,U_7647) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_12,plain,
( hBOOL(hAPP(U_7645,U_7635))
| U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7635)),U_7634)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7649))
| ~ sP445(U_7635,U_7634,U_7636,U_7649,U_7637,U_7645,U_7647) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_13,plain,
( hBOOL(hAPP(U_7645,U_7637))
| U_7647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7649),U_7637)),U_7636)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7636),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),U_7636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7649),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP445(U_7635,U_7634,U_7636,U_7649,U_7637,U_7645,U_7647) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_14,plain,
( U_7650 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP446(U_7650,U_7646) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_15,plain,
( ~ hBOOL(hAPP(U_7646,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP446(U_7650,U_7646) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_16,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7650))
| ~ sP447(U_7650,U_7646,U_7648) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_17,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK155(U_7650,U_7648,U_7646)))
| ~ sP447(U_7650,U_7646,U_7648) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_18,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK155(U_7650,U_7648,U_7646)),U_7650))
| ~ sP447(U_7650,U_7646,U_7648) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_19,plain,
( U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),sK154(U_7650,U_7648,U_7646))),sK155(U_7650,U_7648,U_7646))
| ~ sP447(U_7650,U_7646,U_7648) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_20,plain,
( ~ hBOOL(hAPP(U_7646,sK154(U_7650,U_7648,U_7646)))
| ~ sP447(U_7650,U_7646,U_7648) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_21,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP448(U_7650,U_7646,U_7648) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_22,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7650),sK157(U_7650,U_7648,U_7646)))
| ~ sP448(U_7650,U_7646,U_7648) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_23,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK157(U_7650,U_7648,U_7646)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP448(U_7650,U_7646,U_7648) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_24,plain,
( U_7648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7650),sK156(U_7650,U_7648,U_7646))),sK157(U_7650,U_7648,U_7646))
| ~ sP448(U_7650,U_7646,U_7648) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
cnf(f_1846_25,plain,
( ~ hBOOL(hAPP(U_7646,sK156(U_7650,U_7648,U_7646)))
| ~ sP448(U_7650,U_7646,U_7648) ),
inference(clausify,[status(thm)],[f_1846_8]) ).
fof(f_1847_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_1847_2,plain,
! [U_7654,U_7653,U_7652,U_7651] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7651),U_7652) = U_7653
| U_7652 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7654),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7652),U_7654)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7652)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7654),U_7652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7654)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7652)) )
| U_7651 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7652),U_7653)),U_7654) ),
inference(variable_rename,[status(thm)],[f_1847_1]) ).
fof(f_1847_3,plain,
( ! [U_7654,U_7652] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7654),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7652),U_7654))
| ~ sP450(U_7654,U_7652) )
& ! [U_7654,U_7652] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7652))
| ~ sP450(U_7654,U_7652) )
& ! [U_7654,U_7652] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7654),U_7652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7654))
| ~ sP449(U_7654,U_7652) )
& ! [U_7654,U_7652] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7652))
| ~ sP449(U_7654,U_7652) )
& ! [U_7653,U_7651,U_7654,U_7652] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7651),U_7652) = U_7653
| U_7652 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP450(U_7654,U_7652)
| sP449(U_7654,U_7652)
| U_7651 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7652),U_7653)),U_7654) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP449,sP450])],[f_1847_2]) ).
cnf(f_1847_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7651),U_7652) = U_7653
| U_7652 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP450(U_7654,U_7652)
| sP449(U_7654,U_7652)
| U_7651 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7652),U_7653)),U_7654) ),
inference(clausify,[status(thm)],[f_1847_3]) ).
cnf(f_1847_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7652))
| ~ sP449(U_7654,U_7652) ),
inference(clausify,[status(thm)],[f_1847_3]) ).
cnf(f_1847_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7654),U_7652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7654))
| ~ sP449(U_7654,U_7652) ),
inference(clausify,[status(thm)],[f_1847_3]) ).
cnf(f_1847_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7652))
| ~ sP450(U_7654,U_7652) ),
inference(clausify,[status(thm)],[f_1847_3]) ).
cnf(f_1847_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7654),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7652),U_7654))
| ~ sP450(U_7654,U_7652) ),
inference(clausify,[status(thm)],[f_1847_3]) ).
fof(f_1848_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_1848_2,plain,
! [U_7656,U_7655] :
( 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_7655,U_7656)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7655)) ),
inference(variable_rename,[status(thm)],[f_1848_1]) ).
fof(f_1848_3,plain,
! [U_7655,U_7656] :
( 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_7655,U_7656)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7655)) ),
inference(definitional_conversion,[status(esa)],[f_1848_2]) ).
cnf(f_1848_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_7655,U_7656)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7655)) ),
inference(clausify,[status(thm)],[f_1848_3]) ).
fof(f_1849_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_1849_2,plain,
! [U_7658,U_7657] :
( c_Nat__Transfer_Otsub(U_7658,U_7657) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7658),U_7657)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7657),U_7658)) ),
inference(variable_rename,[status(thm)],[f_1849_1]) ).
fof(f_1849_3,plain,
! [U_7658,U_7657] :
( c_Nat__Transfer_Otsub(U_7658,U_7657) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7658),U_7657)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7657),U_7658)) ),
inference(definitional_conversion,[status(esa)],[f_1849_2]) ).
cnf(f_1849_4,plain,
( c_Nat__Transfer_Otsub(U_7658,U_7657) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7658),U_7657)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7657),U_7658)) ),
inference(clausify,[status(thm)],[f_1849_3]) ).
fof(f_1850_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_1850_2,plain,
! [U_7660,U_7659] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7659),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7660)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7659),U_7660)),
inference(variable_rename,[status(thm)],[f_1850_1]) ).
fof(f_1850_3,plain,
! [U_7660,U_7659] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7659),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7660)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7659),U_7660)),
inference(definitional_conversion,[status(esa)],[f_1850_2]) ).
cnf(f_1850_4,plain,
c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7659),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7660)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7659),U_7660)),
inference(clausify,[status(thm)],[f_1850_3]) ).
fof(f_1851_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I15_J]) ).
fof(f_1851_2,plain,
! [U_7664,U_7663,U_7662,U_7661] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7661,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7661,U_7662,U_7663)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7661,U_7663),U_7664)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7661,U_7662,U_7664)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7661),U_7663),U_7664))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7661),U_7662),U_7663))
| ~ class_Orderings_Olinorder(U_7661) ),
inference(variable_rename,[status(thm)],[f_1851_1]) ).
fof(f_1851_3,plain,
! [U_7661,U_7663,U_7662,U_7664] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7661,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7661,U_7662,U_7663)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7661,U_7663),U_7664)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7661,U_7662,U_7664)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7661),U_7663),U_7664))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7661),U_7662),U_7663))
| ~ class_Orderings_Olinorder(U_7661) ),
inference(definitional_conversion,[status(esa)],[f_1851_2]) ).
cnf(f_1851_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7661,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7661,U_7662,U_7663)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7661,U_7663),U_7664)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7661,U_7662,U_7664)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7661),U_7663),U_7664))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7661),U_7662),U_7663))
| ~ class_Orderings_Olinorder(U_7661) ),
inference(clausify,[status(thm)],[f_1851_3]) ).
fof(f_1852_1,plain,
! [V_com_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_com_Osize_I6_J]) ).
fof(f_1852_2,plain,
! [U_7666,U_7665] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_7665,U_7666)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_7666)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1852_1]) ).
fof(f_1852_3,plain,
! [U_7666,U_7665] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_7665,U_7666)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_7666)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_1852_2]) ).
cnf(f_1852_4,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_7665,U_7666)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_7666)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1852_3]) ).
fof(f_1853_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_1853_2,plain,
! [U_7668,U_7667] :
( ( c_SMT_Oz3div(U_7668,U_7667) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7668),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7667)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7667)) )
& ( c_SMT_Oz3div(U_7668,U_7667) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7668),U_7667)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7667)) ) ),
inference(variable_rename,[status(thm)],[f_1853_1]) ).
fof(f_1853_3,plain,
( ! [U_7672,U_7670] :
( c_SMT_Oz3div(U_7672,U_7670) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7672),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7670)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7670)) )
& ! [U_7671,U_7669] :
( c_SMT_Oz3div(U_7671,U_7669) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7671),U_7669)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7669)) ) ),
inference(miniscope,[status(thm)],[f_1853_2]) ).
fof(f_1853_4,plain,
( ! [U_7670,U_7672] :
( c_SMT_Oz3div(U_7672,U_7670) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7672),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7670)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7670)) )
& ! [U_7671,U_7669] :
( c_SMT_Oz3div(U_7671,U_7669) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7671),U_7669)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7669)) ) ),
inference(definitional_conversion,[status(esa)],[f_1853_3]) ).
cnf(f_1853_5,plain,
( c_SMT_Oz3div(U_7671,U_7669) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7671),U_7669)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7669)) ),
inference(clausify,[status(thm)],[f_1853_4]) ).
cnf(f_1853_6,plain,
( c_SMT_Oz3div(U_7672,U_7670) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7672),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7670)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7670)) ),
inference(clausify,[status(thm)],[f_1853_4]) ).
fof(f_1854_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I4_J]) ).
fof(f_1854_2,plain,
! [U_7675,U_7674,U_7673] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7673,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7673,U_7674,U_7675)),hAPP(hAPP(c_Set_Oinsert(U_7673),U_7675),c_Orderings_Obot__class_Obot(tc_fun(U_7673,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7673,U_7674,U_7675)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7673),U_7674),U_7675))
| ~ class_Orderings_Olinorder(U_7673) ),
inference(variable_rename,[status(thm)],[f_1854_1]) ).
fof(f_1854_3,plain,
! [U_7673,U_7674,U_7675] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7673,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7673,U_7674,U_7675)),hAPP(hAPP(c_Set_Oinsert(U_7673),U_7675),c_Orderings_Obot__class_Obot(tc_fun(U_7673,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7673,U_7674,U_7675)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7673),U_7674),U_7675))
| ~ class_Orderings_Olinorder(U_7673) ),
inference(definitional_conversion,[status(esa)],[f_1854_2]) ).
cnf(f_1854_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7673,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7673,U_7674,U_7675)),hAPP(hAPP(c_Set_Oinsert(U_7673),U_7675),c_Orderings_Obot__class_Obot(tc_fun(U_7673,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7673,U_7674,U_7675)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7673),U_7674),U_7675))
| ~ class_Orderings_Olinorder(U_7673) ),
inference(clausify,[status(thm)],[f_1854_3]) ).
fof(f_1855_1,plain,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_c,V_A_2)),c_Predicate_OPowp(T_c,V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Powp__mono]) ).
fof(f_1855_2,plain,
! [U_7678,U_7677,U_7676] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7676,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_7676,U_7677)),c_Predicate_OPowp(U_7676,U_7678)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7676,tc_HOL_Obool)),U_7677),U_7678)) ),
inference(variable_rename,[status(thm)],[f_1855_1]) ).
fof(f_1855_3,plain,
! [U_7676,U_7677,U_7678] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7676,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_7676,U_7677)),c_Predicate_OPowp(U_7676,U_7678)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7676,tc_HOL_Obool)),U_7677),U_7678)) ),
inference(definitional_conversion,[status(esa)],[f_1855_2]) ).
cnf(f_1855_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7676,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_7676,U_7677)),c_Predicate_OPowp(U_7676,U_7678)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7676,tc_HOL_Obool)),U_7677),U_7678)) ),
inference(clausify,[status(thm)],[f_1855_3]) ).
fof(f_1856_1,plain,
! [V_B_2,T_d,V_A_2,T_c] :
( ( hAPP(c_Finite__Set_Ocard(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) )
& ( hAPP(c_Finite__Set_Ocard(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_card__Plus__conv__if]) ).
fof(f_1856_2,plain,
! [U_7682,U_7681,U_7680,U_7679] :
( ( hAPP(c_Finite__Set_Ocard(tc_sum(U_7679,U_7681)),c_Sum__Type_OPlus(U_7679,U_7681,U_7680,U_7682)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7681),U_7682))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_7679),U_7680)) ) )
& ( hAPP(c_Finite__Set_Ocard(tc_sum(U_7679,U_7681)),c_Sum__Type_OPlus(U_7679,U_7681,U_7680,U_7682)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7679),U_7680)),hAPP(c_Finite__Set_Ocard(U_7681),U_7682))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7681),U_7682))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7679),U_7680)) ) ),
inference(variable_rename,[status(thm)],[f_1856_1]) ).
fof(f_1856_3,plain,
( ! [U_7690,U_7688,U_7686,U_7684] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_7684,U_7688)),c_Sum__Type_OPlus(U_7684,U_7688,U_7686,U_7690)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7688),U_7690))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_7684),U_7686)) ) )
& ! [U_7689,U_7687,U_7685,U_7683] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_7683,U_7687)),c_Sum__Type_OPlus(U_7683,U_7687,U_7685,U_7689)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7683),U_7685)),hAPP(c_Finite__Set_Ocard(U_7687),U_7689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7687),U_7689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7683),U_7685)) ) ),
inference(miniscope,[status(thm)],[f_1856_2]) ).
fof(f_1856_4,plain,
( ! [U_7684,U_7686,U_7688,U_7690] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7688),U_7690))
| ~ sP451(U_7684,U_7686,U_7688,U_7690) )
& ! [U_7684,U_7686,U_7688,U_7690] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7684),U_7686))
| ~ sP451(U_7684,U_7686,U_7688,U_7690) )
& ! [U_7684,U_7686,U_7688,U_7690] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_7684,U_7688)),c_Sum__Type_OPlus(U_7684,U_7688,U_7686,U_7690)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP451(U_7684,U_7686,U_7688,U_7690) )
& ! [U_7683,U_7685,U_7687,U_7689] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_7683,U_7687)),c_Sum__Type_OPlus(U_7683,U_7687,U_7685,U_7689)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7683),U_7685)),hAPP(c_Finite__Set_Ocard(U_7687),U_7689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7687),U_7689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7683),U_7685)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP451])],[f_1856_3]) ).
cnf(f_1856_5,plain,
( hAPP(c_Finite__Set_Ocard(tc_sum(U_7683,U_7687)),c_Sum__Type_OPlus(U_7683,U_7687,U_7685,U_7689)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7683),U_7685)),hAPP(c_Finite__Set_Ocard(U_7687),U_7689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7687),U_7689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7683),U_7685)) ),
inference(clausify,[status(thm)],[f_1856_4]) ).
cnf(f_1856_6,plain,
( hAPP(c_Finite__Set_Ocard(tc_sum(U_7684,U_7688)),c_Sum__Type_OPlus(U_7684,U_7688,U_7686,U_7690)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP451(U_7684,U_7686,U_7688,U_7690) ),
inference(clausify,[status(thm)],[f_1856_4]) ).
cnf(f_1856_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7684),U_7686))
| ~ sP451(U_7684,U_7686,U_7688,U_7690) ),
inference(clausify,[status(thm)],[f_1856_4]) ).
cnf(f_1856_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7688),U_7690))
| ~ sP451(U_7684,U_7686,U_7688,U_7690) ),
inference(clausify,[status(thm)],[f_1856_4]) ).
fof(f_1857_1,plain,
! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_com_Osize_I12_J]) ).
fof(f_1857_2,plain,
! [U_7692,U_7691] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_7691,U_7692)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_7691)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_7692))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1857_1]) ).
fof(f_1857_3,plain,
! [U_7692,U_7691] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_7691,U_7692)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_7691)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_7692))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_1857_2]) ).
cnf(f_1857_4,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_7691,U_7692)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_7691)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_7692))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1857_3]) ).
fof(f_1858_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_1858_2,plain,
! [U_7694,U_7693] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7693,U_7694))),
inference(variable_rename,[status(thm)],[f_1858_1]) ).
fof(f_1858_3,plain,
! [U_7693,U_7694] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7693,U_7694))),
inference(definitional_conversion,[status(esa)],[f_1858_2]) ).
cnf(f_1858_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7693,U_7694))),
inference(clausify,[status(thm)],[f_1858_3]) ).
fof(f_1859_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_1859_2,plain,
! [U_7696,U_7695] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7695,U_7696))),
inference(variable_rename,[status(thm)],[f_1859_1]) ).
fof(f_1859_3,plain,
! [U_7695,U_7696] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7695,U_7696))),
inference(definitional_conversion,[status(esa)],[f_1859_2]) ).
cnf(f_1859_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7695,U_7696))),
inference(clausify,[status(thm)],[f_1859_3]) ).
fof(f_1860_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_1860_2,plain,
! [U_7699,U_7698,U_7697] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7698),U_7699)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7697),U_7698)),U_7699),
inference(variable_rename,[status(thm)],[f_1860_1]) ).
fof(f_1860_3,plain,
! [U_7697,U_7698,U_7699] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7698),U_7699)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7697),U_7698)),U_7699),
inference(definitional_conversion,[status(esa)],[f_1860_2]) ).
cnf(f_1860_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7698),U_7699)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7697),U_7698)),U_7699),
inference(clausify,[status(thm)],[f_1860_3]) ).
fof(f_1861_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_1861_2,plain,
! [U_7701,U_7700] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7700),U_7701)),U_7700)),
inference(variable_rename,[status(thm)],[f_1861_1]) ).
fof(f_1861_3,plain,
! [U_7700,U_7701] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7700),U_7701)),U_7700)),
inference(definitional_conversion,[status(esa)],[f_1861_2]) ).
cnf(f_1861_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_7700),U_7701)),U_7700)),
inference(clausify,[status(thm)],[f_1861_3]) ).
fof(f_1862_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_1862_2,plain,
! [U_7704,U_7703,U_7702] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7702),U_7704)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7703),U_7704)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7702),U_7703)) ),
inference(variable_rename,[status(thm)],[f_1862_1]) ).
fof(f_1862_3,plain,
! [U_7702,U_7703,U_7704] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7702),U_7704)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7703),U_7704)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7702),U_7703)) ),
inference(definitional_conversion,[status(esa)],[f_1862_2]) ).
cnf(f_1862_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_7702),U_7704)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7703),U_7704)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7702),U_7703)) ),
inference(clausify,[status(thm)],[f_1862_3]) ).
fof(f_1863_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_1863_2,plain,
! [U_7705] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7705),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_7705,
inference(variable_rename,[status(thm)],[f_1863_1]) ).
fof(f_1863_3,plain,
! [U_7705] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7705),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_7705,
inference(definitional_conversion,[status(esa)],[f_1863_2]) ).
cnf(f_1863_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7705),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_7705,
inference(clausify,[status(thm)],[f_1863_3]) ).
fof(f_1864_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_1864_2,plain,
! [U_7707,U_7706] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7706),U_7707) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7706),U_7707)) ),
inference(variable_rename,[status(thm)],[f_1864_1]) ).
fof(f_1864_3,plain,
! [U_7706,U_7707] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7706),U_7707) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7706),U_7707)) ),
inference(definitional_conversion,[status(esa)],[f_1864_2]) ).
cnf(f_1864_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7706),U_7707) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7706),U_7707)) ),
inference(clausify,[status(thm)],[f_1864_3]) ).
fof(f_1865_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_1865_2,plain,
! [U_7710,U_7709,U_7708] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7708),U_7709)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7708),U_7710)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7709),U_7710)
| U_7708 = 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_7708),U_7709)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7708),U_7710)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7708 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1865_1]) ).
fof(f_1865_3,plain,
( ! [U_7716,U_7714,U_7712] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7714)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7716)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7714),U_7716)
| U_7712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_7715,U_7713,U_7711] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7711),U_7713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7711),U_7715)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7711 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1865_2]) ).
fof(f_1865_4,plain,
( ! [U_7714,U_7712,U_7716] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7714)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7716)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7714),U_7716)
| U_7712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_7711,U_7713,U_7715] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7711),U_7713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7711),U_7715)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7711 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1865_3]) ).
cnf(f_1865_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7711),U_7713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7711),U_7715)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7711 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1865_4]) ).
cnf(f_1865_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7714)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7716)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7714),U_7716)
| U_7712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1865_4]) ).
fof(f_1866_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_1866_2,plain,
! [U_7718,U_7717] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7717),U_7718)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7717)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7718)),
inference(variable_rename,[status(thm)],[f_1866_1]) ).
fof(f_1866_3,plain,
! [U_7717,U_7718] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7717),U_7718)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7717)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7718)),
inference(definitional_conversion,[status(esa)],[f_1866_2]) ).
cnf(f_1866_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7717),U_7718)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7717)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7718)),
inference(clausify,[status(thm)],[f_1866_3]) ).
fof(f_1867_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_1867_2,plain,
! [U_7720,U_7719] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7719)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7720)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7719),U_7720)),
inference(variable_rename,[status(thm)],[f_1867_1]) ).
fof(f_1867_3,plain,
! [U_7719,U_7720] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7719)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7720)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7719),U_7720)),
inference(definitional_conversion,[status(esa)],[f_1867_2]) ).
cnf(f_1867_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7719)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7720)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7719),U_7720)),
inference(clausify,[status(thm)],[f_1867_3]) ).
fof(f_1868_1,plain,
! [V_k_2,V_l_2,T_c] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_k_2))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty]) ).
fof(f_1868_2,plain,
! [U_7723,U_7722,U_7721] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_7721,U_7723,U_7722) = c_Orderings_Obot__class_Obot(tc_fun(U_7721,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7721),U_7722),U_7723))
| ~ class_Orderings_Oorder(U_7721) ),
inference(variable_rename,[status(thm)],[f_1868_1]) ).
fof(f_1868_3,plain,
! [U_7721,U_7722,U_7723] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_7721,U_7723,U_7722) = c_Orderings_Obot__class_Obot(tc_fun(U_7721,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7721),U_7722),U_7723))
| ~ class_Orderings_Oorder(U_7721) ),
inference(definitional_conversion,[status(esa)],[f_1868_2]) ).
cnf(f_1868_4,plain,
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_7721,U_7723,U_7722) = c_Orderings_Obot__class_Obot(tc_fun(U_7721,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7721),U_7722),U_7723))
| ~ class_Orderings_Oorder(U_7721) ),
inference(clausify,[status(thm)],[f_1868_3]) ).
fof(f_1869_1,plain,
! [V_l_2,V_k_2,T_c] :
( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_k_2),V_l_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_k_2),V_l_2))
| c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_k_2,V_l_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty__iff]) ).
fof(f_1869_2,plain,
! [U_7726,U_7725,U_7724] :
( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_7724,U_7725,U_7726) = c_Orderings_Obot__class_Obot(tc_fun(U_7724,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7724),U_7725),U_7726)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7724),U_7725),U_7726))
| c_SetInterval_Oord__class_OgreaterThanAtMost(U_7724,U_7725,U_7726) != c_Orderings_Obot__class_Obot(tc_fun(U_7724,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(U_7724) ),
inference(variable_rename,[status(thm)],[f_1869_1]) ).
fof(f_1869_3,plain,
( ! [U_7724,U_7725,U_7726] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_7724,U_7725,U_7726) = c_Orderings_Obot__class_Obot(tc_fun(U_7724,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7724),U_7725),U_7726))
| ~ sP452(U_7724,U_7725,U_7726) )
& ! [U_7724,U_7725,U_7726] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7724),U_7725),U_7726))
| c_SetInterval_Oord__class_OgreaterThanAtMost(U_7724,U_7725,U_7726) != c_Orderings_Obot__class_Obot(tc_fun(U_7724,tc_HOL_Obool))
| ~ sP452(U_7724,U_7725,U_7726) )
& ! [U_7724,U_7725,U_7726] :
( sP452(U_7724,U_7725,U_7726)
| ~ class_Orderings_Oorder(U_7724) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP452])],[f_1869_2]) ).
cnf(f_1869_4,plain,
( sP452(U_7724,U_7725,U_7726)
| ~ class_Orderings_Oorder(U_7724) ),
inference(clausify,[status(thm)],[f_1869_3]) ).
cnf(f_1869_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7724),U_7725),U_7726))
| c_SetInterval_Oord__class_OgreaterThanAtMost(U_7724,U_7725,U_7726) != c_Orderings_Obot__class_Obot(tc_fun(U_7724,tc_HOL_Obool))
| ~ sP452(U_7724,U_7725,U_7726) ),
inference(clausify,[status(thm)],[f_1869_3]) ).
cnf(f_1869_6,plain,
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_7724,U_7725,U_7726) = c_Orderings_Obot__class_Obot(tc_fun(U_7724,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7724),U_7725),U_7726))
| ~ sP452(U_7724,U_7725,U_7726) ),
inference(clausify,[status(thm)],[f_1869_3]) ).
fof(f_1870_1,plain,
! [V_l_2,V_k_2,T_c] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_k_2,V_l_2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_k_2),V_l_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_k_2),V_l_2))
| c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_k_2,V_l_2) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty__iff2]) ).
fof(f_1870_2,plain,
! [U_7729,U_7728,U_7727] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_7727,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7727,U_7728,U_7729)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7727),U_7728),U_7729)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7727),U_7728),U_7729))
| c_Orderings_Obot__class_Obot(tc_fun(U_7727,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_7727,U_7728,U_7729) ) )
| ~ class_Orderings_Oorder(U_7727) ),
inference(variable_rename,[status(thm)],[f_1870_1]) ).
fof(f_1870_3,plain,
( ! [U_7728,U_7727,U_7729] :
( c_Orderings_Obot__class_Obot(tc_fun(U_7727,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7727,U_7728,U_7729)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7727),U_7728),U_7729))
| ~ sP453(U_7728,U_7727,U_7729) )
& ! [U_7728,U_7727,U_7729] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7727),U_7728),U_7729))
| c_Orderings_Obot__class_Obot(tc_fun(U_7727,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_7727,U_7728,U_7729)
| ~ sP453(U_7728,U_7727,U_7729) )
& ! [U_7728,U_7727,U_7729] :
( sP453(U_7728,U_7727,U_7729)
| ~ class_Orderings_Oorder(U_7727) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP453])],[f_1870_2]) ).
cnf(f_1870_4,plain,
( sP453(U_7728,U_7727,U_7729)
| ~ class_Orderings_Oorder(U_7727) ),
inference(clausify,[status(thm)],[f_1870_3]) ).
cnf(f_1870_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7727),U_7728),U_7729))
| c_Orderings_Obot__class_Obot(tc_fun(U_7727,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_7727,U_7728,U_7729)
| ~ sP453(U_7728,U_7727,U_7729) ),
inference(clausify,[status(thm)],[f_1870_3]) ).
cnf(f_1870_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_7727,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7727,U_7728,U_7729)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7727),U_7728),U_7729))
| ~ sP453(U_7728,U_7727,U_7729) ),
inference(clausify,[status(thm)],[f_1870_3]) ).
fof(f_1871_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I20_J]) ).
fof(f_1871_2,plain,
! [U_7733,U_7732,U_7731,U_7730] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7730,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7730,U_7731,U_7732)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7730,U_7732,U_7733)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7730,U_7731,U_7733)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7730),U_7732),U_7733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7730),U_7731),U_7732))
| ~ class_Orderings_Olinorder(U_7730) ),
inference(variable_rename,[status(thm)],[f_1871_1]) ).
fof(f_1871_3,plain,
! [U_7730,U_7731,U_7732,U_7733] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7730,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7730,U_7731,U_7732)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7730,U_7732,U_7733)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7730,U_7731,U_7733)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7730),U_7732),U_7733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7730),U_7731),U_7732))
| ~ class_Orderings_Olinorder(U_7730) ),
inference(definitional_conversion,[status(esa)],[f_1871_2]) ).
cnf(f_1871_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7730,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7730,U_7731,U_7732)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7730,U_7732,U_7733)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7730,U_7731,U_7733)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7730),U_7732),U_7733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7730),U_7731),U_7732))
| ~ class_Orderings_Olinorder(U_7730) ),
inference(clausify,[status(thm)],[f_1871_3]) ).
fof(f_1872_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I14_J]) ).
fof(f_1872_2,plain,
! [U_7737,U_7736,U_7735,U_7734] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7734,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7734,U_7735,U_7736)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7734,U_7736,U_7737)) = c_Orderings_Obot__class_Obot(tc_fun(U_7734,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7734) ),
inference(variable_rename,[status(thm)],[f_1872_1]) ).
fof(f_1872_3,plain,
! [U_7734,U_7735,U_7736,U_7737] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7734,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7734,U_7735,U_7736)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7734,U_7736,U_7737)) = c_Orderings_Obot__class_Obot(tc_fun(U_7734,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7734) ),
inference(definitional_conversion,[status(esa)],[f_1872_2]) ).
cnf(f_1872_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7734,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7734,U_7735,U_7736)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7734,U_7736,U_7737)) = c_Orderings_Obot__class_Obot(tc_fun(U_7734,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7734) ),
inference(clausify,[status(thm)],[f_1872_3]) ).
fof(f_1873_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_1873_2,plain,
! [U_7740,U_7739,U_7738] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7740),U_7739)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7740),U_7738)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7738),U_7739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7738)) ),
inference(variable_rename,[status(thm)],[f_1873_1]) ).
fof(f_1873_3,plain,
! [U_7738,U_7739,U_7740] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7740),U_7739)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7740),U_7738)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7738),U_7739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7738)) ),
inference(definitional_conversion,[status(esa)],[f_1873_2]) ).
cnf(f_1873_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_7740),U_7739)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7740),U_7738)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7738),U_7739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7738)) ),
inference(clausify,[status(thm)],[f_1873_3]) ).
fof(f_1874_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_1874_2,plain,
! [U_7743,U_7742,U_7741] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7741),U_7742)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7741),U_7743)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7742),U_7743)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7741)) ),
inference(variable_rename,[status(thm)],[f_1874_1]) ).
fof(f_1874_3,plain,
! [U_7741,U_7742,U_7743] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7741),U_7742)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7741),U_7743)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7742),U_7743)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7741)) ),
inference(definitional_conversion,[status(esa)],[f_1874_2]) ).
cnf(f_1874_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7741),U_7742)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7741),U_7743)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7742),U_7743)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7741)) ),
inference(clausify,[status(thm)],[f_1874_3]) ).
fof(f_1875_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_1875_2,plain,
! [U_7745,U_7744] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7744),U_7745)),U_7744) = U_7745
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7744)) ),
inference(variable_rename,[status(thm)],[f_1875_1]) ).
fof(f_1875_3,plain,
! [U_7744,U_7745] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7744),U_7745)),U_7744) = U_7745
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7744)) ),
inference(definitional_conversion,[status(esa)],[f_1875_2]) ).
cnf(f_1875_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7744),U_7745)),U_7744) = U_7745
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7744)) ),
inference(clausify,[status(thm)],[f_1875_3]) ).
fof(f_1876_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_1876_2,plain,
! [U_7747,U_7746] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7747),U_7746)),U_7746) = U_7747
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7746)) ),
inference(variable_rename,[status(thm)],[f_1876_1]) ).
fof(f_1876_3,plain,
! [U_7746,U_7747] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7747),U_7746)),U_7746) = U_7747
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7746)) ),
inference(definitional_conversion,[status(esa)],[f_1876_2]) ).
cnf(f_1876_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7747),U_7746)),U_7746) = U_7747
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7746)) ),
inference(clausify,[status(thm)],[f_1876_3]) ).
fof(f_1877_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_1877_2,plain,
! [U_7749,U_7748] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7749),U_7748)),U_7749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7748)) ),
inference(variable_rename,[status(thm)],[f_1877_1]) ).
fof(f_1877_3,plain,
! [U_7748,U_7749] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7749),U_7748)),U_7749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7748)) ),
inference(definitional_conversion,[status(esa)],[f_1877_2]) ).
cnf(f_1877_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7749),U_7748)),U_7749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7749))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7748)) ),
inference(clausify,[status(thm)],[f_1877_3]) ).
fof(f_1878_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_1878_2,plain,
! [U_7751,U_7750] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7750,U_7751)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7751),U_7750),
inference(variable_rename,[status(thm)],[f_1878_1]) ).
fof(f_1878_3,plain,
! [U_7751,U_7750] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7750,U_7751)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7751),U_7750),
inference(definitional_conversion,[status(esa)],[f_1878_2]) ).
cnf(f_1878_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7750,U_7751)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7751),U_7750),
inference(clausify,[status(thm)],[f_1878_3]) ).
fof(f_1879_1,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_com_Osize_I9_J]) ).
fof(f_1879_2,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1879_1]) ).
cnf(f_1879_3,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1879_2]) ).
fof(f_1880_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_1880_2,plain,
! [U_7753,U_7752] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7753),U_7752) = 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_7753),U_7752)),U_7752))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7753),U_7752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7752)) ),
inference(variable_rename,[status(thm)],[f_1880_1]) ).
fof(f_1880_3,plain,
! [U_7752,U_7753] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7753),U_7752) = 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_7753),U_7752)),U_7752))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7753),U_7752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7752)) ),
inference(definitional_conversion,[status(esa)],[f_1880_2]) ).
cnf(f_1880_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7753),U_7752) = 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_7753),U_7752)),U_7752))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7753),U_7752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7752)) ),
inference(clausify,[status(thm)],[f_1880_3]) ).
fof(f_1881_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_1881_2,plain,
! [U_7755,U_7754] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7755),U_7754) = 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_7755),U_7754)),U_7754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7755),U_7754)) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7755),U_7754) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7755),U_7754)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7754)) ),
inference(variable_rename,[status(thm)],[f_1881_1]) ).
fof(f_1881_3,plain,
( ! [U_7754,U_7755] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7755),U_7754) = 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_7755),U_7754)),U_7754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7755),U_7754))
| ~ sP454(U_7754,U_7755) )
& ! [U_7754,U_7755] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7755),U_7754) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7755),U_7754))
| ~ sP454(U_7754,U_7755) )
& ! [U_7754,U_7755] :
( sP454(U_7754,U_7755)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7754)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP454])],[f_1881_2]) ).
cnf(f_1881_4,plain,
( sP454(U_7754,U_7755)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7754)) ),
inference(clausify,[status(thm)],[f_1881_3]) ).
cnf(f_1881_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7755),U_7754) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7755),U_7754))
| ~ sP454(U_7754,U_7755) ),
inference(clausify,[status(thm)],[f_1881_3]) ).
cnf(f_1881_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7755),U_7754) = 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_7755),U_7754)),U_7754))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7755),U_7754))
| ~ sP454(U_7754,U_7755) ),
inference(clausify,[status(thm)],[f_1881_3]) ).
fof(f_1882_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_1882_2,plain,
! [U_7762,U_7761,U_7760] :
( ( hBOOL(hAPP(U_7760,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7761),U_7762)))
| ( ? [U_7759,U_7758] :
( ~ hBOOL(hAPP(U_7760,U_7759))
& U_7761 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7762),U_7759)),U_7758)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7758),U_7762)) )
& U_7762 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7760,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7762 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [U_7757,U_7756] :
( hBOOL(hAPP(U_7760,U_7757))
| U_7761 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7762),U_7757)),U_7756)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7756),U_7762)) )
| U_7762 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7760,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7762 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7760,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7761),U_7762))) ) ),
inference(variable_rename,[status(thm)],[f_1882_1]) ).
fof(f_1882_3,plain,
( ! [U_7768,U_7766,U_7764] :
( hBOOL(hAPP(U_7764,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7766),U_7768)))
| ( ? [U_7759,U_7758] :
( ~ hBOOL(hAPP(U_7764,U_7759))
& U_7766 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7768),U_7759)),U_7758)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7758),U_7768)) )
& U_7768 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7764,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_7767,U_7765,U_7763] :
( ( ( ! [U_7757,U_7756] :
( hBOOL(hAPP(U_7763,U_7757))
| U_7765 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7767),U_7757)),U_7756)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7756),U_7767)) )
| U_7767 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7767 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7765),U_7767))) ) ),
inference(miniscope,[status(thm)],[f_1882_2]) ).
fof(f_1882_4,plain,
( ! [U_7768,U_7766,U_7764] :
( hBOOL(hAPP(U_7764,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7766),U_7768)))
| ( ? [U_7758] :
( ~ hBOOL(hAPP(U_7764,sK158(U_7768,U_7766,U_7764)))
& U_7766 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7768),sK158(U_7768,U_7766,U_7764))),U_7758)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7758),U_7768)) )
& U_7768 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7764,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_7767,U_7765,U_7763] :
( ( ( ! [U_7757,U_7756] :
( hBOOL(hAPP(U_7763,U_7757))
| U_7765 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7767),U_7757)),U_7756)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7756),U_7767)) )
| U_7767 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7767 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7765),U_7767))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_7759,sK158(U_7768,U_7766,U_7764))],[f_1882_3]) ).
fof(f_1882_5,plain,
( ! [U_7768,U_7766,U_7764] :
( hBOOL(hAPP(U_7764,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7766),U_7768)))
| ( ~ hBOOL(hAPP(U_7764,sK158(U_7768,U_7766,U_7764)))
& U_7766 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7768),sK158(U_7768,U_7766,U_7764))),sK159(U_7768,U_7766,U_7764))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK159(U_7768,U_7766,U_7764)),U_7768))
& U_7768 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_7764,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_7767,U_7765,U_7763] :
( ( ( ! [U_7757,U_7756] :
( hBOOL(hAPP(U_7763,U_7757))
| U_7765 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7767),U_7757)),U_7756)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7756),U_7767)) )
| U_7767 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_7763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7767 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_7763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7765),U_7767))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_7758,sK159(U_7768,U_7766,U_7764))],[f_1882_4]) ).
fof(f_1882_6,plain,
( ! [U_7766,U_7764,U_7768] :
( ~ hBOOL(hAPP(U_7764,sK158(U_7768,U_7766,U_7764)))
| ~ sP457(U_7766,U_7764,U_7768) )
& ! [U_7766,U_7764,U_7768] :
( U_7766 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7768),sK158(U_7768,U_7766,U_7764))),sK159(U_7768,U_7766,U_7764))
| ~ sP457(U_7766,U_7764,U_7768) )
& ! [U_7766,U_7764,U_7768] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK159(U_7768,U_7766,U_7764)),U_7768))
| ~ sP457(U_7766,U_7764,U_7768) )
& ! [U_7766,U_7764,U_7768] :
( U_7768 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP457(U_7766,U_7764,U_7768) )
& ! [U_7764,U_7768] :
( ~ hBOOL(hAPP(U_7764,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP456(U_7764,U_7768) )
& ! [U_7764,U_7768] :
( U_7768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP456(U_7764,U_7768) )
& ! [U_7756,U_7757,U_7767,U_7763,U_7765] :
( hBOOL(hAPP(U_7763,U_7757))
| U_7765 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7767),U_7757)),U_7756)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7756),U_7767))
| U_7767 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP455(U_7756,U_7757,U_7767,U_7763,U_7765) )
& ! [U_7756,U_7757,U_7767,U_7763,U_7765] :
( hBOOL(hAPP(U_7763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7767 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP455(U_7756,U_7757,U_7767,U_7763,U_7765) )
& ! [U_7766,U_7764,U_7768] :
( hBOOL(hAPP(U_7764,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7766),U_7768)))
| sP457(U_7766,U_7764,U_7768)
| sP456(U_7764,U_7768) )
& ! [U_7756,U_7757,U_7767,U_7763,U_7765] :
( sP455(U_7756,U_7757,U_7767,U_7763,U_7765)
| ~ hBOOL(hAPP(U_7763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7765),U_7767))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP455,sP456,sP457])],[f_1882_5]) ).
cnf(f_1882_7,plain,
( sP455(U_7756,U_7757,U_7767,U_7763,U_7765)
| ~ hBOOL(hAPP(U_7763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7765),U_7767))) ),
inference(clausify,[status(thm)],[f_1882_6]) ).
cnf(f_1882_8,plain,
( hBOOL(hAPP(U_7764,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7766),U_7768)))
| sP457(U_7766,U_7764,U_7768)
| sP456(U_7764,U_7768) ),
inference(clausify,[status(thm)],[f_1882_6]) ).
cnf(f_1882_9,plain,
( hBOOL(hAPP(U_7763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7767 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP455(U_7756,U_7757,U_7767,U_7763,U_7765) ),
inference(clausify,[status(thm)],[f_1882_6]) ).
cnf(f_1882_10,plain,
( hBOOL(hAPP(U_7763,U_7757))
| U_7765 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7767),U_7757)),U_7756)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7756),U_7767))
| U_7767 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP455(U_7756,U_7757,U_7767,U_7763,U_7765) ),
inference(clausify,[status(thm)],[f_1882_6]) ).
cnf(f_1882_11,plain,
( U_7768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP456(U_7764,U_7768) ),
inference(clausify,[status(thm)],[f_1882_6]) ).
cnf(f_1882_12,plain,
( ~ hBOOL(hAPP(U_7764,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP456(U_7764,U_7768) ),
inference(clausify,[status(thm)],[f_1882_6]) ).
cnf(f_1882_13,plain,
( U_7768 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP457(U_7766,U_7764,U_7768) ),
inference(clausify,[status(thm)],[f_1882_6]) ).
cnf(f_1882_14,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK159(U_7768,U_7766,U_7764)),U_7768))
| ~ sP457(U_7766,U_7764,U_7768) ),
inference(clausify,[status(thm)],[f_1882_6]) ).
cnf(f_1882_15,plain,
( U_7766 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7768),sK158(U_7768,U_7766,U_7764))),sK159(U_7768,U_7766,U_7764))
| ~ sP457(U_7766,U_7764,U_7768) ),
inference(clausify,[status(thm)],[f_1882_6]) ).
cnf(f_1882_16,plain,
( ~ hBOOL(hAPP(U_7764,sK158(U_7768,U_7766,U_7764)))
| ~ sP457(U_7766,U_7764,U_7768) ),
inference(clausify,[status(thm)],[f_1882_6]) ).
fof(f_1883_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost]) ).
fof(f_1883_2,plain,
! [U_7773,U_7772,U_7771,U_7770,U_7769] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7769,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7769,U_7770,U_7771)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7769,U_7772,U_7773)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7769,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_7769),U_7770),U_7772),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_7769),U_7771),U_7773))
| ~ class_Orderings_Olinorder(U_7769) ),
inference(variable_rename,[status(thm)],[f_1883_1]) ).
fof(f_1883_3,plain,
! [U_7770,U_7771,U_7773,U_7772,U_7769] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7769,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7769,U_7770,U_7771)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7769,U_7772,U_7773)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7769,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_7769),U_7770),U_7772),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_7769),U_7771),U_7773))
| ~ class_Orderings_Olinorder(U_7769) ),
inference(definitional_conversion,[status(esa)],[f_1883_2]) ).
cnf(f_1883_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7769,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7769,U_7770,U_7771)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7769,U_7772,U_7773)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7769,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_7769),U_7770),U_7772),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_7769),U_7771),U_7773))
| ~ class_Orderings_Olinorder(U_7769) ),
inference(clausify,[status(thm)],[f_1883_3]) ).
fof(f_1884_1,plain,
! [V_y_2,V_x_2,T_c] :
( hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan]) ).
fof(f_1884_2,plain,
! [U_7776,U_7775,U_7774] :
( hAPP(c_Set_Oimage(U_7774,U_7774,c_Groups_Ouminus__class_Ouminus(U_7774)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7774,U_7775),U_7776)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7774,hAPP(c_Groups_Ouminus__class_Ouminus(U_7774),U_7776),hAPP(c_Groups_Ouminus__class_Ouminus(U_7774),U_7775))
| ~ class_Groups_Oordered__ab__group__add(U_7774) ),
inference(variable_rename,[status(thm)],[f_1884_1]) ).
fof(f_1884_3,plain,
! [U_7774,U_7775,U_7776] :
( hAPP(c_Set_Oimage(U_7774,U_7774,c_Groups_Ouminus__class_Ouminus(U_7774)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7774,U_7775),U_7776)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7774,hAPP(c_Groups_Ouminus__class_Ouminus(U_7774),U_7776),hAPP(c_Groups_Ouminus__class_Ouminus(U_7774),U_7775))
| ~ class_Groups_Oordered__ab__group__add(U_7774) ),
inference(definitional_conversion,[status(esa)],[f_1884_2]) ).
cnf(f_1884_4,plain,
( hAPP(c_Set_Oimage(U_7774,U_7774,c_Groups_Ouminus__class_Ouminus(U_7774)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7774,U_7775),U_7776)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7774,hAPP(c_Groups_Ouminus__class_Ouminus(U_7774),U_7776),hAPP(c_Groups_Ouminus__class_Ouminus(U_7774),U_7775))
| ~ class_Groups_Oordered__ab__group__add(U_7774) ),
inference(clausify,[status(thm)],[f_1884_3]) ).
fof(f_1885_1,plain,
! [V_y_2,V_x_2,T_c] :
( hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost]) ).
fof(f_1885_2,plain,
! [U_7779,U_7778,U_7777] :
( hAPP(c_Set_Oimage(U_7777,U_7777,c_Groups_Ouminus__class_Ouminus(U_7777)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7777,U_7778,U_7779)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7777,hAPP(c_Groups_Ouminus__class_Ouminus(U_7777),U_7779)),hAPP(c_Groups_Ouminus__class_Ouminus(U_7777),U_7778))
| ~ class_Groups_Oordered__ab__group__add(U_7777) ),
inference(variable_rename,[status(thm)],[f_1885_1]) ).
fof(f_1885_3,plain,
! [U_7779,U_7778,U_7777] :
( hAPP(c_Set_Oimage(U_7777,U_7777,c_Groups_Ouminus__class_Ouminus(U_7777)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7777,U_7778,U_7779)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7777,hAPP(c_Groups_Ouminus__class_Ouminus(U_7777),U_7779)),hAPP(c_Groups_Ouminus__class_Ouminus(U_7777),U_7778))
| ~ class_Groups_Oordered__ab__group__add(U_7777) ),
inference(definitional_conversion,[status(esa)],[f_1885_2]) ).
cnf(f_1885_4,plain,
( hAPP(c_Set_Oimage(U_7777,U_7777,c_Groups_Ouminus__class_Ouminus(U_7777)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7777,U_7778,U_7779)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7777,hAPP(c_Groups_Ouminus__class_Ouminus(U_7777),U_7779)),hAPP(c_Groups_Ouminus__class_Ouminus(U_7777),U_7778))
| ~ class_Groups_Oordered__ab__group__add(U_7777) ),
inference(clausify,[status(thm)],[f_1885_3]) ).
fof(f_1886_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J]) ).
fof(f_1886_2,plain,
! [U_7783,U_7782,U_7781,U_7780] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7780,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7780,U_7781,U_7782)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7780,U_7782,U_7783)) = c_Orderings_Obot__class_Obot(tc_fun(U_7780,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7780) ),
inference(variable_rename,[status(thm)],[f_1886_1]) ).
fof(f_1886_3,plain,
! [U_7780,U_7781,U_7782,U_7783] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7780,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7780,U_7781,U_7782)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7780,U_7782,U_7783)) = c_Orderings_Obot__class_Obot(tc_fun(U_7780,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7780) ),
inference(definitional_conversion,[status(esa)],[f_1886_2]) ).
cnf(f_1886_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_7780,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7780,U_7781,U_7782)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7780,U_7782,U_7783)) = c_Orderings_Obot__class_Obot(tc_fun(U_7780,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7780) ),
inference(clausify,[status(thm)],[f_1886_3]) ).
fof(f_1887_1,plain,
! [V_B_2,V_A_2,T_d,T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff]) ).
fof(f_1887_2,plain,
! [U_7787,U_7786,U_7785,U_7784] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7784,U_7785)),c_Sum__Type_OPlus(U_7784,U_7785,U_7786,U_7787)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7785),U_7787))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7784),U_7786)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7785),U_7787))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_7784),U_7786)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7784,U_7785)),c_Sum__Type_OPlus(U_7784,U_7785,U_7786,U_7787))) ) ),
inference(variable_rename,[status(thm)],[f_1887_1]) ).
fof(f_1887_3,plain,
( ! [U_7795,U_7793,U_7791,U_7789] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7789,U_7791)),c_Sum__Type_OPlus(U_7789,U_7791,U_7793,U_7795)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7791),U_7795))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7789),U_7793)) )
& ! [U_7794,U_7792,U_7790,U_7788] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7790),U_7794))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_7788),U_7792)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7788,U_7790)),c_Sum__Type_OPlus(U_7788,U_7790,U_7792,U_7794))) ) ),
inference(miniscope,[status(thm)],[f_1887_2]) ).
fof(f_1887_4,plain,
( ! [U_7788,U_7790,U_7794,U_7792] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7790),U_7794))
| ~ sP458(U_7788,U_7790,U_7794,U_7792) )
& ! [U_7788,U_7790,U_7794,U_7792] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7788),U_7792))
| ~ sP458(U_7788,U_7790,U_7794,U_7792) )
& ! [U_7791,U_7789,U_7795,U_7793] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7789,U_7791)),c_Sum__Type_OPlus(U_7789,U_7791,U_7793,U_7795)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7791),U_7795))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7789),U_7793)) )
& ! [U_7788,U_7790,U_7794,U_7792] :
( sP458(U_7788,U_7790,U_7794,U_7792)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7788,U_7790)),c_Sum__Type_OPlus(U_7788,U_7790,U_7792,U_7794))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP458])],[f_1887_3]) ).
cnf(f_1887_5,plain,
( sP458(U_7788,U_7790,U_7794,U_7792)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7788,U_7790)),c_Sum__Type_OPlus(U_7788,U_7790,U_7792,U_7794))) ),
inference(clausify,[status(thm)],[f_1887_4]) ).
cnf(f_1887_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7789,U_7791)),c_Sum__Type_OPlus(U_7789,U_7791,U_7793,U_7795)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7791),U_7795))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7789),U_7793)) ),
inference(clausify,[status(thm)],[f_1887_4]) ).
cnf(f_1887_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7788),U_7792))
| ~ sP458(U_7788,U_7790,U_7794,U_7792) ),
inference(clausify,[status(thm)],[f_1887_4]) ).
cnf(f_1887_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7790),U_7794))
| ~ sP458(U_7788,U_7790,U_7794,U_7792) ),
inference(clausify,[status(thm)],[f_1887_4]) ).
fof(f_1888_1,plain,
! [V_B_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Plus]) ).
fof(f_1888_2,plain,
! [U_7799,U_7798,U_7797,U_7796] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7796,U_7798)),c_Sum__Type_OPlus(U_7796,U_7798,U_7797,U_7799)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7798),U_7799))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7796),U_7797)) ),
inference(variable_rename,[status(thm)],[f_1888_1]) ).
fof(f_1888_3,plain,
! [U_7796,U_7797,U_7798,U_7799] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7796,U_7798)),c_Sum__Type_OPlus(U_7796,U_7798,U_7797,U_7799)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7798),U_7799))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7796),U_7797)) ),
inference(definitional_conversion,[status(esa)],[f_1888_2]) ).
cnf(f_1888_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7796,U_7798)),c_Sum__Type_OPlus(U_7796,U_7798,U_7797,U_7799)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7798),U_7799))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7796),U_7797)) ),
inference(clausify,[status(thm)],[f_1888_3]) ).
fof(f_1889_1,plain,
! [V_B_2,V_A_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J]) ).
fof(f_1889_2,plain,
! [U_7803,U_7802,U_7801,U_7800] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7800),U_7802))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7800,U_7801)),c_Sum__Type_OPlus(U_7800,U_7801,U_7802,U_7803))) ),
inference(variable_rename,[status(thm)],[f_1889_1]) ).
fof(f_1889_3,plain,
! [U_7800,U_7801,U_7802,U_7803] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7800),U_7802))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7800,U_7801)),c_Sum__Type_OPlus(U_7800,U_7801,U_7802,U_7803))) ),
inference(definitional_conversion,[status(esa)],[f_1889_2]) ).
cnf(f_1889_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7800),U_7802))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7800,U_7801)),c_Sum__Type_OPlus(U_7800,U_7801,U_7802,U_7803))) ),
inference(clausify,[status(thm)],[f_1889_3]) ).
fof(f_1890_1,plain,
! [V_B_2,V_A_2,T_d,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J]) ).
fof(f_1890_2,plain,
! [U_7807,U_7806,U_7805,U_7804] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7805),U_7807))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7804,U_7805)),c_Sum__Type_OPlus(U_7804,U_7805,U_7806,U_7807))) ),
inference(variable_rename,[status(thm)],[f_1890_1]) ).
fof(f_1890_3,plain,
! [U_7807,U_7806,U_7805] :
( ! [U_7804] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7804,U_7805)),c_Sum__Type_OPlus(U_7804,U_7805,U_7806,U_7807)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7805),U_7807)) ),
inference(miniscope,[status(thm)],[f_1890_2]) ).
fof(f_1890_4,plain,
! [U_7804,U_7805,U_7806,U_7807] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7804,U_7805)),c_Sum__Type_OPlus(U_7804,U_7805,U_7806,U_7807)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7805),U_7807)) ),
inference(definitional_conversion,[status(esa)],[f_1890_3]) ).
cnf(f_1890_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7804,U_7805)),c_Sum__Type_OPlus(U_7804,U_7805,U_7806,U_7807)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7805),U_7807)) ),
inference(clausify,[status(thm)],[f_1890_4]) ).
fof(f_1891_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_1891_2,plain,
! [U_7809,U_7808] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7809),U_7808) = 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_7809),U_7808)),U_7808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7808),U_7809))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7808)) ),
inference(variable_rename,[status(thm)],[f_1891_1]) ).
fof(f_1891_3,plain,
! [U_7808,U_7809] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7809),U_7808) = 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_7809),U_7808)),U_7808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7808),U_7809))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7808)) ),
inference(definitional_conversion,[status(esa)],[f_1891_2]) ).
cnf(f_1891_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7809),U_7808) = 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_7809),U_7808)),U_7808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7808),U_7809))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7808)) ),
inference(clausify,[status(thm)],[f_1891_3]) ).
fof(f_1892_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_1892_2,plain,
! [U_7814,U_7813,U_7812] :
( ( hBOOL(hAPP(U_7812,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7813),U_7814)))
| ( ! [U_7811] :
( ~ hBOOL(hAPP(U_7812,U_7811))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7814),hAPP(c_Nat_OSuc,U_7811))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7814),U_7811)),U_7813)) )
& ( ~ hBOOL(hAPP(U_7812,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7814 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ( ? [U_7810] :
( hBOOL(hAPP(U_7812,U_7810))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7814),hAPP(c_Nat_OSuc,U_7810))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7814),U_7810)),U_7813)) )
| ( hBOOL(hAPP(U_7812,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_7812,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7813),U_7814))) ) ),
inference(variable_rename,[status(thm)],[f_1892_1]) ).
fof(f_1892_3,plain,
( ! [U_7820,U_7818,U_7816] :
( hBOOL(hAPP(U_7816,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7818),U_7820)))
| ( ! [U_7811] :
( ~ hBOOL(hAPP(U_7816,U_7811))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7820),hAPP(c_Nat_OSuc,U_7811))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7820),U_7811)),U_7818)) )
& ( ~ hBOOL(hAPP(U_7816,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7820 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ! [U_7819,U_7817,U_7815] :
( ? [U_7810] :
( hBOOL(hAPP(U_7815,U_7810))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7819),hAPP(c_Nat_OSuc,U_7810))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7819),U_7810)),U_7817)) )
| ( hBOOL(hAPP(U_7815,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_7815,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7817),U_7819))) ) ),
inference(miniscope,[status(thm)],[f_1892_2]) ).
fof(f_1892_4,plain,
( ! [U_7820,U_7818,U_7816] :
( hBOOL(hAPP(U_7816,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7818),U_7820)))
| ( ! [U_7811] :
( ~ hBOOL(hAPP(U_7816,U_7811))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7820),hAPP(c_Nat_OSuc,U_7811))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7820),U_7811)),U_7818)) )
& ( ~ hBOOL(hAPP(U_7816,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7820 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ! [U_7819,U_7817,U_7815] :
( ( hBOOL(hAPP(U_7815,sK160(U_7819,U_7817,U_7815)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7819),hAPP(c_Nat_OSuc,sK160(U_7819,U_7817,U_7815)))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7819),sK160(U_7819,U_7817,U_7815))),U_7817)) )
| ( hBOOL(hAPP(U_7815,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_7819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_7815,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7817),U_7819))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_7810,sK160(U_7819,U_7817,U_7815))],[f_1892_3]) ).
fof(f_1892_5,plain,
( ! [U_7811,U_7818,U_7816,U_7820] :
( ~ hBOOL(hAPP(U_7816,U_7811))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7820),hAPP(c_Nat_OSuc,U_7811))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7820),U_7811)),U_7818))
| ~ sP461(U_7811,U_7818,U_7816,U_7820) )
& ! [U_7811,U_7818,U_7816,U_7820] :
( ~ hBOOL(hAPP(U_7816,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7820 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP461(U_7811,U_7818,U_7816,U_7820) )
& ! [U_7819,U_7815,U_7817] :
( hBOOL(hAPP(U_7815,sK160(U_7819,U_7817,U_7815)))
| ~ sP460(U_7819,U_7815,U_7817) )
& ! [U_7819,U_7815,U_7817] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7819),hAPP(c_Nat_OSuc,sK160(U_7819,U_7817,U_7815)))))
| ~ sP460(U_7819,U_7815,U_7817) )
& ! [U_7819,U_7815,U_7817] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7819),sK160(U_7819,U_7817,U_7815))),U_7817))
| ~ sP460(U_7819,U_7815,U_7817) )
& ! [U_7819,U_7815] :
( hBOOL(hAPP(U_7815,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP459(U_7819,U_7815) )
& ! [U_7819,U_7815] :
( U_7819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP459(U_7819,U_7815) )
& ! [U_7811,U_7818,U_7816,U_7820] :
( hBOOL(hAPP(U_7816,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7818),U_7820)))
| sP461(U_7811,U_7818,U_7816,U_7820) )
& ! [U_7819,U_7815,U_7817] :
( sP460(U_7819,U_7815,U_7817)
| sP459(U_7819,U_7815)
| ~ hBOOL(hAPP(U_7815,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7817),U_7819))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP459,sP460,sP461])],[f_1892_4]) ).
cnf(f_1892_6,plain,
( sP460(U_7819,U_7815,U_7817)
| sP459(U_7819,U_7815)
| ~ hBOOL(hAPP(U_7815,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7817),U_7819))) ),
inference(clausify,[status(thm)],[f_1892_5]) ).
cnf(f_1892_7,plain,
( hBOOL(hAPP(U_7816,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7818),U_7820)))
| sP461(U_7811,U_7818,U_7816,U_7820) ),
inference(clausify,[status(thm)],[f_1892_5]) ).
cnf(f_1892_8,plain,
( U_7819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP459(U_7819,U_7815) ),
inference(clausify,[status(thm)],[f_1892_5]) ).
cnf(f_1892_9,plain,
( hBOOL(hAPP(U_7815,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP459(U_7819,U_7815) ),
inference(clausify,[status(thm)],[f_1892_5]) ).
cnf(f_1892_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_7819),sK160(U_7819,U_7817,U_7815))),U_7817))
| ~ sP460(U_7819,U_7815,U_7817) ),
inference(clausify,[status(thm)],[f_1892_5]) ).
cnf(f_1892_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7819),hAPP(c_Nat_OSuc,sK160(U_7819,U_7817,U_7815)))))
| ~ sP460(U_7819,U_7815,U_7817) ),
inference(clausify,[status(thm)],[f_1892_5]) ).
cnf(f_1892_12,plain,
( hBOOL(hAPP(U_7815,sK160(U_7819,U_7817,U_7815)))
| ~ sP460(U_7819,U_7815,U_7817) ),
inference(clausify,[status(thm)],[f_1892_5]) ).
cnf(f_1892_13,plain,
( ~ hBOOL(hAPP(U_7816,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_7820 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP461(U_7811,U_7818,U_7816,U_7820) ),
inference(clausify,[status(thm)],[f_1892_5]) ).
cnf(f_1892_14,plain,
( ~ hBOOL(hAPP(U_7816,U_7811))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7820),hAPP(c_Nat_OSuc,U_7811))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7820),U_7811)),U_7818))
| ~ sP461(U_7811,U_7818,U_7816,U_7820) ),
inference(clausify,[status(thm)],[f_1892_5]) ).
fof(f_1893_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_1893_2,plain,
! [U_7823,U_7822,U_7821] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7821),hAPP(c_Nat_OSuc,U_7822))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7821),U_7822)),U_7823)) )
| U_7822 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7823),U_7821) )
& ( U_7822 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7823),U_7821)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7821),hAPP(c_Nat_OSuc,U_7822))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7821),U_7822)),U_7823)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7821)) ),
inference(variable_rename,[status(thm)],[f_1893_1]) ).
fof(f_1893_3,plain,
( ! [U_7821,U_7822,U_7823] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7821),hAPP(c_Nat_OSuc,U_7822))))
| ~ sP462(U_7821,U_7822,U_7823) )
& ! [U_7821,U_7822,U_7823] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7821),U_7822)),U_7823))
| ~ sP462(U_7821,U_7822,U_7823) )
& ! [U_7821,U_7822,U_7823] :
( sP462(U_7821,U_7822,U_7823)
| U_7822 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7823),U_7821)
| ~ sP463(U_7821,U_7822,U_7823) )
& ! [U_7821,U_7822,U_7823] :
( U_7822 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7823),U_7821)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7821),hAPP(c_Nat_OSuc,U_7822))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7821),U_7822)),U_7823))
| ~ sP463(U_7821,U_7822,U_7823) )
& ! [U_7821,U_7822,U_7823] :
( sP463(U_7821,U_7822,U_7823)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7821)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP462,sP463])],[f_1893_2]) ).
cnf(f_1893_4,plain,
( sP463(U_7821,U_7822,U_7823)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7821)) ),
inference(clausify,[status(thm)],[f_1893_3]) ).
cnf(f_1893_5,plain,
( U_7822 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7823),U_7821)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7821),hAPP(c_Nat_OSuc,U_7822))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7821),U_7822)),U_7823))
| ~ sP463(U_7821,U_7822,U_7823) ),
inference(clausify,[status(thm)],[f_1893_3]) ).
cnf(f_1893_6,plain,
( sP462(U_7821,U_7822,U_7823)
| U_7822 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7823),U_7821)
| ~ sP463(U_7821,U_7822,U_7823) ),
inference(clausify,[status(thm)],[f_1893_3]) ).
cnf(f_1893_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_7821),U_7822)),U_7823))
| ~ sP462(U_7821,U_7822,U_7823) ),
inference(clausify,[status(thm)],[f_1893_3]) ).
cnf(f_1893_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7821),hAPP(c_Nat_OSuc,U_7822))))
| ~ sP462(U_7821,U_7822,U_7823) ),
inference(clausify,[status(thm)],[f_1893_3]) ).
fof(f_1894_1,plain,
! [V_B_2,T_d,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(tc_sum(T_c,T_d)),c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)),hAPP(c_Finite__Set_Ocard(T_d),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Plus]) ).
fof(f_1894_2,plain,
! [U_7827,U_7826,U_7825,U_7824] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_7824,U_7826)),c_Sum__Type_OPlus(U_7824,U_7826,U_7825,U_7827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7824),U_7825)),hAPP(c_Finite__Set_Ocard(U_7826),U_7827))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7826),U_7827))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7824),U_7825)) ),
inference(variable_rename,[status(thm)],[f_1894_1]) ).
fof(f_1894_3,plain,
! [U_7826,U_7827,U_7825,U_7824] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_7824,U_7826)),c_Sum__Type_OPlus(U_7824,U_7826,U_7825,U_7827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7824),U_7825)),hAPP(c_Finite__Set_Ocard(U_7826),U_7827))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7826),U_7827))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7824),U_7825)) ),
inference(definitional_conversion,[status(esa)],[f_1894_2]) ).
cnf(f_1894_4,plain,
( hAPP(c_Finite__Set_Ocard(tc_sum(U_7824,U_7826)),c_Sum__Type_OPlus(U_7824,U_7826,U_7825,U_7827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7824),U_7825)),hAPP(c_Finite__Set_Ocard(U_7826),U_7827))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7826),U_7827))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7824),U_7825)) ),
inference(clausify,[status(thm)],[f_1894_3]) ).
fof(f_1895_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I16_J]) ).
fof(f_1895_2,plain,
! [U_7831,U_7830,U_7829,U_7828] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7828,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7828,U_7829,U_7830)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7828,U_7830,U_7831)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7828,U_7829,U_7831)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7828),U_7830),U_7831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7828),U_7829),U_7830))
| ~ class_Orderings_Olinorder(U_7828) ),
inference(variable_rename,[status(thm)],[f_1895_1]) ).
fof(f_1895_3,plain,
! [U_7828,U_7829,U_7830,U_7831] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7828,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7828,U_7829,U_7830)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7828,U_7830,U_7831)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7828,U_7829,U_7831)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7828),U_7830),U_7831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7828),U_7829),U_7830))
| ~ class_Orderings_Olinorder(U_7828) ),
inference(definitional_conversion,[status(esa)],[f_1895_2]) ).
cnf(f_1895_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7828,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7828,U_7829,U_7830)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7828,U_7830,U_7831)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7828,U_7829,U_7831)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7828),U_7830),U_7831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7828),U_7829),U_7830))
| ~ class_Orderings_Olinorder(U_7828) ),
inference(clausify,[status(thm)],[f_1895_3]) ).
fof(f_1896_1,plain,
! [V_com_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_com_Osize_I14_J]) ).
fof(f_1896_2,plain,
! [U_7833,U_7832] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_7832,U_7833)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_7833)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1896_1]) ).
fof(f_1896_3,plain,
! [U_7832,U_7833] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_7832,U_7833)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_7833)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_1896_2]) ).
cnf(f_1896_4,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_7832,U_7833)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_7833)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1896_3]) ).
fof(f_1897_1,plain,
! [T_d,T_c] : c_Sum__Type_OPlus(T_c,T_d,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_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_c,T_d),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_UNIV__Plus__UNIV]) ).
fof(f_1897_2,plain,
! [U_7835,U_7834] : c_Sum__Type_OPlus(U_7834,U_7835,c_Orderings_Otop__class_Otop(tc_fun(U_7834,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7835,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_7834,U_7835),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_1897_1]) ).
fof(f_1897_3,plain,
! [U_7834,U_7835] : c_Sum__Type_OPlus(U_7834,U_7835,c_Orderings_Otop__class_Otop(tc_fun(U_7834,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7835,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_7834,U_7835),tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_1897_2]) ).
cnf(f_1897_4,plain,
c_Sum__Type_OPlus(U_7834,U_7835,c_Orderings_Otop__class_Otop(tc_fun(U_7834,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_7835,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_7834,U_7835),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_1897_3]) ).
fof(f_1898_1,plain,
! [V_B_2,V_A_2,T_d,T_c] :
( ( c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_c,T_d),tc_HOL_Obool))
| V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
& V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
| c_Sum__Type_OPlus(T_c,T_d,V_A_2,V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_c,T_d),tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv]) ).
fof(f_1898_2,plain,
! [U_7839,U_7838,U_7837,U_7836] :
( ( c_Sum__Type_OPlus(U_7836,U_7837,U_7838,U_7839) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_7836,U_7837),tc_HOL_Obool))
| U_7839 != c_Orderings_Obot__class_Obot(tc_fun(U_7837,tc_HOL_Obool))
| U_7838 != c_Orderings_Obot__class_Obot(tc_fun(U_7836,tc_HOL_Obool)) )
& ( ( U_7839 = c_Orderings_Obot__class_Obot(tc_fun(U_7837,tc_HOL_Obool))
& U_7838 = c_Orderings_Obot__class_Obot(tc_fun(U_7836,tc_HOL_Obool)) )
| c_Sum__Type_OPlus(U_7836,U_7837,U_7838,U_7839) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_7836,U_7837),tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_1898_1]) ).
fof(f_1898_3,plain,
( ! [U_7847,U_7845,U_7843,U_7841] :
( c_Sum__Type_OPlus(U_7841,U_7843,U_7845,U_7847) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_7841,U_7843),tc_HOL_Obool))
| U_7847 != c_Orderings_Obot__class_Obot(tc_fun(U_7843,tc_HOL_Obool))
| U_7845 != c_Orderings_Obot__class_Obot(tc_fun(U_7841,tc_HOL_Obool)) )
& ! [U_7846,U_7844,U_7842,U_7840] :
( ( U_7846 = c_Orderings_Obot__class_Obot(tc_fun(U_7842,tc_HOL_Obool))
& U_7844 = c_Orderings_Obot__class_Obot(tc_fun(U_7840,tc_HOL_Obool)) )
| c_Sum__Type_OPlus(U_7840,U_7842,U_7844,U_7846) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_7840,U_7842),tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_1898_2]) ).
fof(f_1898_4,plain,
( ! [U_7842,U_7840,U_7844,U_7846] :
( U_7846 = c_Orderings_Obot__class_Obot(tc_fun(U_7842,tc_HOL_Obool))
| ~ sP464(U_7842,U_7840,U_7844,U_7846) )
& ! [U_7842,U_7840,U_7844,U_7846] :
( U_7844 = c_Orderings_Obot__class_Obot(tc_fun(U_7840,tc_HOL_Obool))
| ~ sP464(U_7842,U_7840,U_7844,U_7846) )
& ! [U_7845,U_7847,U_7841,U_7843] :
( c_Sum__Type_OPlus(U_7841,U_7843,U_7845,U_7847) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_7841,U_7843),tc_HOL_Obool))
| U_7847 != c_Orderings_Obot__class_Obot(tc_fun(U_7843,tc_HOL_Obool))
| U_7845 != c_Orderings_Obot__class_Obot(tc_fun(U_7841,tc_HOL_Obool)) )
& ! [U_7842,U_7840,U_7844,U_7846] :
( sP464(U_7842,U_7840,U_7844,U_7846)
| c_Sum__Type_OPlus(U_7840,U_7842,U_7844,U_7846) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_7840,U_7842),tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP464])],[f_1898_3]) ).
cnf(f_1898_5,plain,
( sP464(U_7842,U_7840,U_7844,U_7846)
| c_Sum__Type_OPlus(U_7840,U_7842,U_7844,U_7846) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_7840,U_7842),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1898_4]) ).
cnf(f_1898_6,plain,
( c_Sum__Type_OPlus(U_7841,U_7843,U_7845,U_7847) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_7841,U_7843),tc_HOL_Obool))
| U_7847 != c_Orderings_Obot__class_Obot(tc_fun(U_7843,tc_HOL_Obool))
| U_7845 != c_Orderings_Obot__class_Obot(tc_fun(U_7841,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_1898_4]) ).
cnf(f_1898_7,plain,
( U_7844 = c_Orderings_Obot__class_Obot(tc_fun(U_7840,tc_HOL_Obool))
| ~ sP464(U_7842,U_7840,U_7844,U_7846) ),
inference(clausify,[status(thm)],[f_1898_4]) ).
cnf(f_1898_8,plain,
( U_7846 = c_Orderings_Obot__class_Obot(tc_fun(U_7842,tc_HOL_Obool))
| ~ sP464(U_7842,U_7840,U_7844,U_7846) ),
inference(clausify,[status(thm)],[f_1898_4]) ).
fof(f_1899_1,plain,
! [V_a_2,V_f_2,V_A_2,T_c,T_d] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) )
| hAPP(V_f_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_d)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Fields_Ofield(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__diff1]) ).
fof(f_1899_2,plain,
! [U_7852,U_7851,U_7850,U_7849,U_7848] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7849,U_7848),U_7851),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7849,tc_HOL_Obool)),U_7850),hAPP(hAPP(c_Set_Oinsert(U_7849),U_7852),c_Orderings_Obot__class_Obot(tc_fun(U_7849,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7849,U_7848),U_7851),U_7850)
| hBOOL(hAPP(hAPP(c_member(U_7849),U_7852),U_7850)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7849,U_7848),U_7851),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7849,tc_HOL_Obool)),U_7850),hAPP(hAPP(c_Set_Oinsert(U_7849),U_7852),c_Orderings_Obot__class_Obot(tc_fun(U_7849,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7848),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7849,U_7848),U_7851),U_7850)),hAPP(U_7851,U_7852))
| ~ hBOOL(hAPP(hAPP(c_member(U_7849),U_7852),U_7850)) ) )
| hAPP(U_7851,U_7852) = c_Groups_Ozero__class_Ozero(U_7848)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7849),U_7850))
| ~ class_Fields_Ofield(U_7848) ),
inference(variable_rename,[status(thm)],[f_1899_1]) ).
fof(f_1899_3,plain,
( ! [U_7848,U_7849,U_7850,U_7851,U_7852] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7849,U_7848),U_7851),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7849,tc_HOL_Obool)),U_7850),hAPP(hAPP(c_Set_Oinsert(U_7849),U_7852),c_Orderings_Obot__class_Obot(tc_fun(U_7849,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7849,U_7848),U_7851),U_7850)
| hBOOL(hAPP(hAPP(c_member(U_7849),U_7852),U_7850))
| ~ sP465(U_7848,U_7849,U_7850,U_7851,U_7852) )
& ! [U_7848,U_7849,U_7850,U_7851,U_7852] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7849,U_7848),U_7851),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7849,tc_HOL_Obool)),U_7850),hAPP(hAPP(c_Set_Oinsert(U_7849),U_7852),c_Orderings_Obot__class_Obot(tc_fun(U_7849,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7848),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7849,U_7848),U_7851),U_7850)),hAPP(U_7851,U_7852))
| ~ hBOOL(hAPP(hAPP(c_member(U_7849),U_7852),U_7850))
| ~ sP465(U_7848,U_7849,U_7850,U_7851,U_7852) )
& ! [U_7848,U_7849,U_7850,U_7851,U_7852] :
( sP465(U_7848,U_7849,U_7850,U_7851,U_7852)
| hAPP(U_7851,U_7852) = c_Groups_Ozero__class_Ozero(U_7848)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7849),U_7850))
| ~ class_Fields_Ofield(U_7848) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP465])],[f_1899_2]) ).
cnf(f_1899_4,plain,
( sP465(U_7848,U_7849,U_7850,U_7851,U_7852)
| hAPP(U_7851,U_7852) = c_Groups_Ozero__class_Ozero(U_7848)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7849),U_7850))
| ~ class_Fields_Ofield(U_7848) ),
inference(clausify,[status(thm)],[f_1899_3]) ).
cnf(f_1899_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7849,U_7848),U_7851),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7849,tc_HOL_Obool)),U_7850),hAPP(hAPP(c_Set_Oinsert(U_7849),U_7852),c_Orderings_Obot__class_Obot(tc_fun(U_7849,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7848),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7849,U_7848),U_7851),U_7850)),hAPP(U_7851,U_7852))
| ~ hBOOL(hAPP(hAPP(c_member(U_7849),U_7852),U_7850))
| ~ sP465(U_7848,U_7849,U_7850,U_7851,U_7852) ),
inference(clausify,[status(thm)],[f_1899_3]) ).
cnf(f_1899_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7849,U_7848),U_7851),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7849,tc_HOL_Obool)),U_7850),hAPP(hAPP(c_Set_Oinsert(U_7849),U_7852),c_Orderings_Obot__class_Obot(tc_fun(U_7849,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7849,U_7848),U_7851),U_7850)
| hBOOL(hAPP(hAPP(c_member(U_7849),U_7852),U_7850))
| ~ sP465(U_7848,U_7849,U_7850,U_7851,U_7852) ),
inference(clausify,[status(thm)],[f_1899_3]) ).
fof(f_1900_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_1900_2,plain,
! [U_7853] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7853) = 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_7853)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7853)) ),
inference(variable_rename,[status(thm)],[f_1900_1]) ).
fof(f_1900_3,plain,
! [U_7853] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7853) = 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_7853)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7853)) ),
inference(definitional_conversion,[status(esa)],[f_1900_2]) ).
cnf(f_1900_4,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7853) = 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_7853)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7853)) ),
inference(clausify,[status(thm)],[f_1900_3]) ).
fof(f_1901_1,plain,
! [V_i_2,V_f_2,V_s_2,T_c,T_d] :
( hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_d)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),V_s_2))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_s_2) != c_Groups_Ozero__class_Ozero(T_d)
| ? [B_i] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_i)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_s_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_s_2))
| ~ class_Groups_Oordered__ab__group__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__0]) ).
fof(f_1901_2,plain,
! [U_7859,U_7858,U_7857,U_7856,U_7855] :
( hAPP(U_7858,U_7859) = c_Groups_Ozero__class_Ozero(U_7855)
| ~ hBOOL(hAPP(hAPP(c_member(U_7856),U_7859),U_7857))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7856,U_7855),U_7858),U_7857) != c_Groups_Ozero__class_Ozero(U_7855)
| ? [U_7854] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7855),c_Groups_Ozero__class_Ozero(U_7855)),hAPP(U_7858,U_7854)))
& hBOOL(hAPP(hAPP(c_member(U_7856),U_7854),U_7857)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7856),U_7857))
| ~ class_Groups_Oordered__ab__group__add(U_7855) ),
inference(variable_rename,[status(thm)],[f_1901_1]) ).
fof(f_1901_3,plain,
! [U_7859,U_7858,U_7857,U_7856,U_7855] :
( hAPP(U_7858,U_7859) = c_Groups_Ozero__class_Ozero(U_7855)
| ~ hBOOL(hAPP(hAPP(c_member(U_7856),U_7859),U_7857))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7856,U_7855),U_7858),U_7857) != c_Groups_Ozero__class_Ozero(U_7855)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7855),c_Groups_Ozero__class_Ozero(U_7855)),hAPP(U_7858,sK161(U_7859,U_7858,U_7857,U_7856,U_7855))))
& hBOOL(hAPP(hAPP(c_member(U_7856),sK161(U_7859,U_7858,U_7857,U_7856,U_7855)),U_7857)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7856),U_7857))
| ~ class_Groups_Oordered__ab__group__add(U_7855) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_7854,sK161(U_7859,U_7858,U_7857,U_7856,U_7855))],[f_1901_2]) ).
fof(f_1901_4,plain,
( ! [U_7855,U_7856,U_7857,U_7858,U_7859] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7855),c_Groups_Ozero__class_Ozero(U_7855)),hAPP(U_7858,sK161(U_7859,U_7858,U_7857,U_7856,U_7855))))
| ~ sP466(U_7855,U_7856,U_7857,U_7858,U_7859) )
& ! [U_7855,U_7856,U_7857,U_7858,U_7859] :
( hBOOL(hAPP(hAPP(c_member(U_7856),sK161(U_7859,U_7858,U_7857,U_7856,U_7855)),U_7857))
| ~ sP466(U_7855,U_7856,U_7857,U_7858,U_7859) )
& ! [U_7855,U_7856,U_7857,U_7858,U_7859] :
( hAPP(U_7858,U_7859) = c_Groups_Ozero__class_Ozero(U_7855)
| ~ hBOOL(hAPP(hAPP(c_member(U_7856),U_7859),U_7857))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7856,U_7855),U_7858),U_7857) != c_Groups_Ozero__class_Ozero(U_7855)
| sP466(U_7855,U_7856,U_7857,U_7858,U_7859)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7856),U_7857))
| ~ class_Groups_Oordered__ab__group__add(U_7855) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP466])],[f_1901_3]) ).
cnf(f_1901_5,plain,
( hAPP(U_7858,U_7859) = c_Groups_Ozero__class_Ozero(U_7855)
| ~ hBOOL(hAPP(hAPP(c_member(U_7856),U_7859),U_7857))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7856,U_7855),U_7858),U_7857) != c_Groups_Ozero__class_Ozero(U_7855)
| sP466(U_7855,U_7856,U_7857,U_7858,U_7859)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7856),U_7857))
| ~ class_Groups_Oordered__ab__group__add(U_7855) ),
inference(clausify,[status(thm)],[f_1901_4]) ).
cnf(f_1901_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_7856),sK161(U_7859,U_7858,U_7857,U_7856,U_7855)),U_7857))
| ~ sP466(U_7855,U_7856,U_7857,U_7858,U_7859) ),
inference(clausify,[status(thm)],[f_1901_4]) ).
cnf(f_1901_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7855),c_Groups_Ozero__class_Ozero(U_7855)),hAPP(U_7858,sK161(U_7859,U_7858,U_7857,U_7856,U_7855))))
| ~ sP466(U_7855,U_7856,U_7857,U_7858,U_7859) ),
inference(clausify,[status(thm)],[f_1901_4]) ).
fof(f_1902_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_1902_2,plain,
! [U_7863,U_7862,U_7861,U_7860] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7860),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7860),U_7861),U_7862)),U_7863) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7860),hAPP(hAPP(c_Power_Opower__class_Opower(U_7860),U_7861),U_7863)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7860),U_7862),U_7863))
| ~ class_Fields_Ofield__inverse__zero(U_7860) ),
inference(variable_rename,[status(thm)],[f_1902_1]) ).
fof(f_1902_3,plain,
! [U_7862,U_7863,U_7860,U_7861] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7860),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7860),U_7861),U_7862)),U_7863) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7860),hAPP(hAPP(c_Power_Opower__class_Opower(U_7860),U_7861),U_7863)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7860),U_7862),U_7863))
| ~ class_Fields_Ofield__inverse__zero(U_7860) ),
inference(definitional_conversion,[status(esa)],[f_1902_2]) ).
cnf(f_1902_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7860),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7860),U_7861),U_7862)),U_7863) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7860),hAPP(hAPP(c_Power_Opower__class_Opower(U_7860),U_7861),U_7863)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7860),U_7862),U_7863))
| ~ class_Fields_Ofield__inverse__zero(U_7860) ),
inference(clausify,[status(thm)],[f_1902_3]) ).
fof(f_1903_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_1903_2,plain,
! [U_7864] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7864)) = U_7864,
inference(variable_rename,[status(thm)],[f_1903_1]) ).
fof(f_1903_3,plain,
! [U_7864] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7864)) = U_7864,
inference(definitional_conversion,[status(esa)],[f_1903_2]) ).
cnf(f_1903_4,plain,
hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7864)) = U_7864,
inference(clausify,[status(thm)],[f_1903_3]) ).
fof(f_1904_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_1904_2,plain,
! [U_7866,U_7865] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7865),c_Groups_Ozero__class_Ozero(U_7865)),U_7866) = c_Groups_Ozero__class_Ozero(U_7865)
| ~ class_Rings_Odivision__ring(U_7865) ),
inference(variable_rename,[status(thm)],[f_1904_1]) ).
fof(f_1904_3,plain,
! [U_7865,U_7866] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7865),c_Groups_Ozero__class_Ozero(U_7865)),U_7866) = c_Groups_Ozero__class_Ozero(U_7865)
| ~ class_Rings_Odivision__ring(U_7865) ),
inference(definitional_conversion,[status(esa)],[f_1904_2]) ).
cnf(f_1904_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7865),c_Groups_Ozero__class_Ozero(U_7865)),U_7866) = c_Groups_Ozero__class_Ozero(U_7865)
| ~ class_Rings_Odivision__ring(U_7865) ),
inference(clausify,[status(thm)],[f_1904_3]) ).
fof(f_1905_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_1905_2,plain,
! [U_7868,U_7867] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7867),U_7868),c_Groups_Ozero__class_Ozero(U_7867)) = c_Groups_Ozero__class_Ozero(U_7867)
| ~ class_Rings_Odivision__ring__inverse__zero(U_7867) ),
inference(variable_rename,[status(thm)],[f_1905_1]) ).
fof(f_1905_3,plain,
! [U_7867,U_7868] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7867),U_7868),c_Groups_Ozero__class_Ozero(U_7867)) = c_Groups_Ozero__class_Ozero(U_7867)
| ~ class_Rings_Odivision__ring__inverse__zero(U_7867) ),
inference(definitional_conversion,[status(esa)],[f_1905_2]) ).
cnf(f_1905_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7867),U_7868),c_Groups_Ozero__class_Ozero(U_7867)) = c_Groups_Ozero__class_Ozero(U_7867)
| ~ class_Rings_Odivision__ring__inverse__zero(U_7867) ),
inference(clausify,[status(thm)],[f_1905_3]) ).
fof(f_1906_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_1906_2,plain,
! [U_7871,U_7870,U_7869] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7869),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),U_7870),U_7871)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),hAPP(c_Groups_Ouminus__class_Ouminus(U_7869),U_7870)),U_7871)
| ~ class_Rings_Odivision__ring(U_7869) ),
inference(variable_rename,[status(thm)],[f_1906_1]) ).
fof(f_1906_3,plain,
! [U_7869,U_7870,U_7871] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7869),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),U_7870),U_7871)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),hAPP(c_Groups_Ouminus__class_Ouminus(U_7869),U_7870)),U_7871)
| ~ class_Rings_Odivision__ring(U_7869) ),
inference(definitional_conversion,[status(esa)],[f_1906_2]) ).
cnf(f_1906_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7869),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),U_7870),U_7871)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7869),hAPP(c_Groups_Ouminus__class_Ouminus(U_7869),U_7870)),U_7871)
| ~ class_Rings_Odivision__ring(U_7869) ),
inference(clausify,[status(thm)],[f_1906_3]) ).
fof(f_1907_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_1907_2,plain,
! [U_7873,U_7872] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7872),U_7873),c_Groups_Oone__class_Oone(U_7872)) = U_7873
| ~ class_Rings_Odivision__ring(U_7872) ),
inference(variable_rename,[status(thm)],[f_1907_1]) ).
fof(f_1907_3,plain,
! [U_7872,U_7873] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7872),U_7873),c_Groups_Oone__class_Oone(U_7872)) = U_7873
| ~ class_Rings_Odivision__ring(U_7872) ),
inference(definitional_conversion,[status(esa)],[f_1907_2]) ).
cnf(f_1907_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7872),U_7873),c_Groups_Oone__class_Oone(U_7872)) = U_7873
| ~ class_Rings_Odivision__ring(U_7872) ),
inference(clausify,[status(thm)],[f_1907_3]) ).
fof(f_1908_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_1908_2,plain,
! [U_7877,U_7876,U_7875,U_7874] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7874),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7874),U_7875),U_7876)),U_7877) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7874),U_7875),U_7877)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7874),U_7876),U_7877))
| ~ class_Rings_Odivision__ring(U_7874) ),
inference(variable_rename,[status(thm)],[f_1908_1]) ).
fof(f_1908_3,plain,
! [U_7874,U_7875,U_7876,U_7877] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7874),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7874),U_7875),U_7876)),U_7877) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7874),U_7875),U_7877)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7874),U_7876),U_7877))
| ~ class_Rings_Odivision__ring(U_7874) ),
inference(definitional_conversion,[status(esa)],[f_1908_2]) ).
cnf(f_1908_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7874),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7874),U_7875),U_7876)),U_7877) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7874),U_7875),U_7877)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7874),U_7876),U_7877))
| ~ class_Rings_Odivision__ring(U_7874) ),
inference(clausify,[status(thm)],[f_1908_3]) ).
fof(f_1909_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_1909_2,plain,
! [U_7881,U_7880,U_7879,U_7878] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7878),U_7879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7878),U_7880),U_7881)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7878),U_7879),U_7880)),U_7881)
| ~ class_Rings_Odivision__ring(U_7878) ),
inference(variable_rename,[status(thm)],[f_1909_1]) ).
fof(f_1909_3,plain,
! [U_7878,U_7879,U_7880,U_7881] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7878),U_7879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7878),U_7880),U_7881)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7878),U_7879),U_7880)),U_7881)
| ~ class_Rings_Odivision__ring(U_7878) ),
inference(definitional_conversion,[status(esa)],[f_1909_2]) ).
cnf(f_1909_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7878),U_7879),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7878),U_7880),U_7881)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7878),U_7879),U_7880)),U_7881)
| ~ class_Rings_Odivision__ring(U_7878) ),
inference(clausify,[status(thm)],[f_1909_3]) ).
fof(f_1910_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_1910_2,plain,
! [U_7885,U_7884,U_7883,U_7882] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7882),U_7883),U_7884)),U_7885) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7882),U_7883),U_7885)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7882),U_7884),U_7885))
| ~ class_Rings_Odivision__ring(U_7882) ),
inference(variable_rename,[status(thm)],[f_1910_1]) ).
fof(f_1910_3,plain,
! [U_7882,U_7883,U_7884,U_7885] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7882),U_7883),U_7884)),U_7885) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7882),U_7883),U_7885)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7882),U_7884),U_7885))
| ~ class_Rings_Odivision__ring(U_7882) ),
inference(definitional_conversion,[status(esa)],[f_1910_2]) ).
cnf(f_1910_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7882),U_7883),U_7884)),U_7885) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7882),U_7883),U_7885)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7882),U_7884),U_7885))
| ~ class_Rings_Odivision__ring(U_7882) ),
inference(clausify,[status(thm)],[f_1910_3]) ).
fof(f_1911_1,plain,
! [V_r_2,V_A_2,V_f_2,T_d,T_c] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBC(T_d,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_d),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_r_2)),V_A_2)
| ~ class_Fields_Ofield(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__divide__distrib]) ).
fof(f_1911_2,plain,
! [U_7890,U_7889,U_7888,U_7887,U_7886] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7886),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7887,U_7886),U_7888),U_7889)),U_7890) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7887,U_7886),hAPP(hAPP(c_COMBC(U_7887,U_7886,U_7886),hAPP(hAPP(c_COMBB(U_7886,tc_fun(U_7886,U_7886),U_7887),c_Rings_Oinverse__class_Odivide(U_7886)),U_7888)),U_7890)),U_7889)
| ~ class_Fields_Ofield(U_7886) ),
inference(variable_rename,[status(thm)],[f_1911_1]) ).
fof(f_1911_3,plain,
! [U_7888,U_7889,U_7890,U_7886,U_7887] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7886),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7887,U_7886),U_7888),U_7889)),U_7890) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7887,U_7886),hAPP(hAPP(c_COMBC(U_7887,U_7886,U_7886),hAPP(hAPP(c_COMBB(U_7886,tc_fun(U_7886,U_7886),U_7887),c_Rings_Oinverse__class_Odivide(U_7886)),U_7888)),U_7890)),U_7889)
| ~ class_Fields_Ofield(U_7886) ),
inference(definitional_conversion,[status(esa)],[f_1911_2]) ).
cnf(f_1911_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7886),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7887,U_7886),U_7888),U_7889)),U_7890) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7887,U_7886),hAPP(hAPP(c_COMBC(U_7887,U_7886,U_7886),hAPP(hAPP(c_COMBB(U_7886,tc_fun(U_7886,U_7886),U_7887),c_Rings_Oinverse__class_Odivide(U_7886)),U_7888)),U_7890)),U_7889)
| ~ class_Fields_Ofield(U_7886) ),
inference(clausify,[status(thm)],[f_1911_3]) ).
fof(f_1912_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_1912_2,plain,
! [U_7894,U_7893,U_7892,U_7891] :
( U_7893 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7891),U_7894),U_7892)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7891),U_7893),U_7892) != U_7894
| U_7892 = c_Groups_Ozero__class_Ozero(U_7891)
| ~ class_Rings_Odivision__ring(U_7891) ),
inference(variable_rename,[status(thm)],[f_1912_1]) ).
fof(f_1912_3,plain,
! [U_7891,U_7892,U_7893,U_7894] :
( U_7893 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7891),U_7894),U_7892)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7891),U_7893),U_7892) != U_7894
| U_7892 = c_Groups_Ozero__class_Ozero(U_7891)
| ~ class_Rings_Odivision__ring(U_7891) ),
inference(definitional_conversion,[status(esa)],[f_1912_2]) ).
cnf(f_1912_4,plain,
( U_7893 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7891),U_7894),U_7892)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7891),U_7893),U_7892) != U_7894
| U_7892 = c_Groups_Ozero__class_Ozero(U_7891)
| ~ class_Rings_Odivision__ring(U_7891) ),
inference(clausify,[status(thm)],[f_1912_3]) ).
fof(f_1913_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_1913_2,plain,
! [U_7898,U_7897,U_7896,U_7895] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7895),U_7897),U_7896) = U_7898
| U_7897 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7895),U_7898),U_7896)
| U_7896 = c_Groups_Ozero__class_Ozero(U_7895)
| ~ class_Rings_Odivision__ring(U_7895) ),
inference(variable_rename,[status(thm)],[f_1913_1]) ).
fof(f_1913_3,plain,
! [U_7895,U_7896,U_7897,U_7898] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7895),U_7897),U_7896) = U_7898
| U_7897 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7895),U_7898),U_7896)
| U_7896 = c_Groups_Ozero__class_Ozero(U_7895)
| ~ class_Rings_Odivision__ring(U_7895) ),
inference(definitional_conversion,[status(esa)],[f_1913_2]) ).
cnf(f_1913_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7895),U_7897),U_7896) = U_7898
| U_7897 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7895),U_7898),U_7896)
| U_7896 = c_Groups_Ozero__class_Ozero(U_7895)
| ~ class_Rings_Odivision__ring(U_7895) ),
inference(clausify,[status(thm)],[f_1913_3]) ).
fof(f_1914_1,plain,
! [V_a_2,V_b_2,V_c_2,T_c] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) = V_a_2
| V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) != V_a_2 ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(T_c)
| ~ class_Rings_Odivision__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq]) ).
fof(f_1914_2,plain,
! [U_7902,U_7901,U_7900,U_7899] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7899),U_7901),U_7900) = U_7902
| U_7901 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7899),U_7902),U_7900) )
& ( U_7901 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7899),U_7902),U_7900)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7899),U_7901),U_7900) != U_7902 ) )
| U_7900 = c_Groups_Ozero__class_Ozero(U_7899)
| ~ class_Rings_Odivision__ring(U_7899) ),
inference(variable_rename,[status(thm)],[f_1914_1]) ).
fof(f_1914_3,plain,
( ! [U_7900,U_7901,U_7902,U_7899] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7899),U_7901),U_7900) = U_7902
| U_7901 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7899),U_7902),U_7900)
| ~ sP467(U_7900,U_7901,U_7902,U_7899) )
& ! [U_7900,U_7901,U_7902,U_7899] :
( U_7901 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7899),U_7902),U_7900)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7899),U_7901),U_7900) != U_7902
| ~ sP467(U_7900,U_7901,U_7902,U_7899) )
& ! [U_7900,U_7901,U_7902,U_7899] :
( sP467(U_7900,U_7901,U_7902,U_7899)
| U_7900 = c_Groups_Ozero__class_Ozero(U_7899)
| ~ class_Rings_Odivision__ring(U_7899) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP467])],[f_1914_2]) ).
cnf(f_1914_4,plain,
( sP467(U_7900,U_7901,U_7902,U_7899)
| U_7900 = c_Groups_Ozero__class_Ozero(U_7899)
| ~ class_Rings_Odivision__ring(U_7899) ),
inference(clausify,[status(thm)],[f_1914_3]) ).
cnf(f_1914_5,plain,
( U_7901 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7899),U_7902),U_7900)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7899),U_7901),U_7900) != U_7902
| ~ sP467(U_7900,U_7901,U_7902,U_7899) ),
inference(clausify,[status(thm)],[f_1914_3]) ).
cnf(f_1914_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7899),U_7901),U_7900) = U_7902
| U_7901 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7899),U_7902),U_7900)
| ~ sP467(U_7900,U_7901,U_7902,U_7899) ),
inference(clausify,[status(thm)],[f_1914_3]) ).
fof(f_1915_1,plain,
! [V_b_2,V_a_2,V_c_2,T_c] :
( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2) != V_b_2 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2) = V_b_2
| V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(T_c)
| ~ class_Rings_Odivision__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq]) ).
fof(f_1915_2,plain,
! [U_7906,U_7905,U_7904,U_7903] :
( ( ( U_7905 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7906),U_7904)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7905),U_7904) != U_7906 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7905),U_7904) = U_7906
| U_7905 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7906),U_7904) ) )
| U_7904 = c_Groups_Ozero__class_Ozero(U_7903)
| ~ class_Rings_Odivision__ring(U_7903) ),
inference(variable_rename,[status(thm)],[f_1915_1]) ).
fof(f_1915_3,plain,
( ! [U_7903,U_7905,U_7904,U_7906] :
( U_7905 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7906),U_7904)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7905),U_7904) != U_7906
| ~ sP468(U_7903,U_7905,U_7904,U_7906) )
& ! [U_7903,U_7905,U_7904,U_7906] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7905),U_7904) = U_7906
| U_7905 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7906),U_7904)
| ~ sP468(U_7903,U_7905,U_7904,U_7906) )
& ! [U_7903,U_7905,U_7904,U_7906] :
( sP468(U_7903,U_7905,U_7904,U_7906)
| U_7904 = c_Groups_Ozero__class_Ozero(U_7903)
| ~ class_Rings_Odivision__ring(U_7903) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP468])],[f_1915_2]) ).
cnf(f_1915_4,plain,
( sP468(U_7903,U_7905,U_7904,U_7906)
| U_7904 = c_Groups_Ozero__class_Ozero(U_7903)
| ~ class_Rings_Odivision__ring(U_7903) ),
inference(clausify,[status(thm)],[f_1915_3]) ).
cnf(f_1915_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7905),U_7904) = U_7906
| U_7905 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7906),U_7904)
| ~ sP468(U_7903,U_7905,U_7904,U_7906) ),
inference(clausify,[status(thm)],[f_1915_3]) ).
cnf(f_1915_6,plain,
( U_7905 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7903),U_7906),U_7904)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7903),U_7905),U_7904) != U_7906
| ~ sP468(U_7903,U_7905,U_7904,U_7906) ),
inference(clausify,[status(thm)],[f_1915_3]) ).
fof(f_1916_1,plain,
! [V_a_2,V_b_2,T_c] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_c)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2) != c_Groups_Oone__class_Oone(T_c) ) )
| V_b_2 = c_Groups_Ozero__class_Ozero(T_c)
| ~ class_Rings_Odivision__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_right__inverse__eq]) ).
fof(f_1916_2,plain,
! [U_7909,U_7908,U_7907] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7909),U_7908) = c_Groups_Oone__class_Oone(U_7907)
| U_7909 != U_7908 )
& ( U_7909 = U_7908
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7909),U_7908) != c_Groups_Oone__class_Oone(U_7907) ) )
| U_7908 = c_Groups_Ozero__class_Ozero(U_7907)
| ~ class_Rings_Odivision__ring(U_7907) ),
inference(variable_rename,[status(thm)],[f_1916_1]) ).
fof(f_1916_3,plain,
( ! [U_7909,U_7908,U_7907] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7909),U_7908) = c_Groups_Oone__class_Oone(U_7907)
| U_7909 != U_7908
| ~ sP469(U_7909,U_7908,U_7907) )
& ! [U_7909,U_7908,U_7907] :
( U_7909 = U_7908
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7909),U_7908) != c_Groups_Oone__class_Oone(U_7907)
| ~ sP469(U_7909,U_7908,U_7907) )
& ! [U_7909,U_7908,U_7907] :
( sP469(U_7909,U_7908,U_7907)
| U_7908 = c_Groups_Ozero__class_Ozero(U_7907)
| ~ class_Rings_Odivision__ring(U_7907) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP469])],[f_1916_2]) ).
cnf(f_1916_4,plain,
( sP469(U_7909,U_7908,U_7907)
| U_7908 = c_Groups_Ozero__class_Ozero(U_7907)
| ~ class_Rings_Odivision__ring(U_7907) ),
inference(clausify,[status(thm)],[f_1916_3]) ).
cnf(f_1916_5,plain,
( U_7909 = U_7908
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7909),U_7908) != c_Groups_Oone__class_Oone(U_7907)
| ~ sP469(U_7909,U_7908,U_7907) ),
inference(clausify,[status(thm)],[f_1916_3]) ).
cnf(f_1916_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7907),U_7909),U_7908) = c_Groups_Oone__class_Oone(U_7907)
| U_7909 != U_7908
| ~ sP469(U_7909,U_7908,U_7907) ),
inference(clausify,[status(thm)],[f_1916_3]) ).
fof(f_1917_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_1917_2,plain,
! [U_7911,U_7910] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7910),U_7911),U_7911) = c_Groups_Oone__class_Oone(U_7910)
| U_7911 = c_Groups_Ozero__class_Ozero(U_7910)
| ~ class_Rings_Odivision__ring(U_7910) ),
inference(variable_rename,[status(thm)],[f_1917_1]) ).
fof(f_1917_3,plain,
! [U_7911,U_7910] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7910),U_7911),U_7911) = c_Groups_Oone__class_Oone(U_7910)
| U_7911 = c_Groups_Ozero__class_Ozero(U_7910)
| ~ class_Rings_Odivision__ring(U_7910) ),
inference(definitional_conversion,[status(esa)],[f_1917_2]) ).
cnf(f_1917_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7910),U_7911),U_7911) = c_Groups_Oone__class_Oone(U_7910)
| U_7911 = c_Groups_Ozero__class_Ozero(U_7910)
| ~ class_Rings_Odivision__ring(U_7910) ),
inference(clausify,[status(thm)],[f_1917_3]) ).
fof(f_1918_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_1918_2,plain,
! [U_7913,U_7912] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7912),U_7913),U_7913) = c_Groups_Oone__class_Oone(U_7912)
| U_7913 = c_Groups_Ozero__class_Ozero(U_7912) )
& ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7912),U_7913),U_7913) = c_Groups_Ozero__class_Ozero(U_7912)
| U_7913 != c_Groups_Ozero__class_Ozero(U_7912) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(U_7912) ),
inference(variable_rename,[status(thm)],[f_1918_1]) ).
fof(f_1918_3,plain,
( ! [U_7912,U_7913] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7912),U_7913),U_7913) = c_Groups_Oone__class_Oone(U_7912)
| U_7913 = c_Groups_Ozero__class_Ozero(U_7912)
| ~ sP470(U_7912,U_7913) )
& ! [U_7912,U_7913] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7912),U_7913),U_7913) = c_Groups_Ozero__class_Ozero(U_7912)
| U_7913 != c_Groups_Ozero__class_Ozero(U_7912)
| ~ sP470(U_7912,U_7913) )
& ! [U_7912,U_7913] :
( sP470(U_7912,U_7913)
| ~ class_Rings_Odivision__ring__inverse__zero(U_7912) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP470])],[f_1918_2]) ).
cnf(f_1918_4,plain,
( sP470(U_7912,U_7913)
| ~ class_Rings_Odivision__ring__inverse__zero(U_7912) ),
inference(clausify,[status(thm)],[f_1918_3]) ).
cnf(f_1918_5,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7912),U_7913),U_7913) = c_Groups_Ozero__class_Ozero(U_7912)
| U_7913 != c_Groups_Ozero__class_Ozero(U_7912)
| ~ sP470(U_7912,U_7913) ),
inference(clausify,[status(thm)],[f_1918_3]) ).
cnf(f_1918_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7912),U_7913),U_7913) = c_Groups_Oone__class_Oone(U_7912)
| U_7913 = c_Groups_Ozero__class_Ozero(U_7912)
| ~ sP470(U_7912,U_7913) ),
inference(clausify,[status(thm)],[f_1918_3]) ).
fof(f_1919_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_1919_2,plain,
! [U_7916,U_7915,U_7914] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7914),hAPP(c_Groups_Ouminus__class_Ouminus(U_7914),U_7916)),hAPP(c_Groups_Ouminus__class_Ouminus(U_7914),U_7915)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7914),U_7916),U_7915)
| U_7915 = c_Groups_Ozero__class_Ozero(U_7914)
| ~ class_Rings_Odivision__ring(U_7914) ),
inference(variable_rename,[status(thm)],[f_1919_1]) ).
fof(f_1919_3,plain,
! [U_7916,U_7914,U_7915] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7914),hAPP(c_Groups_Ouminus__class_Ouminus(U_7914),U_7916)),hAPP(c_Groups_Ouminus__class_Ouminus(U_7914),U_7915)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7914),U_7916),U_7915)
| U_7915 = c_Groups_Ozero__class_Ozero(U_7914)
| ~ class_Rings_Odivision__ring(U_7914) ),
inference(definitional_conversion,[status(esa)],[f_1919_2]) ).
cnf(f_1919_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7914),hAPP(c_Groups_Ouminus__class_Ouminus(U_7914),U_7916)),hAPP(c_Groups_Ouminus__class_Ouminus(U_7914),U_7915)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7914),U_7916),U_7915)
| U_7915 = c_Groups_Ozero__class_Ozero(U_7914)
| ~ class_Rings_Odivision__ring(U_7914) ),
inference(clausify,[status(thm)],[f_1919_3]) ).
fof(f_1920_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_1920_2,plain,
! [U_7919,U_7918,U_7917] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7917),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7917),U_7919),U_7918)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7917),U_7919),hAPP(c_Groups_Ouminus__class_Ouminus(U_7917),U_7918))
| U_7918 = c_Groups_Ozero__class_Ozero(U_7917)
| ~ class_Rings_Odivision__ring(U_7917) ),
inference(variable_rename,[status(thm)],[f_1920_1]) ).
fof(f_1920_3,plain,
! [U_7917,U_7918,U_7919] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7917),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7917),U_7919),U_7918)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7917),U_7919),hAPP(c_Groups_Ouminus__class_Ouminus(U_7917),U_7918))
| U_7918 = c_Groups_Ozero__class_Ozero(U_7917)
| ~ class_Rings_Odivision__ring(U_7917) ),
inference(definitional_conversion,[status(esa)],[f_1920_2]) ).
cnf(f_1920_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_7917),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7917),U_7919),U_7918)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7917),U_7919),hAPP(c_Groups_Ouminus__class_Ouminus(U_7917),U_7918))
| U_7918 = c_Groups_Ozero__class_Ozero(U_7917)
| ~ class_Rings_Odivision__ring(U_7917) ),
inference(clausify,[status(thm)],[f_1920_3]) ).
fof(f_1921_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_1921_2,plain,
! [U_7923,U_7922,U_7921,U_7920] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7920),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7920),U_7922),U_7921)),U_7923) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7920),hAPP(hAPP(c_Power_Opower__class_Opower(U_7920),U_7922),U_7923)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7920),U_7921),U_7923))
| U_7921 = c_Groups_Ozero__class_Ozero(U_7920)
| ~ class_Fields_Ofield(U_7920) ),
inference(variable_rename,[status(thm)],[f_1921_1]) ).
fof(f_1921_3,plain,
! [U_7920,U_7921,U_7922,U_7923] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7920),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7920),U_7922),U_7921)),U_7923) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7920),hAPP(hAPP(c_Power_Opower__class_Opower(U_7920),U_7922),U_7923)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7920),U_7921),U_7923))
| U_7921 = c_Groups_Ozero__class_Ozero(U_7920)
| ~ class_Fields_Ofield(U_7920) ),
inference(definitional_conversion,[status(esa)],[f_1921_2]) ).
cnf(f_1921_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_7920),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7920),U_7922),U_7921)),U_7923) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7920),hAPP(hAPP(c_Power_Opower__class_Opower(U_7920),U_7922),U_7923)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7920),U_7921),U_7923))
| U_7921 = c_Groups_Ozero__class_Ozero(U_7920)
| ~ class_Fields_Ofield(U_7920) ),
inference(clausify,[status(thm)],[f_1921_3]) ).
fof(f_1922_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_1922_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_1922_1]) ).
cnf(f_1922_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_1922_2]) ).
fof(f_1923_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_1923_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_1923_1]) ).
cnf(f_1923_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_1923_2]) ).
fof(f_1924_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_1924_2,plain,
! [U_7925,U_7924] :
( ( ( hAPP(c_Int_Onat,U_7924) = hAPP(c_Int_Onat,U_7925)
| U_7924 != U_7925 )
& ( U_7924 = U_7925
| hAPP(c_Int_Onat,U_7924) != hAPP(c_Int_Onat,U_7925) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7924)) ),
inference(variable_rename,[status(thm)],[f_1924_1]) ).
fof(f_1924_3,plain,
( ! [U_7925,U_7924] :
( hAPP(c_Int_Onat,U_7924) = hAPP(c_Int_Onat,U_7925)
| U_7924 != U_7925
| ~ sP471(U_7925,U_7924) )
& ! [U_7925,U_7924] :
( U_7924 = U_7925
| hAPP(c_Int_Onat,U_7924) != hAPP(c_Int_Onat,U_7925)
| ~ sP471(U_7925,U_7924) )
& ! [U_7925,U_7924] :
( sP471(U_7925,U_7924)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7924)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP471])],[f_1924_2]) ).
cnf(f_1924_4,plain,
( sP471(U_7925,U_7924)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7924)) ),
inference(clausify,[status(thm)],[f_1924_3]) ).
cnf(f_1924_5,plain,
( U_7924 = U_7925
| hAPP(c_Int_Onat,U_7924) != hAPP(c_Int_Onat,U_7925)
| ~ sP471(U_7925,U_7924) ),
inference(clausify,[status(thm)],[f_1924_3]) ).
cnf(f_1924_6,plain,
( hAPP(c_Int_Onat,U_7924) = hAPP(c_Int_Onat,U_7925)
| U_7924 != U_7925
| ~ sP471(U_7925,U_7924) ),
inference(clausify,[status(thm)],[f_1924_3]) ).
fof(f_1925_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_1925_2,plain,
! [U_7927,U_7926] :
( ( ( hAPP(c_Int_Onat,U_7926) = hAPP(c_Int_Onat,U_7927)
| U_7926 != U_7927 )
& ( U_7926 = U_7927
| hAPP(c_Int_Onat,U_7926) != hAPP(c_Int_Onat,U_7927) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7926)) ),
inference(variable_rename,[status(thm)],[f_1925_1]) ).
fof(f_1925_3,plain,
( ! [U_7926,U_7927] :
( hAPP(c_Int_Onat,U_7926) = hAPP(c_Int_Onat,U_7927)
| U_7926 != U_7927
| ~ sP472(U_7926,U_7927) )
& ! [U_7926,U_7927] :
( U_7926 = U_7927
| hAPP(c_Int_Onat,U_7926) != hAPP(c_Int_Onat,U_7927)
| ~ sP472(U_7926,U_7927) )
& ! [U_7926,U_7927] :
( sP472(U_7926,U_7927)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7926)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP472])],[f_1925_2]) ).
cnf(f_1925_4,plain,
( sP472(U_7926,U_7927)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7926)) ),
inference(clausify,[status(thm)],[f_1925_3]) ).
cnf(f_1925_5,plain,
( U_7926 = U_7927
| hAPP(c_Int_Onat,U_7926) != hAPP(c_Int_Onat,U_7927)
| ~ sP472(U_7926,U_7927) ),
inference(clausify,[status(thm)],[f_1925_3]) ).
cnf(f_1925_6,plain,
( hAPP(c_Int_Onat,U_7926) = hAPP(c_Int_Onat,U_7927)
| U_7926 != U_7927
| ~ sP472(U_7926,U_7927) ),
inference(clausify,[status(thm)],[f_1925_3]) ).
fof(f_1926_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_1926_2,plain,
! [U_7932] :
( ( ! [U_7931] : hBOOL(hAPP(U_7932,U_7931))
| ? [U_7930] :
( ~ hBOOL(hAPP(U_7932,hAPP(c_Int_Onat,U_7930)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7930)) ) )
& ( ! [U_7929] :
( hBOOL(hAPP(U_7932,hAPP(c_Int_Onat,U_7929)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7929)) )
| ? [U_7928] : ~ hBOOL(hAPP(U_7932,U_7928)) ) ),
inference(variable_rename,[status(thm)],[f_1926_1]) ).
fof(f_1926_3,plain,
( ! [U_7934] :
( ! [U_7931] : hBOOL(hAPP(U_7934,U_7931))
| ? [U_7930] :
( ~ hBOOL(hAPP(U_7934,hAPP(c_Int_Onat,U_7930)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7930)) ) )
& ! [U_7933] :
( ! [U_7929] :
( hBOOL(hAPP(U_7933,hAPP(c_Int_Onat,U_7929)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7929)) )
| ? [U_7928] : ~ hBOOL(hAPP(U_7933,U_7928)) ) ),
inference(miniscope,[status(thm)],[f_1926_2]) ).
fof(f_1926_4,plain,
( ! [U_7934] :
( ! [U_7931] : hBOOL(hAPP(U_7934,U_7931))
| ? [U_7930] :
( ~ hBOOL(hAPP(U_7934,hAPP(c_Int_Onat,U_7930)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7930)) ) )
& ! [U_7933] :
( ! [U_7929] :
( hBOOL(hAPP(U_7933,hAPP(c_Int_Onat,U_7929)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7929)) )
| ~ hBOOL(hAPP(U_7933,sK162(U_7933))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_7928,sK162(U_7933))],[f_1926_3]) ).
fof(f_1926_5,plain,
( ! [U_7934] :
( ! [U_7931] : hBOOL(hAPP(U_7934,U_7931))
| ( ~ hBOOL(hAPP(U_7934,hAPP(c_Int_Onat,sK163(U_7934))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK163(U_7934))) ) )
& ! [U_7933] :
( ! [U_7929] :
( hBOOL(hAPP(U_7933,hAPP(c_Int_Onat,U_7929)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7929)) )
| ~ hBOOL(hAPP(U_7933,sK162(U_7933))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_7930,sK163(U_7934))],[f_1926_4]) ).
fof(f_1926_6,plain,
( ! [U_7934] :
( ~ hBOOL(hAPP(U_7934,hAPP(c_Int_Onat,sK163(U_7934))))
| ~ sP473(U_7934) )
& ! [U_7934] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK163(U_7934)))
| ~ sP473(U_7934) )
& ! [U_7931,U_7934] :
( hBOOL(hAPP(U_7934,U_7931))
| sP473(U_7934) )
& ! [U_7929,U_7933] :
( hBOOL(hAPP(U_7933,hAPP(c_Int_Onat,U_7929)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7929))
| ~ hBOOL(hAPP(U_7933,sK162(U_7933))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP473])],[f_1926_5]) ).
cnf(f_1926_7,plain,
( hBOOL(hAPP(U_7933,hAPP(c_Int_Onat,U_7929)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7929))
| ~ hBOOL(hAPP(U_7933,sK162(U_7933))) ),
inference(clausify,[status(thm)],[f_1926_6]) ).
cnf(f_1926_8,plain,
( hBOOL(hAPP(U_7934,U_7931))
| sP473(U_7934) ),
inference(clausify,[status(thm)],[f_1926_6]) ).
cnf(f_1926_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK163(U_7934)))
| ~ sP473(U_7934) ),
inference(clausify,[status(thm)],[f_1926_6]) ).
cnf(f_1926_10,plain,
( ~ hBOOL(hAPP(U_7934,hAPP(c_Int_Onat,sK163(U_7934))))
| ~ sP473(U_7934) ),
inference(clausify,[status(thm)],[f_1926_6]) ).
fof(f_1927_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_1927_2,plain,
! [U_7939] :
( ( ? [U_7938] : hBOOL(hAPP(U_7939,U_7938))
| ! [U_7937] :
( ~ hBOOL(hAPP(U_7939,hAPP(c_Int_Onat,U_7937)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7937)) ) )
& ( ? [U_7936] :
( hBOOL(hAPP(U_7939,hAPP(c_Int_Onat,U_7936)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7936)) )
| ! [U_7935] : ~ hBOOL(hAPP(U_7939,U_7935)) ) ),
inference(variable_rename,[status(thm)],[f_1927_1]) ).
fof(f_1927_3,plain,
( ! [U_7941] :
( ? [U_7938] : hBOOL(hAPP(U_7941,U_7938))
| ! [U_7937] :
( ~ hBOOL(hAPP(U_7941,hAPP(c_Int_Onat,U_7937)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7937)) ) )
& ! [U_7940] :
( ? [U_7936] :
( hBOOL(hAPP(U_7940,hAPP(c_Int_Onat,U_7936)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7936)) )
| ! [U_7935] : ~ hBOOL(hAPP(U_7940,U_7935)) ) ),
inference(miniscope,[status(thm)],[f_1927_2]) ).
fof(f_1927_4,plain,
( ! [U_7941] :
( ? [U_7938] : hBOOL(hAPP(U_7941,U_7938))
| ! [U_7937] :
( ~ hBOOL(hAPP(U_7941,hAPP(c_Int_Onat,U_7937)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7937)) ) )
& ! [U_7940] :
( ( hBOOL(hAPP(U_7940,hAPP(c_Int_Onat,sK164(U_7940))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK164(U_7940))) )
| ! [U_7935] : ~ hBOOL(hAPP(U_7940,U_7935)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_7936,sK164(U_7940))],[f_1927_3]) ).
fof(f_1927_5,plain,
( ! [U_7941] :
( hBOOL(hAPP(U_7941,sK165(U_7941)))
| ! [U_7937] :
( ~ hBOOL(hAPP(U_7941,hAPP(c_Int_Onat,U_7937)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7937)) ) )
& ! [U_7940] :
( ( hBOOL(hAPP(U_7940,hAPP(c_Int_Onat,sK164(U_7940))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK164(U_7940))) )
| ! [U_7935] : ~ hBOOL(hAPP(U_7940,U_7935)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_7938,sK165(U_7941))],[f_1927_4]) ).
fof(f_1927_6,plain,
( ! [U_7940] :
( hBOOL(hAPP(U_7940,hAPP(c_Int_Onat,sK164(U_7940))))
| ~ sP474(U_7940) )
& ! [U_7940] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK164(U_7940)))
| ~ sP474(U_7940) )
& ! [U_7937,U_7941] :
( hBOOL(hAPP(U_7941,sK165(U_7941)))
| ~ hBOOL(hAPP(U_7941,hAPP(c_Int_Onat,U_7937)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7937)) )
& ! [U_7935,U_7940] :
( sP474(U_7940)
| ~ hBOOL(hAPP(U_7940,U_7935)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP474])],[f_1927_5]) ).
cnf(f_1927_7,plain,
( sP474(U_7940)
| ~ hBOOL(hAPP(U_7940,U_7935)) ),
inference(clausify,[status(thm)],[f_1927_6]) ).
cnf(f_1927_8,plain,
( hBOOL(hAPP(U_7941,sK165(U_7941)))
| ~ hBOOL(hAPP(U_7941,hAPP(c_Int_Onat,U_7937)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7937)) ),
inference(clausify,[status(thm)],[f_1927_6]) ).
cnf(f_1927_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK164(U_7940)))
| ~ sP474(U_7940) ),
inference(clausify,[status(thm)],[f_1927_6]) ).
cnf(f_1927_10,plain,
( hBOOL(hAPP(U_7940,hAPP(c_Int_Onat,sK164(U_7940))))
| ~ sP474(U_7940) ),
inference(clausify,[status(thm)],[f_1927_6]) ).
fof(f_1928_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_1928_2,plain,
! [U_7944,U_7943,U_7942] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7942),c_Groups_Oone__class_Oone(U_7942)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7942),U_7943),U_7944)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7942),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7942),c_Groups_Oone__class_Oone(U_7942)),U_7943)),U_7944)
| ~ class_Fields_Ofield__inverse__zero(U_7942) ),
inference(variable_rename,[status(thm)],[f_1928_1]) ).
fof(f_1928_3,plain,
! [U_7943,U_7942,U_7944] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7942),c_Groups_Oone__class_Oone(U_7942)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7942),U_7943),U_7944)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7942),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7942),c_Groups_Oone__class_Oone(U_7942)),U_7943)),U_7944)
| ~ class_Fields_Ofield__inverse__zero(U_7942) ),
inference(definitional_conversion,[status(esa)],[f_1928_2]) ).
cnf(f_1928_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7942),c_Groups_Oone__class_Oone(U_7942)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7942),U_7943),U_7944)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7942),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7942),c_Groups_Oone__class_Oone(U_7942)),U_7943)),U_7944)
| ~ class_Fields_Ofield__inverse__zero(U_7942) ),
inference(clausify,[status(thm)],[f_1928_3]) ).
fof(f_1929_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_1929_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_1929_1]) ).
cnf(f_1929_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_1929_2]) ).
fof(f_1930_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_1930_2,plain,
! [U_7946,U_7945] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7945),U_7946) = 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_7945)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7946))),
inference(variable_rename,[status(thm)],[f_1930_1]) ).
fof(f_1930_3,plain,
! [U_7945,U_7946] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7945),U_7946) = 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_7945)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7946))),
inference(definitional_conversion,[status(esa)],[f_1930_2]) ).
cnf(f_1930_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7945),U_7946) = 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_7945)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7946))),
inference(clausify,[status(thm)],[f_1930_3]) ).
fof(f_1931_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_1931_2,plain,
! [U_7947] : 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_7947)) = U_7947,
inference(variable_rename,[status(thm)],[f_1931_1]) ).
fof(f_1931_3,plain,
! [U_7947] : 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_7947)) = U_7947,
inference(definitional_conversion,[status(esa)],[f_1931_2]) ).
cnf(f_1931_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_7947)) = U_7947,
inference(clausify,[status(thm)],[f_1931_3]) ).
fof(f_1932_1,plain,
! [V_g_2,V_f_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_c),c_Rings_Oinverse__class_Odivide(T_d)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_g_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Fields_Ofield__inverse__zero(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__dividef]) ).
fof(f_1932_2,plain,
! [U_7952,U_7951,U_7950,U_7949,U_7948] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7949,U_7948),hAPP(hAPP(c_COMBS(U_7949,U_7948,U_7948),hAPP(hAPP(c_COMBB(U_7948,tc_fun(U_7948,U_7948),U_7949),c_Rings_Oinverse__class_Odivide(U_7948)),U_7951)),U_7952)),U_7950) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7948),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7949,U_7948),U_7951),U_7950)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7949,U_7948),U_7952),U_7950))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7949),U_7950))
| ~ class_Fields_Ofield__inverse__zero(U_7948) ),
inference(variable_rename,[status(thm)],[f_1932_1]) ).
fof(f_1932_3,plain,
! [U_7948,U_7949,U_7950,U_7951,U_7952] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7949,U_7948),hAPP(hAPP(c_COMBS(U_7949,U_7948,U_7948),hAPP(hAPP(c_COMBB(U_7948,tc_fun(U_7948,U_7948),U_7949),c_Rings_Oinverse__class_Odivide(U_7948)),U_7951)),U_7952)),U_7950) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7948),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7949,U_7948),U_7951),U_7950)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7949,U_7948),U_7952),U_7950))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7949),U_7950))
| ~ class_Fields_Ofield__inverse__zero(U_7948) ),
inference(definitional_conversion,[status(esa)],[f_1932_2]) ).
cnf(f_1932_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7949,U_7948),hAPP(hAPP(c_COMBS(U_7949,U_7948,U_7948),hAPP(hAPP(c_COMBB(U_7948,tc_fun(U_7948,U_7948),U_7949),c_Rings_Oinverse__class_Odivide(U_7948)),U_7951)),U_7952)),U_7950) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7948),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7949,U_7948),U_7951),U_7950)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_7949,U_7948),U_7952),U_7950))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7949),U_7950))
| ~ class_Fields_Ofield__inverse__zero(U_7948) ),
inference(clausify,[status(thm)],[f_1932_3]) ).
fof(f_1933_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_1933_2,plain,
! [U_7954,U_7953] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7953,U_7954)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7954),U_7953)),
inference(variable_rename,[status(thm)],[f_1933_1]) ).
fof(f_1933_3,plain,
! [U_7954,U_7953] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7953,U_7954)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7954),U_7953)),
inference(definitional_conversion,[status(esa)],[f_1933_2]) ).
cnf(f_1933_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7953,U_7954)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7954),U_7953)),
inference(clausify,[status(thm)],[f_1933_3]) ).
fof(f_1934_1,plain,
! [V_A_2,V_f_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J]) ).
fof(f_1934_2,plain,
! [U_7957,U_7956,U_7955] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_7955),U_7956),U_7957) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_7955),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7955,tc_Int_Oint),U_7956),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7957))
| ~ class_Groups_Ocomm__monoid__mult(U_7955)
| ~ class_Groups_Ocomm__monoid__add(U_7955) ),
inference(variable_rename,[status(thm)],[f_1934_1]) ).
fof(f_1934_3,plain,
! [U_7955,U_7956,U_7957] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_7955),U_7956),U_7957) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_7955),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7955,tc_Int_Oint),U_7956),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7957))
| ~ class_Groups_Ocomm__monoid__mult(U_7955)
| ~ class_Groups_Ocomm__monoid__add(U_7955) ),
inference(definitional_conversion,[status(esa)],[f_1934_2]) ).
cnf(f_1934_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_7955),U_7956),U_7957) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_7955),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7955,tc_Int_Oint),U_7956),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7957))
| ~ class_Groups_Ocomm__monoid__mult(U_7955)
| ~ class_Groups_Ocomm__monoid__add(U_7955) ),
inference(clausify,[status(thm)],[f_1934_3]) ).
fof(f_1935_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_1935_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_1935_1]) ).
cnf(f_1935_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_1935_2]) ).
fof(f_1936_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_1936_2,plain,
! [U_7958] :
( ( hAPP(c_Int_Onat,U_7958) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7958),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7958),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_7958) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1936_1]) ).
fof(f_1936_3,plain,
( ! [U_7960] :
( hAPP(c_Int_Onat,U_7960) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7960),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7959] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7959),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_7959) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1936_2]) ).
fof(f_1936_4,plain,
( ! [U_7960] :
( hAPP(c_Int_Onat,U_7960) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7960),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_7959] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7959),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_7959) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_1936_3]) ).
cnf(f_1936_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7959),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_7959) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1936_4]) ).
cnf(f_1936_6,plain,
( hAPP(c_Int_Onat,U_7960) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7960),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1936_4]) ).
fof(f_1937_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_1937_2,plain,
! [U_7961] :
( hAPP(c_Int_Onat,U_7961) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7961),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1937_1]) ).
fof(f_1937_3,plain,
! [U_7961] :
( hAPP(c_Int_Onat,U_7961) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7961),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1937_2]) ).
cnf(f_1937_4,plain,
( hAPP(c_Int_Onat,U_7961) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7961),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1937_3]) ).
fof(f_1938_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_1938_2,plain,
! [U_7963,U_7962] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7962)),hAPP(c_Int_Onat,U_7963)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7962),U_7963))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7963)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7962),U_7963))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7963)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7962)),hAPP(c_Int_Onat,U_7963))) ) ),
inference(variable_rename,[status(thm)],[f_1938_1]) ).
fof(f_1938_3,plain,
( ! [U_7967,U_7965] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7965)),hAPP(c_Int_Onat,U_7967)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7965),U_7967))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7967)) )
& ! [U_7966,U_7964] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7964),U_7966))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7966)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7964)),hAPP(c_Int_Onat,U_7966))) ) ),
inference(miniscope,[status(thm)],[f_1938_2]) ).
fof(f_1938_4,plain,
( ! [U_7966,U_7964] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7964),U_7966))
| ~ sP475(U_7966,U_7964) )
& ! [U_7966,U_7964] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7966))
| ~ sP475(U_7966,U_7964) )
& ! [U_7967,U_7965] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7965)),hAPP(c_Int_Onat,U_7967)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7965),U_7967))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7967)) )
& ! [U_7966,U_7964] :
( sP475(U_7966,U_7964)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7964)),hAPP(c_Int_Onat,U_7966))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP475])],[f_1938_3]) ).
cnf(f_1938_5,plain,
( sP475(U_7966,U_7964)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7964)),hAPP(c_Int_Onat,U_7966))) ),
inference(clausify,[status(thm)],[f_1938_4]) ).
cnf(f_1938_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7965)),hAPP(c_Int_Onat,U_7967)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7965),U_7967))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7967)) ),
inference(clausify,[status(thm)],[f_1938_4]) ).
cnf(f_1938_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7966))
| ~ sP475(U_7966,U_7964) ),
inference(clausify,[status(thm)],[f_1938_4]) ).
cnf(f_1938_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7964),U_7966))
| ~ sP475(U_7966,U_7964) ),
inference(clausify,[status(thm)],[f_1938_4]) ).
fof(f_1939_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_1939_2,plain,
! [U_7969,U_7968] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7969)),hAPP(c_Int_Onat,U_7968)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7969),U_7968)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7969),U_7968))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7969)),hAPP(c_Int_Onat,U_7968))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7968)) ),
inference(variable_rename,[status(thm)],[f_1939_1]) ).
fof(f_1939_3,plain,
( ! [U_7968,U_7969] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7969)),hAPP(c_Int_Onat,U_7968)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7969),U_7968))
| ~ sP476(U_7968,U_7969) )
& ! [U_7968,U_7969] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7969),U_7968))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7969)),hAPP(c_Int_Onat,U_7968)))
| ~ sP476(U_7968,U_7969) )
& ! [U_7968,U_7969] :
( sP476(U_7968,U_7969)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7968)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP476])],[f_1939_2]) ).
cnf(f_1939_4,plain,
( sP476(U_7968,U_7969)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7968)) ),
inference(clausify,[status(thm)],[f_1939_3]) ).
cnf(f_1939_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7969),U_7968))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7969)),hAPP(c_Int_Onat,U_7968)))
| ~ sP476(U_7968,U_7969) ),
inference(clausify,[status(thm)],[f_1939_3]) ).
cnf(f_1939_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7969)),hAPP(c_Int_Onat,U_7968)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7969),U_7968))
| ~ sP476(U_7968,U_7969) ),
inference(clausify,[status(thm)],[f_1939_3]) ).
fof(f_1940_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_1940_2,plain,
! [U_7971,U_7970] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7970)),hAPP(c_Int_Onat,U_7971)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7970),U_7971)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7970),U_7971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7970)),hAPP(c_Int_Onat,U_7971))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7970)) ),
inference(variable_rename,[status(thm)],[f_1940_1]) ).
fof(f_1940_3,plain,
( ! [U_7971,U_7970] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7970)),hAPP(c_Int_Onat,U_7971)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7970),U_7971))
| ~ sP477(U_7971,U_7970) )
& ! [U_7971,U_7970] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7970),U_7971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7970)),hAPP(c_Int_Onat,U_7971)))
| ~ sP477(U_7971,U_7970) )
& ! [U_7971,U_7970] :
( sP477(U_7971,U_7970)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7970)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP477])],[f_1940_2]) ).
cnf(f_1940_4,plain,
( sP477(U_7971,U_7970)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7970)) ),
inference(clausify,[status(thm)],[f_1940_3]) ).
cnf(f_1940_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7970),U_7971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7970)),hAPP(c_Int_Onat,U_7971)))
| ~ sP477(U_7971,U_7970) ),
inference(clausify,[status(thm)],[f_1940_3]) ).
cnf(f_1940_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7970)),hAPP(c_Int_Onat,U_7971)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7970),U_7971))
| ~ sP477(U_7971,U_7970) ),
inference(clausify,[status(thm)],[f_1940_3]) ).
fof(f_1941_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_1941_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_1941_1]) ).
cnf(f_1941_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_1941_2]) ).
fof(f_1942_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_1942_2,plain,
! [U_7972] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7972)) = 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_7972)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7972)) = U_7972
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7972)) ) ),
inference(variable_rename,[status(thm)],[f_1942_1]) ).
fof(f_1942_3,plain,
( ! [U_7974] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7974)) = 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_7974)) )
& ! [U_7973] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7973)) = U_7973
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7973)) ) ),
inference(miniscope,[status(thm)],[f_1942_2]) ).
fof(f_1942_4,plain,
( ! [U_7974] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7974)) = 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_7974)) )
& ! [U_7973] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7973)) = U_7973
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7973)) ) ),
inference(definitional_conversion,[status(esa)],[f_1942_3]) ).
cnf(f_1942_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7973)) = U_7973
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7973)) ),
inference(clausify,[status(thm)],[f_1942_4]) ).
cnf(f_1942_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7974)) = 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_7974)) ),
inference(clausify,[status(thm)],[f_1942_4]) ).
fof(f_1943_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_1943_2,plain,
! [U_7976,U_7975] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7975) = U_7976
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7976))
| U_7975 != hAPP(c_Int_Onat,U_7976) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7976))
& U_7975 = hAPP(c_Int_Onat,U_7976) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7975) != U_7976 ) ),
inference(variable_rename,[status(thm)],[f_1943_1]) ).
fof(f_1943_3,plain,
( ! [U_7980,U_7978] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7978) = U_7980
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7980))
| U_7978 != hAPP(c_Int_Onat,U_7980) )
& ! [U_7979,U_7977] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7979))
& U_7977 = hAPP(c_Int_Onat,U_7979) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7977) != U_7979 ) ),
inference(miniscope,[status(thm)],[f_1943_2]) ).
fof(f_1943_4,plain,
( ! [U_7979,U_7977] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7979))
| ~ sP478(U_7979,U_7977) )
& ! [U_7979,U_7977] :
( U_7977 = hAPP(c_Int_Onat,U_7979)
| ~ sP478(U_7979,U_7977) )
& ! [U_7978,U_7980] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7978) = U_7980
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7980))
| U_7978 != hAPP(c_Int_Onat,U_7980) )
& ! [U_7979,U_7977] :
( sP478(U_7979,U_7977)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7977) != U_7979 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP478])],[f_1943_3]) ).
cnf(f_1943_5,plain,
( sP478(U_7979,U_7977)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7977) != U_7979 ),
inference(clausify,[status(thm)],[f_1943_4]) ).
cnf(f_1943_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7978) = U_7980
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7980))
| U_7978 != hAPP(c_Int_Onat,U_7980) ),
inference(clausify,[status(thm)],[f_1943_4]) ).
cnf(f_1943_7,plain,
( U_7977 = hAPP(c_Int_Onat,U_7979)
| ~ sP478(U_7979,U_7977) ),
inference(clausify,[status(thm)],[f_1943_4]) ).
cnf(f_1943_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7979))
| ~ sP478(U_7979,U_7977) ),
inference(clausify,[status(thm)],[f_1943_4]) ).
fof(f_1944_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_1944_2,plain,
! [U_7981] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7981)) = U_7981
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7981)) ),
inference(variable_rename,[status(thm)],[f_1944_1]) ).
fof(f_1944_3,plain,
! [U_7981] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7981)) = U_7981
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7981)) ),
inference(definitional_conversion,[status(esa)],[f_1944_2]) ).
cnf(f_1944_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7981)) = U_7981
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7981)) ),
inference(clausify,[status(thm)],[f_1944_3]) ).
fof(f_1945_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_1945_2,plain,
! [U_7983,U_7982] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7982),hAPP(c_Int_Onat,U_7983)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7982)),U_7983)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7982)),U_7983))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7982),hAPP(c_Int_Onat,U_7983))) ) ),
inference(variable_rename,[status(thm)],[f_1945_1]) ).
fof(f_1945_3,plain,
( ! [U_7987,U_7985] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7985),hAPP(c_Int_Onat,U_7987)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7985)),U_7987)) )
& ! [U_7986,U_7984] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7984)),U_7986))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7984),hAPP(c_Int_Onat,U_7986))) ) ),
inference(miniscope,[status(thm)],[f_1945_2]) ).
fof(f_1945_4,plain,
( ! [U_7985,U_7987] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7985),hAPP(c_Int_Onat,U_7987)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7985)),U_7987)) )
& ! [U_7986,U_7984] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7984)),U_7986))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7984),hAPP(c_Int_Onat,U_7986))) ) ),
inference(definitional_conversion,[status(esa)],[f_1945_3]) ).
cnf(f_1945_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_7984)),U_7986))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7984),hAPP(c_Int_Onat,U_7986))) ),
inference(clausify,[status(thm)],[f_1945_4]) ).
cnf(f_1945_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7985),hAPP(c_Int_Onat,U_7987)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7985)),U_7987)) ),
inference(clausify,[status(thm)],[f_1945_4]) ).
fof(f_1946_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_1946_2,plain,
! [U_7989,U_7988] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7988)),hAPP(c_Int_Onat,U_7989)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7988),U_7989))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7989))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7988)) ),
inference(variable_rename,[status(thm)],[f_1946_1]) ).
fof(f_1946_3,plain,
! [U_7988,U_7989] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7988)),hAPP(c_Int_Onat,U_7989)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7988),U_7989))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7989))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7988)) ),
inference(definitional_conversion,[status(esa)],[f_1946_2]) ).
cnf(f_1946_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7988)),hAPP(c_Int_Onat,U_7989)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7988),U_7989))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7989))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7988)) ),
inference(clausify,[status(thm)],[f_1946_3]) ).
fof(f_1947_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_1947_2,plain,
! [U_7991,U_7990] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7990),U_7991)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7990)),hAPP(c_Int_Onat,U_7991))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7990)) ),
inference(variable_rename,[status(thm)],[f_1947_1]) ).
fof(f_1947_3,plain,
! [U_7990,U_7991] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7990),U_7991)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7990)),hAPP(c_Int_Onat,U_7991))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7990)) ),
inference(definitional_conversion,[status(esa)],[f_1947_2]) ).
cnf(f_1947_4,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7990),U_7991)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7990)),hAPP(c_Int_Onat,U_7991))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7990)) ),
inference(clausify,[status(thm)],[f_1947_3]) ).
fof(f_1948_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_1948_2,plain,
! [U_7992] : 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_7992))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1948_1]) ).
fof(f_1948_3,plain,
! [U_7992] : 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_7992))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1948_2]) ).
cnf(f_1948_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_7992))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1948_3]) ).
fof(f_1949_1,plain,
! [V_A_2,V_f_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J]) ).
fof(f_1949_2,plain,
! [U_7995,U_7994,U_7993] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7993),U_7994),U_7995) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_7993),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7993,tc_Int_Oint),U_7994),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7995))
| ~ class_Groups_Ocomm__monoid__mult(U_7993)
| ~ class_Groups_Ocomm__monoid__add(U_7993) ),
inference(variable_rename,[status(thm)],[f_1949_1]) ).
fof(f_1949_3,plain,
! [U_7993,U_7994,U_7995] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7993),U_7994),U_7995) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_7993),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7993,tc_Int_Oint),U_7994),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7995))
| ~ class_Groups_Ocomm__monoid__mult(U_7993)
| ~ class_Groups_Ocomm__monoid__add(U_7993) ),
inference(definitional_conversion,[status(esa)],[f_1949_2]) ).
cnf(f_1949_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_7993),U_7994),U_7995) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_7993),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_7993,tc_Int_Oint),U_7994),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7995))
| ~ class_Groups_Ocomm__monoid__mult(U_7993)
| ~ class_Groups_Ocomm__monoid__add(U_7993) ),
inference(clausify,[status(thm)],[f_1949_3]) ).
fof(f_1950_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_1950_2,plain,
! [U_7996] : 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_7996)) = hAPP(c_Int_Onat,U_7996),
inference(variable_rename,[status(thm)],[f_1950_1]) ).
fof(f_1950_3,plain,
! [U_7996] : 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_7996)) = hAPP(c_Int_Onat,U_7996),
inference(definitional_conversion,[status(esa)],[f_1950_2]) ).
cnf(f_1950_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_7996)) = hAPP(c_Int_Onat,U_7996),
inference(clausify,[status(thm)],[f_1950_3]) ).
fof(f_1951_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_1951_2,plain,
! [U_7998,U_7997] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7997),U_7998)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7998),U_7997)),
inference(variable_rename,[status(thm)],[f_1951_1]) ).
fof(f_1951_3,plain,
! [U_7997,U_7998] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7997),U_7998)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7998),U_7997)),
inference(definitional_conversion,[status(esa)],[f_1951_2]) ).
cnf(f_1951_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7997),U_7998)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7998),U_7997)),
inference(clausify,[status(thm)],[f_1951_3]) ).
fof(f_1952_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_1952_2,plain,
! [U_7999] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7999)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7999)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7999))) ) ),
inference(variable_rename,[status(thm)],[f_1952_1]) ).
fof(f_1952_3,plain,
( ! [U_8001] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_8001)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8001)) )
& ! [U_8000] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_8000))) ) ),
inference(miniscope,[status(thm)],[f_1952_2]) ).
fof(f_1952_4,plain,
( ! [U_8001] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_8001)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8001)) )
& ! [U_8000] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_8000))) ) ),
inference(definitional_conversion,[status(esa)],[f_1952_3]) ).
cnf(f_1952_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_8000))) ),
inference(clausify,[status(thm)],[f_1952_4]) ).
cnf(f_1952_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_8001)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8001)) ),
inference(clausify,[status(thm)],[f_1952_4]) ).
fof(f_1953_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_1953_2,plain,
! [U_8005,U_8004,U_8003,U_8002] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8005),U_8004)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8002),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),U_8005)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),U_8004))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8004),U_8005))
| U_8003 = c_Groups_Ozero__class_Ozero(U_8002)
| ~ class_Fields_Ofield(U_8002) ),
inference(variable_rename,[status(thm)],[f_1953_1]) ).
fof(f_1953_3,plain,
! [U_8002,U_8003,U_8004,U_8005] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8005),U_8004)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8002),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),U_8005)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),U_8004))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8004),U_8005))
| U_8003 = c_Groups_Ozero__class_Ozero(U_8002)
| ~ class_Fields_Ofield(U_8002) ),
inference(definitional_conversion,[status(esa)],[f_1953_2]) ).
cnf(f_1953_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8005),U_8004)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8002),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),U_8005)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),U_8004))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8004),U_8005))
| U_8003 = c_Groups_Ozero__class_Ozero(U_8002)
| ~ class_Fields_Ofield(U_8002) ),
inference(clausify,[status(thm)],[f_1953_3]) ).
fof(f_1954_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_1954_2,plain,
! [U_8007,U_8006] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8006)),hAPP(c_Int_Onat,U_8007)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8006),U_8007)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8006),U_8007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8006)),hAPP(c_Int_Onat,U_8007))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8006)) ),
inference(variable_rename,[status(thm)],[f_1954_1]) ).
fof(f_1954_3,plain,
( ! [U_8006,U_8007] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8006)),hAPP(c_Int_Onat,U_8007)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8006),U_8007))
| ~ sP479(U_8006,U_8007) )
& ! [U_8006,U_8007] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8006),U_8007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8006)),hAPP(c_Int_Onat,U_8007)))
| ~ sP479(U_8006,U_8007) )
& ! [U_8006,U_8007] :
( sP479(U_8006,U_8007)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8006)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP479])],[f_1954_2]) ).
cnf(f_1954_4,plain,
( sP479(U_8006,U_8007)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8006)) ),
inference(clausify,[status(thm)],[f_1954_3]) ).
cnf(f_1954_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8006),U_8007))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8006)),hAPP(c_Int_Onat,U_8007)))
| ~ sP479(U_8006,U_8007) ),
inference(clausify,[status(thm)],[f_1954_3]) ).
cnf(f_1954_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8006)),hAPP(c_Int_Onat,U_8007)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8006),U_8007))
| ~ sP479(U_8006,U_8007) ),
inference(clausify,[status(thm)],[f_1954_3]) ).
fof(f_1955_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_1955_2,plain,
! [U_8009,U_8008] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8008)),hAPP(c_Int_Onat,U_8009)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8008),U_8009)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8008),U_8009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8008)),hAPP(c_Int_Onat,U_8009))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8008)) ),
inference(variable_rename,[status(thm)],[f_1955_1]) ).
fof(f_1955_3,plain,
( ! [U_8009,U_8008] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8008)),hAPP(c_Int_Onat,U_8009)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8008),U_8009))
| ~ sP480(U_8009,U_8008) )
& ! [U_8009,U_8008] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8008),U_8009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8008)),hAPP(c_Int_Onat,U_8009)))
| ~ sP480(U_8009,U_8008) )
& ! [U_8009,U_8008] :
( sP480(U_8009,U_8008)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8008)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP480])],[f_1955_2]) ).
cnf(f_1955_4,plain,
( sP480(U_8009,U_8008)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8008)) ),
inference(clausify,[status(thm)],[f_1955_3]) ).
cnf(f_1955_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8008),U_8009))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8008)),hAPP(c_Int_Onat,U_8009)))
| ~ sP480(U_8009,U_8008) ),
inference(clausify,[status(thm)],[f_1955_3]) ).
cnf(f_1955_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8008)),hAPP(c_Int_Onat,U_8009)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8008),U_8009))
| ~ sP480(U_8009,U_8008) ),
inference(clausify,[status(thm)],[f_1955_3]) ).
fof(f_1956_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_1956_2,plain,
! [U_8011,U_8010] :
( ( hAPP(c_Int_Onat,U_8010) = U_8011
| ( U_8011 != 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_8010)) )
| ( U_8010 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8011)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8010)) ) )
& ( ( ( U_8011 = 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_8010)) )
& ( U_8010 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8011)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8010)) ) )
| hAPP(c_Int_Onat,U_8010) != U_8011 ) ),
inference(variable_rename,[status(thm)],[f_1956_1]) ).
fof(f_1956_3,plain,
( ! [U_8015,U_8013] :
( hAPP(c_Int_Onat,U_8013) = U_8015
| ( U_8015 != 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_8013)) )
| ( U_8013 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8015)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8013)) ) )
& ! [U_8014,U_8012] :
( ( ( U_8014 = 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_8012)) )
& ( U_8012 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8014)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8012)) ) )
| hAPP(c_Int_Onat,U_8012) != U_8014 ) ),
inference(miniscope,[status(thm)],[f_1956_2]) ).
fof(f_1956_4,plain,
( ! [U_8015,U_8013] :
( U_8015 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP483(U_8015,U_8013) )
& ! [U_8015,U_8013] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8013))
| ~ sP483(U_8015,U_8013) )
& ! [U_8015,U_8013] :
( U_8013 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8015)
| ~ sP482(U_8015,U_8013) )
& ! [U_8015,U_8013] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8013))
| ~ sP482(U_8015,U_8013) )
& ! [U_8012,U_8014] :
( U_8014 = 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_8012))
| ~ sP481(U_8012,U_8014) )
& ! [U_8012,U_8014] :
( U_8012 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8014)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8012))
| ~ sP481(U_8012,U_8014) )
& ! [U_8015,U_8013] :
( hAPP(c_Int_Onat,U_8013) = U_8015
| sP483(U_8015,U_8013)
| sP482(U_8015,U_8013) )
& ! [U_8012,U_8014] :
( sP481(U_8012,U_8014)
| hAPP(c_Int_Onat,U_8012) != U_8014 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP481,sP482,sP483])],[f_1956_3]) ).
cnf(f_1956_5,plain,
( sP481(U_8012,U_8014)
| hAPP(c_Int_Onat,U_8012) != U_8014 ),
inference(clausify,[status(thm)],[f_1956_4]) ).
cnf(f_1956_6,plain,
( hAPP(c_Int_Onat,U_8013) = U_8015
| sP483(U_8015,U_8013)
| sP482(U_8015,U_8013) ),
inference(clausify,[status(thm)],[f_1956_4]) ).
cnf(f_1956_7,plain,
( U_8012 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8014)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8012))
| ~ sP481(U_8012,U_8014) ),
inference(clausify,[status(thm)],[f_1956_4]) ).
cnf(f_1956_8,plain,
( U_8014 = 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_8012))
| ~ sP481(U_8012,U_8014) ),
inference(clausify,[status(thm)],[f_1956_4]) ).
cnf(f_1956_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8013))
| ~ sP482(U_8015,U_8013) ),
inference(clausify,[status(thm)],[f_1956_4]) ).
cnf(f_1956_10,plain,
( U_8013 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8015)
| ~ sP482(U_8015,U_8013) ),
inference(clausify,[status(thm)],[f_1956_4]) ).
cnf(f_1956_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8013))
| ~ sP483(U_8015,U_8013) ),
inference(clausify,[status(thm)],[f_1956_4]) ).
cnf(f_1956_12,plain,
( U_8015 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP483(U_8015,U_8013) ),
inference(clausify,[status(thm)],[f_1956_4]) ).
fof(f_1957_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_1957_2,plain,
! [U_8017,U_8016] :
( ( U_8016 = hAPP(c_Int_Onat,U_8017)
| ( U_8016 != 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_8017)) )
| ( U_8017 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8016)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8017)) ) )
& ( ( ( U_8016 = 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_8017)) )
& ( U_8017 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8016)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8017)) ) )
| U_8016 != hAPP(c_Int_Onat,U_8017) ) ),
inference(variable_rename,[status(thm)],[f_1957_1]) ).
fof(f_1957_3,plain,
( ! [U_8021,U_8019] :
( U_8019 = hAPP(c_Int_Onat,U_8021)
| ( U_8019 != 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_8021)) )
| ( U_8021 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8019)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8021)) ) )
& ! [U_8020,U_8018] :
( ( ( U_8018 = 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_8020)) )
& ( U_8020 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8018)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8020)) ) )
| U_8018 != hAPP(c_Int_Onat,U_8020) ) ),
inference(miniscope,[status(thm)],[f_1957_2]) ).
fof(f_1957_4,plain,
( ! [U_8021,U_8019] :
( U_8019 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP486(U_8021,U_8019) )
& ! [U_8021,U_8019] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8021))
| ~ sP486(U_8021,U_8019) )
& ! [U_8021,U_8019] :
( U_8021 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8019)
| ~ sP485(U_8021,U_8019) )
& ! [U_8021,U_8019] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8021))
| ~ sP485(U_8021,U_8019) )
& ! [U_8020,U_8018] :
( U_8018 = 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_8020))
| ~ sP484(U_8020,U_8018) )
& ! [U_8020,U_8018] :
( U_8020 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8018)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8020))
| ~ sP484(U_8020,U_8018) )
& ! [U_8021,U_8019] :
( U_8019 = hAPP(c_Int_Onat,U_8021)
| sP486(U_8021,U_8019)
| sP485(U_8021,U_8019) )
& ! [U_8020,U_8018] :
( sP484(U_8020,U_8018)
| U_8018 != hAPP(c_Int_Onat,U_8020) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP484,sP485,sP486])],[f_1957_3]) ).
cnf(f_1957_5,plain,
( sP484(U_8020,U_8018)
| U_8018 != hAPP(c_Int_Onat,U_8020) ),
inference(clausify,[status(thm)],[f_1957_4]) ).
cnf(f_1957_6,plain,
( U_8019 = hAPP(c_Int_Onat,U_8021)
| sP486(U_8021,U_8019)
| sP485(U_8021,U_8019) ),
inference(clausify,[status(thm)],[f_1957_4]) ).
cnf(f_1957_7,plain,
( U_8020 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8018)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8020))
| ~ sP484(U_8020,U_8018) ),
inference(clausify,[status(thm)],[f_1957_4]) ).
cnf(f_1957_8,plain,
( U_8018 = 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_8020))
| ~ sP484(U_8020,U_8018) ),
inference(clausify,[status(thm)],[f_1957_4]) ).
cnf(f_1957_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8021))
| ~ sP485(U_8021,U_8019) ),
inference(clausify,[status(thm)],[f_1957_4]) ).
cnf(f_1957_10,plain,
( U_8021 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8019)
| ~ sP485(U_8021,U_8019) ),
inference(clausify,[status(thm)],[f_1957_4]) ).
cnf(f_1957_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8021))
| ~ sP486(U_8021,U_8019) ),
inference(clausify,[status(thm)],[f_1957_4]) ).
cnf(f_1957_12,plain,
( U_8019 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP486(U_8021,U_8019) ),
inference(clausify,[status(thm)],[f_1957_4]) ).
fof(f_1958_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_1958_2,plain,
! [U_8023,U_8022] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_8022)),hAPP(c_Int_Onat,U_8023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8022),U_8023)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8022),U_8023))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_8022)),hAPP(c_Int_Onat,U_8023))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8023))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8022)) ) ),
inference(variable_rename,[status(thm)],[f_1958_1]) ).
fof(f_1958_3,plain,
( ! [U_8022,U_8023] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_8022)),hAPP(c_Int_Onat,U_8023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8022),U_8023))
| ~ sP488(U_8022,U_8023) )
& ! [U_8022,U_8023] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8022),U_8023))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_8022)),hAPP(c_Int_Onat,U_8023)))
| ~ sP488(U_8022,U_8023) )
& ! [U_8022,U_8023] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8023))
| ~ sP487(U_8022,U_8023) )
& ! [U_8022,U_8023] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8022))
| ~ sP487(U_8022,U_8023) )
& ! [U_8022,U_8023] :
( sP488(U_8022,U_8023)
| sP487(U_8022,U_8023) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP487,sP488])],[f_1958_2]) ).
cnf(f_1958_4,plain,
( sP488(U_8022,U_8023)
| sP487(U_8022,U_8023) ),
inference(clausify,[status(thm)],[f_1958_3]) ).
cnf(f_1958_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8022))
| ~ sP487(U_8022,U_8023) ),
inference(clausify,[status(thm)],[f_1958_3]) ).
cnf(f_1958_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8023))
| ~ sP487(U_8022,U_8023) ),
inference(clausify,[status(thm)],[f_1958_3]) ).
cnf(f_1958_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8022),U_8023))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_8022)),hAPP(c_Int_Onat,U_8023)))
| ~ sP488(U_8022,U_8023) ),
inference(clausify,[status(thm)],[f_1958_3]) ).
cnf(f_1958_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_8022)),hAPP(c_Int_Onat,U_8023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8022),U_8023))
| ~ sP488(U_8022,U_8023) ),
inference(clausify,[status(thm)],[f_1958_3]) ).
fof(f_1959_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_1959_2,plain,
! [U_8027,U_8026] :
( ( hBOOL(hAPP(U_8026,hAPP(c_Int_Onat,U_8027)))
| ( ~ hBOOL(hAPP(U_8026,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [U_8025] :
( ~ hBOOL(hAPP(U_8026,U_8025))
& U_8027 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8025) ) )
& ( ( ( hBOOL(hAPP(U_8026,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_8024] :
( hBOOL(hAPP(U_8026,U_8024))
| U_8027 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8024) ) )
| ~ hBOOL(hAPP(U_8026,hAPP(c_Int_Onat,U_8027))) ) ),
inference(variable_rename,[status(thm)],[f_1959_1]) ).
fof(f_1959_3,plain,
( ! [U_8031,U_8029] :
( hBOOL(hAPP(U_8029,hAPP(c_Int_Onat,U_8031)))
| ( ~ hBOOL(hAPP(U_8029,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8031),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [U_8025] :
( ~ hBOOL(hAPP(U_8029,U_8025))
& U_8031 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8025) ) )
& ! [U_8030,U_8028] :
( ( ( hBOOL(hAPP(U_8028,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8030),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_8024] :
( hBOOL(hAPP(U_8028,U_8024))
| U_8030 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8024) ) )
| ~ hBOOL(hAPP(U_8028,hAPP(c_Int_Onat,U_8030))) ) ),
inference(miniscope,[status(thm)],[f_1959_2]) ).
fof(f_1959_4,plain,
( ! [U_8031,U_8029] :
( hBOOL(hAPP(U_8029,hAPP(c_Int_Onat,U_8031)))
| ( ~ hBOOL(hAPP(U_8029,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8031),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_8029,sK166(U_8031,U_8029)))
& U_8031 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK166(U_8031,U_8029)) ) )
& ! [U_8030,U_8028] :
( ( ( hBOOL(hAPP(U_8028,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8030),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_8024] :
( hBOOL(hAPP(U_8028,U_8024))
| U_8030 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8024) ) )
| ~ hBOOL(hAPP(U_8028,hAPP(c_Int_Onat,U_8030))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_8025,sK166(U_8031,U_8029))],[f_1959_3]) ).
fof(f_1959_5,plain,
( ! [U_8029,U_8031] :
( ~ hBOOL(hAPP(U_8029,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP491(U_8029,U_8031) )
& ! [U_8029,U_8031] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8031),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP491(U_8029,U_8031) )
& ! [U_8029,U_8031] :
( ~ hBOOL(hAPP(U_8029,sK166(U_8031,U_8029)))
| ~ sP490(U_8029,U_8031) )
& ! [U_8029,U_8031] :
( U_8031 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK166(U_8031,U_8029))
| ~ sP490(U_8029,U_8031) )
& ! [U_8024,U_8028,U_8030] :
( hBOOL(hAPP(U_8028,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8030),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP489(U_8024,U_8028,U_8030) )
& ! [U_8024,U_8028,U_8030] :
( hBOOL(hAPP(U_8028,U_8024))
| U_8030 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8024)
| ~ sP489(U_8024,U_8028,U_8030) )
& ! [U_8029,U_8031] :
( hBOOL(hAPP(U_8029,hAPP(c_Int_Onat,U_8031)))
| sP491(U_8029,U_8031)
| sP490(U_8029,U_8031) )
& ! [U_8024,U_8028,U_8030] :
( sP489(U_8024,U_8028,U_8030)
| ~ hBOOL(hAPP(U_8028,hAPP(c_Int_Onat,U_8030))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP489,sP490,sP491])],[f_1959_4]) ).
cnf(f_1959_6,plain,
( sP489(U_8024,U_8028,U_8030)
| ~ hBOOL(hAPP(U_8028,hAPP(c_Int_Onat,U_8030))) ),
inference(clausify,[status(thm)],[f_1959_5]) ).
cnf(f_1959_7,plain,
( hBOOL(hAPP(U_8029,hAPP(c_Int_Onat,U_8031)))
| sP491(U_8029,U_8031)
| sP490(U_8029,U_8031) ),
inference(clausify,[status(thm)],[f_1959_5]) ).
cnf(f_1959_8,plain,
( hBOOL(hAPP(U_8028,U_8024))
| U_8030 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8024)
| ~ sP489(U_8024,U_8028,U_8030) ),
inference(clausify,[status(thm)],[f_1959_5]) ).
cnf(f_1959_9,plain,
( hBOOL(hAPP(U_8028,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8030),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP489(U_8024,U_8028,U_8030) ),
inference(clausify,[status(thm)],[f_1959_5]) ).
cnf(f_1959_10,plain,
( U_8031 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK166(U_8031,U_8029))
| ~ sP490(U_8029,U_8031) ),
inference(clausify,[status(thm)],[f_1959_5]) ).
cnf(f_1959_11,plain,
( ~ hBOOL(hAPP(U_8029,sK166(U_8031,U_8029)))
| ~ sP490(U_8029,U_8031) ),
inference(clausify,[status(thm)],[f_1959_5]) ).
cnf(f_1959_12,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8031),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP491(U_8029,U_8031) ),
inference(clausify,[status(thm)],[f_1959_5]) ).
cnf(f_1959_13,plain,
( ~ hBOOL(hAPP(U_8029,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP491(U_8029,U_8031) ),
inference(clausify,[status(thm)],[f_1959_5]) ).
fof(f_1960_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_1960_2,plain,
! [U_8033,U_8032] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8032),U_8033)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8032)),hAPP(c_Int_Onat,U_8033))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(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)),U_8032)) ),
inference(variable_rename,[status(thm)],[f_1960_1]) ).
fof(f_1960_3,plain,
! [U_8033,U_8032] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8032),U_8033)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8032)),hAPP(c_Int_Onat,U_8033))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(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)),U_8032)) ),
inference(definitional_conversion,[status(esa)],[f_1960_2]) ).
cnf(f_1960_4,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8032),U_8033)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8032)),hAPP(c_Int_Onat,U_8033))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(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)),U_8032)) ),
inference(clausify,[status(thm)],[f_1960_3]) ).
fof(f_1961_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_1961_2,plain,
! [U_8035,U_8034] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8034)),hAPP(c_Int_Onat,U_8035)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8034),U_8035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(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)),U_8034)) ),
inference(variable_rename,[status(thm)],[f_1961_1]) ).
fof(f_1961_3,plain,
! [U_8034,U_8035] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8034)),hAPP(c_Int_Onat,U_8035)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8034),U_8035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(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)),U_8034)) ),
inference(definitional_conversion,[status(esa)],[f_1961_2]) ).
cnf(f_1961_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8034)),hAPP(c_Int_Onat,U_8035)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8034),U_8035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(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)),U_8034)) ),
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,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_1962_2,plain,
! [U_8037,U_8036] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8036),U_8037)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_8036)),hAPP(c_Int_Onat,U_8037))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8036)) ),
inference(variable_rename,[status(thm)],[f_1962_1]) ).
fof(f_1962_3,plain,
! [U_8036,U_8037] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8036),U_8037)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_8036)),hAPP(c_Int_Onat,U_8037))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8036)) ),
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_8036),U_8037)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_8036)),hAPP(c_Int_Onat,U_8037))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8036)) ),
inference(clausify,[status(thm)],[f_1962_3]) ).
fof(f_1963_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_1963_2,plain,
! [U_8039,U_8038] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_8038)),hAPP(c_Int_Onat,U_8039)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8038),U_8039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8038)) ),
inference(variable_rename,[status(thm)],[f_1963_1]) ).
fof(f_1963_3,plain,
! [U_8038,U_8039] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_8038)),hAPP(c_Int_Onat,U_8039)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8038),U_8039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8038)) ),
inference(definitional_conversion,[status(esa)],[f_1963_2]) ).
cnf(f_1963_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_8038)),hAPP(c_Int_Onat,U_8039)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8038),U_8039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8039))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8038)) ),
inference(clausify,[status(thm)],[f_1963_3]) ).
fof(f_1964_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_1964_2,plain,
! [U_8041,U_8040] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8040),U_8041) = 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_8040)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8041))),
inference(variable_rename,[status(thm)],[f_1964_1]) ).
fof(f_1964_3,plain,
! [U_8040,U_8041] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8040),U_8041) = 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_8040)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8041))),
inference(definitional_conversion,[status(esa)],[f_1964_2]) ).
cnf(f_1964_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8040),U_8041) = 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_8040)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8041))),
inference(clausify,[status(thm)],[f_1964_3]) ).
fof(f_1965_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_1965_2,plain,
! [U_8043,U_8042] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8043),U_8042)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8043)),hAPP(c_Int_Onat,U_8042))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8042),U_8043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8042)) ),
inference(variable_rename,[status(thm)],[f_1965_1]) ).
fof(f_1965_3,plain,
! [U_8042,U_8043] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8043),U_8042)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8043)),hAPP(c_Int_Onat,U_8042))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8042),U_8043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8042)) ),
inference(definitional_conversion,[status(esa)],[f_1965_2]) ).
cnf(f_1965_4,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8043),U_8042)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8043)),hAPP(c_Int_Onat,U_8042))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8042),U_8043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8042)) ),
inference(clausify,[status(thm)],[f_1965_3]) ).
fof(f_1966_1,plain,
! [V_A_2,V_f_2,T_c] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_c),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_1966_2,plain,
! [U_8046,U_8045,U_8044] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8044,tc_Nat_Onat),U_8045),U_8046) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8044,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_8044),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8045)),U_8046)),
inference(variable_rename,[status(thm)],[f_1966_1]) ).
fof(f_1966_3,plain,
! [U_8044,U_8045,U_8046] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8044,tc_Nat_Onat),U_8045),U_8046) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8044,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_8044),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8045)),U_8046)),
inference(definitional_conversion,[status(esa)],[f_1966_2]) ).
cnf(f_1966_4,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8044,tc_Nat_Onat),U_8045),U_8046) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8044,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_8044),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8045)),U_8046)),
inference(clausify,[status(thm)],[f_1966_3]) ).
fof(f_1967_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_1967_2,plain,
! [U_8048,U_8047] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_8047)),U_8048) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8047),U_8048))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8047)) ),
inference(variable_rename,[status(thm)],[f_1967_1]) ).
fof(f_1967_3,plain,
! [U_8047,U_8048] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_8047)),U_8048) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8047),U_8048))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8047)) ),
inference(definitional_conversion,[status(esa)],[f_1967_2]) ).
cnf(f_1967_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_8047)),U_8048) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8047),U_8048))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8047)) ),
inference(clausify,[status(thm)],[f_1967_3]) ).
fof(f_1968_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_1968_2,plain,
! [U_8050,U_8049] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8049),U_8050)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_8049)),U_8050)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8049)) ),
inference(variable_rename,[status(thm)],[f_1968_1]) ).
fof(f_1968_3,plain,
! [U_8049,U_8050] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8049),U_8050)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_8049)),U_8050)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8049)) ),
inference(definitional_conversion,[status(esa)],[f_1968_2]) ).
cnf(f_1968_4,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8049),U_8050)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_8049)),U_8050)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8049)) ),
inference(clausify,[status(thm)],[f_1968_3]) ).
fof(f_1969_1,plain,
! [V_A_2,V_f_2,T_c] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_c),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_1969_2,plain,
! [U_8053,U_8052,U_8051] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8051,tc_Nat_Onat),U_8052),U_8053) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8051,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_8051),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8052)),U_8053)),
inference(variable_rename,[status(thm)],[f_1969_1]) ).
fof(f_1969_3,plain,
! [U_8051,U_8052,U_8053] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8051,tc_Nat_Onat),U_8052),U_8053) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8051,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_8051),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8052)),U_8053)),
inference(definitional_conversion,[status(esa)],[f_1969_2]) ).
cnf(f_1969_4,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8051,tc_Nat_Onat),U_8052),U_8053) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8051,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_8051),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8052)),U_8053)),
inference(clausify,[status(thm)],[f_1969_3]) ).
fof(f_1970_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_1970_2,plain,
! [U_8055,U_8054] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8054)),hAPP(c_Int_Onat,U_8055)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_8054,U_8055))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8055))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8054)) ),
inference(variable_rename,[status(thm)],[f_1970_1]) ).
fof(f_1970_3,plain,
! [U_8054,U_8055] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8054)),hAPP(c_Int_Onat,U_8055)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_8054,U_8055))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8055))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8054)) ),
inference(definitional_conversion,[status(esa)],[f_1970_2]) ).
cnf(f_1970_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8054)),hAPP(c_Int_Onat,U_8055)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_8054,U_8055))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8055))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8054)) ),
inference(clausify,[status(thm)],[f_1970_3]) ).
fof(f_1971_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_1971_2,plain,
! [U_8056] :
( ( 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_8056)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8056)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8056))
| ~ 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_8056))) ) ),
inference(variable_rename,[status(thm)],[f_1971_1]) ).
fof(f_1971_3,plain,
( ! [U_8058] :
( 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_8058)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8058)) )
& ! [U_8057] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8057))
| ~ 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_8057))) ) ),
inference(miniscope,[status(thm)],[f_1971_2]) ).
fof(f_1971_4,plain,
( ! [U_8058] :
( 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_8058)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8058)) )
& ! [U_8057] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8057))
| ~ 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_8057))) ) ),
inference(definitional_conversion,[status(esa)],[f_1971_3]) ).
cnf(f_1971_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8057))
| ~ 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_8057))) ),
inference(clausify,[status(thm)],[f_1971_4]) ).
cnf(f_1971_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_8058)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8058)) ),
inference(clausify,[status(thm)],[f_1971_4]) ).
fof(f_1972_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_1972_2,plain,
! [U_8060,U_8059] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8059)),U_8060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8059),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8060))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8059),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8060)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8059)),U_8060)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8059)) ),
inference(variable_rename,[status(thm)],[f_1972_1]) ).
fof(f_1972_3,plain,
( ! [U_8060,U_8059] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8059)),U_8060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8059),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8060)))
| ~ sP492(U_8060,U_8059) )
& ! [U_8060,U_8059] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8059),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8060)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8059)),U_8060))
| ~ sP492(U_8060,U_8059) )
& ! [U_8060,U_8059] :
( sP492(U_8060,U_8059)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8059)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP492])],[f_1972_2]) ).
cnf(f_1972_4,plain,
( sP492(U_8060,U_8059)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8059)) ),
inference(clausify,[status(thm)],[f_1972_3]) ).
cnf(f_1972_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8059),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8060)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8059)),U_8060))
| ~ sP492(U_8060,U_8059) ),
inference(clausify,[status(thm)],[f_1972_3]) ).
cnf(f_1972_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_8059)),U_8060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8059),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8060)))
| ~ sP492(U_8060,U_8059) ),
inference(clausify,[status(thm)],[f_1972_3]) ).
fof(f_1973_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_1973_2,plain,
! [U_8061] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_8061)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_1973_1]) ).
fof(f_1973_3,plain,
! [U_8061] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_8061)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_1973_2]) ).
cnf(f_1973_4,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_8061)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),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_1973_3]) ).
fof(f_1974_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_1974_2,plain,
! [U_8063,U_8062] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8062),U_8063)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8062))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8063)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8062),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1974_1]) ).
fof(f_1974_3,plain,
! [U_8062,U_8063] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8062),U_8063)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8062))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8063)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8062),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_1974_2]) ).
cnf(f_1974_4,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8062),U_8063)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8062))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8063)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8062),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1974_3]) ).
fof(f_1975_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_1975_2,plain,
! [U_8065,U_8064] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_8064,U_8065)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8065),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8064),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_1975_1]) ).
fof(f_1975_3,plain,
! [U_8064,U_8065] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_8064,U_8065)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8065),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8064),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(definitional_conversion,[status(esa)],[f_1975_2]) ).
cnf(f_1975_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_8064,U_8065)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8065),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8064),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_1975_3]) ).
fof(f_1976_1,plain,
! [V_n_2,V_x_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(c_Power_Opower__class_Opower(T_c),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_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_c))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),V_x_2),c_Groups_Oone__class_Oone(T_c)))
| V_x_2 = c_Groups_Oone__class_Oone(T_c)
| ~ class_Fields_Ofield(T_c) ),
inference(fof_nnf,[status(thm)],[fact_geometric__sum]) ).
fof(f_1976_2,plain,
! [U_8068,U_8067,U_8066] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8066),hAPP(c_Power_Opower__class_Opower(U_8066),U_8067)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8068)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8066),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8066),hAPP(hAPP(c_Power_Opower__class_Opower(U_8066),U_8067),U_8068)),c_Groups_Oone__class_Oone(U_8066))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8066),U_8067),c_Groups_Oone__class_Oone(U_8066)))
| U_8067 = c_Groups_Oone__class_Oone(U_8066)
| ~ class_Fields_Ofield(U_8066) ),
inference(variable_rename,[status(thm)],[f_1976_1]) ).
fof(f_1976_3,plain,
! [U_8066,U_8067,U_8068] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8066),hAPP(c_Power_Opower__class_Opower(U_8066),U_8067)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8068)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8066),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8066),hAPP(hAPP(c_Power_Opower__class_Opower(U_8066),U_8067),U_8068)),c_Groups_Oone__class_Oone(U_8066))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8066),U_8067),c_Groups_Oone__class_Oone(U_8066)))
| U_8067 = c_Groups_Oone__class_Oone(U_8066)
| ~ class_Fields_Ofield(U_8066) ),
inference(definitional_conversion,[status(esa)],[f_1976_2]) ).
cnf(f_1976_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8066),hAPP(c_Power_Opower__class_Opower(U_8066),U_8067)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8068)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8066),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8066),hAPP(hAPP(c_Power_Opower__class_Opower(U_8066),U_8067),U_8068)),c_Groups_Oone__class_Oone(U_8066))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8066),U_8067),c_Groups_Oone__class_Oone(U_8066)))
| U_8067 = c_Groups_Oone__class_Oone(U_8066)
| ~ class_Fields_Ofield(U_8066) ),
inference(clausify,[status(thm)],[f_1976_3]) ).
fof(f_1977_1,plain,
! [V_c_2,V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq]) ).
fof(f_1977_2,plain,
! [U_8072,U_8071,U_8070,U_8069] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8070),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8069),U_8071),U_8072)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8070),c_Groups_Ozero__class_Ozero(U_8069)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),U_8072),c_Groups_Ozero__class_Ozero(U_8069))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8071),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8069),U_8070),U_8072)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),U_8072),c_Groups_Ozero__class_Ozero(U_8069))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),c_Groups_Ozero__class_Ozero(U_8069)),U_8072)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8069),U_8070),U_8072)),U_8071))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),c_Groups_Ozero__class_Ozero(U_8069)),U_8072)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8070),c_Groups_Ozero__class_Ozero(U_8069)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),U_8072),c_Groups_Ozero__class_Ozero(U_8069))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8071),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8069),U_8070),U_8072)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),U_8072),c_Groups_Ozero__class_Ozero(U_8069))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),c_Groups_Ozero__class_Ozero(U_8069)),U_8072)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8069),U_8070),U_8072)),U_8071))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),c_Groups_Ozero__class_Ozero(U_8069)),U_8072)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8070),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8069),U_8071),U_8072))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8069) ),
inference(variable_rename,[status(thm)],[f_1977_1]) ).
fof(f_1977_3,plain,
( ! [U_8069,U_8070,U_8072] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8070),c_Groups_Ozero__class_Ozero(U_8069)))
| ~ sP497(U_8069,U_8070,U_8072) )
& ! [U_8069,U_8070,U_8072] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),U_8072),c_Groups_Ozero__class_Ozero(U_8069)))
| ~ sP497(U_8069,U_8070,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8071),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8069),U_8070),U_8072)))
| ~ sP496(U_8069,U_8070,U_8071,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),U_8072),c_Groups_Ozero__class_Ozero(U_8069)))
| ~ sP496(U_8069,U_8070,U_8071,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( sP497(U_8069,U_8070,U_8072)
| sP496(U_8069,U_8070,U_8071,U_8072)
| ~ sP498(U_8069,U_8070,U_8071,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),c_Groups_Ozero__class_Ozero(U_8069)),U_8072))
| ~ sP498(U_8069,U_8070,U_8071,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8069),U_8070),U_8072)),U_8071))
| ~ sP495(U_8069,U_8070,U_8071,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),c_Groups_Ozero__class_Ozero(U_8069)),U_8072))
| ~ sP495(U_8069,U_8070,U_8071,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8070),c_Groups_Ozero__class_Ozero(U_8069)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),U_8072),c_Groups_Ozero__class_Ozero(U_8069)))
| ~ sP493(U_8069,U_8070,U_8071,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8071),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8069),U_8070),U_8072)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),U_8072),c_Groups_Ozero__class_Ozero(U_8069)))
| ~ sP493(U_8069,U_8070,U_8071,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( sP493(U_8069,U_8070,U_8071,U_8072)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),c_Groups_Ozero__class_Ozero(U_8069)),U_8072))
| ~ sP494(U_8069,U_8070,U_8071,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8069),U_8070),U_8072)),U_8071))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),c_Groups_Ozero__class_Ozero(U_8069)),U_8072))
| ~ sP494(U_8069,U_8070,U_8071,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8070),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8069),U_8071),U_8072)))
| sP498(U_8069,U_8070,U_8071,U_8072)
| sP495(U_8069,U_8070,U_8071,U_8072)
| ~ sP499(U_8069,U_8070,U_8071,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( sP494(U_8069,U_8070,U_8071,U_8072)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8070),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8069),U_8071),U_8072)))
| ~ sP499(U_8069,U_8070,U_8071,U_8072) )
& ! [U_8069,U_8070,U_8071,U_8072] :
( sP499(U_8069,U_8070,U_8071,U_8072)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8069) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP493,sP494,sP495,sP496,sP497,sP498,sP499])],[f_1977_2]) ).
cnf(f_1977_4,plain,
( sP499(U_8069,U_8070,U_8071,U_8072)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8069) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_5,plain,
( sP494(U_8069,U_8070,U_8071,U_8072)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8070),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8069),U_8071),U_8072)))
| ~ sP499(U_8069,U_8070,U_8071,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8070),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8069),U_8071),U_8072)))
| sP498(U_8069,U_8070,U_8071,U_8072)
| sP495(U_8069,U_8070,U_8071,U_8072)
| ~ sP499(U_8069,U_8070,U_8071,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8069),U_8070),U_8072)),U_8071))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),c_Groups_Ozero__class_Ozero(U_8069)),U_8072))
| ~ sP494(U_8069,U_8070,U_8071,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_8,plain,
( sP493(U_8069,U_8070,U_8071,U_8072)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),c_Groups_Ozero__class_Ozero(U_8069)),U_8072))
| ~ sP494(U_8069,U_8070,U_8071,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8071),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8069),U_8070),U_8072)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),U_8072),c_Groups_Ozero__class_Ozero(U_8069)))
| ~ sP493(U_8069,U_8070,U_8071,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8070),c_Groups_Ozero__class_Ozero(U_8069)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),U_8072),c_Groups_Ozero__class_Ozero(U_8069)))
| ~ sP493(U_8069,U_8070,U_8071,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),c_Groups_Ozero__class_Ozero(U_8069)),U_8072))
| ~ sP495(U_8069,U_8070,U_8071,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8069),U_8070),U_8072)),U_8071))
| ~ sP495(U_8069,U_8070,U_8071,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),c_Groups_Ozero__class_Ozero(U_8069)),U_8072))
| ~ sP498(U_8069,U_8070,U_8071,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_14,plain,
( sP497(U_8069,U_8070,U_8072)
| sP496(U_8069,U_8070,U_8071,U_8072)
| ~ sP498(U_8069,U_8070,U_8071,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),U_8072),c_Groups_Ozero__class_Ozero(U_8069)))
| ~ sP496(U_8069,U_8070,U_8071,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8071),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8069),U_8070),U_8072)))
| ~ sP496(U_8069,U_8070,U_8071,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8069),U_8072),c_Groups_Ozero__class_Ozero(U_8069)))
| ~ sP497(U_8069,U_8070,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
cnf(f_1977_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8069),U_8070),c_Groups_Ozero__class_Ozero(U_8069)))
| ~ sP497(U_8069,U_8070,U_8072) ),
inference(clausify,[status(thm)],[f_1977_3]) ).
fof(f_1978_1,plain,
! [V_a_2,V_c_2,V_b_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq]) ).
fof(f_1978_2,plain,
! [U_8076,U_8075,U_8074,U_8073] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8073),U_8074),U_8075)),U_8076))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8076))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),U_8075),c_Groups_Ozero__class_Ozero(U_8073))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8073),U_8076),U_8075)),U_8074))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),U_8075),c_Groups_Ozero__class_Ozero(U_8073))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8075)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8073),U_8076),U_8075)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8075)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8076))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),U_8075),c_Groups_Ozero__class_Ozero(U_8073))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8073),U_8076),U_8075)),U_8074))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),U_8075),c_Groups_Ozero__class_Ozero(U_8073))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8075)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8073),U_8076),U_8075)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8075)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8073),U_8074),U_8075)),U_8076)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8073) ),
inference(variable_rename,[status(thm)],[f_1978_1]) ).
fof(f_1978_3,plain,
( ! [U_8076,U_8073,U_8075] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8076))
| ~ sP504(U_8076,U_8073,U_8075) )
& ! [U_8076,U_8073,U_8075] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),U_8075),c_Groups_Ozero__class_Ozero(U_8073)))
| ~ sP504(U_8076,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8073),U_8076),U_8075)),U_8074))
| ~ sP503(U_8076,U_8074,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),U_8075),c_Groups_Ozero__class_Ozero(U_8073)))
| ~ sP503(U_8076,U_8074,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( sP504(U_8076,U_8073,U_8075)
| sP503(U_8076,U_8074,U_8073,U_8075)
| ~ sP505(U_8076,U_8074,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8075))
| ~ sP505(U_8076,U_8074,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8073),U_8076),U_8075)))
| ~ sP502(U_8076,U_8074,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8075))
| ~ sP502(U_8076,U_8074,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8076))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),U_8075),c_Groups_Ozero__class_Ozero(U_8073)))
| ~ sP500(U_8076,U_8074,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8073),U_8076),U_8075)),U_8074))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),U_8075),c_Groups_Ozero__class_Ozero(U_8073)))
| ~ sP500(U_8076,U_8074,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( sP500(U_8076,U_8074,U_8073,U_8075)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8075))
| ~ sP501(U_8076,U_8074,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8073),U_8076),U_8075)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8075))
| ~ sP501(U_8076,U_8074,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8073),U_8074),U_8075)),U_8076))
| sP505(U_8076,U_8074,U_8073,U_8075)
| sP502(U_8076,U_8074,U_8073,U_8075)
| ~ sP506(U_8076,U_8074,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( sP501(U_8076,U_8074,U_8073,U_8075)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8073),U_8074),U_8075)),U_8076))
| ~ sP506(U_8076,U_8074,U_8073,U_8075) )
& ! [U_8076,U_8074,U_8073,U_8075] :
( sP506(U_8076,U_8074,U_8073,U_8075)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8073) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP500,sP501,sP502,sP503,sP504,sP505,sP506])],[f_1978_2]) ).
cnf(f_1978_4,plain,
( sP506(U_8076,U_8074,U_8073,U_8075)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8073) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_5,plain,
( sP501(U_8076,U_8074,U_8073,U_8075)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8073),U_8074),U_8075)),U_8076))
| ~ sP506(U_8076,U_8074,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8073),U_8074),U_8075)),U_8076))
| sP505(U_8076,U_8074,U_8073,U_8075)
| sP502(U_8076,U_8074,U_8073,U_8075)
| ~ sP506(U_8076,U_8074,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8073),U_8076),U_8075)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8075))
| ~ sP501(U_8076,U_8074,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_8,plain,
( sP500(U_8076,U_8074,U_8073,U_8075)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8075))
| ~ sP501(U_8076,U_8074,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8073),U_8076),U_8075)),U_8074))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),U_8075),c_Groups_Ozero__class_Ozero(U_8073)))
| ~ sP500(U_8076,U_8074,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8076))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),U_8075),c_Groups_Ozero__class_Ozero(U_8073)))
| ~ sP500(U_8076,U_8074,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8075))
| ~ sP502(U_8076,U_8074,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),U_8074),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8073),U_8076),U_8075)))
| ~ sP502(U_8076,U_8074,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8075))
| ~ sP505(U_8076,U_8074,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_14,plain,
( sP504(U_8076,U_8073,U_8075)
| sP503(U_8076,U_8074,U_8073,U_8075)
| ~ sP505(U_8076,U_8074,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),U_8075),c_Groups_Ozero__class_Ozero(U_8073)))
| ~ sP503(U_8076,U_8074,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8073),U_8076),U_8075)),U_8074))
| ~ sP503(U_8076,U_8074,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8073),U_8075),c_Groups_Ozero__class_Ozero(U_8073)))
| ~ sP504(U_8076,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
cnf(f_1978_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8073),c_Groups_Ozero__class_Ozero(U_8073)),U_8076))
| ~ sP504(U_8076,U_8073,U_8075) ),
inference(clausify,[status(thm)],[f_1978_3]) ).
fof(f_1979_1,plain,
! [V_b_2,V_a_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
| ~ class_Fields_Olinordered__field(T_c) ),
inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq]) ).
fof(f_1979_2,plain,
! [U_8080,U_8079,U_8078,U_8077] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8077),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8077),U_8080),U_8078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8077),U_8079),U_8078)),U_8080)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8077),U_8079),U_8078)),U_8080))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8077),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8077),U_8080),U_8078))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8077),c_Groups_Ozero__class_Ozero(U_8077)),U_8078))
| ~ class_Fields_Olinordered__field(U_8077) ),
inference(variable_rename,[status(thm)],[f_1979_1]) ).
fof(f_1979_3,plain,
( ! [U_8080,U_8078,U_8079,U_8077] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8077),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8077),U_8080),U_8078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8077),U_8079),U_8078)),U_8080))
| ~ sP507(U_8080,U_8078,U_8079,U_8077) )
& ! [U_8080,U_8078,U_8079,U_8077] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8077),U_8079),U_8078)),U_8080))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8077),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8077),U_8080),U_8078)))
| ~ sP507(U_8080,U_8078,U_8079,U_8077) )
& ! [U_8080,U_8078,U_8079,U_8077] :
( sP507(U_8080,U_8078,U_8079,U_8077)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8077),c_Groups_Ozero__class_Ozero(U_8077)),U_8078))
| ~ class_Fields_Olinordered__field(U_8077) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP507])],[f_1979_2]) ).
cnf(f_1979_4,plain,
( sP507(U_8080,U_8078,U_8079,U_8077)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8077),c_Groups_Ozero__class_Ozero(U_8077)),U_8078))
| ~ class_Fields_Olinordered__field(U_8077) ),
inference(clausify,[status(thm)],[f_1979_3]) ).
cnf(f_1979_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8077),U_8079),U_8078)),U_8080))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8077),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8077),U_8080),U_8078)))
| ~ sP507(U_8080,U_8078,U_8079,U_8077) ),
inference(clausify,[status(thm)],[f_1979_3]) ).
cnf(f_1979_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8077),U_8079),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8077),U_8080),U_8078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8077),U_8079),U_8078)),U_8080))
| ~ sP507(U_8080,U_8078,U_8079,U_8077) ),
inference(clausify,[status(thm)],[f_1979_3]) ).
fof(f_1980_1,plain,
! [V_a_2,V_b_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
| ~ class_Fields_Olinordered__field(T_c) ),
inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq]) ).
fof(f_1980_2,plain,
! [U_8084,U_8083,U_8082,U_8081] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8081),U_8083),U_8082)),U_8084))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8081),U_8083),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8081),U_8084),U_8082))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8081),U_8083),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8081),U_8084),U_8082)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8081),U_8083),U_8082)),U_8084)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8081),c_Groups_Ozero__class_Ozero(U_8081)),U_8082))
| ~ class_Fields_Olinordered__field(U_8081) ),
inference(variable_rename,[status(thm)],[f_1980_1]) ).
fof(f_1980_3,plain,
( ! [U_8082,U_8083,U_8084,U_8081] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8081),U_8083),U_8082)),U_8084))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8081),U_8083),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8081),U_8084),U_8082)))
| ~ sP508(U_8082,U_8083,U_8084,U_8081) )
& ! [U_8082,U_8083,U_8084,U_8081] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8081),U_8083),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8081),U_8084),U_8082)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8081),U_8083),U_8082)),U_8084))
| ~ sP508(U_8082,U_8083,U_8084,U_8081) )
& ! [U_8082,U_8083,U_8084,U_8081] :
( sP508(U_8082,U_8083,U_8084,U_8081)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8081),c_Groups_Ozero__class_Ozero(U_8081)),U_8082))
| ~ class_Fields_Olinordered__field(U_8081) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP508])],[f_1980_2]) ).
cnf(f_1980_4,plain,
( sP508(U_8082,U_8083,U_8084,U_8081)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8081),c_Groups_Ozero__class_Ozero(U_8081)),U_8082))
| ~ class_Fields_Olinordered__field(U_8081) ),
inference(clausify,[status(thm)],[f_1980_3]) ).
cnf(f_1980_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8081),U_8083),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8081),U_8084),U_8082)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8081),U_8083),U_8082)),U_8084))
| ~ sP508(U_8082,U_8083,U_8084,U_8081) ),
inference(clausify,[status(thm)],[f_1980_3]) ).
cnf(f_1980_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8081),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8081),U_8083),U_8082)),U_8084))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8081),U_8083),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8081),U_8084),U_8082)))
| ~ sP508(U_8082,U_8083,U_8084,U_8081) ),
inference(clausify,[status(thm)],[f_1980_3]) ).
fof(f_1981_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_1981_2,plain,
! [U_8088,U_8087,U_8086,U_8085] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8085),U_8087),U_8086)),U_8088))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8085),U_8087),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8085),U_8088),U_8086)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8085),c_Groups_Ozero__class_Ozero(U_8085)),U_8086))
| ~ class_Fields_Olinordered__field(U_8085) ),
inference(variable_rename,[status(thm)],[f_1981_1]) ).
fof(f_1981_3,plain,
! [U_8088,U_8087,U_8085,U_8086] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8085),U_8087),U_8086)),U_8088))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8085),U_8087),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8085),U_8088),U_8086)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8085),c_Groups_Ozero__class_Ozero(U_8085)),U_8086))
| ~ class_Fields_Olinordered__field(U_8085) ),
inference(definitional_conversion,[status(esa)],[f_1981_2]) ).
cnf(f_1981_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8085),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8085),U_8087),U_8086)),U_8088))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8085),U_8087),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8085),U_8088),U_8086)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8085),c_Groups_Ozero__class_Ozero(U_8085)),U_8086))
| ~ class_Fields_Olinordered__field(U_8085) ),
inference(clausify,[status(thm)],[f_1981_3]) ).
fof(f_1982_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_1982_2,plain,
! [U_8093,U_8092,U_8091,U_8090,U_8089] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8089),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8089),U_8090),U_8091)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8089),U_8092),U_8093)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8089),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8089),U_8090),U_8092)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8089),U_8091),U_8093))
| ~ class_Fields_Ofield__inverse__zero(U_8089) ),
inference(variable_rename,[status(thm)],[f_1982_1]) ).
fof(f_1982_3,plain,
! [U_8090,U_8089,U_8091,U_8092,U_8093] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8089),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8089),U_8090),U_8091)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8089),U_8092),U_8093)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8089),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8089),U_8090),U_8092)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8089),U_8091),U_8093))
| ~ class_Fields_Ofield__inverse__zero(U_8089) ),
inference(definitional_conversion,[status(esa)],[f_1982_2]) ).
cnf(f_1982_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8089),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8089),U_8090),U_8091)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8089),U_8092),U_8093)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8089),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8089),U_8090),U_8092)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8089),U_8091),U_8093))
| ~ class_Fields_Ofield__inverse__zero(U_8089) ),
inference(clausify,[status(thm)],[f_1982_3]) ).
fof(f_1983_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_1983_2,plain,
! [U_8096,U_8095,U_8094] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8094),hAPP(c_Groups_Ouminus__class_Ouminus(U_8094),U_8095)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8094),U_8096)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8094),U_8095),U_8096)
| ~ class_Fields_Ofield__inverse__zero(U_8094) ),
inference(variable_rename,[status(thm)],[f_1983_1]) ).
fof(f_1983_3,plain,
! [U_8094,U_8095,U_8096] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8094),hAPP(c_Groups_Ouminus__class_Ouminus(U_8094),U_8095)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8094),U_8096)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8094),U_8095),U_8096)
| ~ class_Fields_Ofield__inverse__zero(U_8094) ),
inference(definitional_conversion,[status(esa)],[f_1983_2]) ).
cnf(f_1983_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8094),hAPP(c_Groups_Ouminus__class_Ouminus(U_8094),U_8095)),hAPP(c_Groups_Ouminus__class_Ouminus(U_8094),U_8096)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8094),U_8095),U_8096)
| ~ class_Fields_Ofield__inverse__zero(U_8094) ),
inference(clausify,[status(thm)],[f_1983_3]) ).
fof(f_1984_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_1984_2,plain,
! [U_8099,U_8098,U_8097] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8097),U_8098),U_8099)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8097),U_8098),hAPP(c_Groups_Ouminus__class_Ouminus(U_8097),U_8099))
| ~ class_Fields_Ofield__inverse__zero(U_8097) ),
inference(variable_rename,[status(thm)],[f_1984_1]) ).
fof(f_1984_3,plain,
! [U_8097,U_8098,U_8099] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8097),U_8098),U_8099)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8097),U_8098),hAPP(c_Groups_Ouminus__class_Ouminus(U_8097),U_8099))
| ~ class_Fields_Ofield__inverse__zero(U_8097) ),
inference(definitional_conversion,[status(esa)],[f_1984_2]) ).
cnf(f_1984_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_8097),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8097),U_8098),U_8099)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8097),U_8098),hAPP(c_Groups_Ouminus__class_Ouminus(U_8097),U_8099))
| ~ class_Fields_Ofield__inverse__zero(U_8097) ),
inference(clausify,[status(thm)],[f_1984_3]) ).
fof(f_1985_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff]) ).
fof(f_1985_2,plain,
! [U_8102,U_8101,U_8100] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8100),U_8101),U_8102)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),U_8102),c_Groups_Ozero__class_Ozero(U_8100)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),U_8101),c_Groups_Ozero__class_Ozero(U_8100))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),U_8102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),U_8101)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),U_8102),c_Groups_Ozero__class_Ozero(U_8100)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),U_8101),c_Groups_Ozero__class_Ozero(U_8100))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),U_8102))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),U_8101)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8100),U_8101),U_8102))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8100) ),
inference(variable_rename,[status(thm)],[f_1985_1]) ).
fof(f_1985_3,plain,
( ! [U_8100,U_8101,U_8102] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),U_8102),c_Groups_Ozero__class_Ozero(U_8100)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),U_8101),c_Groups_Ozero__class_Ozero(U_8100)))
| ~ sP511(U_8100,U_8101,U_8102) )
& ! [U_8100,U_8101,U_8102] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),U_8102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),U_8101))
| ~ sP511(U_8100,U_8101,U_8102) )
& ! [U_8100,U_8101,U_8102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),U_8102),c_Groups_Ozero__class_Ozero(U_8100)))
| ~ sP510(U_8100,U_8101,U_8102) )
& ! [U_8100,U_8101,U_8102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),U_8101),c_Groups_Ozero__class_Ozero(U_8100)))
| ~ sP510(U_8100,U_8101,U_8102) )
& ! [U_8100,U_8101,U_8102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),U_8102))
| ~ sP509(U_8100,U_8101,U_8102) )
& ! [U_8100,U_8101,U_8102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),U_8101))
| ~ sP509(U_8100,U_8101,U_8102) )
& ! [U_8100,U_8101,U_8102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8100),U_8101),U_8102)))
| sP511(U_8100,U_8101,U_8102)
| ~ sP512(U_8100,U_8101,U_8102) )
& ! [U_8100,U_8101,U_8102] :
( sP510(U_8100,U_8101,U_8102)
| sP509(U_8100,U_8101,U_8102)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8100),U_8101),U_8102)))
| ~ sP512(U_8100,U_8101,U_8102) )
& ! [U_8100,U_8101,U_8102] :
( sP512(U_8100,U_8101,U_8102)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8100) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP509,sP510,sP511,sP512])],[f_1985_2]) ).
cnf(f_1985_4,plain,
( sP512(U_8100,U_8101,U_8102)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8100) ),
inference(clausify,[status(thm)],[f_1985_3]) ).
cnf(f_1985_5,plain,
( sP510(U_8100,U_8101,U_8102)
| sP509(U_8100,U_8101,U_8102)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8100),U_8101),U_8102)))
| ~ sP512(U_8100,U_8101,U_8102) ),
inference(clausify,[status(thm)],[f_1985_3]) ).
cnf(f_1985_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8100),U_8101),U_8102)))
| sP511(U_8100,U_8101,U_8102)
| ~ sP512(U_8100,U_8101,U_8102) ),
inference(clausify,[status(thm)],[f_1985_3]) ).
cnf(f_1985_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),U_8101))
| ~ sP509(U_8100,U_8101,U_8102) ),
inference(clausify,[status(thm)],[f_1985_3]) ).
cnf(f_1985_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),U_8102))
| ~ sP509(U_8100,U_8101,U_8102) ),
inference(clausify,[status(thm)],[f_1985_3]) ).
cnf(f_1985_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),U_8101),c_Groups_Ozero__class_Ozero(U_8100)))
| ~ sP510(U_8100,U_8101,U_8102) ),
inference(clausify,[status(thm)],[f_1985_3]) ).
cnf(f_1985_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),U_8102),c_Groups_Ozero__class_Ozero(U_8100)))
| ~ sP510(U_8100,U_8101,U_8102) ),
inference(clausify,[status(thm)],[f_1985_3]) ).
cnf(f_1985_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),U_8102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),c_Groups_Ozero__class_Ozero(U_8100)),U_8101))
| ~ sP511(U_8100,U_8101,U_8102) ),
inference(clausify,[status(thm)],[f_1985_3]) ).
cnf(f_1985_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),U_8102),c_Groups_Ozero__class_Ozero(U_8100)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8100),U_8101),c_Groups_Ozero__class_Ozero(U_8100)))
| ~ sP511(U_8100,U_8101,U_8102) ),
inference(clausify,[status(thm)],[f_1985_3]) ).
fof(f_1986_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff]) ).
fof(f_1986_2,plain,
! [U_8105,U_8104,U_8103] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8103),U_8104),U_8105)),c_Groups_Ozero__class_Ozero(U_8103)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),c_Groups_Ozero__class_Ozero(U_8103)),U_8105))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),U_8104),c_Groups_Ozero__class_Ozero(U_8103))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),U_8105),c_Groups_Ozero__class_Ozero(U_8103)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),c_Groups_Ozero__class_Ozero(U_8103)),U_8104)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),c_Groups_Ozero__class_Ozero(U_8103)),U_8105))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),U_8104),c_Groups_Ozero__class_Ozero(U_8103))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),U_8105),c_Groups_Ozero__class_Ozero(U_8103)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),c_Groups_Ozero__class_Ozero(U_8103)),U_8104)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8103),U_8104),U_8105)),c_Groups_Ozero__class_Ozero(U_8103))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8103) ),
inference(variable_rename,[status(thm)],[f_1986_1]) ).
fof(f_1986_3,plain,
( ! [U_8103,U_8104,U_8105] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),c_Groups_Ozero__class_Ozero(U_8103)),U_8105))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),U_8104),c_Groups_Ozero__class_Ozero(U_8103)))
| ~ sP515(U_8103,U_8104,U_8105) )
& ! [U_8103,U_8104,U_8105] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),U_8105),c_Groups_Ozero__class_Ozero(U_8103)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),c_Groups_Ozero__class_Ozero(U_8103)),U_8104))
| ~ sP515(U_8103,U_8104,U_8105) )
& ! [U_8103,U_8104,U_8105] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),c_Groups_Ozero__class_Ozero(U_8103)),U_8105))
| ~ sP514(U_8103,U_8104,U_8105) )
& ! [U_8103,U_8104,U_8105] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),U_8104),c_Groups_Ozero__class_Ozero(U_8103)))
| ~ sP514(U_8103,U_8104,U_8105) )
& ! [U_8103,U_8104,U_8105] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),U_8105),c_Groups_Ozero__class_Ozero(U_8103)))
| ~ sP513(U_8103,U_8104,U_8105) )
& ! [U_8103,U_8104,U_8105] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),c_Groups_Ozero__class_Ozero(U_8103)),U_8104))
| ~ sP513(U_8103,U_8104,U_8105) )
& ! [U_8103,U_8104,U_8105] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8103),U_8104),U_8105)),c_Groups_Ozero__class_Ozero(U_8103)))
| sP515(U_8103,U_8104,U_8105)
| ~ sP516(U_8103,U_8104,U_8105) )
& ! [U_8103,U_8104,U_8105] :
( sP514(U_8103,U_8104,U_8105)
| sP513(U_8103,U_8104,U_8105)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8103),U_8104),U_8105)),c_Groups_Ozero__class_Ozero(U_8103)))
| ~ sP516(U_8103,U_8104,U_8105) )
& ! [U_8103,U_8104,U_8105] :
( sP516(U_8103,U_8104,U_8105)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8103) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP513,sP514,sP515,sP516])],[f_1986_2]) ).
cnf(f_1986_4,plain,
( sP516(U_8103,U_8104,U_8105)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8103) ),
inference(clausify,[status(thm)],[f_1986_3]) ).
cnf(f_1986_5,plain,
( sP514(U_8103,U_8104,U_8105)
| sP513(U_8103,U_8104,U_8105)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8103),U_8104),U_8105)),c_Groups_Ozero__class_Ozero(U_8103)))
| ~ sP516(U_8103,U_8104,U_8105) ),
inference(clausify,[status(thm)],[f_1986_3]) ).
cnf(f_1986_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8103),U_8104),U_8105)),c_Groups_Ozero__class_Ozero(U_8103)))
| sP515(U_8103,U_8104,U_8105)
| ~ sP516(U_8103,U_8104,U_8105) ),
inference(clausify,[status(thm)],[f_1986_3]) ).
cnf(f_1986_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),c_Groups_Ozero__class_Ozero(U_8103)),U_8104))
| ~ sP513(U_8103,U_8104,U_8105) ),
inference(clausify,[status(thm)],[f_1986_3]) ).
cnf(f_1986_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),U_8105),c_Groups_Ozero__class_Ozero(U_8103)))
| ~ sP513(U_8103,U_8104,U_8105) ),
inference(clausify,[status(thm)],[f_1986_3]) ).
cnf(f_1986_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),U_8104),c_Groups_Ozero__class_Ozero(U_8103)))
| ~ sP514(U_8103,U_8104,U_8105) ),
inference(clausify,[status(thm)],[f_1986_3]) ).
cnf(f_1986_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),c_Groups_Ozero__class_Ozero(U_8103)),U_8105))
| ~ sP514(U_8103,U_8104,U_8105) ),
inference(clausify,[status(thm)],[f_1986_3]) ).
cnf(f_1986_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),U_8105),c_Groups_Ozero__class_Ozero(U_8103)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),c_Groups_Ozero__class_Ozero(U_8103)),U_8104))
| ~ sP515(U_8103,U_8104,U_8105) ),
inference(clausify,[status(thm)],[f_1986_3]) ).
cnf(f_1986_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),c_Groups_Ozero__class_Ozero(U_8103)),U_8105))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8103),U_8104),c_Groups_Ozero__class_Ozero(U_8103)))
| ~ sP515(U_8103,U_8104,U_8105) ),
inference(clausify,[status(thm)],[f_1986_3]) ).
fof(f_1987_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_1987_2,plain,
! [U_8109,U_8108,U_8107,U_8106] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8106),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8106),U_8107),U_8109)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8106),U_8108),U_8109)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8106),c_Groups_Ozero__class_Ozero(U_8106)),U_8109))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8106),U_8107),U_8108))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8106) ),
inference(variable_rename,[status(thm)],[f_1987_1]) ).
fof(f_1987_3,plain,
! [U_8108,U_8106,U_8107,U_8109] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8106),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8106),U_8107),U_8109)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8106),U_8108),U_8109)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8106),c_Groups_Ozero__class_Ozero(U_8106)),U_8109))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8106),U_8107),U_8108))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8106) ),
inference(definitional_conversion,[status(esa)],[f_1987_2]) ).
cnf(f_1987_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8106),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8106),U_8107),U_8109)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8106),U_8108),U_8109)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8106),c_Groups_Ozero__class_Ozero(U_8106)),U_8109))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8106),U_8107),U_8108))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8106) ),
inference(clausify,[status(thm)],[f_1987_3]) ).
fof(f_1988_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_1988_2,plain,
! [U_8113,U_8112,U_8111,U_8110] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8110),U_8112),U_8113)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8110),U_8111),U_8113)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8110),U_8113),c_Groups_Ozero__class_Ozero(U_8110)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8110),U_8111),U_8112))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8110) ),
inference(variable_rename,[status(thm)],[f_1988_1]) ).
fof(f_1988_3,plain,
! [U_8110,U_8111,U_8112,U_8113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8110),U_8112),U_8113)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8110),U_8111),U_8113)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8110),U_8113),c_Groups_Ozero__class_Ozero(U_8110)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8110),U_8111),U_8112))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8110) ),
inference(definitional_conversion,[status(esa)],[f_1988_2]) ).
cnf(f_1988_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8110),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8110),U_8112),U_8113)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8110),U_8111),U_8113)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8110),U_8113),c_Groups_Ozero__class_Ozero(U_8110)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8110),U_8111),U_8112))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8110) ),
inference(clausify,[status(thm)],[f_1988_3]) ).
fof(f_1989_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff]) ).
fof(f_1989_2,plain,
! [U_8116,U_8115,U_8114] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8114),U_8115),U_8116)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),U_8116),c_Groups_Ozero__class_Ozero(U_8114)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),U_8115),c_Groups_Ozero__class_Ozero(U_8114))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),U_8116))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),U_8115)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),U_8116),c_Groups_Ozero__class_Ozero(U_8114)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),U_8115),c_Groups_Ozero__class_Ozero(U_8114))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),U_8116))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),U_8115)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8114),U_8115),U_8116))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8114) ),
inference(variable_rename,[status(thm)],[f_1989_1]) ).
fof(f_1989_3,plain,
( ! [U_8114,U_8115,U_8116] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),U_8116),c_Groups_Ozero__class_Ozero(U_8114)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),U_8115),c_Groups_Ozero__class_Ozero(U_8114)))
| ~ sP519(U_8114,U_8115,U_8116) )
& ! [U_8114,U_8115,U_8116] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),U_8116))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),U_8115))
| ~ sP519(U_8114,U_8115,U_8116) )
& ! [U_8114,U_8115,U_8116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),U_8116),c_Groups_Ozero__class_Ozero(U_8114)))
| ~ sP518(U_8114,U_8115,U_8116) )
& ! [U_8114,U_8115,U_8116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),U_8115),c_Groups_Ozero__class_Ozero(U_8114)))
| ~ sP518(U_8114,U_8115,U_8116) )
& ! [U_8114,U_8115,U_8116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),U_8116))
| ~ sP517(U_8114,U_8115,U_8116) )
& ! [U_8114,U_8115,U_8116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),U_8115))
| ~ sP517(U_8114,U_8115,U_8116) )
& ! [U_8114,U_8115,U_8116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8114),U_8115),U_8116)))
| sP519(U_8114,U_8115,U_8116)
| ~ sP520(U_8114,U_8115,U_8116) )
& ! [U_8114,U_8115,U_8116] :
( sP518(U_8114,U_8115,U_8116)
| sP517(U_8114,U_8115,U_8116)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8114),U_8115),U_8116)))
| ~ sP520(U_8114,U_8115,U_8116) )
& ! [U_8114,U_8115,U_8116] :
( sP520(U_8114,U_8115,U_8116)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8114) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP517,sP518,sP519,sP520])],[f_1989_2]) ).
cnf(f_1989_4,plain,
( sP520(U_8114,U_8115,U_8116)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8114) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
cnf(f_1989_5,plain,
( sP518(U_8114,U_8115,U_8116)
| sP517(U_8114,U_8115,U_8116)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8114),U_8115),U_8116)))
| ~ sP520(U_8114,U_8115,U_8116) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
cnf(f_1989_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8114),U_8115),U_8116)))
| sP519(U_8114,U_8115,U_8116)
| ~ sP520(U_8114,U_8115,U_8116) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
cnf(f_1989_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),U_8115))
| ~ sP517(U_8114,U_8115,U_8116) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
cnf(f_1989_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),U_8116))
| ~ sP517(U_8114,U_8115,U_8116) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
cnf(f_1989_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),U_8115),c_Groups_Ozero__class_Ozero(U_8114)))
| ~ sP518(U_8114,U_8115,U_8116) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
cnf(f_1989_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),U_8116),c_Groups_Ozero__class_Ozero(U_8114)))
| ~ sP518(U_8114,U_8115,U_8116) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
cnf(f_1989_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),U_8116))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),c_Groups_Ozero__class_Ozero(U_8114)),U_8115))
| ~ sP519(U_8114,U_8115,U_8116) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
cnf(f_1989_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),U_8116),c_Groups_Ozero__class_Ozero(U_8114)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8114),U_8115),c_Groups_Ozero__class_Ozero(U_8114)))
| ~ sP519(U_8114,U_8115,U_8116) ),
inference(clausify,[status(thm)],[f_1989_3]) ).
fof(f_1990_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),c_Groups_Ozero__class_Ozero(T_c)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff]) ).
fof(f_1990_2,plain,
! [U_8119,U_8118,U_8117] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8117),U_8118),U_8119)),c_Groups_Ozero__class_Ozero(U_8117)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),c_Groups_Ozero__class_Ozero(U_8117)),U_8119))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),U_8118),c_Groups_Ozero__class_Ozero(U_8117))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),U_8119),c_Groups_Ozero__class_Ozero(U_8117)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),c_Groups_Ozero__class_Ozero(U_8117)),U_8118)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),c_Groups_Ozero__class_Ozero(U_8117)),U_8119))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),U_8118),c_Groups_Ozero__class_Ozero(U_8117))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),U_8119),c_Groups_Ozero__class_Ozero(U_8117)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),c_Groups_Ozero__class_Ozero(U_8117)),U_8118)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8117),U_8118),U_8119)),c_Groups_Ozero__class_Ozero(U_8117))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8117) ),
inference(variable_rename,[status(thm)],[f_1990_1]) ).
fof(f_1990_3,plain,
( ! [U_8118,U_8119,U_8117] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),c_Groups_Ozero__class_Ozero(U_8117)),U_8119))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),U_8118),c_Groups_Ozero__class_Ozero(U_8117)))
| ~ sP523(U_8118,U_8119,U_8117) )
& ! [U_8118,U_8119,U_8117] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),U_8119),c_Groups_Ozero__class_Ozero(U_8117)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),c_Groups_Ozero__class_Ozero(U_8117)),U_8118))
| ~ sP523(U_8118,U_8119,U_8117) )
& ! [U_8118,U_8119,U_8117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),c_Groups_Ozero__class_Ozero(U_8117)),U_8119))
| ~ sP522(U_8118,U_8119,U_8117) )
& ! [U_8118,U_8119,U_8117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),U_8118),c_Groups_Ozero__class_Ozero(U_8117)))
| ~ sP522(U_8118,U_8119,U_8117) )
& ! [U_8118,U_8119,U_8117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),U_8119),c_Groups_Ozero__class_Ozero(U_8117)))
| ~ sP521(U_8118,U_8119,U_8117) )
& ! [U_8118,U_8119,U_8117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),c_Groups_Ozero__class_Ozero(U_8117)),U_8118))
| ~ sP521(U_8118,U_8119,U_8117) )
& ! [U_8118,U_8119,U_8117] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8117),U_8118),U_8119)),c_Groups_Ozero__class_Ozero(U_8117)))
| sP523(U_8118,U_8119,U_8117)
| ~ sP524(U_8118,U_8119,U_8117) )
& ! [U_8118,U_8119,U_8117] :
( sP522(U_8118,U_8119,U_8117)
| sP521(U_8118,U_8119,U_8117)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8117),U_8118),U_8119)),c_Groups_Ozero__class_Ozero(U_8117)))
| ~ sP524(U_8118,U_8119,U_8117) )
& ! [U_8118,U_8119,U_8117] :
( sP524(U_8118,U_8119,U_8117)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8117) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP521,sP522,sP523,sP524])],[f_1990_2]) ).
cnf(f_1990_4,plain,
( sP524(U_8118,U_8119,U_8117)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8117) ),
inference(clausify,[status(thm)],[f_1990_3]) ).
cnf(f_1990_5,plain,
( sP522(U_8118,U_8119,U_8117)
| sP521(U_8118,U_8119,U_8117)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8117),U_8118),U_8119)),c_Groups_Ozero__class_Ozero(U_8117)))
| ~ sP524(U_8118,U_8119,U_8117) ),
inference(clausify,[status(thm)],[f_1990_3]) ).
cnf(f_1990_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8117),U_8118),U_8119)),c_Groups_Ozero__class_Ozero(U_8117)))
| sP523(U_8118,U_8119,U_8117)
| ~ sP524(U_8118,U_8119,U_8117) ),
inference(clausify,[status(thm)],[f_1990_3]) ).
cnf(f_1990_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),c_Groups_Ozero__class_Ozero(U_8117)),U_8118))
| ~ sP521(U_8118,U_8119,U_8117) ),
inference(clausify,[status(thm)],[f_1990_3]) ).
cnf(f_1990_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),U_8119),c_Groups_Ozero__class_Ozero(U_8117)))
| ~ sP521(U_8118,U_8119,U_8117) ),
inference(clausify,[status(thm)],[f_1990_3]) ).
cnf(f_1990_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),U_8118),c_Groups_Ozero__class_Ozero(U_8117)))
| ~ sP522(U_8118,U_8119,U_8117) ),
inference(clausify,[status(thm)],[f_1990_3]) ).
cnf(f_1990_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),c_Groups_Ozero__class_Ozero(U_8117)),U_8119))
| ~ sP522(U_8118,U_8119,U_8117) ),
inference(clausify,[status(thm)],[f_1990_3]) ).
cnf(f_1990_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),U_8119),c_Groups_Ozero__class_Ozero(U_8117)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),c_Groups_Ozero__class_Ozero(U_8117)),U_8118))
| ~ sP523(U_8118,U_8119,U_8117) ),
inference(clausify,[status(thm)],[f_1990_3]) ).
cnf(f_1990_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),c_Groups_Ozero__class_Ozero(U_8117)),U_8119))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8117),U_8118),c_Groups_Ozero__class_Ozero(U_8117)))
| ~ sP523(U_8118,U_8119,U_8117) ),
inference(clausify,[status(thm)],[f_1990_3]) ).
fof(f_1991_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_1991_2,plain,
! [U_8122,U_8121,U_8120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8120),c_Groups_Ozero__class_Ozero(U_8120)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8120),U_8121),U_8122)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8120),c_Groups_Ozero__class_Ozero(U_8120)),U_8122))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8120),c_Groups_Ozero__class_Ozero(U_8120)),U_8121))
| ~ class_Fields_Olinordered__field(U_8120) ),
inference(variable_rename,[status(thm)],[f_1991_1]) ).
fof(f_1991_3,plain,
! [U_8121,U_8122,U_8120] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8120),c_Groups_Ozero__class_Ozero(U_8120)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8120),U_8121),U_8122)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8120),c_Groups_Ozero__class_Ozero(U_8120)),U_8122))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8120),c_Groups_Ozero__class_Ozero(U_8120)),U_8121))
| ~ class_Fields_Olinordered__field(U_8120) ),
inference(definitional_conversion,[status(esa)],[f_1991_2]) ).
cnf(f_1991_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8120),c_Groups_Ozero__class_Ozero(U_8120)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8120),U_8121),U_8122)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8120),c_Groups_Ozero__class_Ozero(U_8120)),U_8122))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8120),c_Groups_Ozero__class_Ozero(U_8120)),U_8121))
| ~ class_Fields_Olinordered__field(U_8120) ),
inference(clausify,[status(thm)],[f_1991_3]) ).
fof(f_1992_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_1992_2,plain,
! [U_8125,U_8124,U_8123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8123),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8123),U_8124),U_8125)),c_Groups_Ozero__class_Ozero(U_8123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8123),U_8125),c_Groups_Ozero__class_Ozero(U_8123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8123),c_Groups_Ozero__class_Ozero(U_8123)),U_8124))
| ~ class_Fields_Olinordered__field(U_8123) ),
inference(variable_rename,[status(thm)],[f_1992_1]) ).
fof(f_1992_3,plain,
! [U_8123,U_8125,U_8124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8123),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8123),U_8124),U_8125)),c_Groups_Ozero__class_Ozero(U_8123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8123),U_8125),c_Groups_Ozero__class_Ozero(U_8123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8123),c_Groups_Ozero__class_Ozero(U_8123)),U_8124))
| ~ class_Fields_Olinordered__field(U_8123) ),
inference(definitional_conversion,[status(esa)],[f_1992_2]) ).
cnf(f_1992_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8123),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8123),U_8124),U_8125)),c_Groups_Ozero__class_Ozero(U_8123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8123),U_8125),c_Groups_Ozero__class_Ozero(U_8123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8123),c_Groups_Ozero__class_Ozero(U_8123)),U_8124))
| ~ class_Fields_Olinordered__field(U_8123) ),
inference(clausify,[status(thm)],[f_1992_3]) ).
fof(f_1993_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_1993_2,plain,
! [U_8128,U_8127,U_8126] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8126),U_8127),U_8128)),c_Groups_Ozero__class_Ozero(U_8126)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),c_Groups_Ozero__class_Ozero(U_8126)),U_8128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),U_8127),c_Groups_Ozero__class_Ozero(U_8126)))
| ~ class_Fields_Olinordered__field(U_8126) ),
inference(variable_rename,[status(thm)],[f_1993_1]) ).
fof(f_1993_3,plain,
! [U_8127,U_8128,U_8126] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8126),U_8127),U_8128)),c_Groups_Ozero__class_Ozero(U_8126)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),c_Groups_Ozero__class_Ozero(U_8126)),U_8128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),U_8127),c_Groups_Ozero__class_Ozero(U_8126)))
| ~ class_Fields_Olinordered__field(U_8126) ),
inference(definitional_conversion,[status(esa)],[f_1993_2]) ).
cnf(f_1993_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8126),U_8127),U_8128)),c_Groups_Ozero__class_Ozero(U_8126)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),c_Groups_Ozero__class_Ozero(U_8126)),U_8128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8126),U_8127),c_Groups_Ozero__class_Ozero(U_8126)))
| ~ class_Fields_Olinordered__field(U_8126) ),
inference(clausify,[status(thm)],[f_1993_3]) ).
fof(f_1994_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_1994_2,plain,
! [U_8131,U_8130,U_8129] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8129),c_Groups_Ozero__class_Ozero(U_8129)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8129),U_8130),U_8131)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8129),U_8131),c_Groups_Ozero__class_Ozero(U_8129)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8129),U_8130),c_Groups_Ozero__class_Ozero(U_8129)))
| ~ class_Fields_Olinordered__field(U_8129) ),
inference(variable_rename,[status(thm)],[f_1994_1]) ).
fof(f_1994_3,plain,
! [U_8129,U_8130,U_8131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8129),c_Groups_Ozero__class_Ozero(U_8129)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8129),U_8130),U_8131)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8129),U_8131),c_Groups_Ozero__class_Ozero(U_8129)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8129),U_8130),c_Groups_Ozero__class_Ozero(U_8129)))
| ~ class_Fields_Olinordered__field(U_8129) ),
inference(definitional_conversion,[status(esa)],[f_1994_2]) ).
cnf(f_1994_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8129),c_Groups_Ozero__class_Ozero(U_8129)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8129),U_8130),U_8131)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8129),U_8131),c_Groups_Ozero__class_Ozero(U_8129)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8129),U_8130),c_Groups_Ozero__class_Ozero(U_8129)))
| ~ class_Fields_Olinordered__field(U_8129) ),
inference(clausify,[status(thm)],[f_1994_3]) ).
fof(f_1995_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_1995_2,plain,
! [U_8135,U_8134,U_8133,U_8132] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8132),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8132),U_8133),U_8135)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8132),U_8134),U_8135)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8132),c_Groups_Ozero__class_Ozero(U_8132)),U_8135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8132),U_8133),U_8134))
| ~ class_Fields_Olinordered__field(U_8132) ),
inference(variable_rename,[status(thm)],[f_1995_1]) ).
fof(f_1995_3,plain,
! [U_8132,U_8133,U_8134,U_8135] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8132),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8132),U_8133),U_8135)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8132),U_8134),U_8135)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8132),c_Groups_Ozero__class_Ozero(U_8132)),U_8135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8132),U_8133),U_8134))
| ~ class_Fields_Olinordered__field(U_8132) ),
inference(definitional_conversion,[status(esa)],[f_1995_2]) ).
cnf(f_1995_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8132),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8132),U_8133),U_8135)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8132),U_8134),U_8135)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8132),c_Groups_Ozero__class_Ozero(U_8132)),U_8135))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8132),U_8133),U_8134))
| ~ class_Fields_Olinordered__field(U_8132) ),
inference(clausify,[status(thm)],[f_1995_3]) ).
fof(f_1996_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_1996_2,plain,
! [U_8139,U_8138,U_8137,U_8136] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8136),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8136),U_8138),U_8139)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8136),U_8137),U_8139)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8136),U_8139),c_Groups_Ozero__class_Ozero(U_8136)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8136),U_8137),U_8138))
| ~ class_Fields_Olinordered__field(U_8136) ),
inference(variable_rename,[status(thm)],[f_1996_1]) ).
fof(f_1996_3,plain,
! [U_8136,U_8137,U_8138,U_8139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8136),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8136),U_8138),U_8139)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8136),U_8137),U_8139)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8136),U_8139),c_Groups_Ozero__class_Ozero(U_8136)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8136),U_8137),U_8138))
| ~ class_Fields_Olinordered__field(U_8136) ),
inference(definitional_conversion,[status(esa)],[f_1996_2]) ).
cnf(f_1996_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8136),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8136),U_8138),U_8139)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8136),U_8137),U_8139)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8136),U_8139),c_Groups_Ozero__class_Ozero(U_8136)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8136),U_8137),U_8138))
| ~ class_Fields_Olinordered__field(U_8136) ),
inference(clausify,[status(thm)],[f_1996_3]) ).
fof(f_1997_1,plain,
! [V_w_2,V_x_2,V_z_2,V_y_2,T_c] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_w_2),V_z_2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_z_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_w_2),V_y_2) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_w_2),V_y_2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_x_2),V_y_2) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_w_2),V_z_2) ) )
| V_z_2 = c_Groups_Ozero__class_Ozero(T_c)
| V_y_2 = c_Groups_Ozero__class_Ozero(T_c)
| ~ class_Fields_Ofield(T_c) ),
inference(fof_nnf,[status(thm)],[fact_frac__eq__eq]) ).
fof(f_1997_2,plain,
! [U_8144,U_8143,U_8142,U_8141,U_8140] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8140),U_8143),U_8141) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8140),U_8144),U_8142)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8140),U_8143),U_8142) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8140),U_8144),U_8141) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8140),U_8143),U_8142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8140),U_8144),U_8141)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8140),U_8143),U_8141) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8140),U_8144),U_8142) ) )
| U_8142 = c_Groups_Ozero__class_Ozero(U_8140)
| U_8141 = c_Groups_Ozero__class_Ozero(U_8140)
| ~ class_Fields_Ofield(U_8140) ),
inference(variable_rename,[status(thm)],[f_1997_1]) ).
fof(f_1997_3,plain,
( ! [U_8140,U_8141,U_8142,U_8143,U_8144] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8140),U_8143),U_8141) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8140),U_8144),U_8142)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8140),U_8143),U_8142) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8140),U_8144),U_8141)
| ~ sP525(U_8140,U_8141,U_8142,U_8143,U_8144) )
& ! [U_8140,U_8141,U_8142,U_8143,U_8144] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8140),U_8143),U_8142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8140),U_8144),U_8141)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8140),U_8143),U_8141) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8140),U_8144),U_8142)
| ~ sP525(U_8140,U_8141,U_8142,U_8143,U_8144) )
& ! [U_8140,U_8141,U_8142,U_8143,U_8144] :
( sP525(U_8140,U_8141,U_8142,U_8143,U_8144)
| U_8142 = c_Groups_Ozero__class_Ozero(U_8140)
| U_8141 = c_Groups_Ozero__class_Ozero(U_8140)
| ~ class_Fields_Ofield(U_8140) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP525])],[f_1997_2]) ).
cnf(f_1997_4,plain,
( sP525(U_8140,U_8141,U_8142,U_8143,U_8144)
| U_8142 = c_Groups_Ozero__class_Ozero(U_8140)
| U_8141 = c_Groups_Ozero__class_Ozero(U_8140)
| ~ class_Fields_Ofield(U_8140) ),
inference(clausify,[status(thm)],[f_1997_3]) ).
cnf(f_1997_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8140),U_8143),U_8142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8140),U_8144),U_8141)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8140),U_8143),U_8141) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8140),U_8144),U_8142)
| ~ sP525(U_8140,U_8141,U_8142,U_8143,U_8144) ),
inference(clausify,[status(thm)],[f_1997_3]) ).
cnf(f_1997_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8140),U_8143),U_8141) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8140),U_8144),U_8142)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8140),U_8143),U_8142) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8140),U_8144),U_8141)
| ~ sP525(U_8140,U_8141,U_8142,U_8143,U_8144) ),
inference(clausify,[status(thm)],[f_1997_3]) ).
fof(f_1998_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_1998_2,plain,
! [U_8148,U_8147,U_8146,U_8145] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8145),U_8146),U_8147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8145),U_8146),U_8148)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8145),U_8147),U_8148)
| U_8146 = c_Groups_Ozero__class_Ozero(U_8145)
| ~ class_Fields_Ofield__inverse__zero(U_8145) ),
inference(variable_rename,[status(thm)],[f_1998_1]) ).
fof(f_1998_3,plain,
! [U_8146,U_8147,U_8145,U_8148] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8145),U_8146),U_8147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8145),U_8146),U_8148)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8145),U_8147),U_8148)
| U_8146 = c_Groups_Ozero__class_Ozero(U_8145)
| ~ class_Fields_Ofield__inverse__zero(U_8145) ),
inference(definitional_conversion,[status(esa)],[f_1998_2]) ).
cnf(f_1998_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8145),U_8146),U_8147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8145),U_8146),U_8148)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8145),U_8147),U_8148)
| U_8146 = c_Groups_Ozero__class_Ozero(U_8145)
| ~ class_Fields_Ofield__inverse__zero(U_8145) ),
inference(clausify,[status(thm)],[f_1998_3]) ).
fof(f_1999_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_1999_2,plain,
! [U_8152,U_8151,U_8150,U_8149] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8149),U_8151),U_8150)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8149),U_8152),U_8150)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8149),U_8151),U_8152)
| U_8150 = c_Groups_Ozero__class_Ozero(U_8149)
| ~ class_Fields_Ofield__inverse__zero(U_8149) ),
inference(variable_rename,[status(thm)],[f_1999_1]) ).
fof(f_1999_3,plain,
! [U_8149,U_8150,U_8151,U_8152] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8149),U_8151),U_8150)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8149),U_8152),U_8150)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8149),U_8151),U_8152)
| U_8150 = c_Groups_Ozero__class_Ozero(U_8149)
| ~ class_Fields_Ofield__inverse__zero(U_8149) ),
inference(definitional_conversion,[status(esa)],[f_1999_2]) ).
cnf(f_1999_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8149),U_8151),U_8150)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8149),U_8152),U_8150)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8149),U_8151),U_8152)
| U_8150 = c_Groups_Ozero__class_Ozero(U_8149)
| ~ class_Fields_Ofield__inverse__zero(U_8149) ),
inference(clausify,[status(thm)],[f_1999_3]) ).
fof(f_2000_1,plain,
! [V_a_2,V_c_2,V_b_2,T_c] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) = V_a_2
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_c)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_c) )
| ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)
& V_c_2 != c_Groups_Ozero__class_Ozero(T_c) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)
| V_c_2 = c_Groups_Ozero__class_Ozero(T_c) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) != V_a_2 ) )
| ~ class_Fields_Ofield__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq]) ).
fof(f_2000_2,plain,
! [U_8156,U_8155,U_8154,U_8153] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8153),U_8154),U_8155) = U_8156
| ( U_8156 != c_Groups_Ozero__class_Ozero(U_8153)
& U_8155 = c_Groups_Ozero__class_Ozero(U_8153) )
| ( U_8154 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8153),U_8156),U_8155)
& U_8155 != c_Groups_Ozero__class_Ozero(U_8153) ) )
& ( ( ( U_8156 = c_Groups_Ozero__class_Ozero(U_8153)
| U_8155 != c_Groups_Ozero__class_Ozero(U_8153) )
& ( U_8154 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8153),U_8156),U_8155)
| U_8155 = c_Groups_Ozero__class_Ozero(U_8153) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8153),U_8154),U_8155) != U_8156 ) )
| ~ class_Fields_Ofield__inverse__zero(U_8153) ),
inference(variable_rename,[status(thm)],[f_2000_1]) ).
fof(f_2000_3,plain,
( ! [U_8153,U_8155,U_8156] :
( U_8156 != c_Groups_Ozero__class_Ozero(U_8153)
| ~ sP528(U_8153,U_8155,U_8156) )
& ! [U_8153,U_8155,U_8156] :
( U_8155 = c_Groups_Ozero__class_Ozero(U_8153)
| ~ sP528(U_8153,U_8155,U_8156) )
& ! [U_8154,U_8153,U_8155,U_8156] :
( U_8154 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8153),U_8156),U_8155)
| ~ sP527(U_8154,U_8153,U_8155,U_8156) )
& ! [U_8154,U_8153,U_8155,U_8156] :
( U_8155 != c_Groups_Ozero__class_Ozero(U_8153)
| ~ sP527(U_8154,U_8153,U_8155,U_8156) )
& ! [U_8154,U_8153,U_8155,U_8156] :
( U_8156 = c_Groups_Ozero__class_Ozero(U_8153)
| U_8155 != c_Groups_Ozero__class_Ozero(U_8153)
| ~ sP526(U_8154,U_8153,U_8155,U_8156) )
& ! [U_8154,U_8153,U_8155,U_8156] :
( U_8154 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8153),U_8156),U_8155)
| U_8155 = c_Groups_Ozero__class_Ozero(U_8153)
| ~ sP526(U_8154,U_8153,U_8155,U_8156) )
& ! [U_8154,U_8153,U_8155,U_8156] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8153),U_8154),U_8155) = U_8156
| sP528(U_8153,U_8155,U_8156)
| sP527(U_8154,U_8153,U_8155,U_8156)
| ~ sP529(U_8154,U_8153,U_8155,U_8156) )
& ! [U_8154,U_8153,U_8155,U_8156] :
( sP526(U_8154,U_8153,U_8155,U_8156)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8153),U_8154),U_8155) != U_8156
| ~ sP529(U_8154,U_8153,U_8155,U_8156) )
& ! [U_8154,U_8153,U_8155,U_8156] :
( sP529(U_8154,U_8153,U_8155,U_8156)
| ~ class_Fields_Ofield__inverse__zero(U_8153) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP526,sP527,sP528,sP529])],[f_2000_2]) ).
cnf(f_2000_4,plain,
( sP529(U_8154,U_8153,U_8155,U_8156)
| ~ class_Fields_Ofield__inverse__zero(U_8153) ),
inference(clausify,[status(thm)],[f_2000_3]) ).
cnf(f_2000_5,plain,
( sP526(U_8154,U_8153,U_8155,U_8156)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8153),U_8154),U_8155) != U_8156
| ~ sP529(U_8154,U_8153,U_8155,U_8156) ),
inference(clausify,[status(thm)],[f_2000_3]) ).
cnf(f_2000_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8153),U_8154),U_8155) = U_8156
| sP528(U_8153,U_8155,U_8156)
| sP527(U_8154,U_8153,U_8155,U_8156)
| ~ sP529(U_8154,U_8153,U_8155,U_8156) ),
inference(clausify,[status(thm)],[f_2000_3]) ).
cnf(f_2000_7,plain,
( U_8154 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8153),U_8156),U_8155)
| U_8155 = c_Groups_Ozero__class_Ozero(U_8153)
| ~ sP526(U_8154,U_8153,U_8155,U_8156) ),
inference(clausify,[status(thm)],[f_2000_3]) ).
cnf(f_2000_8,plain,
( U_8156 = c_Groups_Ozero__class_Ozero(U_8153)
| U_8155 != c_Groups_Ozero__class_Ozero(U_8153)
| ~ sP526(U_8154,U_8153,U_8155,U_8156) ),
inference(clausify,[status(thm)],[f_2000_3]) ).
cnf(f_2000_9,plain,
( U_8155 != c_Groups_Ozero__class_Ozero(U_8153)
| ~ sP527(U_8154,U_8153,U_8155,U_8156) ),
inference(clausify,[status(thm)],[f_2000_3]) ).
cnf(f_2000_10,plain,
( U_8154 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8153),U_8156),U_8155)
| ~ sP527(U_8154,U_8153,U_8155,U_8156) ),
inference(clausify,[status(thm)],[f_2000_3]) ).
cnf(f_2000_11,plain,
( U_8155 = c_Groups_Ozero__class_Ozero(U_8153)
| ~ sP528(U_8153,U_8155,U_8156) ),
inference(clausify,[status(thm)],[f_2000_3]) ).
cnf(f_2000_12,plain,
( U_8156 != c_Groups_Ozero__class_Ozero(U_8153)
| ~ sP528(U_8153,U_8155,U_8156) ),
inference(clausify,[status(thm)],[f_2000_3]) ).
fof(f_2001_1,plain,
! [V_c_2,V_b_2,V_a_2,T_c] :
( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_c)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_c) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2) != V_b_2
& V_c_2 != c_Groups_Ozero__class_Ozero(T_c) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2) = V_b_2
| V_c_2 = c_Groups_Ozero__class_Ozero(T_c) ) )
| V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) ) )
| ~ class_Fields_Ofield__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq]) ).
fof(f_2001_2,plain,
! [U_8160,U_8159,U_8158,U_8157] :
( ( ( U_8158 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8157),U_8159),U_8160)
| ( U_8158 != c_Groups_Ozero__class_Ozero(U_8157)
& U_8160 = c_Groups_Ozero__class_Ozero(U_8157) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8157),U_8158),U_8160) != U_8159
& U_8160 != c_Groups_Ozero__class_Ozero(U_8157) ) )
& ( ( ( U_8158 = c_Groups_Ozero__class_Ozero(U_8157)
| U_8160 != c_Groups_Ozero__class_Ozero(U_8157) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8157),U_8158),U_8160) = U_8159
| U_8160 = c_Groups_Ozero__class_Ozero(U_8157) ) )
| U_8158 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8157),U_8159),U_8160) ) )
| ~ class_Fields_Ofield__inverse__zero(U_8157) ),
inference(variable_rename,[status(thm)],[f_2001_1]) ).
fof(f_2001_3,plain,
( ! [U_8157,U_8160,U_8158] :
( U_8158 != c_Groups_Ozero__class_Ozero(U_8157)
| ~ sP532(U_8157,U_8160,U_8158) )
& ! [U_8157,U_8160,U_8158] :
( U_8160 = c_Groups_Ozero__class_Ozero(U_8157)
| ~ sP532(U_8157,U_8160,U_8158) )
& ! [U_8157,U_8159,U_8160,U_8158] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8157),U_8158),U_8160) != U_8159
| ~ sP531(U_8157,U_8159,U_8160,U_8158) )
& ! [U_8157,U_8159,U_8160,U_8158] :
( U_8160 != c_Groups_Ozero__class_Ozero(U_8157)
| ~ sP531(U_8157,U_8159,U_8160,U_8158) )
& ! [U_8157,U_8159,U_8160,U_8158] :
( U_8158 = c_Groups_Ozero__class_Ozero(U_8157)
| U_8160 != c_Groups_Ozero__class_Ozero(U_8157)
| ~ sP530(U_8157,U_8159,U_8160,U_8158) )
& ! [U_8157,U_8159,U_8160,U_8158] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8157),U_8158),U_8160) = U_8159
| U_8160 = c_Groups_Ozero__class_Ozero(U_8157)
| ~ sP530(U_8157,U_8159,U_8160,U_8158) )
& ! [U_8157,U_8159,U_8160,U_8158] :
( U_8158 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8157),U_8159),U_8160)
| sP532(U_8157,U_8160,U_8158)
| sP531(U_8157,U_8159,U_8160,U_8158)
| ~ sP533(U_8157,U_8159,U_8160,U_8158) )
& ! [U_8157,U_8159,U_8160,U_8158] :
( sP530(U_8157,U_8159,U_8160,U_8158)
| U_8158 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8157),U_8159),U_8160)
| ~ sP533(U_8157,U_8159,U_8160,U_8158) )
& ! [U_8157,U_8159,U_8160,U_8158] :
( sP533(U_8157,U_8159,U_8160,U_8158)
| ~ class_Fields_Ofield__inverse__zero(U_8157) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP530,sP531,sP532,sP533])],[f_2001_2]) ).
cnf(f_2001_4,plain,
( sP533(U_8157,U_8159,U_8160,U_8158)
| ~ class_Fields_Ofield__inverse__zero(U_8157) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
cnf(f_2001_5,plain,
( sP530(U_8157,U_8159,U_8160,U_8158)
| U_8158 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8157),U_8159),U_8160)
| ~ sP533(U_8157,U_8159,U_8160,U_8158) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
cnf(f_2001_6,plain,
( U_8158 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8157),U_8159),U_8160)
| sP532(U_8157,U_8160,U_8158)
| sP531(U_8157,U_8159,U_8160,U_8158)
| ~ sP533(U_8157,U_8159,U_8160,U_8158) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
cnf(f_2001_7,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8157),U_8158),U_8160) = U_8159
| U_8160 = c_Groups_Ozero__class_Ozero(U_8157)
| ~ sP530(U_8157,U_8159,U_8160,U_8158) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
cnf(f_2001_8,plain,
( U_8158 = c_Groups_Ozero__class_Ozero(U_8157)
| U_8160 != c_Groups_Ozero__class_Ozero(U_8157)
| ~ sP530(U_8157,U_8159,U_8160,U_8158) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
cnf(f_2001_9,plain,
( U_8160 != c_Groups_Ozero__class_Ozero(U_8157)
| ~ sP531(U_8157,U_8159,U_8160,U_8158) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
cnf(f_2001_10,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8157),U_8158),U_8160) != U_8159
| ~ sP531(U_8157,U_8159,U_8160,U_8158) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
cnf(f_2001_11,plain,
( U_8160 = c_Groups_Ozero__class_Ozero(U_8157)
| ~ sP532(U_8157,U_8160,U_8158) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
cnf(f_2001_12,plain,
( U_8158 != c_Groups_Ozero__class_Ozero(U_8157)
| ~ sP532(U_8157,U_8160,U_8158) ),
inference(clausify,[status(thm)],[f_2001_3]) ).
fof(f_2002_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_2002_2,plain,
! [U_8163,U_8162,U_8161] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8161),c_Groups_Ozero__class_Ozero(U_8161)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8161),U_8162),U_8163)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8161),c_Groups_Ozero__class_Ozero(U_8161)),U_8163))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8161),c_Groups_Ozero__class_Ozero(U_8161)),U_8162))
| ~ class_Fields_Olinordered__field(U_8161) ),
inference(variable_rename,[status(thm)],[f_2002_1]) ).
fof(f_2002_3,plain,
! [U_8162,U_8163,U_8161] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8161),c_Groups_Ozero__class_Ozero(U_8161)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8161),U_8162),U_8163)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8161),c_Groups_Ozero__class_Ozero(U_8161)),U_8163))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8161),c_Groups_Ozero__class_Ozero(U_8161)),U_8162))
| ~ class_Fields_Olinordered__field(U_8161) ),
inference(definitional_conversion,[status(esa)],[f_2002_2]) ).
cnf(f_2002_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8161),c_Groups_Ozero__class_Ozero(U_8161)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8161),U_8162),U_8163)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8161),c_Groups_Ozero__class_Ozero(U_8161)),U_8163))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8161),c_Groups_Ozero__class_Ozero(U_8161)),U_8162))
| ~ class_Fields_Olinordered__field(U_8161) ),
inference(clausify,[status(thm)],[f_2002_3]) ).
fof(f_2003_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_2003_2,plain,
! [U_8166,U_8165,U_8164] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8164),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8164),U_8165),U_8166)),c_Groups_Ozero__class_Ozero(U_8164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8164),U_8166),c_Groups_Ozero__class_Ozero(U_8164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8164),c_Groups_Ozero__class_Ozero(U_8164)),U_8165))
| ~ class_Fields_Olinordered__field(U_8164) ),
inference(variable_rename,[status(thm)],[f_2003_1]) ).
fof(f_2003_3,plain,
! [U_8164,U_8165,U_8166] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8164),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8164),U_8165),U_8166)),c_Groups_Ozero__class_Ozero(U_8164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8164),U_8166),c_Groups_Ozero__class_Ozero(U_8164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8164),c_Groups_Ozero__class_Ozero(U_8164)),U_8165))
| ~ class_Fields_Olinordered__field(U_8164) ),
inference(definitional_conversion,[status(esa)],[f_2003_2]) ).
cnf(f_2003_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8164),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8164),U_8165),U_8166)),c_Groups_Ozero__class_Ozero(U_8164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8164),U_8166),c_Groups_Ozero__class_Ozero(U_8164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8164),c_Groups_Ozero__class_Ozero(U_8164)),U_8165))
| ~ class_Fields_Olinordered__field(U_8164) ),
inference(clausify,[status(thm)],[f_2003_3]) ).
fof(f_2004_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_2004_2,plain,
! [U_8171,U_8170,U_8169,U_8168,U_8167] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8167),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8167),U_8168),U_8171)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8167),U_8169),U_8170)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8167),U_8170),U_8171))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8167),c_Groups_Ozero__class_Ozero(U_8167)),U_8170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8167),U_8168),U_8169))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8167),c_Groups_Ozero__class_Ozero(U_8167)),U_8168))
| ~ class_Fields_Olinordered__field(U_8167) ),
inference(variable_rename,[status(thm)],[f_2004_1]) ).
fof(f_2004_3,plain,
! [U_8168,U_8167,U_8169,U_8170,U_8171] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8167),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8167),U_8168),U_8171)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8167),U_8169),U_8170)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8167),U_8170),U_8171))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8167),c_Groups_Ozero__class_Ozero(U_8167)),U_8170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8167),U_8168),U_8169))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8167),c_Groups_Ozero__class_Ozero(U_8167)),U_8168))
| ~ class_Fields_Olinordered__field(U_8167) ),
inference(definitional_conversion,[status(esa)],[f_2004_2]) ).
cnf(f_2004_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8167),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8167),U_8168),U_8171)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8167),U_8169),U_8170)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8167),U_8170),U_8171))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8167),c_Groups_Ozero__class_Ozero(U_8167)),U_8170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8167),U_8168),U_8169))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8167),c_Groups_Ozero__class_Ozero(U_8167)),U_8168))
| ~ class_Fields_Olinordered__field(U_8167) ),
inference(clausify,[status(thm)],[f_2004_3]) ).
fof(f_2005_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_2005_2,plain,
! [U_8176,U_8175,U_8174,U_8173,U_8172] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8172),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8172),U_8173),U_8176)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8172),U_8174),U_8175)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8172),U_8175),U_8176))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8172),c_Groups_Ozero__class_Ozero(U_8172)),U_8175))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8172),U_8173),U_8174))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8172),c_Groups_Ozero__class_Ozero(U_8172)),U_8173))
| ~ class_Fields_Olinordered__field(U_8172) ),
inference(variable_rename,[status(thm)],[f_2005_1]) ).
fof(f_2005_3,plain,
! [U_8174,U_8173,U_8175,U_8172,U_8176] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8172),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8172),U_8173),U_8176)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8172),U_8174),U_8175)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8172),U_8175),U_8176))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8172),c_Groups_Ozero__class_Ozero(U_8172)),U_8175))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8172),U_8173),U_8174))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8172),c_Groups_Ozero__class_Ozero(U_8172)),U_8173))
| ~ class_Fields_Olinordered__field(U_8172) ),
inference(definitional_conversion,[status(esa)],[f_2005_2]) ).
cnf(f_2005_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8172),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8172),U_8173),U_8176)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8172),U_8174),U_8175)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8172),U_8175),U_8176))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8172),c_Groups_Ozero__class_Ozero(U_8172)),U_8175))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8172),U_8173),U_8174))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8172),c_Groups_Ozero__class_Ozero(U_8172)),U_8173))
| ~ class_Fields_Olinordered__field(U_8172) ),
inference(clausify,[status(thm)],[f_2005_3]) ).
fof(f_2006_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_2006_2,plain,
! [U_8181,U_8180,U_8179,U_8178,U_8177] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8177),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8177),U_8178),U_8181)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8177),U_8179),U_8180)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8177),U_8180),U_8181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8177),c_Groups_Ozero__class_Ozero(U_8177)),U_8180))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8177),U_8178),U_8179))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8177),c_Groups_Ozero__class_Ozero(U_8177)),U_8178))
| ~ class_Fields_Olinordered__field(U_8177) ),
inference(variable_rename,[status(thm)],[f_2006_1]) ).
fof(f_2006_3,plain,
! [U_8177,U_8178,U_8180,U_8179,U_8181] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8177),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8177),U_8178),U_8181)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8177),U_8179),U_8180)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8177),U_8180),U_8181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8177),c_Groups_Ozero__class_Ozero(U_8177)),U_8180))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8177),U_8178),U_8179))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8177),c_Groups_Ozero__class_Ozero(U_8177)),U_8178))
| ~ class_Fields_Olinordered__field(U_8177) ),
inference(definitional_conversion,[status(esa)],[f_2006_2]) ).
cnf(f_2006_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8177),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8177),U_8178),U_8181)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8177),U_8179),U_8180)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8177),U_8180),U_8181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8177),c_Groups_Ozero__class_Ozero(U_8177)),U_8180))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8177),U_8178),U_8179))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8177),c_Groups_Ozero__class_Ozero(U_8177)),U_8178))
| ~ class_Fields_Olinordered__field(U_8177) ),
inference(clausify,[status(thm)],[f_2006_3]) ).
fof(f_2007_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_2007_2,plain,
! [U_8184,U_8183,U_8182] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8182),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8182),U_8183),U_8184)),c_Groups_Ozero__class_Ozero(U_8182)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8182),c_Groups_Ozero__class_Ozero(U_8182)),U_8184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8182),U_8183),c_Groups_Ozero__class_Ozero(U_8182)))
| ~ class_Fields_Olinordered__field(U_8182) ),
inference(variable_rename,[status(thm)],[f_2007_1]) ).
fof(f_2007_3,plain,
! [U_8183,U_8182,U_8184] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8182),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8182),U_8183),U_8184)),c_Groups_Ozero__class_Ozero(U_8182)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8182),c_Groups_Ozero__class_Ozero(U_8182)),U_8184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8182),U_8183),c_Groups_Ozero__class_Ozero(U_8182)))
| ~ class_Fields_Olinordered__field(U_8182) ),
inference(definitional_conversion,[status(esa)],[f_2007_2]) ).
cnf(f_2007_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8182),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8182),U_8183),U_8184)),c_Groups_Ozero__class_Ozero(U_8182)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8182),c_Groups_Ozero__class_Ozero(U_8182)),U_8184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8182),U_8183),c_Groups_Ozero__class_Ozero(U_8182)))
| ~ class_Fields_Olinordered__field(U_8182) ),
inference(clausify,[status(thm)],[f_2007_3]) ).
fof(f_2008_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_2008_2,plain,
! [U_8187,U_8186,U_8185] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8185),c_Groups_Ozero__class_Ozero(U_8185)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8185),U_8186),U_8187)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8185),U_8187),c_Groups_Ozero__class_Ozero(U_8185)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8185),U_8186),c_Groups_Ozero__class_Ozero(U_8185)))
| ~ class_Fields_Olinordered__field(U_8185) ),
inference(variable_rename,[status(thm)],[f_2008_1]) ).
fof(f_2008_3,plain,
! [U_8185,U_8186,U_8187] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8185),c_Groups_Ozero__class_Ozero(U_8185)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8185),U_8186),U_8187)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8185),U_8187),c_Groups_Ozero__class_Ozero(U_8185)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8185),U_8186),c_Groups_Ozero__class_Ozero(U_8185)))
| ~ class_Fields_Olinordered__field(U_8185) ),
inference(definitional_conversion,[status(esa)],[f_2008_2]) ).
cnf(f_2008_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8185),c_Groups_Ozero__class_Ozero(U_8185)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8185),U_8186),U_8187)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8185),U_8187),c_Groups_Ozero__class_Ozero(U_8185)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8185),U_8186),c_Groups_Ozero__class_Ozero(U_8185)))
| ~ class_Fields_Olinordered__field(U_8185) ),
inference(clausify,[status(thm)],[f_2008_3]) ).
fof(f_2009_1,plain,
! [V_c_2,V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq]) ).
fof(f_2009_2,plain,
! [U_8191,U_8190,U_8189,U_8188] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8189),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8188),U_8190),U_8191)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8189),c_Groups_Ozero__class_Ozero(U_8188)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8191),c_Groups_Ozero__class_Ozero(U_8188))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8190),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8188),U_8189),U_8191)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8191),c_Groups_Ozero__class_Ozero(U_8188))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),c_Groups_Ozero__class_Ozero(U_8188)),U_8191)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8188),U_8189),U_8191)),U_8190))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),c_Groups_Ozero__class_Ozero(U_8188)),U_8191)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8189),c_Groups_Ozero__class_Ozero(U_8188)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8191),c_Groups_Ozero__class_Ozero(U_8188))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8190),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8188),U_8189),U_8191)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8191),c_Groups_Ozero__class_Ozero(U_8188))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),c_Groups_Ozero__class_Ozero(U_8188)),U_8191)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8188),U_8189),U_8191)),U_8190))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),c_Groups_Ozero__class_Ozero(U_8188)),U_8191)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8189),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8188),U_8190),U_8191))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8188) ),
inference(variable_rename,[status(thm)],[f_2009_1]) ).
fof(f_2009_3,plain,
( ! [U_8188,U_8189,U_8191] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8189),c_Groups_Ozero__class_Ozero(U_8188)))
| ~ sP538(U_8188,U_8189,U_8191) )
& ! [U_8188,U_8189,U_8191] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8191),c_Groups_Ozero__class_Ozero(U_8188)))
| ~ sP538(U_8188,U_8189,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8190),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8188),U_8189),U_8191)))
| ~ sP537(U_8188,U_8189,U_8190,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8191),c_Groups_Ozero__class_Ozero(U_8188)))
| ~ sP537(U_8188,U_8189,U_8190,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( sP538(U_8188,U_8189,U_8191)
| sP537(U_8188,U_8189,U_8190,U_8191)
| ~ sP539(U_8188,U_8189,U_8190,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),c_Groups_Ozero__class_Ozero(U_8188)),U_8191))
| ~ sP539(U_8188,U_8189,U_8190,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8188),U_8189),U_8191)),U_8190))
| ~ sP536(U_8188,U_8189,U_8190,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),c_Groups_Ozero__class_Ozero(U_8188)),U_8191))
| ~ sP536(U_8188,U_8189,U_8190,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8189),c_Groups_Ozero__class_Ozero(U_8188)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8191),c_Groups_Ozero__class_Ozero(U_8188)))
| ~ sP534(U_8188,U_8189,U_8190,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8190),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8188),U_8189),U_8191)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8191),c_Groups_Ozero__class_Ozero(U_8188)))
| ~ sP534(U_8188,U_8189,U_8190,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( sP534(U_8188,U_8189,U_8190,U_8191)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),c_Groups_Ozero__class_Ozero(U_8188)),U_8191))
| ~ sP535(U_8188,U_8189,U_8190,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8188),U_8189),U_8191)),U_8190))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),c_Groups_Ozero__class_Ozero(U_8188)),U_8191))
| ~ sP535(U_8188,U_8189,U_8190,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8189),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8188),U_8190),U_8191)))
| sP539(U_8188,U_8189,U_8190,U_8191)
| sP536(U_8188,U_8189,U_8190,U_8191)
| ~ sP540(U_8188,U_8189,U_8190,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( sP535(U_8188,U_8189,U_8190,U_8191)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8189),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8188),U_8190),U_8191)))
| ~ sP540(U_8188,U_8189,U_8190,U_8191) )
& ! [U_8188,U_8189,U_8190,U_8191] :
( sP540(U_8188,U_8189,U_8190,U_8191)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8188) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP534,sP535,sP536,sP537,sP538,sP539,sP540])],[f_2009_2]) ).
cnf(f_2009_4,plain,
( sP540(U_8188,U_8189,U_8190,U_8191)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8188) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_5,plain,
( sP535(U_8188,U_8189,U_8190,U_8191)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8189),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8188),U_8190),U_8191)))
| ~ sP540(U_8188,U_8189,U_8190,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8189),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8188),U_8190),U_8191)))
| sP539(U_8188,U_8189,U_8190,U_8191)
| sP536(U_8188,U_8189,U_8190,U_8191)
| ~ sP540(U_8188,U_8189,U_8190,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8188),U_8189),U_8191)),U_8190))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),c_Groups_Ozero__class_Ozero(U_8188)),U_8191))
| ~ sP535(U_8188,U_8189,U_8190,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_8,plain,
( sP534(U_8188,U_8189,U_8190,U_8191)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),c_Groups_Ozero__class_Ozero(U_8188)),U_8191))
| ~ sP535(U_8188,U_8189,U_8190,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8190),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8188),U_8189),U_8191)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8191),c_Groups_Ozero__class_Ozero(U_8188)))
| ~ sP534(U_8188,U_8189,U_8190,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8189),c_Groups_Ozero__class_Ozero(U_8188)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8191),c_Groups_Ozero__class_Ozero(U_8188)))
| ~ sP534(U_8188,U_8189,U_8190,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),c_Groups_Ozero__class_Ozero(U_8188)),U_8191))
| ~ sP536(U_8188,U_8189,U_8190,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8188),U_8189),U_8191)),U_8190))
| ~ sP536(U_8188,U_8189,U_8190,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),c_Groups_Ozero__class_Ozero(U_8188)),U_8191))
| ~ sP539(U_8188,U_8189,U_8190,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_14,plain,
( sP538(U_8188,U_8189,U_8191)
| sP537(U_8188,U_8189,U_8190,U_8191)
| ~ sP539(U_8188,U_8189,U_8190,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8191),c_Groups_Ozero__class_Ozero(U_8188)))
| ~ sP537(U_8188,U_8189,U_8190,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8190),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8188),U_8189),U_8191)))
| ~ sP537(U_8188,U_8189,U_8190,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8191),c_Groups_Ozero__class_Ozero(U_8188)))
| ~ sP538(U_8188,U_8189,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
cnf(f_2009_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8188),U_8189),c_Groups_Ozero__class_Ozero(U_8188)))
| ~ sP538(U_8188,U_8189,U_8191) ),
inference(clausify,[status(thm)],[f_2009_3]) ).
fof(f_2010_1,plain,
! [V_a_2,V_c_2,V_b_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq]) ).
fof(f_2010_2,plain,
! [U_8195,U_8194,U_8193,U_8192] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8192),U_8193),U_8194)),U_8195))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8195))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8194),c_Groups_Ozero__class_Ozero(U_8192))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8192),U_8195),U_8194)),U_8193))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8194),c_Groups_Ozero__class_Ozero(U_8192))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8194)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8192),U_8195),U_8194)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8194)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8195))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8194),c_Groups_Ozero__class_Ozero(U_8192))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8192),U_8195),U_8194)),U_8193))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8194),c_Groups_Ozero__class_Ozero(U_8192))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8194)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8192),U_8195),U_8194)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8194)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8192),U_8193),U_8194)),U_8195)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8192) ),
inference(variable_rename,[status(thm)],[f_2010_1]) ).
fof(f_2010_3,plain,
( ! [U_8195,U_8194,U_8192] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8195))
| ~ sP545(U_8195,U_8194,U_8192) )
& ! [U_8195,U_8194,U_8192] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8194),c_Groups_Ozero__class_Ozero(U_8192)))
| ~ sP545(U_8195,U_8194,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8192),U_8195),U_8194)),U_8193))
| ~ sP544(U_8195,U_8194,U_8193,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8194),c_Groups_Ozero__class_Ozero(U_8192)))
| ~ sP544(U_8195,U_8194,U_8193,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( sP545(U_8195,U_8194,U_8192)
| sP544(U_8195,U_8194,U_8193,U_8192)
| ~ sP546(U_8195,U_8194,U_8193,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8194))
| ~ sP546(U_8195,U_8194,U_8193,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8192),U_8195),U_8194)))
| ~ sP543(U_8195,U_8194,U_8193,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8194))
| ~ sP543(U_8195,U_8194,U_8193,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8195))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8194),c_Groups_Ozero__class_Ozero(U_8192)))
| ~ sP541(U_8195,U_8194,U_8193,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8192),U_8195),U_8194)),U_8193))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8194),c_Groups_Ozero__class_Ozero(U_8192)))
| ~ sP541(U_8195,U_8194,U_8193,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( sP541(U_8195,U_8194,U_8193,U_8192)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8194))
| ~ sP542(U_8195,U_8194,U_8193,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8192),U_8195),U_8194)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8194))
| ~ sP542(U_8195,U_8194,U_8193,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8192),U_8193),U_8194)),U_8195))
| sP546(U_8195,U_8194,U_8193,U_8192)
| sP543(U_8195,U_8194,U_8193,U_8192)
| ~ sP547(U_8195,U_8194,U_8193,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( sP542(U_8195,U_8194,U_8193,U_8192)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8192),U_8193),U_8194)),U_8195))
| ~ sP547(U_8195,U_8194,U_8193,U_8192) )
& ! [U_8195,U_8194,U_8193,U_8192] :
( sP547(U_8195,U_8194,U_8193,U_8192)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8192) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP541,sP542,sP543,sP544,sP545,sP546,sP547])],[f_2010_2]) ).
cnf(f_2010_4,plain,
( sP547(U_8195,U_8194,U_8193,U_8192)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_5,plain,
( sP542(U_8195,U_8194,U_8193,U_8192)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8192),U_8193),U_8194)),U_8195))
| ~ sP547(U_8195,U_8194,U_8193,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8192),U_8193),U_8194)),U_8195))
| sP546(U_8195,U_8194,U_8193,U_8192)
| sP543(U_8195,U_8194,U_8193,U_8192)
| ~ sP547(U_8195,U_8194,U_8193,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8192),U_8195),U_8194)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8194))
| ~ sP542(U_8195,U_8194,U_8193,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_8,plain,
( sP541(U_8195,U_8194,U_8193,U_8192)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8194))
| ~ sP542(U_8195,U_8194,U_8193,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8192),U_8195),U_8194)),U_8193))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8194),c_Groups_Ozero__class_Ozero(U_8192)))
| ~ sP541(U_8195,U_8194,U_8193,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8195))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8194),c_Groups_Ozero__class_Ozero(U_8192)))
| ~ sP541(U_8195,U_8194,U_8193,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8194))
| ~ sP543(U_8195,U_8194,U_8193,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8192),U_8195),U_8194)))
| ~ sP543(U_8195,U_8194,U_8193,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8194))
| ~ sP546(U_8195,U_8194,U_8193,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_14,plain,
( sP545(U_8195,U_8194,U_8192)
| sP544(U_8195,U_8194,U_8193,U_8192)
| ~ sP546(U_8195,U_8194,U_8193,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8194),c_Groups_Ozero__class_Ozero(U_8192)))
| ~ sP544(U_8195,U_8194,U_8193,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8192),U_8195),U_8194)),U_8193))
| ~ sP544(U_8195,U_8194,U_8193,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),U_8194),c_Groups_Ozero__class_Ozero(U_8192)))
| ~ sP545(U_8195,U_8194,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
cnf(f_2010_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8192),c_Groups_Ozero__class_Ozero(U_8192)),U_8195))
| ~ sP545(U_8195,U_8194,U_8192) ),
inference(clausify,[status(thm)],[f_2010_3]) ).
fof(f_2011_1,plain,
! [V_b_2,V_a_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
| ~ class_Fields_Olinordered__field(T_c) ),
inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq]) ).
fof(f_2011_2,plain,
! [U_8199,U_8198,U_8197,U_8196] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),U_8198),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8196),U_8199),U_8197)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8196),U_8198),U_8197)),U_8199)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8196),U_8198),U_8197)),U_8199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),U_8198),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8196),U_8199),U_8197))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),c_Groups_Ozero__class_Ozero(U_8196)),U_8197))
| ~ class_Fields_Olinordered__field(U_8196) ),
inference(variable_rename,[status(thm)],[f_2011_1]) ).
fof(f_2011_3,plain,
( ! [U_8199,U_8197,U_8198,U_8196] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),U_8198),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8196),U_8199),U_8197)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8196),U_8198),U_8197)),U_8199))
| ~ sP548(U_8199,U_8197,U_8198,U_8196) )
& ! [U_8199,U_8197,U_8198,U_8196] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8196),U_8198),U_8197)),U_8199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),U_8198),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8196),U_8199),U_8197)))
| ~ sP548(U_8199,U_8197,U_8198,U_8196) )
& ! [U_8199,U_8197,U_8198,U_8196] :
( sP548(U_8199,U_8197,U_8198,U_8196)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),c_Groups_Ozero__class_Ozero(U_8196)),U_8197))
| ~ class_Fields_Olinordered__field(U_8196) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP548])],[f_2011_2]) ).
cnf(f_2011_4,plain,
( sP548(U_8199,U_8197,U_8198,U_8196)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),c_Groups_Ozero__class_Ozero(U_8196)),U_8197))
| ~ class_Fields_Olinordered__field(U_8196) ),
inference(clausify,[status(thm)],[f_2011_3]) ).
cnf(f_2011_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8196),U_8198),U_8197)),U_8199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),U_8198),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8196),U_8199),U_8197)))
| ~ sP548(U_8199,U_8197,U_8198,U_8196) ),
inference(clausify,[status(thm)],[f_2011_3]) ).
cnf(f_2011_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),U_8198),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8196),U_8199),U_8197)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8196),U_8198),U_8197)),U_8199))
| ~ sP548(U_8199,U_8197,U_8198,U_8196) ),
inference(clausify,[status(thm)],[f_2011_3]) ).
fof(f_2012_1,plain,
! [V_a_2,V_b_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2))
| ~ class_Fields_Olinordered__field(T_c) ),
inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq]) ).
fof(f_2012_2,plain,
! [U_8203,U_8202,U_8201,U_8200] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8200),U_8202),U_8201)),U_8203))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),U_8202),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8200),U_8203),U_8201))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),U_8202),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8200),U_8203),U_8201)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8200),U_8202),U_8201)),U_8203)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),c_Groups_Ozero__class_Ozero(U_8200)),U_8201))
| ~ class_Fields_Olinordered__field(U_8200) ),
inference(variable_rename,[status(thm)],[f_2012_1]) ).
fof(f_2012_3,plain,
( ! [U_8200,U_8201,U_8203,U_8202] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8200),U_8202),U_8201)),U_8203))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),U_8202),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8200),U_8203),U_8201)))
| ~ sP549(U_8200,U_8201,U_8203,U_8202) )
& ! [U_8200,U_8201,U_8203,U_8202] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),U_8202),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8200),U_8203),U_8201)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8200),U_8202),U_8201)),U_8203))
| ~ sP549(U_8200,U_8201,U_8203,U_8202) )
& ! [U_8200,U_8201,U_8203,U_8202] :
( sP549(U_8200,U_8201,U_8203,U_8202)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),c_Groups_Ozero__class_Ozero(U_8200)),U_8201))
| ~ class_Fields_Olinordered__field(U_8200) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP549])],[f_2012_2]) ).
cnf(f_2012_4,plain,
( sP549(U_8200,U_8201,U_8203,U_8202)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),c_Groups_Ozero__class_Ozero(U_8200)),U_8201))
| ~ class_Fields_Olinordered__field(U_8200) ),
inference(clausify,[status(thm)],[f_2012_3]) ).
cnf(f_2012_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),U_8202),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8200),U_8203),U_8201)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8200),U_8202),U_8201)),U_8203))
| ~ sP549(U_8200,U_8201,U_8203,U_8202) ),
inference(clausify,[status(thm)],[f_2012_3]) ).
cnf(f_2012_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8200),U_8202),U_8201)),U_8203))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8200),U_8202),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8200),U_8203),U_8201)))
| ~ sP549(U_8200,U_8201,U_8203,U_8202) ),
inference(clausify,[status(thm)],[f_2012_3]) ).
fof(f_2013_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_2013_2,plain,
! [U_8207,U_8206,U_8205,U_8204] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8204),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8204),U_8206),U_8205)),U_8207))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8204),U_8206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8204),U_8207),U_8205)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8204),c_Groups_Ozero__class_Ozero(U_8204)),U_8205))
| ~ class_Fields_Olinordered__field(U_8204) ),
inference(variable_rename,[status(thm)],[f_2013_1]) ).
fof(f_2013_3,plain,
! [U_8204,U_8207,U_8206,U_8205] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8204),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8204),U_8206),U_8205)),U_8207))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8204),U_8206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8204),U_8207),U_8205)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8204),c_Groups_Ozero__class_Ozero(U_8204)),U_8205))
| ~ class_Fields_Olinordered__field(U_8204) ),
inference(definitional_conversion,[status(esa)],[f_2013_2]) ).
cnf(f_2013_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8204),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8204),U_8206),U_8205)),U_8207))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8204),U_8206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8204),U_8207),U_8205)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8204),c_Groups_Ozero__class_Ozero(U_8204)),U_8205))
| ~ class_Fields_Olinordered__field(U_8204) ),
inference(clausify,[status(thm)],[f_2013_3]) ).
fof(f_2014_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_2014_2,plain,
! [U_8211,U_8210,U_8209,U_8208] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8208),U_8210),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8208),U_8211),U_8209)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8208),U_8210),U_8209)),U_8211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8208),c_Groups_Ozero__class_Ozero(U_8208)),U_8209))
| ~ class_Fields_Olinordered__field(U_8208) ),
inference(variable_rename,[status(thm)],[f_2014_1]) ).
fof(f_2014_3,plain,
! [U_8210,U_8208,U_8209,U_8211] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8208),U_8210),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8208),U_8211),U_8209)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8208),U_8210),U_8209)),U_8211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8208),c_Groups_Ozero__class_Ozero(U_8208)),U_8209))
| ~ class_Fields_Olinordered__field(U_8208) ),
inference(definitional_conversion,[status(esa)],[f_2014_2]) ).
cnf(f_2014_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8208),U_8210),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8208),U_8211),U_8209)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8208),U_8210),U_8209)),U_8211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8208),c_Groups_Ozero__class_Ozero(U_8208)),U_8209))
| ~ class_Fields_Olinordered__field(U_8208) ),
inference(clausify,[status(thm)],[f_2014_3]) ).
fof(f_2015_1,plain,
! [V_b_2,V_a_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ class_Fields_Olinordered__field(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq]) ).
fof(f_2015_2,plain,
! [U_8215,U_8214,U_8213,U_8212] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8214),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8212),U_8215),U_8213)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8212),U_8214),U_8213))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8212),U_8214),U_8213)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8214),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8212),U_8215),U_8213))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8213),c_Groups_Ozero__class_Ozero(U_8212)))
| ~ class_Fields_Olinordered__field(U_8212) ),
inference(variable_rename,[status(thm)],[f_2015_1]) ).
fof(f_2015_3,plain,
( ! [U_8213,U_8212,U_8214,U_8215] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8214),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8212),U_8215),U_8213)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8212),U_8214),U_8213)))
| ~ sP550(U_8213,U_8212,U_8214,U_8215) )
& ! [U_8213,U_8212,U_8214,U_8215] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8212),U_8214),U_8213)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8214),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8212),U_8215),U_8213)))
| ~ sP550(U_8213,U_8212,U_8214,U_8215) )
& ! [U_8213,U_8212,U_8214,U_8215] :
( sP550(U_8213,U_8212,U_8214,U_8215)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8213),c_Groups_Ozero__class_Ozero(U_8212)))
| ~ class_Fields_Olinordered__field(U_8212) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP550])],[f_2015_2]) ).
cnf(f_2015_4,plain,
( sP550(U_8213,U_8212,U_8214,U_8215)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8213),c_Groups_Ozero__class_Ozero(U_8212)))
| ~ class_Fields_Olinordered__field(U_8212) ),
inference(clausify,[status(thm)],[f_2015_3]) ).
cnf(f_2015_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8212),U_8214),U_8213)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8214),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8212),U_8215),U_8213)))
| ~ sP550(U_8213,U_8212,U_8214,U_8215) ),
inference(clausify,[status(thm)],[f_2015_3]) ).
cnf(f_2015_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8214),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8212),U_8215),U_8213)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8212),U_8215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8212),U_8214),U_8213)))
| ~ sP550(U_8213,U_8212,U_8214,U_8215) ),
inference(clausify,[status(thm)],[f_2015_3]) ).
fof(f_2016_1,plain,
! [V_a_2,V_b_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ class_Fields_Olinordered__field(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq]) ).
fof(f_2016_2,plain,
! [U_8219,U_8218,U_8217,U_8216] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8216),U_8218),U_8217)),U_8219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8216),U_8219),U_8217)),U_8218)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8216),U_8219),U_8217)),U_8218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8216),U_8218),U_8217)),U_8219)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),U_8217),c_Groups_Ozero__class_Ozero(U_8216)))
| ~ class_Fields_Olinordered__field(U_8216) ),
inference(variable_rename,[status(thm)],[f_2016_1]) ).
fof(f_2016_3,plain,
( ! [U_8217,U_8216,U_8218,U_8219] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8216),U_8218),U_8217)),U_8219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8216),U_8219),U_8217)),U_8218))
| ~ sP551(U_8217,U_8216,U_8218,U_8219) )
& ! [U_8217,U_8216,U_8218,U_8219] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8216),U_8219),U_8217)),U_8218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8216),U_8218),U_8217)),U_8219))
| ~ sP551(U_8217,U_8216,U_8218,U_8219) )
& ! [U_8217,U_8216,U_8218,U_8219] :
( sP551(U_8217,U_8216,U_8218,U_8219)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),U_8217),c_Groups_Ozero__class_Ozero(U_8216)))
| ~ class_Fields_Olinordered__field(U_8216) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP551])],[f_2016_2]) ).
cnf(f_2016_4,plain,
( sP551(U_8217,U_8216,U_8218,U_8219)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),U_8217),c_Groups_Ozero__class_Ozero(U_8216)))
| ~ class_Fields_Olinordered__field(U_8216) ),
inference(clausify,[status(thm)],[f_2016_3]) ).
cnf(f_2016_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8216),U_8219),U_8217)),U_8218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8216),U_8218),U_8217)),U_8219))
| ~ sP551(U_8217,U_8216,U_8218,U_8219) ),
inference(clausify,[status(thm)],[f_2016_3]) ).
cnf(f_2016_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8216),U_8218),U_8217)),U_8219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8216),U_8219),U_8217)),U_8218))
| ~ sP551(U_8217,U_8216,U_8218,U_8219) ),
inference(clausify,[status(thm)],[f_2016_3]) ).
fof(f_2017_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_2017_2,plain,
! [U_8223,U_8222,U_8221,U_8220] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8220),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8220),U_8223),U_8222)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8220),U_8223),U_8221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8220),c_Groups_Ozero__class_Ozero(U_8220)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8220),U_8222),U_8221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8220),c_Groups_Ozero__class_Ozero(U_8220)),U_8223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8220),U_8221),U_8222))
| ~ class_Fields_Olinordered__field(U_8220) ),
inference(variable_rename,[status(thm)],[f_2017_1]) ).
fof(f_2017_3,plain,
! [U_8220,U_8221,U_8222,U_8223] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8220),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8220),U_8223),U_8222)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8220),U_8223),U_8221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8220),c_Groups_Ozero__class_Ozero(U_8220)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8220),U_8222),U_8221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8220),c_Groups_Ozero__class_Ozero(U_8220)),U_8223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8220),U_8221),U_8222))
| ~ class_Fields_Olinordered__field(U_8220) ),
inference(definitional_conversion,[status(esa)],[f_2017_2]) ).
cnf(f_2017_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8220),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8220),U_8223),U_8222)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8220),U_8223),U_8221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8220),c_Groups_Ozero__class_Ozero(U_8220)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8220),U_8222),U_8221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8220),c_Groups_Ozero__class_Ozero(U_8220)),U_8223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8220),U_8221),U_8222))
| ~ class_Fields_Olinordered__field(U_8220) ),
inference(clausify,[status(thm)],[f_2017_3]) ).
fof(f_2018_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_2018_2,plain,
! [U_8227,U_8226,U_8225,U_8224] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8224),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8224),U_8227),U_8225)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8224),U_8227),U_8226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8224),c_Groups_Ozero__class_Ozero(U_8224)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8224),U_8225),U_8226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8224),U_8227),c_Groups_Ozero__class_Ozero(U_8224)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8224),U_8225),U_8226))
| ~ class_Fields_Olinordered__field(U_8224) ),
inference(variable_rename,[status(thm)],[f_2018_1]) ).
fof(f_2018_3,plain,
! [U_8225,U_8226,U_8224,U_8227] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8224),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8224),U_8227),U_8225)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8224),U_8227),U_8226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8224),c_Groups_Ozero__class_Ozero(U_8224)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8224),U_8225),U_8226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8224),U_8227),c_Groups_Ozero__class_Ozero(U_8224)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8224),U_8225),U_8226))
| ~ class_Fields_Olinordered__field(U_8224) ),
inference(definitional_conversion,[status(esa)],[f_2018_2]) ).
cnf(f_2018_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8224),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8224),U_8227),U_8225)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8224),U_8227),U_8226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8224),c_Groups_Ozero__class_Ozero(U_8224)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8224),U_8225),U_8226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8224),U_8227),c_Groups_Ozero__class_Ozero(U_8224)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8224),U_8225),U_8226))
| ~ class_Fields_Olinordered__field(U_8224) ),
inference(clausify,[status(thm)],[f_2018_3]) ).
fof(f_2019_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_2019_2,plain,
! [U_8232,U_8231,U_8230,U_8229,U_8228] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8228),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8228),U_8231),U_8229)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8228),U_8232),U_8230)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8228),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8228),U_8231),U_8230)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8228),U_8232),U_8229))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8228),U_8229),U_8230))
| U_8230 = c_Groups_Ozero__class_Ozero(U_8228)
| U_8229 = c_Groups_Ozero__class_Ozero(U_8228)
| ~ class_Fields_Ofield(U_8228) ),
inference(variable_rename,[status(thm)],[f_2019_1]) ).
fof(f_2019_3,plain,
! [U_8228,U_8229,U_8230,U_8231,U_8232] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8228),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8228),U_8231),U_8229)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8228),U_8232),U_8230)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8228),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8228),U_8231),U_8230)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8228),U_8232),U_8229))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8228),U_8229),U_8230))
| U_8230 = c_Groups_Ozero__class_Ozero(U_8228)
| U_8229 = c_Groups_Ozero__class_Ozero(U_8228)
| ~ class_Fields_Ofield(U_8228) ),
inference(definitional_conversion,[status(esa)],[f_2019_2]) ).
cnf(f_2019_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8228),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8228),U_8231),U_8229)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8228),U_8232),U_8230)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8228),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8228),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8228),U_8231),U_8230)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8228),U_8232),U_8229))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8228),U_8229),U_8230))
| U_8230 = c_Groups_Ozero__class_Ozero(U_8228)
| U_8229 = c_Groups_Ozero__class_Ozero(U_8228)
| ~ class_Fields_Ofield(U_8228) ),
inference(clausify,[status(thm)],[f_2019_3]) ).
fof(f_2020_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_2020_2,plain,
! [U_8236,U_8235,U_8234,U_8233] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8233),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8233),U_8235),U_8234)),U_8236) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8233),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8233),U_8235),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8233),U_8234),U_8236))),U_8234)
| U_8234 = c_Groups_Ozero__class_Ozero(U_8233)
| ~ class_Fields_Ofield(U_8233) ),
inference(variable_rename,[status(thm)],[f_2020_1]) ).
fof(f_2020_3,plain,
! [U_8233,U_8234,U_8235,U_8236] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8233),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8233),U_8235),U_8234)),U_8236) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8233),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8233),U_8235),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8233),U_8234),U_8236))),U_8234)
| U_8234 = c_Groups_Ozero__class_Ozero(U_8233)
| ~ class_Fields_Ofield(U_8233) ),
inference(definitional_conversion,[status(esa)],[f_2020_2]) ).
cnf(f_2020_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8233),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8233),U_8235),U_8234)),U_8236) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8233),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8233),U_8235),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8233),U_8234),U_8236))),U_8234)
| U_8234 = c_Groups_Ozero__class_Ozero(U_8233)
| ~ class_Fields_Ofield(U_8233) ),
inference(clausify,[status(thm)],[f_2020_3]) ).
fof(f_2021_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_2021_2,plain,
! [U_8240,U_8239,U_8238,U_8237] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8237),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8237),U_8239),U_8238)),U_8240) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8237),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8237),U_8239),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8237),U_8240),U_8238))),U_8238)
| U_8238 = c_Groups_Ozero__class_Ozero(U_8237)
| ~ class_Fields_Ofield__inverse__zero(U_8237) ),
inference(variable_rename,[status(thm)],[f_2021_1]) ).
fof(f_2021_3,plain,
! [U_8237,U_8238,U_8239,U_8240] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8237),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8237),U_8239),U_8238)),U_8240) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8237),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8237),U_8239),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8237),U_8240),U_8238))),U_8238)
| U_8238 = c_Groups_Ozero__class_Ozero(U_8237)
| ~ class_Fields_Ofield__inverse__zero(U_8237) ),
inference(definitional_conversion,[status(esa)],[f_2021_2]) ).
cnf(f_2021_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8237),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8237),U_8239),U_8238)),U_8240) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8237),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8237),U_8239),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8237),U_8240),U_8238))),U_8238)
| U_8238 = c_Groups_Ozero__class_Ozero(U_8237)
| ~ class_Fields_Ofield__inverse__zero(U_8237) ),
inference(clausify,[status(thm)],[f_2021_3]) ).
fof(f_2022_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_2022_2,plain,
! [U_8244,U_8243,U_8242,U_8241] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8241),U_8243),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8241),U_8244),U_8242)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8241),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8241),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8241),U_8242),U_8243)),U_8244)),U_8242)
| U_8242 = c_Groups_Ozero__class_Ozero(U_8241)
| ~ class_Fields_Ofield(U_8241) ),
inference(variable_rename,[status(thm)],[f_2022_1]) ).
fof(f_2022_3,plain,
! [U_8241,U_8242,U_8243,U_8244] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8241),U_8243),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8241),U_8244),U_8242)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8241),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8241),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8241),U_8242),U_8243)),U_8244)),U_8242)
| U_8242 = c_Groups_Ozero__class_Ozero(U_8241)
| ~ class_Fields_Ofield(U_8241) ),
inference(definitional_conversion,[status(esa)],[f_2022_2]) ).
cnf(f_2022_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8241),U_8243),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8241),U_8244),U_8242)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8241),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8241),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8241),U_8242),U_8243)),U_8244)),U_8242)
| U_8242 = c_Groups_Ozero__class_Ozero(U_8241)
| ~ class_Fields_Ofield(U_8241) ),
inference(clausify,[status(thm)],[f_2022_3]) ).
fof(f_2023_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_2023_2,plain,
! [U_8248,U_8247,U_8246,U_8245] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8245),U_8247),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8245),U_8248),U_8246)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8245),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8245),U_8248),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8245),U_8247),U_8246))),U_8246)
| U_8246 = c_Groups_Ozero__class_Ozero(U_8245)
| ~ class_Fields_Ofield__inverse__zero(U_8245) ),
inference(variable_rename,[status(thm)],[f_2023_1]) ).
fof(f_2023_3,plain,
! [U_8245,U_8246,U_8247,U_8248] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8245),U_8247),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8245),U_8248),U_8246)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8245),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8245),U_8248),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8245),U_8247),U_8246))),U_8246)
| U_8246 = c_Groups_Ozero__class_Ozero(U_8245)
| ~ class_Fields_Ofield__inverse__zero(U_8245) ),
inference(definitional_conversion,[status(esa)],[f_2023_2]) ).
cnf(f_2023_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8245),U_8247),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8245),U_8248),U_8246)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8245),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8245),U_8248),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8245),U_8247),U_8246))),U_8246)
| U_8246 = c_Groups_Ozero__class_Ozero(U_8245)
| ~ class_Fields_Ofield__inverse__zero(U_8245) ),
inference(clausify,[status(thm)],[f_2023_3]) ).
fof(f_2024_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_2024_2,plain,
! [U_8253,U_8252,U_8251,U_8250,U_8249] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8249),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8249),U_8252),U_8250)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8249),U_8253),U_8251)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8249),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8249),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8249),U_8252),U_8251)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8249),U_8253),U_8250))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8249),U_8250),U_8251))
| U_8251 = c_Groups_Ozero__class_Ozero(U_8249)
| U_8250 = c_Groups_Ozero__class_Ozero(U_8249)
| ~ class_Fields_Ofield(U_8249) ),
inference(variable_rename,[status(thm)],[f_2024_1]) ).
fof(f_2024_3,plain,
! [U_8249,U_8250,U_8251,U_8252,U_8253] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8249),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8249),U_8252),U_8250)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8249),U_8253),U_8251)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8249),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8249),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8249),U_8252),U_8251)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8249),U_8253),U_8250))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8249),U_8250),U_8251))
| U_8251 = c_Groups_Ozero__class_Ozero(U_8249)
| U_8250 = c_Groups_Ozero__class_Ozero(U_8249)
| ~ class_Fields_Ofield(U_8249) ),
inference(definitional_conversion,[status(esa)],[f_2024_2]) ).
cnf(f_2024_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8249),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8249),U_8252),U_8250)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8249),U_8253),U_8251)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8249),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8249),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8249),U_8252),U_8251)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8249),U_8253),U_8250))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8249),U_8250),U_8251))
| U_8251 = c_Groups_Ozero__class_Ozero(U_8249)
| U_8250 = c_Groups_Ozero__class_Ozero(U_8249)
| ~ class_Fields_Ofield(U_8249) ),
inference(clausify,[status(thm)],[f_2024_3]) ).
fof(f_2025_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_2025_2,plain,
! [U_8257,U_8256,U_8255,U_8254] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8254),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8254),U_8256),U_8255)),U_8257) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8254),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8254),U_8256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8254),U_8255),U_8257))),U_8255)
| U_8255 = c_Groups_Ozero__class_Ozero(U_8254)
| ~ class_Fields_Ofield(U_8254) ),
inference(variable_rename,[status(thm)],[f_2025_1]) ).
fof(f_2025_3,plain,
! [U_8255,U_8254,U_8256,U_8257] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8254),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8254),U_8256),U_8255)),U_8257) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8254),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8254),U_8256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8254),U_8255),U_8257))),U_8255)
| U_8255 = c_Groups_Ozero__class_Ozero(U_8254)
| ~ class_Fields_Ofield(U_8254) ),
inference(definitional_conversion,[status(esa)],[f_2025_2]) ).
cnf(f_2025_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8254),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8254),U_8256),U_8255)),U_8257) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8254),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8254),U_8256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8254),U_8255),U_8257))),U_8255)
| U_8255 = c_Groups_Ozero__class_Ozero(U_8254)
| ~ class_Fields_Ofield(U_8254) ),
inference(clausify,[status(thm)],[f_2025_3]) ).
fof(f_2026_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_2026_2,plain,
! [U_8261,U_8260,U_8259,U_8258] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8258),U_8260),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8258),U_8261),U_8259)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8258),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8258),U_8259),U_8260)),U_8261)),U_8259)
| U_8259 = c_Groups_Ozero__class_Ozero(U_8258)
| ~ class_Fields_Ofield(U_8258) ),
inference(variable_rename,[status(thm)],[f_2026_1]) ).
fof(f_2026_3,plain,
! [U_8258,U_8259,U_8260,U_8261] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8258),U_8260),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8258),U_8261),U_8259)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8258),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8258),U_8259),U_8260)),U_8261)),U_8259)
| U_8259 = c_Groups_Ozero__class_Ozero(U_8258)
| ~ class_Fields_Ofield(U_8258) ),
inference(definitional_conversion,[status(esa)],[f_2026_2]) ).
cnf(f_2026_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8258),U_8260),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8258),U_8261),U_8259)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8258),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8258),U_8259),U_8260)),U_8261)),U_8259)
| U_8259 = c_Groups_Ozero__class_Ozero(U_8258)
| ~ class_Fields_Ofield(U_8258) ),
inference(clausify,[status(thm)],[f_2026_3]) ).
fof(f_2027_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_2027_2,plain,
! [U_8264,U_8263,U_8262] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8262),U_8263),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8262),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8262),U_8263),U_8264)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8262),c_Groups_Oone__class_Oone(U_8262)),c_Groups_Oone__class_Oone(U_8262)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8262),U_8263),U_8264))
| ~ class_Fields_Olinordered__field(U_8262) ),
inference(variable_rename,[status(thm)],[f_2027_1]) ).
fof(f_2027_3,plain,
! [U_8262,U_8263,U_8264] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8262),U_8263),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8262),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8262),U_8263),U_8264)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8262),c_Groups_Oone__class_Oone(U_8262)),c_Groups_Oone__class_Oone(U_8262)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8262),U_8263),U_8264))
| ~ class_Fields_Olinordered__field(U_8262) ),
inference(definitional_conversion,[status(esa)],[f_2027_2]) ).
cnf(f_2027_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8262),U_8263),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8262),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8262),U_8263),U_8264)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8262),c_Groups_Oone__class_Oone(U_8262)),c_Groups_Oone__class_Oone(U_8262)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8262),U_8263),U_8264))
| ~ class_Fields_Olinordered__field(U_8262) ),
inference(clausify,[status(thm)],[f_2027_3]) ).
fof(f_2028_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_2028_2,plain,
! [U_8267,U_8266,U_8265] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8265),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8265),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8265),U_8266),U_8267)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8265),c_Groups_Oone__class_Oone(U_8265)),c_Groups_Oone__class_Oone(U_8265)))),U_8267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8265),U_8266),U_8267))
| ~ class_Fields_Olinordered__field(U_8265) ),
inference(variable_rename,[status(thm)],[f_2028_1]) ).
fof(f_2028_3,plain,
! [U_8265,U_8266,U_8267] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8265),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8265),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8265),U_8266),U_8267)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8265),c_Groups_Oone__class_Oone(U_8265)),c_Groups_Oone__class_Oone(U_8265)))),U_8267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8265),U_8266),U_8267))
| ~ class_Fields_Olinordered__field(U_8265) ),
inference(definitional_conversion,[status(esa)],[f_2028_2]) ).
cnf(f_2028_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8265),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8265),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8265),U_8266),U_8267)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8265),c_Groups_Oone__class_Oone(U_8265)),c_Groups_Oone__class_Oone(U_8265)))),U_8267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8265),U_8266),U_8267))
| ~ class_Fields_Olinordered__field(U_8265) ),
inference(clausify,[status(thm)],[f_2028_3]) ).
fof(f_2029_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_2029_2,plain,
! [U_8271,U_8270,U_8269,U_8268] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8268),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8268),U_8271),U_8269)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8268),U_8271),U_8270)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8268),c_Groups_Ozero__class_Ozero(U_8268)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8268),U_8269),U_8270)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8268),U_8271),c_Groups_Ozero__class_Ozero(U_8268)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8268),U_8269),U_8270))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8268) ),
inference(variable_rename,[status(thm)],[f_2029_1]) ).
fof(f_2029_3,plain,
! [U_8268,U_8269,U_8270,U_8271] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8268),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8268),U_8271),U_8269)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8268),U_8271),U_8270)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8268),c_Groups_Ozero__class_Ozero(U_8268)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8268),U_8269),U_8270)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8268),U_8271),c_Groups_Ozero__class_Ozero(U_8268)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8268),U_8269),U_8270))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8268) ),
inference(definitional_conversion,[status(esa)],[f_2029_2]) ).
cnf(f_2029_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8268),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8268),U_8271),U_8269)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8268),U_8271),U_8270)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8268),c_Groups_Ozero__class_Ozero(U_8268)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8268),U_8269),U_8270)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8268),U_8271),c_Groups_Ozero__class_Ozero(U_8268)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8268),U_8269),U_8270))
| ~ class_Fields_Olinordered__field__inverse__zero(U_8268) ),
inference(clausify,[status(thm)],[f_2029_3]) ).
fof(f_2030_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_2030_2,plain,
! [U_8275,U_8274,U_8273,U_8272] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8272),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8272),U_8275),U_8274)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8272),U_8275),U_8273)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8272),c_Groups_Ozero__class_Ozero(U_8272)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8272),U_8274),U_8273)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8272),c_Groups_Ozero__class_Ozero(U_8272)),U_8275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8272),U_8273),U_8274))
| ~ class_Fields_Olinordered__field(U_8272) ),
inference(variable_rename,[status(thm)],[f_2030_1]) ).
fof(f_2030_3,plain,
! [U_8272,U_8273,U_8274,U_8275] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8272),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8272),U_8275),U_8274)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8272),U_8275),U_8273)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8272),c_Groups_Ozero__class_Ozero(U_8272)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8272),U_8274),U_8273)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8272),c_Groups_Ozero__class_Ozero(U_8272)),U_8275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8272),U_8273),U_8274))
| ~ class_Fields_Olinordered__field(U_8272) ),
inference(definitional_conversion,[status(esa)],[f_2030_2]) ).
cnf(f_2030_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8272),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8272),U_8275),U_8274)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8272),U_8275),U_8273)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8272),c_Groups_Ozero__class_Ozero(U_8272)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8272),U_8274),U_8273)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8272),c_Groups_Ozero__class_Ozero(U_8272)),U_8275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8272),U_8273),U_8274))
| ~ class_Fields_Olinordered__field(U_8272) ),
inference(clausify,[status(thm)],[f_2030_3]) ).
fof(f_2031_1,plain,
! [V_a_2,V_b_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ class_Fields_Olinordered__field(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq]) ).
fof(f_2031_2,plain,
! [U_8279,U_8278,U_8277,U_8276] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8276),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8276),U_8278),U_8277)),U_8279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8276),U_8279),U_8277)),U_8278)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8276),U_8279),U_8277)),U_8278))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8276),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8276),U_8278),U_8277)),U_8279)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),U_8277),c_Groups_Ozero__class_Ozero(U_8276)))
| ~ class_Fields_Olinordered__field(U_8276) ),
inference(variable_rename,[status(thm)],[f_2031_1]) ).
fof(f_2031_3,plain,
( ! [U_8277,U_8276,U_8278,U_8279] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8276),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8276),U_8278),U_8277)),U_8279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8276),U_8279),U_8277)),U_8278))
| ~ sP552(U_8277,U_8276,U_8278,U_8279) )
& ! [U_8277,U_8276,U_8278,U_8279] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8276),U_8279),U_8277)),U_8278))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8276),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8276),U_8278),U_8277)),U_8279))
| ~ sP552(U_8277,U_8276,U_8278,U_8279) )
& ! [U_8277,U_8276,U_8278,U_8279] :
( sP552(U_8277,U_8276,U_8278,U_8279)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),U_8277),c_Groups_Ozero__class_Ozero(U_8276)))
| ~ class_Fields_Olinordered__field(U_8276) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP552])],[f_2031_2]) ).
cnf(f_2031_4,plain,
( sP552(U_8277,U_8276,U_8278,U_8279)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),U_8277),c_Groups_Ozero__class_Ozero(U_8276)))
| ~ class_Fields_Olinordered__field(U_8276) ),
inference(clausify,[status(thm)],[f_2031_3]) ).
cnf(f_2031_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8276),U_8279),U_8277)),U_8278))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8276),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8276),U_8278),U_8277)),U_8279))
| ~ sP552(U_8277,U_8276,U_8278,U_8279) ),
inference(clausify,[status(thm)],[f_2031_3]) ).
cnf(f_2031_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8276),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8276),U_8278),U_8277)),U_8279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8276),U_8279),U_8277)),U_8278))
| ~ sP552(U_8277,U_8276,U_8278,U_8279) ),
inference(clausify,[status(thm)],[f_2031_3]) ).
fof(f_2032_1,plain,
! [V_b_2,V_a_2,V_c_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ class_Fields_Olinordered__field(T_c) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq]) ).
fof(f_2032_2,plain,
! [U_8283,U_8282,U_8281,U_8280] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8280),U_8282),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8280),U_8283),U_8281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8280),U_8283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8280),U_8282),U_8281))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8280),U_8283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8280),U_8282),U_8281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8280),U_8282),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8280),U_8283),U_8281))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8280),U_8281),c_Groups_Ozero__class_Ozero(U_8280)))
| ~ class_Fields_Olinordered__field(U_8280) ),
inference(variable_rename,[status(thm)],[f_2032_1]) ).
fof(f_2032_3,plain,
( ! [U_8281,U_8280,U_8282,U_8283] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8280),U_8282),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8280),U_8283),U_8281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8280),U_8283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8280),U_8282),U_8281)))
| ~ sP553(U_8281,U_8280,U_8282,U_8283) )
& ! [U_8281,U_8280,U_8282,U_8283] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8280),U_8283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8280),U_8282),U_8281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8280),U_8282),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8280),U_8283),U_8281)))
| ~ sP553(U_8281,U_8280,U_8282,U_8283) )
& ! [U_8281,U_8280,U_8282,U_8283] :
( sP553(U_8281,U_8280,U_8282,U_8283)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8280),U_8281),c_Groups_Ozero__class_Ozero(U_8280)))
| ~ class_Fields_Olinordered__field(U_8280) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP553])],[f_2032_2]) ).
cnf(f_2032_4,plain,
( sP553(U_8281,U_8280,U_8282,U_8283)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8280),U_8281),c_Groups_Ozero__class_Ozero(U_8280)))
| ~ class_Fields_Olinordered__field(U_8280) ),
inference(clausify,[status(thm)],[f_2032_3]) ).
cnf(f_2032_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8280),U_8283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8280),U_8282),U_8281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8280),U_8282),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8280),U_8283),U_8281)))
| ~ sP553(U_8281,U_8280,U_8282,U_8283) ),
inference(clausify,[status(thm)],[f_2032_3]) ).
cnf(f_2032_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8280),U_8282),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8280),U_8283),U_8281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8280),U_8283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8280),U_8282),U_8281)))
| ~ sP553(U_8281,U_8280,U_8282,U_8283) ),
inference(clausify,[status(thm)],[f_2032_3]) ).
fof(f_2033_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_2033_2,plain,
! [U_8287,U_8286,U_8285,U_8284] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8284),U_8286),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8284),U_8287),U_8285)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8284),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8284),U_8286),U_8285)),U_8287))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8284),c_Groups_Ozero__class_Ozero(U_8284)),U_8285))
| ~ class_Fields_Olinordered__field(U_8284) ),
inference(variable_rename,[status(thm)],[f_2033_1]) ).
fof(f_2033_3,plain,
! [U_8285,U_8284,U_8286,U_8287] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8284),U_8286),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8284),U_8287),U_8285)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8284),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8284),U_8286),U_8285)),U_8287))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8284),c_Groups_Ozero__class_Ozero(U_8284)),U_8285))
| ~ class_Fields_Olinordered__field(U_8284) ),
inference(definitional_conversion,[status(esa)],[f_2033_2]) ).
cnf(f_2033_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8284),U_8286),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8284),U_8287),U_8285)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8284),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8284),U_8286),U_8285)),U_8287))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8284),c_Groups_Ozero__class_Ozero(U_8284)),U_8285))
| ~ class_Fields_Olinordered__field(U_8284) ),
inference(clausify,[status(thm)],[f_2033_3]) ).
fof(f_2034_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_2034_2,plain,
! [U_8289,U_8288] : c_Int_Onat__aux(U_8288,U_8289) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8288)),U_8289),
inference(variable_rename,[status(thm)],[f_2034_1]) ).
fof(f_2034_3,plain,
! [U_8288,U_8289] : c_Int_Onat__aux(U_8288,U_8289) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8288)),U_8289),
inference(definitional_conversion,[status(esa)],[f_2034_2]) ).
cnf(f_2034_4,plain,
c_Int_Onat__aux(U_8288,U_8289) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_8288)),U_8289),
inference(clausify,[status(thm)],[f_2034_3]) ).
fof(f_2035_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_2035_2,plain,
! [U_8291,U_8290] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8290),U_8291) = 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_8290)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8291)))
| ~ c_Nat__Transfer_Onat__set(U_8291)
| ~ c_Nat__Transfer_Onat__set(U_8290) ),
inference(variable_rename,[status(thm)],[f_2035_1]) ).
fof(f_2035_3,plain,
! [U_8290,U_8291] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8290),U_8291) = 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_8290)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8291)))
| ~ c_Nat__Transfer_Onat__set(U_8291)
| ~ c_Nat__Transfer_Onat__set(U_8290) ),
inference(definitional_conversion,[status(esa)],[f_2035_2]) ).
cnf(f_2035_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8290),U_8291) = 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_8290)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8291)))
| ~ c_Nat__Transfer_Onat__set(U_8291)
| ~ c_Nat__Transfer_Onat__set(U_8290) ),
inference(clausify,[status(thm)],[f_2035_3]) ).
fof(f_2036_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_2036_2,plain,
! [U_8293,U_8292] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8292),U_8293) = 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_8292)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8293)))
| ~ c_Nat__Transfer_Onat__set(U_8293)
| ~ c_Nat__Transfer_Onat__set(U_8292) ),
inference(variable_rename,[status(thm)],[f_2036_1]) ).
fof(f_2036_3,plain,
! [U_8293,U_8292] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8292),U_8293) = 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_8292)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8293)))
| ~ c_Nat__Transfer_Onat__set(U_8293)
| ~ c_Nat__Transfer_Onat__set(U_8292) ),
inference(definitional_conversion,[status(esa)],[f_2036_2]) ).
cnf(f_2036_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8292),U_8293) = 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_8292)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8293)))
| ~ c_Nat__Transfer_Onat__set(U_8293)
| ~ c_Nat__Transfer_Onat__set(U_8292) ),
inference(clausify,[status(thm)],[f_2036_3]) ).
fof(f_2037_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_2037_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_2037_1]) ).
cnf(f_2037_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_2037_2]) ).
fof(f_2038_1,plain,
! [V_f_2,V_A_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_c,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_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J]) ).
fof(f_2038_2,plain,
! [U_8296,U_8295,U_8294] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8294),U_8296),U_8295) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_8294),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8294,tc_Nat_Onat),U_8296),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8295))
| ~ c_Nat__Transfer_Onat__set(U_8295)
| ~ class_Groups_Ocomm__monoid__mult(U_8294)
| ~ class_Groups_Ocomm__monoid__add(U_8294) ),
inference(variable_rename,[status(thm)],[f_2038_1]) ).
fof(f_2038_3,plain,
! [U_8295,U_8294,U_8296] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8294),U_8296),U_8295) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_8294),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8294,tc_Nat_Onat),U_8296),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8295))
| ~ c_Nat__Transfer_Onat__set(U_8295)
| ~ class_Groups_Ocomm__monoid__mult(U_8294)
| ~ class_Groups_Ocomm__monoid__add(U_8294) ),
inference(definitional_conversion,[status(esa)],[f_2038_2]) ).
cnf(f_2038_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8294),U_8296),U_8295) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_8294),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8294,tc_Nat_Onat),U_8296),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8295))
| ~ c_Nat__Transfer_Onat__set(U_8295)
| ~ class_Groups_Ocomm__monoid__mult(U_8294)
| ~ class_Groups_Ocomm__monoid__add(U_8294) ),
inference(clausify,[status(thm)],[f_2038_3]) ).
fof(f_2039_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_2039_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_2039_1]) ).
cnf(f_2039_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_2039_2]) ).
fof(f_2040_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_2040_2,plain,
! [U_8298,U_8297] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8297),U_8298))
| ~ c_Nat__Transfer_Onat__set(U_8298)
| ~ c_Nat__Transfer_Onat__set(U_8297) ),
inference(variable_rename,[status(thm)],[f_2040_1]) ).
fof(f_2040_3,plain,
! [U_8297,U_8298] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8297),U_8298))
| ~ c_Nat__Transfer_Onat__set(U_8298)
| ~ c_Nat__Transfer_Onat__set(U_8297) ),
inference(definitional_conversion,[status(esa)],[f_2040_2]) ).
cnf(f_2040_4,plain,
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8297),U_8298))
| ~ c_Nat__Transfer_Onat__set(U_8298)
| ~ c_Nat__Transfer_Onat__set(U_8297) ),
inference(clausify,[status(thm)],[f_2040_3]) ).
fof(f_2041_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_2041_2,plain,
! [U_8300,U_8299] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8299),U_8300))
| ~ c_Nat__Transfer_Onat__set(U_8300)
| ~ c_Nat__Transfer_Onat__set(U_8299) ),
inference(variable_rename,[status(thm)],[f_2041_1]) ).
fof(f_2041_3,plain,
! [U_8300,U_8299] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8299),U_8300))
| ~ c_Nat__Transfer_Onat__set(U_8300)
| ~ c_Nat__Transfer_Onat__set(U_8299) ),
inference(definitional_conversion,[status(esa)],[f_2041_2]) ).
cnf(f_2041_4,plain,
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8299),U_8300))
| ~ c_Nat__Transfer_Onat__set(U_8300)
| ~ c_Nat__Transfer_Onat__set(U_8299) ),
inference(clausify,[status(thm)],[f_2041_3]) ).
fof(f_2042_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_2042_2,plain,
! [U_8303] :
( ( c_Nat__Transfer_Onat__set(U_8303)
| ? [U_8302] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8302))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8302),U_8303)) ) )
& ( ! [U_8301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8301))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8301),U_8303)) )
| ~ c_Nat__Transfer_Onat__set(U_8303) ) ),
inference(variable_rename,[status(thm)],[f_2042_1]) ).
fof(f_2042_3,plain,
( ! [U_8305] :
( c_Nat__Transfer_Onat__set(U_8305)
| ? [U_8302] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8302))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8302),U_8305)) ) )
& ! [U_8304] :
( ! [U_8301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8301))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8301),U_8304)) )
| ~ c_Nat__Transfer_Onat__set(U_8304) ) ),
inference(miniscope,[status(thm)],[f_2042_2]) ).
fof(f_2042_4,plain,
( ! [U_8305] :
( c_Nat__Transfer_Onat__set(U_8305)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK167(U_8305)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK167(U_8305)),U_8305)) ) )
& ! [U_8304] :
( ! [U_8301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8301))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8301),U_8304)) )
| ~ c_Nat__Transfer_Onat__set(U_8304) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_8302,sK167(U_8305))],[f_2042_3]) ).
fof(f_2042_5,plain,
( ! [U_8305] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK167(U_8305)))
| ~ sP554(U_8305) )
& ! [U_8305] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK167(U_8305)),U_8305))
| ~ sP554(U_8305) )
& ! [U_8305] :
( c_Nat__Transfer_Onat__set(U_8305)
| sP554(U_8305) )
& ! [U_8301,U_8304] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8301))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8301),U_8304))
| ~ c_Nat__Transfer_Onat__set(U_8304) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP554])],[f_2042_4]) ).
cnf(f_2042_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8301))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8301),U_8304))
| ~ c_Nat__Transfer_Onat__set(U_8304) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
cnf(f_2042_7,plain,
( c_Nat__Transfer_Onat__set(U_8305)
| sP554(U_8305) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
cnf(f_2042_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK167(U_8305)),U_8305))
| ~ sP554(U_8305) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
cnf(f_2042_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK167(U_8305)))
| ~ sP554(U_8305) ),
inference(clausify,[status(thm)],[f_2042_5]) ).
fof(f_2043_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_2043_2,plain,
! [U_8306] : 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_8306)),
inference(variable_rename,[status(thm)],[f_2043_1]) ).
fof(f_2043_3,plain,
! [U_8306] : 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_8306)),
inference(definitional_conversion,[status(esa)],[f_2043_2]) ).
cnf(f_2043_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_8306)),
inference(clausify,[status(thm)],[f_2043_3]) ).
fof(f_2044_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_2044_2,plain,
! [U_8308,U_8307] :
( ( ( U_8307 = U_8308
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8307) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8308) )
& ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8307) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8308)
| U_8307 != U_8308 ) )
| ~ c_Nat__Transfer_Onat__set(U_8308)
| ~ c_Nat__Transfer_Onat__set(U_8307) ),
inference(variable_rename,[status(thm)],[f_2044_1]) ).
fof(f_2044_3,plain,
( ! [U_8307,U_8308] :
( U_8307 = U_8308
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8307) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8308)
| ~ sP555(U_8307,U_8308) )
& ! [U_8307,U_8308] :
( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8307) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8308)
| U_8307 != U_8308
| ~ sP555(U_8307,U_8308) )
& ! [U_8307,U_8308] :
( sP555(U_8307,U_8308)
| ~ c_Nat__Transfer_Onat__set(U_8308)
| ~ c_Nat__Transfer_Onat__set(U_8307) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP555])],[f_2044_2]) ).
cnf(f_2044_4,plain,
( sP555(U_8307,U_8308)
| ~ c_Nat__Transfer_Onat__set(U_8308)
| ~ c_Nat__Transfer_Onat__set(U_8307) ),
inference(clausify,[status(thm)],[f_2044_3]) ).
cnf(f_2044_5,plain,
( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8307) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8308)
| U_8307 != U_8308
| ~ sP555(U_8307,U_8308) ),
inference(clausify,[status(thm)],[f_2044_3]) ).
cnf(f_2044_6,plain,
( U_8307 = U_8308
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8307) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8308)
| ~ sP555(U_8307,U_8308) ),
inference(clausify,[status(thm)],[f_2044_3]) ).
fof(f_2045_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_2045_2,plain,
! [U_8310,U_8309] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8310),U_8309))
| ~ c_Nat__Transfer_Onat__set(U_8309) ),
inference(variable_rename,[status(thm)],[f_2045_1]) ).
fof(f_2045_3,plain,
! [U_8309,U_8310] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8310),U_8309))
| ~ c_Nat__Transfer_Onat__set(U_8309) ),
inference(definitional_conversion,[status(esa)],[f_2045_2]) ).
cnf(f_2045_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8310),U_8309))
| ~ c_Nat__Transfer_Onat__set(U_8309) ),
inference(clausify,[status(thm)],[f_2045_3]) ).
fof(f_2046_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_2046_2,plain,
! [U_8311] :
( 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_8311)) = U_8311
| ~ c_Nat__Transfer_Onat__set(U_8311) ),
inference(variable_rename,[status(thm)],[f_2046_1]) ).
fof(f_2046_3,plain,
! [U_8311] :
( 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_8311)) = U_8311
| ~ c_Nat__Transfer_Onat__set(U_8311) ),
inference(definitional_conversion,[status(esa)],[f_2046_2]) ).
cnf(f_2046_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_8311)) = U_8311
| ~ c_Nat__Transfer_Onat__set(U_8311) ),
inference(clausify,[status(thm)],[f_2046_3]) ).
fof(f_2047_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_2047_2,plain,
! [U_8312] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8312))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8312))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8312)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8312)) ) )
| ~ c_Nat__Transfer_Onat__set(U_8312) ),
inference(variable_rename,[status(thm)],[f_2047_1]) ).
fof(f_2047_3,plain,
( ! [U_8312] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8312))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8312)))
| ~ sP556(U_8312) )
& ! [U_8312] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8312)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8312))
| ~ sP556(U_8312) )
& ! [U_8312] :
( sP556(U_8312)
| ~ c_Nat__Transfer_Onat__set(U_8312) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP556])],[f_2047_2]) ).
cnf(f_2047_4,plain,
( sP556(U_8312)
| ~ c_Nat__Transfer_Onat__set(U_8312) ),
inference(clausify,[status(thm)],[f_2047_3]) ).
cnf(f_2047_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_8312)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8312))
| ~ sP556(U_8312) ),
inference(clausify,[status(thm)],[f_2047_3]) ).
cnf(f_2047_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8312))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8312)))
| ~ sP556(U_8312) ),
inference(clausify,[status(thm)],[f_2047_3]) ).
fof(f_2048_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_2048_2,plain,
! [U_8313] :
( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_8313) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8313))
| ~ c_Nat__Transfer_Onat__set(U_8313) ),
inference(variable_rename,[status(thm)],[f_2048_1]) ).
fof(f_2048_3,plain,
! [U_8313] :
( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_8313) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8313))
| ~ c_Nat__Transfer_Onat__set(U_8313) ),
inference(definitional_conversion,[status(esa)],[f_2048_2]) ).
cnf(f_2048_4,plain,
( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_8313) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8313))
| ~ c_Nat__Transfer_Onat__set(U_8313) ),
inference(clausify,[status(thm)],[f_2048_3]) ).
fof(f_2049_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_2049_2,plain,
! [U_8315,U_8314] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8314),U_8315))
| ~ 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_8314)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8315))) )
& ( 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_8314)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8315)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8314),U_8315)) ) )
| ~ c_Nat__Transfer_Onat__set(U_8315)
| ~ c_Nat__Transfer_Onat__set(U_8314) ),
inference(variable_rename,[status(thm)],[f_2049_1]) ).
fof(f_2049_3,plain,
( ! [U_8315,U_8314] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8314),U_8315))
| ~ 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_8314)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8315)))
| ~ sP557(U_8315,U_8314) )
& ! [U_8315,U_8314] :
( 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_8314)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8315)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8314),U_8315))
| ~ sP557(U_8315,U_8314) )
& ! [U_8315,U_8314] :
( sP557(U_8315,U_8314)
| ~ c_Nat__Transfer_Onat__set(U_8315)
| ~ c_Nat__Transfer_Onat__set(U_8314) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP557])],[f_2049_2]) ).
cnf(f_2049_4,plain,
( sP557(U_8315,U_8314)
| ~ c_Nat__Transfer_Onat__set(U_8315)
| ~ c_Nat__Transfer_Onat__set(U_8314) ),
inference(clausify,[status(thm)],[f_2049_3]) ).
cnf(f_2049_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_8314)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8315)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8314),U_8315))
| ~ sP557(U_8315,U_8314) ),
inference(clausify,[status(thm)],[f_2049_3]) ).
cnf(f_2049_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8314),U_8315))
| ~ 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_8314)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8315)))
| ~ sP557(U_8315,U_8314) ),
inference(clausify,[status(thm)],[f_2049_3]) ).
fof(f_2050_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_2050_2,plain,
! [U_8317,U_8316] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8316),U_8317))
| ~ 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_8316)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8317))) )
& ( 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_8316)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8316),U_8317)) ) )
| ~ c_Nat__Transfer_Onat__set(U_8317)
| ~ c_Nat__Transfer_Onat__set(U_8316) ),
inference(variable_rename,[status(thm)],[f_2050_1]) ).
fof(f_2050_3,plain,
( ! [U_8317,U_8316] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8316),U_8317))
| ~ 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_8316)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8317)))
| ~ sP558(U_8317,U_8316) )
& ! [U_8317,U_8316] :
( 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_8316)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8316),U_8317))
| ~ sP558(U_8317,U_8316) )
& ! [U_8317,U_8316] :
( sP558(U_8317,U_8316)
| ~ c_Nat__Transfer_Onat__set(U_8317)
| ~ c_Nat__Transfer_Onat__set(U_8316) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP558])],[f_2050_2]) ).
cnf(f_2050_4,plain,
( sP558(U_8317,U_8316)
| ~ c_Nat__Transfer_Onat__set(U_8317)
| ~ c_Nat__Transfer_Onat__set(U_8316) ),
inference(clausify,[status(thm)],[f_2050_3]) ).
cnf(f_2050_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_8316)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8316),U_8317))
| ~ sP558(U_8317,U_8316) ),
inference(clausify,[status(thm)],[f_2050_3]) ).
cnf(f_2050_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8316),U_8317))
| ~ 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_8316)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8317)))
| ~ sP558(U_8317,U_8316) ),
inference(clausify,[status(thm)],[f_2050_3]) ).
fof(f_2051_1,plain,
! [V_f_2,V_A_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_c,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_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J]) ).
fof(f_2051_2,plain,
! [U_8320,U_8319,U_8318] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_8318),U_8320),U_8319) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8318),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8318,tc_Nat_Onat),U_8320),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8319))
| ~ c_Nat__Transfer_Onat__set(U_8319)
| ~ class_Groups_Ocomm__monoid__mult(U_8318)
| ~ class_Groups_Ocomm__monoid__add(U_8318) ),
inference(variable_rename,[status(thm)],[f_2051_1]) ).
fof(f_2051_3,plain,
! [U_8319,U_8320,U_8318] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_8318),U_8320),U_8319) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8318),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8318,tc_Nat_Onat),U_8320),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8319))
| ~ c_Nat__Transfer_Onat__set(U_8319)
| ~ class_Groups_Ocomm__monoid__mult(U_8318)
| ~ class_Groups_Ocomm__monoid__add(U_8318) ),
inference(definitional_conversion,[status(esa)],[f_2051_2]) ).
cnf(f_2051_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_8318),U_8320),U_8319) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8318),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8318,tc_Nat_Onat),U_8320),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8319))
| ~ c_Nat__Transfer_Onat__set(U_8319)
| ~ class_Groups_Ocomm__monoid__mult(U_8318)
| ~ class_Groups_Ocomm__monoid__add(U_8318) ),
inference(clausify,[status(thm)],[f_2051_3]) ).
fof(f_2052_1,plain,
! [V_f_2,V_B_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),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_Rings_Oinverse__class_Odivide(T_d),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ? [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_d)
& 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))
| ~ class_Fields_Ofield(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Un]) ).
fof(f_2052_2,plain,
! [U_8326,U_8325,U_8324,U_8323,U_8322] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8323,tc_HOL_Obool)),U_8324),U_8325)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8322),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8322),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),U_8324)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),U_8325))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8323,tc_HOL_Obool)),U_8324),U_8325)))
| ? [U_8321] :
( hAPP(U_8326,U_8321) = c_Groups_Ozero__class_Ozero(U_8322)
& hBOOL(hAPP(hAPP(c_member(U_8323),U_8321),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8323,tc_HOL_Obool)),U_8324),U_8325))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8323),U_8325))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8323),U_8324))
| ~ class_Fields_Ofield(U_8322) ),
inference(variable_rename,[status(thm)],[f_2052_1]) ).
fof(f_2052_3,plain,
! [U_8326,U_8325,U_8324,U_8323,U_8322] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8323,tc_HOL_Obool)),U_8324),U_8325)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8322),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8322),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),U_8324)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),U_8325))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8323,tc_HOL_Obool)),U_8324),U_8325)))
| ( hAPP(U_8326,sK168(U_8326,U_8325,U_8324,U_8323,U_8322)) = c_Groups_Ozero__class_Ozero(U_8322)
& hBOOL(hAPP(hAPP(c_member(U_8323),sK168(U_8326,U_8325,U_8324,U_8323,U_8322)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8323,tc_HOL_Obool)),U_8324),U_8325))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8323),U_8325))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8323),U_8324))
| ~ class_Fields_Ofield(U_8322) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_8321,sK168(U_8326,U_8325,U_8324,U_8323,U_8322))],[f_2052_2]) ).
fof(f_2052_4,plain,
( ! [U_8324,U_8325,U_8326,U_8322,U_8323] :
( hAPP(U_8326,sK168(U_8326,U_8325,U_8324,U_8323,U_8322)) = c_Groups_Ozero__class_Ozero(U_8322)
| ~ sP559(U_8324,U_8325,U_8326,U_8322,U_8323) )
& ! [U_8324,U_8325,U_8326,U_8322,U_8323] :
( hBOOL(hAPP(hAPP(c_member(U_8323),sK168(U_8326,U_8325,U_8324,U_8323,U_8322)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8323,tc_HOL_Obool)),U_8324),U_8325)))
| ~ sP559(U_8324,U_8325,U_8326,U_8322,U_8323) )
& ! [U_8324,U_8325,U_8326,U_8322,U_8323] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8323,tc_HOL_Obool)),U_8324),U_8325)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8322),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8322),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),U_8324)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),U_8325))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8323,tc_HOL_Obool)),U_8324),U_8325)))
| sP559(U_8324,U_8325,U_8326,U_8322,U_8323)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8323),U_8325))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8323),U_8324))
| ~ class_Fields_Ofield(U_8322) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP559])],[f_2052_3]) ).
cnf(f_2052_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8323,tc_HOL_Obool)),U_8324),U_8325)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8322),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8322),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),U_8324)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),U_8325))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8323,U_8322),U_8326),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8323,tc_HOL_Obool)),U_8324),U_8325)))
| sP559(U_8324,U_8325,U_8326,U_8322,U_8323)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8323),U_8325))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8323),U_8324))
| ~ class_Fields_Ofield(U_8322) ),
inference(clausify,[status(thm)],[f_2052_4]) ).
cnf(f_2052_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8323),sK168(U_8326,U_8325,U_8324,U_8323,U_8322)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8323,tc_HOL_Obool)),U_8324),U_8325)))
| ~ sP559(U_8324,U_8325,U_8326,U_8322,U_8323) ),
inference(clausify,[status(thm)],[f_2052_4]) ).
cnf(f_2052_7,plain,
( hAPP(U_8326,sK168(U_8326,U_8325,U_8324,U_8323,U_8322)) = c_Groups_Ozero__class_Ozero(U_8322)
| ~ sP559(U_8324,U_8325,U_8326,U_8322,U_8323) ),
inference(clausify,[status(thm)],[f_2052_4]) ).
fof(f_2053_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_2053_2,plain,
! [U_8328,U_8327] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8327),U_8328))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8327)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8328))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8327)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8328)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8327),U_8328)) ) )
| ~ c_Nat__Transfer_Onat__set(U_8328)
| ~ c_Nat__Transfer_Ois__nat(U_8327) ),
inference(variable_rename,[status(thm)],[f_2053_1]) ).
fof(f_2053_3,plain,
( ! [U_8327,U_8328] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8327),U_8328))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8327)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8328)))
| ~ sP560(U_8327,U_8328) )
& ! [U_8327,U_8328] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8327)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8328)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8327),U_8328))
| ~ sP560(U_8327,U_8328) )
& ! [U_8327,U_8328] :
( sP560(U_8327,U_8328)
| ~ c_Nat__Transfer_Onat__set(U_8328)
| ~ c_Nat__Transfer_Ois__nat(U_8327) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP560])],[f_2053_2]) ).
cnf(f_2053_4,plain,
( sP560(U_8327,U_8328)
| ~ c_Nat__Transfer_Onat__set(U_8328)
| ~ c_Nat__Transfer_Ois__nat(U_8327) ),
inference(clausify,[status(thm)],[f_2053_3]) ).
cnf(f_2053_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8327)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8328)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8327),U_8328))
| ~ sP560(U_8327,U_8328) ),
inference(clausify,[status(thm)],[f_2053_3]) ).
cnf(f_2053_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8327),U_8328))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8327)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8328)))
| ~ sP560(U_8327,U_8328) ),
inference(clausify,[status(thm)],[f_2053_3]) ).
fof(f_2054_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_2054_2,plain,
! [U_8330,U_8329] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_8329),U_8330) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8329),hAPP(c_Int_Onat,U_8330))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8330),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(U_8329),U_8330) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8329),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8329),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8330))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8330),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ class_Rings_Oring__1(U_8329) ),
inference(variable_rename,[status(thm)],[f_2054_1]) ).
fof(f_2054_3,plain,
( ! [U_8329,U_8330] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8329),U_8330) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8329),hAPP(c_Int_Onat,U_8330))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8330),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP561(U_8329,U_8330) )
& ! [U_8329,U_8330] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8329),U_8330) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8329),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8329),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8330))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8330),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP561(U_8329,U_8330) )
& ! [U_8329,U_8330] :
( sP561(U_8329,U_8330)
| ~ class_Rings_Oring__1(U_8329) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP561])],[f_2054_2]) ).
cnf(f_2054_4,plain,
( sP561(U_8329,U_8330)
| ~ class_Rings_Oring__1(U_8329) ),
inference(clausify,[status(thm)],[f_2054_3]) ).
cnf(f_2054_5,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8329),U_8330) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8329),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8329),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8330))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8330),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP561(U_8329,U_8330) ),
inference(clausify,[status(thm)],[f_2054_3]) ).
cnf(f_2054_6,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8329),U_8330) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8329),hAPP(c_Int_Onat,U_8330))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8330),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP561(U_8329,U_8330) ),
inference(clausify,[status(thm)],[f_2054_3]) ).
fof(f_2055_1,plain,
! [V_i_2,V_B_2,V_f_2,V_s_2,T_c,T_d] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),hAPP(V_f_2,V_i_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),V_s_2))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_s_2) != V_B_2
| ? [B_i] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_d),c_Groups_Ozero__class_Ozero(T_d)),hAPP(V_f_2,B_i)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_s_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_s_2))
| ~ class_Groups_Oordered__ab__group__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__leq__bound]) ).
fof(f_2055_2,plain,
! [U_8337,U_8336,U_8335,U_8334,U_8333,U_8332] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8332),hAPP(U_8335,U_8337)),U_8336))
| ~ hBOOL(hAPP(hAPP(c_member(U_8333),U_8337),U_8334))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8333,U_8332),U_8335),U_8334) != U_8336
| ? [U_8331] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8332),c_Groups_Ozero__class_Ozero(U_8332)),hAPP(U_8335,U_8331)))
& hBOOL(hAPP(hAPP(c_member(U_8333),U_8331),U_8334)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8333),U_8334))
| ~ class_Groups_Oordered__ab__group__add(U_8332) ),
inference(variable_rename,[status(thm)],[f_2055_1]) ).
fof(f_2055_3,plain,
! [U_8337,U_8336,U_8335,U_8334,U_8333,U_8332] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8332),hAPP(U_8335,U_8337)),U_8336))
| ~ hBOOL(hAPP(hAPP(c_member(U_8333),U_8337),U_8334))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8333,U_8332),U_8335),U_8334) != U_8336
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8332),c_Groups_Ozero__class_Ozero(U_8332)),hAPP(U_8335,sK169(U_8337,U_8336,U_8335,U_8334,U_8333,U_8332))))
& hBOOL(hAPP(hAPP(c_member(U_8333),sK169(U_8337,U_8336,U_8335,U_8334,U_8333,U_8332)),U_8334)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8333),U_8334))
| ~ class_Groups_Oordered__ab__group__add(U_8332) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_8331,sK169(U_8337,U_8336,U_8335,U_8334,U_8333,U_8332))],[f_2055_2]) ).
fof(f_2055_4,plain,
( ! [U_8332,U_8333,U_8334,U_8335,U_8336,U_8337] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8332),c_Groups_Ozero__class_Ozero(U_8332)),hAPP(U_8335,sK169(U_8337,U_8336,U_8335,U_8334,U_8333,U_8332))))
| ~ sP562(U_8332,U_8333,U_8334,U_8335,U_8336,U_8337) )
& ! [U_8332,U_8333,U_8334,U_8335,U_8336,U_8337] :
( hBOOL(hAPP(hAPP(c_member(U_8333),sK169(U_8337,U_8336,U_8335,U_8334,U_8333,U_8332)),U_8334))
| ~ sP562(U_8332,U_8333,U_8334,U_8335,U_8336,U_8337) )
& ! [U_8332,U_8333,U_8334,U_8335,U_8336,U_8337] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8332),hAPP(U_8335,U_8337)),U_8336))
| ~ hBOOL(hAPP(hAPP(c_member(U_8333),U_8337),U_8334))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8333,U_8332),U_8335),U_8334) != U_8336
| sP562(U_8332,U_8333,U_8334,U_8335,U_8336,U_8337)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8333),U_8334))
| ~ class_Groups_Oordered__ab__group__add(U_8332) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP562])],[f_2055_3]) ).
cnf(f_2055_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8332),hAPP(U_8335,U_8337)),U_8336))
| ~ hBOOL(hAPP(hAPP(c_member(U_8333),U_8337),U_8334))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8333,U_8332),U_8335),U_8334) != U_8336
| sP562(U_8332,U_8333,U_8334,U_8335,U_8336,U_8337)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8333),U_8334))
| ~ class_Groups_Oordered__ab__group__add(U_8332) ),
inference(clausify,[status(thm)],[f_2055_4]) ).
cnf(f_2055_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8333),sK169(U_8337,U_8336,U_8335,U_8334,U_8333,U_8332)),U_8334))
| ~ sP562(U_8332,U_8333,U_8334,U_8335,U_8336,U_8337) ),
inference(clausify,[status(thm)],[f_2055_4]) ).
cnf(f_2055_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8332),c_Groups_Ozero__class_Ozero(U_8332)),hAPP(U_8335,sK169(U_8337,U_8336,U_8335,U_8334,U_8333,U_8332))))
| ~ sP562(U_8332,U_8333,U_8334,U_8335,U_8336,U_8337) ),
inference(clausify,[status(thm)],[f_2055_4]) ).
fof(f_2056_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_2056_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_2056_1]) ).
cnf(f_2056_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_2056_2]) ).
fof(f_2057_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_x_2) != hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_y_2) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff]) ).
fof(f_2057_2,plain,
! [U_8340,U_8339,U_8338] :
( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8338),U_8339) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8338),U_8340)
| U_8339 != U_8340 )
& ( U_8339 = U_8340
| hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8338),U_8339) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8338),U_8340) ) )
| ~ class_Orderings_Olinorder(U_8338) ),
inference(variable_rename,[status(thm)],[f_2057_1]) ).
fof(f_2057_3,plain,
( ! [U_8338,U_8340,U_8339] :
( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8338),U_8339) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8338),U_8340)
| U_8339 != U_8340
| ~ sP563(U_8338,U_8340,U_8339) )
& ! [U_8338,U_8340,U_8339] :
( U_8339 = U_8340
| hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8338),U_8339) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8338),U_8340)
| ~ sP563(U_8338,U_8340,U_8339) )
& ! [U_8338,U_8340,U_8339] :
( sP563(U_8338,U_8340,U_8339)
| ~ class_Orderings_Olinorder(U_8338) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP563])],[f_2057_2]) ).
cnf(f_2057_4,plain,
( sP563(U_8338,U_8340,U_8339)
| ~ class_Orderings_Olinorder(U_8338) ),
inference(clausify,[status(thm)],[f_2057_3]) ).
cnf(f_2057_5,plain,
( U_8339 = U_8340
| hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8338),U_8339) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8338),U_8340)
| ~ sP563(U_8338,U_8340,U_8339) ),
inference(clausify,[status(thm)],[f_2057_3]) ).
cnf(f_2057_6,plain,
( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8338),U_8339) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8338),U_8340)
| U_8339 != U_8340
| ~ sP563(U_8338,U_8340,U_8339) ),
inference(clausify,[status(thm)],[f_2057_3]) ).
fof(f_2058_1,plain,
! [V_z_2,V_w_2,T_c] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)
| V_w_2 != V_z_2 )
& ( V_w_2 = V_z_2
| hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_w_2) != hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2) ) )
| ~ class_Int_Oring__char__0(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff]) ).
fof(f_2058_2,plain,
! [U_8343,U_8342,U_8341] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_8341),U_8342) = hAPP(c_Int_Oring__1__class_Oof__int(U_8341),U_8343)
| U_8342 != U_8343 )
& ( U_8342 = U_8343
| hAPP(c_Int_Oring__1__class_Oof__int(U_8341),U_8342) != hAPP(c_Int_Oring__1__class_Oof__int(U_8341),U_8343) ) )
| ~ class_Int_Oring__char__0(U_8341) ),
inference(variable_rename,[status(thm)],[f_2058_1]) ).
fof(f_2058_3,plain,
( ! [U_8343,U_8341,U_8342] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8341),U_8342) = hAPP(c_Int_Oring__1__class_Oof__int(U_8341),U_8343)
| U_8342 != U_8343
| ~ sP564(U_8343,U_8341,U_8342) )
& ! [U_8343,U_8341,U_8342] :
( U_8342 = U_8343
| hAPP(c_Int_Oring__1__class_Oof__int(U_8341),U_8342) != hAPP(c_Int_Oring__1__class_Oof__int(U_8341),U_8343)
| ~ sP564(U_8343,U_8341,U_8342) )
& ! [U_8343,U_8341,U_8342] :
( sP564(U_8343,U_8341,U_8342)
| ~ class_Int_Oring__char__0(U_8341) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP564])],[f_2058_2]) ).
cnf(f_2058_4,plain,
( sP564(U_8343,U_8341,U_8342)
| ~ class_Int_Oring__char__0(U_8341) ),
inference(clausify,[status(thm)],[f_2058_3]) ).
cnf(f_2058_5,plain,
( U_8342 = U_8343
| hAPP(c_Int_Oring__1__class_Oof__int(U_8341),U_8342) != hAPP(c_Int_Oring__1__class_Oof__int(U_8341),U_8343)
| ~ sP564(U_8343,U_8341,U_8342) ),
inference(clausify,[status(thm)],[f_2058_3]) ).
cnf(f_2058_6,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8341),U_8342) = hAPP(c_Int_Oring__1__class_Oof__int(U_8341),U_8343)
| U_8342 != U_8343
| ~ sP564(U_8343,U_8341,U_8342) ),
inference(clausify,[status(thm)],[f_2058_3]) ).
fof(f_2059_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_2059_2,plain,
! [U_8344] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8344)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8344),
inference(variable_rename,[status(thm)],[f_2059_1]) ).
fof(f_2059_3,plain,
! [U_8344] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8344)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8344),
inference(definitional_conversion,[status(esa)],[f_2059_2]) ).
cnf(f_2059_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_8344)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8344),
inference(clausify,[status(thm)],[f_2059_3]) ).
fof(f_2060_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_2060_2,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_2060_1]) ).
cnf(f_2060_3,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_2060_2]) ).
fof(f_2061_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_2061_2,plain,
! [U_8346,U_8345] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8345),U_8346))
| ~ c_Nat__Transfer_Ois__nat(U_8346)
| ~ c_Nat__Transfer_Ois__nat(U_8345) ),
inference(variable_rename,[status(thm)],[f_2061_1]) ).
fof(f_2061_3,plain,
! [U_8345,U_8346] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8345),U_8346))
| ~ c_Nat__Transfer_Ois__nat(U_8346)
| ~ c_Nat__Transfer_Ois__nat(U_8345) ),
inference(definitional_conversion,[status(esa)],[f_2061_2]) ).
cnf(f_2061_4,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8345),U_8346))
| ~ c_Nat__Transfer_Ois__nat(U_8346)
| ~ c_Nat__Transfer_Ois__nat(U_8345) ),
inference(clausify,[status(thm)],[f_2061_3]) ).
fof(f_2062_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_2062_2,plain,
! [U_8347] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8347)),
inference(variable_rename,[status(thm)],[f_2062_1]) ).
fof(f_2062_3,plain,
! [U_8347] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8347)),
inference(definitional_conversion,[status(esa)],[f_2062_2]) ).
cnf(f_2062_4,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8347)),
inference(clausify,[status(thm)],[f_2062_3]) ).
fof(f_2063_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_2063_2,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_2063_1]) ).
cnf(f_2063_3,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_2063_2]) ).
fof(f_2064_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_2064_2,plain,
! [U_8349,U_8348] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8348),U_8349))
| ~ c_Nat__Transfer_Ois__nat(U_8349)
| ~ c_Nat__Transfer_Ois__nat(U_8348) ),
inference(variable_rename,[status(thm)],[f_2064_1]) ).
fof(f_2064_3,plain,
! [U_8348,U_8349] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8348),U_8349))
| ~ c_Nat__Transfer_Ois__nat(U_8349)
| ~ c_Nat__Transfer_Ois__nat(U_8348) ),
inference(definitional_conversion,[status(esa)],[f_2064_2]) ).
cnf(f_2064_4,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8348),U_8349))
| ~ c_Nat__Transfer_Ois__nat(U_8349)
| ~ c_Nat__Transfer_Ois__nat(U_8348) ),
inference(clausify,[status(thm)],[f_2064_3]) ).
fof(f_2065_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_2065_2,plain,
! [U_8351,U_8350] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8350),U_8351))
| ~ c_Nat__Transfer_Ois__nat(U_8351)
| ~ c_Nat__Transfer_Ois__nat(U_8350) ),
inference(variable_rename,[status(thm)],[f_2065_1]) ).
fof(f_2065_3,plain,
! [U_8351,U_8350] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8350),U_8351))
| ~ c_Nat__Transfer_Ois__nat(U_8351)
| ~ c_Nat__Transfer_Ois__nat(U_8350) ),
inference(definitional_conversion,[status(esa)],[f_2065_2]) ).
cnf(f_2065_4,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8350),U_8351))
| ~ c_Nat__Transfer_Ois__nat(U_8351)
| ~ c_Nat__Transfer_Ois__nat(U_8350) ),
inference(clausify,[status(thm)],[f_2065_3]) ).
fof(f_2066_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_2066_2,plain,
! [U_8353,U_8352] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8352),U_8353))
| ~ c_Nat__Transfer_Ois__nat(U_8352) ),
inference(variable_rename,[status(thm)],[f_2066_1]) ).
fof(f_2066_3,plain,
! [U_8353,U_8352] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8352),U_8353))
| ~ c_Nat__Transfer_Ois__nat(U_8352) ),
inference(definitional_conversion,[status(esa)],[f_2066_2]) ).
cnf(f_2066_4,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8352),U_8353))
| ~ c_Nat__Transfer_Ois__nat(U_8352) ),
inference(clausify,[status(thm)],[f_2066_3]) ).
fof(f_2067_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_2067_2,plain,
! [U_8355,U_8354] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_8354,U_8355))
| ~ c_Nat__Transfer_Ois__nat(U_8355)
| ~ c_Nat__Transfer_Ois__nat(U_8354) ),
inference(variable_rename,[status(thm)],[f_2067_1]) ).
fof(f_2067_3,plain,
! [U_8354,U_8355] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_8354,U_8355))
| ~ c_Nat__Transfer_Ois__nat(U_8355)
| ~ c_Nat__Transfer_Ois__nat(U_8354) ),
inference(definitional_conversion,[status(esa)],[f_2067_2]) ).
cnf(f_2067_4,plain,
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_8354,U_8355))
| ~ c_Nat__Transfer_Ois__nat(U_8355)
| ~ c_Nat__Transfer_Ois__nat(U_8354) ),
inference(clausify,[status(thm)],[f_2067_3]) ).
fof(f_2068_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_2068_2,plain,
! [U_8356] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8356),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_8356)
| ~ class_Rings_Oring__1(U_8356) ),
inference(variable_rename,[status(thm)],[f_2068_1]) ).
fof(f_2068_3,plain,
! [U_8356] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8356),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_8356)
| ~ class_Rings_Oring__1(U_8356) ),
inference(definitional_conversion,[status(esa)],[f_2068_2]) ).
cnf(f_2068_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8356),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_8356)
| ~ class_Rings_Oring__1(U_8356) ),
inference(clausify,[status(thm)],[f_2068_3]) ).
fof(f_2069_1,plain,
! [V_z_2,T_c] :
( ( ( c_Groups_Ozero__class_Ozero(T_c) = hAPP(c_Int_Oring__1__class_Oof__int(T_c),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_c) != hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2) ) )
| ~ class_Int_Oring__char__0(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__int__0__eq__iff]) ).
fof(f_2069_2,plain,
! [U_8358,U_8357] :
( ( ( c_Groups_Ozero__class_Ozero(U_8357) = hAPP(c_Int_Oring__1__class_Oof__int(U_8357),U_8358)
| U_8358 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_8358 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(U_8357) != hAPP(c_Int_Oring__1__class_Oof__int(U_8357),U_8358) ) )
| ~ class_Int_Oring__char__0(U_8357) ),
inference(variable_rename,[status(thm)],[f_2069_1]) ).
fof(f_2069_3,plain,
( ! [U_8357,U_8358] :
( c_Groups_Ozero__class_Ozero(U_8357) = hAPP(c_Int_Oring__1__class_Oof__int(U_8357),U_8358)
| U_8358 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP565(U_8357,U_8358) )
& ! [U_8357,U_8358] :
( U_8358 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(U_8357) != hAPP(c_Int_Oring__1__class_Oof__int(U_8357),U_8358)
| ~ sP565(U_8357,U_8358) )
& ! [U_8357,U_8358] :
( sP565(U_8357,U_8358)
| ~ class_Int_Oring__char__0(U_8357) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP565])],[f_2069_2]) ).
cnf(f_2069_4,plain,
( sP565(U_8357,U_8358)
| ~ class_Int_Oring__char__0(U_8357) ),
inference(clausify,[status(thm)],[f_2069_3]) ).
cnf(f_2069_5,plain,
( U_8358 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(U_8357) != hAPP(c_Int_Oring__1__class_Oof__int(U_8357),U_8358)
| ~ sP565(U_8357,U_8358) ),
inference(clausify,[status(thm)],[f_2069_3]) ).
cnf(f_2069_6,plain,
( c_Groups_Ozero__class_Ozero(U_8357) = hAPP(c_Int_Oring__1__class_Oof__int(U_8357),U_8358)
| U_8358 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP565(U_8357,U_8358) ),
inference(clausify,[status(thm)],[f_2069_3]) ).
fof(f_2070_1,plain,
! [V_z_2,T_c] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2) = c_Groups_Ozero__class_Ozero(T_c)
| 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_c),V_z_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ class_Int_Oring__char__0(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff]) ).
fof(f_2070_2,plain,
! [U_8360,U_8359] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_8359),U_8360) = c_Groups_Ozero__class_Ozero(U_8359)
| U_8360 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_8360 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(U_8359),U_8360) != c_Groups_Ozero__class_Ozero(U_8359) ) )
| ~ class_Int_Oring__char__0(U_8359) ),
inference(variable_rename,[status(thm)],[f_2070_1]) ).
fof(f_2070_3,plain,
( ! [U_8360,U_8359] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8359),U_8360) = c_Groups_Ozero__class_Ozero(U_8359)
| U_8360 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP566(U_8360,U_8359) )
& ! [U_8360,U_8359] :
( U_8360 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(U_8359),U_8360) != c_Groups_Ozero__class_Ozero(U_8359)
| ~ sP566(U_8360,U_8359) )
& ! [U_8360,U_8359] :
( sP566(U_8360,U_8359)
| ~ class_Int_Oring__char__0(U_8359) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP566])],[f_2070_2]) ).
cnf(f_2070_4,plain,
( sP566(U_8360,U_8359)
| ~ class_Int_Oring__char__0(U_8359) ),
inference(clausify,[status(thm)],[f_2070_3]) ).
cnf(f_2070_5,plain,
( U_8360 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(U_8359),U_8360) != c_Groups_Ozero__class_Ozero(U_8359)
| ~ sP566(U_8360,U_8359) ),
inference(clausify,[status(thm)],[f_2070_3]) ).
cnf(f_2070_6,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8359),U_8360) = c_Groups_Ozero__class_Ozero(U_8359)
| U_8360 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP566(U_8360,U_8359) ),
inference(clausify,[status(thm)],[f_2070_3]) ).
fof(f_2071_1,plain,
! [V_z_2,V_w_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),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_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2))) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__int__le__iff]) ).
fof(f_2071_2,plain,
! [U_8363,U_8362,U_8361] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8361),hAPP(c_Int_Oring__1__class_Oof__int(U_8361),U_8362)),hAPP(c_Int_Oring__1__class_Oof__int(U_8361),U_8363)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8362),U_8363)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8362),U_8363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8361),hAPP(c_Int_Oring__1__class_Oof__int(U_8361),U_8362)),hAPP(c_Int_Oring__1__class_Oof__int(U_8361),U_8363))) ) )
| ~ class_Rings_Olinordered__idom(U_8361) ),
inference(variable_rename,[status(thm)],[f_2071_1]) ).
fof(f_2071_3,plain,
( ! [U_8362,U_8361,U_8363] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8361),hAPP(c_Int_Oring__1__class_Oof__int(U_8361),U_8362)),hAPP(c_Int_Oring__1__class_Oof__int(U_8361),U_8363)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8362),U_8363))
| ~ sP567(U_8362,U_8361,U_8363) )
& ! [U_8362,U_8361,U_8363] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8362),U_8363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8361),hAPP(c_Int_Oring__1__class_Oof__int(U_8361),U_8362)),hAPP(c_Int_Oring__1__class_Oof__int(U_8361),U_8363)))
| ~ sP567(U_8362,U_8361,U_8363) )
& ! [U_8362,U_8361,U_8363] :
( sP567(U_8362,U_8361,U_8363)
| ~ class_Rings_Olinordered__idom(U_8361) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP567])],[f_2071_2]) ).
cnf(f_2071_4,plain,
( sP567(U_8362,U_8361,U_8363)
| ~ class_Rings_Olinordered__idom(U_8361) ),
inference(clausify,[status(thm)],[f_2071_3]) ).
cnf(f_2071_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8362),U_8363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8361),hAPP(c_Int_Oring__1__class_Oof__int(U_8361),U_8362)),hAPP(c_Int_Oring__1__class_Oof__int(U_8361),U_8363)))
| ~ sP567(U_8362,U_8361,U_8363) ),
inference(clausify,[status(thm)],[f_2071_3]) ).
cnf(f_2071_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8361),hAPP(c_Int_Oring__1__class_Oof__int(U_8361),U_8362)),hAPP(c_Int_Oring__1__class_Oof__int(U_8361),U_8363)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8362),U_8363))
| ~ sP567(U_8362,U_8361,U_8363) ),
inference(clausify,[status(thm)],[f_2071_3]) ).
fof(f_2072_1,plain,
! [V_z_2,V_w_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),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_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2))) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__int__less__iff]) ).
fof(f_2072_2,plain,
! [U_8366,U_8365,U_8364] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8364),hAPP(c_Int_Oring__1__class_Oof__int(U_8364),U_8365)),hAPP(c_Int_Oring__1__class_Oof__int(U_8364),U_8366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8365),U_8366)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8365),U_8366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8364),hAPP(c_Int_Oring__1__class_Oof__int(U_8364),U_8365)),hAPP(c_Int_Oring__1__class_Oof__int(U_8364),U_8366))) ) )
| ~ class_Rings_Olinordered__idom(U_8364) ),
inference(variable_rename,[status(thm)],[f_2072_1]) ).
fof(f_2072_3,plain,
( ! [U_8366,U_8365,U_8364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8364),hAPP(c_Int_Oring__1__class_Oof__int(U_8364),U_8365)),hAPP(c_Int_Oring__1__class_Oof__int(U_8364),U_8366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8365),U_8366))
| ~ sP568(U_8366,U_8365,U_8364) )
& ! [U_8366,U_8365,U_8364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8365),U_8366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8364),hAPP(c_Int_Oring__1__class_Oof__int(U_8364),U_8365)),hAPP(c_Int_Oring__1__class_Oof__int(U_8364),U_8366)))
| ~ sP568(U_8366,U_8365,U_8364) )
& ! [U_8366,U_8365,U_8364] :
( sP568(U_8366,U_8365,U_8364)
| ~ class_Rings_Olinordered__idom(U_8364) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP568])],[f_2072_2]) ).
cnf(f_2072_4,plain,
( sP568(U_8366,U_8365,U_8364)
| ~ class_Rings_Olinordered__idom(U_8364) ),
inference(clausify,[status(thm)],[f_2072_3]) ).
cnf(f_2072_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8365),U_8366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8364),hAPP(c_Int_Oring__1__class_Oof__int(U_8364),U_8365)),hAPP(c_Int_Oring__1__class_Oof__int(U_8364),U_8366)))
| ~ sP568(U_8366,U_8365,U_8364) ),
inference(clausify,[status(thm)],[f_2072_3]) ).
cnf(f_2072_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8364),hAPP(c_Int_Oring__1__class_Oof__int(U_8364),U_8365)),hAPP(c_Int_Oring__1__class_Oof__int(U_8364),U_8366)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8365),U_8366))
| ~ sP568(U_8366,U_8365,U_8364) ),
inference(clausify,[status(thm)],[f_2072_3]) ).
fof(f_2073_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_2073_2,plain,
! [U_8369,U_8368,U_8367] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8368),U_8369)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8367),hAPP(c_Int_Oring__1__class_Oof__int(U_8367),U_8368)),hAPP(c_Int_Oring__1__class_Oof__int(U_8367),U_8369))
| ~ class_Rings_Oring__1(U_8367) ),
inference(variable_rename,[status(thm)],[f_2073_1]) ).
fof(f_2073_3,plain,
! [U_8369,U_8368,U_8367] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8368),U_8369)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8367),hAPP(c_Int_Oring__1__class_Oof__int(U_8367),U_8368)),hAPP(c_Int_Oring__1__class_Oof__int(U_8367),U_8369))
| ~ class_Rings_Oring__1(U_8367) ),
inference(definitional_conversion,[status(esa)],[f_2073_2]) ).
cnf(f_2073_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8367),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8368),U_8369)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8367),hAPP(c_Int_Oring__1__class_Oof__int(U_8367),U_8368)),hAPP(c_Int_Oring__1__class_Oof__int(U_8367),U_8369))
| ~ class_Rings_Oring__1(U_8367) ),
inference(clausify,[status(thm)],[f_2073_3]) ).
fof(f_2074_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_2074_2,plain,
! [U_8372,U_8371,U_8370] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8371),U_8372)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8370),hAPP(c_Int_Oring__1__class_Oof__int(U_8370),U_8371)),hAPP(c_Int_Oring__1__class_Oof__int(U_8370),U_8372))
| ~ class_Rings_Oring__1(U_8370) ),
inference(variable_rename,[status(thm)],[f_2074_1]) ).
fof(f_2074_3,plain,
! [U_8370,U_8371,U_8372] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8371),U_8372)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8370),hAPP(c_Int_Oring__1__class_Oof__int(U_8370),U_8371)),hAPP(c_Int_Oring__1__class_Oof__int(U_8370),U_8372))
| ~ class_Rings_Oring__1(U_8370) ),
inference(definitional_conversion,[status(esa)],[f_2074_2]) ).
cnf(f_2074_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8371),U_8372)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8370),hAPP(c_Int_Oring__1__class_Oof__int(U_8370),U_8371)),hAPP(c_Int_Oring__1__class_Oof__int(U_8370),U_8372))
| ~ class_Rings_Oring__1(U_8370) ),
inference(clausify,[status(thm)],[f_2074_3]) ).
fof(f_2075_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_2075_2,plain,
! [U_8373] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8373),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_8373)
| ~ class_Rings_Oring__1(U_8373) ),
inference(variable_rename,[status(thm)],[f_2075_1]) ).
fof(f_2075_3,plain,
! [U_8373] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8373),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_8373)
| ~ class_Rings_Oring__1(U_8373) ),
inference(definitional_conversion,[status(esa)],[f_2075_2]) ).
cnf(f_2075_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8373),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_8373)
| ~ class_Rings_Oring__1(U_8373) ),
inference(clausify,[status(thm)],[f_2075_3]) ).
fof(f_2076_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_2076_2,plain,
! [U_8376,U_8375,U_8374] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8374),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8375),U_8376)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8374),hAPP(c_Int_Oring__1__class_Oof__int(U_8374),U_8375)),hAPP(c_Int_Oring__1__class_Oof__int(U_8374),U_8376))
| ~ class_Rings_Oring__1(U_8374) ),
inference(variable_rename,[status(thm)],[f_2076_1]) ).
fof(f_2076_3,plain,
! [U_8374,U_8375,U_8376] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8374),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8375),U_8376)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8374),hAPP(c_Int_Oring__1__class_Oof__int(U_8374),U_8375)),hAPP(c_Int_Oring__1__class_Oof__int(U_8374),U_8376))
| ~ class_Rings_Oring__1(U_8374) ),
inference(definitional_conversion,[status(esa)],[f_2076_2]) ).
cnf(f_2076_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8374),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8375),U_8376)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8374),hAPP(c_Int_Oring__1__class_Oof__int(U_8374),U_8375)),hAPP(c_Int_Oring__1__class_Oof__int(U_8374),U_8376))
| ~ class_Rings_Oring__1(U_8374) ),
inference(clausify,[status(thm)],[f_2076_3]) ).
fof(f_2077_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_2077_2,plain,
! [U_8378,U_8377] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8377),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8378)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8377),U_8378)
| ~ class_Rings_Oring__1(U_8377) ),
inference(variable_rename,[status(thm)],[f_2077_1]) ).
fof(f_2077_3,plain,
! [U_8377,U_8378] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8377),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8378)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8377),U_8378)
| ~ class_Rings_Oring__1(U_8377) ),
inference(definitional_conversion,[status(esa)],[f_2077_2]) ).
cnf(f_2077_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8377),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8378)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8377),U_8378)
| ~ class_Rings_Oring__1(U_8377) ),
inference(clausify,[status(thm)],[f_2077_3]) ).
fof(f_2078_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_2078_2,plain,
! [U_8380,U_8379] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8379),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8380)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8379),hAPP(c_Int_Oring__1__class_Oof__int(U_8379),U_8380))
| ~ class_Rings_Oring__1(U_8379) ),
inference(variable_rename,[status(thm)],[f_2078_1]) ).
fof(f_2078_3,plain,
! [U_8379,U_8380] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8379),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8380)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8379),hAPP(c_Int_Oring__1__class_Oof__int(U_8379),U_8380))
| ~ class_Rings_Oring__1(U_8379) ),
inference(definitional_conversion,[status(esa)],[f_2078_2]) ).
cnf(f_2078_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8379),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8380)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8379),hAPP(c_Int_Oring__1__class_Oof__int(U_8379),U_8380))
| ~ class_Rings_Oring__1(U_8379) ),
inference(clausify,[status(thm)],[f_2078_3]) ).
fof(f_2079_1,plain,
! [V_z_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Rings_Oring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__of__int]) ).
fof(f_2079_2,plain,
! [U_8382,U_8381] :
( hBOOL(hAPP(hAPP(c_member(U_8381),hAPP(c_Int_Oring__1__class_Oof__int(U_8381),U_8382)),c_Int_Oring__1__class_OInts(U_8381)))
| ~ class_Rings_Oring__1(U_8381) ),
inference(variable_rename,[status(thm)],[f_2079_1]) ).
fof(f_2079_3,plain,
! [U_8381,U_8382] :
( hBOOL(hAPP(hAPP(c_member(U_8381),hAPP(c_Int_Oring__1__class_Oof__int(U_8381),U_8382)),c_Int_Oring__1__class_OInts(U_8381)))
| ~ class_Rings_Oring__1(U_8381) ),
inference(definitional_conversion,[status(esa)],[f_2079_2]) ).
cnf(f_2079_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8381),hAPP(c_Int_Oring__1__class_Oof__int(U_8381),U_8382)),c_Int_Oring__1__class_OInts(U_8381)))
| ~ class_Rings_Oring__1(U_8381) ),
inference(clausify,[status(thm)],[f_2079_3]) ).
fof(f_2080_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_2080_2,plain,
! [U_8385,U_8384,U_8383] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8383),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8384),U_8385)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8383),hAPP(c_Int_Oring__1__class_Oof__int(U_8383),U_8384)),U_8385)
| ~ class_Rings_Oring__1(U_8383) ),
inference(variable_rename,[status(thm)],[f_2080_1]) ).
fof(f_2080_3,plain,
! [U_8383,U_8384,U_8385] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8383),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8384),U_8385)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8383),hAPP(c_Int_Oring__1__class_Oof__int(U_8383),U_8384)),U_8385)
| ~ class_Rings_Oring__1(U_8383) ),
inference(definitional_conversion,[status(esa)],[f_2080_2]) ).
cnf(f_2080_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8383),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8384),U_8385)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8383),hAPP(c_Int_Oring__1__class_Oof__int(U_8383),U_8384)),U_8385)
| ~ class_Rings_Oring__1(U_8383) ),
inference(clausify,[status(thm)],[f_2080_3]) ).
fof(f_2081_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_2081_2,plain,
! [U_8386] :
( ( c_Nat__Transfer_Ois__nat(U_8386)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8386)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8386))
| ~ c_Nat__Transfer_Ois__nat(U_8386) ) ),
inference(variable_rename,[status(thm)],[f_2081_1]) ).
fof(f_2081_3,plain,
( ! [U_8388] :
( c_Nat__Transfer_Ois__nat(U_8388)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8388)) )
& ! [U_8387] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8387))
| ~ c_Nat__Transfer_Ois__nat(U_8387) ) ),
inference(miniscope,[status(thm)],[f_2081_2]) ).
fof(f_2081_4,plain,
( ! [U_8388] :
( c_Nat__Transfer_Ois__nat(U_8388)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8388)) )
& ! [U_8387] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8387))
| ~ c_Nat__Transfer_Ois__nat(U_8387) ) ),
inference(definitional_conversion,[status(esa)],[f_2081_3]) ).
cnf(f_2081_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8387))
| ~ c_Nat__Transfer_Ois__nat(U_8387) ),
inference(clausify,[status(thm)],[f_2081_4]) ).
cnf(f_2081_6,plain,
( c_Nat__Transfer_Ois__nat(U_8388)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8388)) ),
inference(clausify,[status(thm)],[f_2081_4]) ).
fof(f_2082_1,plain,
! [V_k_2,V_i_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_k_2),V_i_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_k_2))) ) )
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_greaterThan__iff]) ).
fof(f_2082_2,plain,
! [U_8391,U_8390,U_8389] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_8389),U_8390),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8389),U_8391)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8389),U_8391),U_8390)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8389),U_8391),U_8390))
| ~ hBOOL(hAPP(hAPP(c_member(U_8389),U_8390),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8389),U_8391))) ) )
| ~ class_Orderings_Oord(U_8389) ),
inference(variable_rename,[status(thm)],[f_2082_1]) ).
fof(f_2082_3,plain,
( ! [U_8389,U_8390,U_8391] :
( hBOOL(hAPP(hAPP(c_member(U_8389),U_8390),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8389),U_8391)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8389),U_8391),U_8390))
| ~ sP569(U_8389,U_8390,U_8391) )
& ! [U_8389,U_8390,U_8391] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8389),U_8391),U_8390))
| ~ hBOOL(hAPP(hAPP(c_member(U_8389),U_8390),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8389),U_8391)))
| ~ sP569(U_8389,U_8390,U_8391) )
& ! [U_8389,U_8390,U_8391] :
( sP569(U_8389,U_8390,U_8391)
| ~ class_Orderings_Oord(U_8389) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP569])],[f_2082_2]) ).
cnf(f_2082_4,plain,
( sP569(U_8389,U_8390,U_8391)
| ~ class_Orderings_Oord(U_8389) ),
inference(clausify,[status(thm)],[f_2082_3]) ).
cnf(f_2082_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8389),U_8391),U_8390))
| ~ hBOOL(hAPP(hAPP(c_member(U_8389),U_8390),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8389),U_8391)))
| ~ sP569(U_8389,U_8390,U_8391) ),
inference(clausify,[status(thm)],[f_2082_3]) ).
cnf(f_2082_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8389),U_8390),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8389),U_8391)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8389),U_8391),U_8390))
| ~ sP569(U_8389,U_8390,U_8391) ),
inference(clausify,[status(thm)],[f_2082_3]) ).
fof(f_2083_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_y_2))) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff]) ).
fof(f_2083_2,plain,
! [U_8394,U_8393,U_8392] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8392,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8392),U_8393)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8392),U_8394)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8392),U_8394),U_8393)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8392),U_8394),U_8393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8392,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8392),U_8393)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8392),U_8394))) ) )
| ~ class_Orderings_Olinorder(U_8392) ),
inference(variable_rename,[status(thm)],[f_2083_1]) ).
fof(f_2083_3,plain,
( ! [U_8393,U_8394,U_8392] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8392,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8392),U_8393)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8392),U_8394)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8392),U_8394),U_8393))
| ~ sP570(U_8393,U_8394,U_8392) )
& ! [U_8393,U_8394,U_8392] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8392),U_8394),U_8393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8392,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8392),U_8393)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8392),U_8394)))
| ~ sP570(U_8393,U_8394,U_8392) )
& ! [U_8393,U_8394,U_8392] :
( sP570(U_8393,U_8394,U_8392)
| ~ class_Orderings_Olinorder(U_8392) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP570])],[f_2083_2]) ).
cnf(f_2083_4,plain,
( sP570(U_8393,U_8394,U_8392)
| ~ class_Orderings_Olinorder(U_8392) ),
inference(clausify,[status(thm)],[f_2083_3]) ).
cnf(f_2083_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8392),U_8394),U_8393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8392,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8392),U_8393)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8392),U_8394)))
| ~ sP570(U_8393,U_8394,U_8392) ),
inference(clausify,[status(thm)],[f_2083_3]) ).
cnf(f_2083_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8392,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8392),U_8393)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8392),U_8394)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8392),U_8394),U_8393))
| ~ sP570(U_8393,U_8394,U_8392) ),
inference(clausify,[status(thm)],[f_2083_3]) ).
fof(f_2084_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Int_Oring__1__class_Oof__int(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_c,T_d),c_Int_Oring__1__class_Oof__int(T_c)),V_f_2)),V_A_2)
| ~ class_Rings_Oring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__int__setsum]) ).
fof(f_2084_2,plain,
! [U_8398,U_8397,U_8396,U_8395] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8395),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8396,tc_Int_Oint),U_8397),U_8398)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8396,U_8395),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8395,U_8396),c_Int_Oring__1__class_Oof__int(U_8395)),U_8397)),U_8398)
| ~ class_Rings_Oring__1(U_8395) ),
inference(variable_rename,[status(thm)],[f_2084_1]) ).
fof(f_2084_3,plain,
! [U_8395,U_8396,U_8397,U_8398] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8395),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8396,tc_Int_Oint),U_8397),U_8398)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8396,U_8395),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8395,U_8396),c_Int_Oring__1__class_Oof__int(U_8395)),U_8397)),U_8398)
| ~ class_Rings_Oring__1(U_8395) ),
inference(definitional_conversion,[status(esa)],[f_2084_2]) ).
cnf(f_2084_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8395),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8396,tc_Int_Oint),U_8397),U_8398)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8396,U_8395),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8395,U_8396),c_Int_Oring__1__class_Oof__int(U_8395)),U_8397)),U_8398)
| ~ class_Rings_Oring__1(U_8395) ),
inference(clausify,[status(thm)],[f_2084_3]) ).
fof(f_2085_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_2085_2,plain,
! [U_8400,U_8399] :
( c_Nat__Transfer_Ois__nat(U_8400)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8400),U_8399))
| ~ c_Nat__Transfer_Onat__set(U_8399) ),
inference(variable_rename,[status(thm)],[f_2085_1]) ).
fof(f_2085_3,plain,
! [U_8400,U_8399] :
( c_Nat__Transfer_Ois__nat(U_8400)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8400),U_8399))
| ~ c_Nat__Transfer_Onat__set(U_8399) ),
inference(definitional_conversion,[status(esa)],[f_2085_2]) ).
cnf(f_2085_4,plain,
( c_Nat__Transfer_Ois__nat(U_8400)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8400),U_8399))
| ~ c_Nat__Transfer_Onat__set(U_8399) ),
inference(clausify,[status(thm)],[f_2085_3]) ).
fof(f_2086_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Int_Oring__1__class_Oof__int(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_c,T_d),c_Int_Oring__1__class_Oof__int(T_c)),V_f_2)),V_A_2)
| ~ class_Rings_Oring__1(T_c)
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__int__setprod]) ).
fof(f_2086_2,plain,
! [U_8404,U_8403,U_8402,U_8401] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8401),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8402,tc_Int_Oint),U_8403),U_8404)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8402,U_8401),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8401,U_8402),c_Int_Oring__1__class_Oof__int(U_8401)),U_8403)),U_8404)
| ~ class_Rings_Oring__1(U_8401)
| ~ class_Groups_Ocomm__monoid__mult(U_8401) ),
inference(variable_rename,[status(thm)],[f_2086_1]) ).
fof(f_2086_3,plain,
! [U_8401,U_8402,U_8403,U_8404] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_8401),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8402,tc_Int_Oint),U_8403),U_8404)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8402,U_8401),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8401,U_8402),c_Int_Oring__1__class_Oof__int(U_8401)),U_8403)),U_8404)
| ~ class_Rings_Oring__1(U_8401)
| ~ class_Groups_Ocomm__monoid__mult(U_8401) ),
inference(definitional_conversion,[status(esa)],[f_2086_2]) ).
cnf(f_2086_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_8401),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8402,tc_Int_Oint),U_8403),U_8404)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8402,U_8401),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8401,U_8402),c_Int_Oring__1__class_Oof__int(U_8401)),U_8403)),U_8404)
| ~ class_Rings_Oring__1(U_8401)
| ~ class_Groups_Ocomm__monoid__mult(U_8401) ),
inference(clausify,[status(thm)],[f_2086_3]) ).
fof(f_2087_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_2087_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_2087_1]) ).
cnf(f_2087_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_2087_2]) ).
fof(f_2088_1,plain,
! [V_z_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),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_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2))) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff]) ).
fof(f_2088_2,plain,
! [U_8406,U_8405] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8405),c_Groups_Ozero__class_Ozero(U_8405)),hAPP(c_Int_Oring__1__class_Oof__int(U_8405),U_8406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8406)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8406))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8405),c_Groups_Ozero__class_Ozero(U_8405)),hAPP(c_Int_Oring__1__class_Oof__int(U_8405),U_8406))) ) )
| ~ class_Rings_Olinordered__idom(U_8405) ),
inference(variable_rename,[status(thm)],[f_2088_1]) ).
fof(f_2088_3,plain,
( ! [U_8405,U_8406] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8405),c_Groups_Ozero__class_Ozero(U_8405)),hAPP(c_Int_Oring__1__class_Oof__int(U_8405),U_8406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8406))
| ~ sP571(U_8405,U_8406) )
& ! [U_8405,U_8406] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8406))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8405),c_Groups_Ozero__class_Ozero(U_8405)),hAPP(c_Int_Oring__1__class_Oof__int(U_8405),U_8406)))
| ~ sP571(U_8405,U_8406) )
& ! [U_8405,U_8406] :
( sP571(U_8405,U_8406)
| ~ class_Rings_Olinordered__idom(U_8405) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP571])],[f_2088_2]) ).
cnf(f_2088_4,plain,
( sP571(U_8405,U_8406)
| ~ class_Rings_Olinordered__idom(U_8405) ),
inference(clausify,[status(thm)],[f_2088_3]) ).
cnf(f_2088_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8406))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8405),c_Groups_Ozero__class_Ozero(U_8405)),hAPP(c_Int_Oring__1__class_Oof__int(U_8405),U_8406)))
| ~ sP571(U_8405,U_8406) ),
inference(clausify,[status(thm)],[f_2088_3]) ).
cnf(f_2088_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8405),c_Groups_Ozero__class_Ozero(U_8405)),hAPP(c_Int_Oring__1__class_Oof__int(U_8405),U_8406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8406))
| ~ sP571(U_8405,U_8406) ),
inference(clausify,[status(thm)],[f_2088_3]) ).
fof(f_2089_1,plain,
! [V_z_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ 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_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__int__le__0__iff]) ).
fof(f_2089_2,plain,
! [U_8408,U_8407] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8407),hAPP(c_Int_Oring__1__class_Oof__int(U_8407),U_8408)),c_Groups_Ozero__class_Ozero(U_8407)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8408),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8408),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8407),hAPP(c_Int_Oring__1__class_Oof__int(U_8407),U_8408)),c_Groups_Ozero__class_Ozero(U_8407))) ) )
| ~ class_Rings_Olinordered__idom(U_8407) ),
inference(variable_rename,[status(thm)],[f_2089_1]) ).
fof(f_2089_3,plain,
( ! [U_8408,U_8407] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8407),hAPP(c_Int_Oring__1__class_Oof__int(U_8407),U_8408)),c_Groups_Ozero__class_Ozero(U_8407)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8408),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP572(U_8408,U_8407) )
& ! [U_8408,U_8407] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8408),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8407),hAPP(c_Int_Oring__1__class_Oof__int(U_8407),U_8408)),c_Groups_Ozero__class_Ozero(U_8407)))
| ~ sP572(U_8408,U_8407) )
& ! [U_8408,U_8407] :
( sP572(U_8408,U_8407)
| ~ class_Rings_Olinordered__idom(U_8407) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP572])],[f_2089_2]) ).
cnf(f_2089_4,plain,
( sP572(U_8408,U_8407)
| ~ class_Rings_Olinordered__idom(U_8407) ),
inference(clausify,[status(thm)],[f_2089_3]) ).
cnf(f_2089_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8408),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8407),hAPP(c_Int_Oring__1__class_Oof__int(U_8407),U_8408)),c_Groups_Ozero__class_Ozero(U_8407)))
| ~ sP572(U_8408,U_8407) ),
inference(clausify,[status(thm)],[f_2089_3]) ).
cnf(f_2089_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8407),hAPP(c_Int_Oring__1__class_Oof__int(U_8407),U_8408)),c_Groups_Ozero__class_Ozero(U_8407)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8408),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP572(U_8408,U_8407) ),
inference(clausify,[status(thm)],[f_2089_3]) ).
fof(f_2090_1,plain,
! [V_z_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),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_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2))) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__int__0__less__iff]) ).
fof(f_2090_2,plain,
! [U_8410,U_8409] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8409),c_Groups_Ozero__class_Ozero(U_8409)),hAPP(c_Int_Oring__1__class_Oof__int(U_8409),U_8410)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8410)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8410))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8409),c_Groups_Ozero__class_Ozero(U_8409)),hAPP(c_Int_Oring__1__class_Oof__int(U_8409),U_8410))) ) )
| ~ class_Rings_Olinordered__idom(U_8409) ),
inference(variable_rename,[status(thm)],[f_2090_1]) ).
fof(f_2090_3,plain,
( ! [U_8410,U_8409] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8409),c_Groups_Ozero__class_Ozero(U_8409)),hAPP(c_Int_Oring__1__class_Oof__int(U_8409),U_8410)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8410))
| ~ sP573(U_8410,U_8409) )
& ! [U_8410,U_8409] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8410))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8409),c_Groups_Ozero__class_Ozero(U_8409)),hAPP(c_Int_Oring__1__class_Oof__int(U_8409),U_8410)))
| ~ sP573(U_8410,U_8409) )
& ! [U_8410,U_8409] :
( sP573(U_8410,U_8409)
| ~ class_Rings_Olinordered__idom(U_8409) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP573])],[f_2090_2]) ).
cnf(f_2090_4,plain,
( sP573(U_8410,U_8409)
| ~ class_Rings_Olinordered__idom(U_8409) ),
inference(clausify,[status(thm)],[f_2090_3]) ).
cnf(f_2090_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8410))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8409),c_Groups_Ozero__class_Ozero(U_8409)),hAPP(c_Int_Oring__1__class_Oof__int(U_8409),U_8410)))
| ~ sP573(U_8410,U_8409) ),
inference(clausify,[status(thm)],[f_2090_3]) ).
cnf(f_2090_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8409),c_Groups_Ozero__class_Ozero(U_8409)),hAPP(c_Int_Oring__1__class_Oof__int(U_8409),U_8410)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8410))
| ~ sP573(U_8410,U_8409) ),
inference(clausify,[status(thm)],[f_2090_3]) ).
fof(f_2091_1,plain,
! [V_z_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ 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_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_z_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__int__less__0__iff]) ).
fof(f_2091_2,plain,
! [U_8412,U_8411] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8411),hAPP(c_Int_Oring__1__class_Oof__int(U_8411),U_8412)),c_Groups_Ozero__class_Ozero(U_8411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8412),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8412),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8411),hAPP(c_Int_Oring__1__class_Oof__int(U_8411),U_8412)),c_Groups_Ozero__class_Ozero(U_8411))) ) )
| ~ class_Rings_Olinordered__idom(U_8411) ),
inference(variable_rename,[status(thm)],[f_2091_1]) ).
fof(f_2091_3,plain,
( ! [U_8412,U_8411] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8411),hAPP(c_Int_Oring__1__class_Oof__int(U_8411),U_8412)),c_Groups_Ozero__class_Ozero(U_8411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8412),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP574(U_8412,U_8411) )
& ! [U_8412,U_8411] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8412),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8411),hAPP(c_Int_Oring__1__class_Oof__int(U_8411),U_8412)),c_Groups_Ozero__class_Ozero(U_8411)))
| ~ sP574(U_8412,U_8411) )
& ! [U_8412,U_8411] :
( sP574(U_8412,U_8411)
| ~ class_Rings_Olinordered__idom(U_8411) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP574])],[f_2091_2]) ).
cnf(f_2091_4,plain,
( sP574(U_8412,U_8411)
| ~ class_Rings_Olinordered__idom(U_8411) ),
inference(clausify,[status(thm)],[f_2091_3]) ).
cnf(f_2091_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8412),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8411),hAPP(c_Int_Oring__1__class_Oof__int(U_8411),U_8412)),c_Groups_Ozero__class_Ozero(U_8411)))
| ~ sP574(U_8412,U_8411) ),
inference(clausify,[status(thm)],[f_2091_3]) ).
cnf(f_2091_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8411),hAPP(c_Int_Oring__1__class_Oof__int(U_8411),U_8412)),c_Groups_Ozero__class_Ozero(U_8411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8412),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP574(U_8412,U_8411) ),
inference(clausify,[status(thm)],[f_2091_3]) ).
fof(f_2092_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_2092_2,plain,
! [U_8414,U_8413] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8413),hAPP(c_Int_Onat,U_8414)) = hAPP(c_Int_Oring__1__class_Oof__int(U_8413),U_8414)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8414))
| ~ class_Rings_Oring__1(U_8413) ),
inference(variable_rename,[status(thm)],[f_2092_1]) ).
fof(f_2092_3,plain,
! [U_8413,U_8414] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8413),hAPP(c_Int_Onat,U_8414)) = hAPP(c_Int_Oring__1__class_Oof__int(U_8413),U_8414)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8414))
| ~ class_Rings_Oring__1(U_8413) ),
inference(definitional_conversion,[status(esa)],[f_2092_2]) ).
cnf(f_2092_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8413),hAPP(c_Int_Onat,U_8414)) = hAPP(c_Int_Oring__1__class_Oof__int(U_8413),U_8414)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8414))
| ~ class_Rings_Oring__1(U_8413) ),
inference(clausify,[status(thm)],[f_2092_3]) ).
fof(f_2093_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_l_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J]) ).
fof(f_2093_2,plain,
! [U_8417,U_8416,U_8415] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8415,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8415,U_8416,U_8417)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8415),U_8417)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8415),U_8416)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8415),U_8416),U_8417))
| ~ class_Orderings_Olinorder(U_8415) ),
inference(variable_rename,[status(thm)],[f_2093_1]) ).
fof(f_2093_3,plain,
! [U_8415,U_8416,U_8417] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8415,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8415,U_8416,U_8417)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8415),U_8417)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8415),U_8416)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8415),U_8416),U_8417))
| ~ class_Orderings_Olinorder(U_8415) ),
inference(definitional_conversion,[status(esa)],[f_2093_2]) ).
cnf(f_2093_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8415,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8415,U_8416,U_8417)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8415),U_8417)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8415),U_8416)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8415),U_8416),U_8417))
| ~ class_Orderings_Olinorder(U_8415) ),
inference(clausify,[status(thm)],[f_2093_3]) ).
fof(f_2094_1,plain,
! [V_x_2,T_c] :
( hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__lessThan]) ).
fof(f_2094_2,plain,
! [U_8419,U_8418] :
( hAPP(c_Set_Oimage(U_8418,U_8418,c_Groups_Ouminus__class_Ouminus(U_8418)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8418),U_8419)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8418),hAPP(c_Groups_Ouminus__class_Ouminus(U_8418),U_8419))
| ~ class_Groups_Oordered__ab__group__add(U_8418) ),
inference(variable_rename,[status(thm)],[f_2094_1]) ).
fof(f_2094_3,plain,
! [U_8418,U_8419] :
( hAPP(c_Set_Oimage(U_8418,U_8418,c_Groups_Ouminus__class_Ouminus(U_8418)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8418),U_8419)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8418),hAPP(c_Groups_Ouminus__class_Ouminus(U_8418),U_8419))
| ~ class_Groups_Oordered__ab__group__add(U_8418) ),
inference(definitional_conversion,[status(esa)],[f_2094_2]) ).
cnf(f_2094_4,plain,
( hAPP(c_Set_Oimage(U_8418,U_8418,c_Groups_Ouminus__class_Ouminus(U_8418)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8418),U_8419)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8418),hAPP(c_Groups_Ouminus__class_Ouminus(U_8418),U_8419))
| ~ class_Groups_Oordered__ab__group__add(U_8418) ),
inference(clausify,[status(thm)],[f_2094_3]) ).
fof(f_2095_1,plain,
! [V_x_2,T_c] :
( hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan]) ).
fof(f_2095_2,plain,
! [U_8421,U_8420] :
( hAPP(c_Set_Oimage(U_8420,U_8420,c_Groups_Ouminus__class_Ouminus(U_8420)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8420),U_8421)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_8420),hAPP(c_Groups_Ouminus__class_Ouminus(U_8420),U_8421))
| ~ class_Groups_Oordered__ab__group__add(U_8420) ),
inference(variable_rename,[status(thm)],[f_2095_1]) ).
fof(f_2095_3,plain,
! [U_8420,U_8421] :
( hAPP(c_Set_Oimage(U_8420,U_8420,c_Groups_Ouminus__class_Ouminus(U_8420)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8420),U_8421)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_8420),hAPP(c_Groups_Ouminus__class_Ouminus(U_8420),U_8421))
| ~ class_Groups_Oordered__ab__group__add(U_8420) ),
inference(definitional_conversion,[status(esa)],[f_2095_2]) ).
cnf(f_2095_4,plain,
( hAPP(c_Set_Oimage(U_8420,U_8420,c_Groups_Ouminus__class_Ouminus(U_8420)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8420),U_8421)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_8420),hAPP(c_Groups_Ouminus__class_Ouminus(U_8420),U_8421))
| ~ class_Groups_Oordered__ab__group__add(U_8420) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
fof(f_2096_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J]) ).
fof(f_2096_2,plain,
! [U_8424,U_8423,U_8422] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8422,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8422,U_8423,U_8424)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8422),U_8424)) = c_Orderings_Obot__class_Obot(tc_fun(U_8422,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8422) ),
inference(variable_rename,[status(thm)],[f_2096_1]) ).
fof(f_2096_3,plain,
! [U_8422,U_8423,U_8424] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8422,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8422,U_8423,U_8424)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8422),U_8424)) = c_Orderings_Obot__class_Obot(tc_fun(U_8422,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8422) ),
inference(definitional_conversion,[status(esa)],[f_2096_2]) ).
cnf(f_2096_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8422,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8422,U_8423,U_8424)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8422),U_8424)) = c_Orderings_Obot__class_Obot(tc_fun(U_8422,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8422) ),
inference(clausify,[status(thm)],[f_2096_3]) ).
fof(f_2097_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_2097_2,plain,
! [U_8425] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8425)) = 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_8425)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8425)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2097_1]) ).
fof(f_2097_3,plain,
! [U_8425] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8425)) = 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_8425)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8425)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_2097_2]) ).
cnf(f_2097_4,plain,
hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8425)) = 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_8425)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8425)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2097_3]) ).
fof(f_2098_1,plain,
! [V_f_2,V_A_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,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_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_c),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_c),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I2_J]) ).
fof(f_2098_2,plain,
! [U_8429,U_8428,U_8427] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8427,tc_Int_Oint),U_8429),U_8428) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8427,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8427),c_Int_Onat),U_8429)),U_8428))
| ? [U_8426] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8429,U_8426))
& hBOOL(hAPP(hAPP(c_member(U_8427),U_8426),U_8428)) ) ),
inference(variable_rename,[status(thm)],[f_2098_1]) ).
fof(f_2098_3,plain,
! [U_8429,U_8428,U_8427] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8427,tc_Int_Oint),U_8429),U_8428) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8427,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8427),c_Int_Onat),U_8429)),U_8428))
| ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8429,sK170(U_8429,U_8428,U_8427)))
& hBOOL(hAPP(hAPP(c_member(U_8427),sK170(U_8429,U_8428,U_8427)),U_8428)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_8426,sK170(U_8429,U_8428,U_8427))],[f_2098_2]) ).
fof(f_2098_4,plain,
( ! [U_8427,U_8428,U_8429] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8429,sK170(U_8429,U_8428,U_8427)))
| ~ sP575(U_8427,U_8428,U_8429) )
& ! [U_8427,U_8428,U_8429] :
( hBOOL(hAPP(hAPP(c_member(U_8427),sK170(U_8429,U_8428,U_8427)),U_8428))
| ~ sP575(U_8427,U_8428,U_8429) )
& ! [U_8427,U_8428,U_8429] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8427,tc_Int_Oint),U_8429),U_8428) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8427,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8427),c_Int_Onat),U_8429)),U_8428))
| sP575(U_8427,U_8428,U_8429) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP575])],[f_2098_3]) ).
cnf(f_2098_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8427,tc_Int_Oint),U_8429),U_8428) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8427,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8427),c_Int_Onat),U_8429)),U_8428))
| sP575(U_8427,U_8428,U_8429) ),
inference(clausify,[status(thm)],[f_2098_4]) ).
cnf(f_2098_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8427),sK170(U_8429,U_8428,U_8427)),U_8428))
| ~ sP575(U_8427,U_8428,U_8429) ),
inference(clausify,[status(thm)],[f_2098_4]) ).
cnf(f_2098_7,plain,
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8429,sK170(U_8429,U_8428,U_8427)))
| ~ sP575(U_8427,U_8428,U_8429) ),
inference(clausify,[status(thm)],[f_2098_4]) ).
fof(f_2099_1,plain,
! [V_f_2,V_A_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_c),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_c),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I1_J]) ).
fof(f_2099_2,plain,
! [U_8433,U_8432,U_8431] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8431,tc_Int_Oint),U_8433),U_8432) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8431,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8431),c_Int_Onat),U_8433)),U_8432))
| ? [U_8430] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8433,U_8430))
& hBOOL(hAPP(hAPP(c_member(U_8431),U_8430),U_8432)) ) ),
inference(variable_rename,[status(thm)],[f_2099_1]) ).
fof(f_2099_3,plain,
! [U_8433,U_8432,U_8431] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8431,tc_Int_Oint),U_8433),U_8432) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8431,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8431),c_Int_Onat),U_8433)),U_8432))
| ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8433,sK171(U_8433,U_8432,U_8431)))
& hBOOL(hAPP(hAPP(c_member(U_8431),sK171(U_8433,U_8432,U_8431)),U_8432)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_8430,sK171(U_8433,U_8432,U_8431))],[f_2099_2]) ).
fof(f_2099_4,plain,
( ! [U_8431,U_8432,U_8433] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8433,sK171(U_8433,U_8432,U_8431)))
| ~ sP576(U_8431,U_8432,U_8433) )
& ! [U_8431,U_8432,U_8433] :
( hBOOL(hAPP(hAPP(c_member(U_8431),sK171(U_8433,U_8432,U_8431)),U_8432))
| ~ sP576(U_8431,U_8432,U_8433) )
& ! [U_8431,U_8432,U_8433] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8431,tc_Int_Oint),U_8433),U_8432) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8431,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8431),c_Int_Onat),U_8433)),U_8432))
| sP576(U_8431,U_8432,U_8433) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP576])],[f_2099_3]) ).
cnf(f_2099_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8431,tc_Int_Oint),U_8433),U_8432) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8431,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8431),c_Int_Onat),U_8433)),U_8432))
| sP576(U_8431,U_8432,U_8433) ),
inference(clausify,[status(thm)],[f_2099_4]) ).
cnf(f_2099_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8431),sK171(U_8433,U_8432,U_8431)),U_8432))
| ~ sP576(U_8431,U_8432,U_8433) ),
inference(clausify,[status(thm)],[f_2099_4]) ).
cnf(f_2099_7,plain,
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8433,sK171(U_8433,U_8432,U_8431)))
| ~ sP576(U_8431,U_8432,U_8433) ),
inference(clausify,[status(thm)],[f_2099_4]) ).
fof(f_2100_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_2100_2,plain,
! [U_8437,U_8436,U_8435] :
( 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_8436),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8437))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8435),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8437))) = 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_8436)),U_8435)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8437))
| ? [U_8434] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_8435,U_8434)),hAPP(U_8436,U_8434))) ),
inference(variable_rename,[status(thm)],[f_2100_1]) ).
fof(f_2100_3,plain,
! [U_8437,U_8436,U_8435] :
( 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_8436),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8437))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8435),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8437))) = 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_8436)),U_8435)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8437))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_8435,sK172(U_8437,U_8436,U_8435))),hAPP(U_8436,sK172(U_8437,U_8436,U_8435)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_8434,sK172(U_8437,U_8436,U_8435))],[f_2100_2]) ).
fof(f_2100_4,plain,
! [U_8435,U_8436,U_8437] :
( 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_8436),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8437))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8435),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8437))) = 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_8436)),U_8435)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8437))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_8435,sK172(U_8437,U_8436,U_8435))),hAPP(U_8436,sK172(U_8437,U_8436,U_8435)))) ),
inference(definitional_conversion,[status(esa)],[f_2100_3]) ).
cnf(f_2100_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_8436),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8437))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8435),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8437))) = 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_8436)),U_8435)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8437))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_8435,sK172(U_8437,U_8436,U_8435))),hAPP(U_8436,sK172(U_8437,U_8436,U_8435)))) ),
inference(clausify,[status(thm)],[f_2100_4]) ).
fof(f_2101_1,plain,
! [V_f_2,V_n_2,V_m_2,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_c)
| 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_c),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_c)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_c),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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__natinterval__difff]) ).
fof(f_2101_2,plain,
! [U_8441,U_8440,U_8439,U_8438] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8438),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_8438,U_8438),hAPP(hAPP(c_COMBB(U_8438,tc_fun(U_8438,U_8438),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_8438)),U_8441)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8438,tc_Nat_Onat),U_8441),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_8439,U_8440)) = c_Groups_Ozero__class_Ozero(U_8438)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8439),U_8440)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8438),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_8438,U_8438),hAPP(hAPP(c_COMBB(U_8438,tc_fun(U_8438,U_8438),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_8438)),U_8441)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8438,tc_Nat_Onat),U_8441),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_8439,U_8440)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8438),hAPP(U_8441,U_8439)),hAPP(U_8441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8440),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8439),U_8440)) ) )
| ~ class_Groups_Oab__group__add(U_8438) ),
inference(variable_rename,[status(thm)],[f_2101_1]) ).
fof(f_2101_3,plain,
( ! [U_8438,U_8439,U_8440,U_8441] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8438),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_8438,U_8438),hAPP(hAPP(c_COMBB(U_8438,tc_fun(U_8438,U_8438),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_8438)),U_8441)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8438,tc_Nat_Onat),U_8441),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_8439,U_8440)) = c_Groups_Ozero__class_Ozero(U_8438)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8439),U_8440))
| ~ sP577(U_8438,U_8439,U_8440,U_8441) )
& ! [U_8438,U_8439,U_8440,U_8441] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8438),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_8438,U_8438),hAPP(hAPP(c_COMBB(U_8438,tc_fun(U_8438,U_8438),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_8438)),U_8441)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8438,tc_Nat_Onat),U_8441),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_8439,U_8440)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8438),hAPP(U_8441,U_8439)),hAPP(U_8441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8440),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8439),U_8440))
| ~ sP577(U_8438,U_8439,U_8440,U_8441) )
& ! [U_8438,U_8439,U_8440,U_8441] :
( sP577(U_8438,U_8439,U_8440,U_8441)
| ~ class_Groups_Oab__group__add(U_8438) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP577])],[f_2101_2]) ).
cnf(f_2101_4,plain,
( sP577(U_8438,U_8439,U_8440,U_8441)
| ~ class_Groups_Oab__group__add(U_8438) ),
inference(clausify,[status(thm)],[f_2101_3]) ).
cnf(f_2101_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8438),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_8438,U_8438),hAPP(hAPP(c_COMBB(U_8438,tc_fun(U_8438,U_8438),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_8438)),U_8441)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8438,tc_Nat_Onat),U_8441),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_8439,U_8440)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8438),hAPP(U_8441,U_8439)),hAPP(U_8441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8440),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8439),U_8440))
| ~ sP577(U_8438,U_8439,U_8440,U_8441) ),
inference(clausify,[status(thm)],[f_2101_3]) ).
cnf(f_2101_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8438),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_8438,U_8438),hAPP(hAPP(c_COMBB(U_8438,tc_fun(U_8438,U_8438),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_8438)),U_8441)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8438,tc_Nat_Onat),U_8441),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_8439,U_8440)) = c_Groups_Ozero__class_Ozero(U_8438)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8439),U_8440))
| ~ sP577(U_8438,U_8439,U_8440,U_8441) ),
inference(clausify,[status(thm)],[f_2101_3]) ).
fof(f_2102_1,plain,
! [V_n_2,T_c] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),c_Groups_Oone__class_Oone(T_c)),c_Groups_Oone__class_Oone(T_c))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_c)),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_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),c_Groups_Oone__class_Oone(T_c)))
| ~ class_Rings_Ocomm__semiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_gauss__sum]) ).
fof(f_2102_2,plain,
! [U_8443,U_8442] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8442),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8442),c_Groups_Oone__class_Oone(U_8442)),c_Groups_Oone__class_Oone(U_8442))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8442),c_Nat_Osemiring__1__class_Oof__nat(U_8442)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_8443))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8442),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8442),U_8443)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8442),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8442),U_8443)),c_Groups_Oone__class_Oone(U_8442)))
| ~ class_Rings_Ocomm__semiring__1(U_8442) ),
inference(variable_rename,[status(thm)],[f_2102_1]) ).
fof(f_2102_3,plain,
! [U_8443,U_8442] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8442),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8442),c_Groups_Oone__class_Oone(U_8442)),c_Groups_Oone__class_Oone(U_8442))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8442),c_Nat_Osemiring__1__class_Oof__nat(U_8442)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_8443))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8442),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8442),U_8443)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8442),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8442),U_8443)),c_Groups_Oone__class_Oone(U_8442)))
| ~ class_Rings_Ocomm__semiring__1(U_8442) ),
inference(definitional_conversion,[status(esa)],[f_2102_2]) ).
cnf(f_2102_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8442),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8442),c_Groups_Oone__class_Oone(U_8442)),c_Groups_Oone__class_Oone(U_8442))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8442),c_Nat_Osemiring__1__class_Oof__nat(U_8442)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_8443))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8442),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8442),U_8443)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8442),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8442),U_8443)),c_Groups_Oone__class_Oone(U_8442)))
| ~ class_Rings_Ocomm__semiring__1(U_8442) ),
inference(clausify,[status(thm)],[f_2102_3]) ).
fof(f_2103_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_2103_2,plain,
! [U_8445,U_8444] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8444,U_8445))),
inference(variable_rename,[status(thm)],[f_2103_1]) ).
fof(f_2103_3,plain,
! [U_8444,U_8445] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8444,U_8445))),
inference(definitional_conversion,[status(esa)],[f_2103_2]) ).
cnf(f_2103_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8444,U_8445))),
inference(clausify,[status(thm)],[f_2103_3]) ).
fof(f_2104_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_2104_2,plain,
! [U_8451,U_8450] :
( ( ! [U_8449] :
( hBOOL(hAPP(U_8451,U_8449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8449),U_8450)) )
| ? [U_8448] :
( ~ hBOOL(hAPP(U_8451,U_8448))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8448),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8450))) ) )
& ( ! [U_8447] :
( hBOOL(hAPP(U_8451,U_8447))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8447),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8450))) )
| ? [U_8446] :
( ~ hBOOL(hAPP(U_8451,U_8446))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8446),U_8450)) ) ) ),
inference(variable_rename,[status(thm)],[f_2104_1]) ).
fof(f_2104_3,plain,
( ! [U_8455,U_8453] :
( ! [U_8449] :
( hBOOL(hAPP(U_8455,U_8449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8449),U_8453)) )
| ? [U_8448] :
( ~ hBOOL(hAPP(U_8455,U_8448))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8448),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8453))) ) )
& ! [U_8454,U_8452] :
( ! [U_8447] :
( hBOOL(hAPP(U_8454,U_8447))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8447),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8452))) )
| ? [U_8446] :
( ~ hBOOL(hAPP(U_8454,U_8446))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8446),U_8452)) ) ) ),
inference(miniscope,[status(thm)],[f_2104_2]) ).
fof(f_2104_4,plain,
( ! [U_8455,U_8453] :
( ! [U_8449] :
( hBOOL(hAPP(U_8455,U_8449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8449),U_8453)) )
| ? [U_8448] :
( ~ hBOOL(hAPP(U_8455,U_8448))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8448),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8453))) ) )
& ! [U_8454,U_8452] :
( ! [U_8447] :
( hBOOL(hAPP(U_8454,U_8447))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8447),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8452))) )
| ( ~ hBOOL(hAPP(U_8454,sK173(U_8454,U_8452)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK173(U_8454,U_8452)),U_8452)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_8446,sK173(U_8454,U_8452))],[f_2104_3]) ).
fof(f_2104_5,plain,
( ! [U_8455,U_8453] :
( ! [U_8449] :
( hBOOL(hAPP(U_8455,U_8449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8449),U_8453)) )
| ( ~ hBOOL(hAPP(U_8455,sK174(U_8455,U_8453)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK174(U_8455,U_8453)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8453))) ) )
& ! [U_8454,U_8452] :
( ! [U_8447] :
( hBOOL(hAPP(U_8454,U_8447))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8447),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8452))) )
| ( ~ hBOOL(hAPP(U_8454,sK173(U_8454,U_8452)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK173(U_8454,U_8452)),U_8452)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_8448,sK174(U_8455,U_8453))],[f_2104_4]) ).
fof(f_2104_6,plain,
( ! [U_8455,U_8453] :
( ~ hBOOL(hAPP(U_8455,sK174(U_8455,U_8453)))
| ~ sP579(U_8455,U_8453) )
& ! [U_8455,U_8453] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK174(U_8455,U_8453)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8453)))
| ~ sP579(U_8455,U_8453) )
& ! [U_8452,U_8454] :
( ~ hBOOL(hAPP(U_8454,sK173(U_8454,U_8452)))
| ~ sP578(U_8452,U_8454) )
& ! [U_8452,U_8454] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK173(U_8454,U_8452)),U_8452))
| ~ sP578(U_8452,U_8454) )
& ! [U_8455,U_8449,U_8453] :
( hBOOL(hAPP(U_8455,U_8449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8449),U_8453))
| sP579(U_8455,U_8453) )
& ! [U_8447,U_8452,U_8454] :
( hBOOL(hAPP(U_8454,U_8447))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8447),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8452)))
| sP578(U_8452,U_8454) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP578,sP579])],[f_2104_5]) ).
cnf(f_2104_7,plain,
( hBOOL(hAPP(U_8454,U_8447))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8447),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8452)))
| sP578(U_8452,U_8454) ),
inference(clausify,[status(thm)],[f_2104_6]) ).
cnf(f_2104_8,plain,
( hBOOL(hAPP(U_8455,U_8449))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8449),U_8453))
| sP579(U_8455,U_8453) ),
inference(clausify,[status(thm)],[f_2104_6]) ).
cnf(f_2104_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK173(U_8454,U_8452)),U_8452))
| ~ sP578(U_8452,U_8454) ),
inference(clausify,[status(thm)],[f_2104_6]) ).
cnf(f_2104_10,plain,
( ~ hBOOL(hAPP(U_8454,sK173(U_8454,U_8452)))
| ~ sP578(U_8452,U_8454) ),
inference(clausify,[status(thm)],[f_2104_6]) ).
cnf(f_2104_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK174(U_8455,U_8453)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8453)))
| ~ sP579(U_8455,U_8453) ),
inference(clausify,[status(thm)],[f_2104_6]) ).
cnf(f_2104_12,plain,
( ~ hBOOL(hAPP(U_8455,sK174(U_8455,U_8453)))
| ~ sP579(U_8455,U_8453) ),
inference(clausify,[status(thm)],[f_2104_6]) ).
fof(f_2105_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_2105_2,plain,
! [U_8461,U_8460] :
( ( ? [U_8459] :
( hBOOL(hAPP(U_8461,U_8459))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8459),U_8460)) )
| ! [U_8458] :
( ~ hBOOL(hAPP(U_8461,U_8458))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8458),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8460))) ) )
& ( ? [U_8457] :
( hBOOL(hAPP(U_8461,U_8457))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8457),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8460))) )
| ! [U_8456] :
( ~ hBOOL(hAPP(U_8461,U_8456))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8456),U_8460)) ) ) ),
inference(variable_rename,[status(thm)],[f_2105_1]) ).
fof(f_2105_3,plain,
( ! [U_8465,U_8463] :
( ? [U_8459] :
( hBOOL(hAPP(U_8465,U_8459))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8459),U_8463)) )
| ! [U_8458] :
( ~ hBOOL(hAPP(U_8465,U_8458))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8458),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8463))) ) )
& ! [U_8464,U_8462] :
( ? [U_8457] :
( hBOOL(hAPP(U_8464,U_8457))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8457),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8462))) )
| ! [U_8456] :
( ~ hBOOL(hAPP(U_8464,U_8456))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8456),U_8462)) ) ) ),
inference(miniscope,[status(thm)],[f_2105_2]) ).
fof(f_2105_4,plain,
( ! [U_8465,U_8463] :
( ? [U_8459] :
( hBOOL(hAPP(U_8465,U_8459))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8459),U_8463)) )
| ! [U_8458] :
( ~ hBOOL(hAPP(U_8465,U_8458))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8458),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8463))) ) )
& ! [U_8464,U_8462] :
( ( hBOOL(hAPP(U_8464,sK175(U_8464,U_8462)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK175(U_8464,U_8462)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8462))) )
| ! [U_8456] :
( ~ hBOOL(hAPP(U_8464,U_8456))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8456),U_8462)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_8457,sK175(U_8464,U_8462))],[f_2105_3]) ).
fof(f_2105_5,plain,
( ! [U_8465,U_8463] :
( ( hBOOL(hAPP(U_8465,sK176(U_8465,U_8463)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK176(U_8465,U_8463)),U_8463)) )
| ! [U_8458] :
( ~ hBOOL(hAPP(U_8465,U_8458))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8458),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8463))) ) )
& ! [U_8464,U_8462] :
( ( hBOOL(hAPP(U_8464,sK175(U_8464,U_8462)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK175(U_8464,U_8462)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8462))) )
| ! [U_8456] :
( ~ hBOOL(hAPP(U_8464,U_8456))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8456),U_8462)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_8459,sK176(U_8465,U_8463))],[f_2105_4]) ).
fof(f_2105_6,plain,
( ! [U_8463,U_8465] :
( hBOOL(hAPP(U_8465,sK176(U_8465,U_8463)))
| ~ sP581(U_8463,U_8465) )
& ! [U_8463,U_8465] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK176(U_8465,U_8463)),U_8463))
| ~ sP581(U_8463,U_8465) )
& ! [U_8462,U_8464] :
( hBOOL(hAPP(U_8464,sK175(U_8464,U_8462)))
| ~ sP580(U_8462,U_8464) )
& ! [U_8462,U_8464] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK175(U_8464,U_8462)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8462)))
| ~ sP580(U_8462,U_8464) )
& ! [U_8458,U_8463,U_8465] :
( sP581(U_8463,U_8465)
| ~ hBOOL(hAPP(U_8465,U_8458))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8458),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8463))) )
& ! [U_8456,U_8462,U_8464] :
( sP580(U_8462,U_8464)
| ~ hBOOL(hAPP(U_8464,U_8456))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8456),U_8462)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP580,sP581])],[f_2105_5]) ).
cnf(f_2105_7,plain,
( sP580(U_8462,U_8464)
| ~ hBOOL(hAPP(U_8464,U_8456))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8456),U_8462)) ),
inference(clausify,[status(thm)],[f_2105_6]) ).
cnf(f_2105_8,plain,
( sP581(U_8463,U_8465)
| ~ hBOOL(hAPP(U_8465,U_8458))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8458),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8463))) ),
inference(clausify,[status(thm)],[f_2105_6]) ).
cnf(f_2105_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK175(U_8464,U_8462)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8462)))
| ~ sP580(U_8462,U_8464) ),
inference(clausify,[status(thm)],[f_2105_6]) ).
cnf(f_2105_10,plain,
( hBOOL(hAPP(U_8464,sK175(U_8464,U_8462)))
| ~ sP580(U_8462,U_8464) ),
inference(clausify,[status(thm)],[f_2105_6]) ).
cnf(f_2105_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK176(U_8465,U_8463)),U_8463))
| ~ sP581(U_8463,U_8465) ),
inference(clausify,[status(thm)],[f_2105_6]) ).
cnf(f_2105_12,plain,
( hBOOL(hAPP(U_8465,sK176(U_8465,U_8463)))
| ~ sP581(U_8463,U_8465) ),
inference(clausify,[status(thm)],[f_2105_6]) ).
fof(f_2106_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_2106_2,plain,
! [U_8467,U_8466] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8466),hAPP(c_Nat_OSuc,U_8467)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8466,U_8467),
inference(variable_rename,[status(thm)],[f_2106_1]) ).
fof(f_2106_3,plain,
! [U_8467,U_8466] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8466),hAPP(c_Nat_OSuc,U_8467)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8466,U_8467),
inference(definitional_conversion,[status(esa)],[f_2106_2]) ).
cnf(f_2106_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8466),hAPP(c_Nat_OSuc,U_8467)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8466,U_8467),
inference(clausify,[status(thm)],[f_2106_3]) ).
fof(f_2107_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2))
| c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).
fof(f_2107_2,plain,
! [U_8470,U_8469,U_8468] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_8468,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8468,U_8469,U_8470)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8468),U_8469),U_8470)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8468),U_8469),U_8470))
| c_Orderings_Obot__class_Obot(tc_fun(U_8468,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_8468,U_8469,U_8470) ) )
| ~ class_Orderings_Oorder(U_8468) ),
inference(variable_rename,[status(thm)],[f_2107_1]) ).
fof(f_2107_3,plain,
( ! [U_8469,U_8468,U_8470] :
( c_Orderings_Obot__class_Obot(tc_fun(U_8468,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8468,U_8469,U_8470)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8468),U_8469),U_8470))
| ~ sP582(U_8469,U_8468,U_8470) )
& ! [U_8469,U_8468,U_8470] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8468),U_8469),U_8470))
| c_Orderings_Obot__class_Obot(tc_fun(U_8468,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_8468,U_8469,U_8470)
| ~ sP582(U_8469,U_8468,U_8470) )
& ! [U_8469,U_8468,U_8470] :
( sP582(U_8469,U_8468,U_8470)
| ~ class_Orderings_Oorder(U_8468) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP582])],[f_2107_2]) ).
cnf(f_2107_4,plain,
( sP582(U_8469,U_8468,U_8470)
| ~ class_Orderings_Oorder(U_8468) ),
inference(clausify,[status(thm)],[f_2107_3]) ).
cnf(f_2107_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8468),U_8469),U_8470))
| c_Orderings_Obot__class_Obot(tc_fun(U_8468,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_8468,U_8469,U_8470)
| ~ sP582(U_8469,U_8468,U_8470) ),
inference(clausify,[status(thm)],[f_2107_3]) ).
cnf(f_2107_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_8468,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8468,U_8469,U_8470)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8468),U_8469),U_8470))
| ~ sP582(U_8469,U_8468,U_8470) ),
inference(clausify,[status(thm)],[f_2107_3]) ).
fof(f_2108_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2))
| c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty__iff]) ).
fof(f_2108_2,plain,
! [U_8473,U_8472,U_8471] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_8471,U_8472,U_8473) = c_Orderings_Obot__class_Obot(tc_fun(U_8471,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8471),U_8472),U_8473)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8471),U_8472),U_8473))
| c_SetInterval_Oord__class_OatLeastAtMost(U_8471,U_8472,U_8473) != c_Orderings_Obot__class_Obot(tc_fun(U_8471,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(U_8471) ),
inference(variable_rename,[status(thm)],[f_2108_1]) ).
fof(f_2108_3,plain,
( ! [U_8473,U_8472,U_8471] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_8471,U_8472,U_8473) = c_Orderings_Obot__class_Obot(tc_fun(U_8471,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8471),U_8472),U_8473))
| ~ sP583(U_8473,U_8472,U_8471) )
& ! [U_8473,U_8472,U_8471] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8471),U_8472),U_8473))
| c_SetInterval_Oord__class_OatLeastAtMost(U_8471,U_8472,U_8473) != c_Orderings_Obot__class_Obot(tc_fun(U_8471,tc_HOL_Obool))
| ~ sP583(U_8473,U_8472,U_8471) )
& ! [U_8473,U_8472,U_8471] :
( sP583(U_8473,U_8472,U_8471)
| ~ class_Orderings_Oorder(U_8471) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP583])],[f_2108_2]) ).
cnf(f_2108_4,plain,
( sP583(U_8473,U_8472,U_8471)
| ~ class_Orderings_Oorder(U_8471) ),
inference(clausify,[status(thm)],[f_2108_3]) ).
cnf(f_2108_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8471),U_8472),U_8473))
| c_SetInterval_Oord__class_OatLeastAtMost(U_8471,U_8472,U_8473) != c_Orderings_Obot__class_Obot(tc_fun(U_8471,tc_HOL_Obool))
| ~ sP583(U_8473,U_8472,U_8471) ),
inference(clausify,[status(thm)],[f_2108_3]) ).
cnf(f_2108_6,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_8471,U_8472,U_8473) = c_Orderings_Obot__class_Obot(tc_fun(U_8471,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8471),U_8472),U_8473))
| ~ sP583(U_8473,U_8472,U_8471) ),
inference(clausify,[status(thm)],[f_2108_3]) ).
fof(f_2109_1,plain,
! [V_a_2,V_b_2,T_c] :
( c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_a_2))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty]) ).
fof(f_2109_2,plain,
! [U_8476,U_8475,U_8474] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_8474,U_8476,U_8475) = c_Orderings_Obot__class_Obot(tc_fun(U_8474,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8474),U_8475),U_8476))
| ~ class_Orderings_Oorder(U_8474) ),
inference(variable_rename,[status(thm)],[f_2109_1]) ).
fof(f_2109_3,plain,
! [U_8475,U_8474,U_8476] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_8474,U_8476,U_8475) = c_Orderings_Obot__class_Obot(tc_fun(U_8474,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8474),U_8475),U_8476))
| ~ class_Orderings_Oorder(U_8474) ),
inference(definitional_conversion,[status(esa)],[f_2109_2]) ).
cnf(f_2109_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_8474,U_8476,U_8475) = c_Orderings_Obot__class_Obot(tc_fun(U_8474,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8474),U_8475),U_8476))
| ~ class_Orderings_Oorder(U_8474) ),
inference(clausify,[status(thm)],[f_2109_3]) ).
fof(f_2110_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2))) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__subset__iff]) ).
fof(f_2110_2,plain,
! [U_8481,U_8480,U_8479,U_8478,U_8477] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8477,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8477,U_8478,U_8479)),c_SetInterval_Oord__class_OatLeastAtMost(U_8477,U_8480,U_8481)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8479),U_8481))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8480),U_8478)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8478),U_8479)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8479),U_8481))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8480),U_8478)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8478),U_8479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8477,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8477,U_8478,U_8479)),c_SetInterval_Oord__class_OatLeastAtMost(U_8477,U_8480,U_8481))) ) )
| ~ class_Orderings_Oorder(U_8477) ),
inference(variable_rename,[status(thm)],[f_2110_1]) ).
fof(f_2110_3,plain,
( ! [U_8477,U_8478,U_8479,U_8480,U_8481] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8479),U_8481))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8480),U_8478))
| ~ sP585(U_8477,U_8478,U_8479,U_8480,U_8481) )
& ! [U_8477,U_8478,U_8479,U_8480,U_8481] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8478),U_8479))
| ~ sP585(U_8477,U_8478,U_8479,U_8480,U_8481) )
& ! [U_8477,U_8478,U_8479,U_8480,U_8481] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8479),U_8481))
| ~ sP584(U_8477,U_8478,U_8479,U_8480,U_8481) )
& ! [U_8477,U_8478,U_8479,U_8480,U_8481] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8480),U_8478))
| ~ sP584(U_8477,U_8478,U_8479,U_8480,U_8481) )
& ! [U_8477,U_8478,U_8479,U_8480,U_8481] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8477,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8477,U_8478,U_8479)),c_SetInterval_Oord__class_OatLeastAtMost(U_8477,U_8480,U_8481)))
| sP585(U_8477,U_8478,U_8479,U_8480,U_8481)
| ~ sP586(U_8477,U_8478,U_8479,U_8480,U_8481) )
& ! [U_8477,U_8478,U_8479,U_8480,U_8481] :
( sP584(U_8477,U_8478,U_8479,U_8480,U_8481)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8478),U_8479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8477,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8477,U_8478,U_8479)),c_SetInterval_Oord__class_OatLeastAtMost(U_8477,U_8480,U_8481)))
| ~ sP586(U_8477,U_8478,U_8479,U_8480,U_8481) )
& ! [U_8477,U_8478,U_8479,U_8480,U_8481] :
( sP586(U_8477,U_8478,U_8479,U_8480,U_8481)
| ~ class_Orderings_Oorder(U_8477) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP584,sP585,sP586])],[f_2110_2]) ).
cnf(f_2110_4,plain,
( sP586(U_8477,U_8478,U_8479,U_8480,U_8481)
| ~ class_Orderings_Oorder(U_8477) ),
inference(clausify,[status(thm)],[f_2110_3]) ).
cnf(f_2110_5,plain,
( sP584(U_8477,U_8478,U_8479,U_8480,U_8481)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8478),U_8479))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8477,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8477,U_8478,U_8479)),c_SetInterval_Oord__class_OatLeastAtMost(U_8477,U_8480,U_8481)))
| ~ sP586(U_8477,U_8478,U_8479,U_8480,U_8481) ),
inference(clausify,[status(thm)],[f_2110_3]) ).
cnf(f_2110_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8477,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8477,U_8478,U_8479)),c_SetInterval_Oord__class_OatLeastAtMost(U_8477,U_8480,U_8481)))
| sP585(U_8477,U_8478,U_8479,U_8480,U_8481)
| ~ sP586(U_8477,U_8478,U_8479,U_8480,U_8481) ),
inference(clausify,[status(thm)],[f_2110_3]) ).
cnf(f_2110_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8480),U_8478))
| ~ sP584(U_8477,U_8478,U_8479,U_8480,U_8481) ),
inference(clausify,[status(thm)],[f_2110_3]) ).
cnf(f_2110_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8479),U_8481))
| ~ sP584(U_8477,U_8478,U_8479,U_8480,U_8481) ),
inference(clausify,[status(thm)],[f_2110_3]) ).
cnf(f_2110_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8478),U_8479))
| ~ sP585(U_8477,U_8478,U_8479,U_8480,U_8481) ),
inference(clausify,[status(thm)],[f_2110_3]) ).
cnf(f_2110_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8479),U_8481))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8480),U_8478))
| ~ sP585(U_8477,U_8478,U_8479,U_8480,U_8481) ),
inference(clausify,[status(thm)],[f_2110_3]) ).
fof(f_2111_1,plain,
! [V_b_2,V_a_2,T_c] :
( c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_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_a_2 != V_b_2
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H]) ).
fof(f_2111_2,plain,
! [U_8484,U_8483,U_8482] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_8482,U_8483,U_8484) = hAPP(hAPP(c_Set_Oinsert(U_8482),U_8483),c_Orderings_Obot__class_Obot(tc_fun(U_8482,tc_HOL_Obool)))
| U_8483 != U_8484
| ~ class_Orderings_Oorder(U_8482) ),
inference(variable_rename,[status(thm)],[f_2111_1]) ).
fof(f_2111_3,plain,
! [U_8484,U_8482,U_8483] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_8482,U_8483,U_8484) = hAPP(hAPP(c_Set_Oinsert(U_8482),U_8483),c_Orderings_Obot__class_Obot(tc_fun(U_8482,tc_HOL_Obool)))
| U_8483 != U_8484
| ~ class_Orderings_Oorder(U_8482) ),
inference(definitional_conversion,[status(esa)],[f_2111_2]) ).
cnf(f_2111_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_8482,U_8483,U_8484) = hAPP(hAPP(c_Set_Oinsert(U_8482),U_8483),c_Orderings_Obot__class_Obot(tc_fun(U_8482,tc_HOL_Obool)))
| U_8483 != U_8484
| ~ class_Orderings_Oorder(U_8482) ),
inference(clausify,[status(thm)],[f_2111_3]) ).
fof(f_2112_1,plain,
! [V_c_2,V_b_2,V_a_2,T_c] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
| V_b_2 != V_c_2
| V_a_2 != V_b_2 )
& ( ( V_b_2 = V_c_2
& V_a_2 = V_b_2 )
| c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2) != hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff]) ).
fof(f_2112_2,plain,
! [U_8488,U_8487,U_8486,U_8485] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_8485,U_8486,U_8487) = hAPP(hAPP(c_Set_Oinsert(U_8485),U_8488),c_Orderings_Obot__class_Obot(tc_fun(U_8485,tc_HOL_Obool)))
| U_8487 != U_8488
| U_8486 != U_8487 )
& ( ( U_8487 = U_8488
& U_8486 = U_8487 )
| c_SetInterval_Oord__class_OatLeastAtMost(U_8485,U_8486,U_8487) != hAPP(hAPP(c_Set_Oinsert(U_8485),U_8488),c_Orderings_Obot__class_Obot(tc_fun(U_8485,tc_HOL_Obool))) ) )
| ~ class_Orderings_Oorder(U_8485) ),
inference(variable_rename,[status(thm)],[f_2112_1]) ).
fof(f_2112_3,plain,
( ! [U_8488,U_8486,U_8487] :
( U_8487 = U_8488
| ~ sP587(U_8488,U_8486,U_8487) )
& ! [U_8488,U_8486,U_8487] :
( U_8486 = U_8487
| ~ sP587(U_8488,U_8486,U_8487) )
& ! [U_8488,U_8486,U_8487,U_8485] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_8485,U_8486,U_8487) = hAPP(hAPP(c_Set_Oinsert(U_8485),U_8488),c_Orderings_Obot__class_Obot(tc_fun(U_8485,tc_HOL_Obool)))
| U_8487 != U_8488
| U_8486 != U_8487
| ~ sP588(U_8488,U_8486,U_8487,U_8485) )
& ! [U_8488,U_8486,U_8487,U_8485] :
( sP587(U_8488,U_8486,U_8487)
| c_SetInterval_Oord__class_OatLeastAtMost(U_8485,U_8486,U_8487) != hAPP(hAPP(c_Set_Oinsert(U_8485),U_8488),c_Orderings_Obot__class_Obot(tc_fun(U_8485,tc_HOL_Obool)))
| ~ sP588(U_8488,U_8486,U_8487,U_8485) )
& ! [U_8488,U_8486,U_8487,U_8485] :
( sP588(U_8488,U_8486,U_8487,U_8485)
| ~ class_Orderings_Oorder(U_8485) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP587,sP588])],[f_2112_2]) ).
cnf(f_2112_4,plain,
( sP588(U_8488,U_8486,U_8487,U_8485)
| ~ class_Orderings_Oorder(U_8485) ),
inference(clausify,[status(thm)],[f_2112_3]) ).
cnf(f_2112_5,plain,
( sP587(U_8488,U_8486,U_8487)
| c_SetInterval_Oord__class_OatLeastAtMost(U_8485,U_8486,U_8487) != hAPP(hAPP(c_Set_Oinsert(U_8485),U_8488),c_Orderings_Obot__class_Obot(tc_fun(U_8485,tc_HOL_Obool)))
| ~ sP588(U_8488,U_8486,U_8487,U_8485) ),
inference(clausify,[status(thm)],[f_2112_3]) ).
cnf(f_2112_6,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_8485,U_8486,U_8487) = hAPP(hAPP(c_Set_Oinsert(U_8485),U_8488),c_Orderings_Obot__class_Obot(tc_fun(U_8485,tc_HOL_Obool)))
| U_8487 != U_8488
| U_8486 != U_8487
| ~ sP588(U_8488,U_8486,U_8487,U_8485) ),
inference(clausify,[status(thm)],[f_2112_3]) ).
cnf(f_2112_7,plain,
( U_8486 = U_8487
| ~ sP587(U_8488,U_8486,U_8487) ),
inference(clausify,[status(thm)],[f_2112_3]) ).
cnf(f_2112_8,plain,
( U_8487 = U_8488
| ~ sP587(U_8488,U_8486,U_8487) ),
inference(clausify,[status(thm)],[f_2112_3]) ).
fof(f_2113_1,plain,
! [V_a_2,T_c] :
( c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton]) ).
fof(f_2113_2,plain,
! [U_8490,U_8489] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_8489,U_8490,U_8490) = hAPP(hAPP(c_Set_Oinsert(U_8489),U_8490),c_Orderings_Obot__class_Obot(tc_fun(U_8489,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_8489) ),
inference(variable_rename,[status(thm)],[f_2113_1]) ).
fof(f_2113_3,plain,
! [U_8489,U_8490] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_8489,U_8490,U_8490) = hAPP(hAPP(c_Set_Oinsert(U_8489),U_8490),c_Orderings_Obot__class_Obot(tc_fun(U_8489,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_8489) ),
inference(definitional_conversion,[status(esa)],[f_2113_2]) ).
cnf(f_2113_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_8489,U_8490,U_8490) = hAPP(hAPP(c_Set_Oinsert(U_8489),U_8490),c_Orderings_Obot__class_Obot(tc_fun(U_8489,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_8489) ),
inference(clausify,[status(thm)],[f_2113_3]) ).
fof(f_2114_1,plain,
! [V_y_2,V_x_2,T_c] :
( hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost]) ).
fof(f_2114_2,plain,
! [U_8493,U_8492,U_8491] :
( hAPP(c_Set_Oimage(U_8491,U_8491,c_Groups_Ouminus__class_Ouminus(U_8491)),c_SetInterval_Oord__class_OatLeastAtMost(U_8491,U_8492,U_8493)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8491,hAPP(c_Groups_Ouminus__class_Ouminus(U_8491),U_8493),hAPP(c_Groups_Ouminus__class_Ouminus(U_8491),U_8492))
| ~ class_Groups_Oordered__ab__group__add(U_8491) ),
inference(variable_rename,[status(thm)],[f_2114_1]) ).
fof(f_2114_3,plain,
! [U_8492,U_8491,U_8493] :
( hAPP(c_Set_Oimage(U_8491,U_8491,c_Groups_Ouminus__class_Ouminus(U_8491)),c_SetInterval_Oord__class_OatLeastAtMost(U_8491,U_8492,U_8493)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8491,hAPP(c_Groups_Ouminus__class_Ouminus(U_8491),U_8493),hAPP(c_Groups_Ouminus__class_Ouminus(U_8491),U_8492))
| ~ class_Groups_Oordered__ab__group__add(U_8491) ),
inference(definitional_conversion,[status(esa)],[f_2114_2]) ).
cnf(f_2114_4,plain,
( hAPP(c_Set_Oimage(U_8491,U_8491,c_Groups_Ouminus__class_Ouminus(U_8491)),c_SetInterval_Oord__class_OatLeastAtMost(U_8491,U_8492,U_8493)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8491,hAPP(c_Groups_Ouminus__class_Ouminus(U_8491),U_8493),hAPP(c_Groups_Ouminus__class_Ouminus(U_8491),U_8492))
| ~ class_Groups_Oordered__ab__group__add(U_8491) ),
inference(clausify,[status(thm)],[f_2114_3]) ).
fof(f_2115_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_2115_2,plain,
! [U_8495,U_8494] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8494,U_8495)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8494),hAPP(c_Nat_OSuc,U_8495)),
inference(variable_rename,[status(thm)],[f_2115_1]) ).
fof(f_2115_3,plain,
! [U_8494,U_8495] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8494,U_8495)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8494),hAPP(c_Nat_OSuc,U_8495)),
inference(definitional_conversion,[status(esa)],[f_2115_2]) ).
cnf(f_2115_4,plain,
hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8494,U_8495)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8494),hAPP(c_Nat_OSuc,U_8495)),
inference(clausify,[status(thm)],[f_2115_3]) ).
fof(f_2116_1,plain,
! [V_n_2,V_m_2,V_f_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl]) ).
fof(f_2116_2,plain,
! [U_8499,U_8498,U_8497,U_8496] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8496),U_8497),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8498),hAPP(c_Nat_OSuc,U_8499))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8496),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8496,tc_Nat_Onat),U_8497),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8498,U_8499))
| ~ class_Groups_Ocomm__monoid__add(U_8496) ),
inference(variable_rename,[status(thm)],[f_2116_1]) ).
fof(f_2116_3,plain,
! [U_8496,U_8497,U_8498,U_8499] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8496),U_8497),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8498),hAPP(c_Nat_OSuc,U_8499))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8496),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8496,tc_Nat_Onat),U_8497),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8498,U_8499))
| ~ class_Groups_Ocomm__monoid__add(U_8496) ),
inference(definitional_conversion,[status(esa)],[f_2116_2]) ).
cnf(f_2116_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8496),U_8497),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8498),hAPP(c_Nat_OSuc,U_8499))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8496),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8496,tc_Nat_Onat),U_8497),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8498,U_8499))
| ~ class_Groups_Ocomm__monoid__add(U_8496) ),
inference(clausify,[status(thm)],[f_2116_3]) ).
fof(f_2117_1,plain,
! [V_n_2,V_k_2,V_m_2,V_f_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl]) ).
fof(f_2117_2,plain,
! [U_8504,U_8503,U_8502,U_8501,U_8500] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8500),U_8501),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8502),U_8503),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8504),U_8503))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8500),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8500,tc_Nat_Onat),U_8501),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_8503))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8502,U_8504))
| ~ class_Groups_Ocomm__monoid__add(U_8500) ),
inference(variable_rename,[status(thm)],[f_2117_1]) ).
fof(f_2117_3,plain,
! [U_8501,U_8500,U_8502,U_8503,U_8504] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8500),U_8501),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8502),U_8503),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8504),U_8503))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8500),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8500,tc_Nat_Onat),U_8501),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_8503))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8502,U_8504))
| ~ class_Groups_Ocomm__monoid__add(U_8500) ),
inference(definitional_conversion,[status(esa)],[f_2117_2]) ).
cnf(f_2117_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8500),U_8501),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8502),U_8503),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8504),U_8503))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8500),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8500,tc_Nat_Onat),U_8501),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_8503))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8502,U_8504))
| ~ class_Groups_Ocomm__monoid__add(U_8500) ),
inference(clausify,[status(thm)],[f_2117_3]) ).
fof(f_2118_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_2118_2,plain,
! [U_8506,U_8505] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8505),U_8506) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_8505,U_8506),
inference(variable_rename,[status(thm)],[f_2118_1]) ).
fof(f_2118_3,plain,
! [U_8505,U_8506] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8505),U_8506) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_8505,U_8506),
inference(definitional_conversion,[status(esa)],[f_2118_2]) ).
cnf(f_2118_4,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8505),U_8506) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_8505,U_8506),
inference(clausify,[status(thm)],[f_2118_3]) ).
fof(f_2119_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_2119_2,plain,
! [U_8509,U_8508,U_8507] : 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_8507)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8508,U_8509)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8508),U_8507),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8509),U_8507)),
inference(variable_rename,[status(thm)],[f_2119_1]) ).
fof(f_2119_3,plain,
! [U_8507,U_8508,U_8509] : 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_8507)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8508,U_8509)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8508),U_8507),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8509),U_8507)),
inference(definitional_conversion,[status(esa)],[f_2119_2]) ).
cnf(f_2119_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_8507)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8508,U_8509)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8508),U_8507),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8509),U_8507)),
inference(clausify,[status(thm)],[f_2119_3]) ).
fof(f_2120_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_2120_2,plain,
! [U_8511,U_8510] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8510,U_8511)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8511)),U_8510),
inference(variable_rename,[status(thm)],[f_2120_1]) ).
fof(f_2120_3,plain,
! [U_8510,U_8511] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8510,U_8511)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8511)),U_8510),
inference(definitional_conversion,[status(esa)],[f_2120_2]) ).
cnf(f_2120_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8510,U_8511)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8511)),U_8510),
inference(clausify,[status(thm)],[f_2120_3]) ).
fof(f_2121_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_2121_2,plain,
! [U_8513,U_8512] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8512,hAPP(c_Nat_OSuc,U_8513)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8513)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8512,U_8513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8512),hAPP(c_Nat_OSuc,U_8513))) ),
inference(variable_rename,[status(thm)],[f_2121_1]) ).
fof(f_2121_3,plain,
! [U_8512,U_8513] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8512,hAPP(c_Nat_OSuc,U_8513)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8513)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8512,U_8513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8512),hAPP(c_Nat_OSuc,U_8513))) ),
inference(definitional_conversion,[status(esa)],[f_2121_2]) ).
cnf(f_2121_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8512,hAPP(c_Nat_OSuc,U_8513)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8513)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8512,U_8513))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8512),hAPP(c_Nat_OSuc,U_8513))) ),
inference(clausify,[status(thm)],[f_2121_3]) ).
fof(f_2122_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_2122_2,plain,
! [U_8515,U_8514] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8514),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8515)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8514),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8515))
| hAPP(U_8514,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_2122_1]) ).
fof(f_2122_3,plain,
! [U_8514,U_8515] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8514),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8515)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8514),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8515))
| hAPP(U_8514,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_2122_2]) ).
cnf(f_2122_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8514),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8515)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_8514),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8515))
| hAPP(U_8514,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2122_3]) ).
fof(f_2123_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I21_J]) ).
fof(f_2123_2,plain,
! [U_8519,U_8518,U_8517,U_8516] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8516,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8516,U_8517),U_8518)),c_SetInterval_Oord__class_OatLeastAtMost(U_8516,U_8518,U_8519)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8516,U_8517,U_8519)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8516),U_8518),U_8519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8516),U_8517),U_8518))
| ~ class_Orderings_Olinorder(U_8516) ),
inference(variable_rename,[status(thm)],[f_2123_1]) ).
fof(f_2123_3,plain,
! [U_8516,U_8517,U_8518,U_8519] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8516,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8516,U_8517),U_8518)),c_SetInterval_Oord__class_OatLeastAtMost(U_8516,U_8518,U_8519)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8516,U_8517,U_8519)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8516),U_8518),U_8519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8516),U_8517),U_8518))
| ~ class_Orderings_Olinorder(U_8516) ),
inference(definitional_conversion,[status(esa)],[f_2123_2]) ).
cnf(f_2123_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8516,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8516,U_8517),U_8518)),c_SetInterval_Oord__class_OatLeastAtMost(U_8516,U_8518,U_8519)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8516,U_8517,U_8519)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8516),U_8518),U_8519))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8516),U_8517),U_8518))
| ~ class_Orderings_Olinorder(U_8516) ),
inference(clausify,[status(thm)],[f_2123_3]) ).
fof(f_2124_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J]) ).
fof(f_2124_2,plain,
! [U_8523,U_8522,U_8521,U_8520] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8520,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8520,U_8521),U_8522)),c_SetInterval_Oord__class_OatLeastAtMost(U_8520,U_8522,U_8523)) = c_Orderings_Obot__class_Obot(tc_fun(U_8520,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8520) ),
inference(variable_rename,[status(thm)],[f_2124_1]) ).
fof(f_2124_3,plain,
! [U_8521,U_8522,U_8520,U_8523] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8520,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8520,U_8521),U_8522)),c_SetInterval_Oord__class_OatLeastAtMost(U_8520,U_8522,U_8523)) = c_Orderings_Obot__class_Obot(tc_fun(U_8520,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8520) ),
inference(definitional_conversion,[status(esa)],[f_2124_2]) ).
cnf(f_2124_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8520,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8520,U_8521),U_8522)),c_SetInterval_Oord__class_OatLeastAtMost(U_8520,U_8522,U_8523)) = c_Orderings_Obot__class_Obot(tc_fun(U_8520,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8520) ),
inference(clausify,[status(thm)],[f_2124_3]) ).
fof(f_2125_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost]) ).
fof(f_2125_2,plain,
! [U_8528,U_8527,U_8526,U_8525,U_8524] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8524,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8524,U_8525,U_8526)),c_SetInterval_Oord__class_OatLeastAtMost(U_8524,U_8527,U_8528)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8524,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8524),U_8525),U_8527),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8524),U_8526),U_8528))
| ~ class_Orderings_Olinorder(U_8524) ),
inference(variable_rename,[status(thm)],[f_2125_1]) ).
fof(f_2125_3,plain,
! [U_8524,U_8525,U_8526,U_8527,U_8528] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8524,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8524,U_8525,U_8526)),c_SetInterval_Oord__class_OatLeastAtMost(U_8524,U_8527,U_8528)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8524,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8524),U_8525),U_8527),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8524),U_8526),U_8528))
| ~ class_Orderings_Olinorder(U_8524) ),
inference(definitional_conversion,[status(esa)],[f_2125_2]) ).
cnf(f_2125_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8524,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8524,U_8525,U_8526)),c_SetInterval_Oord__class_OatLeastAtMost(U_8524,U_8527,U_8528)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8524,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8524),U_8525),U_8527),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8524),U_8526),U_8528))
| ~ class_Orderings_Olinorder(U_8524) ),
inference(clausify,[status(thm)],[f_2125_3]) ).
fof(f_2126_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_d_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_d_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_d_2))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),V_d_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2))) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).
fof(f_2126_2,plain,
! [U_8533,U_8532,U_8531,U_8530,U_8529] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8529,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8529,U_8530,U_8531)),c_SetInterval_Oord__class_OatLeastAtMost(U_8529,U_8532,U_8533)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8533))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8529),U_8531),U_8533))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8529),U_8532),U_8530)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8531),U_8533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8530)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8530),U_8531)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8533))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8529),U_8531),U_8533))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8529),U_8532),U_8530)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8531),U_8533))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8530)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8530),U_8531)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8529,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8529,U_8530,U_8531)),c_SetInterval_Oord__class_OatLeastAtMost(U_8529,U_8532,U_8533))) ) )
| ~ class_Orderings_Oorder(U_8529) ),
inference(variable_rename,[status(thm)],[f_2126_1]) ).
fof(f_2126_3,plain,
( ! [U_8529,U_8530,U_8531,U_8532,U_8533] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8529),U_8531),U_8533))
| ~ sP591(U_8529,U_8530,U_8531,U_8532,U_8533) )
& ! [U_8529,U_8530,U_8531,U_8532,U_8533] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8529),U_8532),U_8530))
| ~ sP591(U_8529,U_8530,U_8531,U_8532,U_8533) )
& ! [U_8529,U_8530,U_8531,U_8532,U_8533] :
( sP591(U_8529,U_8530,U_8531,U_8532,U_8533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8531),U_8533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8530))
| ~ sP592(U_8529,U_8530,U_8531,U_8532,U_8533) )
& ! [U_8529,U_8530,U_8531,U_8532,U_8533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8530),U_8531))
| ~ sP592(U_8529,U_8530,U_8531,U_8532,U_8533) )
& ! [U_8529,U_8530,U_8531,U_8532,U_8533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8529),U_8531),U_8533))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8529),U_8532),U_8530))
| ~ sP589(U_8529,U_8530,U_8531,U_8532,U_8533) )
& ! [U_8529,U_8530,U_8531,U_8532,U_8533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8531),U_8533))
| ~ sP589(U_8529,U_8530,U_8531,U_8532,U_8533) )
& ! [U_8529,U_8530,U_8531,U_8532,U_8533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8530))
| ~ sP589(U_8529,U_8530,U_8531,U_8532,U_8533) )
& ! [U_8529,U_8530,U_8531,U_8532,U_8533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8533))
| ~ sP590(U_8529,U_8530,U_8531,U_8532,U_8533) )
& ! [U_8529,U_8530,U_8531,U_8532,U_8533] :
( sP589(U_8529,U_8530,U_8531,U_8532,U_8533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8530),U_8531))
| ~ sP590(U_8529,U_8530,U_8531,U_8532,U_8533) )
& ! [U_8529,U_8530,U_8531,U_8532,U_8533] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8529,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8529,U_8530,U_8531)),c_SetInterval_Oord__class_OatLeastAtMost(U_8529,U_8532,U_8533)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8533))
| sP592(U_8529,U_8530,U_8531,U_8532,U_8533)
| ~ sP593(U_8529,U_8530,U_8531,U_8532,U_8533) )
& ! [U_8529,U_8530,U_8531,U_8532,U_8533] :
( sP590(U_8529,U_8530,U_8531,U_8532,U_8533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8529,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8529,U_8530,U_8531)),c_SetInterval_Oord__class_OatLeastAtMost(U_8529,U_8532,U_8533)))
| ~ sP593(U_8529,U_8530,U_8531,U_8532,U_8533) )
& ! [U_8529,U_8530,U_8531,U_8532,U_8533] :
( sP593(U_8529,U_8530,U_8531,U_8532,U_8533)
| ~ class_Orderings_Oorder(U_8529) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP589,sP590,sP591,sP592,sP593])],[f_2126_2]) ).
cnf(f_2126_4,plain,
( sP593(U_8529,U_8530,U_8531,U_8532,U_8533)
| ~ class_Orderings_Oorder(U_8529) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_5,plain,
( sP590(U_8529,U_8530,U_8531,U_8532,U_8533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8529,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8529,U_8530,U_8531)),c_SetInterval_Oord__class_OatLeastAtMost(U_8529,U_8532,U_8533)))
| ~ sP593(U_8529,U_8530,U_8531,U_8532,U_8533) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8529,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8529,U_8530,U_8531)),c_SetInterval_Oord__class_OatLeastAtMost(U_8529,U_8532,U_8533)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8533))
| sP592(U_8529,U_8530,U_8531,U_8532,U_8533)
| ~ sP593(U_8529,U_8530,U_8531,U_8532,U_8533) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_7,plain,
( sP589(U_8529,U_8530,U_8531,U_8532,U_8533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8530),U_8531))
| ~ sP590(U_8529,U_8530,U_8531,U_8532,U_8533) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8533))
| ~ sP590(U_8529,U_8530,U_8531,U_8532,U_8533) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8530))
| ~ sP589(U_8529,U_8530,U_8531,U_8532,U_8533) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8531),U_8533))
| ~ sP589(U_8529,U_8530,U_8531,U_8532,U_8533) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8529),U_8531),U_8533))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8529),U_8532),U_8530))
| ~ sP589(U_8529,U_8530,U_8531,U_8532,U_8533) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_12,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8530),U_8531))
| ~ sP592(U_8529,U_8530,U_8531,U_8532,U_8533) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_13,plain,
( sP591(U_8529,U_8530,U_8531,U_8532,U_8533)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8531),U_8533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8529),U_8532),U_8530))
| ~ sP592(U_8529,U_8530,U_8531,U_8532,U_8533) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8529),U_8532),U_8530))
| ~ sP591(U_8529,U_8530,U_8531,U_8532,U_8533) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
cnf(f_2126_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8529),U_8531),U_8533))
| ~ sP591(U_8529,U_8530,U_8531,U_8532,U_8533) ),
inference(clausify,[status(thm)],[f_2126_3]) ).
fof(f_2127_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I22_J]) ).
fof(f_2127_2,plain,
! [U_8537,U_8536,U_8535,U_8534] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8534,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8534,U_8535,U_8536)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8534,U_8536,U_8537)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8534,U_8535,U_8537)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8536),U_8537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8535),U_8536))
| ~ class_Orderings_Olinorder(U_8534) ),
inference(variable_rename,[status(thm)],[f_2127_1]) ).
fof(f_2127_3,plain,
! [U_8537,U_8536,U_8535,U_8534] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8534,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8534,U_8535,U_8536)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8534,U_8536,U_8537)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8534,U_8535,U_8537)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8536),U_8537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8535),U_8536))
| ~ class_Orderings_Olinorder(U_8534) ),
inference(definitional_conversion,[status(esa)],[f_2127_2]) ).
cnf(f_2127_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8534,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8534,U_8535,U_8536)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8534,U_8536,U_8537)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8534,U_8535,U_8537)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8536),U_8537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8535),U_8536))
| ~ class_Orderings_Olinorder(U_8534) ),
inference(clausify,[status(thm)],[f_2127_3]) ).
fof(f_2128_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I4_J]) ).
fof(f_2128_2,plain,
! [U_8540,U_8539,U_8538] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8538,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8538),U_8539)),c_SetInterval_Oord__class_OatLeastAtMost(U_8538,U_8539,U_8540)) = c_Orderings_Obot__class_Obot(tc_fun(U_8538,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8538) ),
inference(variable_rename,[status(thm)],[f_2128_1]) ).
fof(f_2128_3,plain,
! [U_8538,U_8540,U_8539] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8538,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8538),U_8539)),c_SetInterval_Oord__class_OatLeastAtMost(U_8538,U_8539,U_8540)) = c_Orderings_Obot__class_Obot(tc_fun(U_8538,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8538) ),
inference(definitional_conversion,[status(esa)],[f_2128_2]) ).
cnf(f_2128_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8538,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8538),U_8539)),c_SetInterval_Oord__class_OatLeastAtMost(U_8538,U_8539,U_8540)) = c_Orderings_Obot__class_Obot(tc_fun(U_8538,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8538) ),
inference(clausify,[status(thm)],[f_2128_3]) ).
fof(f_2129_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J]) ).
fof(f_2129_2,plain,
! [U_8544,U_8543,U_8542,U_8541] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8541,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8541,U_8542,U_8543)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8541,U_8543,U_8544)) = c_Orderings_Obot__class_Obot(tc_fun(U_8541,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8541) ),
inference(variable_rename,[status(thm)],[f_2129_1]) ).
fof(f_2129_3,plain,
! [U_8541,U_8543,U_8544,U_8542] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8541,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8541,U_8542,U_8543)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8541,U_8543,U_8544)) = c_Orderings_Obot__class_Obot(tc_fun(U_8541,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8541) ),
inference(definitional_conversion,[status(esa)],[f_2129_2]) ).
cnf(f_2129_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8541,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8541,U_8542,U_8543)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8541,U_8543,U_8544)) = c_Orderings_Obot__class_Obot(tc_fun(U_8541,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8541) ),
inference(clausify,[status(thm)],[f_2129_3]) ).
fof(f_2130_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J]) ).
fof(f_2130_2,plain,
! [U_8548,U_8547,U_8546,U_8545] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8545,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8545,U_8546,U_8547)),c_SetInterval_Oord__class_OatLeastAtMost(U_8545,U_8547,U_8548)) = c_Orderings_Obot__class_Obot(tc_fun(U_8545,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8545) ),
inference(variable_rename,[status(thm)],[f_2130_1]) ).
fof(f_2130_3,plain,
! [U_8545,U_8546,U_8547,U_8548] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8545,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8545,U_8546,U_8547)),c_SetInterval_Oord__class_OatLeastAtMost(U_8545,U_8547,U_8548)) = c_Orderings_Obot__class_Obot(tc_fun(U_8545,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8545) ),
inference(definitional_conversion,[status(esa)],[f_2130_2]) ).
cnf(f_2130_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8545,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8545,U_8546,U_8547)),c_SetInterval_Oord__class_OatLeastAtMost(U_8545,U_8547,U_8548)) = c_Orderings_Obot__class_Obot(tc_fun(U_8545,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8545) ),
inference(clausify,[status(thm)],[f_2130_3]) ).
fof(f_2131_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I12_J]) ).
fof(f_2131_2,plain,
! [U_8552,U_8551,U_8550,U_8549] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8549,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8549,U_8550,U_8551)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8549,U_8551,U_8552)) = c_Orderings_Obot__class_Obot(tc_fun(U_8549,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8549) ),
inference(variable_rename,[status(thm)],[f_2131_1]) ).
fof(f_2131_3,plain,
! [U_8549,U_8550,U_8551,U_8552] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8549,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8549,U_8550,U_8551)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8549,U_8551,U_8552)) = c_Orderings_Obot__class_Obot(tc_fun(U_8549,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8549) ),
inference(definitional_conversion,[status(esa)],[f_2131_2]) ).
cnf(f_2131_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8549,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8549,U_8550,U_8551)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8549,U_8551,U_8552)) = c_Orderings_Obot__class_Obot(tc_fun(U_8549,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8549) ),
inference(clausify,[status(thm)],[f_2131_3]) ).
fof(f_2132_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J]) ).
fof(f_2132_2,plain,
! [U_8555,U_8554,U_8553] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8553,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8553,U_8554,U_8555)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8553),U_8555)) = c_Orderings_Obot__class_Obot(tc_fun(U_8553,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8553) ),
inference(variable_rename,[status(thm)],[f_2132_1]) ).
fof(f_2132_3,plain,
! [U_8553,U_8554,U_8555] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8553,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8553,U_8554,U_8555)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8553),U_8555)) = c_Orderings_Obot__class_Obot(tc_fun(U_8553,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8553) ),
inference(definitional_conversion,[status(esa)],[f_2132_2]) ).
cnf(f_2132_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8553,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8553,U_8554,U_8555)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8553),U_8555)) = c_Orderings_Obot__class_Obot(tc_fun(U_8553,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8553) ),
inference(clausify,[status(thm)],[f_2132_3]) ).
fof(f_2133_1,plain,
! [V_f_2,V_n_2,V_m_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc]) ).
fof(f_2133_2,plain,
! [U_8559,U_8558,U_8557,U_8556] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8556),U_8559),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8557,U_8558)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8556),hAPP(U_8559,U_8557)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8556),U_8559),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8557),U_8558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8557),U_8558))
| ~ class_Groups_Ocomm__monoid__add(U_8556) ),
inference(variable_rename,[status(thm)],[f_2133_1]) ).
fof(f_2133_3,plain,
! [U_8556,U_8557,U_8558,U_8559] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8556),U_8559),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8557,U_8558)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8556),hAPP(U_8559,U_8557)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8556),U_8559),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8557),U_8558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8557),U_8558))
| ~ class_Groups_Ocomm__monoid__add(U_8556) ),
inference(definitional_conversion,[status(esa)],[f_2133_2]) ).
cnf(f_2133_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8556),U_8559),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8557,U_8558)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8556),hAPP(U_8559,U_8557)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8556),U_8559),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8557),U_8558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8557),U_8558))
| ~ class_Groups_Ocomm__monoid__add(U_8556) ),
inference(clausify,[status(thm)],[f_2133_3]) ).
fof(f_2134_1,plain,
! [V_f_2,V_m_2,V_n_2,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_c)
| ~ 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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).
fof(f_2134_2,plain,
! [U_8563,U_8562,U_8561,U_8560] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8560),U_8563),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8562,hAPP(c_Nat_OSuc,U_8561))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8560),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8560),U_8563),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8562,U_8561))),hAPP(U_8563,hAPP(c_Nat_OSuc,U_8561)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8561)),U_8562)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8560),U_8563),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8562,hAPP(c_Nat_OSuc,U_8561))) = c_Groups_Ozero__class_Ozero(U_8560)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8561)),U_8562)) ) )
| ~ class_Groups_Ocomm__monoid__add(U_8560) ),
inference(variable_rename,[status(thm)],[f_2134_1]) ).
fof(f_2134_3,plain,
( ! [U_8560,U_8561,U_8562,U_8563] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8560),U_8563),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8562,hAPP(c_Nat_OSuc,U_8561))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8560),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8560),U_8563),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8562,U_8561))),hAPP(U_8563,hAPP(c_Nat_OSuc,U_8561)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8561)),U_8562))
| ~ sP594(U_8560,U_8561,U_8562,U_8563) )
& ! [U_8560,U_8561,U_8562,U_8563] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8560),U_8563),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8562,hAPP(c_Nat_OSuc,U_8561))) = c_Groups_Ozero__class_Ozero(U_8560)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8561)),U_8562))
| ~ sP594(U_8560,U_8561,U_8562,U_8563) )
& ! [U_8560,U_8561,U_8562,U_8563] :
( sP594(U_8560,U_8561,U_8562,U_8563)
| ~ class_Groups_Ocomm__monoid__add(U_8560) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP594])],[f_2134_2]) ).
cnf(f_2134_4,plain,
( sP594(U_8560,U_8561,U_8562,U_8563)
| ~ class_Groups_Ocomm__monoid__add(U_8560) ),
inference(clausify,[status(thm)],[f_2134_3]) ).
cnf(f_2134_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8560),U_8563),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8562,hAPP(c_Nat_OSuc,U_8561))) = c_Groups_Ozero__class_Ozero(U_8560)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8561)),U_8562))
| ~ sP594(U_8560,U_8561,U_8562,U_8563) ),
inference(clausify,[status(thm)],[f_2134_3]) ).
cnf(f_2134_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8560),U_8563),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8562,hAPP(c_Nat_OSuc,U_8561))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8560),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8560),U_8563),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8562,U_8561))),hAPP(U_8563,hAPP(c_Nat_OSuc,U_8561)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8561)),U_8562))
| ~ sP594(U_8560,U_8561,U_8562,U_8563) ),
inference(clausify,[status(thm)],[f_2134_3]) ).
fof(f_2135_1,plain,
! [V_Pa_2,V_n_2,V_m_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__head]) ).
fof(f_2135_2,plain,
! [U_8567,U_8566,U_8565,U_8564] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8564),U_8567),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8565,U_8566)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8564),hAPP(U_8567,U_8565)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8564),U_8567),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_8565,U_8566)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8565),U_8566))
| ~ class_Groups_Ocomm__monoid__add(U_8564) ),
inference(variable_rename,[status(thm)],[f_2135_1]) ).
fof(f_2135_3,plain,
! [U_8566,U_8567,U_8565,U_8564] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8564),U_8567),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8565,U_8566)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8564),hAPP(U_8567,U_8565)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8564),U_8567),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_8565,U_8566)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8565),U_8566))
| ~ class_Groups_Ocomm__monoid__add(U_8564) ),
inference(definitional_conversion,[status(esa)],[f_2135_2]) ).
cnf(f_2135_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8564),U_8567),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8565,U_8566)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8564),hAPP(U_8567,U_8565)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8564),U_8567),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_8565,U_8566)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8565),U_8566))
| ~ class_Groups_Ocomm__monoid__add(U_8564) ),
inference(clausify,[status(thm)],[f_2135_3]) ).
fof(f_2136_1,plain,
! [V_p_2,V_f_2,V_n_2,V_m_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat]) ).
fof(f_2136_2,plain,
! [U_8572,U_8571,U_8570,U_8569,U_8568] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8568),U_8571),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8569,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8570),U_8572))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8568),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8568),U_8571),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8569,U_8570))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8568),U_8571),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8570),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8570),U_8572))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8569),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8570),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Ocomm__monoid__add(U_8568) ),
inference(variable_rename,[status(thm)],[f_2136_1]) ).
fof(f_2136_3,plain,
! [U_8569,U_8568,U_8570,U_8571,U_8572] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8568),U_8571),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8569,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8570),U_8572))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8568),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8568),U_8571),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8569,U_8570))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8568),U_8571),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8570),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8570),U_8572))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8569),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8570),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Ocomm__monoid__add(U_8568) ),
inference(definitional_conversion,[status(esa)],[f_2136_2]) ).
cnf(f_2136_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8568),U_8571),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8569,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8570),U_8572))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8568),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8568),U_8571),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8569,U_8570))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8568),U_8571),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8570),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8570),U_8572))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8569),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8570),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Ocomm__monoid__add(U_8568) ),
inference(clausify,[status(thm)],[f_2136_3]) ).
fof(f_2137_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J]) ).
fof(f_2137_2,plain,
! [U_8575,U_8574,U_8573] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8573,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8573,U_8574),U_8575)),hAPP(hAPP(c_Set_Oinsert(U_8573),U_8575),c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_8573,U_8574,U_8575)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8573),U_8574),U_8575))
| ~ class_Orderings_Olinorder(U_8573) ),
inference(variable_rename,[status(thm)],[f_2137_1]) ).
fof(f_2137_3,plain,
! [U_8575,U_8573,U_8574] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8573,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8573,U_8574),U_8575)),hAPP(hAPP(c_Set_Oinsert(U_8573),U_8575),c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_8573,U_8574,U_8575)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8573),U_8574),U_8575))
| ~ class_Orderings_Olinorder(U_8573) ),
inference(definitional_conversion,[status(esa)],[f_2137_2]) ).
cnf(f_2137_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8573,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8573,U_8574),U_8575)),hAPP(hAPP(c_Set_Oinsert(U_8573),U_8575),c_Orderings_Obot__class_Obot(tc_fun(U_8573,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_8573,U_8574,U_8575)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8573),U_8574),U_8575))
| ~ class_Orderings_Olinorder(U_8573) ),
inference(clausify,[status(thm)],[f_2137_3]) ).
fof(f_2138_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I5_J]) ).
fof(f_2138_2,plain,
! [U_8578,U_8577,U_8576] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8576,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8576),U_8577),c_Orderings_Obot__class_Obot(tc_fun(U_8576,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8576,U_8577,U_8578)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8576,U_8577,U_8578)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8576),U_8577),U_8578))
| ~ class_Orderings_Olinorder(U_8576) ),
inference(variable_rename,[status(thm)],[f_2138_1]) ).
fof(f_2138_3,plain,
! [U_8576,U_8577,U_8578] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8576,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8576),U_8577),c_Orderings_Obot__class_Obot(tc_fun(U_8576,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8576,U_8577,U_8578)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8576,U_8577,U_8578)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8576),U_8577),U_8578))
| ~ class_Orderings_Olinorder(U_8576) ),
inference(definitional_conversion,[status(esa)],[f_2138_2]) ).
cnf(f_2138_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8576,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8576),U_8577),c_Orderings_Obot__class_Obot(tc_fun(U_8576,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8576,U_8577,U_8578)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8576,U_8577,U_8578)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8576),U_8577),U_8578))
| ~ class_Orderings_Olinorder(U_8576) ),
inference(clausify,[status(thm)],[f_2138_3]) ).
fof(f_2139_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J]) ).
fof(f_2139_2,plain,
! [U_8582,U_8581,U_8580,U_8579] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8579,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8579,U_8580,U_8581)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8579,U_8581,U_8582)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8579,U_8580),U_8582)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),U_8581),U_8582))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8579),U_8580),U_8581))
| ~ class_Orderings_Olinorder(U_8579) ),
inference(variable_rename,[status(thm)],[f_2139_1]) ).
fof(f_2139_3,plain,
! [U_8579,U_8580,U_8581,U_8582] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8579,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8579,U_8580,U_8581)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8579,U_8581,U_8582)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8579,U_8580),U_8582)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),U_8581),U_8582))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8579),U_8580),U_8581))
| ~ class_Orderings_Olinorder(U_8579) ),
inference(definitional_conversion,[status(esa)],[f_2139_2]) ).
cnf(f_2139_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8579,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8579,U_8580,U_8581)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8579,U_8581,U_8582)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8579,U_8580),U_8582)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8579),U_8581),U_8582))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8579),U_8580),U_8581))
| ~ class_Orderings_Olinorder(U_8579) ),
inference(clausify,[status(thm)],[f_2139_3]) ).
fof(f_2140_1,plain,
! [V_u_2,V_m_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I19_J]) ).
fof(f_2140_2,plain,
! [U_8586,U_8585,U_8584,U_8583] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8583,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8583,U_8584,U_8585)),c_SetInterval_Oord__class_OatLeastAtMost(U_8583,U_8585,U_8586)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8583,U_8584,U_8586)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8583),U_8585),U_8586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),U_8585))
| ~ class_Orderings_Olinorder(U_8583) ),
inference(variable_rename,[status(thm)],[f_2140_1]) ).
fof(f_2140_3,plain,
! [U_8583,U_8584,U_8585,U_8586] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8583,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8583,U_8584,U_8585)),c_SetInterval_Oord__class_OatLeastAtMost(U_8583,U_8585,U_8586)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8583,U_8584,U_8586)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8583),U_8585),U_8586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),U_8585))
| ~ class_Orderings_Olinorder(U_8583) ),
inference(definitional_conversion,[status(esa)],[f_2140_2]) ).
cnf(f_2140_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8583,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8583,U_8584,U_8585)),c_SetInterval_Oord__class_OatLeastAtMost(U_8583,U_8585,U_8586)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8583,U_8584,U_8586)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8583),U_8585),U_8586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8583),U_8584),U_8585))
| ~ class_Orderings_Olinorder(U_8583) ),
inference(clausify,[status(thm)],[f_2140_3]) ).
fof(f_2141_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_2141_2,plain,
! [U_8587] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8587)) = 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_8587)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8587),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2141_1]) ).
fof(f_2141_3,plain,
! [U_8587] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8587)) = 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_8587)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8587),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_2141_2]) ).
cnf(f_2141_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8587)) = 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_8587)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8587),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2141_3]) ).
fof(f_2142_1,plain,
! [V_M_2,V_n_2,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_2142_2,plain,
! [U_8590,U_8589,U_8588] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_8588,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8589)),U_8590) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8588,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_8588,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_8589)),U_8590)),hAPP(U_8590,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2142_1]) ).
fof(f_2142_3,plain,
! [U_8588,U_8589,U_8590] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_8588,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8589)),U_8590) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8588,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_8588,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_8589)),U_8590)),hAPP(U_8590,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_2142_2]) ).
cnf(f_2142_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_8588,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8589)),U_8590) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8588,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_8588,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_8589)),U_8590)),hAPP(U_8590,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2142_3]) ).
fof(f_2143_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_l_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I12_J]) ).
fof(f_2143_2,plain,
! [U_8593,U_8592,U_8591] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8591,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8591,U_8592,U_8593)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8591),U_8593)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8591),U_8592)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8591),U_8592),U_8593))
| ~ class_Orderings_Olinorder(U_8591) ),
inference(variable_rename,[status(thm)],[f_2143_1]) ).
fof(f_2143_3,plain,
! [U_8591,U_8592,U_8593] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8591,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8591,U_8592,U_8593)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8591),U_8593)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8591),U_8592)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8591),U_8592),U_8593))
| ~ class_Orderings_Olinorder(U_8591) ),
inference(definitional_conversion,[status(esa)],[f_2143_2]) ).
cnf(f_2143_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8591,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8591,U_8592,U_8593)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8591),U_8593)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8591),U_8592)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8591),U_8592),U_8593))
| ~ class_Orderings_Olinorder(U_8591) ),
inference(clausify,[status(thm)],[f_2143_3]) ).
fof(f_2144_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_2144_2,plain,
! [U_8598,U_8597,U_8596] :
( ! [U_8595] :
( hBOOL(hAPP(U_8597,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8598),U_8596))))
| ~ hBOOL(hAPP(U_8597,U_8595)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8598))
| ? [U_8594] :
( ~ hBOOL(hAPP(U_8597,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8594),U_8596)))
& hBOOL(hAPP(U_8597,U_8594)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8596)) ),
inference(variable_rename,[status(thm)],[f_2144_1]) ).
fof(f_2144_3,plain,
! [U_8598,U_8597,U_8596] :
( ! [U_8595] :
( hBOOL(hAPP(U_8597,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8598),U_8596))))
| ~ hBOOL(hAPP(U_8597,U_8595)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8598))
| ( ~ hBOOL(hAPP(U_8597,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK177(U_8598,U_8597,U_8596)),U_8596)))
& hBOOL(hAPP(U_8597,sK177(U_8598,U_8597,U_8596))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8596)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_8594,sK177(U_8598,U_8597,U_8596))],[f_2144_2]) ).
fof(f_2144_4,plain,
( ! [U_8596,U_8597,U_8598] :
( ~ hBOOL(hAPP(U_8597,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK177(U_8598,U_8597,U_8596)),U_8596)))
| ~ sP595(U_8596,U_8597,U_8598) )
& ! [U_8596,U_8597,U_8598] :
( hBOOL(hAPP(U_8597,sK177(U_8598,U_8597,U_8596)))
| ~ sP595(U_8596,U_8597,U_8598) )
& ! [U_8595,U_8596,U_8597,U_8598] :
( hBOOL(hAPP(U_8597,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8598),U_8596))))
| ~ hBOOL(hAPP(U_8597,U_8595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8598))
| sP595(U_8596,U_8597,U_8598)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8596)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP595])],[f_2144_3]) ).
cnf(f_2144_5,plain,
( hBOOL(hAPP(U_8597,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8598),U_8596))))
| ~ hBOOL(hAPP(U_8597,U_8595))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8598))
| sP595(U_8596,U_8597,U_8598)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8596)) ),
inference(clausify,[status(thm)],[f_2144_4]) ).
cnf(f_2144_6,plain,
( hBOOL(hAPP(U_8597,sK177(U_8598,U_8597,U_8596)))
| ~ sP595(U_8596,U_8597,U_8598) ),
inference(clausify,[status(thm)],[f_2144_4]) ).
cnf(f_2144_7,plain,
( ~ hBOOL(hAPP(U_8597,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK177(U_8598,U_8597,U_8596)),U_8596)))
| ~ sP595(U_8596,U_8597,U_8598) ),
inference(clausify,[status(thm)],[f_2144_4]) ).
fof(f_2145_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_2145_2,plain,
! [U_8600] :
( ? [U_8599] : U_8600 = 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_8599)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8600),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2145_1]) ).
fof(f_2145_3,plain,
! [U_8600] :
( U_8600 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK178(U_8600))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8600),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_8599,sK178(U_8600))],[f_2145_2]) ).
fof(f_2145_4,plain,
! [U_8600] :
( U_8600 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK178(U_8600))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8600),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2145_3]) ).
cnf(f_2145_5,plain,
( U_8600 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK178(U_8600))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8600),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2145_4]) ).
fof(f_2146_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_2146_2,plain,
! [U_8602,U_8601] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8601,U_8602))),
inference(variable_rename,[status(thm)],[f_2146_1]) ).
fof(f_2146_3,plain,
! [U_8602,U_8601] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8601,U_8602))),
inference(definitional_conversion,[status(esa)],[f_2146_2]) ).
cnf(f_2146_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8601,U_8602))),
inference(clausify,[status(thm)],[f_2146_3]) ).
fof(f_2147_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_2147_2,plain,
! [U_8603] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8603))),
inference(variable_rename,[status(thm)],[f_2147_1]) ).
fof(f_2147_3,plain,
! [U_8603] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8603))),
inference(definitional_conversion,[status(esa)],[f_2147_2]) ).
cnf(f_2147_4,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8603))),
inference(clausify,[status(thm)],[f_2147_3]) ).
fof(f_2148_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_x_2) != hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_y_2) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff]) ).
fof(f_2148_2,plain,
! [U_8606,U_8605,U_8604] :
( ( ( hAPP(c_SetInterval_Oord__class_OatMost(U_8604),U_8605) = hAPP(c_SetInterval_Oord__class_OatMost(U_8604),U_8606)
| U_8605 != U_8606 )
& ( U_8605 = U_8606
| hAPP(c_SetInterval_Oord__class_OatMost(U_8604),U_8605) != hAPP(c_SetInterval_Oord__class_OatMost(U_8604),U_8606) ) )
| ~ class_Orderings_Olinorder(U_8604) ),
inference(variable_rename,[status(thm)],[f_2148_1]) ).
fof(f_2148_3,plain,
( ! [U_8604,U_8605,U_8606] :
( hAPP(c_SetInterval_Oord__class_OatMost(U_8604),U_8605) = hAPP(c_SetInterval_Oord__class_OatMost(U_8604),U_8606)
| U_8605 != U_8606
| ~ sP596(U_8604,U_8605,U_8606) )
& ! [U_8604,U_8605,U_8606] :
( U_8605 = U_8606
| hAPP(c_SetInterval_Oord__class_OatMost(U_8604),U_8605) != hAPP(c_SetInterval_Oord__class_OatMost(U_8604),U_8606)
| ~ sP596(U_8604,U_8605,U_8606) )
& ! [U_8604,U_8605,U_8606] :
( sP596(U_8604,U_8605,U_8606)
| ~ class_Orderings_Olinorder(U_8604) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP596])],[f_2148_2]) ).
cnf(f_2148_4,plain,
( sP596(U_8604,U_8605,U_8606)
| ~ class_Orderings_Olinorder(U_8604) ),
inference(clausify,[status(thm)],[f_2148_3]) ).
cnf(f_2148_5,plain,
( U_8605 = U_8606
| hAPP(c_SetInterval_Oord__class_OatMost(U_8604),U_8605) != hAPP(c_SetInterval_Oord__class_OatMost(U_8604),U_8606)
| ~ sP596(U_8604,U_8605,U_8606) ),
inference(clausify,[status(thm)],[f_2148_3]) ).
cnf(f_2148_6,plain,
( hAPP(c_SetInterval_Oord__class_OatMost(U_8604),U_8605) = hAPP(c_SetInterval_Oord__class_OatMost(U_8604),U_8606)
| U_8605 != U_8606
| ~ sP596(U_8604,U_8605,U_8606) ),
inference(clausify,[status(thm)],[f_2148_3]) ).
fof(f_2149_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_x_2) != hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_y_2) ) )
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff]) ).
fof(f_2149_2,plain,
! [U_8609,U_8608,U_8607] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(U_8607),U_8608) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8607),U_8609)
| U_8608 != U_8609 )
& ( U_8608 = U_8609
| hAPP(c_SetInterval_Oord__class_OatLeast(U_8607),U_8608) != hAPP(c_SetInterval_Oord__class_OatLeast(U_8607),U_8609) ) )
| ~ class_Orderings_Olinorder(U_8607) ),
inference(variable_rename,[status(thm)],[f_2149_1]) ).
fof(f_2149_3,plain,
( ! [U_8609,U_8608,U_8607] :
( hAPP(c_SetInterval_Oord__class_OatLeast(U_8607),U_8608) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8607),U_8609)
| U_8608 != U_8609
| ~ sP597(U_8609,U_8608,U_8607) )
& ! [U_8609,U_8608,U_8607] :
( U_8608 = U_8609
| hAPP(c_SetInterval_Oord__class_OatLeast(U_8607),U_8608) != hAPP(c_SetInterval_Oord__class_OatLeast(U_8607),U_8609)
| ~ sP597(U_8609,U_8608,U_8607) )
& ! [U_8609,U_8608,U_8607] :
( sP597(U_8609,U_8608,U_8607)
| ~ class_Orderings_Olinorder(U_8607) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP597])],[f_2149_2]) ).
cnf(f_2149_4,plain,
( sP597(U_8609,U_8608,U_8607)
| ~ class_Orderings_Olinorder(U_8607) ),
inference(clausify,[status(thm)],[f_2149_3]) ).
cnf(f_2149_5,plain,
( U_8608 = U_8609
| hAPP(c_SetInterval_Oord__class_OatLeast(U_8607),U_8608) != hAPP(c_SetInterval_Oord__class_OatLeast(U_8607),U_8609)
| ~ sP597(U_8609,U_8608,U_8607) ),
inference(clausify,[status(thm)],[f_2149_3]) ).
cnf(f_2149_6,plain,
( hAPP(c_SetInterval_Oord__class_OatLeast(U_8607),U_8608) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8607),U_8609)
| U_8608 != U_8609
| ~ sP597(U_8609,U_8608,U_8607) ),
inference(clausify,[status(thm)],[f_2149_3]) ).
fof(f_2150_1,plain,
! [V_x_2,T_c] :
( hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost]) ).
fof(f_2150_2,plain,
! [U_8611,U_8610] :
( hAPP(c_Set_Oimage(U_8610,U_8610,c_Groups_Ouminus__class_Ouminus(U_8610)),hAPP(c_SetInterval_Oord__class_OatMost(U_8610),U_8611)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8610),hAPP(c_Groups_Ouminus__class_Ouminus(U_8610),U_8611))
| ~ class_Groups_Oordered__ab__group__add(U_8610) ),
inference(variable_rename,[status(thm)],[f_2150_1]) ).
fof(f_2150_3,plain,
! [U_8611,U_8610] :
( hAPP(c_Set_Oimage(U_8610,U_8610,c_Groups_Ouminus__class_Ouminus(U_8610)),hAPP(c_SetInterval_Oord__class_OatMost(U_8610),U_8611)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8610),hAPP(c_Groups_Ouminus__class_Ouminus(U_8610),U_8611))
| ~ class_Groups_Oordered__ab__group__add(U_8610) ),
inference(definitional_conversion,[status(esa)],[f_2150_2]) ).
cnf(f_2150_4,plain,
( hAPP(c_Set_Oimage(U_8610,U_8610,c_Groups_Ouminus__class_Ouminus(U_8610)),hAPP(c_SetInterval_Oord__class_OatMost(U_8610),U_8611)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8610),hAPP(c_Groups_Ouminus__class_Ouminus(U_8610),U_8611))
| ~ class_Groups_Oordered__ab__group__add(U_8610) ),
inference(clausify,[status(thm)],[f_2150_3]) ).
fof(f_2151_1,plain,
! [V_x_2,T_c] :
( hAPP(c_Set_Oimage(T_c,T_c,c_Groups_Ouminus__class_Ouminus(T_c)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast]) ).
fof(f_2151_2,plain,
! [U_8613,U_8612] :
( hAPP(c_Set_Oimage(U_8612,U_8612,c_Groups_Ouminus__class_Ouminus(U_8612)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8612),U_8613)) = hAPP(c_SetInterval_Oord__class_OatMost(U_8612),hAPP(c_Groups_Ouminus__class_Ouminus(U_8612),U_8613))
| ~ class_Groups_Oordered__ab__group__add(U_8612) ),
inference(variable_rename,[status(thm)],[f_2151_1]) ).
fof(f_2151_3,plain,
! [U_8612,U_8613] :
( hAPP(c_Set_Oimage(U_8612,U_8612,c_Groups_Ouminus__class_Ouminus(U_8612)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8612),U_8613)) = hAPP(c_SetInterval_Oord__class_OatMost(U_8612),hAPP(c_Groups_Ouminus__class_Ouminus(U_8612),U_8613))
| ~ class_Groups_Oordered__ab__group__add(U_8612) ),
inference(definitional_conversion,[status(esa)],[f_2151_2]) ).
cnf(f_2151_4,plain,
( hAPP(c_Set_Oimage(U_8612,U_8612,c_Groups_Ouminus__class_Ouminus(U_8612)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8612),U_8613)) = hAPP(c_SetInterval_Oord__class_OatMost(U_8612),hAPP(c_Groups_Ouminus__class_Ouminus(U_8612),U_8613))
| ~ class_Groups_Oordered__ab__group__add(U_8612) ),
inference(clausify,[status(thm)],[f_2151_3]) ).
fof(f_2152_1,plain,
! [V_n_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast]) ).
fof(f_2152_2,plain,
! [U_8615,U_8614] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8614,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8614),U_8615)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8614),U_8615)) = hAPP(hAPP(c_Set_Oinsert(U_8614),U_8615),c_Orderings_Obot__class_Obot(tc_fun(U_8614,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_8614) ),
inference(variable_rename,[status(thm)],[f_2152_1]) ).
fof(f_2152_3,plain,
! [U_8614,U_8615] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8614,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8614),U_8615)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8614),U_8615)) = hAPP(hAPP(c_Set_Oinsert(U_8614),U_8615),c_Orderings_Obot__class_Obot(tc_fun(U_8614,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_8614) ),
inference(definitional_conversion,[status(esa)],[f_2152_2]) ).
cnf(f_2152_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8614,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8614),U_8615)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8614),U_8615)) = hAPP(hAPP(c_Set_Oinsert(U_8614),U_8615),c_Orderings_Obot__class_Obot(tc_fun(U_8614,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_8614) ),
inference(clausify,[status(thm)],[f_2152_3]) ).
fof(f_2153_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_2153_2,plain,
! [U_8616] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8616) = 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_8616))),
inference(variable_rename,[status(thm)],[f_2153_1]) ).
fof(f_2153_3,plain,
! [U_8616] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8616) = 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_8616))),
inference(definitional_conversion,[status(esa)],[f_2153_2]) ).
cnf(f_2153_4,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8616) = 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_8616))),
inference(clausify,[status(thm)],[f_2153_3]) ).
fof(f_2154_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_2154_2,plain,
! [U_8618,U_8617] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8617,U_8618))
| ~ c_Nat__Transfer_Ois__nat(U_8617) ),
inference(variable_rename,[status(thm)],[f_2154_1]) ).
fof(f_2154_3,plain,
! [U_8618,U_8617] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8617,U_8618))
| ~ c_Nat__Transfer_Ois__nat(U_8617) ),
inference(definitional_conversion,[status(esa)],[f_2154_2]) ).
cnf(f_2154_4,plain,
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8617,U_8618))
| ~ c_Nat__Transfer_Ois__nat(U_8617) ),
inference(clausify,[status(thm)],[f_2154_3]) ).
fof(f_2155_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_2155_2,plain,
! [U_8619] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8619) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8619),
inference(variable_rename,[status(thm)],[f_2155_1]) ).
fof(f_2155_3,plain,
! [U_8619] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8619) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8619),
inference(definitional_conversion,[status(esa)],[f_2155_2]) ).
cnf(f_2155_4,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_8619) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8619),
inference(clausify,[status(thm)],[f_2155_3]) ).
fof(f_2156_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_2156_2,plain,
! [U_8620] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8620)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8620),
inference(variable_rename,[status(thm)],[f_2156_1]) ).
fof(f_2156_3,plain,
! [U_8620] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8620)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8620),
inference(definitional_conversion,[status(esa)],[f_2156_2]) ).
cnf(f_2156_4,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8620)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8620),
inference(clausify,[status(thm)],[f_2156_3]) ).
fof(f_2157_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_2157_2,plain,
! [U_8621] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8621)) = hAPP(c_Nat_OSuc,U_8621),
inference(variable_rename,[status(thm)],[f_2157_1]) ).
fof(f_2157_3,plain,
! [U_8621] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8621)) = hAPP(c_Nat_OSuc,U_8621),
inference(definitional_conversion,[status(esa)],[f_2157_2]) ).
cnf(f_2157_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8621)) = hAPP(c_Nat_OSuc,U_8621),
inference(clausify,[status(thm)],[f_2157_3]) ).
fof(f_2158_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_2158_2,plain,
! [U_8622] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8622)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8622)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8622)),
inference(variable_rename,[status(thm)],[f_2158_1]) ).
fof(f_2158_3,plain,
! [U_8622] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8622)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8622)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8622)),
inference(definitional_conversion,[status(esa)],[f_2158_2]) ).
cnf(f_2158_4,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8622)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8622)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8622)),
inference(clausify,[status(thm)],[f_2158_3]) ).
fof(f_2159_1,plain,
! [V_k_2,V_i_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_i_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_k_2))) ) )
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atMost__iff]) ).
fof(f_2159_2,plain,
! [U_8625,U_8624,U_8623] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_8623),U_8624),hAPP(c_SetInterval_Oord__class_OatMost(U_8623),U_8625)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8623),U_8624),U_8625)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8623),U_8624),U_8625))
| ~ hBOOL(hAPP(hAPP(c_member(U_8623),U_8624),hAPP(c_SetInterval_Oord__class_OatMost(U_8623),U_8625))) ) )
| ~ class_Orderings_Oord(U_8623) ),
inference(variable_rename,[status(thm)],[f_2159_1]) ).
fof(f_2159_3,plain,
( ! [U_8623,U_8624,U_8625] :
( hBOOL(hAPP(hAPP(c_member(U_8623),U_8624),hAPP(c_SetInterval_Oord__class_OatMost(U_8623),U_8625)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8623),U_8624),U_8625))
| ~ sP598(U_8623,U_8624,U_8625) )
& ! [U_8623,U_8624,U_8625] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8623),U_8624),U_8625))
| ~ hBOOL(hAPP(hAPP(c_member(U_8623),U_8624),hAPP(c_SetInterval_Oord__class_OatMost(U_8623),U_8625)))
| ~ sP598(U_8623,U_8624,U_8625) )
& ! [U_8623,U_8624,U_8625] :
( sP598(U_8623,U_8624,U_8625)
| ~ class_Orderings_Oord(U_8623) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP598])],[f_2159_2]) ).
cnf(f_2159_4,plain,
( sP598(U_8623,U_8624,U_8625)
| ~ class_Orderings_Oord(U_8623) ),
inference(clausify,[status(thm)],[f_2159_3]) ).
cnf(f_2159_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8623),U_8624),U_8625))
| ~ hBOOL(hAPP(hAPP(c_member(U_8623),U_8624),hAPP(c_SetInterval_Oord__class_OatMost(U_8623),U_8625)))
| ~ sP598(U_8623,U_8624,U_8625) ),
inference(clausify,[status(thm)],[f_2159_3]) ).
cnf(f_2159_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8623),U_8624),hAPP(c_SetInterval_Oord__class_OatMost(U_8623),U_8625)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8623),U_8624),U_8625))
| ~ sP598(U_8623,U_8624,U_8625) ),
inference(clausify,[status(thm)],[f_2159_3]) ).
fof(f_2160_1,plain,
! [V_k_2,V_i_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_k_2),V_i_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_k_2))) ) )
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeast__iff]) ).
fof(f_2160_2,plain,
! [U_8628,U_8627,U_8626] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_8626),U_8627),hAPP(c_SetInterval_Oord__class_OatLeast(U_8626),U_8628)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8626),U_8628),U_8627)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8626),U_8628),U_8627))
| ~ hBOOL(hAPP(hAPP(c_member(U_8626),U_8627),hAPP(c_SetInterval_Oord__class_OatLeast(U_8626),U_8628))) ) )
| ~ class_Orderings_Oord(U_8626) ),
inference(variable_rename,[status(thm)],[f_2160_1]) ).
fof(f_2160_3,plain,
( ! [U_8627,U_8628,U_8626] :
( hBOOL(hAPP(hAPP(c_member(U_8626),U_8627),hAPP(c_SetInterval_Oord__class_OatLeast(U_8626),U_8628)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8626),U_8628),U_8627))
| ~ sP599(U_8627,U_8628,U_8626) )
& ! [U_8627,U_8628,U_8626] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8626),U_8628),U_8627))
| ~ hBOOL(hAPP(hAPP(c_member(U_8626),U_8627),hAPP(c_SetInterval_Oord__class_OatLeast(U_8626),U_8628)))
| ~ sP599(U_8627,U_8628,U_8626) )
& ! [U_8627,U_8628,U_8626] :
( sP599(U_8627,U_8628,U_8626)
| ~ class_Orderings_Oord(U_8626) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP599])],[f_2160_2]) ).
cnf(f_2160_4,plain,
( sP599(U_8627,U_8628,U_8626)
| ~ class_Orderings_Oord(U_8626) ),
inference(clausify,[status(thm)],[f_2160_3]) ).
cnf(f_2160_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8626),U_8628),U_8627))
| ~ hBOOL(hAPP(hAPP(c_member(U_8626),U_8627),hAPP(c_SetInterval_Oord__class_OatLeast(U_8626),U_8628)))
| ~ sP599(U_8627,U_8628,U_8626) ),
inference(clausify,[status(thm)],[f_2160_3]) ).
cnf(f_2160_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8626),U_8627),hAPP(c_SetInterval_Oord__class_OatLeast(U_8626),U_8628)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8626),U_8628),U_8627))
| ~ sP599(U_8627,U_8628,U_8626) ),
inference(clausify,[status(thm)],[f_2160_3]) ).
fof(f_2161_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_y_2))) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff]) ).
fof(f_2161_2,plain,
! [U_8631,U_8630,U_8629] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8629,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8629),U_8630)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8629),U_8631)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8629),U_8631),U_8630)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8629),U_8631),U_8630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8629,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8629),U_8630)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8629),U_8631))) ) )
| ~ class_Orderings_Oorder(U_8629) ),
inference(variable_rename,[status(thm)],[f_2161_1]) ).
fof(f_2161_3,plain,
( ! [U_8630,U_8629,U_8631] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8629,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8629),U_8630)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8629),U_8631)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8629),U_8631),U_8630))
| ~ sP600(U_8630,U_8629,U_8631) )
& ! [U_8630,U_8629,U_8631] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8629),U_8631),U_8630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8629,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8629),U_8630)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8629),U_8631)))
| ~ sP600(U_8630,U_8629,U_8631) )
& ! [U_8630,U_8629,U_8631] :
( sP600(U_8630,U_8629,U_8631)
| ~ class_Orderings_Oorder(U_8629) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP600])],[f_2161_2]) ).
cnf(f_2161_4,plain,
( sP600(U_8630,U_8629,U_8631)
| ~ class_Orderings_Oorder(U_8629) ),
inference(clausify,[status(thm)],[f_2161_3]) ).
cnf(f_2161_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8629),U_8631),U_8630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8629,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8629),U_8630)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8629),U_8631)))
| ~ sP600(U_8630,U_8629,U_8631) ),
inference(clausify,[status(thm)],[f_2161_3]) ).
cnf(f_2161_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8629,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8629),U_8630)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8629),U_8631)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8629),U_8631),U_8630))
| ~ sP600(U_8630,U_8629,U_8631) ),
inference(clausify,[status(thm)],[f_2161_3]) ).
fof(f_2162_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_y_2))) ) )
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff]) ).
fof(f_2162_2,plain,
! [U_8634,U_8633,U_8632] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8632,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8632),U_8633)),hAPP(c_SetInterval_Oord__class_OatMost(U_8632),U_8634)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8632),U_8633),U_8634)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8632),U_8633),U_8634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8632,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8632),U_8633)),hAPP(c_SetInterval_Oord__class_OatMost(U_8632),U_8634))) ) )
| ~ class_Orderings_Oorder(U_8632) ),
inference(variable_rename,[status(thm)],[f_2162_1]) ).
fof(f_2162_3,plain,
( ! [U_8632,U_8633,U_8634] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8632,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8632),U_8633)),hAPP(c_SetInterval_Oord__class_OatMost(U_8632),U_8634)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8632),U_8633),U_8634))
| ~ sP601(U_8632,U_8633,U_8634) )
& ! [U_8632,U_8633,U_8634] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8632),U_8633),U_8634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8632,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8632),U_8633)),hAPP(c_SetInterval_Oord__class_OatMost(U_8632),U_8634)))
| ~ sP601(U_8632,U_8633,U_8634) )
& ! [U_8632,U_8633,U_8634] :
( sP601(U_8632,U_8633,U_8634)
| ~ class_Orderings_Oorder(U_8632) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP601])],[f_2162_2]) ).
cnf(f_2162_4,plain,
( sP601(U_8632,U_8633,U_8634)
| ~ class_Orderings_Oorder(U_8632) ),
inference(clausify,[status(thm)],[f_2162_3]) ).
cnf(f_2162_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8632),U_8633),U_8634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8632,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8632),U_8633)),hAPP(c_SetInterval_Oord__class_OatMost(U_8632),U_8634)))
| ~ sP601(U_8632,U_8633,U_8634) ),
inference(clausify,[status(thm)],[f_2162_3]) ).
cnf(f_2162_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8632,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8632),U_8633)),hAPP(c_SetInterval_Oord__class_OatMost(U_8632),U_8634)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8632),U_8633),U_8634))
| ~ sP601(U_8632,U_8633,U_8634) ),
inference(clausify,[status(thm)],[f_2162_3]) ).
fof(f_2163_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_2163_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_2163_1]) ).
cnf(f_2163_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_2163_2]) ).
fof(f_2164_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_2164_2,plain,
! [U_8636,U_8635] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8635,U_8636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8635)) ),
inference(variable_rename,[status(thm)],[f_2164_1]) ).
fof(f_2164_3,plain,
! [U_8635,U_8636] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8635,U_8636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8635)) ),
inference(definitional_conversion,[status(esa)],[f_2164_2]) ).
cnf(f_2164_4,plain,
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8635,U_8636))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8635)) ),
inference(clausify,[status(thm)],[f_2164_3]) ).
fof(f_2165_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_2165_2,plain,
! [U_8638,U_8637] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_8637),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8638),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8637,U_8638),
inference(variable_rename,[status(thm)],[f_2165_1]) ).
fof(f_2165_3,plain,
! [U_8637,U_8638] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_8637),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8638),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8637,U_8638),
inference(definitional_conversion,[status(esa)],[f_2165_2]) ).
cnf(f_2165_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_8637),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8638),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8637,U_8638),
inference(clausify,[status(thm)],[f_2165_3]) ).
fof(f_2166_1,plain,
! [V_k_2,T_c] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Compl__atLeast]) ).
fof(f_2166_2,plain,
! [U_8640,U_8639] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8639,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8639),U_8640)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_8639),U_8640)
| ~ class_Orderings_Olinorder(U_8639) ),
inference(variable_rename,[status(thm)],[f_2166_1]) ).
fof(f_2166_3,plain,
! [U_8639,U_8640] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8639,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8639),U_8640)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_8639),U_8640)
| ~ class_Orderings_Olinorder(U_8639) ),
inference(definitional_conversion,[status(esa)],[f_2166_2]) ).
cnf(f_2166_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8639,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8639),U_8640)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_8639),U_8640)
| ~ class_Orderings_Olinorder(U_8639) ),
inference(clausify,[status(thm)],[f_2166_3]) ).
fof(f_2167_1,plain,
! [V_k_2,T_c] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_k_2)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Compl__lessThan]) ).
fof(f_2167_2,plain,
! [U_8642,U_8641] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8641,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8641),U_8642)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8641),U_8642)
| ~ class_Orderings_Olinorder(U_8641) ),
inference(variable_rename,[status(thm)],[f_2167_1]) ).
fof(f_2167_3,plain,
! [U_8641,U_8642] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8641,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8641),U_8642)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8641),U_8642)
| ~ class_Orderings_Olinorder(U_8641) ),
inference(definitional_conversion,[status(esa)],[f_2167_2]) ).
cnf(f_2167_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8641,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8641),U_8642)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8641),U_8642)
| ~ class_Orderings_Olinorder(U_8641) ),
inference(clausify,[status(thm)],[f_2167_3]) ).
fof(f_2168_1,plain,
! [V_k_2,T_c] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_k_2)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan]) ).
fof(f_2168_2,plain,
! [U_8644,U_8643] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8643,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8643),U_8644)) = hAPP(c_SetInterval_Oord__class_OatMost(U_8643),U_8644)
| ~ class_Orderings_Olinorder(U_8643) ),
inference(variable_rename,[status(thm)],[f_2168_1]) ).
fof(f_2168_3,plain,
! [U_8643,U_8644] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8643,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8643),U_8644)) = hAPP(c_SetInterval_Oord__class_OatMost(U_8643),U_8644)
| ~ class_Orderings_Olinorder(U_8643) ),
inference(definitional_conversion,[status(esa)],[f_2168_2]) ).
cnf(f_2168_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8643,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8643),U_8644)) = hAPP(c_SetInterval_Oord__class_OatMost(U_8643),U_8644)
| ~ class_Orderings_Olinorder(U_8643) ),
inference(clausify,[status(thm)],[f_2168_3]) ).
fof(f_2169_1,plain,
! [V_k_2,T_c] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_k_2)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Compl__atMost]) ).
fof(f_2169_2,plain,
! [U_8646,U_8645] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8645,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8645),U_8646)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8645),U_8646)
| ~ class_Orderings_Olinorder(U_8645) ),
inference(variable_rename,[status(thm)],[f_2169_1]) ).
fof(f_2169_3,plain,
! [U_8645,U_8646] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8645,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8645),U_8646)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8645),U_8646)
| ~ class_Orderings_Olinorder(U_8645) ),
inference(definitional_conversion,[status(esa)],[f_2169_2]) ).
cnf(f_2169_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8645,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8645),U_8646)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8645),U_8646)
| ~ class_Orderings_Olinorder(U_8645) ),
inference(clausify,[status(thm)],[f_2169_3]) ).
fof(f_2170_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_2170_2,plain,
! [U_8648,U_8647] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8647),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8648) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_8647,U_8648),
inference(variable_rename,[status(thm)],[f_2170_1]) ).
fof(f_2170_3,plain,
! [U_8647,U_8648] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8647),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8648) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_8647,U_8648),
inference(definitional_conversion,[status(esa)],[f_2170_2]) ).
cnf(f_2170_4,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8647),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8648) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_8647,U_8648),
inference(clausify,[status(thm)],[f_2170_3]) ).
fof(f_2171_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_2171_2,plain,
! [U_8649] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8649)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_8649),
inference(variable_rename,[status(thm)],[f_2171_1]) ).
fof(f_2171_3,plain,
! [U_8649] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8649)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_8649),
inference(definitional_conversion,[status(esa)],[f_2171_2]) ).
cnf(f_2171_4,plain,
hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8649)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_8649),
inference(clausify,[status(thm)],[f_2171_3]) ).
fof(f_2172_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_2172_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_2172_1]) ).
cnf(f_2172_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_2172_2]) ).
fof(f_2173_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_2173_2,plain,
! [U_8651,U_8650] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8650,U_8651) = 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_8650),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8651))),
inference(variable_rename,[status(thm)],[f_2173_1]) ).
fof(f_2173_3,plain,
! [U_8650,U_8651] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8650,U_8651) = 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_8650),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8651))),
inference(definitional_conversion,[status(esa)],[f_2173_2]) ).
cnf(f_2173_4,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8650,U_8651) = 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_8650),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8651))),
inference(clausify,[status(thm)],[f_2173_3]) ).
fof(f_2174_1,plain,
! [V_n_2,V_f_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_c),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_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc]) ).
fof(f_2174_2,plain,
! [U_8654,U_8653,U_8652] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8652),U_8653),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8654))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8652),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8652),U_8653),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8654))),hAPP(U_8653,hAPP(c_Nat_OSuc,U_8654)))
| ~ class_Groups_Ocomm__monoid__add(U_8652) ),
inference(variable_rename,[status(thm)],[f_2174_1]) ).
fof(f_2174_3,plain,
! [U_8652,U_8653,U_8654] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8652),U_8653),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8654))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8652),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8652),U_8653),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8654))),hAPP(U_8653,hAPP(c_Nat_OSuc,U_8654)))
| ~ class_Groups_Ocomm__monoid__add(U_8652) ),
inference(definitional_conversion,[status(esa)],[f_2174_2]) ).
cnf(f_2174_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8652),U_8653),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8654))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8652),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8652),U_8653),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8654))),hAPP(U_8653,hAPP(c_Nat_OSuc,U_8654)))
| ~ class_Groups_Ocomm__monoid__add(U_8652) ),
inference(clausify,[status(thm)],[f_2174_3]) ).
fof(f_2175_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_2175_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_2175_1]) ).
cnf(f_2175_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_2175_2]) ).
fof(f_2176_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_l_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J]) ).
fof(f_2176_2,plain,
! [U_8657,U_8656,U_8655] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8655,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8655,U_8656),U_8657)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8655),U_8657)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8655),U_8656)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8655),U_8656),U_8657))
| ~ class_Orderings_Olinorder(U_8655) ),
inference(variable_rename,[status(thm)],[f_2176_1]) ).
fof(f_2176_3,plain,
! [U_8655,U_8656,U_8657] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8655,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8655,U_8656),U_8657)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8655),U_8657)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8655),U_8656)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8655),U_8656),U_8657))
| ~ class_Orderings_Olinorder(U_8655) ),
inference(definitional_conversion,[status(esa)],[f_2176_2]) ).
cnf(f_2176_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8655,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8655,U_8656),U_8657)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8655),U_8657)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8655),U_8656)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8655),U_8656),U_8657))
| ~ class_Orderings_Olinorder(U_8655) ),
inference(clausify,[status(thm)],[f_2176_3]) ).
fof(f_2177_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_2177_2,plain,
! [U_8659,U_8658] :
( ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8659,U_8658) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_8659),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8659),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8658))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8658),U_8659)) )
& ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8659,U_8658) = 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_8658),U_8659)) ) ),
inference(variable_rename,[status(thm)],[f_2177_1]) ).
fof(f_2177_3,plain,
( ! [U_8663,U_8661] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8663,U_8661) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_8663),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8663),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8661))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8661),U_8663)) )
& ! [U_8662,U_8660] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8662,U_8660) = 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_8660),U_8662)) ) ),
inference(miniscope,[status(thm)],[f_2177_2]) ).
fof(f_2177_4,plain,
( ! [U_8663,U_8661] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8663,U_8661) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_8663),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8663),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8661))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8661),U_8663)) )
& ! [U_8662,U_8660] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8662,U_8660) = 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_8660),U_8662)) ) ),
inference(definitional_conversion,[status(esa)],[f_2177_3]) ).
cnf(f_2177_5,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8662,U_8660) = 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_8660),U_8662)) ),
inference(clausify,[status(thm)],[f_2177_4]) ).
cnf(f_2177_6,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8663,U_8661) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_8663),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8663),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8661))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8661),U_8663)) ),
inference(clausify,[status(thm)],[f_2177_4]) ).
fof(f_2178_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_c,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J]) ).
fof(f_2178_2,plain,
! [U_8666,U_8665,U_8664] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8664,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8664,U_8665),U_8666)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8664),U_8666)) = c_Orderings_Obot__class_Obot(tc_fun(U_8664,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8664) ),
inference(variable_rename,[status(thm)],[f_2178_1]) ).
fof(f_2178_3,plain,
! [U_8664,U_8665,U_8666] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8664,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8664,U_8665),U_8666)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8664),U_8666)) = c_Orderings_Obot__class_Obot(tc_fun(U_8664,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8664) ),
inference(definitional_conversion,[status(esa)],[f_2178_2]) ).
cnf(f_2178_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8664,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8664,U_8665),U_8666)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8664),U_8666)) = c_Orderings_Obot__class_Obot(tc_fun(U_8664,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8664) ),
inference(clausify,[status(thm)],[f_2178_3]) ).
fof(f_2179_1,plain,
! [V_d_2,V_c_2,V_b_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1]) ).
fof(f_2179_2,plain,
! [U_8670,U_8669,U_8668,U_8667] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8667,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8667),U_8668)),c_SetInterval_Oord__class_OatLeastAtMost(U_8667,U_8669,U_8670)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8667,U_8669,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8667),U_8668),U_8670))
| ~ class_Orderings_Olinorder(U_8667) ),
inference(variable_rename,[status(thm)],[f_2179_1]) ).
fof(f_2179_3,plain,
! [U_8667,U_8668,U_8669,U_8670] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8667,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8667),U_8668)),c_SetInterval_Oord__class_OatLeastAtMost(U_8667,U_8669,U_8670)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8667,U_8669,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8667),U_8668),U_8670))
| ~ class_Orderings_Olinorder(U_8667) ),
inference(definitional_conversion,[status(esa)],[f_2179_2]) ).
cnf(f_2179_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8667,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8667),U_8668)),c_SetInterval_Oord__class_OatLeastAtMost(U_8667,U_8669,U_8670)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8667,U_8669,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8667),U_8668),U_8670))
| ~ class_Orderings_Olinorder(U_8667) ),
inference(clausify,[status(thm)],[f_2179_3]) ).
fof(f_2180_1,plain,
! [V_d_2,V_b_2,V_a_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1]) ).
fof(f_2180_2,plain,
! [U_8674,U_8673,U_8672,U_8671] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8671,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8671,U_8672,U_8673)),hAPP(c_SetInterval_Oord__class_OatMost(U_8671),U_8674)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8671,U_8672,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8671),U_8673),U_8674))
| ~ class_Orderings_Olinorder(U_8671) ),
inference(variable_rename,[status(thm)],[f_2180_1]) ).
fof(f_2180_3,plain,
! [U_8671,U_8672,U_8673,U_8674] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8671,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8671,U_8672,U_8673)),hAPP(c_SetInterval_Oord__class_OatMost(U_8671),U_8674)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8671,U_8672,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8671),U_8673),U_8674))
| ~ class_Orderings_Olinorder(U_8671) ),
inference(definitional_conversion,[status(esa)],[f_2180_2]) ).
cnf(f_2180_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8671,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8671,U_8672,U_8673)),hAPP(c_SetInterval_Oord__class_OatMost(U_8671),U_8674)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8671,U_8672,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_8671),U_8673),U_8674))
| ~ class_Orderings_Olinorder(U_8671) ),
inference(clausify,[status(thm)],[f_2180_3]) ).
fof(f_2181_1,plain,
! [V_d_2,V_c_2,V_a_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),V_d_2)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2]) ).
fof(f_2181_2,plain,
! [U_8678,U_8677,U_8676,U_8675] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8675,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8675),U_8676)),c_SetInterval_Oord__class_OatLeastAtMost(U_8675,U_8677,U_8678)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8675,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8675),U_8676),U_8677),U_8678)
| ~ class_Orderings_Olinorder(U_8675) ),
inference(variable_rename,[status(thm)],[f_2181_1]) ).
fof(f_2181_3,plain,
! [U_8675,U_8676,U_8677,U_8678] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8675,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8675),U_8676)),c_SetInterval_Oord__class_OatLeastAtMost(U_8675,U_8677,U_8678)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8675,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8675),U_8676),U_8677),U_8678)
| ~ class_Orderings_Olinorder(U_8675) ),
inference(definitional_conversion,[status(esa)],[f_2181_2]) ).
cnf(f_2181_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8675,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8675),U_8676)),c_SetInterval_Oord__class_OatLeastAtMost(U_8675,U_8677,U_8678)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8675,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8675),U_8676),U_8677),U_8678)
| ~ class_Orderings_Olinorder(U_8675) ),
inference(clausify,[status(thm)],[f_2181_3]) ).
fof(f_2182_1,plain,
! [V_c_2,V_b_2,V_a_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_c,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_a_2),V_c_2),V_b_2)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2]) ).
fof(f_2182_2,plain,
! [U_8682,U_8681,U_8680,U_8679] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8679,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8679,U_8680,U_8681)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8679),U_8682)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8679,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8679),U_8680),U_8682),U_8681)
| ~ class_Orderings_Olinorder(U_8679) ),
inference(variable_rename,[status(thm)],[f_2182_1]) ).
fof(f_2182_3,plain,
! [U_8679,U_8680,U_8681,U_8682] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8679,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8679,U_8680,U_8681)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8679),U_8682)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8679,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8679),U_8680),U_8682),U_8681)
| ~ class_Orderings_Olinorder(U_8679) ),
inference(definitional_conversion,[status(esa)],[f_2182_2]) ).
cnf(f_2182_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8679,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8679,U_8680,U_8681)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8679),U_8682)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8679,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_8679),U_8680),U_8682),U_8681)
| ~ class_Orderings_Olinorder(U_8679) ),
inference(clausify,[status(thm)],[f_2182_3]) ).
fof(f_2183_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_2183_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_2183_1]) ).
cnf(f_2183_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_2183_2]) ).
fof(f_2184_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I9_J]) ).
fof(f_2184_2,plain,
! [U_8685,U_8684,U_8683] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8683,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8683),U_8684)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8683,U_8684,U_8685)) = hAPP(c_SetInterval_Oord__class_OatMost(U_8683),U_8685)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8683),U_8684),U_8685))
| ~ class_Orderings_Olinorder(U_8683) ),
inference(variable_rename,[status(thm)],[f_2184_1]) ).
fof(f_2184_3,plain,
! [U_8683,U_8684,U_8685] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8683,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8683),U_8684)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8683,U_8684,U_8685)) = hAPP(c_SetInterval_Oord__class_OatMost(U_8683),U_8685)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8683),U_8684),U_8685))
| ~ class_Orderings_Olinorder(U_8683) ),
inference(definitional_conversion,[status(esa)],[f_2184_2]) ).
cnf(f_2184_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8683,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8683),U_8684)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8683,U_8684,U_8685)) = hAPP(c_SetInterval_Oord__class_OatMost(U_8683),U_8685)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8683),U_8684),U_8685))
| ~ class_Orderings_Olinorder(U_8683) ),
inference(clausify,[status(thm)],[f_2184_3]) ).
fof(f_2185_1,plain,
! [V_k_2,V_M_2,V_n_2,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_c,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_c,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_c,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_2185_2,plain,
! [U_8689,U_8688,U_8687,U_8686] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_8686,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8687)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8686,tc_HOL_Obool),tc_Nat_Onat),U_8688),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_8689))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_8686,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8689,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8687),U_8689))),U_8688),
inference(variable_rename,[status(thm)],[f_2185_1]) ).
fof(f_2185_3,plain,
! [U_8686,U_8687,U_8688,U_8689] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_8686,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8687)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8686,tc_HOL_Obool),tc_Nat_Onat),U_8688),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_8689))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_8686,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8689,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8687),U_8689))),U_8688),
inference(definitional_conversion,[status(esa)],[f_2185_2]) ).
cnf(f_2185_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_8686,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_8687)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8686,tc_HOL_Obool),tc_Nat_Onat),U_8688),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_8689))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_8686,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_8689,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8687),U_8689))),U_8688),
inference(clausify,[status(thm)],[f_2185_3]) ).
fof(f_2186_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_c,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J]) ).
fof(f_2186_2,plain,
! [U_8692,U_8691,U_8690] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8690,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8690),U_8691)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8690,U_8691,U_8692)) = c_Orderings_Obot__class_Obot(tc_fun(U_8690,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8690) ),
inference(variable_rename,[status(thm)],[f_2186_1]) ).
fof(f_2186_3,plain,
! [U_8690,U_8691,U_8692] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8690,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8690),U_8691)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8690,U_8691,U_8692)) = c_Orderings_Obot__class_Obot(tc_fun(U_8690,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8690) ),
inference(definitional_conversion,[status(esa)],[f_2186_2]) ).
cnf(f_2186_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8690,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8690),U_8691)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8690,U_8691,U_8692)) = c_Orderings_Obot__class_Obot(tc_fun(U_8690,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8690) ),
inference(clausify,[status(thm)],[f_2186_3]) ).
fof(f_2187_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J]) ).
fof(f_2187_2,plain,
! [U_8695,U_8694,U_8693] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8693,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8693),U_8694)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8693,U_8694,U_8695)) = c_Orderings_Obot__class_Obot(tc_fun(U_8693,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8693) ),
inference(variable_rename,[status(thm)],[f_2187_1]) ).
fof(f_2187_3,plain,
! [U_8693,U_8694,U_8695] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8693,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8693),U_8694)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8693,U_8694,U_8695)) = c_Orderings_Obot__class_Obot(tc_fun(U_8693,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8693) ),
inference(definitional_conversion,[status(esa)],[f_2187_2]) ).
cnf(f_2187_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8693,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8693),U_8694)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8693,U_8694,U_8695)) = c_Orderings_Obot__class_Obot(tc_fun(U_8693,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8693) ),
inference(clausify,[status(thm)],[f_2187_3]) ).
fof(f_2188_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J]) ).
fof(f_2188_2,plain,
! [U_8698,U_8697,U_8696] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8696,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8696,U_8697,U_8698)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8696),U_8698)) = c_Orderings_Obot__class_Obot(tc_fun(U_8696,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8696) ),
inference(variable_rename,[status(thm)],[f_2188_1]) ).
fof(f_2188_3,plain,
! [U_8696,U_8697,U_8698] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8696,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8696,U_8697,U_8698)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8696),U_8698)) = c_Orderings_Obot__class_Obot(tc_fun(U_8696,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8696) ),
inference(definitional_conversion,[status(esa)],[f_2188_2]) ).
cnf(f_2188_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8696,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8696,U_8697,U_8698)),hAPP(c_SetInterval_Oord__class_OatLeast(U_8696),U_8698)) = c_Orderings_Obot__class_Obot(tc_fun(U_8696,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8696) ),
inference(clausify,[status(thm)],[f_2188_3]) ).
fof(f_2189_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_2189_2,plain,
! [U_8700,U_8699] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8699,U_8700)) = 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_8700),U_8699)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_2189_1]) ).
fof(f_2189_3,plain,
! [U_8699,U_8700] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8699,U_8700)) = 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_8700),U_8699)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_2189_2]) ).
cnf(f_2189_4,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8699,U_8700)) = 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_8700),U_8699)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_2189_3]) ).
fof(f_2190_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_2190_2,plain,
! [U_8702,U_8701] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8701,U_8702) = 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_8701),hAPP(c_Int_Onat,U_8702)))
| ~ c_Nat__Transfer_Ois__nat(U_8702)
| ~ c_Nat__Transfer_Ois__nat(U_8701) ),
inference(variable_rename,[status(thm)],[f_2190_1]) ).
fof(f_2190_3,plain,
! [U_8701,U_8702] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8701,U_8702) = 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_8701),hAPP(c_Int_Onat,U_8702)))
| ~ c_Nat__Transfer_Ois__nat(U_8702)
| ~ c_Nat__Transfer_Ois__nat(U_8701) ),
inference(definitional_conversion,[status(esa)],[f_2190_2]) ).
cnf(f_2190_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8701,U_8702) = 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_8701),hAPP(c_Int_Onat,U_8702)))
| ~ c_Nat__Transfer_Ois__nat(U_8702)
| ~ c_Nat__Transfer_Ois__nat(U_8701) ),
inference(clausify,[status(thm)],[f_2190_3]) ).
fof(f_2191_1,plain,
! [V_u_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_c),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_u_2)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J]) ).
fof(f_2191_2,plain,
! [U_8704,U_8703] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8703,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8703),U_8704)),hAPP(hAPP(c_Set_Oinsert(U_8703),U_8704),c_Orderings_Obot__class_Obot(tc_fun(U_8703,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_8703),U_8704)
| ~ class_Orderings_Olinorder(U_8703) ),
inference(variable_rename,[status(thm)],[f_2191_1]) ).
fof(f_2191_3,plain,
! [U_8703,U_8704] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8703,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8703),U_8704)),hAPP(hAPP(c_Set_Oinsert(U_8703),U_8704),c_Orderings_Obot__class_Obot(tc_fun(U_8703,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_8703),U_8704)
| ~ class_Orderings_Olinorder(U_8703) ),
inference(definitional_conversion,[status(esa)],[f_2191_2]) ).
cnf(f_2191_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8703,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8703),U_8704)),hAPP(hAPP(c_Set_Oinsert(U_8703),U_8704),c_Orderings_Obot__class_Obot(tc_fun(U_8703,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_8703),U_8704)
| ~ class_Orderings_Olinorder(U_8703) ),
inference(clausify,[status(thm)],[f_2191_3]) ).
fof(f_2192_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I10_J]) ).
fof(f_2192_2,plain,
! [U_8707,U_8706,U_8705] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8705,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8705),U_8706)),c_SetInterval_Oord__class_OatLeastAtMost(U_8705,U_8706,U_8707)) = hAPP(c_SetInterval_Oord__class_OatMost(U_8705),U_8707)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8705),U_8706),U_8707))
| ~ class_Orderings_Olinorder(U_8705) ),
inference(variable_rename,[status(thm)],[f_2192_1]) ).
fof(f_2192_3,plain,
! [U_8705,U_8706,U_8707] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8705,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8705),U_8706)),c_SetInterval_Oord__class_OatLeastAtMost(U_8705,U_8706,U_8707)) = hAPP(c_SetInterval_Oord__class_OatMost(U_8705),U_8707)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8705),U_8706),U_8707))
| ~ class_Orderings_Olinorder(U_8705) ),
inference(definitional_conversion,[status(esa)],[f_2192_2]) ).
cnf(f_2192_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8705,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8705),U_8706)),c_SetInterval_Oord__class_OatLeastAtMost(U_8705,U_8706,U_8707)) = hAPP(c_SetInterval_Oord__class_OatMost(U_8705),U_8707)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8705),U_8706),U_8707))
| ~ class_Orderings_Olinorder(U_8705) ),
inference(clausify,[status(thm)],[f_2192_3]) ).
fof(f_2193_1,plain,
! [V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_l_2)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J]) ).
fof(f_2193_2,plain,
! [U_8709,U_8708] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8708,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8708),U_8709),c_Orderings_Obot__class_Obot(tc_fun(U_8708,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8708),U_8709)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8708),U_8709)
| ~ class_Orderings_Olinorder(U_8708) ),
inference(variable_rename,[status(thm)],[f_2193_1]) ).
fof(f_2193_3,plain,
! [U_8708,U_8709] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8708,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8708),U_8709),c_Orderings_Obot__class_Obot(tc_fun(U_8708,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8708),U_8709)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8708),U_8709)
| ~ class_Orderings_Olinorder(U_8708) ),
inference(definitional_conversion,[status(esa)],[f_2193_2]) ).
cnf(f_2193_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8708,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8708),U_8709),c_Orderings_Obot__class_Obot(tc_fun(U_8708,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8708),U_8709)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8708),U_8709)
| ~ class_Orderings_Olinorder(U_8708) ),
inference(clausify,[status(thm)],[f_2193_3]) ).
fof(f_2194_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_c,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_c),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_c),V_l_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I13_J]) ).
fof(f_2194_2,plain,
! [U_8712,U_8711,U_8710] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8710,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8710,U_8711,U_8712)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8710),U_8712)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8710),U_8711)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8710),U_8711),U_8712))
| ~ class_Orderings_Olinorder(U_8710) ),
inference(variable_rename,[status(thm)],[f_2194_1]) ).
fof(f_2194_3,plain,
! [U_8710,U_8711,U_8712] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8710,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8710,U_8711,U_8712)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8710),U_8712)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8710),U_8711)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8710),U_8711),U_8712))
| ~ class_Orderings_Olinorder(U_8710) ),
inference(definitional_conversion,[status(esa)],[f_2194_2]) ).
cnf(f_2194_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8710,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_8710,U_8711,U_8712)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8710),U_8712)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8710),U_8711)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8710),U_8711),U_8712))
| ~ class_Orderings_Olinorder(U_8710) ),
inference(clausify,[status(thm)],[f_2194_3]) ).
fof(f_2195_1,plain,
! [V_u_2,V_l_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_c),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_c,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_c),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J]) ).
fof(f_2195_2,plain,
! [U_8715,U_8714,U_8713] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8713,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8713),U_8714)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8713,U_8714,U_8715)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_8713),U_8715)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8713),U_8714),U_8715))
| ~ class_Orderings_Olinorder(U_8713) ),
inference(variable_rename,[status(thm)],[f_2195_1]) ).
fof(f_2195_3,plain,
! [U_8713,U_8714,U_8715] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8713,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8713),U_8714)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8713,U_8714,U_8715)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_8713),U_8715)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8713),U_8714),U_8715))
| ~ class_Orderings_Olinorder(U_8713) ),
inference(definitional_conversion,[status(esa)],[f_2195_2]) ).
cnf(f_2195_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8713,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_8713),U_8714)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8713,U_8714,U_8715)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_8713),U_8715)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8713),U_8714),U_8715))
| ~ class_Orderings_Olinorder(U_8713) ),
inference(clausify,[status(thm)],[f_2195_3]) ).
fof(f_2196_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_2196_2,plain,
! [U_8721,U_8720,U_8719] :
( ! [U_8718] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8718),U_8719)),U_8720))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8718),U_8720))
| ? [U_8717] :
( ? [U_8716] :
( U_8718 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8716),U_8717)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8716),U_8721)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8717),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8719))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8720),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8719)) ),
inference(variable_rename,[status(thm)],[f_2196_1]) ).
fof(f_2196_3,plain,
! [U_8721,U_8720,U_8719] :
( ! [U_8718] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8718),U_8719)),U_8720))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8718),U_8720))
| ( ? [U_8716] :
( U_8718 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8716),sK179(U_8721,U_8720,U_8719,U_8718))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8716),U_8721)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK179(U_8721,U_8720,U_8719,U_8718)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8719))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8720),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8719)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_8717,sK179(U_8721,U_8720,U_8719,U_8718))],[f_2196_2]) ).
fof(f_2196_4,plain,
! [U_8721,U_8720,U_8719] :
( ! [U_8718] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8718),U_8719)),U_8720))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8718),U_8720))
| ( U_8718 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK180(U_8721,U_8720,U_8719,U_8718)),sK179(U_8721,U_8720,U_8719,U_8718))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK180(U_8721,U_8720,U_8719,U_8718)),U_8721))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK179(U_8721,U_8720,U_8719,U_8718)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8719))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8720),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8719)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_8716,sK180(U_8721,U_8720,U_8719,U_8718))],[f_2196_3]) ).
fof(f_2196_5,plain,
( ! [U_8718,U_8719,U_8720,U_8721] :
( U_8718 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK180(U_8721,U_8720,U_8719,U_8718)),sK179(U_8721,U_8720,U_8719,U_8718))
| ~ sP602(U_8718,U_8719,U_8720,U_8721) )
& ! [U_8718,U_8719,U_8720,U_8721] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK180(U_8721,U_8720,U_8719,U_8718)),U_8721))
| ~ sP602(U_8718,U_8719,U_8720,U_8721) )
& ! [U_8718,U_8719,U_8720,U_8721] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK179(U_8721,U_8720,U_8719,U_8718)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8719)))
| ~ sP602(U_8718,U_8719,U_8720,U_8721) )
& ! [U_8718,U_8719,U_8720,U_8721] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8718),U_8719)),U_8720))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8718),U_8720))
| sP602(U_8718,U_8719,U_8720,U_8721)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8720),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8719)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP602])],[f_2196_4]) ).
cnf(f_2196_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_8718),U_8719)),U_8720))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8718),U_8720))
| sP602(U_8718,U_8719,U_8720,U_8721)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8720),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8719)) ),
inference(clausify,[status(thm)],[f_2196_5]) ).
cnf(f_2196_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK179(U_8721,U_8720,U_8719,U_8718)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8719)))
| ~ sP602(U_8718,U_8719,U_8720,U_8721) ),
inference(clausify,[status(thm)],[f_2196_5]) ).
cnf(f_2196_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK180(U_8721,U_8720,U_8719,U_8718)),U_8721))
| ~ sP602(U_8718,U_8719,U_8720,U_8721) ),
inference(clausify,[status(thm)],[f_2196_5]) ).
cnf(f_2196_9,plain,
( U_8718 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK180(U_8721,U_8720,U_8719,U_8718)),sK179(U_8721,U_8720,U_8719,U_8718))
| ~ sP602(U_8718,U_8719,U_8720,U_8721) ),
inference(clausify,[status(thm)],[f_2196_5]) ).
fof(f_2197_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_2197_2,plain,
! [U_8727,U_8726,U_8725] :
( ! [U_8724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8726),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8724),U_8725)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8726),U_8724))
| ? [U_8723] :
( ? [U_8722] :
( U_8724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8722),U_8723)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8722),U_8727)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8723),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8725))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8726),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8727))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8725)) ),
inference(variable_rename,[status(thm)],[f_2197_1]) ).
fof(f_2197_3,plain,
! [U_8727,U_8726,U_8725] :
( ! [U_8724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8726),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8724),U_8725)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8726),U_8724))
| ( ? [U_8722] :
( U_8724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8722),sK181(U_8727,U_8726,U_8725,U_8724))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8722),U_8727)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK181(U_8727,U_8726,U_8725,U_8724)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8725))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8726),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8727))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8725)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_8723,sK181(U_8727,U_8726,U_8725,U_8724))],[f_2197_2]) ).
fof(f_2197_4,plain,
! [U_8727,U_8726,U_8725] :
( ! [U_8724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8726),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8724),U_8725)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8726),U_8724))
| ( U_8724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK182(U_8727,U_8726,U_8725,U_8724)),sK181(U_8727,U_8726,U_8725,U_8724))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK182(U_8727,U_8726,U_8725,U_8724)),U_8727))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK181(U_8727,U_8726,U_8725,U_8724)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8725))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8726),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8727))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8725)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_8722,sK182(U_8727,U_8726,U_8725,U_8724))],[f_2197_3]) ).
fof(f_2197_5,plain,
( ! [U_8724,U_8727,U_8726,U_8725] :
( U_8724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK182(U_8727,U_8726,U_8725,U_8724)),sK181(U_8727,U_8726,U_8725,U_8724))
| ~ sP603(U_8724,U_8727,U_8726,U_8725) )
& ! [U_8724,U_8727,U_8726,U_8725] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK182(U_8727,U_8726,U_8725,U_8724)),U_8727))
| ~ sP603(U_8724,U_8727,U_8726,U_8725) )
& ! [U_8724,U_8727,U_8726,U_8725] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK181(U_8727,U_8726,U_8725,U_8724)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8725)))
| ~ sP603(U_8724,U_8727,U_8726,U_8725) )
& ! [U_8724,U_8727,U_8726,U_8725] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8726),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8724),U_8725)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8726),U_8724))
| sP603(U_8724,U_8727,U_8726,U_8725)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8726),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8727))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8725)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP603])],[f_2197_4]) ).
cnf(f_2197_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8726),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8724),U_8725)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8726),U_8724))
| sP603(U_8724,U_8727,U_8726,U_8725)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8726),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8727))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8725)) ),
inference(clausify,[status(thm)],[f_2197_5]) ).
cnf(f_2197_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK181(U_8727,U_8726,U_8725,U_8724)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8725)))
| ~ sP603(U_8724,U_8727,U_8726,U_8725) ),
inference(clausify,[status(thm)],[f_2197_5]) ).
cnf(f_2197_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK182(U_8727,U_8726,U_8725,U_8724)),U_8727))
| ~ sP603(U_8724,U_8727,U_8726,U_8725) ),
inference(clausify,[status(thm)],[f_2197_5]) ).
cnf(f_2197_9,plain,
( U_8724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK182(U_8727,U_8726,U_8725,U_8724)),sK181(U_8727,U_8726,U_8725,U_8724))
| ~ sP603(U_8724,U_8727,U_8726,U_8725) ),
inference(clausify,[status(thm)],[f_2197_5]) ).
fof(f_2198_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_2198_2,plain,
! [U_8733,U_8732,U_8731] :
( ! [U_8730] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8730),U_8731) != U_8732
| U_8730 = U_8732
| ? [U_8729] :
( ? [U_8728] :
( U_8730 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8728),U_8729)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8728),U_8733)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8729),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8731))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8732),U_8733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8731)) ),
inference(variable_rename,[status(thm)],[f_2198_1]) ).
fof(f_2198_3,plain,
! [U_8733,U_8732,U_8731] :
( ! [U_8730] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8730),U_8731) != U_8732
| U_8730 = U_8732
| ( ? [U_8728] :
( U_8730 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8728),sK183(U_8733,U_8732,U_8731,U_8730))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8728),U_8733)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK183(U_8733,U_8732,U_8731,U_8730)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8731))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8732),U_8733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8731)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_8729,sK183(U_8733,U_8732,U_8731,U_8730))],[f_2198_2]) ).
fof(f_2198_4,plain,
! [U_8733,U_8732,U_8731] :
( ! [U_8730] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8730),U_8731) != U_8732
| U_8730 = U_8732
| ( U_8730 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK184(U_8733,U_8732,U_8731,U_8730)),sK183(U_8733,U_8732,U_8731,U_8730))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK184(U_8733,U_8732,U_8731,U_8730)),U_8733))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK183(U_8733,U_8732,U_8731,U_8730)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8731))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8732),U_8733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8731)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_8728,sK184(U_8733,U_8732,U_8731,U_8730))],[f_2198_3]) ).
fof(f_2198_5,plain,
( ! [U_8731,U_8730,U_8732,U_8733] :
( U_8730 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK184(U_8733,U_8732,U_8731,U_8730)),sK183(U_8733,U_8732,U_8731,U_8730))
| ~ sP604(U_8731,U_8730,U_8732,U_8733) )
& ! [U_8731,U_8730,U_8732,U_8733] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK184(U_8733,U_8732,U_8731,U_8730)),U_8733))
| ~ sP604(U_8731,U_8730,U_8732,U_8733) )
& ! [U_8731,U_8730,U_8732,U_8733] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK183(U_8733,U_8732,U_8731,U_8730)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8731)))
| ~ sP604(U_8731,U_8730,U_8732,U_8733) )
& ! [U_8731,U_8730,U_8732,U_8733] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8730),U_8731) != U_8732
| U_8730 = U_8732
| sP604(U_8731,U_8730,U_8732,U_8733)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8732),U_8733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8731)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP604])],[f_2198_4]) ).
cnf(f_2198_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8730),U_8731) != U_8732
| U_8730 = U_8732
| sP604(U_8731,U_8730,U_8732,U_8733)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8732),U_8733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8731)) ),
inference(clausify,[status(thm)],[f_2198_5]) ).
cnf(f_2198_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK183(U_8733,U_8732,U_8731,U_8730)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8731)))
| ~ sP604(U_8731,U_8730,U_8732,U_8733) ),
inference(clausify,[status(thm)],[f_2198_5]) ).
cnf(f_2198_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK184(U_8733,U_8732,U_8731,U_8730)),U_8733))
| ~ sP604(U_8731,U_8730,U_8732,U_8733) ),
inference(clausify,[status(thm)],[f_2198_5]) ).
cnf(f_2198_9,plain,
( U_8730 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK184(U_8733,U_8732,U_8731,U_8730)),sK183(U_8733,U_8732,U_8731,U_8730))
| ~ sP604(U_8731,U_8730,U_8732,U_8733) ),
inference(clausify,[status(thm)],[f_2198_5]) ).
fof(f_2199_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_2199_2,plain,
! [U_8739,U_8738,U_8737] :
( ! [U_8736] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8736),U_8737) != U_8738
| U_8736 = U_8738
| ? [U_8735] :
( ? [U_8734] :
( U_8736 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8734),U_8735)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8734),U_8739)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8735),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8737))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8738),U_8739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8737)) ),
inference(variable_rename,[status(thm)],[f_2199_1]) ).
fof(f_2199_3,plain,
! [U_8739,U_8738,U_8737] :
( ! [U_8736] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8736),U_8737) != U_8738
| U_8736 = U_8738
| ( ? [U_8734] :
( U_8736 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8734),sK185(U_8739,U_8738,U_8737,U_8736))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8734),U_8739)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK185(U_8739,U_8738,U_8737,U_8736)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8737))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8738),U_8739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8737)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_8735,sK185(U_8739,U_8738,U_8737,U_8736))],[f_2199_2]) ).
fof(f_2199_4,plain,
! [U_8739,U_8738,U_8737] :
( ! [U_8736] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8736),U_8737) != U_8738
| U_8736 = U_8738
| ( U_8736 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK186(U_8739,U_8738,U_8737,U_8736)),sK185(U_8739,U_8738,U_8737,U_8736))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK186(U_8739,U_8738,U_8737,U_8736)),U_8739))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK185(U_8739,U_8738,U_8737,U_8736)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8737))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8738),U_8739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8737)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_8734,sK186(U_8739,U_8738,U_8737,U_8736))],[f_2199_3]) ).
fof(f_2199_5,plain,
( ! [U_8739,U_8738,U_8736,U_8737] :
( U_8736 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK186(U_8739,U_8738,U_8737,U_8736)),sK185(U_8739,U_8738,U_8737,U_8736))
| ~ sP605(U_8739,U_8738,U_8736,U_8737) )
& ! [U_8739,U_8738,U_8736,U_8737] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK186(U_8739,U_8738,U_8737,U_8736)),U_8739))
| ~ sP605(U_8739,U_8738,U_8736,U_8737) )
& ! [U_8739,U_8738,U_8736,U_8737] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK185(U_8739,U_8738,U_8737,U_8736)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8737)))
| ~ sP605(U_8739,U_8738,U_8736,U_8737) )
& ! [U_8739,U_8738,U_8736,U_8737] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8736),U_8737) != U_8738
| U_8736 = U_8738
| sP605(U_8739,U_8738,U_8736,U_8737)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8738),U_8739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8737)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP605])],[f_2199_4]) ).
cnf(f_2199_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8736),U_8737) != U_8738
| U_8736 = U_8738
| sP605(U_8739,U_8738,U_8736,U_8737)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8738),U_8739))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8737)) ),
inference(clausify,[status(thm)],[f_2199_5]) ).
cnf(f_2199_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK185(U_8739,U_8738,U_8737,U_8736)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8737)))
| ~ sP605(U_8739,U_8738,U_8736,U_8737) ),
inference(clausify,[status(thm)],[f_2199_5]) ).
cnf(f_2199_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK186(U_8739,U_8738,U_8737,U_8736)),U_8739))
| ~ sP605(U_8739,U_8738,U_8736,U_8737) ),
inference(clausify,[status(thm)],[f_2199_5]) ).
cnf(f_2199_9,plain,
( U_8736 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK186(U_8739,U_8738,U_8737,U_8736)),sK185(U_8739,U_8738,U_8737,U_8736))
| ~ sP605(U_8739,U_8738,U_8736,U_8737) ),
inference(clausify,[status(thm)],[f_2199_5]) ).
fof(f_2200_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_2200_2,plain,
! [U_8745,U_8744,U_8743] :
( ! [U_8742] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8744),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8742),U_8743)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8744),U_8742))
| ? [U_8741] :
( ? [U_8740] :
( U_8742 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8740),U_8741)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8740),U_8745)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8741),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8743))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8744),U_8745))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8743)) ),
inference(variable_rename,[status(thm)],[f_2200_1]) ).
fof(f_2200_3,plain,
! [U_8745,U_8744,U_8743] :
( ! [U_8742] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8744),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8742),U_8743)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8744),U_8742))
| ( ? [U_8740] :
( U_8742 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8740),sK187(U_8745,U_8744,U_8743,U_8742))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8740),U_8745)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK187(U_8745,U_8744,U_8743,U_8742)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8743))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8744),U_8745))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8743)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_8741,sK187(U_8745,U_8744,U_8743,U_8742))],[f_2200_2]) ).
fof(f_2200_4,plain,
! [U_8745,U_8744,U_8743] :
( ! [U_8742] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8744),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8742),U_8743)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8744),U_8742))
| ( U_8742 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK188(U_8745,U_8744,U_8743,U_8742)),sK187(U_8745,U_8744,U_8743,U_8742))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK188(U_8745,U_8744,U_8743,U_8742)),U_8745))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK187(U_8745,U_8744,U_8743,U_8742)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8743))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8744),U_8745))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8743)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_8740,sK188(U_8745,U_8744,U_8743,U_8742))],[f_2200_3]) ).
fof(f_2200_5,plain,
( ! [U_8743,U_8745,U_8744,U_8742] :
( U_8742 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK188(U_8745,U_8744,U_8743,U_8742)),sK187(U_8745,U_8744,U_8743,U_8742))
| ~ sP606(U_8743,U_8745,U_8744,U_8742) )
& ! [U_8743,U_8745,U_8744,U_8742] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK188(U_8745,U_8744,U_8743,U_8742)),U_8745))
| ~ sP606(U_8743,U_8745,U_8744,U_8742) )
& ! [U_8743,U_8745,U_8744,U_8742] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK187(U_8745,U_8744,U_8743,U_8742)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8743)))
| ~ sP606(U_8743,U_8745,U_8744,U_8742) )
& ! [U_8743,U_8745,U_8744,U_8742] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8744),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8742),U_8743)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8744),U_8742))
| sP606(U_8743,U_8745,U_8744,U_8742)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8744),U_8745))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8743)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP606])],[f_2200_4]) ).
cnf(f_2200_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8744),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8742),U_8743)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8744),U_8742))
| sP606(U_8743,U_8745,U_8744,U_8742)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8744),U_8745))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8743)) ),
inference(clausify,[status(thm)],[f_2200_5]) ).
cnf(f_2200_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK187(U_8745,U_8744,U_8743,U_8742)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8743)))
| ~ sP606(U_8743,U_8745,U_8744,U_8742) ),
inference(clausify,[status(thm)],[f_2200_5]) ).
cnf(f_2200_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK188(U_8745,U_8744,U_8743,U_8742)),U_8745))
| ~ sP606(U_8743,U_8745,U_8744,U_8742) ),
inference(clausify,[status(thm)],[f_2200_5]) ).
cnf(f_2200_9,plain,
( U_8742 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK188(U_8745,U_8744,U_8743,U_8742)),sK187(U_8745,U_8744,U_8743,U_8742))
| ~ sP606(U_8743,U_8745,U_8744,U_8742) ),
inference(clausify,[status(thm)],[f_2200_5]) ).
fof(f_2201_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_2201_2,plain,
! [U_8750,U_8749,U_8748] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8749),U_8748) = U_8749
| ? [U_8747] :
( ? [U_8746] :
( U_8749 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8746),U_8747)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8746),U_8750)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8747),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8748))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8749),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8750))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8748)) ),
inference(variable_rename,[status(thm)],[f_2201_1]) ).
fof(f_2201_3,plain,
! [U_8750,U_8749,U_8748] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8749),U_8748) = U_8749
| ( ? [U_8746] :
( U_8749 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8746),sK189(U_8750,U_8749,U_8748))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8746),U_8750)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK189(U_8750,U_8749,U_8748)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8748))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8749),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8750))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8748)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_8747,sK189(U_8750,U_8749,U_8748))],[f_2201_2]) ).
fof(f_2201_4,plain,
! [U_8750,U_8749,U_8748] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8749),U_8748) = U_8749
| ( U_8749 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK190(U_8750,U_8749,U_8748)),sK189(U_8750,U_8749,U_8748))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK190(U_8750,U_8749,U_8748)),U_8750))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK189(U_8750,U_8749,U_8748)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8748))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8749),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8750))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8748)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_8746,sK190(U_8750,U_8749,U_8748))],[f_2201_3]) ).
fof(f_2201_5,plain,
( ! [U_8750,U_8748,U_8749] :
( U_8749 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK190(U_8750,U_8749,U_8748)),sK189(U_8750,U_8749,U_8748))
| ~ sP607(U_8750,U_8748,U_8749) )
& ! [U_8750,U_8748,U_8749] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK190(U_8750,U_8749,U_8748)),U_8750))
| ~ sP607(U_8750,U_8748,U_8749) )
& ! [U_8750,U_8748,U_8749] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK189(U_8750,U_8749,U_8748)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8748)))
| ~ sP607(U_8750,U_8748,U_8749) )
& ! [U_8750,U_8748,U_8749] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8749),U_8748) = U_8749
| sP607(U_8750,U_8748,U_8749)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8749),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8750))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8748)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP607])],[f_2201_4]) ).
cnf(f_2201_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8749),U_8748) = U_8749
| sP607(U_8750,U_8748,U_8749)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8749),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8750))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8748)) ),
inference(clausify,[status(thm)],[f_2201_5]) ).
cnf(f_2201_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK189(U_8750,U_8749,U_8748)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8748)))
| ~ sP607(U_8750,U_8748,U_8749) ),
inference(clausify,[status(thm)],[f_2201_5]) ).
cnf(f_2201_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK190(U_8750,U_8749,U_8748)),U_8750))
| ~ sP607(U_8750,U_8748,U_8749) ),
inference(clausify,[status(thm)],[f_2201_5]) ).
cnf(f_2201_9,plain,
( U_8749 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK190(U_8750,U_8749,U_8748)),sK189(U_8750,U_8749,U_8748))
| ~ sP607(U_8750,U_8748,U_8749) ),
inference(clausify,[status(thm)],[f_2201_5]) ).
fof(f_2202_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_2202_2,plain,
! [U_8755,U_8754,U_8753] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8754),U_8753) = U_8754
| ? [U_8752] :
( ? [U_8751] :
( U_8754 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8751),U_8752)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8751),U_8755)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8752),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8753))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8754),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8753)) ),
inference(variable_rename,[status(thm)],[f_2202_1]) ).
fof(f_2202_3,plain,
! [U_8755,U_8754,U_8753] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8754),U_8753) = U_8754
| ( ? [U_8751] :
( U_8754 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8751),sK191(U_8755,U_8754,U_8753))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8751),U_8755)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK191(U_8755,U_8754,U_8753)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8753))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8754),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8753)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_8752,sK191(U_8755,U_8754,U_8753))],[f_2202_2]) ).
fof(f_2202_4,plain,
! [U_8755,U_8754,U_8753] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8754),U_8753) = U_8754
| ( U_8754 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK192(U_8755,U_8754,U_8753)),sK191(U_8755,U_8754,U_8753))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK192(U_8755,U_8754,U_8753)),U_8755))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK191(U_8755,U_8754,U_8753)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8753))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8754),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8753)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_8751,sK192(U_8755,U_8754,U_8753))],[f_2202_3]) ).
fof(f_2202_5,plain,
( ! [U_8754,U_8755,U_8753] :
( U_8754 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK192(U_8755,U_8754,U_8753)),sK191(U_8755,U_8754,U_8753))
| ~ sP608(U_8754,U_8755,U_8753) )
& ! [U_8754,U_8755,U_8753] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK192(U_8755,U_8754,U_8753)),U_8755))
| ~ sP608(U_8754,U_8755,U_8753) )
& ! [U_8754,U_8755,U_8753] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK191(U_8755,U_8754,U_8753)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8753)))
| ~ sP608(U_8754,U_8755,U_8753) )
& ! [U_8754,U_8755,U_8753] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8754),U_8753) = U_8754
| sP608(U_8754,U_8755,U_8753)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8754),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8753)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP608])],[f_2202_4]) ).
cnf(f_2202_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8754),U_8753) = U_8754
| sP608(U_8754,U_8755,U_8753)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8754),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8755))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8753)) ),
inference(clausify,[status(thm)],[f_2202_5]) ).
cnf(f_2202_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK191(U_8755,U_8754,U_8753)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8753)))
| ~ sP608(U_8754,U_8755,U_8753) ),
inference(clausify,[status(thm)],[f_2202_5]) ).
cnf(f_2202_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK192(U_8755,U_8754,U_8753)),U_8755))
| ~ sP608(U_8754,U_8755,U_8753) ),
inference(clausify,[status(thm)],[f_2202_5]) ).
cnf(f_2202_9,plain,
( U_8754 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK192(U_8755,U_8754,U_8753)),sK191(U_8755,U_8754,U_8753))
| ~ sP608(U_8754,U_8755,U_8753) ),
inference(clausify,[status(thm)],[f_2202_5]) ).
fof(f_2203_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_2203_2,plain,
! [U_8761,U_8760,U_8759] :
( ! [U_8758] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8758),U_8759)),U_8760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8758),U_8760))
| ? [U_8757] :
( ? [U_8756] :
( U_8758 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8756),U_8757)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8756),U_8761)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8757),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8759))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8760),U_8761))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8759)) ),
inference(variable_rename,[status(thm)],[f_2203_1]) ).
fof(f_2203_3,plain,
! [U_8761,U_8760,U_8759] :
( ! [U_8758] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8758),U_8759)),U_8760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8758),U_8760))
| ( ? [U_8756] :
( U_8758 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8756),sK193(U_8761,U_8760,U_8759,U_8758))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8756),U_8761)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK193(U_8761,U_8760,U_8759,U_8758)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8759))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8760),U_8761))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8759)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_8757,sK193(U_8761,U_8760,U_8759,U_8758))],[f_2203_2]) ).
fof(f_2203_4,plain,
! [U_8761,U_8760,U_8759] :
( ! [U_8758] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8758),U_8759)),U_8760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8758),U_8760))
| ( U_8758 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK194(U_8761,U_8760,U_8759,U_8758)),sK193(U_8761,U_8760,U_8759,U_8758))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK194(U_8761,U_8760,U_8759,U_8758)),U_8761))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK193(U_8761,U_8760,U_8759,U_8758)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8759))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8760),U_8761))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8759)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_8756,sK194(U_8761,U_8760,U_8759,U_8758))],[f_2203_3]) ).
fof(f_2203_5,plain,
( ! [U_8758,U_8759,U_8760,U_8761] :
( U_8758 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK194(U_8761,U_8760,U_8759,U_8758)),sK193(U_8761,U_8760,U_8759,U_8758))
| ~ sP609(U_8758,U_8759,U_8760,U_8761) )
& ! [U_8758,U_8759,U_8760,U_8761] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK194(U_8761,U_8760,U_8759,U_8758)),U_8761))
| ~ sP609(U_8758,U_8759,U_8760,U_8761) )
& ! [U_8758,U_8759,U_8760,U_8761] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK193(U_8761,U_8760,U_8759,U_8758)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8759)))
| ~ sP609(U_8758,U_8759,U_8760,U_8761) )
& ! [U_8758,U_8759,U_8760,U_8761] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8758),U_8759)),U_8760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8758),U_8760))
| sP609(U_8758,U_8759,U_8760,U_8761)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8760),U_8761))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8759)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP609])],[f_2203_4]) ).
cnf(f_2203_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8758),U_8759)),U_8760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8758),U_8760))
| sP609(U_8758,U_8759,U_8760,U_8761)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8760),U_8761))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8759)) ),
inference(clausify,[status(thm)],[f_2203_5]) ).
cnf(f_2203_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK193(U_8761,U_8760,U_8759,U_8758)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8759)))
| ~ sP609(U_8758,U_8759,U_8760,U_8761) ),
inference(clausify,[status(thm)],[f_2203_5]) ).
cnf(f_2203_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK194(U_8761,U_8760,U_8759,U_8758)),U_8761))
| ~ sP609(U_8758,U_8759,U_8760,U_8761) ),
inference(clausify,[status(thm)],[f_2203_5]) ).
cnf(f_2203_9,plain,
( U_8758 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK194(U_8761,U_8760,U_8759,U_8758)),sK193(U_8761,U_8760,U_8759,U_8758))
| ~ sP609(U_8758,U_8759,U_8760,U_8761) ),
inference(clausify,[status(thm)],[f_2203_5]) ).
fof(f_2204_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_2204_2,plain,
! [U_8767,U_8766,U_8765] :
( ! [U_8764] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8764),U_8765)),U_8767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8764),U_8767))
| ? [U_8763] :
( ? [U_8762] :
( U_8764 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8762),U_8763)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8762),U_8766)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8763),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8765))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8765)) ),
inference(variable_rename,[status(thm)],[f_2204_1]) ).
fof(f_2204_3,plain,
! [U_8767,U_8766,U_8765] :
( ! [U_8764] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8764),U_8765)),U_8767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8764),U_8767))
| ( ? [U_8762] :
( U_8764 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8762),sK195(U_8767,U_8766,U_8765,U_8764))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8762),U_8766)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK195(U_8767,U_8766,U_8765,U_8764)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8765))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8765)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_8763,sK195(U_8767,U_8766,U_8765,U_8764))],[f_2204_2]) ).
fof(f_2204_4,plain,
! [U_8767,U_8766,U_8765] :
( ! [U_8764] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8764),U_8765)),U_8767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8764),U_8767))
| ( U_8764 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK196(U_8767,U_8766,U_8765,U_8764)),sK195(U_8767,U_8766,U_8765,U_8764))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK196(U_8767,U_8766,U_8765,U_8764)),U_8766))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK195(U_8767,U_8766,U_8765,U_8764)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8765))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8765)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_8762,sK196(U_8767,U_8766,U_8765,U_8764))],[f_2204_3]) ).
fof(f_2204_5,plain,
( ! [U_8765,U_8764,U_8766,U_8767] :
( U_8764 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK196(U_8767,U_8766,U_8765,U_8764)),sK195(U_8767,U_8766,U_8765,U_8764))
| ~ sP610(U_8765,U_8764,U_8766,U_8767) )
& ! [U_8765,U_8764,U_8766,U_8767] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK196(U_8767,U_8766,U_8765,U_8764)),U_8766))
| ~ sP610(U_8765,U_8764,U_8766,U_8767) )
& ! [U_8765,U_8764,U_8766,U_8767] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK195(U_8767,U_8766,U_8765,U_8764)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8765)))
| ~ sP610(U_8765,U_8764,U_8766,U_8767) )
& ! [U_8765,U_8764,U_8766,U_8767] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8764),U_8765)),U_8767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8764),U_8767))
| sP610(U_8765,U_8764,U_8766,U_8767)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8765)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP610])],[f_2204_4]) ).
cnf(f_2204_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_8764),U_8765)),U_8767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8764),U_8767))
| sP610(U_8765,U_8764,U_8766,U_8767)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8765)) ),
inference(clausify,[status(thm)],[f_2204_5]) ).
cnf(f_2204_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK195(U_8767,U_8766,U_8765,U_8764)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8765)))
| ~ sP610(U_8765,U_8764,U_8766,U_8767) ),
inference(clausify,[status(thm)],[f_2204_5]) ).
cnf(f_2204_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK196(U_8767,U_8766,U_8765,U_8764)),U_8766))
| ~ sP610(U_8765,U_8764,U_8766,U_8767) ),
inference(clausify,[status(thm)],[f_2204_5]) ).
cnf(f_2204_9,plain,
( U_8764 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK196(U_8767,U_8766,U_8765,U_8764)),sK195(U_8767,U_8766,U_8765,U_8764))
| ~ sP610(U_8765,U_8764,U_8766,U_8767) ),
inference(clausify,[status(thm)],[f_2204_5]) ).
fof(f_2205_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_2205_2,plain,
! [U_8773,U_8772,U_8771] :
( ! [U_8770] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8770),U_8771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8773),U_8770))
| ? [U_8769] :
( ? [U_8768] :
( U_8770 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8768),U_8769)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8768),U_8772)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8769),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8771))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8771)) ),
inference(variable_rename,[status(thm)],[f_2205_1]) ).
fof(f_2205_3,plain,
! [U_8773,U_8772,U_8771] :
( ! [U_8770] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8770),U_8771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8773),U_8770))
| ( ? [U_8768] :
( U_8770 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8768),sK197(U_8773,U_8772,U_8771,U_8770))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8768),U_8772)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK197(U_8773,U_8772,U_8771,U_8770)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8771))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8771)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_8769,sK197(U_8773,U_8772,U_8771,U_8770))],[f_2205_2]) ).
fof(f_2205_4,plain,
! [U_8773,U_8772,U_8771] :
( ! [U_8770] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8770),U_8771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8773),U_8770))
| ( U_8770 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK198(U_8773,U_8772,U_8771,U_8770)),sK197(U_8773,U_8772,U_8771,U_8770))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK198(U_8773,U_8772,U_8771,U_8770)),U_8772))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK197(U_8773,U_8772,U_8771,U_8770)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8771))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8771)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_8768,sK198(U_8773,U_8772,U_8771,U_8770))],[f_2205_3]) ).
fof(f_2205_5,plain,
( ! [U_8770,U_8773,U_8771,U_8772] :
( U_8770 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK198(U_8773,U_8772,U_8771,U_8770)),sK197(U_8773,U_8772,U_8771,U_8770))
| ~ sP611(U_8770,U_8773,U_8771,U_8772) )
& ! [U_8770,U_8773,U_8771,U_8772] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK198(U_8773,U_8772,U_8771,U_8770)),U_8772))
| ~ sP611(U_8770,U_8773,U_8771,U_8772) )
& ! [U_8770,U_8773,U_8771,U_8772] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK197(U_8773,U_8772,U_8771,U_8770)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8771)))
| ~ sP611(U_8770,U_8773,U_8771,U_8772) )
& ! [U_8770,U_8773,U_8771,U_8772] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8770),U_8771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8773),U_8770))
| sP611(U_8770,U_8773,U_8771,U_8772)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8771)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP611])],[f_2205_4]) ).
cnf(f_2205_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8770),U_8771)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8773),U_8770))
| sP611(U_8770,U_8773,U_8771,U_8772)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8771)) ),
inference(clausify,[status(thm)],[f_2205_5]) ).
cnf(f_2205_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK197(U_8773,U_8772,U_8771,U_8770)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8771)))
| ~ sP611(U_8770,U_8773,U_8771,U_8772) ),
inference(clausify,[status(thm)],[f_2205_5]) ).
cnf(f_2205_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK198(U_8773,U_8772,U_8771,U_8770)),U_8772))
| ~ sP611(U_8770,U_8773,U_8771,U_8772) ),
inference(clausify,[status(thm)],[f_2205_5]) ).
cnf(f_2205_9,plain,
( U_8770 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK198(U_8773,U_8772,U_8771,U_8770)),sK197(U_8773,U_8772,U_8771,U_8770))
| ~ sP611(U_8770,U_8773,U_8771,U_8772) ),
inference(clausify,[status(thm)],[f_2205_5]) ).
fof(f_2206_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_2206_2,plain,
! [U_8781,U_8780] :
( ( ( ? [U_8779] : hBOOL(hAPP(U_8781,U_8779))
| ! [U_8778] :
( ~ hBOOL(hAPP(U_8781,U_8778))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8778),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) ) )
& ( ? [U_8777] :
( hBOOL(hAPP(U_8781,U_8777))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8777),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) )
| ! [U_8776] : ~ hBOOL(hAPP(U_8781,U_8776)) ) )
| ? [U_8775,U_8774] :
( ( ~ hBOOL(hAPP(U_8781,U_8775))
& hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8775),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8774),U_8780)))) )
| ( ~ hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8775),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8774),U_8780))))
& hBOOL(hAPP(U_8781,U_8775)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8780)) ),
inference(variable_rename,[status(thm)],[f_2206_1]) ).
fof(f_2206_3,plain,
! [U_8781,U_8780] :
( ( ( ? [U_8779] : hBOOL(hAPP(U_8781,U_8779))
| ! [U_8778] :
( ~ hBOOL(hAPP(U_8781,U_8778))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8778),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) ) )
& ( ? [U_8777] :
( hBOOL(hAPP(U_8781,U_8777))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8777),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) )
| ! [U_8776] : ~ hBOOL(hAPP(U_8781,U_8776)) ) )
| ? [U_8785] :
( ? [U_8783] : hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8783),U_8780))))
& ~ hBOOL(hAPP(U_8781,U_8785)) )
| ? [U_8784] :
( ? [U_8782] : ~ hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8782),U_8780))))
& hBOOL(hAPP(U_8781,U_8784)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8780)) ),
inference(miniscope,[status(thm)],[f_2206_2]) ).
fof(f_2206_4,plain,
! [U_8781,U_8780] :
( ( ( ? [U_8779] : hBOOL(hAPP(U_8781,U_8779))
| ! [U_8778] :
( ~ hBOOL(hAPP(U_8781,U_8778))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8778),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) ) )
& ( ? [U_8777] :
( hBOOL(hAPP(U_8781,U_8777))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8777),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) )
| ! [U_8776] : ~ hBOOL(hAPP(U_8781,U_8776)) ) )
| ? [U_8785] :
( ? [U_8783] : hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8783),U_8780))))
& ~ hBOOL(hAPP(U_8781,U_8785)) )
| ( ? [U_8782] : ~ hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK199(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8782),U_8780))))
& hBOOL(hAPP(U_8781,sK199(U_8781,U_8780))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8780)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_8784,sK199(U_8781,U_8780))],[f_2206_3]) ).
fof(f_2206_5,plain,
! [U_8781,U_8780] :
( ( ( ? [U_8779] : hBOOL(hAPP(U_8781,U_8779))
| ! [U_8778] :
( ~ hBOOL(hAPP(U_8781,U_8778))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8778),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) ) )
& ( ? [U_8777] :
( hBOOL(hAPP(U_8781,U_8777))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8777),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) )
| ! [U_8776] : ~ hBOOL(hAPP(U_8781,U_8776)) ) )
| ? [U_8785] :
( ? [U_8783] : hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8783),U_8780))))
& ~ hBOOL(hAPP(U_8781,U_8785)) )
| ( ~ hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK199(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK200(U_8781,U_8780)),U_8780))))
& hBOOL(hAPP(U_8781,sK199(U_8781,U_8780))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8780)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_8782,sK200(U_8781,U_8780))],[f_2206_4]) ).
fof(f_2206_6,plain,
! [U_8781,U_8780] :
( ( ( ? [U_8779] : hBOOL(hAPP(U_8781,U_8779))
| ! [U_8778] :
( ~ hBOOL(hAPP(U_8781,U_8778))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8778),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) ) )
& ( ? [U_8777] :
( hBOOL(hAPP(U_8781,U_8777))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8777),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) )
| ! [U_8776] : ~ hBOOL(hAPP(U_8781,U_8776)) ) )
| ( ? [U_8783] : hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK201(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8783),U_8780))))
& ~ hBOOL(hAPP(U_8781,sK201(U_8781,U_8780))) )
| ( ~ hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK199(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK200(U_8781,U_8780)),U_8780))))
& hBOOL(hAPP(U_8781,sK199(U_8781,U_8780))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8780)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_8785,sK201(U_8781,U_8780))],[f_2206_5]) ).
fof(f_2206_7,plain,
! [U_8781,U_8780] :
( ( ( ? [U_8779] : hBOOL(hAPP(U_8781,U_8779))
| ! [U_8778] :
( ~ hBOOL(hAPP(U_8781,U_8778))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8778),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) ) )
& ( ? [U_8777] :
( hBOOL(hAPP(U_8781,U_8777))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8777),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) )
| ! [U_8776] : ~ hBOOL(hAPP(U_8781,U_8776)) ) )
| ( hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK201(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK202(U_8781,U_8780)),U_8780))))
& ~ hBOOL(hAPP(U_8781,sK201(U_8781,U_8780))) )
| ( ~ hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK199(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK200(U_8781,U_8780)),U_8780))))
& hBOOL(hAPP(U_8781,sK199(U_8781,U_8780))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8780)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_8783,sK202(U_8781,U_8780))],[f_2206_6]) ).
fof(f_2206_8,plain,
! [U_8781,U_8780] :
( ( ( ? [U_8779] : hBOOL(hAPP(U_8781,U_8779))
| ! [U_8778] :
( ~ hBOOL(hAPP(U_8781,U_8778))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8778),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) ) )
& ( ( hBOOL(hAPP(U_8781,sK203(U_8781,U_8780)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK203(U_8781,U_8780)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) )
| ! [U_8776] : ~ hBOOL(hAPP(U_8781,U_8776)) ) )
| ( hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK201(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK202(U_8781,U_8780)),U_8780))))
& ~ hBOOL(hAPP(U_8781,sK201(U_8781,U_8780))) )
| ( ~ hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK199(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK200(U_8781,U_8780)),U_8780))))
& hBOOL(hAPP(U_8781,sK199(U_8781,U_8780))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8780)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_8777,sK203(U_8781,U_8780))],[f_2206_7]) ).
fof(f_2206_9,plain,
! [U_8781,U_8780] :
( ( ( hBOOL(hAPP(U_8781,sK204(U_8781,U_8780)))
| ! [U_8778] :
( ~ hBOOL(hAPP(U_8781,U_8778))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8778),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) ) )
& ( ( hBOOL(hAPP(U_8781,sK203(U_8781,U_8780)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK203(U_8781,U_8780)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780))) )
| ! [U_8776] : ~ hBOOL(hAPP(U_8781,U_8776)) ) )
| ( hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK201(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK202(U_8781,U_8780)),U_8780))))
& ~ hBOOL(hAPP(U_8781,sK201(U_8781,U_8780))) )
| ( ~ hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK199(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK200(U_8781,U_8780)),U_8780))))
& hBOOL(hAPP(U_8781,sK199(U_8781,U_8780))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8780)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_8779,sK204(U_8781,U_8780))],[f_2206_8]) ).
fof(f_2206_10,plain,
( ! [U_8780,U_8781] :
( hBOOL(hAPP(U_8781,sK203(U_8781,U_8780)))
| ~ sP614(U_8780,U_8781) )
& ! [U_8780,U_8781] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK203(U_8781,U_8780)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780)))
| ~ sP614(U_8780,U_8781) )
& ! [U_8776,U_8778,U_8780,U_8781] :
( hBOOL(hAPP(U_8781,sK204(U_8781,U_8780)))
| ~ hBOOL(hAPP(U_8781,U_8778))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8778),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780)))
| ~ sP615(U_8776,U_8778,U_8780,U_8781) )
& ! [U_8776,U_8778,U_8780,U_8781] :
( sP614(U_8780,U_8781)
| ~ hBOOL(hAPP(U_8781,U_8776))
| ~ sP615(U_8776,U_8778,U_8780,U_8781) )
& ! [U_8780,U_8781] :
( hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK201(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK202(U_8781,U_8780)),U_8780))))
| ~ sP613(U_8780,U_8781) )
& ! [U_8780,U_8781] :
( ~ hBOOL(hAPP(U_8781,sK201(U_8781,U_8780)))
| ~ sP613(U_8780,U_8781) )
& ! [U_8780,U_8781] :
( ~ hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK199(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK200(U_8781,U_8780)),U_8780))))
| ~ sP612(U_8780,U_8781) )
& ! [U_8780,U_8781] :
( hBOOL(hAPP(U_8781,sK199(U_8781,U_8780)))
| ~ sP612(U_8780,U_8781) )
& ! [U_8776,U_8778,U_8780,U_8781] :
( sP615(U_8776,U_8778,U_8780,U_8781)
| sP613(U_8780,U_8781)
| sP612(U_8780,U_8781)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8780)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP612,sP613,sP614,sP615])],[f_2206_9]) ).
cnf(f_2206_11,plain,
( sP615(U_8776,U_8778,U_8780,U_8781)
| sP613(U_8780,U_8781)
| sP612(U_8780,U_8781)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8780)) ),
inference(clausify,[status(thm)],[f_2206_10]) ).
cnf(f_2206_12,plain,
( hBOOL(hAPP(U_8781,sK199(U_8781,U_8780)))
| ~ sP612(U_8780,U_8781) ),
inference(clausify,[status(thm)],[f_2206_10]) ).
cnf(f_2206_13,plain,
( ~ hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK199(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK200(U_8781,U_8780)),U_8780))))
| ~ sP612(U_8780,U_8781) ),
inference(clausify,[status(thm)],[f_2206_10]) ).
cnf(f_2206_14,plain,
( ~ hBOOL(hAPP(U_8781,sK201(U_8781,U_8780)))
| ~ sP613(U_8780,U_8781) ),
inference(clausify,[status(thm)],[f_2206_10]) ).
cnf(f_2206_15,plain,
( hBOOL(hAPP(U_8781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK201(U_8781,U_8780)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK202(U_8781,U_8780)),U_8780))))
| ~ sP613(U_8780,U_8781) ),
inference(clausify,[status(thm)],[f_2206_10]) ).
cnf(f_2206_16,plain,
( sP614(U_8780,U_8781)
| ~ hBOOL(hAPP(U_8781,U_8776))
| ~ sP615(U_8776,U_8778,U_8780,U_8781) ),
inference(clausify,[status(thm)],[f_2206_10]) ).
cnf(f_2206_17,plain,
( hBOOL(hAPP(U_8781,sK204(U_8781,U_8780)))
| ~ hBOOL(hAPP(U_8781,U_8778))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8778),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780)))
| ~ sP615(U_8776,U_8778,U_8780,U_8781) ),
inference(clausify,[status(thm)],[f_2206_10]) ).
cnf(f_2206_18,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK203(U_8781,U_8780)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8780)))
| ~ sP614(U_8780,U_8781) ),
inference(clausify,[status(thm)],[f_2206_10]) ).
cnf(f_2206_19,plain,
( hBOOL(hAPP(U_8781,sK203(U_8781,U_8780)))
| ~ sP614(U_8780,U_8781) ),
inference(clausify,[status(thm)],[f_2206_10]) ).
fof(f_2207_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_2207_2,plain,
! [U_8791,U_8790,U_8789] :
( ! [U_8788] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8788),U_8789)),U_8791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8788),U_8791))
| ? [U_8787] :
( ? [U_8786] :
( U_8788 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8786),U_8787)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8786),U_8790)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8787),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8789))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8789)) ),
inference(variable_rename,[status(thm)],[f_2207_1]) ).
fof(f_2207_3,plain,
! [U_8791,U_8790,U_8789] :
( ! [U_8788] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8788),U_8789)),U_8791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8788),U_8791))
| ( ? [U_8786] :
( U_8788 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8786),sK205(U_8791,U_8790,U_8789,U_8788))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8786),U_8790)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK205(U_8791,U_8790,U_8789,U_8788)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8789))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8789)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_8787,sK205(U_8791,U_8790,U_8789,U_8788))],[f_2207_2]) ).
fof(f_2207_4,plain,
! [U_8791,U_8790,U_8789] :
( ! [U_8788] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8788),U_8789)),U_8791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8788),U_8791))
| ( U_8788 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK206(U_8791,U_8790,U_8789,U_8788)),sK205(U_8791,U_8790,U_8789,U_8788))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK206(U_8791,U_8790,U_8789,U_8788)),U_8790))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK205(U_8791,U_8790,U_8789,U_8788)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8789))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8789)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_8786,sK206(U_8791,U_8790,U_8789,U_8788))],[f_2207_3]) ).
fof(f_2207_5,plain,
( ! [U_8790,U_8789,U_8788,U_8791] :
( U_8788 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK206(U_8791,U_8790,U_8789,U_8788)),sK205(U_8791,U_8790,U_8789,U_8788))
| ~ sP616(U_8790,U_8789,U_8788,U_8791) )
& ! [U_8790,U_8789,U_8788,U_8791] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK206(U_8791,U_8790,U_8789,U_8788)),U_8790))
| ~ sP616(U_8790,U_8789,U_8788,U_8791) )
& ! [U_8790,U_8789,U_8788,U_8791] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK205(U_8791,U_8790,U_8789,U_8788)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8789)))
| ~ sP616(U_8790,U_8789,U_8788,U_8791) )
& ! [U_8790,U_8789,U_8788,U_8791] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8788),U_8789)),U_8791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8788),U_8791))
| sP616(U_8790,U_8789,U_8788,U_8791)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8789)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP616])],[f_2207_4]) ).
cnf(f_2207_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8788),U_8789)),U_8791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8788),U_8791))
| sP616(U_8790,U_8789,U_8788,U_8791)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8789)) ),
inference(clausify,[status(thm)],[f_2207_5]) ).
cnf(f_2207_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK205(U_8791,U_8790,U_8789,U_8788)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8789)))
| ~ sP616(U_8790,U_8789,U_8788,U_8791) ),
inference(clausify,[status(thm)],[f_2207_5]) ).
cnf(f_2207_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK206(U_8791,U_8790,U_8789,U_8788)),U_8790))
| ~ sP616(U_8790,U_8789,U_8788,U_8791) ),
inference(clausify,[status(thm)],[f_2207_5]) ).
cnf(f_2207_9,plain,
( U_8788 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK206(U_8791,U_8790,U_8789,U_8788)),sK205(U_8791,U_8790,U_8789,U_8788))
| ~ sP616(U_8790,U_8789,U_8788,U_8791) ),
inference(clausify,[status(thm)],[f_2207_5]) ).
fof(f_2208_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_2208_2,plain,
! [U_8797,U_8796,U_8795] :
( ! [U_8794] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8797),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8794),U_8795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8797),U_8794))
| ? [U_8793] :
( ? [U_8792] :
( U_8794 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8792),U_8793)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8792),U_8796)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8793),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8795))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8795)) ),
inference(variable_rename,[status(thm)],[f_2208_1]) ).
fof(f_2208_3,plain,
! [U_8797,U_8796,U_8795] :
( ! [U_8794] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8797),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8794),U_8795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8797),U_8794))
| ( ? [U_8792] :
( U_8794 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8792),sK207(U_8797,U_8796,U_8795,U_8794))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8792),U_8796)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK207(U_8797,U_8796,U_8795,U_8794)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8795))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8795)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_8793,sK207(U_8797,U_8796,U_8795,U_8794))],[f_2208_2]) ).
fof(f_2208_4,plain,
! [U_8797,U_8796,U_8795] :
( ! [U_8794] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8797),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8794),U_8795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8797),U_8794))
| ( U_8794 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK208(U_8797,U_8796,U_8795,U_8794)),sK207(U_8797,U_8796,U_8795,U_8794))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK208(U_8797,U_8796,U_8795,U_8794)),U_8796))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK207(U_8797,U_8796,U_8795,U_8794)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8795))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8795)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_8792,sK208(U_8797,U_8796,U_8795,U_8794))],[f_2208_3]) ).
fof(f_2208_5,plain,
( ! [U_8796,U_8797,U_8794,U_8795] :
( U_8794 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK208(U_8797,U_8796,U_8795,U_8794)),sK207(U_8797,U_8796,U_8795,U_8794))
| ~ sP617(U_8796,U_8797,U_8794,U_8795) )
& ! [U_8796,U_8797,U_8794,U_8795] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK208(U_8797,U_8796,U_8795,U_8794)),U_8796))
| ~ sP617(U_8796,U_8797,U_8794,U_8795) )
& ! [U_8796,U_8797,U_8794,U_8795] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK207(U_8797,U_8796,U_8795,U_8794)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8795)))
| ~ sP617(U_8796,U_8797,U_8794,U_8795) )
& ! [U_8796,U_8797,U_8794,U_8795] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8797),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8794),U_8795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8797),U_8794))
| sP617(U_8796,U_8797,U_8794,U_8795)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8795)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP617])],[f_2208_4]) ).
cnf(f_2208_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8797),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8794),U_8795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8797),U_8794))
| sP617(U_8796,U_8797,U_8794,U_8795)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8795)) ),
inference(clausify,[status(thm)],[f_2208_5]) ).
cnf(f_2208_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK207(U_8797,U_8796,U_8795,U_8794)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8795)))
| ~ sP617(U_8796,U_8797,U_8794,U_8795) ),
inference(clausify,[status(thm)],[f_2208_5]) ).
cnf(f_2208_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK208(U_8797,U_8796,U_8795,U_8794)),U_8796))
| ~ sP617(U_8796,U_8797,U_8794,U_8795) ),
inference(clausify,[status(thm)],[f_2208_5]) ).
cnf(f_2208_9,plain,
( U_8794 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK208(U_8797,U_8796,U_8795,U_8794)),sK207(U_8797,U_8796,U_8795,U_8794))
| ~ sP617(U_8796,U_8797,U_8794,U_8795) ),
inference(clausify,[status(thm)],[f_2208_5]) ).
fof(f_2209_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_2209_2,plain,
! [U_8802,U_8801,U_8800] :
( ! [U_8799] :
( hBOOL(hAPP(U_8801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8802),U_8800))))
| ~ hBOOL(hAPP(U_8801,U_8799)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8802))
| ? [U_8798] :
( ~ hBOOL(hAPP(U_8801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8798),U_8800)))
& hBOOL(hAPP(U_8801,U_8798)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8800)) ),
inference(variable_rename,[status(thm)],[f_2209_1]) ).
fof(f_2209_3,plain,
! [U_8802,U_8801,U_8800] :
( ! [U_8799] :
( hBOOL(hAPP(U_8801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8802),U_8800))))
| ~ hBOOL(hAPP(U_8801,U_8799)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8802))
| ( ~ hBOOL(hAPP(U_8801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK209(U_8802,U_8801,U_8800)),U_8800)))
& hBOOL(hAPP(U_8801,sK209(U_8802,U_8801,U_8800))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8800)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_8798,sK209(U_8802,U_8801,U_8800))],[f_2209_2]) ).
fof(f_2209_4,plain,
( ! [U_8802,U_8800,U_8801] :
( ~ hBOOL(hAPP(U_8801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK209(U_8802,U_8801,U_8800)),U_8800)))
| ~ sP618(U_8802,U_8800,U_8801) )
& ! [U_8802,U_8800,U_8801] :
( hBOOL(hAPP(U_8801,sK209(U_8802,U_8801,U_8800)))
| ~ sP618(U_8802,U_8800,U_8801) )
& ! [U_8802,U_8799,U_8800,U_8801] :
( hBOOL(hAPP(U_8801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8802),U_8800))))
| ~ hBOOL(hAPP(U_8801,U_8799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8802))
| sP618(U_8802,U_8800,U_8801)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8800)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP618])],[f_2209_3]) ).
cnf(f_2209_5,plain,
( hBOOL(hAPP(U_8801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8802),U_8800))))
| ~ hBOOL(hAPP(U_8801,U_8799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8802))
| sP618(U_8802,U_8800,U_8801)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8800)) ),
inference(clausify,[status(thm)],[f_2209_4]) ).
cnf(f_2209_6,plain,
( hBOOL(hAPP(U_8801,sK209(U_8802,U_8801,U_8800)))
| ~ sP618(U_8802,U_8800,U_8801) ),
inference(clausify,[status(thm)],[f_2209_4]) ).
cnf(f_2209_7,plain,
( ~ hBOOL(hAPP(U_8801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK209(U_8802,U_8801,U_8800)),U_8800)))
| ~ sP618(U_8802,U_8800,U_8801) ),
inference(clausify,[status(thm)],[f_2209_4]) ).
fof(f_2210_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_2210_2,plain,
! [U_8806,U_8805] :
( ? [U_8804] :
( hBOOL(hAPP(U_8805,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8804),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_8803] :
( ~ hBOOL(hAPP(U_8805,U_8803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8803),U_8804)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8804),U_8806)) )
| ~ hBOOL(hAPP(U_8805,U_8806))
| hBOOL(hAPP(U_8805,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[f_2210_1]) ).
fof(f_2210_3,plain,
! [U_8806,U_8805] :
( ( hBOOL(hAPP(U_8805,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK210(U_8806,U_8805)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_8803] :
( ~ hBOOL(hAPP(U_8805,U_8803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8803),sK210(U_8806,U_8805))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK210(U_8806,U_8805)),U_8806)) )
| ~ hBOOL(hAPP(U_8805,U_8806))
| hBOOL(hAPP(U_8805,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_8804,sK210(U_8806,U_8805))],[f_2210_2]) ).
fof(f_2210_4,plain,
( ! [U_8806,U_8805,U_8803] :
( hBOOL(hAPP(U_8805,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK210(U_8806,U_8805)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ sP619(U_8806,U_8805,U_8803) )
& ! [U_8806,U_8805,U_8803] :
( ~ hBOOL(hAPP(U_8805,U_8803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8803),sK210(U_8806,U_8805)))
| ~ sP619(U_8806,U_8805,U_8803) )
& ! [U_8806,U_8805,U_8803] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK210(U_8806,U_8805)),U_8806))
| ~ sP619(U_8806,U_8805,U_8803) )
& ! [U_8806,U_8805,U_8803] :
( sP619(U_8806,U_8805,U_8803)
| ~ hBOOL(hAPP(U_8805,U_8806))
| hBOOL(hAPP(U_8805,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP619])],[f_2210_3]) ).
cnf(f_2210_5,plain,
( sP619(U_8806,U_8805,U_8803)
| ~ hBOOL(hAPP(U_8805,U_8806))
| hBOOL(hAPP(U_8805,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_2210_4]) ).
cnf(f_2210_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK210(U_8806,U_8805)),U_8806))
| ~ sP619(U_8806,U_8805,U_8803) ),
inference(clausify,[status(thm)],[f_2210_4]) ).
cnf(f_2210_7,plain,
( ~ hBOOL(hAPP(U_8805,U_8803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8803),sK210(U_8806,U_8805)))
| ~ sP619(U_8806,U_8805,U_8803) ),
inference(clausify,[status(thm)],[f_2210_4]) ).
cnf(f_2210_8,plain,
( hBOOL(hAPP(U_8805,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK210(U_8806,U_8805)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ sP619(U_8806,U_8805,U_8803) ),
inference(clausify,[status(thm)],[f_2210_4]) ).
fof(f_2211_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_2211_2,plain,
! [U_8808] :
( ? [U_8807] :
( U_8808 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8807)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8807)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8808)) ),
inference(variable_rename,[status(thm)],[f_2211_1]) ).
fof(f_2211_3,plain,
! [U_8808] :
( ( U_8808 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK211(U_8808))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK211(U_8808))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8808)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_8807,sK211(U_8808))],[f_2211_2]) ).
fof(f_2211_4,plain,
( ! [U_8808] :
( U_8808 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK211(U_8808))
| ~ sP620(U_8808) )
& ! [U_8808] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK211(U_8808)))
| ~ sP620(U_8808) )
& ! [U_8808] :
( sP620(U_8808)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8808)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP620])],[f_2211_3]) ).
cnf(f_2211_5,plain,
( sP620(U_8808)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8808)) ),
inference(clausify,[status(thm)],[f_2211_4]) ).
cnf(f_2211_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK211(U_8808)))
| ~ sP620(U_8808) ),
inference(clausify,[status(thm)],[f_2211_4]) ).
cnf(f_2211_7,plain,
( U_8808 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK211(U_8808))
| ~ sP620(U_8808) ),
inference(clausify,[status(thm)],[f_2211_4]) ).
fof(f_2212_1,plain,
! [V_f_2,V_S_2,V_T_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_S_2)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_d)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_T_2),V_S_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__right]) ).
fof(f_2212_2,plain,
! [U_8814,U_8813,U_8812,U_8811,U_8810] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8811,U_8810),U_8814),U_8812) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8811,U_8810),U_8814),U_8813)
| ? [U_8809] :
( hAPP(U_8814,U_8809) != c_Groups_Ozero__class_Ozero(U_8810)
& hBOOL(hAPP(hAPP(c_member(U_8811),U_8809),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8811,tc_HOL_Obool)),U_8812),U_8813))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8811,tc_HOL_Obool)),U_8813),U_8812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8811),U_8812))
| ~ class_Groups_Ocomm__monoid__add(U_8810) ),
inference(variable_rename,[status(thm)],[f_2212_1]) ).
fof(f_2212_3,plain,
! [U_8814,U_8813,U_8812,U_8811,U_8810] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8811,U_8810),U_8814),U_8812) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8811,U_8810),U_8814),U_8813)
| ( hAPP(U_8814,sK212(U_8814,U_8813,U_8812,U_8811,U_8810)) != c_Groups_Ozero__class_Ozero(U_8810)
& hBOOL(hAPP(hAPP(c_member(U_8811),sK212(U_8814,U_8813,U_8812,U_8811,U_8810)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8811,tc_HOL_Obool)),U_8812),U_8813))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8811,tc_HOL_Obool)),U_8813),U_8812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8811),U_8812))
| ~ class_Groups_Ocomm__monoid__add(U_8810) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_8809,sK212(U_8814,U_8813,U_8812,U_8811,U_8810))],[f_2212_2]) ).
fof(f_2212_4,plain,
( ! [U_8810,U_8811,U_8812,U_8813,U_8814] :
( hAPP(U_8814,sK212(U_8814,U_8813,U_8812,U_8811,U_8810)) != c_Groups_Ozero__class_Ozero(U_8810)
| ~ sP621(U_8810,U_8811,U_8812,U_8813,U_8814) )
& ! [U_8810,U_8811,U_8812,U_8813,U_8814] :
( hBOOL(hAPP(hAPP(c_member(U_8811),sK212(U_8814,U_8813,U_8812,U_8811,U_8810)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8811,tc_HOL_Obool)),U_8812),U_8813)))
| ~ sP621(U_8810,U_8811,U_8812,U_8813,U_8814) )
& ! [U_8810,U_8811,U_8812,U_8813,U_8814] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8811,U_8810),U_8814),U_8812) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8811,U_8810),U_8814),U_8813)
| sP621(U_8810,U_8811,U_8812,U_8813,U_8814)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8811,tc_HOL_Obool)),U_8813),U_8812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8811),U_8812))
| ~ class_Groups_Ocomm__monoid__add(U_8810) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP621])],[f_2212_3]) ).
cnf(f_2212_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8811,U_8810),U_8814),U_8812) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8811,U_8810),U_8814),U_8813)
| sP621(U_8810,U_8811,U_8812,U_8813,U_8814)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8811,tc_HOL_Obool)),U_8813),U_8812))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8811),U_8812))
| ~ class_Groups_Ocomm__monoid__add(U_8810) ),
inference(clausify,[status(thm)],[f_2212_4]) ).
cnf(f_2212_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8811),sK212(U_8814,U_8813,U_8812,U_8811,U_8810)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8811,tc_HOL_Obool)),U_8812),U_8813)))
| ~ sP621(U_8810,U_8811,U_8812,U_8813,U_8814) ),
inference(clausify,[status(thm)],[f_2212_4]) ).
cnf(f_2212_7,plain,
( hAPP(U_8814,sK212(U_8814,U_8813,U_8812,U_8811,U_8810)) != c_Groups_Ozero__class_Ozero(U_8810)
| ~ sP621(U_8810,U_8811,U_8812,U_8813,U_8814) ),
inference(clausify,[status(thm)],[f_2212_4]) ).
fof(f_2213_1,plain,
! [V_f_2,V_S_2,V_T_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),V_T_2)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_d)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_T_2),V_S_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__left]) ).
fof(f_2213_2,plain,
! [U_8820,U_8819,U_8818,U_8817,U_8816] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8817,U_8816),U_8820),U_8819) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8817,U_8816),U_8820),U_8818)
| ? [U_8815] :
( hAPP(U_8820,U_8815) != c_Groups_Ozero__class_Ozero(U_8816)
& hBOOL(hAPP(hAPP(c_member(U_8817),U_8815),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8817,tc_HOL_Obool)),U_8818),U_8819))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8817,tc_HOL_Obool)),U_8819),U_8818))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8817),U_8818))
| ~ class_Groups_Ocomm__monoid__add(U_8816) ),
inference(variable_rename,[status(thm)],[f_2213_1]) ).
fof(f_2213_3,plain,
! [U_8820,U_8819,U_8818,U_8817,U_8816] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8817,U_8816),U_8820),U_8819) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8817,U_8816),U_8820),U_8818)
| ( hAPP(U_8820,sK213(U_8820,U_8819,U_8818,U_8817,U_8816)) != c_Groups_Ozero__class_Ozero(U_8816)
& hBOOL(hAPP(hAPP(c_member(U_8817),sK213(U_8820,U_8819,U_8818,U_8817,U_8816)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8817,tc_HOL_Obool)),U_8818),U_8819))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8817,tc_HOL_Obool)),U_8819),U_8818))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8817),U_8818))
| ~ class_Groups_Ocomm__monoid__add(U_8816) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_8815,sK213(U_8820,U_8819,U_8818,U_8817,U_8816))],[f_2213_2]) ).
fof(f_2213_4,plain,
( ! [U_8818,U_8816,U_8817,U_8819,U_8820] :
( hAPP(U_8820,sK213(U_8820,U_8819,U_8818,U_8817,U_8816)) != c_Groups_Ozero__class_Ozero(U_8816)
| ~ sP622(U_8818,U_8816,U_8817,U_8819,U_8820) )
& ! [U_8818,U_8816,U_8817,U_8819,U_8820] :
( hBOOL(hAPP(hAPP(c_member(U_8817),sK213(U_8820,U_8819,U_8818,U_8817,U_8816)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8817,tc_HOL_Obool)),U_8818),U_8819)))
| ~ sP622(U_8818,U_8816,U_8817,U_8819,U_8820) )
& ! [U_8818,U_8816,U_8817,U_8819,U_8820] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8817,U_8816),U_8820),U_8819) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8817,U_8816),U_8820),U_8818)
| sP622(U_8818,U_8816,U_8817,U_8819,U_8820)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8817,tc_HOL_Obool)),U_8819),U_8818))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8817),U_8818))
| ~ class_Groups_Ocomm__monoid__add(U_8816) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP622])],[f_2213_3]) ).
cnf(f_2213_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8817,U_8816),U_8820),U_8819) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8817,U_8816),U_8820),U_8818)
| sP622(U_8818,U_8816,U_8817,U_8819,U_8820)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8817,tc_HOL_Obool)),U_8819),U_8818))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8817),U_8818))
| ~ class_Groups_Ocomm__monoid__add(U_8816) ),
inference(clausify,[status(thm)],[f_2213_4]) ).
cnf(f_2213_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8817),sK213(U_8820,U_8819,U_8818,U_8817,U_8816)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8817,tc_HOL_Obool)),U_8818),U_8819)))
| ~ sP622(U_8818,U_8816,U_8817,U_8819,U_8820) ),
inference(clausify,[status(thm)],[f_2213_4]) ).
cnf(f_2213_7,plain,
( hAPP(U_8820,sK213(U_8820,U_8819,U_8818,U_8817,U_8816)) != c_Groups_Ozero__class_Ozero(U_8816)
| ~ sP622(U_8818,U_8816,U_8817,U_8819,U_8820) ),
inference(clausify,[status(thm)],[f_2213_4]) ).
fof(f_2214_1,plain,
! [V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),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_c),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Pow]) ).
fof(f_2214_2,plain,
! [U_8822,U_8821] :
( hAPP(c_Finite__Set_Ocard(tc_fun(U_8821,tc_HOL_Obool)),hAPP(c_Set_OPow(U_8821),U_8822)) = 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_8821),U_8822))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8821),U_8822)) ),
inference(variable_rename,[status(thm)],[f_2214_1]) ).
fof(f_2214_3,plain,
! [U_8822,U_8821] :
( hAPP(c_Finite__Set_Ocard(tc_fun(U_8821,tc_HOL_Obool)),hAPP(c_Set_OPow(U_8821),U_8822)) = 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_8821),U_8822))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8821),U_8822)) ),
inference(definitional_conversion,[status(esa)],[f_2214_2]) ).
cnf(f_2214_4,plain,
( hAPP(c_Finite__Set_Ocard(tc_fun(U_8821,tc_HOL_Obool)),hAPP(c_Set_OPow(U_8821),U_8822)) = 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_8821),U_8822))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8821),U_8822)) ),
inference(clausify,[status(thm)],[f_2214_3]) ).
fof(f_2215_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_2215_2,plain,
! [U_8824,U_8823] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8823),hAPP(c_Nat_OSuc,U_8824)) = 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_8824)),U_8823),
inference(variable_rename,[status(thm)],[f_2215_1]) ).
fof(f_2215_3,plain,
! [U_8823,U_8824] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8823),hAPP(c_Nat_OSuc,U_8824)) = 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_8824)),U_8823),
inference(definitional_conversion,[status(esa)],[f_2215_2]) ).
cnf(f_2215_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_8823),hAPP(c_Nat_OSuc,U_8824)) = 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_8824)),U_8823),
inference(clausify,[status(thm)],[f_2215_3]) ).
fof(f_2216_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_2216_2,plain,
! [U_8826,U_8825] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8825)),U_8826) = 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_8825)),U_8826),
inference(variable_rename,[status(thm)],[f_2216_1]) ).
fof(f_2216_3,plain,
! [U_8825,U_8826] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8825)),U_8826) = 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_8825)),U_8826),
inference(definitional_conversion,[status(esa)],[f_2216_2]) ).
cnf(f_2216_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8825)),U_8826) = 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_8825)),U_8826),
inference(clausify,[status(thm)],[f_2216_3]) ).
fof(f_2217_1,plain,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_PowI]) ).
fof(f_2217_2,plain,
! [U_8829,U_8828,U_8827] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8827,tc_HOL_Obool)),U_8828),hAPP(c_Set_OPow(U_8827),U_8829)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8827,tc_HOL_Obool)),U_8828),U_8829)) ),
inference(variable_rename,[status(thm)],[f_2217_1]) ).
fof(f_2217_3,plain,
! [U_8827,U_8828,U_8829] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8827,tc_HOL_Obool)),U_8828),hAPP(c_Set_OPow(U_8827),U_8829)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8827,tc_HOL_Obool)),U_8828),U_8829)) ),
inference(definitional_conversion,[status(esa)],[f_2217_2]) ).
cnf(f_2217_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8827,tc_HOL_Obool)),U_8828),hAPP(c_Set_OPow(U_8827),U_8829)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8827,tc_HOL_Obool)),U_8828),U_8829)) ),
inference(clausify,[status(thm)],[f_2217_3]) ).
fof(f_2218_1,plain,
! [V_A_2,T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff]) ).
fof(f_2218_2,plain,
! [U_8831,U_8830] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8830,tc_HOL_Obool)),hAPP(c_Set_OPow(U_8830),U_8831)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8830),U_8831)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8830),U_8831))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8830,tc_HOL_Obool)),hAPP(c_Set_OPow(U_8830),U_8831))) ) ),
inference(variable_rename,[status(thm)],[f_2218_1]) ).
fof(f_2218_3,plain,
( ! [U_8835,U_8833] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8833,tc_HOL_Obool)),hAPP(c_Set_OPow(U_8833),U_8835)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8833),U_8835)) )
& ! [U_8834,U_8832] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8832),U_8834))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8832,tc_HOL_Obool)),hAPP(c_Set_OPow(U_8832),U_8834))) ) ),
inference(miniscope,[status(thm)],[f_2218_2]) ).
fof(f_2218_4,plain,
( ! [U_8833,U_8835] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8833,tc_HOL_Obool)),hAPP(c_Set_OPow(U_8833),U_8835)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8833),U_8835)) )
& ! [U_8834,U_8832] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8832),U_8834))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8832,tc_HOL_Obool)),hAPP(c_Set_OPow(U_8832),U_8834))) ) ),
inference(definitional_conversion,[status(esa)],[f_2218_3]) ).
cnf(f_2218_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8832),U_8834))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8832,tc_HOL_Obool)),hAPP(c_Set_OPow(U_8832),U_8834))) ),
inference(clausify,[status(thm)],[f_2218_4]) ).
cnf(f_2218_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_8833,tc_HOL_Obool)),hAPP(c_Set_OPow(U_8833),U_8835)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8833),U_8835)) ),
inference(clausify,[status(thm)],[f_2218_4]) ).
fof(f_2219_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_d] :
( hAPP(c_Set_Oimage(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),c_Set_Oimage(T_d,T_c,V_f_2)),hAPP(c_Set_OPow(T_d),V_A_2)) = hAPP(c_Set_OPow(T_c),V_B_2)
| hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2) != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_image__Pow__surj]) ).
fof(f_2219_2,plain,
! [U_8840,U_8839,U_8838,U_8837,U_8836] :
( hAPP(c_Set_Oimage(tc_fun(U_8836,tc_HOL_Obool),tc_fun(U_8837,tc_HOL_Obool),c_Set_Oimage(U_8836,U_8837,U_8838)),hAPP(c_Set_OPow(U_8836),U_8839)) = hAPP(c_Set_OPow(U_8837),U_8840)
| hAPP(c_Set_Oimage(U_8836,U_8837,U_8838),U_8839) != U_8840 ),
inference(variable_rename,[status(thm)],[f_2219_1]) ).
fof(f_2219_3,plain,
! [U_8836,U_8837,U_8838,U_8839,U_8840] :
( hAPP(c_Set_Oimage(tc_fun(U_8836,tc_HOL_Obool),tc_fun(U_8837,tc_HOL_Obool),c_Set_Oimage(U_8836,U_8837,U_8838)),hAPP(c_Set_OPow(U_8836),U_8839)) = hAPP(c_Set_OPow(U_8837),U_8840)
| hAPP(c_Set_Oimage(U_8836,U_8837,U_8838),U_8839) != U_8840 ),
inference(definitional_conversion,[status(esa)],[f_2219_2]) ).
cnf(f_2219_4,plain,
( hAPP(c_Set_Oimage(tc_fun(U_8836,tc_HOL_Obool),tc_fun(U_8837,tc_HOL_Obool),c_Set_Oimage(U_8836,U_8837,U_8838)),hAPP(c_Set_OPow(U_8836),U_8839)) = hAPP(c_Set_OPow(U_8837),U_8840)
| hAPP(c_Set_Oimage(U_8836,U_8837,U_8838),U_8839) != U_8840 ),
inference(clausify,[status(thm)],[f_2219_3]) ).
fof(f_2220_1,plain,
! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_A_2))),
inference(fof_nnf,[status(thm)],[fact_Pow__top]) ).
fof(f_2220_2,plain,
! [U_8842,U_8841] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_8841,tc_HOL_Obool)),U_8842),hAPP(c_Set_OPow(U_8841),U_8842))),
inference(variable_rename,[status(thm)],[f_2220_1]) ).
fof(f_2220_3,plain,
! [U_8841,U_8842] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_8841,tc_HOL_Obool)),U_8842),hAPP(c_Set_OPow(U_8841),U_8842))),
inference(definitional_conversion,[status(esa)],[f_2220_2]) ).
cnf(f_2220_4,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_8841,tc_HOL_Obool)),U_8842),hAPP(c_Set_OPow(U_8841),U_8842))),
inference(clausify,[status(thm)],[f_2220_3]) ).
fof(f_2221_1,plain,
! [V_A_2,T_c,B_f] : hAPP(c_Set_Oimage(T_c,tc_fun(T_c,tc_HOL_Obool),B_f),V_A_2) != hAPP(c_Set_OPow(T_c),V_A_2),
inference(fof_nnf,[status(thm)],[fact_Cantors__paradox]) ).
fof(f_2221_2,plain,
! [U_8845,U_8844,U_8843] : hAPP(c_Set_Oimage(U_8844,tc_fun(U_8844,tc_HOL_Obool),U_8843),U_8845) != hAPP(c_Set_OPow(U_8844),U_8845),
inference(variable_rename,[status(thm)],[f_2221_1]) ).
fof(f_2221_3,plain,
! [U_8843,U_8844,U_8845] : hAPP(c_Set_Oimage(U_8844,tc_fun(U_8844,tc_HOL_Obool),U_8843),U_8845) != hAPP(c_Set_OPow(U_8844),U_8845),
inference(definitional_conversion,[status(esa)],[f_2221_2]) ).
cnf(f_2221_4,plain,
hAPP(c_Set_Oimage(U_8844,tc_fun(U_8844,tc_HOL_Obool),U_8843),U_8845) != hAPP(c_Set_OPow(U_8844),U_8845),
inference(clausify,[status(thm)],[f_2221_3]) ).
fof(f_2222_1,plain,
! [V_A_2,T_c] : hAPP(c_Set_OPow(T_c),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Pow__not__empty]) ).
fof(f_2222_2,plain,
! [U_8847,U_8846] : hAPP(c_Set_OPow(U_8846),U_8847) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8846,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2222_1]) ).
fof(f_2222_3,plain,
! [U_8846,U_8847] : hAPP(c_Set_OPow(U_8846),U_8847) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8846,tc_HOL_Obool),tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_2222_2]) ).
cnf(f_2222_4,plain,
hAPP(c_Set_OPow(U_8846),U_8847) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8846,tc_HOL_Obool),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2222_3]) ).
fof(f_2223_1,plain,
! [V_B_2,V_A_2,T_d,T_c] : hAPP(c_Set_OPow(T_c),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(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_d),c_Set_OPow(T_c)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Pow__INT__eq]) ).
fof(f_2223_2,plain,
! [U_8851,U_8850,U_8849,U_8848] : hAPP(c_Set_OPow(U_8848),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8849,tc_fun(U_8848,tc_HOL_Obool)),U_8850),U_8851)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8849,tc_fun(tc_fun(U_8848,tc_HOL_Obool),tc_HOL_Obool)),U_8850),hAPP(hAPP(c_COMBB(tc_fun(U_8848,tc_HOL_Obool),tc_fun(tc_fun(U_8848,tc_HOL_Obool),tc_HOL_Obool),U_8849),c_Set_OPow(U_8848)),U_8851)),
inference(variable_rename,[status(thm)],[f_2223_1]) ).
fof(f_2223_3,plain,
! [U_8849,U_8848,U_8850,U_8851] : hAPP(c_Set_OPow(U_8848),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8849,tc_fun(U_8848,tc_HOL_Obool)),U_8850),U_8851)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8849,tc_fun(tc_fun(U_8848,tc_HOL_Obool),tc_HOL_Obool)),U_8850),hAPP(hAPP(c_COMBB(tc_fun(U_8848,tc_HOL_Obool),tc_fun(tc_fun(U_8848,tc_HOL_Obool),tc_HOL_Obool),U_8849),c_Set_OPow(U_8848)),U_8851)),
inference(definitional_conversion,[status(esa)],[f_2223_2]) ).
cnf(f_2223_4,plain,
hAPP(c_Set_OPow(U_8848),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8849,tc_fun(U_8848,tc_HOL_Obool)),U_8850),U_8851)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8849,tc_fun(tc_fun(U_8848,tc_HOL_Obool),tc_HOL_Obool)),U_8850),hAPP(hAPP(c_COMBB(tc_fun(U_8848,tc_HOL_Obool),tc_fun(tc_fun(U_8848,tc_HOL_Obool),tc_HOL_Obool),U_8849),c_Set_OPow(U_8848)),U_8851)),
inference(clausify,[status(thm)],[f_2223_3]) ).
fof(f_2224_1,plain,
! [V_B_2,T_c] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),hAPP(c_Set_OPow(T_c),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Pow__bottom]) ).
fof(f_2224_2,plain,
! [U_8853,U_8852] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_8852,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8852,tc_HOL_Obool))),hAPP(c_Set_OPow(U_8852),U_8853))),
inference(variable_rename,[status(thm)],[f_2224_1]) ).
fof(f_2224_3,plain,
! [U_8852,U_8853] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_8852,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8852,tc_HOL_Obool))),hAPP(c_Set_OPow(U_8852),U_8853))),
inference(definitional_conversion,[status(esa)],[f_2224_2]) ).
cnf(f_2224_4,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_8852,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8852,tc_HOL_Obool))),hAPP(c_Set_OPow(U_8852),U_8853))),
inference(clausify,[status(thm)],[f_2224_3]) ).
fof(f_2225_1,plain,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_PowD]) ).
fof(f_2225_2,plain,
! [U_8856,U_8855,U_8854] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8854,tc_HOL_Obool)),U_8855),U_8856))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_8854,tc_HOL_Obool)),U_8855),hAPP(c_Set_OPow(U_8854),U_8856))) ),
inference(variable_rename,[status(thm)],[f_2225_1]) ).
fof(f_2225_3,plain,
! [U_8854,U_8855,U_8856] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8854,tc_HOL_Obool)),U_8855),U_8856))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_8854,tc_HOL_Obool)),U_8855),hAPP(c_Set_OPow(U_8854),U_8856))) ),
inference(definitional_conversion,[status(esa)],[f_2225_2]) ).
cnf(f_2225_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8854,tc_HOL_Obool)),U_8855),U_8856))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_8854,tc_HOL_Obool)),U_8855),hAPP(c_Set_OPow(U_8854),U_8856))) ),
inference(clausify,[status(thm)],[f_2225_3]) ).
fof(f_2226_1,plain,
! [V_B_2,V_A_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,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)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Pow__iff]) ).
fof(f_2226_2,plain,
! [U_8859,U_8858,U_8857] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8857,tc_HOL_Obool)),U_8858),hAPP(c_Set_OPow(U_8857),U_8859)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8857,tc_HOL_Obool)),U_8858),U_8859)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8857,tc_HOL_Obool)),U_8858),U_8859))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_8857,tc_HOL_Obool)),U_8858),hAPP(c_Set_OPow(U_8857),U_8859))) ) ),
inference(variable_rename,[status(thm)],[f_2226_1]) ).
fof(f_2226_3,plain,
( ! [U_8865,U_8863,U_8861] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8861,tc_HOL_Obool)),U_8863),hAPP(c_Set_OPow(U_8861),U_8865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8861,tc_HOL_Obool)),U_8863),U_8865)) )
& ! [U_8864,U_8862,U_8860] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8860,tc_HOL_Obool)),U_8862),U_8864))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_8860,tc_HOL_Obool)),U_8862),hAPP(c_Set_OPow(U_8860),U_8864))) ) ),
inference(miniscope,[status(thm)],[f_2226_2]) ).
fof(f_2226_4,plain,
( ! [U_8861,U_8863,U_8865] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8861,tc_HOL_Obool)),U_8863),hAPP(c_Set_OPow(U_8861),U_8865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8861,tc_HOL_Obool)),U_8863),U_8865)) )
& ! [U_8862,U_8860,U_8864] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8860,tc_HOL_Obool)),U_8862),U_8864))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_8860,tc_HOL_Obool)),U_8862),hAPP(c_Set_OPow(U_8860),U_8864))) ) ),
inference(definitional_conversion,[status(esa)],[f_2226_3]) ).
cnf(f_2226_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8860,tc_HOL_Obool)),U_8862),U_8864))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_8860,tc_HOL_Obool)),U_8862),hAPP(c_Set_OPow(U_8860),U_8864))) ),
inference(clausify,[status(thm)],[f_2226_4]) ).
cnf(f_2226_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8861,tc_HOL_Obool)),U_8863),hAPP(c_Set_OPow(U_8861),U_8865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8861,tc_HOL_Obool)),U_8863),U_8865)) ),
inference(clausify,[status(thm)],[f_2226_4]) ).
fof(f_2227_1,plain,
! [V_f2_2,V_f1_2,T_c] : c_Nat_Onat_Onat__case(T_c,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_2227_2,plain,
! [U_8868,U_8867,U_8866] : c_Nat_Onat_Onat__case(U_8866,U_8867,U_8868,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8867,
inference(variable_rename,[status(thm)],[f_2227_1]) ).
fof(f_2227_3,plain,
! [U_8867,U_8866,U_8868] : c_Nat_Onat_Onat__case(U_8866,U_8867,U_8868,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8867,
inference(definitional_conversion,[status(esa)],[f_2227_2]) ).
cnf(f_2227_4,plain,
c_Nat_Onat_Onat__case(U_8866,U_8867,U_8868,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_8867,
inference(clausify,[status(thm)],[f_2227_3]) ).
fof(f_2228_1,plain,
! [V_nat_2,V_f2_2,V_f1_2,T_c] : c_Nat_Onat_Onat__case(T_c,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_2228_2,plain,
! [U_8872,U_8871,U_8870,U_8869] : c_Nat_Onat_Onat__case(U_8869,U_8870,U_8871,hAPP(c_Nat_OSuc,U_8872)) = hAPP(U_8871,U_8872),
inference(variable_rename,[status(thm)],[f_2228_1]) ).
fof(f_2228_3,plain,
! [U_8869,U_8870,U_8871,U_8872] : c_Nat_Onat_Onat__case(U_8869,U_8870,U_8871,hAPP(c_Nat_OSuc,U_8872)) = hAPP(U_8871,U_8872),
inference(definitional_conversion,[status(esa)],[f_2228_2]) ).
cnf(f_2228_4,plain,
c_Nat_Onat_Onat__case(U_8869,U_8870,U_8871,hAPP(c_Nat_OSuc,U_8872)) = hAPP(U_8871,U_8872),
inference(clausify,[status(thm)],[f_2228_3]) ).
fof(f_2229_1,plain,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)),hAPP(c_Set_OPow(T_c),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Pow__mono]) ).
fof(f_2229_2,plain,
! [U_8875,U_8874,U_8873] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_8873,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_8873),U_8874)),hAPP(c_Set_OPow(U_8873),U_8875)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8873,tc_HOL_Obool)),U_8874),U_8875)) ),
inference(variable_rename,[status(thm)],[f_2229_1]) ).
fof(f_2229_3,plain,
! [U_8873,U_8874,U_8875] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_8873,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_8873),U_8874)),hAPP(c_Set_OPow(U_8873),U_8875)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8873,tc_HOL_Obool)),U_8874),U_8875)) ),
inference(definitional_conversion,[status(esa)],[f_2229_2]) ).
cnf(f_2229_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_8873,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_8873),U_8874)),hAPP(c_Set_OPow(U_8873),U_8875)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8873,tc_HOL_Obool)),U_8874),U_8875)) ),
inference(clausify,[status(thm)],[f_2229_3]) ).
fof(f_2230_1,plain,
! [V_A_2,V_a_2,T_c] : hAPP(c_Set_OPow(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_c),V_a_2)),hAPP(c_Set_OPow(T_c),V_A_2))),
inference(fof_nnf,[status(thm)],[fact_Pow__insert]) ).
fof(f_2230_2,plain,
! [U_8878,U_8877,U_8876] : hAPP(c_Set_OPow(U_8876),hAPP(hAPP(c_Set_Oinsert(U_8876),U_8877),U_8878)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_8876,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_8876),U_8878)),hAPP(c_Set_Oimage(tc_fun(U_8876,tc_HOL_Obool),tc_fun(U_8876,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_8876),U_8877)),hAPP(c_Set_OPow(U_8876),U_8878))),
inference(variable_rename,[status(thm)],[f_2230_1]) ).
fof(f_2230_3,plain,
! [U_8876,U_8877,U_8878] : hAPP(c_Set_OPow(U_8876),hAPP(hAPP(c_Set_Oinsert(U_8876),U_8877),U_8878)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_8876,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_8876),U_8878)),hAPP(c_Set_Oimage(tc_fun(U_8876,tc_HOL_Obool),tc_fun(U_8876,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_8876),U_8877)),hAPP(c_Set_OPow(U_8876),U_8878))),
inference(definitional_conversion,[status(esa)],[f_2230_2]) ).
cnf(f_2230_4,plain,
hAPP(c_Set_OPow(U_8876),hAPP(hAPP(c_Set_Oinsert(U_8876),U_8877),U_8878)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_8876,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_8876),U_8878)),hAPP(c_Set_Oimage(tc_fun(U_8876,tc_HOL_Obool),tc_fun(U_8876,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_8876),U_8877)),hAPP(c_Set_OPow(U_8876),U_8878))),
inference(clausify,[status(thm)],[f_2230_3]) ).
fof(f_2231_1,plain,
! [T_c] : hAPP(c_Set_OPow(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Pow__UNIV]) ).
fof(f_2231_2,plain,
! [U_8879] : hAPP(c_Set_OPow(U_8879),c_Orderings_Otop__class_Otop(tc_fun(U_8879,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_8879,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2231_1]) ).
fof(f_2231_3,plain,
! [U_8879] : hAPP(c_Set_OPow(U_8879),c_Orderings_Otop__class_Otop(tc_fun(U_8879,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_8879,tc_HOL_Obool),tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_2231_2]) ).
cnf(f_2231_4,plain,
hAPP(c_Set_OPow(U_8879),c_Orderings_Otop__class_Otop(tc_fun(U_8879,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_8879,tc_HOL_Obool),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2231_3]) ).
fof(f_2232_1,plain,
! [V_B_2,V_A_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_d),c_Set_OPow(T_c)),V_B_2))),hAPP(c_Set_OPow(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_UN__Pow__subset]) ).
fof(f_2232_2,plain,
! [U_8883,U_8882,U_8881,U_8880] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_8880,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8881,tc_fun(tc_fun(U_8880,tc_HOL_Obool),tc_HOL_Obool)),U_8882),hAPP(hAPP(c_COMBB(tc_fun(U_8880,tc_HOL_Obool),tc_fun(tc_fun(U_8880,tc_HOL_Obool),tc_HOL_Obool),U_8881),c_Set_OPow(U_8880)),U_8883))),hAPP(c_Set_OPow(U_8880),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8881,tc_fun(U_8880,tc_HOL_Obool)),U_8882),U_8883)))),
inference(variable_rename,[status(thm)],[f_2232_1]) ).
fof(f_2232_3,plain,
! [U_8880,U_8881,U_8882,U_8883] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_8880,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8881,tc_fun(tc_fun(U_8880,tc_HOL_Obool),tc_HOL_Obool)),U_8882),hAPP(hAPP(c_COMBB(tc_fun(U_8880,tc_HOL_Obool),tc_fun(tc_fun(U_8880,tc_HOL_Obool),tc_HOL_Obool),U_8881),c_Set_OPow(U_8880)),U_8883))),hAPP(c_Set_OPow(U_8880),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8881,tc_fun(U_8880,tc_HOL_Obool)),U_8882),U_8883)))),
inference(definitional_conversion,[status(esa)],[f_2232_2]) ).
cnf(f_2232_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_8880,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8881,tc_fun(tc_fun(U_8880,tc_HOL_Obool),tc_HOL_Obool)),U_8882),hAPP(hAPP(c_COMBB(tc_fun(U_8880,tc_HOL_Obool),tc_fun(tc_fun(U_8880,tc_HOL_Obool),tc_HOL_Obool),U_8881),c_Set_OPow(U_8880)),U_8883))),hAPP(c_Set_OPow(U_8880),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8881,tc_fun(U_8880,tc_HOL_Obool)),U_8882),U_8883)))),
inference(clausify,[status(thm)],[f_2232_3]) ).
fof(f_2233_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(c_Set_OPow(T_c),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(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)),hAPP(c_Set_OPow(T_c),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Pow__Int__eq]) ).
fof(f_2233_2,plain,
! [U_8886,U_8885,U_8884] : hAPP(c_Set_OPow(U_8884),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8884,tc_HOL_Obool)),U_8885),U_8886)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_8884,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_8884),U_8885)),hAPP(c_Set_OPow(U_8884),U_8886)),
inference(variable_rename,[status(thm)],[f_2233_1]) ).
fof(f_2233_3,plain,
! [U_8884,U_8885,U_8886] : hAPP(c_Set_OPow(U_8884),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8884,tc_HOL_Obool)),U_8885),U_8886)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_8884,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_8884),U_8885)),hAPP(c_Set_OPow(U_8884),U_8886)),
inference(definitional_conversion,[status(esa)],[f_2233_2]) ).
cnf(f_2233_4,plain,
hAPP(c_Set_OPow(U_8884),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_8884,tc_HOL_Obool)),U_8885),U_8886)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_8884,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_8884),U_8885)),hAPP(c_Set_OPow(U_8884),U_8886)),
inference(clausify,[status(thm)],[f_2233_3]) ).
fof(f_2234_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),c_Set_Oimage(T_d,T_c,V_f_2)),hAPP(c_Set_OPow(T_d),V_A_2))),hAPP(c_Set_OPow(T_c),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__Pow__mono]) ).
fof(f_2234_2,plain,
! [U_8891,U_8890,U_8889,U_8888,U_8887] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_8887,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_8888,tc_HOL_Obool),tc_fun(U_8887,tc_HOL_Obool),c_Set_Oimage(U_8888,U_8887,U_8889)),hAPP(c_Set_OPow(U_8888),U_8890))),hAPP(c_Set_OPow(U_8887),U_8891)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8887,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8888,U_8887,U_8889),U_8890)),U_8891)) ),
inference(variable_rename,[status(thm)],[f_2234_1]) ).
fof(f_2234_3,plain,
! [U_8887,U_8888,U_8889,U_8890,U_8891] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_8887,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_8888,tc_HOL_Obool),tc_fun(U_8887,tc_HOL_Obool),c_Set_Oimage(U_8888,U_8887,U_8889)),hAPP(c_Set_OPow(U_8888),U_8890))),hAPP(c_Set_OPow(U_8887),U_8891)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8887,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8888,U_8887,U_8889),U_8890)),U_8891)) ),
inference(definitional_conversion,[status(esa)],[f_2234_2]) ).
cnf(f_2234_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_8887,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_8888,tc_HOL_Obool),tc_fun(U_8887,tc_HOL_Obool),c_Set_Oimage(U_8888,U_8887,U_8889)),hAPP(c_Set_OPow(U_8888),U_8890))),hAPP(c_Set_OPow(U_8887),U_8891)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8887,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8888,U_8887,U_8889),U_8890)),U_8891)) ),
inference(clausify,[status(thm)],[f_2234_3]) ).
fof(f_2235_1,plain,
! [T_c] : hAPP(c_Set_OPow(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_Pow__empty]) ).
fof(f_2235_2,plain,
! [U_8892] : hAPP(c_Set_OPow(U_8892),c_Orderings_Obot__class_Obot(tc_fun(U_8892,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_8892,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8892,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8892,tc_HOL_Obool),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2235_1]) ).
fof(f_2235_3,plain,
! [U_8892] : hAPP(c_Set_OPow(U_8892),c_Orderings_Obot__class_Obot(tc_fun(U_8892,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_8892,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8892,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8892,tc_HOL_Obool),tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_2235_2]) ).
cnf(f_2235_4,plain,
hAPP(c_Set_OPow(U_8892),c_Orderings_Obot__class_Obot(tc_fun(U_8892,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_8892,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8892,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_8892,tc_HOL_Obool),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2235_3]) ).
fof(f_2236_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_2236_2,plain,
! [U_8894,U_8893] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8893),hAPP(c_Nat_OSuc,U_8894)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8894),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_8894)),U_8893),
inference(variable_rename,[status(thm)],[f_2236_1]) ).
fof(f_2236_3,plain,
! [U_8893,U_8894] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8893),hAPP(c_Nat_OSuc,U_8894)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8894),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_8894)),U_8893),
inference(definitional_conversion,[status(esa)],[f_2236_2]) ).
cnf(f_2236_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_8893),hAPP(c_Nat_OSuc,U_8894)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8894),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_8894)),U_8893),
inference(clausify,[status(thm)],[f_2236_3]) ).
fof(f_2237_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_2237_2,plain,
! [U_8896,U_8895] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8895)),U_8896) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8895),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_8895)),U_8896),
inference(variable_rename,[status(thm)],[f_2237_1]) ).
fof(f_2237_3,plain,
! [U_8895,U_8896] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8895)),U_8896) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8895),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_8895)),U_8896),
inference(definitional_conversion,[status(esa)],[f_2237_2]) ).
cnf(f_2237_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8895)),U_8896) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8895),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_8895)),U_8896),
inference(clausify,[status(thm)],[f_2237_3]) ).
fof(f_2238_1,plain,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_c),V_A_2)),hAPP(c_Set_OPow(T_c),V_B_2))),hAPP(c_Set_OPow(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Un__Pow__subset]) ).
fof(f_2238_2,plain,
! [U_8899,U_8898,U_8897] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_8897,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_8897,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_8897),U_8898)),hAPP(c_Set_OPow(U_8897),U_8899))),hAPP(c_Set_OPow(U_8897),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8897,tc_HOL_Obool)),U_8898),U_8899)))),
inference(variable_rename,[status(thm)],[f_2238_1]) ).
fof(f_2238_3,plain,
! [U_8897,U_8898,U_8899] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_8897,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_8897,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_8897),U_8898)),hAPP(c_Set_OPow(U_8897),U_8899))),hAPP(c_Set_OPow(U_8897),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8897,tc_HOL_Obool)),U_8898),U_8899)))),
inference(definitional_conversion,[status(esa)],[f_2238_2]) ).
cnf(f_2238_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_8897,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_8897,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_8897),U_8898)),hAPP(c_Set_OPow(U_8897),U_8899))),hAPP(c_Set_OPow(U_8897),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8897,tc_HOL_Obool)),U_8898),U_8899)))),
inference(clausify,[status(thm)],[f_2238_3]) ).
fof(f_2239_1,plain,
! [V_x_2,V_A_2,T_c] :
( ( hBOOL(hAPP(c_Predicate_OPowp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_c),V_A_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_c),V_A_2)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq]) ).
fof(f_2239_2,plain,
! [U_8902,U_8901,U_8900] :
( ( hBOOL(hAPP(c_Predicate_OPowp(U_8900,hAPP(hAPP(c_COMBC(U_8900,tc_fun(U_8900,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8900)),U_8901)),U_8902))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_8900,tc_HOL_Obool)),U_8902),hAPP(c_Set_OPow(U_8900),U_8901))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8900,tc_HOL_Obool)),U_8902),hAPP(c_Set_OPow(U_8900),U_8901)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_8900,hAPP(hAPP(c_COMBC(U_8900,tc_fun(U_8900,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8900)),U_8901)),U_8902)) ) ),
inference(variable_rename,[status(thm)],[f_2239_1]) ).
fof(f_2239_3,plain,
( ! [U_8908,U_8906,U_8904] :
( hBOOL(hAPP(c_Predicate_OPowp(U_8904,hAPP(hAPP(c_COMBC(U_8904,tc_fun(U_8904,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8904)),U_8906)),U_8908))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_8904,tc_HOL_Obool)),U_8908),hAPP(c_Set_OPow(U_8904),U_8906))) )
& ! [U_8907,U_8905,U_8903] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8903,tc_HOL_Obool)),U_8907),hAPP(c_Set_OPow(U_8903),U_8905)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_8903,hAPP(hAPP(c_COMBC(U_8903,tc_fun(U_8903,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8903)),U_8905)),U_8907)) ) ),
inference(miniscope,[status(thm)],[f_2239_2]) ).
fof(f_2239_4,plain,
( ! [U_8904,U_8906,U_8908] :
( hBOOL(hAPP(c_Predicate_OPowp(U_8904,hAPP(hAPP(c_COMBC(U_8904,tc_fun(U_8904,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8904)),U_8906)),U_8908))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_8904,tc_HOL_Obool)),U_8908),hAPP(c_Set_OPow(U_8904),U_8906))) )
& ! [U_8905,U_8903,U_8907] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8903,tc_HOL_Obool)),U_8907),hAPP(c_Set_OPow(U_8903),U_8905)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_8903,hAPP(hAPP(c_COMBC(U_8903,tc_fun(U_8903,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8903)),U_8905)),U_8907)) ) ),
inference(definitional_conversion,[status(esa)],[f_2239_3]) ).
cnf(f_2239_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_8903,tc_HOL_Obool)),U_8907),hAPP(c_Set_OPow(U_8903),U_8905)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_8903,hAPP(hAPP(c_COMBC(U_8903,tc_fun(U_8903,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8903)),U_8905)),U_8907)) ),
inference(clausify,[status(thm)],[f_2239_4]) ).
cnf(f_2239_6,plain,
( hBOOL(hAPP(c_Predicate_OPowp(U_8904,hAPP(hAPP(c_COMBC(U_8904,tc_fun(U_8904,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8904)),U_8906)),U_8908))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_8904,tc_HOL_Obool)),U_8908),hAPP(c_Set_OPow(U_8904),U_8906))) ),
inference(clausify,[status(thm)],[f_2239_4]) ).
fof(f_2240_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_2240_2,plain,
! [U_8910,U_8909] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8909),hAPP(c_Nat_OSuc,U_8910)) = 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_8909),U_8910)),
inference(variable_rename,[status(thm)],[f_2240_1]) ).
fof(f_2240_3,plain,
! [U_8909,U_8910] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8909),hAPP(c_Nat_OSuc,U_8910)) = 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_8909),U_8910)),
inference(definitional_conversion,[status(esa)],[f_2240_2]) ).
cnf(f_2240_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8909),hAPP(c_Nat_OSuc,U_8910)) = 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_8909),U_8910)),
inference(clausify,[status(thm)],[f_2240_3]) ).
fof(f_2241_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_2241_2,plain,
! [U_8914,U_8913,U_8912] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8912),U_8913),U_8914))
| ? [U_8911] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8912),U_8911),U_8913)),U_8914))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8912),U_8911),c_Groups_Oone__class_Oone(U_8912)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8912),c_Groups_Ozero__class_Ozero(U_8912)),U_8911)) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8912) ),
inference(variable_rename,[status(thm)],[f_2241_1]) ).
fof(f_2241_3,plain,
! [U_8914,U_8913,U_8912] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8912),U_8913),U_8914))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8912),sK214(U_8914,U_8913,U_8912)),U_8913)),U_8914))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8912),sK214(U_8914,U_8913,U_8912)),c_Groups_Oone__class_Oone(U_8912)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8912),c_Groups_Ozero__class_Ozero(U_8912)),sK214(U_8914,U_8913,U_8912))) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_8912) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_8911,sK214(U_8914,U_8913,U_8912))],[f_2241_2]) ).
fof(f_2241_4,plain,
( ! [U_8912,U_8913,U_8914] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8912),sK214(U_8914,U_8913,U_8912)),U_8913)),U_8914))
| ~ sP623(U_8912,U_8913,U_8914) )
& ! [U_8912,U_8913,U_8914] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8912),sK214(U_8914,U_8913,U_8912)),c_Groups_Oone__class_Oone(U_8912)))
| ~ sP623(U_8912,U_8913,U_8914) )
& ! [U_8912,U_8913,U_8914] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8912),c_Groups_Ozero__class_Ozero(U_8912)),sK214(U_8914,U_8913,U_8912)))
| ~ sP623(U_8912,U_8913,U_8914) )
& ! [U_8912,U_8913,U_8914] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8912),U_8913),U_8914))
| sP623(U_8912,U_8913,U_8914)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8912) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP623])],[f_2241_3]) ).
cnf(f_2241_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8912),U_8913),U_8914))
| sP623(U_8912,U_8913,U_8914)
| ~ class_Fields_Olinordered__field__inverse__zero(U_8912) ),
inference(clausify,[status(thm)],[f_2241_4]) ).
cnf(f_2241_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8912),c_Groups_Ozero__class_Ozero(U_8912)),sK214(U_8914,U_8913,U_8912)))
| ~ sP623(U_8912,U_8913,U_8914) ),
inference(clausify,[status(thm)],[f_2241_4]) ).
cnf(f_2241_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8912),sK214(U_8914,U_8913,U_8912)),c_Groups_Oone__class_Oone(U_8912)))
| ~ sP623(U_8912,U_8913,U_8914) ),
inference(clausify,[status(thm)],[f_2241_4]) ).
cnf(f_2241_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8912),sK214(U_8914,U_8913,U_8912)),U_8913)),U_8914))
| ~ sP623(U_8912,U_8913,U_8914) ),
inference(clausify,[status(thm)],[f_2241_4]) ).
fof(f_2242_1,plain,
! [V_g_2,V_f_2,V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_c),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_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I2_J]) ).
fof(f_2242_2,plain,
! [U_8920,U_8919,U_8918,U_8917,U_8916] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8916),U_8919),U_8917) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8916),U_8920),U_8918)
| ? [U_8915] :
( hAPP(U_8919,U_8915) != hAPP(U_8920,U_8915)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8915)) )
| ~ c_Nat__Transfer_Onat__set(U_8918)
| U_8917 != U_8918
| ~ class_Groups_Ocomm__monoid__mult(U_8916)
| ~ class_Groups_Ocomm__monoid__add(U_8916) ),
inference(variable_rename,[status(thm)],[f_2242_1]) ).
fof(f_2242_3,plain,
! [U_8920,U_8919,U_8918,U_8917,U_8916] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8916),U_8919),U_8917) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8916),U_8920),U_8918)
| ( hAPP(U_8919,sK215(U_8920,U_8919,U_8918,U_8917,U_8916)) != hAPP(U_8920,sK215(U_8920,U_8919,U_8918,U_8917,U_8916))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK215(U_8920,U_8919,U_8918,U_8917,U_8916))) )
| ~ c_Nat__Transfer_Onat__set(U_8918)
| U_8917 != U_8918
| ~ class_Groups_Ocomm__monoid__mult(U_8916)
| ~ class_Groups_Ocomm__monoid__add(U_8916) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_8915,sK215(U_8920,U_8919,U_8918,U_8917,U_8916))],[f_2242_2]) ).
fof(f_2242_4,plain,
( ! [U_8917,U_8918,U_8919,U_8916,U_8920] :
( hAPP(U_8919,sK215(U_8920,U_8919,U_8918,U_8917,U_8916)) != hAPP(U_8920,sK215(U_8920,U_8919,U_8918,U_8917,U_8916))
| ~ sP624(U_8917,U_8918,U_8919,U_8916,U_8920) )
& ! [U_8917,U_8918,U_8919,U_8916,U_8920] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK215(U_8920,U_8919,U_8918,U_8917,U_8916)))
| ~ sP624(U_8917,U_8918,U_8919,U_8916,U_8920) )
& ! [U_8917,U_8918,U_8919,U_8916,U_8920] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8916),U_8919),U_8917) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8916),U_8920),U_8918)
| sP624(U_8917,U_8918,U_8919,U_8916,U_8920)
| ~ c_Nat__Transfer_Onat__set(U_8918)
| U_8917 != U_8918
| ~ class_Groups_Ocomm__monoid__mult(U_8916)
| ~ class_Groups_Ocomm__monoid__add(U_8916) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP624])],[f_2242_3]) ).
cnf(f_2242_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8916),U_8919),U_8917) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_8916),U_8920),U_8918)
| sP624(U_8917,U_8918,U_8919,U_8916,U_8920)
| ~ c_Nat__Transfer_Onat__set(U_8918)
| U_8917 != U_8918
| ~ class_Groups_Ocomm__monoid__mult(U_8916)
| ~ class_Groups_Ocomm__monoid__add(U_8916) ),
inference(clausify,[status(thm)],[f_2242_4]) ).
cnf(f_2242_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK215(U_8920,U_8919,U_8918,U_8917,U_8916)))
| ~ sP624(U_8917,U_8918,U_8919,U_8916,U_8920) ),
inference(clausify,[status(thm)],[f_2242_4]) ).
cnf(f_2242_7,plain,
( hAPP(U_8919,sK215(U_8920,U_8919,U_8918,U_8917,U_8916)) != hAPP(U_8920,sK215(U_8920,U_8919,U_8918,U_8917,U_8916))
| ~ sP624(U_8917,U_8918,U_8919,U_8916,U_8920) ),
inference(clausify,[status(thm)],[f_2242_4]) ).
fof(f_2243_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_2243_2,plain,
! [U_8927,U_8926,U_8925] :
( ( ( hBOOL(hAPP(hAPP(U_8926,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8927),U_8925)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8927,U_8925)))
| ? [U_8924,U_8923] :
( ~ hBOOL(hAPP(hAPP(U_8926,U_8924),U_8923))
& U_8927 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8925),U_8924)),U_8923)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8923),U_8925))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8923)) ) )
& ( ! [U_8922,U_8921] :
( hBOOL(hAPP(hAPP(U_8926,U_8922),U_8921))
| U_8927 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8925),U_8922)),U_8921)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8921),U_8925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8921)) )
| ~ hBOOL(hAPP(hAPP(U_8926,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8927),U_8925)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8927,U_8925))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8925)) ),
inference(variable_rename,[status(thm)],[f_2243_1]) ).
fof(f_2243_3,plain,
! [U_8927,U_8926,U_8925] :
( ( ( hBOOL(hAPP(hAPP(U_8926,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8927),U_8925)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8927,U_8925)))
| ? [U_8923] :
( ~ hBOOL(hAPP(hAPP(U_8926,sK216(U_8927,U_8926,U_8925)),U_8923))
& U_8927 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8925),sK216(U_8927,U_8926,U_8925))),U_8923)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8923),U_8925))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8923)) ) )
& ( ! [U_8922,U_8921] :
( hBOOL(hAPP(hAPP(U_8926,U_8922),U_8921))
| U_8927 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8925),U_8922)),U_8921)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8921),U_8925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8921)) )
| ~ hBOOL(hAPP(hAPP(U_8926,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8927),U_8925)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8927,U_8925))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8925)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_8924,sK216(U_8927,U_8926,U_8925))],[f_2243_2]) ).
fof(f_2243_4,plain,
! [U_8927,U_8926,U_8925] :
( ( ( hBOOL(hAPP(hAPP(U_8926,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8927),U_8925)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8927,U_8925)))
| ( ~ hBOOL(hAPP(hAPP(U_8926,sK216(U_8927,U_8926,U_8925)),sK217(U_8927,U_8926,U_8925)))
& U_8927 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8925),sK216(U_8927,U_8926,U_8925))),sK217(U_8927,U_8926,U_8925))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK217(U_8927,U_8926,U_8925)),U_8925))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK217(U_8927,U_8926,U_8925))) ) )
& ( ! [U_8922,U_8921] :
( hBOOL(hAPP(hAPP(U_8926,U_8922),U_8921))
| U_8927 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8925),U_8922)),U_8921)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8921),U_8925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8921)) )
| ~ hBOOL(hAPP(hAPP(U_8926,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8927),U_8925)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8927,U_8925))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8925)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_8923,sK217(U_8927,U_8926,U_8925))],[f_2243_3]) ).
fof(f_2243_5,plain,
( ! [U_8925,U_8926,U_8927] :
( ~ hBOOL(hAPP(hAPP(U_8926,sK216(U_8927,U_8926,U_8925)),sK217(U_8927,U_8926,U_8925)))
| ~ sP625(U_8925,U_8926,U_8927) )
& ! [U_8925,U_8926,U_8927] :
( U_8927 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8925),sK216(U_8927,U_8926,U_8925))),sK217(U_8927,U_8926,U_8925))
| ~ sP625(U_8925,U_8926,U_8927) )
& ! [U_8925,U_8926,U_8927] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK217(U_8927,U_8926,U_8925)),U_8925))
| ~ sP625(U_8925,U_8926,U_8927) )
& ! [U_8925,U_8926,U_8927] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK217(U_8927,U_8926,U_8925)))
| ~ sP625(U_8925,U_8926,U_8927) )
& ! [U_8922,U_8921,U_8925,U_8926,U_8927] :
( hBOOL(hAPP(hAPP(U_8926,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8927),U_8925)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8927,U_8925)))
| sP625(U_8925,U_8926,U_8927)
| ~ sP626(U_8922,U_8921,U_8925,U_8926,U_8927) )
& ! [U_8922,U_8921,U_8925,U_8926,U_8927] :
( hBOOL(hAPP(hAPP(U_8926,U_8922),U_8921))
| U_8927 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8925),U_8922)),U_8921)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8921),U_8925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8921))
| ~ hBOOL(hAPP(hAPP(U_8926,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8927),U_8925)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8927,U_8925)))
| ~ sP626(U_8922,U_8921,U_8925,U_8926,U_8927) )
& ! [U_8922,U_8921,U_8925,U_8926,U_8927] :
( sP626(U_8922,U_8921,U_8925,U_8926,U_8927)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8925)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP625,sP626])],[f_2243_4]) ).
cnf(f_2243_6,plain,
( sP626(U_8922,U_8921,U_8925,U_8926,U_8927)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8925)) ),
inference(clausify,[status(thm)],[f_2243_5]) ).
cnf(f_2243_7,plain,
( hBOOL(hAPP(hAPP(U_8926,U_8922),U_8921))
| U_8927 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8925),U_8922)),U_8921)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8921),U_8925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8921))
| ~ hBOOL(hAPP(hAPP(U_8926,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8927),U_8925)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8927,U_8925)))
| ~ sP626(U_8922,U_8921,U_8925,U_8926,U_8927) ),
inference(clausify,[status(thm)],[f_2243_5]) ).
cnf(f_2243_8,plain,
( hBOOL(hAPP(hAPP(U_8926,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8927),U_8925)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8927,U_8925)))
| sP625(U_8925,U_8926,U_8927)
| ~ sP626(U_8922,U_8921,U_8925,U_8926,U_8927) ),
inference(clausify,[status(thm)],[f_2243_5]) ).
cnf(f_2243_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK217(U_8927,U_8926,U_8925)))
| ~ sP625(U_8925,U_8926,U_8927) ),
inference(clausify,[status(thm)],[f_2243_5]) ).
cnf(f_2243_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK217(U_8927,U_8926,U_8925)),U_8925))
| ~ sP625(U_8925,U_8926,U_8927) ),
inference(clausify,[status(thm)],[f_2243_5]) ).
cnf(f_2243_11,plain,
( U_8927 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8925),sK216(U_8927,U_8926,U_8925))),sK217(U_8927,U_8926,U_8925))
| ~ sP625(U_8925,U_8926,U_8927) ),
inference(clausify,[status(thm)],[f_2243_5]) ).
cnf(f_2243_12,plain,
( ~ hBOOL(hAPP(hAPP(U_8926,sK216(U_8927,U_8926,U_8925)),sK217(U_8927,U_8926,U_8925)))
| ~ sP625(U_8925,U_8926,U_8927) ),
inference(clausify,[status(thm)],[f_2243_5]) ).
fof(f_2244_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_2244_2,plain,
! [U_8934,U_8933,U_8932] :
( ( ( hBOOL(hAPP(hAPP(U_8933,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8934),U_8932)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8934,U_8932)))
| ? [U_8931,U_8930] :
( ~ hBOOL(hAPP(hAPP(U_8933,U_8931),U_8930))
& U_8934 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8932),U_8931)),U_8930)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8930),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),U_8930)) ) )
& ( ! [U_8929,U_8928] :
( hBOOL(hAPP(hAPP(U_8933,U_8929),U_8928))
| U_8934 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8932),U_8929)),U_8928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8928),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),U_8928)) )
| ~ hBOOL(hAPP(hAPP(U_8933,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8934),U_8932)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8934,U_8932))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2244_1]) ).
fof(f_2244_3,plain,
! [U_8934,U_8933,U_8932] :
( ( ( hBOOL(hAPP(hAPP(U_8933,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8934),U_8932)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8934,U_8932)))
| ? [U_8930] :
( ~ hBOOL(hAPP(hAPP(U_8933,sK218(U_8934,U_8933,U_8932)),U_8930))
& U_8934 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8932),sK218(U_8934,U_8933,U_8932))),U_8930)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8930),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),U_8930)) ) )
& ( ! [U_8929,U_8928] :
( hBOOL(hAPP(hAPP(U_8933,U_8929),U_8928))
| U_8934 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8932),U_8929)),U_8928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8928),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),U_8928)) )
| ~ hBOOL(hAPP(hAPP(U_8933,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8934),U_8932)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8934,U_8932))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_8931,sK218(U_8934,U_8933,U_8932))],[f_2244_2]) ).
fof(f_2244_4,plain,
! [U_8934,U_8933,U_8932] :
( ( ( hBOOL(hAPP(hAPP(U_8933,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8934),U_8932)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8934,U_8932)))
| ( ~ hBOOL(hAPP(hAPP(U_8933,sK218(U_8934,U_8933,U_8932)),sK219(U_8934,U_8933,U_8932)))
& U_8934 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8932),sK218(U_8934,U_8933,U_8932))),sK219(U_8934,U_8933,U_8932))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK219(U_8934,U_8933,U_8932)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),sK219(U_8934,U_8933,U_8932))) ) )
& ( ! [U_8929,U_8928] :
( hBOOL(hAPP(hAPP(U_8933,U_8929),U_8928))
| U_8934 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8932),U_8929)),U_8928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8928),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),U_8928)) )
| ~ hBOOL(hAPP(hAPP(U_8933,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8934),U_8932)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8934,U_8932))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_8930,sK219(U_8934,U_8933,U_8932))],[f_2244_3]) ).
fof(f_2244_5,plain,
( ! [U_8932,U_8933,U_8934] :
( ~ hBOOL(hAPP(hAPP(U_8933,sK218(U_8934,U_8933,U_8932)),sK219(U_8934,U_8933,U_8932)))
| ~ sP627(U_8932,U_8933,U_8934) )
& ! [U_8932,U_8933,U_8934] :
( U_8934 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8932),sK218(U_8934,U_8933,U_8932))),sK219(U_8934,U_8933,U_8932))
| ~ sP627(U_8932,U_8933,U_8934) )
& ! [U_8932,U_8933,U_8934] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK219(U_8934,U_8933,U_8932)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP627(U_8932,U_8933,U_8934) )
& ! [U_8932,U_8933,U_8934] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),sK219(U_8934,U_8933,U_8932)))
| ~ sP627(U_8932,U_8933,U_8934) )
& ! [U_8929,U_8932,U_8933,U_8928,U_8934] :
( hBOOL(hAPP(hAPP(U_8933,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8934),U_8932)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8934,U_8932)))
| sP627(U_8932,U_8933,U_8934)
| ~ sP628(U_8929,U_8932,U_8933,U_8928,U_8934) )
& ! [U_8929,U_8932,U_8933,U_8928,U_8934] :
( hBOOL(hAPP(hAPP(U_8933,U_8929),U_8928))
| U_8934 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8932),U_8929)),U_8928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8928),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),U_8928))
| ~ hBOOL(hAPP(hAPP(U_8933,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8934),U_8932)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8934,U_8932)))
| ~ sP628(U_8929,U_8932,U_8933,U_8928,U_8934) )
& ! [U_8929,U_8932,U_8933,U_8928,U_8934] :
( sP628(U_8929,U_8932,U_8933,U_8928,U_8934)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP627,sP628])],[f_2244_4]) ).
cnf(f_2244_6,plain,
( sP628(U_8929,U_8932,U_8933,U_8928,U_8934)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2244_5]) ).
cnf(f_2244_7,plain,
( hBOOL(hAPP(hAPP(U_8933,U_8929),U_8928))
| U_8934 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8932),U_8929)),U_8928)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8928),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),U_8928))
| ~ hBOOL(hAPP(hAPP(U_8933,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8934),U_8932)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8934,U_8932)))
| ~ sP628(U_8929,U_8932,U_8933,U_8928,U_8934) ),
inference(clausify,[status(thm)],[f_2244_5]) ).
cnf(f_2244_8,plain,
( hBOOL(hAPP(hAPP(U_8933,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8934),U_8932)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8934,U_8932)))
| sP627(U_8932,U_8933,U_8934)
| ~ sP628(U_8929,U_8932,U_8933,U_8928,U_8934) ),
inference(clausify,[status(thm)],[f_2244_5]) ).
cnf(f_2244_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8932),sK219(U_8934,U_8933,U_8932)))
| ~ sP627(U_8932,U_8933,U_8934) ),
inference(clausify,[status(thm)],[f_2244_5]) ).
cnf(f_2244_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK219(U_8934,U_8933,U_8932)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP627(U_8932,U_8933,U_8934) ),
inference(clausify,[status(thm)],[f_2244_5]) ).
cnf(f_2244_11,plain,
( U_8934 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8932),sK218(U_8934,U_8933,U_8932))),sK219(U_8934,U_8933,U_8932))
| ~ sP627(U_8932,U_8933,U_8934) ),
inference(clausify,[status(thm)],[f_2244_5]) ).
cnf(f_2244_12,plain,
( ~ hBOOL(hAPP(hAPP(U_8933,sK218(U_8934,U_8933,U_8932)),sK219(U_8934,U_8933,U_8932)))
| ~ sP627(U_8932,U_8933,U_8934) ),
inference(clausify,[status(thm)],[f_2244_5]) ).
fof(f_2245_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_2245_2,plain,
! [U_8937,U_8936,U_8935] : 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_8935,U_8936)),U_8937),U_8936) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8935),U_8937),U_8936),
inference(variable_rename,[status(thm)],[f_2245_1]) ).
fof(f_2245_3,plain,
! [U_8936,U_8937,U_8935] : 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_8935,U_8936)),U_8937),U_8936) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8935),U_8937),U_8936),
inference(definitional_conversion,[status(esa)],[f_2245_2]) ).
cnf(f_2245_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_8935,U_8936)),U_8937),U_8936) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8935),U_8937),U_8936),
inference(clausify,[status(thm)],[f_2245_3]) ).
fof(f_2246_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_2246_2,plain,
! [U_8940,U_8939,U_8938] : 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_8938,U_8939)),U_8940),U_8939) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8938),U_8940),U_8939),
inference(variable_rename,[status(thm)],[f_2246_1]) ).
fof(f_2246_3,plain,
! [U_8939,U_8938,U_8940] : 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_8938,U_8939)),U_8940),U_8939) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8938),U_8940),U_8939),
inference(definitional_conversion,[status(esa)],[f_2246_2]) ).
cnf(f_2246_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_8938,U_8939)),U_8940),U_8939) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8938),U_8940),U_8939),
inference(clausify,[status(thm)],[f_2246_3]) ).
fof(f_2247_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_2247_2,plain,
! [U_8943,U_8942,U_8941] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8941),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8942,U_8943)),U_8943) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8941),U_8942),U_8943),
inference(variable_rename,[status(thm)],[f_2247_1]) ).
fof(f_2247_3,plain,
! [U_8941,U_8942,U_8943] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8941),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8942,U_8943)),U_8943) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8941),U_8942),U_8943),
inference(definitional_conversion,[status(esa)],[f_2247_2]) ).
cnf(f_2247_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8941),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8942,U_8943)),U_8943) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8941),U_8942),U_8943),
inference(clausify,[status(thm)],[f_2247_3]) ).
fof(f_2248_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_2248_2,plain,
! [U_8949,U_8948,U_8947,U_8946,U_8945,U_8944] :
( c_Divides_Odiv__class_Omod(U_8944,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8944),U_8945),U_8948),U_8946) = c_Divides_Odiv__class_Omod(U_8944,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8944),U_8947),U_8949),U_8946)
| c_Divides_Odiv__class_Omod(U_8944,U_8948,U_8946) != c_Divides_Odiv__class_Omod(U_8944,U_8949,U_8946)
| c_Divides_Odiv__class_Omod(U_8944,U_8945,U_8946) != c_Divides_Odiv__class_Omod(U_8944,U_8947,U_8946)
| ~ class_Divides_Oring__div(U_8944) ),
inference(variable_rename,[status(thm)],[f_2248_1]) ).
fof(f_2248_3,plain,
! [U_8944,U_8945,U_8946,U_8947,U_8948,U_8949] :
( c_Divides_Odiv__class_Omod(U_8944,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8944),U_8945),U_8948),U_8946) = c_Divides_Odiv__class_Omod(U_8944,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8944),U_8947),U_8949),U_8946)
| c_Divides_Odiv__class_Omod(U_8944,U_8948,U_8946) != c_Divides_Odiv__class_Omod(U_8944,U_8949,U_8946)
| c_Divides_Odiv__class_Omod(U_8944,U_8945,U_8946) != c_Divides_Odiv__class_Omod(U_8944,U_8947,U_8946)
| ~ class_Divides_Oring__div(U_8944) ),
inference(definitional_conversion,[status(esa)],[f_2248_2]) ).
cnf(f_2248_4,plain,
( c_Divides_Odiv__class_Omod(U_8944,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8944),U_8945),U_8948),U_8946) = c_Divides_Odiv__class_Omod(U_8944,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8944),U_8947),U_8949),U_8946)
| c_Divides_Odiv__class_Omod(U_8944,U_8948,U_8946) != c_Divides_Odiv__class_Omod(U_8944,U_8949,U_8946)
| c_Divides_Odiv__class_Omod(U_8944,U_8945,U_8946) != c_Divides_Odiv__class_Omod(U_8944,U_8947,U_8946)
| ~ class_Divides_Oring__div(U_8944) ),
inference(clausify,[status(thm)],[f_2248_3]) ).
fof(f_2249_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_2249_2,plain,
! [U_8953,U_8952,U_8951,U_8950] :
( c_Divides_Odiv__class_Omod(U_8950,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8950),U_8951),U_8952),U_8953) = c_Divides_Odiv__class_Omod(U_8950,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8950),c_Divides_Odiv__class_Omod(U_8950,U_8951,U_8953)),c_Divides_Odiv__class_Omod(U_8950,U_8952,U_8953)),U_8953)
| ~ class_Divides_Oring__div(U_8950) ),
inference(variable_rename,[status(thm)],[f_2249_1]) ).
fof(f_2249_3,plain,
! [U_8952,U_8951,U_8950,U_8953] :
( c_Divides_Odiv__class_Omod(U_8950,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8950),U_8951),U_8952),U_8953) = c_Divides_Odiv__class_Omod(U_8950,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8950),c_Divides_Odiv__class_Omod(U_8950,U_8951,U_8953)),c_Divides_Odiv__class_Omod(U_8950,U_8952,U_8953)),U_8953)
| ~ class_Divides_Oring__div(U_8950) ),
inference(definitional_conversion,[status(esa)],[f_2249_2]) ).
cnf(f_2249_4,plain,
( c_Divides_Odiv__class_Omod(U_8950,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8950),U_8951),U_8952),U_8953) = c_Divides_Odiv__class_Omod(U_8950,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8950),c_Divides_Odiv__class_Omod(U_8950,U_8951,U_8953)),c_Divides_Odiv__class_Omod(U_8950,U_8952,U_8953)),U_8953)
| ~ class_Divides_Oring__div(U_8950) ),
inference(clausify,[status(thm)],[f_2249_3]) ).
fof(f_2250_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_2250_2,plain,
! [U_8957,U_8956,U_8955,U_8954] :
( c_Divides_Odiv__class_Omod(U_8954,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8954),U_8955),U_8956),U_8957) = c_Divides_Odiv__class_Omod(U_8954,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8954),c_Divides_Odiv__class_Omod(U_8954,U_8955,U_8957)),U_8956),U_8957)
| ~ class_Divides_Oring__div(U_8954) ),
inference(variable_rename,[status(thm)],[f_2250_1]) ).
fof(f_2250_3,plain,
! [U_8954,U_8955,U_8956,U_8957] :
( c_Divides_Odiv__class_Omod(U_8954,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8954),U_8955),U_8956),U_8957) = c_Divides_Odiv__class_Omod(U_8954,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8954),c_Divides_Odiv__class_Omod(U_8954,U_8955,U_8957)),U_8956),U_8957)
| ~ class_Divides_Oring__div(U_8954) ),
inference(definitional_conversion,[status(esa)],[f_2250_2]) ).
cnf(f_2250_4,plain,
( c_Divides_Odiv__class_Omod(U_8954,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8954),U_8955),U_8956),U_8957) = c_Divides_Odiv__class_Omod(U_8954,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8954),c_Divides_Odiv__class_Omod(U_8954,U_8955,U_8957)),U_8956),U_8957)
| ~ class_Divides_Oring__div(U_8954) ),
inference(clausify,[status(thm)],[f_2250_3]) ).
fof(f_2251_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_2251_2,plain,
! [U_8961,U_8960,U_8959,U_8958] :
( c_Divides_Odiv__class_Omod(U_8958,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8958),U_8959),U_8960),U_8961) = c_Divides_Odiv__class_Omod(U_8958,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8958),U_8959),c_Divides_Odiv__class_Omod(U_8958,U_8960,U_8961)),U_8961)
| ~ class_Divides_Oring__div(U_8958) ),
inference(variable_rename,[status(thm)],[f_2251_1]) ).
fof(f_2251_3,plain,
! [U_8958,U_8959,U_8960,U_8961] :
( c_Divides_Odiv__class_Omod(U_8958,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8958),U_8959),U_8960),U_8961) = c_Divides_Odiv__class_Omod(U_8958,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8958),U_8959),c_Divides_Odiv__class_Omod(U_8958,U_8960,U_8961)),U_8961)
| ~ class_Divides_Oring__div(U_8958) ),
inference(definitional_conversion,[status(esa)],[f_2251_2]) ).
cnf(f_2251_4,plain,
( c_Divides_Odiv__class_Omod(U_8958,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8958),U_8959),U_8960),U_8961) = c_Divides_Odiv__class_Omod(U_8958,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8958),U_8959),c_Divides_Odiv__class_Omod(U_8958,U_8960,U_8961)),U_8961)
| ~ class_Divides_Oring__div(U_8958) ),
inference(clausify,[status(thm)],[f_2251_3]) ).
fof(f_2252_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_2252_2,plain,
! [U_8964,U_8963,U_8962] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8962),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8963,U_8964)),U_8964) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8962),U_8963),U_8964),
inference(variable_rename,[status(thm)],[f_2252_1]) ).
fof(f_2252_3,plain,
! [U_8963,U_8962,U_8964] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8962),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8963,U_8964)),U_8964) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8962),U_8963),U_8964),
inference(definitional_conversion,[status(esa)],[f_2252_2]) ).
cnf(f_2252_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8962),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8963,U_8964)),U_8964) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8962),U_8963),U_8964),
inference(clausify,[status(thm)],[f_2252_3]) ).
fof(f_2253_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_2253_2,plain,
! [U_8967,U_8966,U_8965] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8965),U_8966),U_8967) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8965),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8966,U_8967)),U_8967),
inference(variable_rename,[status(thm)],[f_2253_1]) ).
fof(f_2253_3,plain,
! [U_8965,U_8966,U_8967] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8965),U_8966),U_8967) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8965),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8966,U_8967)),U_8967),
inference(definitional_conversion,[status(esa)],[f_2253_2]) ).
cnf(f_2253_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8965),U_8966),U_8967) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8965),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8966,U_8967)),U_8967),
inference(clausify,[status(thm)],[f_2253_3]) ).
fof(f_2254_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_2254_2,plain,
! [U_8968] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8968,U_8968) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_2254_1]) ).
fof(f_2254_3,plain,
! [U_8968] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8968,U_8968) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_2254_2]) ).
cnf(f_2254_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8968,U_8968) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_2254_3]) ).
fof(f_2255_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_2255_2,plain,
! [U_8969] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_8969) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_2255_1]) ).
fof(f_2255_3,plain,
! [U_8969] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_8969) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_2255_2]) ).
cnf(f_2255_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_8969) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_2255_3]) ).
fof(f_2256_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_2256_2,plain,
! [U_8975,U_8974,U_8973,U_8972,U_8971,U_8970] :
( c_Divides_Odiv__class_Omod(U_8970,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8970),U_8971),U_8974),U_8972) = c_Divides_Odiv__class_Omod(U_8970,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8970),U_8973),U_8975),U_8972)
| c_Divides_Odiv__class_Omod(U_8970,U_8974,U_8972) != c_Divides_Odiv__class_Omod(U_8970,U_8975,U_8972)
| c_Divides_Odiv__class_Omod(U_8970,U_8971,U_8972) != c_Divides_Odiv__class_Omod(U_8970,U_8973,U_8972)
| ~ class_Divides_Osemiring__div(U_8970) ),
inference(variable_rename,[status(thm)],[f_2256_1]) ).
fof(f_2256_3,plain,
! [U_8970,U_8971,U_8972,U_8973,U_8974,U_8975] :
( c_Divides_Odiv__class_Omod(U_8970,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8970),U_8971),U_8974),U_8972) = c_Divides_Odiv__class_Omod(U_8970,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8970),U_8973),U_8975),U_8972)
| c_Divides_Odiv__class_Omod(U_8970,U_8974,U_8972) != c_Divides_Odiv__class_Omod(U_8970,U_8975,U_8972)
| c_Divides_Odiv__class_Omod(U_8970,U_8971,U_8972) != c_Divides_Odiv__class_Omod(U_8970,U_8973,U_8972)
| ~ class_Divides_Osemiring__div(U_8970) ),
inference(definitional_conversion,[status(esa)],[f_2256_2]) ).
cnf(f_2256_4,plain,
( c_Divides_Odiv__class_Omod(U_8970,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8970),U_8971),U_8974),U_8972) = c_Divides_Odiv__class_Omod(U_8970,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8970),U_8973),U_8975),U_8972)
| c_Divides_Odiv__class_Omod(U_8970,U_8974,U_8972) != c_Divides_Odiv__class_Omod(U_8970,U_8975,U_8972)
| c_Divides_Odiv__class_Omod(U_8970,U_8971,U_8972) != c_Divides_Odiv__class_Omod(U_8970,U_8973,U_8972)
| ~ class_Divides_Osemiring__div(U_8970) ),
inference(clausify,[status(thm)],[f_2256_3]) ).
fof(f_2257_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_2257_2,plain,
! [U_8979,U_8978,U_8977,U_8976] :
( c_Divides_Odiv__class_Omod(U_8976,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8976),c_Divides_Odiv__class_Omod(U_8976,U_8977,U_8978)),U_8979),U_8978) = c_Divides_Odiv__class_Omod(U_8976,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8976),U_8977),U_8979),U_8978)
| ~ class_Divides_Osemiring__div(U_8976) ),
inference(variable_rename,[status(thm)],[f_2257_1]) ).
fof(f_2257_3,plain,
! [U_8977,U_8976,U_8979,U_8978] :
( c_Divides_Odiv__class_Omod(U_8976,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8976),c_Divides_Odiv__class_Omod(U_8976,U_8977,U_8978)),U_8979),U_8978) = c_Divides_Odiv__class_Omod(U_8976,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8976),U_8977),U_8979),U_8978)
| ~ class_Divides_Osemiring__div(U_8976) ),
inference(definitional_conversion,[status(esa)],[f_2257_2]) ).
cnf(f_2257_4,plain,
( c_Divides_Odiv__class_Omod(U_8976,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8976),c_Divides_Odiv__class_Omod(U_8976,U_8977,U_8978)),U_8979),U_8978) = c_Divides_Odiv__class_Omod(U_8976,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8976),U_8977),U_8979),U_8978)
| ~ class_Divides_Osemiring__div(U_8976) ),
inference(clausify,[status(thm)],[f_2257_3]) ).
fof(f_2258_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_2258_2,plain,
! [U_8983,U_8982,U_8981,U_8980] :
( c_Divides_Odiv__class_Omod(U_8980,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8980),U_8981),c_Divides_Odiv__class_Omod(U_8980,U_8982,U_8983)),U_8983) = c_Divides_Odiv__class_Omod(U_8980,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8980),U_8981),U_8982),U_8983)
| ~ class_Divides_Osemiring__div(U_8980) ),
inference(variable_rename,[status(thm)],[f_2258_1]) ).
fof(f_2258_3,plain,
! [U_8980,U_8981,U_8982,U_8983] :
( c_Divides_Odiv__class_Omod(U_8980,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8980),U_8981),c_Divides_Odiv__class_Omod(U_8980,U_8982,U_8983)),U_8983) = c_Divides_Odiv__class_Omod(U_8980,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8980),U_8981),U_8982),U_8983)
| ~ class_Divides_Osemiring__div(U_8980) ),
inference(definitional_conversion,[status(esa)],[f_2258_2]) ).
cnf(f_2258_4,plain,
( c_Divides_Odiv__class_Omod(U_8980,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8980),U_8981),c_Divides_Odiv__class_Omod(U_8980,U_8982,U_8983)),U_8983) = c_Divides_Odiv__class_Omod(U_8980,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8980),U_8981),U_8982),U_8983)
| ~ class_Divides_Osemiring__div(U_8980) ),
inference(clausify,[status(thm)],[f_2258_3]) ).
fof(f_2259_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_2259_2,plain,
! [U_8987,U_8986,U_8985,U_8984] :
( c_Divides_Odiv__class_Omod(U_8984,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8984),U_8985),U_8986),U_8987) = c_Divides_Odiv__class_Omod(U_8984,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8984),c_Divides_Odiv__class_Omod(U_8984,U_8985,U_8987)),c_Divides_Odiv__class_Omod(U_8984,U_8986,U_8987)),U_8987)
| ~ class_Divides_Osemiring__div(U_8984) ),
inference(variable_rename,[status(thm)],[f_2259_1]) ).
fof(f_2259_3,plain,
! [U_8984,U_8985,U_8986,U_8987] :
( c_Divides_Odiv__class_Omod(U_8984,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8984),U_8985),U_8986),U_8987) = c_Divides_Odiv__class_Omod(U_8984,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8984),c_Divides_Odiv__class_Omod(U_8984,U_8985,U_8987)),c_Divides_Odiv__class_Omod(U_8984,U_8986,U_8987)),U_8987)
| ~ class_Divides_Osemiring__div(U_8984) ),
inference(definitional_conversion,[status(esa)],[f_2259_2]) ).
cnf(f_2259_4,plain,
( c_Divides_Odiv__class_Omod(U_8984,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8984),U_8985),U_8986),U_8987) = c_Divides_Odiv__class_Omod(U_8984,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8984),c_Divides_Odiv__class_Omod(U_8984,U_8985,U_8987)),c_Divides_Odiv__class_Omod(U_8984,U_8986,U_8987)),U_8987)
| ~ class_Divides_Osemiring__div(U_8984) ),
inference(clausify,[status(thm)],[f_2259_3]) ).
fof(f_2260_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_2260_2,plain,
! [U_8991,U_8990,U_8989,U_8988] :
( c_Divides_Odiv__class_Omod(U_8988,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8988),U_8989),U_8990),U_8991) = c_Divides_Odiv__class_Omod(U_8988,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8988),c_Divides_Odiv__class_Omod(U_8988,U_8989,U_8991)),U_8990),U_8991)
| ~ class_Divides_Osemiring__div(U_8988) ),
inference(variable_rename,[status(thm)],[f_2260_1]) ).
fof(f_2260_3,plain,
! [U_8988,U_8989,U_8990,U_8991] :
( c_Divides_Odiv__class_Omod(U_8988,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8988),U_8989),U_8990),U_8991) = c_Divides_Odiv__class_Omod(U_8988,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8988),c_Divides_Odiv__class_Omod(U_8988,U_8989,U_8991)),U_8990),U_8991)
| ~ class_Divides_Osemiring__div(U_8988) ),
inference(definitional_conversion,[status(esa)],[f_2260_2]) ).
cnf(f_2260_4,plain,
( c_Divides_Odiv__class_Omod(U_8988,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8988),U_8989),U_8990),U_8991) = c_Divides_Odiv__class_Omod(U_8988,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8988),c_Divides_Odiv__class_Omod(U_8988,U_8989,U_8991)),U_8990),U_8991)
| ~ class_Divides_Osemiring__div(U_8988) ),
inference(clausify,[status(thm)],[f_2260_3]) ).
fof(f_2261_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_2261_2,plain,
! [U_8995,U_8994,U_8993,U_8992] :
( c_Divides_Odiv__class_Omod(U_8992,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8992),U_8993),U_8994),U_8995) = c_Divides_Odiv__class_Omod(U_8992,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8992),U_8993),c_Divides_Odiv__class_Omod(U_8992,U_8994,U_8995)),U_8995)
| ~ class_Divides_Osemiring__div(U_8992) ),
inference(variable_rename,[status(thm)],[f_2261_1]) ).
fof(f_2261_3,plain,
! [U_8992,U_8993,U_8994,U_8995] :
( c_Divides_Odiv__class_Omod(U_8992,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8992),U_8993),U_8994),U_8995) = c_Divides_Odiv__class_Omod(U_8992,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8992),U_8993),c_Divides_Odiv__class_Omod(U_8992,U_8994,U_8995)),U_8995)
| ~ class_Divides_Osemiring__div(U_8992) ),
inference(definitional_conversion,[status(esa)],[f_2261_2]) ).
cnf(f_2261_4,plain,
( c_Divides_Odiv__class_Omod(U_8992,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8992),U_8993),U_8994),U_8995) = c_Divides_Odiv__class_Omod(U_8992,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8992),U_8993),c_Divides_Odiv__class_Omod(U_8992,U_8994,U_8995)),U_8995)
| ~ class_Divides_Osemiring__div(U_8992) ),
inference(clausify,[status(thm)],[f_2261_3]) ).
fof(f_2262_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_2262_2,plain,
! [U_8998,U_8997,U_8996] :
( c_Divides_Odiv__class_Omod(U_8996,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8996),U_8997),U_8998),U_8997) = c_Divides_Odiv__class_Omod(U_8996,U_8998,U_8997)
| ~ class_Divides_Osemiring__div(U_8996) ),
inference(variable_rename,[status(thm)],[f_2262_1]) ).
fof(f_2262_3,plain,
! [U_8996,U_8997,U_8998] :
( c_Divides_Odiv__class_Omod(U_8996,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8996),U_8997),U_8998),U_8997) = c_Divides_Odiv__class_Omod(U_8996,U_8998,U_8997)
| ~ class_Divides_Osemiring__div(U_8996) ),
inference(definitional_conversion,[status(esa)],[f_2262_2]) ).
cnf(f_2262_4,plain,
( c_Divides_Odiv__class_Omod(U_8996,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8996),U_8997),U_8998),U_8997) = c_Divides_Odiv__class_Omod(U_8996,U_8998,U_8997)
| ~ class_Divides_Osemiring__div(U_8996) ),
inference(clausify,[status(thm)],[f_2262_3]) ).
fof(f_2263_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_2263_2,plain,
! [U_9001,U_9000,U_8999] :
( c_Divides_Odiv__class_Omod(U_8999,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8999),U_9000),U_9001),U_9001) = c_Divides_Odiv__class_Omod(U_8999,U_9000,U_9001)
| ~ class_Divides_Osemiring__div(U_8999) ),
inference(variable_rename,[status(thm)],[f_2263_1]) ).
fof(f_2263_3,plain,
! [U_8999,U_9000,U_9001] :
( c_Divides_Odiv__class_Omod(U_8999,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8999),U_9000),U_9001),U_9001) = c_Divides_Odiv__class_Omod(U_8999,U_9000,U_9001)
| ~ class_Divides_Osemiring__div(U_8999) ),
inference(definitional_conversion,[status(esa)],[f_2263_2]) ).
cnf(f_2263_4,plain,
( c_Divides_Odiv__class_Omod(U_8999,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8999),U_9000),U_9001),U_9001) = c_Divides_Odiv__class_Omod(U_8999,U_9000,U_9001)
| ~ class_Divides_Osemiring__div(U_8999) ),
inference(clausify,[status(thm)],[f_2263_3]) ).
fof(f_2264_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_2264_2,plain,
! [U_9004,U_9003,U_9002] :
( c_Divides_Odiv__class_Omod(U_9002,hAPP(c_Groups_Ouminus__class_Ouminus(U_9002),U_9003),U_9004) = c_Divides_Odiv__class_Omod(U_9002,hAPP(c_Groups_Ouminus__class_Ouminus(U_9002),c_Divides_Odiv__class_Omod(U_9002,U_9003,U_9004)),U_9004)
| ~ class_Divides_Oring__div(U_9002) ),
inference(variable_rename,[status(thm)],[f_2264_1]) ).
fof(f_2264_3,plain,
! [U_9002,U_9003,U_9004] :
( c_Divides_Odiv__class_Omod(U_9002,hAPP(c_Groups_Ouminus__class_Ouminus(U_9002),U_9003),U_9004) = c_Divides_Odiv__class_Omod(U_9002,hAPP(c_Groups_Ouminus__class_Ouminus(U_9002),c_Divides_Odiv__class_Omod(U_9002,U_9003,U_9004)),U_9004)
| ~ class_Divides_Oring__div(U_9002) ),
inference(definitional_conversion,[status(esa)],[f_2264_2]) ).
cnf(f_2264_4,plain,
( c_Divides_Odiv__class_Omod(U_9002,hAPP(c_Groups_Ouminus__class_Ouminus(U_9002),U_9003),U_9004) = c_Divides_Odiv__class_Omod(U_9002,hAPP(c_Groups_Ouminus__class_Ouminus(U_9002),c_Divides_Odiv__class_Omod(U_9002,U_9003,U_9004)),U_9004)
| ~ class_Divides_Oring__div(U_9002) ),
inference(clausify,[status(thm)],[f_2264_3]) ).
fof(f_2265_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_2265_2,plain,
! [U_9008,U_9007,U_9006,U_9005] :
( c_Divides_Odiv__class_Omod(U_9005,hAPP(c_Groups_Ouminus__class_Ouminus(U_9005),U_9006),U_9007) = c_Divides_Odiv__class_Omod(U_9005,hAPP(c_Groups_Ouminus__class_Ouminus(U_9005),U_9008),U_9007)
| c_Divides_Odiv__class_Omod(U_9005,U_9006,U_9007) != c_Divides_Odiv__class_Omod(U_9005,U_9008,U_9007)
| ~ class_Divides_Oring__div(U_9005) ),
inference(variable_rename,[status(thm)],[f_2265_1]) ).
fof(f_2265_3,plain,
! [U_9005,U_9006,U_9007,U_9008] :
( c_Divides_Odiv__class_Omod(U_9005,hAPP(c_Groups_Ouminus__class_Ouminus(U_9005),U_9006),U_9007) = c_Divides_Odiv__class_Omod(U_9005,hAPP(c_Groups_Ouminus__class_Ouminus(U_9005),U_9008),U_9007)
| c_Divides_Odiv__class_Omod(U_9005,U_9006,U_9007) != c_Divides_Odiv__class_Omod(U_9005,U_9008,U_9007)
| ~ class_Divides_Oring__div(U_9005) ),
inference(definitional_conversion,[status(esa)],[f_2265_2]) ).
cnf(f_2265_4,plain,
( c_Divides_Odiv__class_Omod(U_9005,hAPP(c_Groups_Ouminus__class_Ouminus(U_9005),U_9006),U_9007) = c_Divides_Odiv__class_Omod(U_9005,hAPP(c_Groups_Ouminus__class_Ouminus(U_9005),U_9008),U_9007)
| c_Divides_Odiv__class_Omod(U_9005,U_9006,U_9007) != c_Divides_Odiv__class_Omod(U_9005,U_9008,U_9007)
| ~ class_Divides_Oring__div(U_9005) ),
inference(clausify,[status(thm)],[f_2265_3]) ).
fof(f_2266_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_2266_2,plain,
! [U_9010,U_9009] :
( c_Divides_Odiv__class_Omod(U_9009,U_9010,U_9010) = c_Groups_Ozero__class_Ozero(U_9009)
| ~ class_Divides_Osemiring__div(U_9009) ),
inference(variable_rename,[status(thm)],[f_2266_1]) ).
fof(f_2266_3,plain,
! [U_9010,U_9009] :
( c_Divides_Odiv__class_Omod(U_9009,U_9010,U_9010) = c_Groups_Ozero__class_Ozero(U_9009)
| ~ class_Divides_Osemiring__div(U_9009) ),
inference(definitional_conversion,[status(esa)],[f_2266_2]) ).
cnf(f_2266_4,plain,
( c_Divides_Odiv__class_Omod(U_9009,U_9010,U_9010) = c_Groups_Ozero__class_Ozero(U_9009)
| ~ class_Divides_Osemiring__div(U_9009) ),
inference(clausify,[status(thm)],[f_2266_3]) ).
fof(f_2267_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_2267_2,plain,
! [U_9012,U_9011] :
( c_Divides_Odiv__class_Omod(U_9011,U_9012,c_Groups_Ozero__class_Ozero(U_9011)) = U_9012
| ~ class_Divides_Osemiring__div(U_9011) ),
inference(variable_rename,[status(thm)],[f_2267_1]) ).
fof(f_2267_3,plain,
! [U_9011,U_9012] :
( c_Divides_Odiv__class_Omod(U_9011,U_9012,c_Groups_Ozero__class_Ozero(U_9011)) = U_9012
| ~ class_Divides_Osemiring__div(U_9011) ),
inference(definitional_conversion,[status(esa)],[f_2267_2]) ).
cnf(f_2267_4,plain,
( c_Divides_Odiv__class_Omod(U_9011,U_9012,c_Groups_Ozero__class_Ozero(U_9011)) = U_9012
| ~ class_Divides_Osemiring__div(U_9011) ),
inference(clausify,[status(thm)],[f_2267_3]) ).
fof(f_2268_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_2268_2,plain,
! [U_9014,U_9013] :
( c_Divides_Odiv__class_Omod(U_9013,c_Groups_Ozero__class_Ozero(U_9013),U_9014) = c_Groups_Ozero__class_Ozero(U_9013)
| ~ class_Divides_Osemiring__div(U_9013) ),
inference(variable_rename,[status(thm)],[f_2268_1]) ).
fof(f_2268_3,plain,
! [U_9013,U_9014] :
( c_Divides_Odiv__class_Omod(U_9013,c_Groups_Ozero__class_Ozero(U_9013),U_9014) = c_Groups_Ozero__class_Ozero(U_9013)
| ~ class_Divides_Osemiring__div(U_9013) ),
inference(definitional_conversion,[status(esa)],[f_2268_2]) ).
cnf(f_2268_4,plain,
( c_Divides_Odiv__class_Omod(U_9013,c_Groups_Ozero__class_Ozero(U_9013),U_9014) = c_Groups_Ozero__class_Ozero(U_9013)
| ~ class_Divides_Osemiring__div(U_9013) ),
inference(clausify,[status(thm)],[f_2268_3]) ).
fof(f_2269_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_2269_2,plain,
! [U_9017,U_9016,U_9015] :
( c_Divides_Odiv__class_Omod(U_9015,c_Divides_Odiv__class_Omod(U_9015,U_9016,U_9017),U_9017) = c_Divides_Odiv__class_Omod(U_9015,U_9016,U_9017)
| ~ class_Divides_Osemiring__div(U_9015) ),
inference(variable_rename,[status(thm)],[f_2269_1]) ).
fof(f_2269_3,plain,
! [U_9015,U_9016,U_9017] :
( c_Divides_Odiv__class_Omod(U_9015,c_Divides_Odiv__class_Omod(U_9015,U_9016,U_9017),U_9017) = c_Divides_Odiv__class_Omod(U_9015,U_9016,U_9017)
| ~ class_Divides_Osemiring__div(U_9015) ),
inference(definitional_conversion,[status(esa)],[f_2269_2]) ).
cnf(f_2269_4,plain,
( c_Divides_Odiv__class_Omod(U_9015,c_Divides_Odiv__class_Omod(U_9015,U_9016,U_9017),U_9017) = c_Divides_Odiv__class_Omod(U_9015,U_9016,U_9017)
| ~ class_Divides_Osemiring__div(U_9015) ),
inference(clausify,[status(thm)],[f_2269_3]) ).
fof(f_2270_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_2270_2,plain,
! [U_9023,U_9022,U_9021,U_9020,U_9019,U_9018] :
( c_Divides_Odiv__class_Omod(U_9018,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9018),U_9019),U_9022),U_9020) = c_Divides_Odiv__class_Omod(U_9018,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9018),U_9021),U_9023),U_9020)
| c_Divides_Odiv__class_Omod(U_9018,U_9022,U_9020) != c_Divides_Odiv__class_Omod(U_9018,U_9023,U_9020)
| c_Divides_Odiv__class_Omod(U_9018,U_9019,U_9020) != c_Divides_Odiv__class_Omod(U_9018,U_9021,U_9020)
| ~ class_Divides_Osemiring__div(U_9018) ),
inference(variable_rename,[status(thm)],[f_2270_1]) ).
fof(f_2270_3,plain,
! [U_9018,U_9019,U_9020,U_9021,U_9022,U_9023] :
( c_Divides_Odiv__class_Omod(U_9018,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9018),U_9019),U_9022),U_9020) = c_Divides_Odiv__class_Omod(U_9018,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9018),U_9021),U_9023),U_9020)
| c_Divides_Odiv__class_Omod(U_9018,U_9022,U_9020) != c_Divides_Odiv__class_Omod(U_9018,U_9023,U_9020)
| c_Divides_Odiv__class_Omod(U_9018,U_9019,U_9020) != c_Divides_Odiv__class_Omod(U_9018,U_9021,U_9020)
| ~ class_Divides_Osemiring__div(U_9018) ),
inference(definitional_conversion,[status(esa)],[f_2270_2]) ).
cnf(f_2270_4,plain,
( c_Divides_Odiv__class_Omod(U_9018,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9018),U_9019),U_9022),U_9020) = c_Divides_Odiv__class_Omod(U_9018,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9018),U_9021),U_9023),U_9020)
| c_Divides_Odiv__class_Omod(U_9018,U_9022,U_9020) != c_Divides_Odiv__class_Omod(U_9018,U_9023,U_9020)
| c_Divides_Odiv__class_Omod(U_9018,U_9019,U_9020) != c_Divides_Odiv__class_Omod(U_9018,U_9021,U_9020)
| ~ class_Divides_Osemiring__div(U_9018) ),
inference(clausify,[status(thm)],[f_2270_3]) ).
fof(f_2271_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_2271_2,plain,
! [U_9027,U_9026,U_9025,U_9024] :
( c_Divides_Odiv__class_Omod(U_9024,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9024),c_Divides_Odiv__class_Omod(U_9024,U_9025,U_9026)),U_9027),U_9026) = c_Divides_Odiv__class_Omod(U_9024,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9024),U_9025),U_9027),U_9026)
| ~ class_Divides_Osemiring__div(U_9024) ),
inference(variable_rename,[status(thm)],[f_2271_1]) ).
fof(f_2271_3,plain,
! [U_9024,U_9026,U_9025,U_9027] :
( c_Divides_Odiv__class_Omod(U_9024,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9024),c_Divides_Odiv__class_Omod(U_9024,U_9025,U_9026)),U_9027),U_9026) = c_Divides_Odiv__class_Omod(U_9024,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9024),U_9025),U_9027),U_9026)
| ~ class_Divides_Osemiring__div(U_9024) ),
inference(definitional_conversion,[status(esa)],[f_2271_2]) ).
cnf(f_2271_4,plain,
( c_Divides_Odiv__class_Omod(U_9024,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9024),c_Divides_Odiv__class_Omod(U_9024,U_9025,U_9026)),U_9027),U_9026) = c_Divides_Odiv__class_Omod(U_9024,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9024),U_9025),U_9027),U_9026)
| ~ class_Divides_Osemiring__div(U_9024) ),
inference(clausify,[status(thm)],[f_2271_3]) ).
fof(f_2272_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_2272_2,plain,
! [U_9031,U_9030,U_9029,U_9028] :
( c_Divides_Odiv__class_Omod(U_9028,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9028),U_9029),U_9030),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9028),U_9031),U_9030)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9028),c_Divides_Odiv__class_Omod(U_9028,U_9029,U_9031)),U_9030)
| ~ class_Divides_Osemiring__div(U_9028) ),
inference(variable_rename,[status(thm)],[f_2272_1]) ).
fof(f_2272_3,plain,
! [U_9028,U_9029,U_9030,U_9031] :
( c_Divides_Odiv__class_Omod(U_9028,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9028),U_9029),U_9030),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9028),U_9031),U_9030)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9028),c_Divides_Odiv__class_Omod(U_9028,U_9029,U_9031)),U_9030)
| ~ class_Divides_Osemiring__div(U_9028) ),
inference(definitional_conversion,[status(esa)],[f_2272_2]) ).
cnf(f_2272_4,plain,
( c_Divides_Odiv__class_Omod(U_9028,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9028),U_9029),U_9030),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9028),U_9031),U_9030)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9028),c_Divides_Odiv__class_Omod(U_9028,U_9029,U_9031)),U_9030)
| ~ class_Divides_Osemiring__div(U_9028) ),
inference(clausify,[status(thm)],[f_2272_3]) ).
fof(f_2273_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_2273_2,plain,
! [U_9035,U_9034,U_9033,U_9032] :
( c_Divides_Odiv__class_Omod(U_9032,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9032),U_9033),U_9034),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9032),U_9033),U_9035)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9032),U_9033),c_Divides_Odiv__class_Omod(U_9032,U_9034,U_9035))
| ~ class_Divides_Osemiring__div(U_9032) ),
inference(variable_rename,[status(thm)],[f_2273_1]) ).
fof(f_2273_3,plain,
! [U_9032,U_9033,U_9034,U_9035] :
( c_Divides_Odiv__class_Omod(U_9032,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9032),U_9033),U_9034),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9032),U_9033),U_9035)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9032),U_9033),c_Divides_Odiv__class_Omod(U_9032,U_9034,U_9035))
| ~ class_Divides_Osemiring__div(U_9032) ),
inference(definitional_conversion,[status(esa)],[f_2273_2]) ).
cnf(f_2273_4,plain,
( c_Divides_Odiv__class_Omod(U_9032,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9032),U_9033),U_9034),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9032),U_9033),U_9035)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9032),U_9033),c_Divides_Odiv__class_Omod(U_9032,U_9034,U_9035))
| ~ class_Divides_Osemiring__div(U_9032) ),
inference(clausify,[status(thm)],[f_2273_3]) ).
fof(f_2274_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_2274_2,plain,
! [U_9039,U_9038,U_9037,U_9036] :
( c_Divides_Odiv__class_Omod(U_9036,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9036),U_9037),U_9038),U_9039) = c_Divides_Odiv__class_Omod(U_9036,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9036),c_Divides_Odiv__class_Omod(U_9036,U_9037,U_9039)),c_Divides_Odiv__class_Omod(U_9036,U_9038,U_9039)),U_9039)
| ~ class_Divides_Osemiring__div(U_9036) ),
inference(variable_rename,[status(thm)],[f_2274_1]) ).
fof(f_2274_3,plain,
! [U_9036,U_9037,U_9038,U_9039] :
( c_Divides_Odiv__class_Omod(U_9036,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9036),U_9037),U_9038),U_9039) = c_Divides_Odiv__class_Omod(U_9036,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9036),c_Divides_Odiv__class_Omod(U_9036,U_9037,U_9039)),c_Divides_Odiv__class_Omod(U_9036,U_9038,U_9039)),U_9039)
| ~ class_Divides_Osemiring__div(U_9036) ),
inference(definitional_conversion,[status(esa)],[f_2274_2]) ).
cnf(f_2274_4,plain,
( c_Divides_Odiv__class_Omod(U_9036,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9036),U_9037),U_9038),U_9039) = c_Divides_Odiv__class_Omod(U_9036,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9036),c_Divides_Odiv__class_Omod(U_9036,U_9037,U_9039)),c_Divides_Odiv__class_Omod(U_9036,U_9038,U_9039)),U_9039)
| ~ class_Divides_Osemiring__div(U_9036) ),
inference(clausify,[status(thm)],[f_2274_3]) ).
fof(f_2275_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_2275_2,plain,
! [U_9043,U_9042,U_9041,U_9040] :
( c_Divides_Odiv__class_Omod(U_9040,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9040),U_9041),U_9042),U_9043) = c_Divides_Odiv__class_Omod(U_9040,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9040),c_Divides_Odiv__class_Omod(U_9040,U_9041,U_9043)),U_9042),U_9043)
| ~ class_Divides_Osemiring__div(U_9040) ),
inference(variable_rename,[status(thm)],[f_2275_1]) ).
fof(f_2275_3,plain,
! [U_9040,U_9041,U_9042,U_9043] :
( c_Divides_Odiv__class_Omod(U_9040,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9040),U_9041),U_9042),U_9043) = c_Divides_Odiv__class_Omod(U_9040,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9040),c_Divides_Odiv__class_Omod(U_9040,U_9041,U_9043)),U_9042),U_9043)
| ~ class_Divides_Osemiring__div(U_9040) ),
inference(definitional_conversion,[status(esa)],[f_2275_2]) ).
cnf(f_2275_4,plain,
( c_Divides_Odiv__class_Omod(U_9040,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9040),U_9041),U_9042),U_9043) = c_Divides_Odiv__class_Omod(U_9040,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9040),c_Divides_Odiv__class_Omod(U_9040,U_9041,U_9043)),U_9042),U_9043)
| ~ class_Divides_Osemiring__div(U_9040) ),
inference(clausify,[status(thm)],[f_2275_3]) ).
fof(f_2276_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_2276_2,plain,
! [U_9047,U_9046,U_9045,U_9044] :
( c_Divides_Odiv__class_Omod(U_9044,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9044),U_9045),U_9046),U_9047) = c_Divides_Odiv__class_Omod(U_9044,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9044),U_9045),c_Divides_Odiv__class_Omod(U_9044,U_9046,U_9047)),U_9047)
| ~ class_Divides_Osemiring__div(U_9044) ),
inference(variable_rename,[status(thm)],[f_2276_1]) ).
fof(f_2276_3,plain,
! [U_9044,U_9045,U_9046,U_9047] :
( c_Divides_Odiv__class_Omod(U_9044,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9044),U_9045),U_9046),U_9047) = c_Divides_Odiv__class_Omod(U_9044,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9044),U_9045),c_Divides_Odiv__class_Omod(U_9044,U_9046,U_9047)),U_9047)
| ~ class_Divides_Osemiring__div(U_9044) ),
inference(definitional_conversion,[status(esa)],[f_2276_2]) ).
cnf(f_2276_4,plain,
( c_Divides_Odiv__class_Omod(U_9044,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9044),U_9045),U_9046),U_9047) = c_Divides_Odiv__class_Omod(U_9044,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9044),U_9045),c_Divides_Odiv__class_Omod(U_9044,U_9046,U_9047)),U_9047)
| ~ class_Divides_Osemiring__div(U_9044) ),
inference(clausify,[status(thm)],[f_2276_3]) ).
fof(f_2277_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_2277_2,plain,
! [U_9049,U_9048] : 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_9048,U_9049)),U_9049) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9048),U_9049),
inference(variable_rename,[status(thm)],[f_2277_1]) ).
fof(f_2277_3,plain,
! [U_9049,U_9048] : 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_9048,U_9049)),U_9049) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9048),U_9049),
inference(definitional_conversion,[status(esa)],[f_2277_2]) ).
cnf(f_2277_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_9048,U_9049)),U_9049) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9048),U_9049),
inference(clausify,[status(thm)],[f_2277_3]) ).
fof(f_2278_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_2278_2,plain,
! [U_9051,U_9050] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9050),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9051)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9050,U_9051)),
inference(variable_rename,[status(thm)],[f_2278_1]) ).
fof(f_2278_3,plain,
! [U_9050,U_9051] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9050),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9051)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9050,U_9051)),
inference(definitional_conversion,[status(esa)],[f_2278_2]) ).
cnf(f_2278_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9050),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9051)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9050,U_9051)),
inference(clausify,[status(thm)],[f_2278_3]) ).
fof(f_2279_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_2279_2,plain,
! [U_9053,U_9052] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9052,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9053)) = 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_9052),U_9053)),
inference(variable_rename,[status(thm)],[f_2279_1]) ).
fof(f_2279_3,plain,
! [U_9052,U_9053] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9052,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9053)) = 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_9052),U_9053)),
inference(definitional_conversion,[status(esa)],[f_2279_2]) ).
cnf(f_2279_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9052,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9053)) = 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_9052),U_9053)),
inference(clausify,[status(thm)],[f_2279_3]) ).
fof(f_2280_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_2280_2,plain,
! [U_9055,U_9054] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9054,U_9055))
| ~ c_Nat__Transfer_Ois__nat(U_9055)
| ~ c_Nat__Transfer_Ois__nat(U_9054) ),
inference(variable_rename,[status(thm)],[f_2280_1]) ).
fof(f_2280_3,plain,
! [U_9055,U_9054] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9054,U_9055))
| ~ c_Nat__Transfer_Ois__nat(U_9055)
| ~ c_Nat__Transfer_Ois__nat(U_9054) ),
inference(definitional_conversion,[status(esa)],[f_2280_2]) ).
cnf(f_2280_4,plain,
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9054,U_9055))
| ~ c_Nat__Transfer_Ois__nat(U_9055)
| ~ c_Nat__Transfer_Ois__nat(U_9054) ),
inference(clausify,[status(thm)],[f_2280_3]) ).
fof(f_2281_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_2281_2,plain,
! [U_9058,U_9057,U_9056] :
( c_Divides_Odiv__class_Omod(U_9056,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9056),U_9057),U_9058),U_9057) = c_Groups_Ozero__class_Ozero(U_9056)
| ~ class_Divides_Osemiring__div(U_9056) ),
inference(variable_rename,[status(thm)],[f_2281_1]) ).
fof(f_2281_3,plain,
! [U_9056,U_9057,U_9058] :
( c_Divides_Odiv__class_Omod(U_9056,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9056),U_9057),U_9058),U_9057) = c_Groups_Ozero__class_Ozero(U_9056)
| ~ class_Divides_Osemiring__div(U_9056) ),
inference(definitional_conversion,[status(esa)],[f_2281_2]) ).
cnf(f_2281_4,plain,
( c_Divides_Odiv__class_Omod(U_9056,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9056),U_9057),U_9058),U_9057) = c_Groups_Ozero__class_Ozero(U_9056)
| ~ class_Divides_Osemiring__div(U_9056) ),
inference(clausify,[status(thm)],[f_2281_3]) ).
fof(f_2282_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_2282_2,plain,
! [U_9061,U_9060,U_9059] :
( c_Divides_Odiv__class_Omod(U_9059,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9059),U_9060),U_9061),U_9061) = c_Groups_Ozero__class_Ozero(U_9059)
| ~ class_Divides_Osemiring__div(U_9059) ),
inference(variable_rename,[status(thm)],[f_2282_1]) ).
fof(f_2282_3,plain,
! [U_9059,U_9060,U_9061] :
( c_Divides_Odiv__class_Omod(U_9059,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9059),U_9060),U_9061),U_9061) = c_Groups_Ozero__class_Ozero(U_9059)
| ~ class_Divides_Osemiring__div(U_9059) ),
inference(definitional_conversion,[status(esa)],[f_2282_2]) ).
cnf(f_2282_4,plain,
( c_Divides_Odiv__class_Omod(U_9059,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9059),U_9060),U_9061),U_9061) = c_Groups_Ozero__class_Ozero(U_9059)
| ~ class_Divides_Osemiring__div(U_9059) ),
inference(clausify,[status(thm)],[f_2282_3]) ).
fof(f_2283_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_2283_2,plain,
! [U_9065,U_9064,U_9063,U_9062] :
( c_Divides_Odiv__class_Omod(U_9062,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9062),U_9063),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9062),U_9064),U_9065)),U_9064) = c_Divides_Odiv__class_Omod(U_9062,U_9063,U_9064)
| ~ class_Divides_Osemiring__div(U_9062) ),
inference(variable_rename,[status(thm)],[f_2283_1]) ).
fof(f_2283_3,plain,
! [U_9062,U_9063,U_9064,U_9065] :
( c_Divides_Odiv__class_Omod(U_9062,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9062),U_9063),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9062),U_9064),U_9065)),U_9064) = c_Divides_Odiv__class_Omod(U_9062,U_9063,U_9064)
| ~ class_Divides_Osemiring__div(U_9062) ),
inference(definitional_conversion,[status(esa)],[f_2283_2]) ).
cnf(f_2283_4,plain,
( c_Divides_Odiv__class_Omod(U_9062,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9062),U_9063),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9062),U_9064),U_9065)),U_9064) = c_Divides_Odiv__class_Omod(U_9062,U_9063,U_9064)
| ~ class_Divides_Osemiring__div(U_9062) ),
inference(clausify,[status(thm)],[f_2283_3]) ).
fof(f_2284_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_2284_2,plain,
! [U_9069,U_9068,U_9067,U_9066] :
( c_Divides_Odiv__class_Omod(U_9066,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9066),U_9067),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9066),U_9068),U_9069)),U_9069) = c_Divides_Odiv__class_Omod(U_9066,U_9067,U_9069)
| ~ class_Divides_Osemiring__div(U_9066) ),
inference(variable_rename,[status(thm)],[f_2284_1]) ).
fof(f_2284_3,plain,
! [U_9066,U_9067,U_9068,U_9069] :
( c_Divides_Odiv__class_Omod(U_9066,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9066),U_9067),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9066),U_9068),U_9069)),U_9069) = c_Divides_Odiv__class_Omod(U_9066,U_9067,U_9069)
| ~ class_Divides_Osemiring__div(U_9066) ),
inference(definitional_conversion,[status(esa)],[f_2284_2]) ).
cnf(f_2284_4,plain,
( c_Divides_Odiv__class_Omod(U_9066,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9066),U_9067),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9066),U_9068),U_9069)),U_9069) = c_Divides_Odiv__class_Omod(U_9066,U_9067,U_9069)
| ~ class_Divides_Osemiring__div(U_9066) ),
inference(clausify,[status(thm)],[f_2284_3]) ).
fof(f_2285_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_2285_2,plain,
! [U_9071,U_9070] :
( c_Divides_Odiv__class_Omod(U_9070,U_9071,c_Groups_Oone__class_Oone(U_9070)) = c_Groups_Ozero__class_Ozero(U_9070)
| ~ class_Divides_Osemiring__div(U_9070) ),
inference(variable_rename,[status(thm)],[f_2285_1]) ).
fof(f_2285_3,plain,
! [U_9070,U_9071] :
( c_Divides_Odiv__class_Omod(U_9070,U_9071,c_Groups_Oone__class_Oone(U_9070)) = c_Groups_Ozero__class_Ozero(U_9070)
| ~ class_Divides_Osemiring__div(U_9070) ),
inference(definitional_conversion,[status(esa)],[f_2285_2]) ).
cnf(f_2285_4,plain,
( c_Divides_Odiv__class_Omod(U_9070,U_9071,c_Groups_Oone__class_Oone(U_9070)) = c_Groups_Ozero__class_Ozero(U_9070)
| ~ class_Divides_Osemiring__div(U_9070) ),
inference(clausify,[status(thm)],[f_2285_3]) ).
fof(f_2286_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_2286_2,plain,
! [U_9074,U_9073,U_9072] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9072),c_Divides_Odiv__class_Omod(U_9072,U_9073,U_9074)),U_9074) = c_Groups_Ozero__class_Ozero(U_9072)
| ~ class_Divides_Osemiring__div(U_9072) ),
inference(variable_rename,[status(thm)],[f_2286_1]) ).
fof(f_2286_3,plain,
! [U_9072,U_9073,U_9074] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9072),c_Divides_Odiv__class_Omod(U_9072,U_9073,U_9074)),U_9074) = c_Groups_Ozero__class_Ozero(U_9072)
| ~ class_Divides_Osemiring__div(U_9072) ),
inference(definitional_conversion,[status(esa)],[f_2286_2]) ).
cnf(f_2286_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9072),c_Divides_Odiv__class_Omod(U_9072,U_9073,U_9074)),U_9074) = c_Groups_Ozero__class_Ozero(U_9072)
| ~ class_Divides_Osemiring__div(U_9072) ),
inference(clausify,[status(thm)],[f_2286_3]) ).
fof(f_2287_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_2287_2,plain,
! [U_9076,U_9075] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9075,U_9076)),U_9075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9075)) ),
inference(variable_rename,[status(thm)],[f_2287_1]) ).
fof(f_2287_3,plain,
! [U_9075,U_9076] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9075,U_9076)),U_9075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9075)) ),
inference(definitional_conversion,[status(esa)],[f_2287_2]) ).
cnf(f_2287_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9075,U_9076)),U_9075))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9075)) ),
inference(clausify,[status(thm)],[f_2287_3]) ).
fof(f_2288_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_2288_2,plain,
! [U_9078,U_9077] :
( 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_9077,U_9078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9077)) ),
inference(variable_rename,[status(thm)],[f_2288_1]) ).
fof(f_2288_3,plain,
! [U_9077,U_9078] :
( 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_9077,U_9078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9077)) ),
inference(definitional_conversion,[status(esa)],[f_2288_2]) ).
cnf(f_2288_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_9077,U_9078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9077)) ),
inference(clausify,[status(thm)],[f_2288_3]) ).
fof(f_2289_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_2289_2,plain,
! [U_9080,U_9079] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9080,U_9079)),U_9079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9079)) ),
inference(variable_rename,[status(thm)],[f_2289_1]) ).
fof(f_2289_3,plain,
! [U_9079,U_9080] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9080,U_9079)),U_9079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9079)) ),
inference(definitional_conversion,[status(esa)],[f_2289_2]) ).
cnf(f_2289_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9080,U_9079)),U_9079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9079)) ),
inference(clausify,[status(thm)],[f_2289_3]) ).
fof(f_2290_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_2290_2,plain,
! [U_9082,U_9081] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9081),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9082,U_9081)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9081),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2290_1]) ).
fof(f_2290_3,plain,
! [U_9081,U_9082] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9081),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9082,U_9081)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9081),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2290_2]) ).
cnf(f_2290_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9081),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9082,U_9081)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9081),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2290_3]) ).
fof(f_2291_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_2291_2,plain,
! [U_9086,U_9085] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9085,U_9086) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [U_9084] : U_9085 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9086),U_9084) )
& ( ? [U_9083] : U_9085 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9086),U_9083)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9085,U_9086) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_2291_1]) ).
fof(f_2291_3,plain,
( ! [U_9090,U_9088] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9088,U_9090) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [U_9084] : U_9088 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9090),U_9084) )
& ! [U_9089,U_9087] :
( ? [U_9083] : U_9087 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9089),U_9083)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9087,U_9089) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_2291_2]) ).
fof(f_2291_4,plain,
( ! [U_9090,U_9088] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9088,U_9090) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [U_9084] : U_9088 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9090),U_9084) )
& ! [U_9089,U_9087] :
( U_9087 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9089),sK220(U_9089,U_9087))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9087,U_9089) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_9083,sK220(U_9089,U_9087))],[f_2291_3]) ).
fof(f_2291_5,plain,
( ! [U_9084,U_9088,U_9090] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9088,U_9090) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_9088 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9090),U_9084) )
& ! [U_9087,U_9089] :
( U_9087 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9089),sK220(U_9089,U_9087))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9087,U_9089) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa)],[f_2291_4]) ).
cnf(f_2291_6,plain,
( U_9087 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9089),sK220(U_9089,U_9087))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9087,U_9089) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2291_5]) ).
cnf(f_2291_7,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9088,U_9090) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_9088 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9090),U_9084) ),
inference(clausify,[status(thm)],[f_2291_5]) ).
fof(f_2292_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_2292_2,plain,
! [U_9092,U_9091] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9091,U_9092) != 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_9091),U_9092) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2292_1]) ).
fof(f_2292_3,plain,
! [U_9092,U_9091] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9091,U_9092) != 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_9091),U_9092) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_2292_2]) ).
cnf(f_2292_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9091,U_9092) != 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_9091),U_9092) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2292_3]) ).
fof(f_2293_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_2293_2,plain,
! [U_9094,U_9093] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9093,U_9094) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9093,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9094)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2293_1]) ).
fof(f_2293_3,plain,
! [U_9094,U_9093] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9093,U_9094) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9093,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9094)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_2293_2]) ).
cnf(f_2293_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9093,U_9094) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9093,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9094)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2293_3]) ).
fof(f_2294_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_2294_2,plain,
! [U_9096,U_9095] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9095,U_9096)),U_9096) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_2294_1]) ).
fof(f_2294_3,plain,
! [U_9095,U_9096] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9095,U_9096)),U_9096) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_2294_2]) ).
cnf(f_2294_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9095,U_9096)),U_9096) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_2294_3]) ).
fof(f_2295_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_2295_2,plain,
! [U_9097] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9097,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_9097
& hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9097),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2295_1]) ).
fof(f_2295_3,plain,
( ! [U_9099] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9099,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_9099
& ! [U_9098] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9098),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(miniscope,[status(thm)],[f_2295_2]) ).
fof(f_2295_4,plain,
( ! [U_9099] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9099,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_9099
& ! [U_9098] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9098),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_2295_3]) ).
cnf(f_2295_5,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9098),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_2295_4]) ).
cnf(f_2295_6,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9099,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_9099,
inference(clausify,[status(thm)],[f_2295_4]) ).
fof(f_2296_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_2296_2,plain,
! [U_9102,U_9101,U_9100] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9100),U_9101)),U_9102) = 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_9100),U_9102)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9101),U_9102))),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_9100,U_9102)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9101,U_9102))),U_9102)),
inference(variable_rename,[status(thm)],[f_2296_1]) ).
fof(f_2296_3,plain,
! [U_9100,U_9101,U_9102] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9100),U_9101)),U_9102) = 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_9100),U_9102)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9101),U_9102))),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_9100,U_9102)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9101,U_9102))),U_9102)),
inference(definitional_conversion,[status(esa)],[f_2296_2]) ).
cnf(f_2296_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9100),U_9101)),U_9102) = 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_9100),U_9102)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9101),U_9102))),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_9100,U_9102)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9101,U_9102))),U_9102)),
inference(clausify,[status(thm)],[f_2296_3]) ).
fof(f_2297_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_2297_2,plain,
! [U_9105,U_9104,U_9103] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9103),c_Divides_Odiv__class_Omod(U_9103,U_9104,U_9105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9103),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9103),U_9104),U_9105)),U_9105)) = U_9104
| ~ class_Divides_Osemiring__div(U_9103) ),
inference(variable_rename,[status(thm)],[f_2297_1]) ).
fof(f_2297_3,plain,
! [U_9103,U_9104,U_9105] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9103),c_Divides_Odiv__class_Omod(U_9103,U_9104,U_9105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9103),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9103),U_9104),U_9105)),U_9105)) = U_9104
| ~ class_Divides_Osemiring__div(U_9103) ),
inference(definitional_conversion,[status(esa)],[f_2297_2]) ).
cnf(f_2297_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9103),c_Divides_Odiv__class_Omod(U_9103,U_9104,U_9105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9103),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9103),U_9104),U_9105)),U_9105)) = U_9104
| ~ class_Divides_Osemiring__div(U_9103) ),
inference(clausify,[status(thm)],[f_2297_3]) ).
fof(f_2298_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_2298_2,plain,
! [U_9108,U_9107,U_9106] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9106),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9106),U_9107),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9106),U_9108),U_9107))),c_Divides_Odiv__class_Omod(U_9106,U_9108,U_9107)) = U_9108
| ~ class_Divides_Osemiring__div(U_9106) ),
inference(variable_rename,[status(thm)],[f_2298_1]) ).
fof(f_2298_3,plain,
! [U_9106,U_9107,U_9108] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9106),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9106),U_9107),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9106),U_9108),U_9107))),c_Divides_Odiv__class_Omod(U_9106,U_9108,U_9107)) = U_9108
| ~ class_Divides_Osemiring__div(U_9106) ),
inference(definitional_conversion,[status(esa)],[f_2298_2]) ).
cnf(f_2298_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9106),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9106),U_9107),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9106),U_9108),U_9107))),c_Divides_Odiv__class_Omod(U_9106,U_9108,U_9107)) = U_9108
| ~ class_Divides_Osemiring__div(U_9106) ),
inference(clausify,[status(thm)],[f_2298_3]) ).
fof(f_2299_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_2299_2,plain,
! [U_9111,U_9110,U_9109] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9109),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9109),U_9110),U_9111)),U_9111)),c_Divides_Odiv__class_Omod(U_9109,U_9110,U_9111)) = U_9110
| ~ class_Divides_Osemiring__div(U_9109) ),
inference(variable_rename,[status(thm)],[f_2299_1]) ).
fof(f_2299_3,plain,
! [U_9109,U_9110,U_9111] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9109),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9109),U_9110),U_9111)),U_9111)),c_Divides_Odiv__class_Omod(U_9109,U_9110,U_9111)) = U_9110
| ~ class_Divides_Osemiring__div(U_9109) ),
inference(definitional_conversion,[status(esa)],[f_2299_2]) ).
cnf(f_2299_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9109),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9109),U_9110),U_9111)),U_9111)),c_Divides_Odiv__class_Omod(U_9109,U_9110,U_9111)) = U_9110
| ~ class_Divides_Osemiring__div(U_9109) ),
inference(clausify,[status(thm)],[f_2299_3]) ).
fof(f_2300_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_2300_2,plain,
! [U_9115,U_9114,U_9113,U_9112] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9112),U_9113),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9112),U_9114),U_9113))),c_Divides_Odiv__class_Omod(U_9112,U_9114,U_9113))),U_9115) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9112),U_9114),U_9115)
| ~ class_Divides_Osemiring__div(U_9112) ),
inference(variable_rename,[status(thm)],[f_2300_1]) ).
fof(f_2300_3,plain,
! [U_9112,U_9113,U_9114,U_9115] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9112),U_9113),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9112),U_9114),U_9113))),c_Divides_Odiv__class_Omod(U_9112,U_9114,U_9113))),U_9115) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9112),U_9114),U_9115)
| ~ class_Divides_Osemiring__div(U_9112) ),
inference(definitional_conversion,[status(esa)],[f_2300_2]) ).
cnf(f_2300_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9112),U_9113),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9112),U_9114),U_9113))),c_Divides_Odiv__class_Omod(U_9112,U_9114,U_9113))),U_9115) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9112),U_9114),U_9115)
| ~ class_Divides_Osemiring__div(U_9112) ),
inference(clausify,[status(thm)],[f_2300_3]) ).
fof(f_2301_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_2301_2,plain,
! [U_9119,U_9118,U_9117,U_9116] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9116),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9116),U_9117),U_9118)),U_9118)),c_Divides_Odiv__class_Omod(U_9116,U_9117,U_9118))),U_9119) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9116),U_9117),U_9119)
| ~ class_Divides_Osemiring__div(U_9116) ),
inference(variable_rename,[status(thm)],[f_2301_1]) ).
fof(f_2301_3,plain,
! [U_9116,U_9117,U_9118,U_9119] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9116),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9116),U_9117),U_9118)),U_9118)),c_Divides_Odiv__class_Omod(U_9116,U_9117,U_9118))),U_9119) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9116),U_9117),U_9119)
| ~ class_Divides_Osemiring__div(U_9116) ),
inference(definitional_conversion,[status(esa)],[f_2301_2]) ).
cnf(f_2301_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9116),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_9116),U_9117),U_9118)),U_9118)),c_Divides_Odiv__class_Omod(U_9116,U_9117,U_9118))),U_9119) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9116),U_9117),U_9119)
| ~ class_Divides_Osemiring__div(U_9116) ),
inference(clausify,[status(thm)],[f_2301_3]) ).
fof(f_2302_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_2302_2,plain,
! [U_9121,U_9120] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9120,U_9121) = U_9120
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9121),U_9120))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9120),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2302_1]) ).
fof(f_2302_3,plain,
! [U_9120,U_9121] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9120,U_9121) = U_9120
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9121),U_9120))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9120),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2302_2]) ).
cnf(f_2302_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9120,U_9121) = U_9120
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9121),U_9120))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9120),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2302_3]) ).
fof(f_2303_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_2303_2,plain,
! [U_9123,U_9122] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9122),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9123,U_9122)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9123,U_9122)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9122),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2303_1]) ).
fof(f_2303_3,plain,
( ! [U_9122,U_9123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9122),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9123,U_9122)))
| ~ sP629(U_9122,U_9123) )
& ! [U_9122,U_9123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9123,U_9122)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP629(U_9122,U_9123) )
& ! [U_9122,U_9123] :
( sP629(U_9122,U_9123)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9122),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP629])],[f_2303_2]) ).
cnf(f_2303_4,plain,
( sP629(U_9122,U_9123)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9122),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2303_3]) ).
cnf(f_2303_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9123,U_9122)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP629(U_9122,U_9123) ),
inference(clausify,[status(thm)],[f_2303_3]) ).
cnf(f_2303_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9122),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9123,U_9122)))
| ~ sP629(U_9122,U_9123) ),
inference(clausify,[status(thm)],[f_2303_3]) ).
fof(f_2304_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_2304_2,plain,
! [U_9125,U_9124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9125,U_9124)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9124),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2304_1]) ).
fof(f_2304_3,plain,
! [U_9124,U_9125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9125,U_9124)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9124),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2304_2]) ).
cnf(f_2304_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9125,U_9124)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9124),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2304_3]) ).
fof(f_2305_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_2305_2,plain,
! [U_9127,U_9126] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9126,U_9127) = U_9126
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9126),U_9127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9126)) ),
inference(variable_rename,[status(thm)],[f_2305_1]) ).
fof(f_2305_3,plain,
! [U_9126,U_9127] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9126,U_9127) = U_9126
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9126),U_9127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9126)) ),
inference(definitional_conversion,[status(esa)],[f_2305_2]) ).
cnf(f_2305_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9126,U_9127) = U_9126
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9126),U_9127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9126)) ),
inference(clausify,[status(thm)],[f_2305_3]) ).
fof(f_2306_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_2306_2,plain,
! [U_9129,U_9128] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9129,U_9128)),U_9128))
& 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_9129,U_9128))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9128)) ),
inference(variable_rename,[status(thm)],[f_2306_1]) ).
fof(f_2306_3,plain,
( ! [U_9128,U_9129] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9129,U_9128)),U_9128))
| ~ sP630(U_9128,U_9129) )
& ! [U_9128,U_9129] :
( 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_9129,U_9128)))
| ~ sP630(U_9128,U_9129) )
& ! [U_9128,U_9129] :
( sP630(U_9128,U_9129)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9128)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP630])],[f_2306_2]) ).
cnf(f_2306_4,plain,
( sP630(U_9128,U_9129)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9128)) ),
inference(clausify,[status(thm)],[f_2306_3]) ).
cnf(f_2306_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_9129,U_9128)))
| ~ sP630(U_9128,U_9129) ),
inference(clausify,[status(thm)],[f_2306_3]) ).
cnf(f_2306_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9129,U_9128)),U_9128))
| ~ sP630(U_9128,U_9129) ),
inference(clausify,[status(thm)],[f_2306_3]) ).
fof(f_2307_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_2307_2,plain,
! [U_9131,U_9130] :
( 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_9131,U_9130)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9130)) ),
inference(variable_rename,[status(thm)],[f_2307_1]) ).
fof(f_2307_3,plain,
! [U_9130,U_9131] :
( 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_9131,U_9130)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9130)) ),
inference(definitional_conversion,[status(esa)],[f_2307_2]) ).
cnf(f_2307_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_9131,U_9130)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9130)) ),
inference(clausify,[status(thm)],[f_2307_3]) ).
fof(f_2308_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_2308_2,plain,
! [U_9133,U_9132] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9132,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9132,U_9133)),U_9133)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9132,U_9133) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9132,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9133)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9132,U_9133) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_2308_1]) ).
fof(f_2308_3,plain,
( ! [U_9137,U_9135] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9135,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9137)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9135,U_9137)),U_9137)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9135,U_9137) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_9136,U_9134] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9134,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9136)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9134,U_9136) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_2308_2]) ).
fof(f_2308_4,plain,
( ! [U_9137,U_9135] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9135,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9137)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9135,U_9137)),U_9137)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9135,U_9137) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_9134,U_9136] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9134,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9136)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9134,U_9136) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa)],[f_2308_3]) ).
cnf(f_2308_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9134,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9136)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9134,U_9136) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2308_4]) ).
cnf(f_2308_6,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9135,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9137)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9135,U_9137)),U_9137)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9135,U_9137) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2308_4]) ).
fof(f_2309_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_2309_2,plain,
! [U_9139,U_9138] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9138),U_9139) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9139),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9138,U_9139))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9138,U_9139) = 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_9138),U_9139) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9138,U_9139) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_2309_1]) ).
fof(f_2309_3,plain,
( ! [U_9143,U_9141] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9141),U_9143) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9143),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9141,U_9143))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9141,U_9143) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_9142,U_9140] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9140),U_9142) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9140,U_9142) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_2309_2]) ).
fof(f_2309_4,plain,
( ! [U_9143,U_9141] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9141),U_9143) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9143),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9141,U_9143))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9141,U_9143) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_9140,U_9142] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9140),U_9142) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9140,U_9142) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa)],[f_2309_3]) ).
cnf(f_2309_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9140),U_9142) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9140,U_9142) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2309_4]) ).
cnf(f_2309_6,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9141),U_9143) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9143),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9141,U_9143))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9141,U_9143) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2309_4]) ).
fof(f_2310_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_2310_2,plain,
! [U_9145,U_9144] : U_9144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9145),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9144),U_9145))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9144,U_9145)),
inference(variable_rename,[status(thm)],[f_2310_1]) ).
fof(f_2310_3,plain,
! [U_9144,U_9145] : U_9144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9145),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9144),U_9145))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9144,U_9145)),
inference(definitional_conversion,[status(esa)],[f_2310_2]) ).
cnf(f_2310_4,plain,
U_9144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9145),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9144),U_9145))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9144,U_9145)),
inference(clausify,[status(thm)],[f_2310_3]) ).
fof(f_2311_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_2311_2,plain,
! [U_9148,U_9147,U_9146] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9146),U_9147)),U_9148) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9146),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9147),U_9148))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9146),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9147,U_9148))),U_9148)),
inference(variable_rename,[status(thm)],[f_2311_1]) ).
fof(f_2311_3,plain,
! [U_9146,U_9147,U_9148] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9146),U_9147)),U_9148) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9146),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9147),U_9148))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9146),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9147,U_9148))),U_9148)),
inference(definitional_conversion,[status(esa)],[f_2311_2]) ).
cnf(f_2311_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9146),U_9147)),U_9148) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9146),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9147),U_9148))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9146),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9147,U_9148))),U_9148)),
inference(clausify,[status(thm)],[f_2311_3]) ).
fof(f_2312_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_2312_2,plain,
! [U_9151,U_9150,U_9149] : 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_9149),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9150),U_9149))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9150,U_9149))),U_9151) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9150),U_9151),
inference(variable_rename,[status(thm)],[f_2312_1]) ).
fof(f_2312_3,plain,
! [U_9149,U_9150,U_9151] : 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_9149),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9150),U_9149))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9150,U_9149))),U_9151) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9150),U_9151),
inference(definitional_conversion,[status(esa)],[f_2312_2]) ).
cnf(f_2312_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_9149),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9150),U_9149))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9150,U_9149))),U_9151) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9150),U_9151),
inference(clausify,[status(thm)],[f_2312_3]) ).
fof(f_2313_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_2313_2,plain,
! [U_9154,U_9153,U_9152] : 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_9152),U_9153)),U_9153)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9152,U_9153))),U_9154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9152),U_9154),
inference(variable_rename,[status(thm)],[f_2313_1]) ).
fof(f_2313_3,plain,
! [U_9152,U_9153,U_9154] : 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_9152),U_9153)),U_9153)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9152,U_9153))),U_9154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9152),U_9154),
inference(definitional_conversion,[status(esa)],[f_2313_2]) ).
cnf(f_2313_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_9152),U_9153)),U_9153)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9152,U_9153))),U_9154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9152),U_9154),
inference(clausify,[status(thm)],[f_2313_3]) ).
fof(f_2314_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_2314_2,plain,
! [U_9156,U_9155] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9155),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9156),U_9155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9156),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9156,U_9155)),
inference(variable_rename,[status(thm)],[f_2314_1]) ).
fof(f_2314_3,plain,
! [U_9155,U_9156] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9155),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9156),U_9155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9156),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9156,U_9155)),
inference(definitional_conversion,[status(esa)],[f_2314_2]) ).
cnf(f_2314_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9155),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9156),U_9155)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9156),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9156,U_9155)),
inference(clausify,[status(thm)],[f_2314_3]) ).
fof(f_2315_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_2315_2,plain,
! [U_9158,U_9157] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9157,U_9158) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9157),U_9158)),U_9158)),
inference(variable_rename,[status(thm)],[f_2315_1]) ).
fof(f_2315_3,plain,
! [U_9157,U_9158] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9157,U_9158) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9157),U_9158)),U_9158)),
inference(definitional_conversion,[status(esa)],[f_2315_2]) ).
cnf(f_2315_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9157,U_9158) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9157),U_9158)),U_9158)),
inference(clausify,[status(thm)],[f_2315_3]) ).
fof(f_2316_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_2316_2,plain,
! [U_9160,U_9159] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9159,U_9160) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9159),U_9160)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9159),U_9160)),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_9159)) ),
inference(variable_rename,[status(thm)],[f_2316_1]) ).
fof(f_2316_3,plain,
! [U_9159,U_9160] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9159,U_9160) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9159),U_9160)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9159),U_9160)),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_9159)) ),
inference(definitional_conversion,[status(esa)],[f_2316_2]) ).
cnf(f_2316_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9159,U_9160) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9159),U_9160)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9159),U_9160)),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_9159)) ),
inference(clausify,[status(thm)],[f_2316_3]) ).
fof(f_2317_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_2317_2,plain,
! [U_9164,U_9163,U_9162,U_9161] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9161,U_9162) = U_9164
| U_9162 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9164),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9162),U_9164)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9162)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9164),U_9162))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9164)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9162)) )
| U_9161 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9162),U_9163)),U_9164) ),
inference(variable_rename,[status(thm)],[f_2317_1]) ).
fof(f_2317_3,plain,
( ! [U_9162,U_9164] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9164),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9162),U_9164))
| ~ sP632(U_9162,U_9164) )
& ! [U_9162,U_9164] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9162))
| ~ sP632(U_9162,U_9164) )
& ! [U_9162,U_9164] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9164),U_9162))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9164))
| ~ sP631(U_9162,U_9164) )
& ! [U_9162,U_9164] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9162))
| ~ sP631(U_9162,U_9164) )
& ! [U_9161,U_9162,U_9163,U_9164] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9161,U_9162) = U_9164
| U_9162 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP632(U_9162,U_9164)
| sP631(U_9162,U_9164)
| U_9161 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9162),U_9163)),U_9164) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP631,sP632])],[f_2317_2]) ).
cnf(f_2317_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9161,U_9162) = U_9164
| U_9162 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP632(U_9162,U_9164)
| sP631(U_9162,U_9164)
| U_9161 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9162),U_9163)),U_9164) ),
inference(clausify,[status(thm)],[f_2317_3]) ).
cnf(f_2317_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9162))
| ~ sP631(U_9162,U_9164) ),
inference(clausify,[status(thm)],[f_2317_3]) ).
cnf(f_2317_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9164),U_9162))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9164))
| ~ sP631(U_9162,U_9164) ),
inference(clausify,[status(thm)],[f_2317_3]) ).
cnf(f_2317_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9162))
| ~ sP632(U_9162,U_9164) ),
inference(clausify,[status(thm)],[f_2317_3]) ).
cnf(f_2317_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9164),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9162),U_9164))
| ~ sP632(U_9162,U_9164) ),
inference(clausify,[status(thm)],[f_2317_3]) ).
fof(f_2318_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_2318_2,plain,
! [U_9168,U_9167,U_9166,U_9165] :
( 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_9166),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9168,U_9165))),U_9167)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9167),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9166),U_9167))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9165)) ),
inference(variable_rename,[status(thm)],[f_2318_1]) ).
fof(f_2318_3,plain,
! [U_9165,U_9167,U_9166,U_9168] :
( 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_9166),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9168,U_9165))),U_9167)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9167),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9166),U_9167))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9165)) ),
inference(definitional_conversion,[status(esa)],[f_2318_2]) ).
cnf(f_2318_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_9166),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9168,U_9165))),U_9167)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9167),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9166),U_9167))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9165)) ),
inference(clausify,[status(thm)],[f_2318_3]) ).
fof(f_2319_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_2319_2,plain,
! [U_9172,U_9171,U_9170,U_9169] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9170),U_9169)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9170),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9172,U_9169))),U_9171)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9171),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9170),U_9171))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9169)) ),
inference(variable_rename,[status(thm)],[f_2319_1]) ).
fof(f_2319_3,plain,
! [U_9172,U_9171,U_9169,U_9170] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9170),U_9169)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9170),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9172,U_9169))),U_9171)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9171),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9170),U_9171))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9169)) ),
inference(definitional_conversion,[status(esa)],[f_2319_2]) ).
cnf(f_2319_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9170),U_9169)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9170),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9172,U_9169))),U_9171)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9171),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9170),U_9171))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9169)) ),
inference(clausify,[status(thm)],[f_2319_3]) ).
fof(f_2320_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_2320_2,plain,
! [U_9176,U_9175,U_9174,U_9173] :
( 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_9175),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9176,U_9173))),U_9174)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9175),U_9173)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9174),U_9175))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9174))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9173)) ),
inference(variable_rename,[status(thm)],[f_2320_1]) ).
fof(f_2320_3,plain,
! [U_9173,U_9174,U_9175,U_9176] :
( 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_9175),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9176,U_9173))),U_9174)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9175),U_9173)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9174),U_9175))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9174))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9173)) ),
inference(definitional_conversion,[status(esa)],[f_2320_2]) ).
cnf(f_2320_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_9175),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9176,U_9173))),U_9174)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9175),U_9173)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9174),U_9175))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9174))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9173)) ),
inference(clausify,[status(thm)],[f_2320_3]) ).
fof(f_2321_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_2321_2,plain,
! [U_9180,U_9179,U_9178,U_9177] :
( 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_9179),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9180,U_9177))),U_9178)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9178),U_9179))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9177)) ),
inference(variable_rename,[status(thm)],[f_2321_1]) ).
fof(f_2321_3,plain,
! [U_9177,U_9178,U_9179,U_9180] :
( 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_9179),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9180,U_9177))),U_9178)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9178),U_9179))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9177)) ),
inference(definitional_conversion,[status(esa)],[f_2321_2]) ).
cnf(f_2321_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_9179),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9180,U_9177))),U_9178)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9178),U_9179))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9177)) ),
inference(clausify,[status(thm)],[f_2321_3]) ).
fof(f_2322_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_2322_2,plain,
! [U_9191,U_9190,U_9189] :
( ( hBOOL(hAPP(U_9189,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9190,U_9191)))
| ( ? [U_9188,U_9187] :
( ~ hBOOL(hAPP(U_9189,U_9187))
& U_9190 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9191),U_9188)),U_9187)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9187),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9191),U_9187)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9191),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_9186,U_9185] :
( ~ hBOOL(hAPP(U_9189,U_9185))
& U_9190 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9191),U_9186)),U_9185)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9185),U_9191))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9185)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9191)) )
| ( ~ hBOOL(hAPP(U_9189,U_9190))
& U_9191 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [U_9184,U_9183] :
( hBOOL(hAPP(U_9189,U_9183))
| U_9190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9191),U_9184)),U_9183)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9191),U_9183)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9191),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_9182,U_9181] :
( hBOOL(hAPP(U_9189,U_9181))
| U_9190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9191),U_9182)),U_9181)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9181),U_9191))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9181)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9191)) )
& ( hBOOL(hAPP(U_9189,U_9190))
| U_9191 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_9189,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9190,U_9191))) ) ),
inference(variable_rename,[status(thm)],[f_2322_1]) ).
fof(f_2322_3,plain,
( ! [U_9197,U_9195,U_9193] :
( hBOOL(hAPP(U_9193,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9195,U_9197)))
| ( ? [U_9188,U_9187] :
( ~ hBOOL(hAPP(U_9193,U_9187))
& U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),U_9188)),U_9187)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9187),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),U_9187)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_9186,U_9185] :
( ~ hBOOL(hAPP(U_9193,U_9185))
& U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),U_9186)),U_9185)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9185),U_9197))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9185)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9197)) )
| ( ~ hBOOL(hAPP(U_9193,U_9195))
& U_9197 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_9196,U_9194,U_9192] :
( ( ( ! [U_9184,U_9183] :
( hBOOL(hAPP(U_9192,U_9183))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9184)),U_9183)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),U_9183)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_9182,U_9181] :
( hBOOL(hAPP(U_9192,U_9181))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9182)),U_9181)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9181),U_9196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9181)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9196)) )
& ( hBOOL(hAPP(U_9192,U_9194))
| U_9196 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_9192,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9194,U_9196))) ) ),
inference(miniscope,[status(thm)],[f_2322_2]) ).
fof(f_2322_4,plain,
( ! [U_9197,U_9195,U_9193] :
( hBOOL(hAPP(U_9193,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9195,U_9197)))
| ( ? [U_9188,U_9187] :
( ~ hBOOL(hAPP(U_9193,U_9187))
& U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),U_9188)),U_9187)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9187),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),U_9187)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_9185] :
( ~ hBOOL(hAPP(U_9193,U_9185))
& U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),sK221(U_9197,U_9195,U_9193))),U_9185)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9185),U_9197))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9185)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9197)) )
| ( ~ hBOOL(hAPP(U_9193,U_9195))
& U_9197 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_9196,U_9194,U_9192] :
( ( ( ! [U_9184,U_9183] :
( hBOOL(hAPP(U_9192,U_9183))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9184)),U_9183)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),U_9183)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_9182,U_9181] :
( hBOOL(hAPP(U_9192,U_9181))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9182)),U_9181)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9181),U_9196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9181)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9196)) )
& ( hBOOL(hAPP(U_9192,U_9194))
| U_9196 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_9192,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9194,U_9196))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_9186,sK221(U_9197,U_9195,U_9193))],[f_2322_3]) ).
fof(f_2322_5,plain,
( ! [U_9197,U_9195,U_9193] :
( hBOOL(hAPP(U_9193,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9195,U_9197)))
| ( ? [U_9188,U_9187] :
( ~ hBOOL(hAPP(U_9193,U_9187))
& U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),U_9188)),U_9187)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9187),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),U_9187)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_9193,sK222(U_9197,U_9195,U_9193)))
& U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),sK221(U_9197,U_9195,U_9193))),sK222(U_9197,U_9195,U_9193))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK222(U_9197,U_9195,U_9193)),U_9197))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK222(U_9197,U_9195,U_9193)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9197)) )
| ( ~ hBOOL(hAPP(U_9193,U_9195))
& U_9197 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_9196,U_9194,U_9192] :
( ( ( ! [U_9184,U_9183] :
( hBOOL(hAPP(U_9192,U_9183))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9184)),U_9183)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),U_9183)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_9182,U_9181] :
( hBOOL(hAPP(U_9192,U_9181))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9182)),U_9181)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9181),U_9196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9181)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9196)) )
& ( hBOOL(hAPP(U_9192,U_9194))
| U_9196 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_9192,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9194,U_9196))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_9185,sK222(U_9197,U_9195,U_9193))],[f_2322_4]) ).
fof(f_2322_6,plain,
( ! [U_9197,U_9195,U_9193] :
( hBOOL(hAPP(U_9193,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9195,U_9197)))
| ( ? [U_9187] :
( ~ hBOOL(hAPP(U_9193,U_9187))
& U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),sK223(U_9197,U_9195,U_9193))),U_9187)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9187),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),U_9187)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_9193,sK222(U_9197,U_9195,U_9193)))
& U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),sK221(U_9197,U_9195,U_9193))),sK222(U_9197,U_9195,U_9193))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK222(U_9197,U_9195,U_9193)),U_9197))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK222(U_9197,U_9195,U_9193)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9197)) )
| ( ~ hBOOL(hAPP(U_9193,U_9195))
& U_9197 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_9196,U_9194,U_9192] :
( ( ( ! [U_9184,U_9183] :
( hBOOL(hAPP(U_9192,U_9183))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9184)),U_9183)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),U_9183)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_9182,U_9181] :
( hBOOL(hAPP(U_9192,U_9181))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9182)),U_9181)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9181),U_9196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9181)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9196)) )
& ( hBOOL(hAPP(U_9192,U_9194))
| U_9196 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_9192,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9194,U_9196))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_9188,sK223(U_9197,U_9195,U_9193))],[f_2322_5]) ).
fof(f_2322_7,plain,
( ! [U_9197,U_9195,U_9193] :
( hBOOL(hAPP(U_9193,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9195,U_9197)))
| ( ~ hBOOL(hAPP(U_9193,sK224(U_9197,U_9195,U_9193)))
& U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),sK223(U_9197,U_9195,U_9193))),sK224(U_9197,U_9195,U_9193))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK224(U_9197,U_9195,U_9193)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),sK224(U_9197,U_9195,U_9193)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_9193,sK222(U_9197,U_9195,U_9193)))
& U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),sK221(U_9197,U_9195,U_9193))),sK222(U_9197,U_9195,U_9193))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK222(U_9197,U_9195,U_9193)),U_9197))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK222(U_9197,U_9195,U_9193)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9197)) )
| ( ~ hBOOL(hAPP(U_9193,U_9195))
& U_9197 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_9196,U_9194,U_9192] :
( ( ( ! [U_9184,U_9183] :
( hBOOL(hAPP(U_9192,U_9183))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9184)),U_9183)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),U_9183)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_9182,U_9181] :
( hBOOL(hAPP(U_9192,U_9181))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9182)),U_9181)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9181),U_9196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9181)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9196)) )
& ( hBOOL(hAPP(U_9192,U_9194))
| U_9196 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_9192,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9194,U_9196))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_9187,sK224(U_9197,U_9195,U_9193))],[f_2322_6]) ).
fof(f_2322_8,plain,
( ! [U_9193,U_9197,U_9195] :
( ~ hBOOL(hAPP(U_9193,sK224(U_9197,U_9195,U_9193)))
| ~ sP636(U_9193,U_9197,U_9195) )
& ! [U_9193,U_9197,U_9195] :
( U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),sK223(U_9197,U_9195,U_9193))),sK224(U_9197,U_9195,U_9193))
| ~ sP636(U_9193,U_9197,U_9195) )
& ! [U_9193,U_9197,U_9195] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK224(U_9197,U_9195,U_9193)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP636(U_9193,U_9197,U_9195) )
& ! [U_9193,U_9197,U_9195] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),sK224(U_9197,U_9195,U_9193)))
| ~ sP636(U_9193,U_9197,U_9195) )
& ! [U_9193,U_9197,U_9195] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP636(U_9193,U_9197,U_9195) )
& ! [U_9193,U_9197,U_9195] :
( ~ hBOOL(hAPP(U_9193,sK222(U_9197,U_9195,U_9193)))
| ~ sP635(U_9193,U_9197,U_9195) )
& ! [U_9193,U_9197,U_9195] :
( U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),sK221(U_9197,U_9195,U_9193))),sK222(U_9197,U_9195,U_9193))
| ~ sP635(U_9193,U_9197,U_9195) )
& ! [U_9193,U_9197,U_9195] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK222(U_9197,U_9195,U_9193)),U_9197))
| ~ sP635(U_9193,U_9197,U_9195) )
& ! [U_9193,U_9197,U_9195] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK222(U_9197,U_9195,U_9193)))
| ~ sP635(U_9193,U_9197,U_9195) )
& ! [U_9193,U_9197,U_9195] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9197))
| ~ sP635(U_9193,U_9197,U_9195) )
& ! [U_9193,U_9197,U_9195] :
( ~ hBOOL(hAPP(U_9193,U_9195))
| ~ sP634(U_9193,U_9197,U_9195) )
& ! [U_9193,U_9197,U_9195] :
( U_9197 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP634(U_9193,U_9197,U_9195) )
& ! [U_9181,U_9182,U_9194,U_9183,U_9184,U_9192,U_9196] :
( hBOOL(hAPP(U_9192,U_9183))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9184)),U_9183)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),U_9183))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP633(U_9181,U_9182,U_9194,U_9183,U_9184,U_9192,U_9196) )
& ! [U_9181,U_9182,U_9194,U_9183,U_9184,U_9192,U_9196] :
( hBOOL(hAPP(U_9192,U_9181))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9182)),U_9181)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9181),U_9196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9196))
| ~ sP633(U_9181,U_9182,U_9194,U_9183,U_9184,U_9192,U_9196) )
& ! [U_9181,U_9182,U_9194,U_9183,U_9184,U_9192,U_9196] :
( hBOOL(hAPP(U_9192,U_9194))
| U_9196 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP633(U_9181,U_9182,U_9194,U_9183,U_9184,U_9192,U_9196) )
& ! [U_9193,U_9197,U_9195] :
( hBOOL(hAPP(U_9193,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9195,U_9197)))
| sP636(U_9193,U_9197,U_9195)
| sP635(U_9193,U_9197,U_9195)
| sP634(U_9193,U_9197,U_9195) )
& ! [U_9181,U_9182,U_9194,U_9183,U_9184,U_9192,U_9196] :
( sP633(U_9181,U_9182,U_9194,U_9183,U_9184,U_9192,U_9196)
| ~ hBOOL(hAPP(U_9192,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9194,U_9196))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP633,sP634,sP635,sP636])],[f_2322_7]) ).
cnf(f_2322_9,plain,
( sP633(U_9181,U_9182,U_9194,U_9183,U_9184,U_9192,U_9196)
| ~ hBOOL(hAPP(U_9192,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9194,U_9196))) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_10,plain,
( hBOOL(hAPP(U_9193,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9195,U_9197)))
| sP636(U_9193,U_9197,U_9195)
| sP635(U_9193,U_9197,U_9195)
| sP634(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_11,plain,
( hBOOL(hAPP(U_9192,U_9194))
| U_9196 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP633(U_9181,U_9182,U_9194,U_9183,U_9184,U_9192,U_9196) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_12,plain,
( hBOOL(hAPP(U_9192,U_9181))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9182)),U_9181)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9181),U_9196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9196))
| ~ sP633(U_9181,U_9182,U_9194,U_9183,U_9184,U_9192,U_9196) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_13,plain,
( hBOOL(hAPP(U_9192,U_9183))
| U_9194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9196),U_9184)),U_9183)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),U_9183))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9196),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP633(U_9181,U_9182,U_9194,U_9183,U_9184,U_9192,U_9196) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_14,plain,
( U_9197 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP634(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_15,plain,
( ~ hBOOL(hAPP(U_9193,U_9195))
| ~ sP634(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_16,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9197))
| ~ sP635(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_17,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK222(U_9197,U_9195,U_9193)))
| ~ sP635(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_18,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK222(U_9197,U_9195,U_9193)),U_9197))
| ~ sP635(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_19,plain,
( U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),sK221(U_9197,U_9195,U_9193))),sK222(U_9197,U_9195,U_9193))
| ~ sP635(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_20,plain,
( ~ hBOOL(hAPP(U_9193,sK222(U_9197,U_9195,U_9193)))
| ~ sP635(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_21,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP636(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_22,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9197),sK224(U_9197,U_9195,U_9193)))
| ~ sP636(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_23,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK224(U_9197,U_9195,U_9193)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP636(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_24,plain,
( U_9195 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9197),sK223(U_9197,U_9195,U_9193))),sK224(U_9197,U_9195,U_9193))
| ~ sP636(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
cnf(f_2322_25,plain,
( ~ hBOOL(hAPP(U_9193,sK224(U_9197,U_9195,U_9193)))
| ~ sP636(U_9193,U_9197,U_9195) ),
inference(clausify,[status(thm)],[f_2322_8]) ).
fof(f_2323_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_2323_2,plain,
! [U_9200,U_9199,U_9198] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9199,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9200),U_9198)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9200),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9199),U_9200),U_9198))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9199,U_9200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9198)) ),
inference(variable_rename,[status(thm)],[f_2323_1]) ).
fof(f_2323_3,plain,
! [U_9199,U_9198,U_9200] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9199,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9200),U_9198)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9200),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9199),U_9200),U_9198))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9199,U_9200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9198)) ),
inference(definitional_conversion,[status(esa)],[f_2323_2]) ).
cnf(f_2323_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9199,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9200),U_9198)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9200),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9199),U_9200),U_9198))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9199,U_9200))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9198)) ),
inference(clausify,[status(thm)],[f_2323_3]) ).
fof(f_2324_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_2324_2,plain,
! [U_9202,U_9201] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9202),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9201)) = 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_9202),U_9201))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9202,U_9201) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9202),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9201)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9202),U_9201))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9202,U_9201) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_9201 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2324_1]) ).
fof(f_2324_3,plain,
( ! [U_9202,U_9201] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9202),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9201)) = 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_9202),U_9201))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9202,U_9201) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP637(U_9202,U_9201) )
& ! [U_9202,U_9201] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9202),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9201)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9202),U_9201))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9202,U_9201) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP637(U_9202,U_9201) )
& ! [U_9202,U_9201] :
( sP637(U_9202,U_9201)
| U_9201 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP637])],[f_2324_2]) ).
cnf(f_2324_4,plain,
( sP637(U_9202,U_9201)
| U_9201 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2324_3]) ).
cnf(f_2324_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9202),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9201)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9202),U_9201))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9202,U_9201) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP637(U_9202,U_9201) ),
inference(clausify,[status(thm)],[f_2324_3]) ).
cnf(f_2324_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9202),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9201)) = 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_9202),U_9201))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9202,U_9201) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP637(U_9202,U_9201) ),
inference(clausify,[status(thm)],[f_2324_3]) ).
fof(f_2325_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_2325_2,plain,
! [U_9204,U_9203] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9204)),U_9203) = 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_9204),U_9203))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9204,U_9203) = 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_9204)),U_9203) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9204),U_9203))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9204,U_9203) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_9203 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2325_1]) ).
fof(f_2325_3,plain,
( ! [U_9203,U_9204] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9204)),U_9203) = 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_9204),U_9203))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9204,U_9203) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP638(U_9203,U_9204) )
& ! [U_9203,U_9204] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9204)),U_9203) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9204),U_9203))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9204,U_9203) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP638(U_9203,U_9204) )
& ! [U_9203,U_9204] :
( sP638(U_9203,U_9204)
| U_9203 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP638])],[f_2325_2]) ).
cnf(f_2325_4,plain,
( sP638(U_9203,U_9204)
| U_9203 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2325_3]) ).
cnf(f_2325_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9204)),U_9203) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_9204),U_9203))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9204,U_9203) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP638(U_9203,U_9204) ),
inference(clausify,[status(thm)],[f_2325_3]) ).
cnf(f_2325_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9204)),U_9203) = 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_9204),U_9203))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9204,U_9203) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP638(U_9203,U_9204) ),
inference(clausify,[status(thm)],[f_2325_3]) ).
fof(f_2326_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_2326_2,plain,
! [U_9206,U_9205] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9205)),U_9206))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9205),U_9206)) )
& ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9205),U_9206))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9205)),U_9206)) ) ),
inference(variable_rename,[status(thm)],[f_2326_1]) ).
fof(f_2326_3,plain,
( ! [U_9210,U_9208] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9208)),U_9210))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9208),U_9210)) )
& ! [U_9209,U_9207] :
( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9207),U_9209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9207)),U_9209)) ) ),
inference(miniscope,[status(thm)],[f_2326_2]) ).
fof(f_2326_4,plain,
( ! [U_9210,U_9208] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9208)),U_9210))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9208),U_9210)) )
& ! [U_9207,U_9209] :
( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9207),U_9209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9207)),U_9209)) ) ),
inference(definitional_conversion,[status(esa)],[f_2326_3]) ).
cnf(f_2326_5,plain,
( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9207),U_9209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9207)),U_9209)) ),
inference(clausify,[status(thm)],[f_2326_4]) ).
cnf(f_2326_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_9208)),U_9210))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9208),U_9210)) ),
inference(clausify,[status(thm)],[f_2326_4]) ).
fof(f_2327_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_2327_2,plain,
! [U_9212,U_9211] :
( ( c_SMT_Oz3mod(U_9212,U_9211) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9212,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9211))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9211)) )
& ( c_SMT_Oz3mod(U_9212,U_9211) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9212,U_9211)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9211)) ) ),
inference(variable_rename,[status(thm)],[f_2327_1]) ).
fof(f_2327_3,plain,
( ! [U_9216,U_9214] :
( c_SMT_Oz3mod(U_9216,U_9214) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9216,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9214))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9214)) )
& ! [U_9215,U_9213] :
( c_SMT_Oz3mod(U_9215,U_9213) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9215,U_9213)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9213)) ) ),
inference(miniscope,[status(thm)],[f_2327_2]) ).
fof(f_2327_4,plain,
( ! [U_9216,U_9214] :
( c_SMT_Oz3mod(U_9216,U_9214) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9216,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9214))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9214)) )
& ! [U_9213,U_9215] :
( c_SMT_Oz3mod(U_9215,U_9213) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9215,U_9213)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9213)) ) ),
inference(definitional_conversion,[status(esa)],[f_2327_3]) ).
cnf(f_2327_5,plain,
( c_SMT_Oz3mod(U_9215,U_9213) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9215,U_9213)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9213)) ),
inference(clausify,[status(thm)],[f_2327_4]) ).
cnf(f_2327_6,plain,
( c_SMT_Oz3mod(U_9216,U_9214) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9216,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9214))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9214)) ),
inference(clausify,[status(thm)],[f_2327_4]) ).
fof(f_2328_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_2328_2,plain,
! [U_9218,U_9217] :
( c_Groups_Osgn__class_Osgn(U_9217,U_9218) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9217),c_Groups_Oone__class_Oone(U_9217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9217),U_9218),c_Groups_Ozero__class_Ozero(U_9217)))
| ~ class_Rings_Olinordered__idom(U_9217) ),
inference(variable_rename,[status(thm)],[f_2328_1]) ).
fof(f_2328_3,plain,
! [U_9217,U_9218] :
( c_Groups_Osgn__class_Osgn(U_9217,U_9218) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9217),c_Groups_Oone__class_Oone(U_9217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9217),U_9218),c_Groups_Ozero__class_Ozero(U_9217)))
| ~ class_Rings_Olinordered__idom(U_9217) ),
inference(definitional_conversion,[status(esa)],[f_2328_2]) ).
cnf(f_2328_4,plain,
( c_Groups_Osgn__class_Osgn(U_9217,U_9218) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9217),c_Groups_Oone__class_Oone(U_9217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9217),U_9218),c_Groups_Ozero__class_Ozero(U_9217)))
| ~ class_Rings_Olinordered__idom(U_9217) ),
inference(clausify,[status(thm)],[f_2328_3]) ).
fof(f_2329_1,plain,
! [V_a_2,T_c] :
( ( ( c_Groups_Osgn__class_Osgn(T_c,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Groups_Oone__class_Oone(T_c))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| c_Groups_Osgn__class_Osgn(T_c,V_a_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Groups_Oone__class_Oone(T_c)) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sgn__1__neg]) ).
fof(f_2329_2,plain,
! [U_9220,U_9219] :
( ( ( c_Groups_Osgn__class_Osgn(U_9219,U_9220) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9219),c_Groups_Oone__class_Oone(U_9219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9219),U_9220),c_Groups_Ozero__class_Ozero(U_9219))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9219),U_9220),c_Groups_Ozero__class_Ozero(U_9219)))
| c_Groups_Osgn__class_Osgn(U_9219,U_9220) != hAPP(c_Groups_Ouminus__class_Ouminus(U_9219),c_Groups_Oone__class_Oone(U_9219)) ) )
| ~ class_Rings_Olinordered__idom(U_9219) ),
inference(variable_rename,[status(thm)],[f_2329_1]) ).
fof(f_2329_3,plain,
( ! [U_9219,U_9220] :
( c_Groups_Osgn__class_Osgn(U_9219,U_9220) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9219),c_Groups_Oone__class_Oone(U_9219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9219),U_9220),c_Groups_Ozero__class_Ozero(U_9219)))
| ~ sP639(U_9219,U_9220) )
& ! [U_9219,U_9220] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9219),U_9220),c_Groups_Ozero__class_Ozero(U_9219)))
| c_Groups_Osgn__class_Osgn(U_9219,U_9220) != hAPP(c_Groups_Ouminus__class_Ouminus(U_9219),c_Groups_Oone__class_Oone(U_9219))
| ~ sP639(U_9219,U_9220) )
& ! [U_9219,U_9220] :
( sP639(U_9219,U_9220)
| ~ class_Rings_Olinordered__idom(U_9219) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP639])],[f_2329_2]) ).
cnf(f_2329_4,plain,
( sP639(U_9219,U_9220)
| ~ class_Rings_Olinordered__idom(U_9219) ),
inference(clausify,[status(thm)],[f_2329_3]) ).
cnf(f_2329_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9219),U_9220),c_Groups_Ozero__class_Ozero(U_9219)))
| c_Groups_Osgn__class_Osgn(U_9219,U_9220) != hAPP(c_Groups_Ouminus__class_Ouminus(U_9219),c_Groups_Oone__class_Oone(U_9219))
| ~ sP639(U_9219,U_9220) ),
inference(clausify,[status(thm)],[f_2329_3]) ).
cnf(f_2329_6,plain,
( c_Groups_Osgn__class_Osgn(U_9219,U_9220) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9219),c_Groups_Oone__class_Oone(U_9219))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9219),U_9220),c_Groups_Ozero__class_Ozero(U_9219)))
| ~ sP639(U_9219,U_9220) ),
inference(clausify,[status(thm)],[f_2329_3]) ).
fof(f_2330_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_2330_2,plain,
! [U_9222,U_9221] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(U_9221,U_9222) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9221),c_Groups_Oone__class_Oone(U_9221))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9221),c_Groups_Ozero__class_Ozero(U_9221)),U_9222)) )
& ( c_Groups_Osgn__class_Osgn(U_9221,U_9222) = c_Groups_Oone__class_Oone(U_9221)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9221),c_Groups_Ozero__class_Ozero(U_9221)),U_9222)) ) )
| U_9222 = c_Groups_Ozero__class_Ozero(U_9221) )
& ( c_Groups_Osgn__class_Osgn(U_9221,U_9222) = c_Groups_Ozero__class_Ozero(U_9221)
| U_9222 != c_Groups_Ozero__class_Ozero(U_9221) ) )
| ~ class_Groups_Osgn__if(U_9221) ),
inference(variable_rename,[status(thm)],[f_2330_1]) ).
fof(f_2330_3,plain,
( ! [U_9221,U_9222] :
( c_Groups_Osgn__class_Osgn(U_9221,U_9222) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9221),c_Groups_Oone__class_Oone(U_9221))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9221),c_Groups_Ozero__class_Ozero(U_9221)),U_9222))
| ~ sP640(U_9221,U_9222) )
& ! [U_9221,U_9222] :
( c_Groups_Osgn__class_Osgn(U_9221,U_9222) = c_Groups_Oone__class_Oone(U_9221)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9221),c_Groups_Ozero__class_Ozero(U_9221)),U_9222))
| ~ sP640(U_9221,U_9222) )
& ! [U_9221,U_9222] :
( sP640(U_9221,U_9222)
| U_9222 = c_Groups_Ozero__class_Ozero(U_9221)
| ~ sP641(U_9221,U_9222) )
& ! [U_9221,U_9222] :
( c_Groups_Osgn__class_Osgn(U_9221,U_9222) = c_Groups_Ozero__class_Ozero(U_9221)
| U_9222 != c_Groups_Ozero__class_Ozero(U_9221)
| ~ sP641(U_9221,U_9222) )
& ! [U_9221,U_9222] :
( sP641(U_9221,U_9222)
| ~ class_Groups_Osgn__if(U_9221) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP640,sP641])],[f_2330_2]) ).
cnf(f_2330_4,plain,
( sP641(U_9221,U_9222)
| ~ class_Groups_Osgn__if(U_9221) ),
inference(clausify,[status(thm)],[f_2330_3]) ).
cnf(f_2330_5,plain,
( c_Groups_Osgn__class_Osgn(U_9221,U_9222) = c_Groups_Ozero__class_Ozero(U_9221)
| U_9222 != c_Groups_Ozero__class_Ozero(U_9221)
| ~ sP641(U_9221,U_9222) ),
inference(clausify,[status(thm)],[f_2330_3]) ).
cnf(f_2330_6,plain,
( sP640(U_9221,U_9222)
| U_9222 = c_Groups_Ozero__class_Ozero(U_9221)
| ~ sP641(U_9221,U_9222) ),
inference(clausify,[status(thm)],[f_2330_3]) ).
cnf(f_2330_7,plain,
( c_Groups_Osgn__class_Osgn(U_9221,U_9222) = c_Groups_Oone__class_Oone(U_9221)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9221),c_Groups_Ozero__class_Ozero(U_9221)),U_9222))
| ~ sP640(U_9221,U_9222) ),
inference(clausify,[status(thm)],[f_2330_3]) ).
cnf(f_2330_8,plain,
( c_Groups_Osgn__class_Osgn(U_9221,U_9222) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9221),c_Groups_Oone__class_Oone(U_9221))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9221),c_Groups_Ozero__class_Ozero(U_9221)),U_9222))
| ~ sP640(U_9221,U_9222) ),
inference(clausify,[status(thm)],[f_2330_3]) ).
fof(f_2331_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_2331_2,plain,
! [U_9224,U_9223] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9223,U_9224) = U_9223
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9223),U_9224)) ),
inference(variable_rename,[status(thm)],[f_2331_1]) ).
fof(f_2331_3,plain,
! [U_9224,U_9223] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9223,U_9224) = U_9223
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9223),U_9224)) ),
inference(definitional_conversion,[status(esa)],[f_2331_2]) ).
cnf(f_2331_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9223,U_9224) = U_9223
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9223),U_9224)) ),
inference(clausify,[status(thm)],[f_2331_3]) ).
fof(f_2332_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_2332_2,plain,
! [U_9226,U_9225] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9225),U_9226) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9225,U_9226)),U_9226),
inference(variable_rename,[status(thm)],[f_2332_1]) ).
fof(f_2332_3,plain,
! [U_9226,U_9225] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9225),U_9226) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9225,U_9226)),U_9226),
inference(definitional_conversion,[status(esa)],[f_2332_2]) ).
cnf(f_2332_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9225),U_9226) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9225,U_9226)),U_9226),
inference(clausify,[status(thm)],[f_2332_3]) ).
fof(f_2333_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_2333_2,plain,
! [U_9229,U_9228,U_9227] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9227,U_9228)),U_9229) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9227),U_9229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9228),U_9229)),
inference(variable_rename,[status(thm)],[f_2333_1]) ).
fof(f_2333_3,plain,
! [U_9227,U_9228,U_9229] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9227,U_9228)),U_9229) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9227),U_9229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9228),U_9229)),
inference(definitional_conversion,[status(esa)],[f_2333_2]) ).
cnf(f_2333_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9227,U_9228)),U_9229) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9227),U_9229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9228),U_9229)),
inference(clausify,[status(thm)],[f_2333_3]) ).
fof(f_2334_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_2334_2,plain,
! [U_9232,U_9231,U_9230] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9230),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9231,U_9232)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9230),U_9231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9230),U_9232)),
inference(variable_rename,[status(thm)],[f_2334_1]) ).
fof(f_2334_3,plain,
! [U_9230,U_9231,U_9232] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9230),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9231,U_9232)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9230),U_9231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9230),U_9232)),
inference(definitional_conversion,[status(esa)],[f_2334_2]) ).
cnf(f_2334_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9230),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9231,U_9232)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9230),U_9231),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9230),U_9232)),
inference(clausify,[status(thm)],[f_2334_3]) ).
fof(f_2335_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_2335_2,plain,
! [U_9234,U_9233] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9233,U_9234)),U_9233)),
inference(variable_rename,[status(thm)],[f_2335_1]) ).
fof(f_2335_3,plain,
! [U_9233,U_9234] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9233,U_9234)),U_9233)),
inference(definitional_conversion,[status(esa)],[f_2335_2]) ).
cnf(f_2335_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9233,U_9234)),U_9233)),
inference(clausify,[status(thm)],[f_2335_3]) ).
fof(f_2336_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_2336_2,plain,
! [U_9236,U_9235] :
( c_Groups_Osgn__class_Osgn(U_9235,c_Groups_Osgn__class_Osgn(U_9235,U_9236)) = c_Groups_Osgn__class_Osgn(U_9235,U_9236)
| ~ class_Rings_Olinordered__idom(U_9235) ),
inference(variable_rename,[status(thm)],[f_2336_1]) ).
fof(f_2336_3,plain,
! [U_9235,U_9236] :
( c_Groups_Osgn__class_Osgn(U_9235,c_Groups_Osgn__class_Osgn(U_9235,U_9236)) = c_Groups_Osgn__class_Osgn(U_9235,U_9236)
| ~ class_Rings_Olinordered__idom(U_9235) ),
inference(definitional_conversion,[status(esa)],[f_2336_2]) ).
cnf(f_2336_4,plain,
( c_Groups_Osgn__class_Osgn(U_9235,c_Groups_Osgn__class_Osgn(U_9235,U_9236)) = c_Groups_Osgn__class_Osgn(U_9235,U_9236)
| ~ class_Rings_Olinordered__idom(U_9235) ),
inference(clausify,[status(thm)],[f_2336_3]) ).
fof(f_2337_1,plain,
! [V_a_2,T_c] :
( ( ( c_Groups_Osgn__class_Osgn(T_c,V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| c_Groups_Osgn__class_Osgn(T_c,V_a_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sgn__0__0]) ).
fof(f_2337_2,plain,
! [U_9238,U_9237] :
( ( ( c_Groups_Osgn__class_Osgn(U_9237,U_9238) = c_Groups_Ozero__class_Ozero(U_9237)
| U_9238 != c_Groups_Ozero__class_Ozero(U_9237) )
& ( U_9238 = c_Groups_Ozero__class_Ozero(U_9237)
| c_Groups_Osgn__class_Osgn(U_9237,U_9238) != c_Groups_Ozero__class_Ozero(U_9237) ) )
| ~ class_Rings_Olinordered__idom(U_9237) ),
inference(variable_rename,[status(thm)],[f_2337_1]) ).
fof(f_2337_3,plain,
( ! [U_9237,U_9238] :
( c_Groups_Osgn__class_Osgn(U_9237,U_9238) = c_Groups_Ozero__class_Ozero(U_9237)
| U_9238 != c_Groups_Ozero__class_Ozero(U_9237)
| ~ sP642(U_9237,U_9238) )
& ! [U_9237,U_9238] :
( U_9238 = c_Groups_Ozero__class_Ozero(U_9237)
| c_Groups_Osgn__class_Osgn(U_9237,U_9238) != c_Groups_Ozero__class_Ozero(U_9237)
| ~ sP642(U_9237,U_9238) )
& ! [U_9237,U_9238] :
( sP642(U_9237,U_9238)
| ~ class_Rings_Olinordered__idom(U_9237) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP642])],[f_2337_2]) ).
cnf(f_2337_4,plain,
( sP642(U_9237,U_9238)
| ~ class_Rings_Olinordered__idom(U_9237) ),
inference(clausify,[status(thm)],[f_2337_3]) ).
cnf(f_2337_5,plain,
( U_9238 = c_Groups_Ozero__class_Ozero(U_9237)
| c_Groups_Osgn__class_Osgn(U_9237,U_9238) != c_Groups_Ozero__class_Ozero(U_9237)
| ~ sP642(U_9237,U_9238) ),
inference(clausify,[status(thm)],[f_2337_3]) ).
cnf(f_2337_6,plain,
( c_Groups_Osgn__class_Osgn(U_9237,U_9238) = c_Groups_Ozero__class_Ozero(U_9237)
| U_9238 != c_Groups_Ozero__class_Ozero(U_9237)
| ~ sP642(U_9237,U_9238) ),
inference(clausify,[status(thm)],[f_2337_3]) ).
fof(f_2338_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_2338_2,plain,
! [U_9239] :
( c_Groups_Osgn__class_Osgn(U_9239,c_Groups_Ozero__class_Ozero(U_9239)) = c_Groups_Ozero__class_Ozero(U_9239)
| ~ class_Groups_Osgn__if(U_9239) ),
inference(variable_rename,[status(thm)],[f_2338_1]) ).
fof(f_2338_3,plain,
! [U_9239] :
( c_Groups_Osgn__class_Osgn(U_9239,c_Groups_Ozero__class_Ozero(U_9239)) = c_Groups_Ozero__class_Ozero(U_9239)
| ~ class_Groups_Osgn__if(U_9239) ),
inference(definitional_conversion,[status(esa)],[f_2338_2]) ).
cnf(f_2338_4,plain,
( c_Groups_Osgn__class_Osgn(U_9239,c_Groups_Ozero__class_Ozero(U_9239)) = c_Groups_Ozero__class_Ozero(U_9239)
| ~ class_Groups_Osgn__if(U_9239) ),
inference(clausify,[status(thm)],[f_2338_3]) ).
fof(f_2339_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_2339_2,plain,
! [U_9242,U_9241,U_9240] :
( c_Groups_Osgn__class_Osgn(U_9240,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9240),U_9241),U_9242)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9240),c_Groups_Osgn__class_Osgn(U_9240,U_9241)),c_Groups_Osgn__class_Osgn(U_9240,U_9242))
| ~ class_Rings_Olinordered__idom(U_9240) ),
inference(variable_rename,[status(thm)],[f_2339_1]) ).
fof(f_2339_3,plain,
! [U_9240,U_9241,U_9242] :
( c_Groups_Osgn__class_Osgn(U_9240,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9240),U_9241),U_9242)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9240),c_Groups_Osgn__class_Osgn(U_9240,U_9241)),c_Groups_Osgn__class_Osgn(U_9240,U_9242))
| ~ class_Rings_Olinordered__idom(U_9240) ),
inference(definitional_conversion,[status(esa)],[f_2339_2]) ).
cnf(f_2339_4,plain,
( c_Groups_Osgn__class_Osgn(U_9240,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9240),U_9241),U_9242)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9240),c_Groups_Osgn__class_Osgn(U_9240,U_9241)),c_Groups_Osgn__class_Osgn(U_9240,U_9242))
| ~ class_Rings_Olinordered__idom(U_9240) ),
inference(clausify,[status(thm)],[f_2339_3]) ).
fof(f_2340_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_2340_2,plain,
! [U_9244,U_9243] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9243),U_9244) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9243,U_9244))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9243,U_9244)) = U_9244 )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9243),U_9244) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9243,U_9244)) != U_9244 ) ),
inference(variable_rename,[status(thm)],[f_2340_1]) ).
fof(f_2340_3,plain,
( ! [U_9248,U_9246] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9246),U_9248) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9246,U_9248))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9246,U_9248)) = U_9248 )
& ! [U_9247,U_9245] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9245),U_9247) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9245,U_9247)) != U_9247 ) ),
inference(miniscope,[status(thm)],[f_2340_2]) ).
fof(f_2340_4,plain,
( ! [U_9246,U_9248] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9246),U_9248) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9246,U_9248))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9246,U_9248)) = U_9248 )
& ! [U_9245,U_9247] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9245),U_9247) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9245,U_9247)) != U_9247 ) ),
inference(definitional_conversion,[status(esa)],[f_2340_3]) ).
cnf(f_2340_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9245),U_9247) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9245,U_9247)) != U_9247 ),
inference(clausify,[status(thm)],[f_2340_4]) ).
cnf(f_2340_6,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9246),U_9248) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9246,U_9248))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9246,U_9248)) = U_9248 ),
inference(clausify,[status(thm)],[f_2340_4]) ).
fof(f_2341_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_2341_2,plain,
! [U_9249] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9249,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_2341_1]) ).
fof(f_2341_3,plain,
! [U_9249] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9249,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_2341_2]) ).
cnf(f_2341_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9249,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_2341_3]) ).
fof(f_2342_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_2342_2,plain,
! [U_9251,U_9250] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9251,U_9250)),U_9250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9250)) ),
inference(variable_rename,[status(thm)],[f_2342_1]) ).
fof(f_2342_3,plain,
! [U_9250,U_9251] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9251,U_9250)),U_9250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9250)) ),
inference(definitional_conversion,[status(esa)],[f_2342_2]) ).
cnf(f_2342_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9251,U_9250)),U_9250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9250)) ),
inference(clausify,[status(thm)],[f_2342_3]) ).
fof(f_2343_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_2343_2,plain,
! [U_9255,U_9254] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9254,U_9255) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [U_9253] : U_9254 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9255),U_9253) )
& ( ? [U_9252] : U_9254 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9255),U_9252)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9254,U_9255) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_2343_1]) ).
fof(f_2343_3,plain,
( ! [U_9259,U_9257] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9257,U_9259) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [U_9253] : U_9257 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9259),U_9253) )
& ! [U_9258,U_9256] :
( ? [U_9252] : U_9256 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9258),U_9252)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9256,U_9258) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_2343_2]) ).
fof(f_2343_4,plain,
( ! [U_9259,U_9257] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9257,U_9259) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [U_9253] : U_9257 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9259),U_9253) )
& ! [U_9258,U_9256] :
( U_9256 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9258),sK225(U_9258,U_9256))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9256,U_9258) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_9252,sK225(U_9258,U_9256))],[f_2343_3]) ).
fof(f_2343_5,plain,
( ! [U_9253,U_9257,U_9259] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9257,U_9259) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_9257 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9259),U_9253) )
& ! [U_9256,U_9258] :
( U_9256 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9258),sK225(U_9258,U_9256))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9256,U_9258) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_2343_4]) ).
cnf(f_2343_6,plain,
( U_9256 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9258),sK225(U_9258,U_9256))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9256,U_9258) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2343_5]) ).
cnf(f_2343_7,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9257,U_9259) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_9257 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9259),U_9253) ),
inference(clausify,[status(thm)],[f_2343_5]) ).
fof(f_2344_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_2344_2,plain,
! [U_9261,U_9260] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9260,U_9261) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9260),U_9261),U_9261)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9260),U_9261)) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9260,U_9261) = U_9260
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9260),U_9261)) ) ),
inference(variable_rename,[status(thm)],[f_2344_1]) ).
fof(f_2344_3,plain,
( ! [U_9265,U_9263] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9263,U_9265) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9263),U_9265),U_9265)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9263),U_9265)) )
& ! [U_9264,U_9262] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9262,U_9264) = U_9262
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9262),U_9264)) ) ),
inference(miniscope,[status(thm)],[f_2344_2]) ).
fof(f_2344_4,plain,
( ! [U_9265,U_9263] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9263,U_9265) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9263),U_9265),U_9265)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9263),U_9265)) )
& ! [U_9262,U_9264] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9262,U_9264) = U_9262
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9262),U_9264)) ) ),
inference(definitional_conversion,[status(esa)],[f_2344_3]) ).
cnf(f_2344_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9262,U_9264) = U_9262
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9262),U_9264)) ),
inference(clausify,[status(thm)],[f_2344_4]) ).
cnf(f_2344_6,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9263,U_9265) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9263),U_9265),U_9265)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9263),U_9265)) ),
inference(clausify,[status(thm)],[f_2344_4]) ).
fof(f_2345_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_2345_2,plain,
! [U_9267,U_9266] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9266,U_9267) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9266),U_9267),U_9267)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9266),U_9267)) ),
inference(variable_rename,[status(thm)],[f_2345_1]) ).
fof(f_2345_3,plain,
! [U_9267,U_9266] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9266,U_9267) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9266),U_9267),U_9267)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9266),U_9267)) ),
inference(definitional_conversion,[status(esa)],[f_2345_2]) ).
cnf(f_2345_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9266,U_9267) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9266),U_9267),U_9267)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9266),U_9267)) ),
inference(clausify,[status(thm)],[f_2345_3]) ).
fof(f_2346_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_2346_2,plain,
! [U_9270,U_9269,U_9268] : 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_9268),U_9269)),U_9270),U_9269) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9270,U_9269),
inference(variable_rename,[status(thm)],[f_2346_1]) ).
fof(f_2346_3,plain,
! [U_9268,U_9269,U_9270] : 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_9268),U_9269)),U_9270),U_9269) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9270,U_9269),
inference(definitional_conversion,[status(esa)],[f_2346_2]) ).
cnf(f_2346_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_9268),U_9269)),U_9270),U_9269) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9270,U_9269),
inference(clausify,[status(thm)],[f_2346_3]) ).
fof(f_2347_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_2347_2,plain,
! [U_9272,U_9271] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9272,U_9271) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9272),U_9271),U_9271)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9271),U_9272)) ),
inference(variable_rename,[status(thm)],[f_2347_1]) ).
fof(f_2347_3,plain,
! [U_9271,U_9272] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9272,U_9271) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9272),U_9271),U_9271)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9271),U_9272)) ),
inference(definitional_conversion,[status(esa)],[f_2347_2]) ).
cnf(f_2347_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9272,U_9271) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9272),U_9271),U_9271)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9271),U_9272)) ),
inference(clausify,[status(thm)],[f_2347_3]) ).
fof(f_2348_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_2348_2,plain,
! [U_9274,U_9273] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9273),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9274)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9273,U_9274)),
inference(variable_rename,[status(thm)],[f_2348_1]) ).
fof(f_2348_3,plain,
! [U_9273,U_9274] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9273),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9274)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9273,U_9274)),
inference(definitional_conversion,[status(esa)],[f_2348_2]) ).
cnf(f_2348_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9273),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9274)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9273,U_9274)),
inference(clausify,[status(thm)],[f_2348_3]) ).
fof(f_2349_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_2349_2,plain,
! [U_9276,U_9275] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9275,U_9276)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9275),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9276)),
inference(variable_rename,[status(thm)],[f_2349_1]) ).
fof(f_2349_3,plain,
! [U_9275,U_9276] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9275,U_9276)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9275),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9276)),
inference(definitional_conversion,[status(esa)],[f_2349_2]) ).
cnf(f_2349_4,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9275,U_9276)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9275),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9276)),
inference(clausify,[status(thm)],[f_2349_3]) ).
fof(f_2350_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_2350_2,plain,
! [U_9279,U_9278,U_9277] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9277),U_9278)),U_9279) = 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_9277),U_9279)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9278),U_9279))),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_9277,U_9279)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9278,U_9279))),U_9279)),
inference(variable_rename,[status(thm)],[f_2350_1]) ).
fof(f_2350_3,plain,
! [U_9277,U_9278,U_9279] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9277),U_9278)),U_9279) = 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_9277),U_9279)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9278),U_9279))),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_9277,U_9279)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9278,U_9279))),U_9279)),
inference(definitional_conversion,[status(esa)],[f_2350_2]) ).
cnf(f_2350_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9277),U_9278)),U_9279) = 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_9277),U_9279)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9278),U_9279))),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_9277,U_9279)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9278,U_9279))),U_9279)),
inference(clausify,[status(thm)],[f_2350_3]) ).
fof(f_2351_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_2351_2,plain,
! [U_9281,U_9280] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9281,U_9280)),U_9280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9280)) ),
inference(variable_rename,[status(thm)],[f_2351_1]) ).
fof(f_2351_3,plain,
! [U_9280,U_9281] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9281,U_9280)),U_9280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9280)) ),
inference(definitional_conversion,[status(esa)],[f_2351_2]) ).
cnf(f_2351_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9281,U_9280)),U_9280))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9280)) ),
inference(clausify,[status(thm)],[f_2351_3]) ).
fof(f_2352_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_2352_2,plain,
! [U_9284,U_9283,U_9282] : 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_9282),U_9283)),U_9284)),U_9283) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9284),U_9283),
inference(variable_rename,[status(thm)],[f_2352_1]) ).
fof(f_2352_3,plain,
! [U_9282,U_9283,U_9284] : 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_9282),U_9283)),U_9284)),U_9283) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9284),U_9283),
inference(definitional_conversion,[status(esa)],[f_2352_2]) ).
cnf(f_2352_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_9282),U_9283)),U_9284)),U_9283) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9284),U_9283),
inference(clausify,[status(thm)],[f_2352_3]) ).
fof(f_2353_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Osgn__class_Osgn(T_c,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Osgn__class_Osgn(T_c,V_a_2))) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sgn__greater]) ).
fof(f_2353_2,plain,
! [U_9286,U_9285] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9285),c_Groups_Ozero__class_Ozero(U_9285)),c_Groups_Osgn__class_Osgn(U_9285,U_9286)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9285),c_Groups_Ozero__class_Ozero(U_9285)),U_9286)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9285),c_Groups_Ozero__class_Ozero(U_9285)),U_9286))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9285),c_Groups_Ozero__class_Ozero(U_9285)),c_Groups_Osgn__class_Osgn(U_9285,U_9286))) ) )
| ~ class_Rings_Olinordered__idom(U_9285) ),
inference(variable_rename,[status(thm)],[f_2353_1]) ).
fof(f_2353_3,plain,
( ! [U_9285,U_9286] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9285),c_Groups_Ozero__class_Ozero(U_9285)),c_Groups_Osgn__class_Osgn(U_9285,U_9286)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9285),c_Groups_Ozero__class_Ozero(U_9285)),U_9286))
| ~ sP643(U_9285,U_9286) )
& ! [U_9285,U_9286] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9285),c_Groups_Ozero__class_Ozero(U_9285)),U_9286))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9285),c_Groups_Ozero__class_Ozero(U_9285)),c_Groups_Osgn__class_Osgn(U_9285,U_9286)))
| ~ sP643(U_9285,U_9286) )
& ! [U_9285,U_9286] :
( sP643(U_9285,U_9286)
| ~ class_Rings_Olinordered__idom(U_9285) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP643])],[f_2353_2]) ).
cnf(f_2353_4,plain,
( sP643(U_9285,U_9286)
| ~ class_Rings_Olinordered__idom(U_9285) ),
inference(clausify,[status(thm)],[f_2353_3]) ).
cnf(f_2353_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9285),c_Groups_Ozero__class_Ozero(U_9285)),U_9286))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9285),c_Groups_Ozero__class_Ozero(U_9285)),c_Groups_Osgn__class_Osgn(U_9285,U_9286)))
| ~ sP643(U_9285,U_9286) ),
inference(clausify,[status(thm)],[f_2353_3]) ).
cnf(f_2353_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9285),c_Groups_Ozero__class_Ozero(U_9285)),c_Groups_Osgn__class_Osgn(U_9285,U_9286)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9285),c_Groups_Ozero__class_Ozero(U_9285)),U_9286))
| ~ sP643(U_9285,U_9286) ),
inference(clausify,[status(thm)],[f_2353_3]) ).
fof(f_2354_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Osgn__class_Osgn(T_c,V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Osgn__class_Osgn(T_c,V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sgn__less]) ).
fof(f_2354_2,plain,
! [U_9288,U_9287] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9287),c_Groups_Osgn__class_Osgn(U_9287,U_9288)),c_Groups_Ozero__class_Ozero(U_9287)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9287),U_9288),c_Groups_Ozero__class_Ozero(U_9287))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9287),U_9288),c_Groups_Ozero__class_Ozero(U_9287)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9287),c_Groups_Osgn__class_Osgn(U_9287,U_9288)),c_Groups_Ozero__class_Ozero(U_9287))) ) )
| ~ class_Rings_Olinordered__idom(U_9287) ),
inference(variable_rename,[status(thm)],[f_2354_1]) ).
fof(f_2354_3,plain,
( ! [U_9287,U_9288] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9287),c_Groups_Osgn__class_Osgn(U_9287,U_9288)),c_Groups_Ozero__class_Ozero(U_9287)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9287),U_9288),c_Groups_Ozero__class_Ozero(U_9287)))
| ~ sP644(U_9287,U_9288) )
& ! [U_9287,U_9288] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9287),U_9288),c_Groups_Ozero__class_Ozero(U_9287)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9287),c_Groups_Osgn__class_Osgn(U_9287,U_9288)),c_Groups_Ozero__class_Ozero(U_9287)))
| ~ sP644(U_9287,U_9288) )
& ! [U_9287,U_9288] :
( sP644(U_9287,U_9288)
| ~ class_Rings_Olinordered__idom(U_9287) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP644])],[f_2354_2]) ).
cnf(f_2354_4,plain,
( sP644(U_9287,U_9288)
| ~ class_Rings_Olinordered__idom(U_9287) ),
inference(clausify,[status(thm)],[f_2354_3]) ).
cnf(f_2354_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9287),U_9288),c_Groups_Ozero__class_Ozero(U_9287)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9287),c_Groups_Osgn__class_Osgn(U_9287,U_9288)),c_Groups_Ozero__class_Ozero(U_9287)))
| ~ sP644(U_9287,U_9288) ),
inference(clausify,[status(thm)],[f_2354_3]) ).
cnf(f_2354_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9287),c_Groups_Osgn__class_Osgn(U_9287,U_9288)),c_Groups_Ozero__class_Ozero(U_9287)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9287),U_9288),c_Groups_Ozero__class_Ozero(U_9287)))
| ~ sP644(U_9287,U_9288) ),
inference(clausify,[status(thm)],[f_2354_3]) ).
fof(f_2355_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_2355_2,plain,
! [U_9291,U_9290,U_9289] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9289,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9290),U_9291)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9290),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9289),U_9290),U_9291))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9289,U_9290)),
inference(variable_rename,[status(thm)],[f_2355_1]) ).
fof(f_2355_3,plain,
! [U_9289,U_9290,U_9291] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9289,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9290),U_9291)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9290),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9289),U_9290),U_9291))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9289,U_9290)),
inference(definitional_conversion,[status(esa)],[f_2355_2]) ).
cnf(f_2355_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9289,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9290),U_9291)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9290),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9289),U_9290),U_9291))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9289,U_9290)),
inference(clausify,[status(thm)],[f_2355_3]) ).
fof(f_2356_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_2356_2,plain,
! [U_9294,U_9293,U_9292] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9292),U_9293)),U_9294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9292),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9293),U_9294))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9292),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9293,U_9294))),U_9294)),
inference(variable_rename,[status(thm)],[f_2356_1]) ).
fof(f_2356_3,plain,
! [U_9292,U_9293,U_9294] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9292),U_9293)),U_9294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9292),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9293),U_9294))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9292),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9293,U_9294))),U_9294)),
inference(definitional_conversion,[status(esa)],[f_2356_2]) ).
cnf(f_2356_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9292),U_9293)),U_9294) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9292),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9293),U_9294))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9292),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9293,U_9294))),U_9294)),
inference(clausify,[status(thm)],[f_2356_3]) ).
fof(f_2357_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_2357_2,plain,
! [U_9296,U_9295] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9295),U_9296)),U_9296) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9295),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9295,U_9296)),
inference(variable_rename,[status(thm)],[f_2357_1]) ).
fof(f_2357_3,plain,
! [U_9296,U_9295] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9295),U_9296)),U_9296) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9295),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9295,U_9296)),
inference(definitional_conversion,[status(esa)],[f_2357_2]) ).
cnf(f_2357_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9295),U_9296)),U_9296) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9295),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9295,U_9296)),
inference(clausify,[status(thm)],[f_2357_3]) ).
fof(f_2358_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_2358_2,plain,
! [U_9298,U_9297] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9297),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9298),U_9297)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9298),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9298,U_9297)),
inference(variable_rename,[status(thm)],[f_2358_1]) ).
fof(f_2358_3,plain,
! [U_9297,U_9298] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9297),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9298),U_9297)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9298),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9298,U_9297)),
inference(definitional_conversion,[status(esa)],[f_2358_2]) ).
cnf(f_2358_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9297),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9298),U_9297)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9298),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9298,U_9297)),
inference(clausify,[status(thm)],[f_2358_3]) ).
fof(f_2359_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_2359_2,plain,
! [U_9300,U_9299] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9299,U_9300) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9299),U_9300)),U_9300)),
inference(variable_rename,[status(thm)],[f_2359_1]) ).
fof(f_2359_3,plain,
! [U_9299,U_9300] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9299,U_9300) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9299),U_9300)),U_9300)),
inference(definitional_conversion,[status(esa)],[f_2359_2]) ).
cnf(f_2359_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9299,U_9300) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_9299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_9299),U_9300)),U_9300)),
inference(clausify,[status(thm)],[f_2359_3]) ).
fof(f_2360_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_2360_2,plain,
! [U_9307,U_9306,U_9305] :
( ( hBOOL(hAPP(U_9305,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9306,U_9307)))
| ( ? [U_9304,U_9303] :
( ~ hBOOL(hAPP(U_9305,U_9303))
& U_9306 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9307),U_9304)),U_9303)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9303),U_9307)) )
& U_9307 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_9305,U_9306))
& U_9307 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [U_9302,U_9301] :
( hBOOL(hAPP(U_9305,U_9301))
| U_9306 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9307),U_9302)),U_9301)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9301),U_9307)) )
| U_9307 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_9305,U_9306))
| U_9307 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_9305,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9306,U_9307))) ) ),
inference(variable_rename,[status(thm)],[f_2360_1]) ).
fof(f_2360_3,plain,
( ! [U_9313,U_9311,U_9309] :
( hBOOL(hAPP(U_9309,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9311,U_9313)))
| ( ? [U_9304,U_9303] :
( ~ hBOOL(hAPP(U_9309,U_9303))
& U_9311 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9313),U_9304)),U_9303)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9303),U_9313)) )
& U_9313 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_9309,U_9311))
& U_9313 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_9312,U_9310,U_9308] :
( ( ( ! [U_9302,U_9301] :
( hBOOL(hAPP(U_9308,U_9301))
| U_9310 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9312),U_9302)),U_9301)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9301),U_9312)) )
| U_9312 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_9308,U_9310))
| U_9312 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_9308,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9310,U_9312))) ) ),
inference(miniscope,[status(thm)],[f_2360_2]) ).
fof(f_2360_4,plain,
( ! [U_9313,U_9311,U_9309] :
( hBOOL(hAPP(U_9309,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9311,U_9313)))
| ( ? [U_9303] :
( ~ hBOOL(hAPP(U_9309,U_9303))
& U_9311 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9313),sK226(U_9313,U_9311,U_9309))),U_9303)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9303),U_9313)) )
& U_9313 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_9309,U_9311))
& U_9313 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_9312,U_9310,U_9308] :
( ( ( ! [U_9302,U_9301] :
( hBOOL(hAPP(U_9308,U_9301))
| U_9310 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9312),U_9302)),U_9301)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9301),U_9312)) )
| U_9312 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_9308,U_9310))
| U_9312 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_9308,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9310,U_9312))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_9304,sK226(U_9313,U_9311,U_9309))],[f_2360_3]) ).
fof(f_2360_5,plain,
( ! [U_9313,U_9311,U_9309] :
( hBOOL(hAPP(U_9309,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9311,U_9313)))
| ( ~ hBOOL(hAPP(U_9309,sK227(U_9313,U_9311,U_9309)))
& U_9311 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9313),sK226(U_9313,U_9311,U_9309))),sK227(U_9313,U_9311,U_9309))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK227(U_9313,U_9311,U_9309)),U_9313))
& U_9313 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_9309,U_9311))
& U_9313 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_9312,U_9310,U_9308] :
( ( ( ! [U_9302,U_9301] :
( hBOOL(hAPP(U_9308,U_9301))
| U_9310 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9312),U_9302)),U_9301)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9301),U_9312)) )
| U_9312 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_9308,U_9310))
| U_9312 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_9308,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9310,U_9312))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_9303,sK227(U_9313,U_9311,U_9309))],[f_2360_4]) ).
fof(f_2360_6,plain,
( ! [U_9311,U_9309,U_9313] :
( ~ hBOOL(hAPP(U_9309,sK227(U_9313,U_9311,U_9309)))
| ~ sP647(U_9311,U_9309,U_9313) )
& ! [U_9311,U_9309,U_9313] :
( U_9311 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9313),sK226(U_9313,U_9311,U_9309))),sK227(U_9313,U_9311,U_9309))
| ~ sP647(U_9311,U_9309,U_9313) )
& ! [U_9311,U_9309,U_9313] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK227(U_9313,U_9311,U_9309)),U_9313))
| ~ sP647(U_9311,U_9309,U_9313) )
& ! [U_9311,U_9309,U_9313] :
( U_9313 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP647(U_9311,U_9309,U_9313) )
& ! [U_9311,U_9309,U_9313] :
( ~ hBOOL(hAPP(U_9309,U_9311))
| ~ sP646(U_9311,U_9309,U_9313) )
& ! [U_9311,U_9309,U_9313] :
( U_9313 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP646(U_9311,U_9309,U_9313) )
& ! [U_9301,U_9302,U_9308,U_9312,U_9310] :
( hBOOL(hAPP(U_9308,U_9301))
| U_9310 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9312),U_9302)),U_9301)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9301),U_9312))
| U_9312 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP645(U_9301,U_9302,U_9308,U_9312,U_9310) )
& ! [U_9301,U_9302,U_9308,U_9312,U_9310] :
( hBOOL(hAPP(U_9308,U_9310))
| U_9312 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP645(U_9301,U_9302,U_9308,U_9312,U_9310) )
& ! [U_9311,U_9309,U_9313] :
( hBOOL(hAPP(U_9309,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9311,U_9313)))
| sP647(U_9311,U_9309,U_9313)
| sP646(U_9311,U_9309,U_9313) )
& ! [U_9301,U_9302,U_9308,U_9312,U_9310] :
( sP645(U_9301,U_9302,U_9308,U_9312,U_9310)
| ~ hBOOL(hAPP(U_9308,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9310,U_9312))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP645,sP646,sP647])],[f_2360_5]) ).
cnf(f_2360_7,plain,
( sP645(U_9301,U_9302,U_9308,U_9312,U_9310)
| ~ hBOOL(hAPP(U_9308,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9310,U_9312))) ),
inference(clausify,[status(thm)],[f_2360_6]) ).
cnf(f_2360_8,plain,
( hBOOL(hAPP(U_9309,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9311,U_9313)))
| sP647(U_9311,U_9309,U_9313)
| sP646(U_9311,U_9309,U_9313) ),
inference(clausify,[status(thm)],[f_2360_6]) ).
cnf(f_2360_9,plain,
( hBOOL(hAPP(U_9308,U_9310))
| U_9312 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP645(U_9301,U_9302,U_9308,U_9312,U_9310) ),
inference(clausify,[status(thm)],[f_2360_6]) ).
cnf(f_2360_10,plain,
( hBOOL(hAPP(U_9308,U_9301))
| U_9310 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9312),U_9302)),U_9301)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9301),U_9312))
| U_9312 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP645(U_9301,U_9302,U_9308,U_9312,U_9310) ),
inference(clausify,[status(thm)],[f_2360_6]) ).
cnf(f_2360_11,plain,
( U_9313 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP646(U_9311,U_9309,U_9313) ),
inference(clausify,[status(thm)],[f_2360_6]) ).
cnf(f_2360_12,plain,
( ~ hBOOL(hAPP(U_9309,U_9311))
| ~ sP646(U_9311,U_9309,U_9313) ),
inference(clausify,[status(thm)],[f_2360_6]) ).
cnf(f_2360_13,plain,
( U_9313 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP647(U_9311,U_9309,U_9313) ),
inference(clausify,[status(thm)],[f_2360_6]) ).
cnf(f_2360_14,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK227(U_9313,U_9311,U_9309)),U_9313))
| ~ sP647(U_9311,U_9309,U_9313) ),
inference(clausify,[status(thm)],[f_2360_6]) ).
cnf(f_2360_15,plain,
( U_9311 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9313),sK226(U_9313,U_9311,U_9309))),sK227(U_9313,U_9311,U_9309))
| ~ sP647(U_9311,U_9309,U_9313) ),
inference(clausify,[status(thm)],[f_2360_6]) ).
cnf(f_2360_16,plain,
( ~ hBOOL(hAPP(U_9309,sK227(U_9313,U_9311,U_9309)))
| ~ sP647(U_9311,U_9309,U_9313) ),
inference(clausify,[status(thm)],[f_2360_6]) ).
fof(f_2361_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_2361_2,plain,
! [U_9317,U_9316,U_9315,U_9314] :
( 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_9316),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9317,U_9314))),U_9315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9316),U_9314)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9315),U_9316))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9314)) ),
inference(variable_rename,[status(thm)],[f_2361_1]) ).
fof(f_2361_3,plain,
! [U_9316,U_9317,U_9315,U_9314] :
( 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_9316),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9317,U_9314))),U_9315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9316),U_9314)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9315),U_9316))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9314)) ),
inference(definitional_conversion,[status(esa)],[f_2361_2]) ).
cnf(f_2361_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_9316),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9317,U_9314))),U_9315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9316),U_9314)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9315),U_9316))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9314)) ),
inference(clausify,[status(thm)],[f_2361_3]) ).
fof(f_2362_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_2362_2,plain,
! [U_9319,U_9318] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9318),U_9319)),U_9318) = 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_9318)) ),
inference(variable_rename,[status(thm)],[f_2362_1]) ).
fof(f_2362_3,plain,
! [U_9318,U_9319] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9318),U_9319)),U_9318) = 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_9318)) ),
inference(definitional_conversion,[status(esa)],[f_2362_2]) ).
cnf(f_2362_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_9318),U_9319)),U_9318) = 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_9318)) ),
inference(clausify,[status(thm)],[f_2362_3]) ).
fof(f_2363_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_2363_2,plain,
! [U_9321,U_9320] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_9320),hAPP(c_Int_Onat,U_9321)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9320,U_9321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9320)) ),
inference(variable_rename,[status(thm)],[f_2363_1]) ).
fof(f_2363_3,plain,
! [U_9320,U_9321] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_9320),hAPP(c_Int_Onat,U_9321)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9320,U_9321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9320)) ),
inference(definitional_conversion,[status(esa)],[f_2363_2]) ).
cnf(f_2363_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_9320),hAPP(c_Int_Onat,U_9321)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9320,U_9321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9320)) ),
inference(clausify,[status(thm)],[f_2363_3]) ).
fof(f_2364_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_2364_2,plain,
! [U_9323,U_9322] :
( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9322,U_9323)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_9322),hAPP(c_Int_Onat,U_9323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9322)) ),
inference(variable_rename,[status(thm)],[f_2364_1]) ).
fof(f_2364_3,plain,
! [U_9322,U_9323] :
( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9322,U_9323)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_9322),hAPP(c_Int_Onat,U_9323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9322)) ),
inference(definitional_conversion,[status(esa)],[f_2364_2]) ).
cnf(f_2364_4,plain,
( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_9322,U_9323)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_9322),hAPP(c_Int_Onat,U_9323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9322)) ),
inference(clausify,[status(thm)],[f_2364_3]) ).
fof(f_2365_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_2365_2,plain,
! [U_9325,U_9324] :
( c_Groups_Osgn__class_Osgn(U_9324,U_9325) = c_Groups_Oone__class_Oone(U_9324)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9324),c_Groups_Ozero__class_Ozero(U_9324)),U_9325))
| ~ class_Rings_Olinordered__idom(U_9324) ),
inference(variable_rename,[status(thm)],[f_2365_1]) ).
fof(f_2365_3,plain,
! [U_9324,U_9325] :
( c_Groups_Osgn__class_Osgn(U_9324,U_9325) = c_Groups_Oone__class_Oone(U_9324)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9324),c_Groups_Ozero__class_Ozero(U_9324)),U_9325))
| ~ class_Rings_Olinordered__idom(U_9324) ),
inference(definitional_conversion,[status(esa)],[f_2365_2]) ).
cnf(f_2365_4,plain,
( c_Groups_Osgn__class_Osgn(U_9324,U_9325) = c_Groups_Oone__class_Oone(U_9324)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9324),c_Groups_Ozero__class_Ozero(U_9324)),U_9325))
| ~ class_Rings_Olinordered__idom(U_9324) ),
inference(clausify,[status(thm)],[f_2365_3]) ).
fof(f_2366_1,plain,
! [V_a_2,T_c] :
( ( ( c_Groups_Osgn__class_Osgn(T_c,V_a_2) = c_Groups_Oone__class_Oone(T_c)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
| c_Groups_Osgn__class_Osgn(T_c,V_a_2) != c_Groups_Oone__class_Oone(T_c) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sgn__1__pos]) ).
fof(f_2366_2,plain,
! [U_9327,U_9326] :
( ( ( c_Groups_Osgn__class_Osgn(U_9326,U_9327) = c_Groups_Oone__class_Oone(U_9326)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9326),c_Groups_Ozero__class_Ozero(U_9326)),U_9327)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9326),c_Groups_Ozero__class_Ozero(U_9326)),U_9327))
| c_Groups_Osgn__class_Osgn(U_9326,U_9327) != c_Groups_Oone__class_Oone(U_9326) ) )
| ~ class_Rings_Olinordered__idom(U_9326) ),
inference(variable_rename,[status(thm)],[f_2366_1]) ).
fof(f_2366_3,plain,
( ! [U_9326,U_9327] :
( c_Groups_Osgn__class_Osgn(U_9326,U_9327) = c_Groups_Oone__class_Oone(U_9326)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9326),c_Groups_Ozero__class_Ozero(U_9326)),U_9327))
| ~ sP648(U_9326,U_9327) )
& ! [U_9326,U_9327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9326),c_Groups_Ozero__class_Ozero(U_9326)),U_9327))
| c_Groups_Osgn__class_Osgn(U_9326,U_9327) != c_Groups_Oone__class_Oone(U_9326)
| ~ sP648(U_9326,U_9327) )
& ! [U_9326,U_9327] :
( sP648(U_9326,U_9327)
| ~ class_Rings_Olinordered__idom(U_9326) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP648])],[f_2366_2]) ).
cnf(f_2366_4,plain,
( sP648(U_9326,U_9327)
| ~ class_Rings_Olinordered__idom(U_9326) ),
inference(clausify,[status(thm)],[f_2366_3]) ).
cnf(f_2366_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9326),c_Groups_Ozero__class_Ozero(U_9326)),U_9327))
| c_Groups_Osgn__class_Osgn(U_9326,U_9327) != c_Groups_Oone__class_Oone(U_9326)
| ~ sP648(U_9326,U_9327) ),
inference(clausify,[status(thm)],[f_2366_3]) ).
cnf(f_2366_6,plain,
( c_Groups_Osgn__class_Osgn(U_9326,U_9327) = c_Groups_Oone__class_Oone(U_9326)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9326),c_Groups_Ozero__class_Ozero(U_9326)),U_9327))
| ~ sP648(U_9326,U_9327) ),
inference(clausify,[status(thm)],[f_2366_3]) ).
fof(f_2367_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_2367_2,plain,
! [U_9328] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_9328) = 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_9328)) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_9328) = 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_9328)) ) )
| U_9328 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_9328) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_9328 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_2367_1]) ).
fof(f_2367_3,plain,
( ! [U_9330] :
( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_9330) = 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_9330)) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_9330) = 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_9330)) ) )
| U_9330 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_9329] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_9329) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_9329 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_2367_2]) ).
fof(f_2367_4,plain,
( ! [U_9330] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_9330) = 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_9330))
| ~ sP649(U_9330) )
& ! [U_9330] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_9330) = 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_9330))
| ~ sP649(U_9330) )
& ! [U_9330] :
( sP649(U_9330)
| U_9330 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_9329] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_9329) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_9329 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP649])],[f_2367_3]) ).
cnf(f_2367_5,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_9329) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_9329 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2367_4]) ).
cnf(f_2367_6,plain,
( sP649(U_9330)
| U_9330 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2367_4]) ).
cnf(f_2367_7,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_9330) = 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_9330))
| ~ sP649(U_9330) ),
inference(clausify,[status(thm)],[f_2367_4]) ).
cnf(f_2367_8,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_9330) = 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_9330))
| ~ sP649(U_9330) ),
inference(clausify,[status(thm)],[f_2367_4]) ).
fof(f_2368_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_2368_2,plain,
! [U_9333,U_9332,U_9331] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9332),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_9332),U_9333))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9331))),U_9333))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9331)) ),
inference(variable_rename,[status(thm)],[f_2368_1]) ).
fof(f_2368_3,plain,
! [U_9331,U_9332,U_9333] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9332),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_9332),U_9333))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9331))),U_9333))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9331)) ),
inference(definitional_conversion,[status(esa)],[f_2368_2]) ).
cnf(f_2368_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9332),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_9332),U_9333))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9331))),U_9333))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9331)) ),
inference(clausify,[status(thm)],[f_2368_3]) ).
fof(f_2369_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_2369_2,plain,
! [U_9336,U_9335,U_9334] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9335),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9336),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_9336),U_9335))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9334))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9334)) ),
inference(variable_rename,[status(thm)],[f_2369_1]) ).
fof(f_2369_3,plain,
! [U_9334,U_9335,U_9336] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9335),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9336),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_9336),U_9335))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9334))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9334)) ),
inference(definitional_conversion,[status(esa)],[f_2369_2]) ).
cnf(f_2369_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9335),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9336),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_9336),U_9335))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9334))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9334)) ),
inference(clausify,[status(thm)],[f_2369_3]) ).
fof(f_2370_1,plain,
! [V_g_2,V_f_2,V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_c),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_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I1_J]) ).
fof(f_2370_2,plain,
! [U_9342,U_9341,U_9340,U_9339,U_9338] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_9338),U_9341),U_9339) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_9338),U_9342),U_9340)
| ? [U_9337] :
( hAPP(U_9341,U_9337) != hAPP(U_9342,U_9337)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9337)) )
| ~ c_Nat__Transfer_Onat__set(U_9340)
| U_9339 != U_9340
| ~ class_Groups_Ocomm__monoid__mult(U_9338)
| ~ class_Groups_Ocomm__monoid__add(U_9338) ),
inference(variable_rename,[status(thm)],[f_2370_1]) ).
fof(f_2370_3,plain,
! [U_9342,U_9341,U_9340,U_9339,U_9338] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_9338),U_9341),U_9339) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_9338),U_9342),U_9340)
| ( hAPP(U_9341,sK228(U_9342,U_9341,U_9340,U_9339,U_9338)) != hAPP(U_9342,sK228(U_9342,U_9341,U_9340,U_9339,U_9338))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK228(U_9342,U_9341,U_9340,U_9339,U_9338))) )
| ~ c_Nat__Transfer_Onat__set(U_9340)
| U_9339 != U_9340
| ~ class_Groups_Ocomm__monoid__mult(U_9338)
| ~ class_Groups_Ocomm__monoid__add(U_9338) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_9337,sK228(U_9342,U_9341,U_9340,U_9339,U_9338))],[f_2370_2]) ).
fof(f_2370_4,plain,
( ! [U_9338,U_9339,U_9340,U_9341,U_9342] :
( hAPP(U_9341,sK228(U_9342,U_9341,U_9340,U_9339,U_9338)) != hAPP(U_9342,sK228(U_9342,U_9341,U_9340,U_9339,U_9338))
| ~ sP650(U_9338,U_9339,U_9340,U_9341,U_9342) )
& ! [U_9338,U_9339,U_9340,U_9341,U_9342] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK228(U_9342,U_9341,U_9340,U_9339,U_9338)))
| ~ sP650(U_9338,U_9339,U_9340,U_9341,U_9342) )
& ! [U_9338,U_9339,U_9340,U_9341,U_9342] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_9338),U_9341),U_9339) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_9338),U_9342),U_9340)
| sP650(U_9338,U_9339,U_9340,U_9341,U_9342)
| ~ c_Nat__Transfer_Onat__set(U_9340)
| U_9339 != U_9340
| ~ class_Groups_Ocomm__monoid__mult(U_9338)
| ~ class_Groups_Ocomm__monoid__add(U_9338) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP650])],[f_2370_3]) ).
cnf(f_2370_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_9338),U_9341),U_9339) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_9338),U_9342),U_9340)
| sP650(U_9338,U_9339,U_9340,U_9341,U_9342)
| ~ c_Nat__Transfer_Onat__set(U_9340)
| U_9339 != U_9340
| ~ class_Groups_Ocomm__monoid__mult(U_9338)
| ~ class_Groups_Ocomm__monoid__add(U_9338) ),
inference(clausify,[status(thm)],[f_2370_4]) ).
cnf(f_2370_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK228(U_9342,U_9341,U_9340,U_9339,U_9338)))
| ~ sP650(U_9338,U_9339,U_9340,U_9341,U_9342) ),
inference(clausify,[status(thm)],[f_2370_4]) ).
cnf(f_2370_7,plain,
( hAPP(U_9341,sK228(U_9342,U_9341,U_9340,U_9339,U_9338)) != hAPP(U_9342,sK228(U_9342,U_9341,U_9340,U_9339,U_9338))
| ~ sP650(U_9338,U_9339,U_9340,U_9341,U_9342) ),
inference(clausify,[status(thm)],[f_2370_4]) ).
fof(f_2371_1,plain,
! [V_A_2,T_c] :
( c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),c_Orderings_Obot__class_Obot(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup]) ).
fof(f_2371_2,plain,
! [U_9344,U_9343] :
( c_Complete__Lattice_OSup__class_OSup(U_9343,U_9344) = hAPP(hAPP(c_Finite__Set_Ofold(U_9343,U_9343,c_Lattices_Osemilattice__sup__class_Osup(U_9343)),c_Orderings_Obot__class_Obot(U_9343)),U_9344)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9343),U_9344))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9343) ),
inference(variable_rename,[status(thm)],[f_2371_1]) ).
fof(f_2371_3,plain,
! [U_9343,U_9344] :
( c_Complete__Lattice_OSup__class_OSup(U_9343,U_9344) = hAPP(hAPP(c_Finite__Set_Ofold(U_9343,U_9343,c_Lattices_Osemilattice__sup__class_Osup(U_9343)),c_Orderings_Obot__class_Obot(U_9343)),U_9344)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9343),U_9344))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9343) ),
inference(definitional_conversion,[status(esa)],[f_2371_2]) ).
cnf(f_2371_4,plain,
( c_Complete__Lattice_OSup__class_OSup(U_9343,U_9344) = hAPP(hAPP(c_Finite__Set_Ofold(U_9343,U_9343,c_Lattices_Osemilattice__sup__class_Osup(U_9343)),c_Orderings_Obot__class_Obot(U_9343)),U_9344)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9343),U_9344))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9343) ),
inference(clausify,[status(thm)],[f_2371_3]) ).
fof(f_2372_1,plain,
! [V_A_2,V_C_2,V_X_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_UnionI]) ).
fof(f_2372_2,plain,
! [U_9348,U_9347,U_9346,U_9345] :
( hBOOL(hAPP(hAPP(c_member(U_9345),U_9348),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9345,tc_HOL_Obool),U_9347)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9345),U_9348),U_9346))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9345,tc_HOL_Obool)),U_9346),U_9347)) ),
inference(variable_rename,[status(thm)],[f_2372_1]) ).
fof(f_2372_3,plain,
! [U_9345,U_9347,U_9348,U_9346] :
( hBOOL(hAPP(hAPP(c_member(U_9345),U_9348),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9345,tc_HOL_Obool),U_9347)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9345),U_9348),U_9346))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9345,tc_HOL_Obool)),U_9346),U_9347)) ),
inference(definitional_conversion,[status(esa)],[f_2372_2]) ).
cnf(f_2372_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9345),U_9348),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9345,tc_HOL_Obool),U_9347)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9345),U_9348),U_9346))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9345,tc_HOL_Obool)),U_9346),U_9347)) ),
inference(clausify,[status(thm)],[f_2372_3]) ).
fof(f_2373_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__abs]) ).
fof(f_2373_2,plain,
! [U_9352,U_9351,U_9350,U_9349] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9349),hAPP(c_Groups_Oabs__class_Oabs(U_9349),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9350,U_9349),U_9351),U_9352))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9350,U_9349),hAPP(hAPP(c_COMBB(U_9349,U_9349,U_9350),c_Groups_Oabs__class_Oabs(U_9349)),U_9351)),U_9352)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9349) ),
inference(variable_rename,[status(thm)],[f_2373_1]) ).
fof(f_2373_3,plain,
! [U_9349,U_9350,U_9351,U_9352] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9349),hAPP(c_Groups_Oabs__class_Oabs(U_9349),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9350,U_9349),U_9351),U_9352))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9350,U_9349),hAPP(hAPP(c_COMBB(U_9349,U_9349,U_9350),c_Groups_Oabs__class_Oabs(U_9349)),U_9351)),U_9352)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9349) ),
inference(definitional_conversion,[status(esa)],[f_2373_2]) ).
cnf(f_2373_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9349),hAPP(c_Groups_Oabs__class_Oabs(U_9349),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9350,U_9349),U_9351),U_9352))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9350,U_9349),hAPP(hAPP(c_COMBB(U_9349,U_9349,U_9350),c_Groups_Oabs__class_Oabs(U_9349)),U_9351)),U_9352)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9349) ),
inference(clausify,[status(thm)],[f_2373_3]) ).
fof(f_2374_1,plain,
! [V_A_2,V_f_2,T_d,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__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero]) ).
fof(f_2374_2,plain,
! [U_9356,U_9355,U_9354,U_9353] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9353),c_Groups_Ozero__class_Ozero(U_9353)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9354,U_9353),hAPP(hAPP(c_COMBB(U_9353,U_9353,U_9354),c_Groups_Oabs__class_Oabs(U_9353)),U_9355)),U_9356)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9353) ),
inference(variable_rename,[status(thm)],[f_2374_1]) ).
fof(f_2374_3,plain,
! [U_9353,U_9354,U_9355,U_9356] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9353),c_Groups_Ozero__class_Ozero(U_9353)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9354,U_9353),hAPP(hAPP(c_COMBB(U_9353,U_9353,U_9354),c_Groups_Oabs__class_Oabs(U_9353)),U_9355)),U_9356)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9353) ),
inference(definitional_conversion,[status(esa)],[f_2374_2]) ).
cnf(f_2374_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9353),c_Groups_Ozero__class_Ozero(U_9353)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9354,U_9353),hAPP(hAPP(c_COMBB(U_9353,U_9353,U_9354),c_Groups_Oabs__class_Oabs(U_9353)),U_9355)),U_9356)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9353) ),
inference(clausify,[status(thm)],[f_2374_3]) ).
fof(f_2375_1,plain,
! [V_A_2,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_OPow(T_c),V_A_2)) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Union__Pow__eq]) ).
fof(f_2375_2,plain,
! [U_9358,U_9357] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9357,tc_HOL_Obool),hAPP(c_Set_OPow(U_9357),U_9358)) = U_9358,
inference(variable_rename,[status(thm)],[f_2375_1]) ).
fof(f_2375_3,plain,
! [U_9357,U_9358] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9357,tc_HOL_Obool),hAPP(c_Set_OPow(U_9357),U_9358)) = U_9358,
inference(definitional_conversion,[status(esa)],[f_2375_2]) ).
cnf(f_2375_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9357,tc_HOL_Obool),hAPP(c_Set_OPow(U_9357),U_9358)) = U_9358,
inference(clausify,[status(thm)],[f_2375_3]) ).
fof(f_2376_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_2376_2,plain,
! [U_9361,U_9360,U_9359] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9359),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9359),U_9360),U_9361)) = hAPP(c_Groups_Oabs__class_Oabs(U_9359),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9359),U_9361),U_9360))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9359) ),
inference(variable_rename,[status(thm)],[f_2376_1]) ).
fof(f_2376_3,plain,
! [U_9359,U_9360,U_9361] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9359),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9359),U_9360),U_9361)) = hAPP(c_Groups_Oabs__class_Oabs(U_9359),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9359),U_9361),U_9360))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9359) ),
inference(definitional_conversion,[status(esa)],[f_2376_2]) ).
cnf(f_2376_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9359),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9359),U_9360),U_9361)) = hAPP(c_Groups_Oabs__class_Oabs(U_9359),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9359),U_9361),U_9360))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9359) ),
inference(clausify,[status(thm)],[f_2376_3]) ).
fof(f_2377_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_2377_2,plain,
! [U_9364,U_9363,U_9362] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9362),U_9363),U_9364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9362),hAPP(c_Groups_Oabs__class_Oabs(U_9362),U_9363)),U_9364))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9362) ),
inference(variable_rename,[status(thm)],[f_2377_1]) ).
fof(f_2377_3,plain,
! [U_9362,U_9363,U_9364] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9362),U_9363),U_9364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9362),hAPP(c_Groups_Oabs__class_Oabs(U_9362),U_9363)),U_9364))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9362) ),
inference(definitional_conversion,[status(esa)],[f_2377_2]) ).
cnf(f_2377_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9362),U_9363),U_9364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9362),hAPP(c_Groups_Oabs__class_Oabs(U_9362),U_9363)),U_9364))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9362) ),
inference(clausify,[status(thm)],[f_2377_3]) ).
fof(f_2378_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_2378_2,plain,
! [U_9366,U_9365] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9365),U_9366),hAPP(c_Groups_Oabs__class_Oabs(U_9365),U_9366)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9365) ),
inference(variable_rename,[status(thm)],[f_2378_1]) ).
fof(f_2378_3,plain,
! [U_9365,U_9366] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9365),U_9366),hAPP(c_Groups_Oabs__class_Oabs(U_9365),U_9366)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9365) ),
inference(definitional_conversion,[status(esa)],[f_2378_2]) ).
cnf(f_2378_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9365),U_9366),hAPP(c_Groups_Oabs__class_Oabs(U_9365),U_9366)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9365) ),
inference(clausify,[status(thm)],[f_2378_3]) ).
fof(f_2379_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_2379_2,plain,
! [U_9367] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9367),c_Groups_Oone__class_Oone(U_9367)) = c_Groups_Oone__class_Oone(U_9367)
| ~ class_Rings_Olinordered__idom(U_9367) ),
inference(variable_rename,[status(thm)],[f_2379_1]) ).
fof(f_2379_3,plain,
! [U_9367] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9367),c_Groups_Oone__class_Oone(U_9367)) = c_Groups_Oone__class_Oone(U_9367)
| ~ class_Rings_Olinordered__idom(U_9367) ),
inference(definitional_conversion,[status(esa)],[f_2379_2]) ).
cnf(f_2379_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9367),c_Groups_Oone__class_Oone(U_9367)) = c_Groups_Oone__class_Oone(U_9367)
| ~ class_Rings_Olinordered__idom(U_9367) ),
inference(clausify,[status(thm)],[f_2379_3]) ).
fof(f_2380_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_2380_2,plain,
! [U_9369,U_9368] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9368),hAPP(c_Groups_Ouminus__class_Ouminus(U_9368),U_9369)) = hAPP(c_Groups_Oabs__class_Oabs(U_9368),U_9369)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9368) ),
inference(variable_rename,[status(thm)],[f_2380_1]) ).
fof(f_2380_3,plain,
! [U_9368,U_9369] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9368),hAPP(c_Groups_Ouminus__class_Ouminus(U_9368),U_9369)) = hAPP(c_Groups_Oabs__class_Oabs(U_9368),U_9369)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9368) ),
inference(definitional_conversion,[status(esa)],[f_2380_2]) ).
cnf(f_2380_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9368),hAPP(c_Groups_Ouminus__class_Ouminus(U_9368),U_9369)) = hAPP(c_Groups_Oabs__class_Oabs(U_9368),U_9369)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9368) ),
inference(clausify,[status(thm)],[f_2380_3]) ).
fof(f_2381_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_2381_2,plain,
! [U_9371,U_9370] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9370),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9370),U_9371)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9370),U_9371)
| ~ class_Rings_Olinordered__idom(U_9370) ),
inference(variable_rename,[status(thm)],[f_2381_1]) ).
fof(f_2381_3,plain,
! [U_9370,U_9371] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9370),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9370),U_9371)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9370),U_9371)
| ~ class_Rings_Olinordered__idom(U_9370) ),
inference(definitional_conversion,[status(esa)],[f_2381_2]) ).
cnf(f_2381_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9370),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9370),U_9371)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9370),U_9371)
| ~ class_Rings_Olinordered__idom(U_9370) ),
inference(clausify,[status(thm)],[f_2381_3]) ).
fof(f_2382_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_2382_2,plain,
! [U_9374,U_9373,U_9372] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9372),hAPP(hAPP(c_Power_Opower__class_Opower(U_9372),U_9373),U_9374)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9372),hAPP(c_Groups_Oabs__class_Oabs(U_9372),U_9373)),U_9374)
| ~ class_Rings_Olinordered__idom(U_9372) ),
inference(variable_rename,[status(thm)],[f_2382_1]) ).
fof(f_2382_3,plain,
! [U_9372,U_9373,U_9374] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9372),hAPP(hAPP(c_Power_Opower__class_Opower(U_9372),U_9373),U_9374)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9372),hAPP(c_Groups_Oabs__class_Oabs(U_9372),U_9373)),U_9374)
| ~ class_Rings_Olinordered__idom(U_9372) ),
inference(definitional_conversion,[status(esa)],[f_2382_2]) ).
cnf(f_2382_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9372),hAPP(hAPP(c_Power_Opower__class_Opower(U_9372),U_9373),U_9374)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9372),hAPP(c_Groups_Oabs__class_Oabs(U_9372),U_9373)),U_9374)
| ~ class_Rings_Olinordered__idom(U_9372) ),
inference(clausify,[status(thm)],[f_2382_3]) ).
fof(f_2383_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_2383_2,plain,
! [U_9376,U_9375] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9375),hAPP(c_Groups_Oabs__class_Oabs(U_9375),U_9376)) = hAPP(c_Groups_Oabs__class_Oabs(U_9375),U_9376)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9375) ),
inference(variable_rename,[status(thm)],[f_2383_1]) ).
fof(f_2383_3,plain,
! [U_9375,U_9376] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9375),hAPP(c_Groups_Oabs__class_Oabs(U_9375),U_9376)) = hAPP(c_Groups_Oabs__class_Oabs(U_9375),U_9376)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9375) ),
inference(definitional_conversion,[status(esa)],[f_2383_2]) ).
cnf(f_2383_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9375),hAPP(c_Groups_Oabs__class_Oabs(U_9375),U_9376)) = hAPP(c_Groups_Oabs__class_Oabs(U_9375),U_9376)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9375) ),
inference(clausify,[status(thm)],[f_2383_3]) ).
fof(f_2384_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_2384_2,plain,
! [U_9379,U_9378,U_9377] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9377),U_9378),U_9379)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9377),hAPP(c_Groups_Oabs__class_Oabs(U_9377),U_9378)),hAPP(c_Groups_Oabs__class_Oabs(U_9377),U_9379))
| ~ class_Rings_Olinordered__idom(U_9377) ),
inference(variable_rename,[status(thm)],[f_2384_1]) ).
fof(f_2384_3,plain,
! [U_9377,U_9378,U_9379] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9377),U_9378),U_9379)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9377),hAPP(c_Groups_Oabs__class_Oabs(U_9377),U_9378)),hAPP(c_Groups_Oabs__class_Oabs(U_9377),U_9379))
| ~ class_Rings_Olinordered__idom(U_9377) ),
inference(definitional_conversion,[status(esa)],[f_2384_2]) ).
cnf(f_2384_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9377),U_9378),U_9379)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9377),hAPP(c_Groups_Oabs__class_Oabs(U_9377),U_9378)),hAPP(c_Groups_Oabs__class_Oabs(U_9377),U_9379))
| ~ class_Rings_Olinordered__idom(U_9377) ),
inference(clausify,[status(thm)],[f_2384_3]) ).
fof(f_2385_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_2385_2,plain,
! [U_9381,U_9380] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9380),hAPP(c_Groups_Oabs__class_Oabs(U_9380),U_9381)),hAPP(c_Groups_Oabs__class_Oabs(U_9380),U_9381)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9380),U_9381),U_9381)
| ~ class_Rings_Olinordered__idom(U_9380) ),
inference(variable_rename,[status(thm)],[f_2385_1]) ).
fof(f_2385_3,plain,
! [U_9380,U_9381] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9380),hAPP(c_Groups_Oabs__class_Oabs(U_9380),U_9381)),hAPP(c_Groups_Oabs__class_Oabs(U_9380),U_9381)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9380),U_9381),U_9381)
| ~ class_Rings_Olinordered__idom(U_9380) ),
inference(definitional_conversion,[status(esa)],[f_2385_2]) ).
cnf(f_2385_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9380),hAPP(c_Groups_Oabs__class_Oabs(U_9380),U_9381)),hAPP(c_Groups_Oabs__class_Oabs(U_9380),U_9381)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9380),U_9381),U_9381)
| ~ class_Rings_Olinordered__idom(U_9380) ),
inference(clausify,[status(thm)],[f_2385_3]) ).
fof(f_2386_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_2386_2,plain,
! [U_9384,U_9383,U_9382] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9382),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9382),hAPP(c_Groups_Oabs__class_Oabs(U_9382),U_9383)),hAPP(c_Groups_Oabs__class_Oabs(U_9382),U_9384))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9382),hAPP(c_Groups_Oabs__class_Oabs(U_9382),U_9383)),hAPP(c_Groups_Oabs__class_Oabs(U_9382),U_9384))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9382) ),
inference(variable_rename,[status(thm)],[f_2386_1]) ).
fof(f_2386_3,plain,
! [U_9382,U_9383,U_9384] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9382),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9382),hAPP(c_Groups_Oabs__class_Oabs(U_9382),U_9383)),hAPP(c_Groups_Oabs__class_Oabs(U_9382),U_9384))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9382),hAPP(c_Groups_Oabs__class_Oabs(U_9382),U_9383)),hAPP(c_Groups_Oabs__class_Oabs(U_9382),U_9384))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9382) ),
inference(definitional_conversion,[status(esa)],[f_2386_2]) ).
cnf(f_2386_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9382),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9382),hAPP(c_Groups_Oabs__class_Oabs(U_9382),U_9383)),hAPP(c_Groups_Oabs__class_Oabs(U_9382),U_9384))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9382),hAPP(c_Groups_Oabs__class_Oabs(U_9382),U_9383)),hAPP(c_Groups_Oabs__class_Oabs(U_9382),U_9384))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9382) ),
inference(clausify,[status(thm)],[f_2386_3]) ).
fof(f_2387_1,plain,
! [V_a_2,T_c] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_c) ),
inference(fof_nnf,[status(thm)],[fact_abs__eq__0]) ).
fof(f_2387_2,plain,
! [U_9386,U_9385] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_9385),U_9386) = c_Groups_Ozero__class_Ozero(U_9385)
| U_9386 != c_Groups_Ozero__class_Ozero(U_9385) )
& ( U_9386 = c_Groups_Ozero__class_Ozero(U_9385)
| hAPP(c_Groups_Oabs__class_Oabs(U_9385),U_9386) != c_Groups_Ozero__class_Ozero(U_9385) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_9385) ),
inference(variable_rename,[status(thm)],[f_2387_1]) ).
fof(f_2387_3,plain,
( ! [U_9385,U_9386] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9385),U_9386) = c_Groups_Ozero__class_Ozero(U_9385)
| U_9386 != c_Groups_Ozero__class_Ozero(U_9385)
| ~ sP651(U_9385,U_9386) )
& ! [U_9385,U_9386] :
( U_9386 = c_Groups_Ozero__class_Ozero(U_9385)
| hAPP(c_Groups_Oabs__class_Oabs(U_9385),U_9386) != c_Groups_Ozero__class_Ozero(U_9385)
| ~ sP651(U_9385,U_9386) )
& ! [U_9385,U_9386] :
( sP651(U_9385,U_9386)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9385) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP651])],[f_2387_2]) ).
cnf(f_2387_4,plain,
( sP651(U_9385,U_9386)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9385) ),
inference(clausify,[status(thm)],[f_2387_3]) ).
cnf(f_2387_5,plain,
( U_9386 = c_Groups_Ozero__class_Ozero(U_9385)
| hAPP(c_Groups_Oabs__class_Oabs(U_9385),U_9386) != c_Groups_Ozero__class_Ozero(U_9385)
| ~ sP651(U_9385,U_9386) ),
inference(clausify,[status(thm)],[f_2387_3]) ).
cnf(f_2387_6,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9385),U_9386) = c_Groups_Ozero__class_Ozero(U_9385)
| U_9386 != c_Groups_Ozero__class_Ozero(U_9385)
| ~ sP651(U_9385,U_9386) ),
inference(clausify,[status(thm)],[f_2387_3]) ).
fof(f_2388_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_2388_2,plain,
! [U_9387] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9387),c_Groups_Ozero__class_Ozero(U_9387)) = c_Groups_Ozero__class_Ozero(U_9387)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9387) ),
inference(variable_rename,[status(thm)],[f_2388_1]) ).
fof(f_2388_3,plain,
! [U_9387] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9387),c_Groups_Ozero__class_Ozero(U_9387)) = c_Groups_Ozero__class_Ozero(U_9387)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9387) ),
inference(definitional_conversion,[status(esa)],[f_2388_2]) ).
cnf(f_2388_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9387),c_Groups_Ozero__class_Ozero(U_9387)) = c_Groups_Ozero__class_Ozero(U_9387)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9387) ),
inference(clausify,[status(thm)],[f_2388_3]) ).
fof(f_2389_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_2389_2,plain,
! [U_9388] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9388)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9388),
inference(variable_rename,[status(thm)],[f_2389_1]) ).
fof(f_2389_3,plain,
! [U_9388] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9388)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9388),
inference(definitional_conversion,[status(esa)],[f_2389_2]) ).
cnf(f_2389_4,plain,
hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9388)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9388),
inference(clausify,[status(thm)],[f_2389_3]) ).
fof(f_2390_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_2390_2,plain,
! [U_9391,U_9390,U_9389] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9389),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9389),U_9390),U_9391)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9389),hAPP(c_Groups_Oabs__class_Oabs(U_9389),U_9390)),hAPP(c_Groups_Oabs__class_Oabs(U_9389),U_9391))
| ~ class_Fields_Olinordered__field__inverse__zero(U_9389) ),
inference(variable_rename,[status(thm)],[f_2390_1]) ).
fof(f_2390_3,plain,
! [U_9389,U_9390,U_9391] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9389),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9389),U_9390),U_9391)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9389),hAPP(c_Groups_Oabs__class_Oabs(U_9389),U_9390)),hAPP(c_Groups_Oabs__class_Oabs(U_9389),U_9391))
| ~ class_Fields_Olinordered__field__inverse__zero(U_9389) ),
inference(definitional_conversion,[status(esa)],[f_2390_2]) ).
cnf(f_2390_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9389),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9389),U_9390),U_9391)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9389),hAPP(c_Groups_Oabs__class_Oabs(U_9389),U_9390)),hAPP(c_Groups_Oabs__class_Oabs(U_9389),U_9391))
| ~ class_Fields_Olinordered__field__inverse__zero(U_9389) ),
inference(clausify,[status(thm)],[f_2390_3]) ).
fof(f_2391_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Groups_Oabs__class_Oabs(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2)
| ~ class_Groups_Oordered__ab__group__add__abs(T_c) ),
inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs]) ).
fof(f_2391_2,plain,
! [U_9395,U_9394,U_9393,U_9392] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9392),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9393,U_9392),hAPP(hAPP(c_COMBB(U_9392,U_9392,U_9393),c_Groups_Oabs__class_Oabs(U_9392)),U_9394)),U_9395)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9393,U_9392),hAPP(hAPP(c_COMBB(U_9392,U_9392,U_9393),c_Groups_Oabs__class_Oabs(U_9392)),U_9394)),U_9395)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9392) ),
inference(variable_rename,[status(thm)],[f_2391_1]) ).
fof(f_2391_3,plain,
! [U_9392,U_9393,U_9394,U_9395] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9392),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9393,U_9392),hAPP(hAPP(c_COMBB(U_9392,U_9392,U_9393),c_Groups_Oabs__class_Oabs(U_9392)),U_9394)),U_9395)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9393,U_9392),hAPP(hAPP(c_COMBB(U_9392,U_9392,U_9393),c_Groups_Oabs__class_Oabs(U_9392)),U_9394)),U_9395)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9392) ),
inference(definitional_conversion,[status(esa)],[f_2391_2]) ).
cnf(f_2391_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9392),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9393,U_9392),hAPP(hAPP(c_COMBB(U_9392,U_9392,U_9393),c_Groups_Oabs__class_Oabs(U_9392)),U_9394)),U_9395)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9393,U_9392),hAPP(hAPP(c_COMBB(U_9392,U_9392,U_9393),c_Groups_Oabs__class_Oabs(U_9392)),U_9394)),U_9395)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9392) ),
inference(clausify,[status(thm)],[f_2391_3]) ).
fof(f_2392_1,plain,
! [V_A_2,V_f_2,T_d,T_c] :
( hAPP(c_Groups_Oabs__class_Oabs(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,T_c,T_d),c_Groups_Oabs__class_Oabs(T_c)),V_f_2)),V_A_2)
| ~ class_Fields_Olinordered__field(T_c) ),
inference(fof_nnf,[status(thm)],[fact_abs__setprod]) ).
fof(f_2392_2,plain,
! [U_9399,U_9398,U_9397,U_9396] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9396),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9397,U_9396),U_9398),U_9399)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9397,U_9396),hAPP(hAPP(c_COMBB(U_9396,U_9396,U_9397),c_Groups_Oabs__class_Oabs(U_9396)),U_9398)),U_9399)
| ~ class_Fields_Olinordered__field(U_9396) ),
inference(variable_rename,[status(thm)],[f_2392_1]) ).
fof(f_2392_3,plain,
! [U_9396,U_9397,U_9398,U_9399] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9396),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9397,U_9396),U_9398),U_9399)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9397,U_9396),hAPP(hAPP(c_COMBB(U_9396,U_9396,U_9397),c_Groups_Oabs__class_Oabs(U_9396)),U_9398)),U_9399)
| ~ class_Fields_Olinordered__field(U_9396) ),
inference(definitional_conversion,[status(esa)],[f_2392_2]) ).
cnf(f_2392_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9396),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9397,U_9396),U_9398),U_9399)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9397,U_9396),hAPP(hAPP(c_COMBB(U_9396,U_9396,U_9397),c_Groups_Oabs__class_Oabs(U_9396)),U_9398)),U_9399)
| ~ class_Fields_Olinordered__field(U_9396) ),
inference(clausify,[status(thm)],[f_2392_3]) ).
fof(f_2393_1,plain,
! [V_S_2,V_f_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_d,T_c,V_f_2)),
inference(fof_nnf,[status(thm)],[fact_image__Union]) ).
fof(f_2393_2,plain,
! [U_9403,U_9402,U_9401,U_9400] : hAPP(c_Set_Oimage(U_9400,U_9401,U_9402),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9400,tc_HOL_Obool),U_9403)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9400,tc_HOL_Obool),tc_fun(U_9401,tc_HOL_Obool)),U_9403),c_Set_Oimage(U_9400,U_9401,U_9402)),
inference(variable_rename,[status(thm)],[f_2393_1]) ).
fof(f_2393_3,plain,
! [U_9400,U_9401,U_9402,U_9403] : hAPP(c_Set_Oimage(U_9400,U_9401,U_9402),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9400,tc_HOL_Obool),U_9403)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9400,tc_HOL_Obool),tc_fun(U_9401,tc_HOL_Obool)),U_9403),c_Set_Oimage(U_9400,U_9401,U_9402)),
inference(definitional_conversion,[status(esa)],[f_2393_2]) ).
cnf(f_2393_4,plain,
hAPP(c_Set_Oimage(U_9400,U_9401,U_9402),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9400,tc_HOL_Obool),U_9403)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9400,tc_HOL_Obool),tc_fun(U_9401,tc_HOL_Obool)),U_9403),c_Set_Oimage(U_9400,U_9401,U_9402)),
inference(clausify,[status(thm)],[f_2393_3]) ).
fof(f_2394_1,plain,
! [V_A_2,V_B_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Int__Union2]) ).
fof(f_2394_2,plain,
! [U_9406,U_9405,U_9404] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9404,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9404,tc_HOL_Obool),U_9405)),U_9406) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9404,tc_HOL_Obool),tc_fun(U_9404,tc_HOL_Obool)),U_9405),hAPP(hAPP(c_COMBC(tc_fun(U_9404,tc_HOL_Obool),tc_fun(U_9404,tc_HOL_Obool),tc_fun(U_9404,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9404,tc_HOL_Obool))),U_9406)),
inference(variable_rename,[status(thm)],[f_2394_1]) ).
fof(f_2394_3,plain,
! [U_9404,U_9405,U_9406] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9404,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9404,tc_HOL_Obool),U_9405)),U_9406) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9404,tc_HOL_Obool),tc_fun(U_9404,tc_HOL_Obool)),U_9405),hAPP(hAPP(c_COMBC(tc_fun(U_9404,tc_HOL_Obool),tc_fun(U_9404,tc_HOL_Obool),tc_fun(U_9404,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9404,tc_HOL_Obool))),U_9406)),
inference(definitional_conversion,[status(esa)],[f_2394_2]) ).
cnf(f_2394_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9404,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9404,tc_HOL_Obool),U_9405)),U_9406) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9404,tc_HOL_Obool),tc_fun(U_9404,tc_HOL_Obool)),U_9405),hAPP(hAPP(c_COMBC(tc_fun(U_9404,tc_HOL_Obool),tc_fun(U_9404,tc_HOL_Obool),tc_fun(U_9404,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9404,tc_HOL_Obool))),U_9406)),
inference(clausify,[status(thm)],[f_2394_3]) ).
fof(f_2395_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Int__Union]) ).
fof(f_2395_2,plain,
! [U_9409,U_9408,U_9407] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9407,tc_HOL_Obool)),U_9408),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9407,tc_HOL_Obool),U_9409)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9407,tc_HOL_Obool),tc_fun(U_9407,tc_HOL_Obool)),U_9409),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9407,tc_HOL_Obool)),U_9408)),
inference(variable_rename,[status(thm)],[f_2395_1]) ).
fof(f_2395_3,plain,
! [U_9408,U_9409,U_9407] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9407,tc_HOL_Obool)),U_9408),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9407,tc_HOL_Obool),U_9409)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9407,tc_HOL_Obool),tc_fun(U_9407,tc_HOL_Obool)),U_9409),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9407,tc_HOL_Obool)),U_9408)),
inference(definitional_conversion,[status(esa)],[f_2395_2]) ).
cnf(f_2395_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9407,tc_HOL_Obool)),U_9408),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9407,tc_HOL_Obool),U_9409)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9407,tc_HOL_Obool),tc_fun(U_9407,tc_HOL_Obool)),U_9409),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9407,tc_HOL_Obool)),U_9408)),
inference(clausify,[status(thm)],[f_2395_3]) ).
fof(f_2396_1,plain,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I8_J]) ).
fof(f_2396_2,plain,
! [U_9413,U_9412,U_9411,U_9410] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9410,tc_HOL_Obool),tc_fun(U_9411,tc_HOL_Obool)),U_9412),hAPP(hAPP(c_COMBC(tc_fun(U_9410,tc_HOL_Obool),tc_fun(U_9410,tc_fun(U_9411,tc_HOL_Obool)),tc_fun(U_9411,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9410,tc_fun(U_9411,tc_HOL_Obool))),U_9413)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9410,tc_fun(U_9411,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9410,tc_HOL_Obool),U_9412)),U_9413),
inference(variable_rename,[status(thm)],[f_2396_1]) ).
fof(f_2396_3,plain,
! [U_9410,U_9411,U_9412,U_9413] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9410,tc_HOL_Obool),tc_fun(U_9411,tc_HOL_Obool)),U_9412),hAPP(hAPP(c_COMBC(tc_fun(U_9410,tc_HOL_Obool),tc_fun(U_9410,tc_fun(U_9411,tc_HOL_Obool)),tc_fun(U_9411,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9410,tc_fun(U_9411,tc_HOL_Obool))),U_9413)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9410,tc_fun(U_9411,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9410,tc_HOL_Obool),U_9412)),U_9413),
inference(definitional_conversion,[status(esa)],[f_2396_2]) ).
cnf(f_2396_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9410,tc_HOL_Obool),tc_fun(U_9411,tc_HOL_Obool)),U_9412),hAPP(hAPP(c_COMBC(tc_fun(U_9410,tc_HOL_Obool),tc_fun(U_9410,tc_fun(U_9411,tc_HOL_Obool)),tc_fun(U_9411,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9410,tc_fun(U_9411,tc_HOL_Obool))),U_9413)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9410,tc_fun(U_9411,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9410,tc_HOL_Obool),U_9412)),U_9413),
inference(clausify,[status(thm)],[f_2396_3]) ).
fof(f_2397_1,plain,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I8_J]) ).
fof(f_2397_2,plain,
! [U_9417,U_9416,U_9415,U_9414] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9414,tc_fun(U_9415,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9414,tc_HOL_Obool),U_9416)),U_9417) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9414,tc_HOL_Obool),tc_fun(U_9415,tc_HOL_Obool)),U_9416),hAPP(hAPP(c_COMBC(tc_fun(U_9414,tc_HOL_Obool),tc_fun(U_9414,tc_fun(U_9415,tc_HOL_Obool)),tc_fun(U_9415,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9414,tc_fun(U_9415,tc_HOL_Obool))),U_9417)),
inference(variable_rename,[status(thm)],[f_2397_1]) ).
fof(f_2397_3,plain,
! [U_9414,U_9415,U_9416,U_9417] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9414,tc_fun(U_9415,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9414,tc_HOL_Obool),U_9416)),U_9417) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9414,tc_HOL_Obool),tc_fun(U_9415,tc_HOL_Obool)),U_9416),hAPP(hAPP(c_COMBC(tc_fun(U_9414,tc_HOL_Obool),tc_fun(U_9414,tc_fun(U_9415,tc_HOL_Obool)),tc_fun(U_9415,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9414,tc_fun(U_9415,tc_HOL_Obool))),U_9417)),
inference(definitional_conversion,[status(esa)],[f_2397_2]) ).
cnf(f_2397_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9414,tc_fun(U_9415,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9414,tc_HOL_Obool),U_9416)),U_9417) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9414,tc_HOL_Obool),tc_fun(U_9415,tc_HOL_Obool)),U_9416),hAPP(hAPP(c_COMBC(tc_fun(U_9414,tc_HOL_Obool),tc_fun(U_9414,tc_fun(U_9415,tc_HOL_Obool)),tc_fun(U_9415,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9414,tc_fun(U_9415,tc_HOL_Obool))),U_9417)),
inference(clausify,[status(thm)],[f_2397_3]) ).
fof(f_2398_1,plain,
! [V_b_2,V_A_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2)),V_b_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),V_b_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_c),B_x),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2)),V_b_2)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__le__iff]) ).
fof(f_2398_2,plain,
! [U_9422,U_9421,U_9420] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),c_Complete__Lattice_OSup__class_OSup(U_9420,U_9421)),U_9422))
| ? [U_9419] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),U_9419),U_9422))
& hBOOL(hAPP(hAPP(c_member(U_9420),U_9419),U_9421)) ) )
& ( ! [U_9418] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),U_9418),U_9422))
| ~ hBOOL(hAPP(hAPP(c_member(U_9420),U_9418),U_9421)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),c_Complete__Lattice_OSup__class_OSup(U_9420,U_9421)),U_9422)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9420) ),
inference(variable_rename,[status(thm)],[f_2398_1]) ).
fof(f_2398_3,plain,
! [U_9422,U_9421,U_9420] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),c_Complete__Lattice_OSup__class_OSup(U_9420,U_9421)),U_9422))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),sK229(U_9422,U_9421,U_9420)),U_9422))
& hBOOL(hAPP(hAPP(c_member(U_9420),sK229(U_9422,U_9421,U_9420)),U_9421)) ) )
& ( ! [U_9418] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),U_9418),U_9422))
| ~ hBOOL(hAPP(hAPP(c_member(U_9420),U_9418),U_9421)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),c_Complete__Lattice_OSup__class_OSup(U_9420,U_9421)),U_9422)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9420) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_9419,sK229(U_9422,U_9421,U_9420))],[f_2398_2]) ).
fof(f_2398_4,plain,
( ! [U_9420,U_9421,U_9422] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),sK229(U_9422,U_9421,U_9420)),U_9422))
| ~ sP652(U_9420,U_9421,U_9422) )
& ! [U_9420,U_9421,U_9422] :
( hBOOL(hAPP(hAPP(c_member(U_9420),sK229(U_9422,U_9421,U_9420)),U_9421))
| ~ sP652(U_9420,U_9421,U_9422) )
& ! [U_9418,U_9420,U_9421,U_9422] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),c_Complete__Lattice_OSup__class_OSup(U_9420,U_9421)),U_9422))
| sP652(U_9420,U_9421,U_9422)
| ~ sP653(U_9418,U_9420,U_9421,U_9422) )
& ! [U_9418,U_9420,U_9421,U_9422] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),U_9418),U_9422))
| ~ hBOOL(hAPP(hAPP(c_member(U_9420),U_9418),U_9421))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),c_Complete__Lattice_OSup__class_OSup(U_9420,U_9421)),U_9422))
| ~ sP653(U_9418,U_9420,U_9421,U_9422) )
& ! [U_9418,U_9420,U_9421,U_9422] :
( sP653(U_9418,U_9420,U_9421,U_9422)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9420) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP652,sP653])],[f_2398_3]) ).
cnf(f_2398_5,plain,
( sP653(U_9418,U_9420,U_9421,U_9422)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9420) ),
inference(clausify,[status(thm)],[f_2398_4]) ).
cnf(f_2398_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),U_9418),U_9422))
| ~ hBOOL(hAPP(hAPP(c_member(U_9420),U_9418),U_9421))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),c_Complete__Lattice_OSup__class_OSup(U_9420,U_9421)),U_9422))
| ~ sP653(U_9418,U_9420,U_9421,U_9422) ),
inference(clausify,[status(thm)],[f_2398_4]) ).
cnf(f_2398_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),c_Complete__Lattice_OSup__class_OSup(U_9420,U_9421)),U_9422))
| sP652(U_9420,U_9421,U_9422)
| ~ sP653(U_9418,U_9420,U_9421,U_9422) ),
inference(clausify,[status(thm)],[f_2398_4]) ).
cnf(f_2398_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9420),sK229(U_9422,U_9421,U_9420)),U_9421))
| ~ sP652(U_9420,U_9421,U_9422) ),
inference(clausify,[status(thm)],[f_2398_4]) ).
cnf(f_2398_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9420),sK229(U_9422,U_9421,U_9420)),U_9422))
| ~ sP652(U_9420,U_9421,U_9422) ),
inference(clausify,[status(thm)],[f_2398_4]) ).
fof(f_2399_1,plain,
! [V_S_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_S_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_S_2))) ) )
| ~ class_Orderings_Olinorder(T_c)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__Sup__iff]) ).
fof(f_2399_2,plain,
! [U_9427,U_9426,U_9425] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),c_Complete__Lattice_OSup__class_OSup(U_9425,U_9427)))
| ! [U_9424] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),U_9424))
| ~ hBOOL(hAPP(hAPP(c_member(U_9425),U_9424),U_9427)) ) )
& ( ? [U_9423] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),U_9423))
& hBOOL(hAPP(hAPP(c_member(U_9425),U_9423),U_9427)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),c_Complete__Lattice_OSup__class_OSup(U_9425,U_9427))) ) )
| ~ class_Orderings_Olinorder(U_9425)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9425) ),
inference(variable_rename,[status(thm)],[f_2399_1]) ).
fof(f_2399_3,plain,
! [U_9427,U_9426,U_9425] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),c_Complete__Lattice_OSup__class_OSup(U_9425,U_9427)))
| ! [U_9424] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),U_9424))
| ~ hBOOL(hAPP(hAPP(c_member(U_9425),U_9424),U_9427)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),sK230(U_9427,U_9426,U_9425)))
& hBOOL(hAPP(hAPP(c_member(U_9425),sK230(U_9427,U_9426,U_9425)),U_9427)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),c_Complete__Lattice_OSup__class_OSup(U_9425,U_9427))) ) )
| ~ class_Orderings_Olinorder(U_9425)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9425) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_9423,sK230(U_9427,U_9426,U_9425))],[f_2399_2]) ).
fof(f_2399_4,plain,
( ! [U_9426,U_9427,U_9425] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),sK230(U_9427,U_9426,U_9425)))
| ~ sP654(U_9426,U_9427,U_9425) )
& ! [U_9426,U_9427,U_9425] :
( hBOOL(hAPP(hAPP(c_member(U_9425),sK230(U_9427,U_9426,U_9425)),U_9427))
| ~ sP654(U_9426,U_9427,U_9425) )
& ! [U_9426,U_9427,U_9424,U_9425] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),c_Complete__Lattice_OSup__class_OSup(U_9425,U_9427)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),U_9424))
| ~ hBOOL(hAPP(hAPP(c_member(U_9425),U_9424),U_9427))
| ~ sP655(U_9426,U_9427,U_9424,U_9425) )
& ! [U_9426,U_9427,U_9424,U_9425] :
( sP654(U_9426,U_9427,U_9425)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),c_Complete__Lattice_OSup__class_OSup(U_9425,U_9427)))
| ~ sP655(U_9426,U_9427,U_9424,U_9425) )
& ! [U_9426,U_9427,U_9424,U_9425] :
( sP655(U_9426,U_9427,U_9424,U_9425)
| ~ class_Orderings_Olinorder(U_9425)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9425) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP654,sP655])],[f_2399_3]) ).
cnf(f_2399_5,plain,
( sP655(U_9426,U_9427,U_9424,U_9425)
| ~ class_Orderings_Olinorder(U_9425)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9425) ),
inference(clausify,[status(thm)],[f_2399_4]) ).
cnf(f_2399_6,plain,
( sP654(U_9426,U_9427,U_9425)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),c_Complete__Lattice_OSup__class_OSup(U_9425,U_9427)))
| ~ sP655(U_9426,U_9427,U_9424,U_9425) ),
inference(clausify,[status(thm)],[f_2399_4]) ).
cnf(f_2399_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),c_Complete__Lattice_OSup__class_OSup(U_9425,U_9427)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),U_9424))
| ~ hBOOL(hAPP(hAPP(c_member(U_9425),U_9424),U_9427))
| ~ sP655(U_9426,U_9427,U_9424,U_9425) ),
inference(clausify,[status(thm)],[f_2399_4]) ).
cnf(f_2399_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_9425),sK230(U_9427,U_9426,U_9425)),U_9427))
| ~ sP654(U_9426,U_9427,U_9425) ),
inference(clausify,[status(thm)],[f_2399_4]) ).
cnf(f_2399_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9425),U_9426),sK230(U_9427,U_9426,U_9425)))
| ~ sP654(U_9426,U_9427,U_9425) ),
inference(clausify,[status(thm)],[f_2399_4]) ).
fof(f_2400_1,plain,
! [V_A_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_c,T_d,V_f_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Union]) ).
fof(f_2400_2,plain,
! [U_9431,U_9430,U_9429,U_9428] : hAPP(c_Set_Ovimage(U_9428,U_9429,U_9430),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9429,tc_HOL_Obool),U_9431)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9429,tc_HOL_Obool),tc_fun(U_9428,tc_HOL_Obool)),U_9431),c_Set_Ovimage(U_9428,U_9429,U_9430)),
inference(variable_rename,[status(thm)],[f_2400_1]) ).
fof(f_2400_3,plain,
! [U_9429,U_9430,U_9431,U_9428] : hAPP(c_Set_Ovimage(U_9428,U_9429,U_9430),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9429,tc_HOL_Obool),U_9431)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9429,tc_HOL_Obool),tc_fun(U_9428,tc_HOL_Obool)),U_9431),c_Set_Ovimage(U_9428,U_9429,U_9430)),
inference(definitional_conversion,[status(esa)],[f_2400_2]) ).
cnf(f_2400_4,plain,
hAPP(c_Set_Ovimage(U_9428,U_9429,U_9430),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9429,tc_HOL_Obool),U_9431)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9429,tc_HOL_Obool),tc_fun(U_9428,tc_HOL_Obool)),U_9431),c_Set_Ovimage(U_9428,U_9429,U_9430)),
inference(clausify,[status(thm)],[f_2400_3]) ).
fof(f_2401_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_2401_2,plain,
! [U_9433,U_9432] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9432),c_Groups_Ozero__class_Ozero(U_9432)),hAPP(c_Groups_Oabs__class_Oabs(U_9432),U_9433)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9432) ),
inference(variable_rename,[status(thm)],[f_2401_1]) ).
fof(f_2401_3,plain,
! [U_9432,U_9433] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9432),c_Groups_Ozero__class_Ozero(U_9432)),hAPP(c_Groups_Oabs__class_Oabs(U_9432),U_9433)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9432) ),
inference(definitional_conversion,[status(esa)],[f_2401_2]) ).
cnf(f_2401_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9432),c_Groups_Ozero__class_Ozero(U_9432)),hAPP(c_Groups_Oabs__class_Oabs(U_9432),U_9433)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9432) ),
inference(clausify,[status(thm)],[f_2401_3]) ).
fof(f_2402_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)),c_Groups_Ozero__class_Ozero(T_c)))
| V_a_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_c) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff]) ).
fof(f_2402_2,plain,
! [U_9435,U_9434] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),hAPP(c_Groups_Oabs__class_Oabs(U_9434),U_9435)),c_Groups_Ozero__class_Ozero(U_9434)))
| U_9435 != c_Groups_Ozero__class_Ozero(U_9434) )
& ( U_9435 = c_Groups_Ozero__class_Ozero(U_9434)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),hAPP(c_Groups_Oabs__class_Oabs(U_9434),U_9435)),c_Groups_Ozero__class_Ozero(U_9434))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_9434) ),
inference(variable_rename,[status(thm)],[f_2402_1]) ).
fof(f_2402_3,plain,
( ! [U_9434,U_9435] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),hAPP(c_Groups_Oabs__class_Oabs(U_9434),U_9435)),c_Groups_Ozero__class_Ozero(U_9434)))
| U_9435 != c_Groups_Ozero__class_Ozero(U_9434)
| ~ sP656(U_9434,U_9435) )
& ! [U_9434,U_9435] :
( U_9435 = c_Groups_Ozero__class_Ozero(U_9434)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),hAPP(c_Groups_Oabs__class_Oabs(U_9434),U_9435)),c_Groups_Ozero__class_Ozero(U_9434)))
| ~ sP656(U_9434,U_9435) )
& ! [U_9434,U_9435] :
( sP656(U_9434,U_9435)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9434) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP656])],[f_2402_2]) ).
cnf(f_2402_4,plain,
( sP656(U_9434,U_9435)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9434) ),
inference(clausify,[status(thm)],[f_2402_3]) ).
cnf(f_2402_5,plain,
( U_9435 = c_Groups_Ozero__class_Ozero(U_9434)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),hAPP(c_Groups_Oabs__class_Oabs(U_9434),U_9435)),c_Groups_Ozero__class_Ozero(U_9434)))
| ~ sP656(U_9434,U_9435) ),
inference(clausify,[status(thm)],[f_2402_3]) ).
cnf(f_2402_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),hAPP(c_Groups_Oabs__class_Oabs(U_9434),U_9435)),c_Groups_Ozero__class_Ozero(U_9434)))
| U_9435 != c_Groups_Ozero__class_Ozero(U_9434)
| ~ sP656(U_9434,U_9435) ),
inference(clausify,[status(thm)],[f_2402_3]) ).
fof(f_2403_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_2403_2,plain,
! [U_9437,U_9436] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9436),U_9437) = U_9437
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9436),c_Groups_Ozero__class_Ozero(U_9436)),U_9437))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9436) ),
inference(variable_rename,[status(thm)],[f_2403_1]) ).
fof(f_2403_3,plain,
! [U_9437,U_9436] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9436),U_9437) = U_9437
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9436),c_Groups_Ozero__class_Ozero(U_9436)),U_9437))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9436) ),
inference(definitional_conversion,[status(esa)],[f_2403_2]) ).
cnf(f_2403_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9436),U_9437) = U_9437
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9436),c_Groups_Ozero__class_Ozero(U_9436)),U_9437))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9436) ),
inference(clausify,[status(thm)],[f_2403_3]) ).
fof(f_2404_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_2404_2,plain,
! [U_9439,U_9438] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9438),U_9439) = U_9439
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9438),c_Groups_Ozero__class_Ozero(U_9438)),U_9439))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9438) ),
inference(variable_rename,[status(thm)],[f_2404_1]) ).
fof(f_2404_3,plain,
! [U_9438,U_9439] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9438),U_9439) = U_9439
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9438),c_Groups_Ozero__class_Ozero(U_9438)),U_9439))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9438) ),
inference(definitional_conversion,[status(esa)],[f_2404_2]) ).
cnf(f_2404_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9438),U_9439) = U_9439
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9438),c_Groups_Ozero__class_Ozero(U_9438)),U_9439))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9438) ),
inference(clausify,[status(thm)],[f_2404_3]) ).
fof(f_2405_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)))
| V_a_2 = c_Groups_Ozero__class_Ozero(T_c) )
& ( V_a_2 != c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_c) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff]) ).
fof(f_2405_2,plain,
! [U_9441,U_9440] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9440),c_Groups_Ozero__class_Ozero(U_9440)),hAPP(c_Groups_Oabs__class_Oabs(U_9440),U_9441)))
| U_9441 = c_Groups_Ozero__class_Ozero(U_9440) )
& ( U_9441 != c_Groups_Ozero__class_Ozero(U_9440)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9440),c_Groups_Ozero__class_Ozero(U_9440)),hAPP(c_Groups_Oabs__class_Oabs(U_9440),U_9441))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_9440) ),
inference(variable_rename,[status(thm)],[f_2405_1]) ).
fof(f_2405_3,plain,
( ! [U_9440,U_9441] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9440),c_Groups_Ozero__class_Ozero(U_9440)),hAPP(c_Groups_Oabs__class_Oabs(U_9440),U_9441)))
| U_9441 = c_Groups_Ozero__class_Ozero(U_9440)
| ~ sP657(U_9440,U_9441) )
& ! [U_9440,U_9441] :
( U_9441 != c_Groups_Ozero__class_Ozero(U_9440)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9440),c_Groups_Ozero__class_Ozero(U_9440)),hAPP(c_Groups_Oabs__class_Oabs(U_9440),U_9441)))
| ~ sP657(U_9440,U_9441) )
& ! [U_9440,U_9441] :
( sP657(U_9440,U_9441)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9440) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP657])],[f_2405_2]) ).
cnf(f_2405_4,plain,
( sP657(U_9440,U_9441)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9440) ),
inference(clausify,[status(thm)],[f_2405_3]) ).
cnf(f_2405_5,plain,
( U_9441 != c_Groups_Ozero__class_Ozero(U_9440)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9440),c_Groups_Ozero__class_Ozero(U_9440)),hAPP(c_Groups_Oabs__class_Oabs(U_9440),U_9441)))
| ~ sP657(U_9440,U_9441) ),
inference(clausify,[status(thm)],[f_2405_3]) ).
cnf(f_2405_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9440),c_Groups_Ozero__class_Ozero(U_9440)),hAPP(c_Groups_Oabs__class_Oabs(U_9440),U_9441)))
| U_9441 = c_Groups_Ozero__class_Ozero(U_9440)
| ~ sP657(U_9440,U_9441) ),
inference(clausify,[status(thm)],[f_2405_3]) ).
fof(f_2406_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_2406_2,plain,
! [U_9443,U_9442] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9442),hAPP(c_Groups_Oabs__class_Oabs(U_9442),U_9443)),c_Groups_Ozero__class_Ozero(U_9442)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9442) ),
inference(variable_rename,[status(thm)],[f_2406_1]) ).
fof(f_2406_3,plain,
! [U_9443,U_9442] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9442),hAPP(c_Groups_Oabs__class_Oabs(U_9442),U_9443)),c_Groups_Ozero__class_Ozero(U_9442)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9442) ),
inference(definitional_conversion,[status(esa)],[f_2406_2]) ).
cnf(f_2406_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9442),hAPP(c_Groups_Oabs__class_Oabs(U_9442),U_9443)),c_Groups_Ozero__class_Ozero(U_9442)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9442) ),
inference(clausify,[status(thm)],[f_2406_3]) ).
fof(f_2407_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_2407_2,plain,
! [U_9446,U_9445,U_9444] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9444),hAPP(c_Groups_Oabs__class_Oabs(U_9444),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9444),U_9445),U_9446))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9444),hAPP(c_Groups_Oabs__class_Oabs(U_9444),U_9445)),hAPP(c_Groups_Oabs__class_Oabs(U_9444),U_9446))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9444) ),
inference(variable_rename,[status(thm)],[f_2407_1]) ).
fof(f_2407_3,plain,
! [U_9444,U_9445,U_9446] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9444),hAPP(c_Groups_Oabs__class_Oabs(U_9444),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9444),U_9445),U_9446))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9444),hAPP(c_Groups_Oabs__class_Oabs(U_9444),U_9445)),hAPP(c_Groups_Oabs__class_Oabs(U_9444),U_9446))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9444) ),
inference(definitional_conversion,[status(esa)],[f_2407_2]) ).
cnf(f_2407_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9444),hAPP(c_Groups_Oabs__class_Oabs(U_9444),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9444),U_9445),U_9446))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9444),hAPP(c_Groups_Oabs__class_Oabs(U_9444),U_9445)),hAPP(c_Groups_Oabs__class_Oabs(U_9444),U_9446))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9444) ),
inference(clausify,[status(thm)],[f_2407_3]) ).
fof(f_2408_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_2408_2,plain,
! [U_9451,U_9450,U_9449,U_9448,U_9447] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9447),hAPP(c_Groups_Oabs__class_Oabs(U_9447),U_9448)),hAPP(c_Groups_Oabs__class_Oabs(U_9447),U_9450))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9447),U_9449),U_9451)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9447),hAPP(c_Groups_Oabs__class_Oabs(U_9447),U_9450)),U_9451))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9447),hAPP(c_Groups_Oabs__class_Oabs(U_9447),U_9448)),U_9449))
| ~ class_Rings_Olinordered__idom(U_9447) ),
inference(variable_rename,[status(thm)],[f_2408_1]) ).
fof(f_2408_3,plain,
! [U_9447,U_9448,U_9449,U_9450,U_9451] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9447),hAPP(c_Groups_Oabs__class_Oabs(U_9447),U_9448)),hAPP(c_Groups_Oabs__class_Oabs(U_9447),U_9450))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9447),U_9449),U_9451)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9447),hAPP(c_Groups_Oabs__class_Oabs(U_9447),U_9450)),U_9451))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9447),hAPP(c_Groups_Oabs__class_Oabs(U_9447),U_9448)),U_9449))
| ~ class_Rings_Olinordered__idom(U_9447) ),
inference(definitional_conversion,[status(esa)],[f_2408_2]) ).
cnf(f_2408_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9447),hAPP(c_Groups_Oabs__class_Oabs(U_9447),U_9448)),hAPP(c_Groups_Oabs__class_Oabs(U_9447),U_9450))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9447),U_9449),U_9451)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9447),hAPP(c_Groups_Oabs__class_Oabs(U_9447),U_9450)),U_9451))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9447),hAPP(c_Groups_Oabs__class_Oabs(U_9447),U_9448)),U_9449))
| ~ class_Rings_Olinordered__idom(U_9447) ),
inference(clausify,[status(thm)],[f_2408_3]) ).
fof(f_2409_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_2409_2,plain,
! [U_9454,U_9453,U_9452] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9452),hAPP(c_Groups_Oabs__class_Oabs(U_9452),U_9453)),hAPP(c_Groups_Oabs__class_Oabs(U_9452),U_9454))),hAPP(c_Groups_Oabs__class_Oabs(U_9452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9452),U_9454),U_9453))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9452) ),
inference(variable_rename,[status(thm)],[f_2409_1]) ).
fof(f_2409_3,plain,
! [U_9452,U_9453,U_9454] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9452),hAPP(c_Groups_Oabs__class_Oabs(U_9452),U_9453)),hAPP(c_Groups_Oabs__class_Oabs(U_9452),U_9454))),hAPP(c_Groups_Oabs__class_Oabs(U_9452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9452),U_9454),U_9453))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9452) ),
inference(definitional_conversion,[status(esa)],[f_2409_2]) ).
cnf(f_2409_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9452),hAPP(c_Groups_Oabs__class_Oabs(U_9452),U_9453)),hAPP(c_Groups_Oabs__class_Oabs(U_9452),U_9454))),hAPP(c_Groups_Oabs__class_Oabs(U_9452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9452),U_9454),U_9453))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9452) ),
inference(clausify,[status(thm)],[f_2409_3]) ).
fof(f_2410_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_2410_2,plain,
! [U_9457,U_9456,U_9455] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9455),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9455),hAPP(c_Groups_Oabs__class_Oabs(U_9455),U_9456)),hAPP(c_Groups_Oabs__class_Oabs(U_9455),U_9457))),hAPP(c_Groups_Oabs__class_Oabs(U_9455),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9455),U_9456),U_9457))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9455) ),
inference(variable_rename,[status(thm)],[f_2410_1]) ).
fof(f_2410_3,plain,
! [U_9455,U_9456,U_9457] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9455),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9455),hAPP(c_Groups_Oabs__class_Oabs(U_9455),U_9456)),hAPP(c_Groups_Oabs__class_Oabs(U_9455),U_9457))),hAPP(c_Groups_Oabs__class_Oabs(U_9455),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9455),U_9456),U_9457))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9455) ),
inference(definitional_conversion,[status(esa)],[f_2410_2]) ).
cnf(f_2410_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9455),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9455),hAPP(c_Groups_Oabs__class_Oabs(U_9455),U_9456)),hAPP(c_Groups_Oabs__class_Oabs(U_9455),U_9457))),hAPP(c_Groups_Oabs__class_Oabs(U_9455),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9455),U_9456),U_9457))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9455) ),
inference(clausify,[status(thm)],[f_2410_3]) ).
fof(f_2411_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_2411_2,plain,
! [U_9460,U_9459,U_9458] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9458),hAPP(c_Groups_Oabs__class_Oabs(U_9458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9458),hAPP(c_Groups_Oabs__class_Oabs(U_9458),U_9459)),hAPP(c_Groups_Oabs__class_Oabs(U_9458),U_9460)))),hAPP(c_Groups_Oabs__class_Oabs(U_9458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9458),U_9459),U_9460))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9458) ),
inference(variable_rename,[status(thm)],[f_2411_1]) ).
fof(f_2411_3,plain,
! [U_9458,U_9459,U_9460] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9458),hAPP(c_Groups_Oabs__class_Oabs(U_9458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9458),hAPP(c_Groups_Oabs__class_Oabs(U_9458),U_9459)),hAPP(c_Groups_Oabs__class_Oabs(U_9458),U_9460)))),hAPP(c_Groups_Oabs__class_Oabs(U_9458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9458),U_9459),U_9460))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9458) ),
inference(definitional_conversion,[status(esa)],[f_2411_2]) ).
cnf(f_2411_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9458),hAPP(c_Groups_Oabs__class_Oabs(U_9458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9458),hAPP(c_Groups_Oabs__class_Oabs(U_9458),U_9459)),hAPP(c_Groups_Oabs__class_Oabs(U_9458),U_9460)))),hAPP(c_Groups_Oabs__class_Oabs(U_9458),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9458),U_9459),U_9460))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9458) ),
inference(clausify,[status(thm)],[f_2411_3]) ).
fof(f_2412_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_2412_2,plain,
! [U_9463,U_9462,U_9461] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9461),hAPP(c_Groups_Ouminus__class_Ouminus(U_9461),U_9462)),U_9463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9461),hAPP(c_Groups_Oabs__class_Oabs(U_9461),U_9462)),U_9463))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9461) ),
inference(variable_rename,[status(thm)],[f_2412_1]) ).
fof(f_2412_3,plain,
! [U_9461,U_9462,U_9463] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9461),hAPP(c_Groups_Ouminus__class_Ouminus(U_9461),U_9462)),U_9463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9461),hAPP(c_Groups_Oabs__class_Oabs(U_9461),U_9462)),U_9463))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9461) ),
inference(definitional_conversion,[status(esa)],[f_2412_2]) ).
cnf(f_2412_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9461),hAPP(c_Groups_Ouminus__class_Ouminus(U_9461),U_9462)),U_9463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9461),hAPP(c_Groups_Oabs__class_Oabs(U_9461),U_9462)),U_9463))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9461) ),
inference(clausify,[status(thm)],[f_2412_3]) ).
fof(f_2413_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_2413_2,plain,
! [U_9466,U_9465,U_9464] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9464),hAPP(c_Groups_Oabs__class_Oabs(U_9464),U_9465)),U_9466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9464),hAPP(c_Groups_Ouminus__class_Ouminus(U_9464),U_9465)),U_9466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9464),U_9465),U_9466))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9464) ),
inference(variable_rename,[status(thm)],[f_2413_1]) ).
fof(f_2413_3,plain,
! [U_9464,U_9465,U_9466] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9464),hAPP(c_Groups_Oabs__class_Oabs(U_9464),U_9465)),U_9466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9464),hAPP(c_Groups_Ouminus__class_Ouminus(U_9464),U_9465)),U_9466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9464),U_9465),U_9466))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9464) ),
inference(definitional_conversion,[status(esa)],[f_2413_2]) ).
cnf(f_2413_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9464),hAPP(c_Groups_Oabs__class_Oabs(U_9464),U_9465)),U_9466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9464),hAPP(c_Groups_Ouminus__class_Ouminus(U_9464),U_9465)),U_9466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9464),U_9465),U_9466))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9464) ),
inference(clausify,[status(thm)],[f_2413_3]) ).
fof(f_2414_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),V_b_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_c) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__iff]) ).
fof(f_2414_2,plain,
! [U_9469,U_9468,U_9467] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),hAPP(c_Groups_Oabs__class_Oabs(U_9467),U_9468)),U_9469))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),hAPP(c_Groups_Ouminus__class_Ouminus(U_9467),U_9468)),U_9469))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),U_9468),U_9469)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),hAPP(c_Groups_Ouminus__class_Ouminus(U_9467),U_9468)),U_9469))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),U_9468),U_9469)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),hAPP(c_Groups_Oabs__class_Oabs(U_9467),U_9468)),U_9469)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_9467) ),
inference(variable_rename,[status(thm)],[f_2414_1]) ).
fof(f_2414_3,plain,
( ! [U_9467,U_9468,U_9469] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),hAPP(c_Groups_Ouminus__class_Ouminus(U_9467),U_9468)),U_9469))
| ~ sP658(U_9467,U_9468,U_9469) )
& ! [U_9467,U_9468,U_9469] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),U_9468),U_9469))
| ~ sP658(U_9467,U_9468,U_9469) )
& ! [U_9467,U_9468,U_9469] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),hAPP(c_Groups_Oabs__class_Oabs(U_9467),U_9468)),U_9469))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),hAPP(c_Groups_Ouminus__class_Ouminus(U_9467),U_9468)),U_9469))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),U_9468),U_9469))
| ~ sP659(U_9467,U_9468,U_9469) )
& ! [U_9467,U_9468,U_9469] :
( sP658(U_9467,U_9468,U_9469)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),hAPP(c_Groups_Oabs__class_Oabs(U_9467),U_9468)),U_9469))
| ~ sP659(U_9467,U_9468,U_9469) )
& ! [U_9467,U_9468,U_9469] :
( sP659(U_9467,U_9468,U_9469)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9467) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP658,sP659])],[f_2414_2]) ).
cnf(f_2414_4,plain,
( sP659(U_9467,U_9468,U_9469)
| ~ class_Groups_Oordered__ab__group__add__abs(U_9467) ),
inference(clausify,[status(thm)],[f_2414_3]) ).
cnf(f_2414_5,plain,
( sP658(U_9467,U_9468,U_9469)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),hAPP(c_Groups_Oabs__class_Oabs(U_9467),U_9468)),U_9469))
| ~ sP659(U_9467,U_9468,U_9469) ),
inference(clausify,[status(thm)],[f_2414_3]) ).
cnf(f_2414_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),hAPP(c_Groups_Oabs__class_Oabs(U_9467),U_9468)),U_9469))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),hAPP(c_Groups_Ouminus__class_Ouminus(U_9467),U_9468)),U_9469))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),U_9468),U_9469))
| ~ sP659(U_9467,U_9468,U_9469) ),
inference(clausify,[status(thm)],[f_2414_3]) ).
cnf(f_2414_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),U_9468),U_9469))
| ~ sP658(U_9467,U_9468,U_9469) ),
inference(clausify,[status(thm)],[f_2414_3]) ).
cnf(f_2414_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9467),hAPP(c_Groups_Ouminus__class_Ouminus(U_9467),U_9468)),U_9469))
| ~ sP658(U_9467,U_9468,U_9469) ),
inference(clausify,[status(thm)],[f_2414_3]) ).
fof(f_2415_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_2415_2,plain,
! [U_9471,U_9470] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9470),hAPP(c_Groups_Ouminus__class_Ouminus(U_9470),U_9471)),hAPP(c_Groups_Oabs__class_Oabs(U_9470),U_9471)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9470) ),
inference(variable_rename,[status(thm)],[f_2415_1]) ).
fof(f_2415_3,plain,
! [U_9471,U_9470] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9470),hAPP(c_Groups_Ouminus__class_Ouminus(U_9470),U_9471)),hAPP(c_Groups_Oabs__class_Oabs(U_9470),U_9471)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9470) ),
inference(definitional_conversion,[status(esa)],[f_2415_2]) ).
cnf(f_2415_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9470),hAPP(c_Groups_Ouminus__class_Ouminus(U_9470),U_9471)),hAPP(c_Groups_Oabs__class_Oabs(U_9470),U_9471)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9470) ),
inference(clausify,[status(thm)],[f_2415_3]) ).
fof(f_2416_1,plain,
! [V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(T_c),V_a_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),V_b_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Groups_Oabs__class_Oabs(T_c),V_a_2)),V_b_2)) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_abs__less__iff]) ).
fof(f_2416_2,plain,
! [U_9474,U_9473,U_9472] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),hAPP(c_Groups_Oabs__class_Oabs(U_9472),U_9473)),U_9474))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),hAPP(c_Groups_Ouminus__class_Ouminus(U_9472),U_9473)),U_9474))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),U_9473),U_9474)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),hAPP(c_Groups_Ouminus__class_Ouminus(U_9472),U_9473)),U_9474))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),U_9473),U_9474)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),hAPP(c_Groups_Oabs__class_Oabs(U_9472),U_9473)),U_9474)) ) )
| ~ class_Rings_Olinordered__idom(U_9472) ),
inference(variable_rename,[status(thm)],[f_2416_1]) ).
fof(f_2416_3,plain,
( ! [U_9472,U_9473,U_9474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),hAPP(c_Groups_Ouminus__class_Ouminus(U_9472),U_9473)),U_9474))
| ~ sP660(U_9472,U_9473,U_9474) )
& ! [U_9472,U_9473,U_9474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),U_9473),U_9474))
| ~ sP660(U_9472,U_9473,U_9474) )
& ! [U_9472,U_9473,U_9474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),hAPP(c_Groups_Oabs__class_Oabs(U_9472),U_9473)),U_9474))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),hAPP(c_Groups_Ouminus__class_Ouminus(U_9472),U_9473)),U_9474))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),U_9473),U_9474))
| ~ sP661(U_9472,U_9473,U_9474) )
& ! [U_9472,U_9473,U_9474] :
( sP660(U_9472,U_9473,U_9474)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),hAPP(c_Groups_Oabs__class_Oabs(U_9472),U_9473)),U_9474))
| ~ sP661(U_9472,U_9473,U_9474) )
& ! [U_9472,U_9473,U_9474] :
( sP661(U_9472,U_9473,U_9474)
| ~ class_Rings_Olinordered__idom(U_9472) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP660,sP661])],[f_2416_2]) ).
cnf(f_2416_4,plain,
( sP661(U_9472,U_9473,U_9474)
| ~ class_Rings_Olinordered__idom(U_9472) ),
inference(clausify,[status(thm)],[f_2416_3]) ).
cnf(f_2416_5,plain,
( sP660(U_9472,U_9473,U_9474)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),hAPP(c_Groups_Oabs__class_Oabs(U_9472),U_9473)),U_9474))
| ~ sP661(U_9472,U_9473,U_9474) ),
inference(clausify,[status(thm)],[f_2416_3]) ).
cnf(f_2416_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),hAPP(c_Groups_Oabs__class_Oabs(U_9472),U_9473)),U_9474))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),hAPP(c_Groups_Ouminus__class_Ouminus(U_9472),U_9473)),U_9474))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),U_9473),U_9474))
| ~ sP661(U_9472,U_9473,U_9474) ),
inference(clausify,[status(thm)],[f_2416_3]) ).
cnf(f_2416_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),U_9473),U_9474))
| ~ sP660(U_9472,U_9473,U_9474) ),
inference(clausify,[status(thm)],[f_2416_3]) ).
cnf(f_2416_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9472),hAPP(c_Groups_Ouminus__class_Ouminus(U_9472),U_9473)),U_9474))
| ~ sP660(U_9472,U_9473,U_9474) ),
inference(clausify,[status(thm)],[f_2416_3]) ).
fof(f_2417_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_2417_2,plain,
! [U_9477,U_9476,U_9475] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9475),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9475),U_9477),U_9476)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9475),hAPP(c_Groups_Oabs__class_Oabs(U_9475),U_9477)),hAPP(c_Groups_Oabs__class_Oabs(U_9475),U_9476))
| U_9476 = c_Groups_Ozero__class_Ozero(U_9475)
| ~ class_Fields_Olinordered__field(U_9475) ),
inference(variable_rename,[status(thm)],[f_2417_1]) ).
fof(f_2417_3,plain,
! [U_9476,U_9475,U_9477] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9475),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9475),U_9477),U_9476)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9475),hAPP(c_Groups_Oabs__class_Oabs(U_9475),U_9477)),hAPP(c_Groups_Oabs__class_Oabs(U_9475),U_9476))
| U_9476 = c_Groups_Ozero__class_Ozero(U_9475)
| ~ class_Fields_Olinordered__field(U_9475) ),
inference(definitional_conversion,[status(esa)],[f_2417_2]) ).
cnf(f_2417_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9475),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9475),U_9477),U_9476)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9475),hAPP(c_Groups_Oabs__class_Oabs(U_9475),U_9477)),hAPP(c_Groups_Oabs__class_Oabs(U_9475),U_9476))
| U_9476 = c_Groups_Ozero__class_Ozero(U_9475)
| ~ class_Fields_Olinordered__field(U_9475) ),
inference(clausify,[status(thm)],[f_2417_3]) ).
fof(f_2418_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_2418_2,plain,
! [U_9480,U_9479,U_9478] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9478),hAPP(hAPP(c_Power_Opower__class_Opower(U_9478),hAPP(c_Groups_Ouminus__class_Ouminus(U_9478),U_9479)),U_9480)) = hAPP(c_Groups_Oabs__class_Oabs(U_9478),hAPP(hAPP(c_Power_Opower__class_Opower(U_9478),U_9479),U_9480))
| ~ class_Rings_Olinordered__idom(U_9478) ),
inference(variable_rename,[status(thm)],[f_2418_1]) ).
fof(f_2418_3,plain,
! [U_9478,U_9479,U_9480] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9478),hAPP(hAPP(c_Power_Opower__class_Opower(U_9478),hAPP(c_Groups_Ouminus__class_Ouminus(U_9478),U_9479)),U_9480)) = hAPP(c_Groups_Oabs__class_Oabs(U_9478),hAPP(hAPP(c_Power_Opower__class_Opower(U_9478),U_9479),U_9480))
| ~ class_Rings_Olinordered__idom(U_9478) ),
inference(definitional_conversion,[status(esa)],[f_2418_2]) ).
cnf(f_2418_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9478),hAPP(hAPP(c_Power_Opower__class_Opower(U_9478),hAPP(c_Groups_Ouminus__class_Ouminus(U_9478),U_9479)),U_9480)) = hAPP(c_Groups_Oabs__class_Oabs(U_9478),hAPP(hAPP(c_Power_Opower__class_Opower(U_9478),U_9479),U_9480))
| ~ class_Rings_Olinordered__idom(U_9478) ),
inference(clausify,[status(thm)],[f_2418_3]) ).
fof(f_2419_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_2419_2,plain,
! [U_9482,U_9481] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9481) = 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_9481),U_9482)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2419_1]) ).
fof(f_2419_3,plain,
! [U_9481,U_9482] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9481) = 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_9481),U_9482)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_2419_2]) ).
cnf(f_2419_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9481) = 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_9481),U_9482)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2419_3]) ).
fof(f_2420_1,plain,
! [V_A_2,V_C_2,T_c] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ? [B_x] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),B_x),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_x),V_C_2)) ) )
& ( ! [B_x] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_x),V_C_2)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2)),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Union__disjoint]) ).
fof(f_2420_2,plain,
! [U_9487,U_9486,U_9485] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9485,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9485,tc_HOL_Obool),U_9486)),U_9487) = c_Orderings_Obot__class_Obot(tc_fun(U_9485,tc_HOL_Obool))
| ? [U_9484] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9485,tc_HOL_Obool)),U_9484),U_9487) != c_Orderings_Obot__class_Obot(tc_fun(U_9485,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9485,tc_HOL_Obool)),U_9484),U_9486)) ) )
& ( ! [U_9483] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9485,tc_HOL_Obool)),U_9483),U_9487) = c_Orderings_Obot__class_Obot(tc_fun(U_9485,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9485,tc_HOL_Obool)),U_9483),U_9486)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9485,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9485,tc_HOL_Obool),U_9486)),U_9487) != c_Orderings_Obot__class_Obot(tc_fun(U_9485,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2420_1]) ).
fof(f_2420_3,plain,
( ! [U_9493,U_9491,U_9489] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9489,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9489,tc_HOL_Obool),U_9491)),U_9493) = c_Orderings_Obot__class_Obot(tc_fun(U_9489,tc_HOL_Obool))
| ? [U_9484] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9489,tc_HOL_Obool)),U_9484),U_9493) != c_Orderings_Obot__class_Obot(tc_fun(U_9489,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9489,tc_HOL_Obool)),U_9484),U_9491)) ) )
& ! [U_9492,U_9490,U_9488] :
( ! [U_9483] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9488,tc_HOL_Obool)),U_9483),U_9492) = c_Orderings_Obot__class_Obot(tc_fun(U_9488,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9488,tc_HOL_Obool)),U_9483),U_9490)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9488,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9488,tc_HOL_Obool),U_9490)),U_9492) != c_Orderings_Obot__class_Obot(tc_fun(U_9488,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2420_2]) ).
fof(f_2420_4,plain,
( ! [U_9493,U_9491,U_9489] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9489,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9489,tc_HOL_Obool),U_9491)),U_9493) = c_Orderings_Obot__class_Obot(tc_fun(U_9489,tc_HOL_Obool))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9489,tc_HOL_Obool)),sK231(U_9493,U_9491,U_9489)),U_9493) != c_Orderings_Obot__class_Obot(tc_fun(U_9489,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9489,tc_HOL_Obool)),sK231(U_9493,U_9491,U_9489)),U_9491)) ) )
& ! [U_9492,U_9490,U_9488] :
( ! [U_9483] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9488,tc_HOL_Obool)),U_9483),U_9492) = c_Orderings_Obot__class_Obot(tc_fun(U_9488,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9488,tc_HOL_Obool)),U_9483),U_9490)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9488,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9488,tc_HOL_Obool),U_9490)),U_9492) != c_Orderings_Obot__class_Obot(tc_fun(U_9488,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_9484,sK231(U_9493,U_9491,U_9489))],[f_2420_3]) ).
fof(f_2420_5,plain,
( ! [U_9491,U_9493,U_9489] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9489,tc_HOL_Obool)),sK231(U_9493,U_9491,U_9489)),U_9493) != c_Orderings_Obot__class_Obot(tc_fun(U_9489,tc_HOL_Obool))
| ~ sP662(U_9491,U_9493,U_9489) )
& ! [U_9491,U_9493,U_9489] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9489,tc_HOL_Obool)),sK231(U_9493,U_9491,U_9489)),U_9491))
| ~ sP662(U_9491,U_9493,U_9489) )
& ! [U_9491,U_9493,U_9489] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9489,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9489,tc_HOL_Obool),U_9491)),U_9493) = c_Orderings_Obot__class_Obot(tc_fun(U_9489,tc_HOL_Obool))
| sP662(U_9491,U_9493,U_9489) )
& ! [U_9490,U_9492,U_9483,U_9488] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9488,tc_HOL_Obool)),U_9483),U_9492) = c_Orderings_Obot__class_Obot(tc_fun(U_9488,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9488,tc_HOL_Obool)),U_9483),U_9490))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9488,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9488,tc_HOL_Obool),U_9490)),U_9492) != c_Orderings_Obot__class_Obot(tc_fun(U_9488,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP662])],[f_2420_4]) ).
cnf(f_2420_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9488,tc_HOL_Obool)),U_9483),U_9492) = c_Orderings_Obot__class_Obot(tc_fun(U_9488,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9488,tc_HOL_Obool)),U_9483),U_9490))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9488,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9488,tc_HOL_Obool),U_9490)),U_9492) != c_Orderings_Obot__class_Obot(tc_fun(U_9488,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2420_5]) ).
cnf(f_2420_7,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9489,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9489,tc_HOL_Obool),U_9491)),U_9493) = c_Orderings_Obot__class_Obot(tc_fun(U_9489,tc_HOL_Obool))
| sP662(U_9491,U_9493,U_9489) ),
inference(clausify,[status(thm)],[f_2420_5]) ).
cnf(f_2420_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9489,tc_HOL_Obool)),sK231(U_9493,U_9491,U_9489)),U_9491))
| ~ sP662(U_9491,U_9493,U_9489) ),
inference(clausify,[status(thm)],[f_2420_5]) ).
cnf(f_2420_9,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9489,tc_HOL_Obool)),sK231(U_9493,U_9491,U_9489)),U_9493) != c_Orderings_Obot__class_Obot(tc_fun(U_9489,tc_HOL_Obool))
| ~ sP662(U_9491,U_9493,U_9489) ),
inference(clausify,[status(thm)],[f_2420_5]) ).
fof(f_2421_1,plain,
! [V_A_2,V_B_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Union__upper]) ).
fof(f_2421_2,plain,
! [U_9496,U_9495,U_9494] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9494,tc_HOL_Obool)),U_9495),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9494,tc_HOL_Obool),U_9496)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9494,tc_HOL_Obool)),U_9495),U_9496)) ),
inference(variable_rename,[status(thm)],[f_2421_1]) ).
fof(f_2421_3,plain,
! [U_9496,U_9494,U_9495] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9494,tc_HOL_Obool)),U_9495),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9494,tc_HOL_Obool),U_9496)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9494,tc_HOL_Obool)),U_9495),U_9496)) ),
inference(definitional_conversion,[status(esa)],[f_2421_2]) ).
cnf(f_2421_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9494,tc_HOL_Obool)),U_9495),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9494,tc_HOL_Obool),U_9496)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9494,tc_HOL_Obool)),U_9495),U_9496)) ),
inference(clausify,[status(thm)],[f_2421_3]) ).
fof(f_2422_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_2422_2,plain,
! [U_9498,U_9497] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9497),c_Groups_Osgn__class_Osgn(U_9497,U_9498)),hAPP(c_Groups_Oabs__class_Oabs(U_9497),U_9498)) = U_9498
| ~ class_Rings_Olinordered__idom(U_9497) ),
inference(variable_rename,[status(thm)],[f_2422_1]) ).
fof(f_2422_3,plain,
! [U_9497,U_9498] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9497),c_Groups_Osgn__class_Osgn(U_9497,U_9498)),hAPP(c_Groups_Oabs__class_Oabs(U_9497),U_9498)) = U_9498
| ~ class_Rings_Olinordered__idom(U_9497) ),
inference(definitional_conversion,[status(esa)],[f_2422_2]) ).
cnf(f_2422_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9497),c_Groups_Osgn__class_Osgn(U_9497,U_9498)),hAPP(c_Groups_Oabs__class_Oabs(U_9497),U_9498)) = U_9498
| ~ class_Rings_Olinordered__idom(U_9497) ),
inference(clausify,[status(thm)],[f_2422_3]) ).
fof(f_2423_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_2423_2,plain,
! [U_9500,U_9499] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9499),U_9500) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9499),U_9500),c_Groups_Osgn__class_Osgn(U_9499,U_9500))
| ~ class_Rings_Olinordered__idom(U_9499) ),
inference(variable_rename,[status(thm)],[f_2423_1]) ).
fof(f_2423_3,plain,
! [U_9499,U_9500] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9499),U_9500) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9499),U_9500),c_Groups_Osgn__class_Osgn(U_9499,U_9500))
| ~ class_Rings_Olinordered__idom(U_9499) ),
inference(definitional_conversion,[status(esa)],[f_2423_2]) ).
cnf(f_2423_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9499),U_9500) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9499),U_9500),c_Groups_Osgn__class_Osgn(U_9499,U_9500))
| ~ class_Rings_Olinordered__idom(U_9499) ),
inference(clausify,[status(thm)],[f_2423_3]) ).
fof(f_2424_1,plain,
! [T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Union__empty]) ).
fof(f_2424_2,plain,
! [U_9501] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9501,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9501,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9501,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2424_1]) ).
fof(f_2424_3,plain,
! [U_9501] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9501,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9501,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9501,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_2424_2]) ).
cnf(f_2424_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9501,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9501,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9501,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2424_3]) ).
fof(f_2425_1,plain,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Union__mono]) ).
fof(f_2425_2,plain,
! [U_9504,U_9503,U_9502] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9502,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9502,tc_HOL_Obool),U_9503)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9502,tc_HOL_Obool),U_9504)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_9502,tc_HOL_Obool),tc_HOL_Obool)),U_9503),U_9504)) ),
inference(variable_rename,[status(thm)],[f_2425_1]) ).
fof(f_2425_3,plain,
! [U_9502,U_9503,U_9504] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9502,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9502,tc_HOL_Obool),U_9503)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9502,tc_HOL_Obool),U_9504)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_9502,tc_HOL_Obool),tc_HOL_Obool)),U_9503),U_9504)) ),
inference(definitional_conversion,[status(esa)],[f_2425_2]) ).
cnf(f_2425_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9502,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9502,tc_HOL_Obool),U_9503)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9502,tc_HOL_Obool),U_9504)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_9502,tc_HOL_Obool),tc_HOL_Obool)),U_9503),U_9504)) ),
inference(clausify,[status(thm)],[f_2425_3]) ).
fof(f_2426_1,plain,
! [V_B_2,V_a_2,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(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),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Union__insert]) ).
fof(f_2426_2,plain,
! [U_9507,U_9506,U_9505] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9505,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9505,tc_HOL_Obool)),U_9506),U_9507)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9505,tc_HOL_Obool)),U_9506),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9505,tc_HOL_Obool),U_9507)),
inference(variable_rename,[status(thm)],[f_2426_1]) ).
fof(f_2426_3,plain,
! [U_9505,U_9506,U_9507] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9505,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9505,tc_HOL_Obool)),U_9506),U_9507)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9505,tc_HOL_Obool)),U_9506),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9505,tc_HOL_Obool),U_9507)),
inference(definitional_conversion,[status(esa)],[f_2426_2]) ).
cnf(f_2426_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9505,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9505,tc_HOL_Obool)),U_9506),U_9507)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9505,tc_HOL_Obool)),U_9506),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9505,tc_HOL_Obool),U_9507)),
inference(clausify,[status(thm)],[f_2426_3]) ).
fof(f_2427_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__UnionD]) ).
fof(f_2427_2,plain,
! [U_9509,U_9508] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9508,tc_HOL_Obool)),U_9509))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9508),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9508,tc_HOL_Obool),U_9509))) ),
inference(variable_rename,[status(thm)],[f_2427_1]) ).
fof(f_2427_3,plain,
! [U_9508,U_9509] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9508,tc_HOL_Obool)),U_9509))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9508),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9508,tc_HOL_Obool),U_9509))) ),
inference(definitional_conversion,[status(esa)],[f_2427_2]) ).
cnf(f_2427_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9508,tc_HOL_Obool)),U_9509))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9508),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9508,tc_HOL_Obool),U_9509))) ),
inference(clausify,[status(thm)],[f_2427_3]) ).
fof(f_2428_1,plain,
! [V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)))),
inference(fof_nnf,[status(thm)],[fact_subset__Pow__Union]) ).
fof(f_2428_2,plain,
! [U_9511,U_9510] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_9510,tc_HOL_Obool),tc_HOL_Obool)),U_9511),hAPP(c_Set_OPow(U_9510),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9510,tc_HOL_Obool),U_9511)))),
inference(variable_rename,[status(thm)],[f_2428_1]) ).
fof(f_2428_3,plain,
! [U_9510,U_9511] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_9510,tc_HOL_Obool),tc_HOL_Obool)),U_9511),hAPP(c_Set_OPow(U_9510),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9510,tc_HOL_Obool),U_9511)))),
inference(definitional_conversion,[status(esa)],[f_2428_2]) ).
cnf(f_2428_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_9510,tc_HOL_Obool),tc_HOL_Obool)),U_9511),hAPP(c_Set_OPow(U_9510),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9510,tc_HOL_Obool),U_9511)))),
inference(clausify,[status(thm)],[f_2428_3]) ).
fof(f_2429_1,plain,
! [T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Union__UNIV]) ).
fof(f_2429_2,plain,
! [U_9512] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9512,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_9512,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_9512,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2429_1]) ).
fof(f_2429_3,plain,
! [U_9512] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9512,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_9512,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_9512,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_2429_2]) ).
cnf(f_2429_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9512,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_9512,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_9512,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2429_3]) ).
fof(f_2430_1,plain,
! [V_B_2,V_A_2,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Union__Un__distrib]) ).
fof(f_2430_2,plain,
! [U_9515,U_9514,U_9513] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9513,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_9513,tc_HOL_Obool),tc_HOL_Obool)),U_9514),U_9515)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9513,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9513,tc_HOL_Obool),U_9514)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9513,tc_HOL_Obool),U_9515)),
inference(variable_rename,[status(thm)],[f_2430_1]) ).
fof(f_2430_3,plain,
! [U_9513,U_9514,U_9515] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9513,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_9513,tc_HOL_Obool),tc_HOL_Obool)),U_9514),U_9515)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9513,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9513,tc_HOL_Obool),U_9514)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9513,tc_HOL_Obool),U_9515)),
inference(definitional_conversion,[status(esa)],[f_2430_2]) ).
cnf(f_2430_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9513,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_9513,tc_HOL_Obool),tc_HOL_Obool)),U_9514),U_9515)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9513,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9513,tc_HOL_Obool),U_9514)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9513,tc_HOL_Obool),U_9515)),
inference(clausify,[status(thm)],[f_2430_3]) ).
fof(f_2431_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_2431_2,plain,
! [U_9518,U_9517,U_9516] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9516),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9516),U_9517),U_9518)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9516),hAPP(c_Groups_Oabs__class_Oabs(U_9516),U_9517)),hAPP(c_Groups_Oabs__class_Oabs(U_9516),U_9518))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9516),U_9518),c_Groups_Ozero__class_Ozero(U_9516)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9516),c_Groups_Ozero__class_Ozero(U_9516)),U_9518)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9516),U_9517),c_Groups_Ozero__class_Ozero(U_9516)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9516),c_Groups_Ozero__class_Ozero(U_9516)),U_9517)) )
| ~ class_Rings_Oordered__ring__abs(U_9516) ),
inference(variable_rename,[status(thm)],[f_2431_1]) ).
fof(f_2431_3,plain,
( ! [U_9516,U_9518] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9516),U_9518),c_Groups_Ozero__class_Ozero(U_9516)))
| ~ sP664(U_9516,U_9518) )
& ! [U_9516,U_9518] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9516),c_Groups_Ozero__class_Ozero(U_9516)),U_9518))
| ~ sP664(U_9516,U_9518) )
& ! [U_9516,U_9517] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9516),U_9517),c_Groups_Ozero__class_Ozero(U_9516)))
| ~ sP663(U_9516,U_9517) )
& ! [U_9516,U_9517] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9516),c_Groups_Ozero__class_Ozero(U_9516)),U_9517))
| ~ sP663(U_9516,U_9517) )
& ! [U_9516,U_9517,U_9518] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9516),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9516),U_9517),U_9518)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9516),hAPP(c_Groups_Oabs__class_Oabs(U_9516),U_9517)),hAPP(c_Groups_Oabs__class_Oabs(U_9516),U_9518))
| sP664(U_9516,U_9518)
| sP663(U_9516,U_9517)
| ~ class_Rings_Oordered__ring__abs(U_9516) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP663,sP664])],[f_2431_2]) ).
cnf(f_2431_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9516),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9516),U_9517),U_9518)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9516),hAPP(c_Groups_Oabs__class_Oabs(U_9516),U_9517)),hAPP(c_Groups_Oabs__class_Oabs(U_9516),U_9518))
| sP664(U_9516,U_9518)
| sP663(U_9516,U_9517)
| ~ class_Rings_Oordered__ring__abs(U_9516) ),
inference(clausify,[status(thm)],[f_2431_3]) ).
cnf(f_2431_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9516),c_Groups_Ozero__class_Ozero(U_9516)),U_9517))
| ~ sP663(U_9516,U_9517) ),
inference(clausify,[status(thm)],[f_2431_3]) ).
cnf(f_2431_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9516),U_9517),c_Groups_Ozero__class_Ozero(U_9516)))
| ~ sP663(U_9516,U_9517) ),
inference(clausify,[status(thm)],[f_2431_3]) ).
cnf(f_2431_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9516),c_Groups_Ozero__class_Ozero(U_9516)),U_9518))
| ~ sP664(U_9516,U_9518) ),
inference(clausify,[status(thm)],[f_2431_3]) ).
cnf(f_2431_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9516),U_9518),c_Groups_Ozero__class_Ozero(U_9516)))
| ~ sP664(U_9516,U_9518) ),
inference(clausify,[status(thm)],[f_2431_3]) ).
fof(f_2432_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_2432_2,plain,
! [U_9521,U_9520,U_9519] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9519),hAPP(c_Groups_Oabs__class_Oabs(U_9519),U_9521)),U_9520) = hAPP(c_Groups_Oabs__class_Oabs(U_9519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9519),U_9521),U_9520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9519),c_Groups_Ozero__class_Ozero(U_9519)),U_9520))
| ~ class_Rings_Olinordered__idom(U_9519) ),
inference(variable_rename,[status(thm)],[f_2432_1]) ).
fof(f_2432_3,plain,
! [U_9520,U_9521,U_9519] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9519),hAPP(c_Groups_Oabs__class_Oabs(U_9519),U_9521)),U_9520) = hAPP(c_Groups_Oabs__class_Oabs(U_9519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9519),U_9521),U_9520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9519),c_Groups_Ozero__class_Ozero(U_9519)),U_9520))
| ~ class_Rings_Olinordered__idom(U_9519) ),
inference(definitional_conversion,[status(esa)],[f_2432_2]) ).
cnf(f_2432_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9519),hAPP(c_Groups_Oabs__class_Oabs(U_9519),U_9521)),U_9520) = hAPP(c_Groups_Oabs__class_Oabs(U_9519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9519),U_9521),U_9520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9519),c_Groups_Ozero__class_Ozero(U_9519)),U_9520))
| ~ class_Rings_Olinordered__idom(U_9519) ),
inference(clausify,[status(thm)],[f_2432_3]) ).
fof(f_2433_1,plain,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_UNION__eq__Union__image]) ).
fof(f_2433_2,plain,
! [U_9525,U_9524,U_9523,U_9522] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9522,tc_fun(U_9523,tc_HOL_Obool)),U_9524),U_9525) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9523,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9522,tc_fun(U_9523,tc_HOL_Obool),U_9525),U_9524)),
inference(variable_rename,[status(thm)],[f_2433_1]) ).
fof(f_2433_3,plain,
! [U_9522,U_9523,U_9524,U_9525] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9522,tc_fun(U_9523,tc_HOL_Obool)),U_9524),U_9525) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9523,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9522,tc_fun(U_9523,tc_HOL_Obool),U_9525),U_9524)),
inference(definitional_conversion,[status(esa)],[f_2433_2]) ).
cnf(f_2433_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9522,tc_fun(U_9523,tc_HOL_Obool)),U_9524),U_9525) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9523,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9522,tc_fun(U_9523,tc_HOL_Obool),U_9525),U_9524)),
inference(clausify,[status(thm)],[f_2433_3]) ).
fof(f_2434_1,plain,
! [V_A_2,V_B_2,T_d,T_c] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_A_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),
inference(fof_nnf,[status(thm)],[fact_Union__image__eq]) ).
fof(f_2434_2,plain,
! [U_9529,U_9528,U_9527,U_9526] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9526,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9527,tc_fun(U_9526,tc_HOL_Obool),U_9528),U_9529)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9527,tc_fun(U_9526,tc_HOL_Obool)),U_9529),U_9528),
inference(variable_rename,[status(thm)],[f_2434_1]) ).
fof(f_2434_3,plain,
! [U_9526,U_9527,U_9528,U_9529] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9526,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9527,tc_fun(U_9526,tc_HOL_Obool),U_9528),U_9529)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9527,tc_fun(U_9526,tc_HOL_Obool)),U_9529),U_9528),
inference(definitional_conversion,[status(esa)],[f_2434_2]) ).
cnf(f_2434_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9526,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9527,tc_fun(U_9526,tc_HOL_Obool),U_9528),U_9529)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9527,tc_fun(U_9526,tc_HOL_Obool)),U_9529),U_9528),
inference(clausify,[status(thm)],[f_2434_3]) ).
fof(f_2435_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_2435_2,plain,
! [U_9534,U_9533,U_9532,U_9531,U_9530] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9530),hAPP(c_Groups_Oabs__class_Oabs(U_9530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9530),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9530),U_9531),U_9532)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9530),U_9533),U_9534)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9530),hAPP(c_Groups_Oabs__class_Oabs(U_9530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9530),U_9531),U_9533))),hAPP(c_Groups_Oabs__class_Oabs(U_9530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9530),U_9532),U_9534)))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9530) ),
inference(variable_rename,[status(thm)],[f_2435_1]) ).
fof(f_2435_3,plain,
! [U_9530,U_9531,U_9532,U_9533,U_9534] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9530),hAPP(c_Groups_Oabs__class_Oabs(U_9530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9530),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9530),U_9531),U_9532)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9530),U_9533),U_9534)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9530),hAPP(c_Groups_Oabs__class_Oabs(U_9530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9530),U_9531),U_9533))),hAPP(c_Groups_Oabs__class_Oabs(U_9530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9530),U_9532),U_9534)))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9530) ),
inference(definitional_conversion,[status(esa)],[f_2435_2]) ).
cnf(f_2435_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9530),hAPP(c_Groups_Oabs__class_Oabs(U_9530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9530),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9530),U_9531),U_9532)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9530),U_9533),U_9534)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9530),hAPP(c_Groups_Oabs__class_Oabs(U_9530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9530),U_9531),U_9533))),hAPP(c_Groups_Oabs__class_Oabs(U_9530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9530),U_9532),U_9534)))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9530) ),
inference(clausify,[status(thm)],[f_2435_3]) ).
fof(f_2436_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_2436_2,plain,
! [U_9537,U_9536,U_9535] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9535),hAPP(c_Groups_Oabs__class_Oabs(U_9535),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9535),U_9536),U_9537))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9535),hAPP(c_Groups_Oabs__class_Oabs(U_9535),U_9536)),hAPP(c_Groups_Oabs__class_Oabs(U_9535),U_9537))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9535) ),
inference(variable_rename,[status(thm)],[f_2436_1]) ).
fof(f_2436_3,plain,
! [U_9535,U_9536,U_9537] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9535),hAPP(c_Groups_Oabs__class_Oabs(U_9535),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9535),U_9536),U_9537))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9535),hAPP(c_Groups_Oabs__class_Oabs(U_9535),U_9536)),hAPP(c_Groups_Oabs__class_Oabs(U_9535),U_9537))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9535) ),
inference(definitional_conversion,[status(esa)],[f_2436_2]) ).
cnf(f_2436_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9535),hAPP(c_Groups_Oabs__class_Oabs(U_9535),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9535),U_9536),U_9537))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9535),hAPP(c_Groups_Oabs__class_Oabs(U_9535),U_9536)),hAPP(c_Groups_Oabs__class_Oabs(U_9535),U_9537))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9535) ),
inference(clausify,[status(thm)],[f_2436_3]) ).
fof(f_2437_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_2437_2,plain,
! [U_9539,U_9538] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9538),U_9539) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9538),U_9539)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9538),U_9539),c_Groups_Ozero__class_Ozero(U_9538)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9538) ),
inference(variable_rename,[status(thm)],[f_2437_1]) ).
fof(f_2437_3,plain,
! [U_9538,U_9539] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9538),U_9539) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9538),U_9539)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9538),U_9539),c_Groups_Ozero__class_Ozero(U_9538)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9538) ),
inference(definitional_conversion,[status(esa)],[f_2437_2]) ).
cnf(f_2437_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9538),U_9539) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9538),U_9539)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9538),U_9539),c_Groups_Ozero__class_Ozero(U_9538)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9538) ),
inference(clausify,[status(thm)],[f_2437_3]) ).
fof(f_2438_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_2438_2,plain,
! [U_9541,U_9540] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9540),hAPP(c_Groups_Ouminus__class_Ouminus(U_9540),hAPP(c_Groups_Oabs__class_Oabs(U_9540),U_9541))),c_Groups_Ozero__class_Ozero(U_9540)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9540) ),
inference(variable_rename,[status(thm)],[f_2438_1]) ).
fof(f_2438_3,plain,
! [U_9540,U_9541] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9540),hAPP(c_Groups_Ouminus__class_Ouminus(U_9540),hAPP(c_Groups_Oabs__class_Oabs(U_9540),U_9541))),c_Groups_Ozero__class_Ozero(U_9540)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9540) ),
inference(definitional_conversion,[status(esa)],[f_2438_2]) ).
cnf(f_2438_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9540),hAPP(c_Groups_Ouminus__class_Ouminus(U_9540),hAPP(c_Groups_Oabs__class_Oabs(U_9540),U_9541))),c_Groups_Ozero__class_Ozero(U_9540)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9540) ),
inference(clausify,[status(thm)],[f_2438_3]) ).
fof(f_2439_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_2439_2,plain,
! [U_9543,U_9542] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_9542),U_9543) = U_9543
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9542),U_9543),c_Groups_Ozero__class_Ozero(U_9542))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(U_9542),U_9543) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9542),U_9543)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9542),U_9543),c_Groups_Ozero__class_Ozero(U_9542))) ) )
| ~ class_Groups_Oabs__if(U_9542) ),
inference(variable_rename,[status(thm)],[f_2439_1]) ).
fof(f_2439_3,plain,
( ! [U_9542,U_9543] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9542),U_9543) = U_9543
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9542),U_9543),c_Groups_Ozero__class_Ozero(U_9542)))
| ~ sP665(U_9542,U_9543) )
& ! [U_9542,U_9543] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9542),U_9543) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9542),U_9543)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9542),U_9543),c_Groups_Ozero__class_Ozero(U_9542)))
| ~ sP665(U_9542,U_9543) )
& ! [U_9542,U_9543] :
( sP665(U_9542,U_9543)
| ~ class_Groups_Oabs__if(U_9542) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP665])],[f_2439_2]) ).
cnf(f_2439_4,plain,
( sP665(U_9542,U_9543)
| ~ class_Groups_Oabs__if(U_9542) ),
inference(clausify,[status(thm)],[f_2439_3]) ).
cnf(f_2439_5,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9542),U_9543) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9542),U_9543)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9542),U_9543),c_Groups_Ozero__class_Ozero(U_9542)))
| ~ sP665(U_9542,U_9543) ),
inference(clausify,[status(thm)],[f_2439_3]) ).
cnf(f_2439_6,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9542),U_9543) = U_9543
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9542),U_9543),c_Groups_Ozero__class_Ozero(U_9542)))
| ~ sP665(U_9542,U_9543) ),
inference(clausify,[status(thm)],[f_2439_3]) ).
fof(f_2440_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_2440_2,plain,
! [U_9545,U_9544] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9544),U_9545) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9544),U_9545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9544),U_9545),c_Groups_Ozero__class_Ozero(U_9544)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9544) ),
inference(variable_rename,[status(thm)],[f_2440_1]) ).
fof(f_2440_3,plain,
! [U_9545,U_9544] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9544),U_9545) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9544),U_9545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9544),U_9545),c_Groups_Ozero__class_Ozero(U_9544)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9544) ),
inference(definitional_conversion,[status(esa)],[f_2440_2]) ).
cnf(f_2440_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9544),U_9545) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9544),U_9545)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9544),U_9545),c_Groups_Ozero__class_Ozero(U_9544)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_9544) ),
inference(clausify,[status(thm)],[f_2440_3]) ).
fof(f_2441_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_2441_2,plain,
! [U_9548,U_9547,U_9546] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9546),c_Groups_Ozero__class_Ozero(U_9546)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9546),hAPP(c_Groups_Oabs__class_Oabs(U_9546),U_9547)),U_9548)))
| ~ class_Rings_Olinordered__idom(U_9546) ),
inference(variable_rename,[status(thm)],[f_2441_1]) ).
fof(f_2441_3,plain,
! [U_9546,U_9547,U_9548] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9546),c_Groups_Ozero__class_Ozero(U_9546)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9546),hAPP(c_Groups_Oabs__class_Oabs(U_9546),U_9547)),U_9548)))
| ~ class_Rings_Olinordered__idom(U_9546) ),
inference(definitional_conversion,[status(esa)],[f_2441_2]) ).
cnf(f_2441_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9546),c_Groups_Ozero__class_Ozero(U_9546)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9546),hAPP(c_Groups_Oabs__class_Oabs(U_9546),U_9547)),U_9548)))
| ~ class_Rings_Olinordered__idom(U_9546) ),
inference(clausify,[status(thm)],[f_2441_3]) ).
fof(f_2442_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_2442_2,plain,
! [U_9551,U_9550,U_9549] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9549),hAPP(c_Groups_Oabs__class_Oabs(U_9549),U_9551)),U_9550) = hAPP(c_Groups_Oabs__class_Oabs(U_9549),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9549),U_9551),U_9550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9549),c_Groups_Ozero__class_Ozero(U_9549)),U_9550))
| ~ class_Fields_Olinordered__field__inverse__zero(U_9549) ),
inference(variable_rename,[status(thm)],[f_2442_1]) ).
fof(f_2442_3,plain,
! [U_9549,U_9550,U_9551] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9549),hAPP(c_Groups_Oabs__class_Oabs(U_9549),U_9551)),U_9550) = hAPP(c_Groups_Oabs__class_Oabs(U_9549),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9549),U_9551),U_9550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9549),c_Groups_Ozero__class_Ozero(U_9549)),U_9550))
| ~ class_Fields_Olinordered__field__inverse__zero(U_9549) ),
inference(definitional_conversion,[status(esa)],[f_2442_2]) ).
cnf(f_2442_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9549),hAPP(c_Groups_Oabs__class_Oabs(U_9549),U_9551)),U_9550) = hAPP(c_Groups_Oabs__class_Oabs(U_9549),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9549),U_9551),U_9550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9549),c_Groups_Ozero__class_Ozero(U_9549)),U_9550))
| ~ class_Fields_Olinordered__field__inverse__zero(U_9549) ),
inference(clausify,[status(thm)],[f_2442_3]) ).
fof(f_2443_1,plain,
! [V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__upper]) ).
fof(f_2443_2,plain,
! [U_9554,U_9553,U_9552] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9552),U_9553),c_Complete__Lattice_OSup__class_OSup(U_9552,U_9554)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9552),U_9553),U_9554))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9552) ),
inference(variable_rename,[status(thm)],[f_2443_1]) ).
fof(f_2443_3,plain,
! [U_9552,U_9553,U_9554] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9552),U_9553),c_Complete__Lattice_OSup__class_OSup(U_9552,U_9554)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9552),U_9553),U_9554))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9552) ),
inference(definitional_conversion,[status(esa)],[f_2443_2]) ).
cnf(f_2443_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9552),U_9553),c_Complete__Lattice_OSup__class_OSup(U_9552,U_9554)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9552),U_9553),U_9554))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9552) ),
inference(clausify,[status(thm)],[f_2443_3]) ).
fof(f_2444_1,plain,
! [T_c] :
( c_Complete__Lattice_OSup__class_OSup(T_c,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_c)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__empty]) ).
fof(f_2444_2,plain,
! [U_9555] :
( c_Complete__Lattice_OSup__class_OSup(U_9555,c_Orderings_Obot__class_Obot(tc_fun(U_9555,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_9555)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9555) ),
inference(variable_rename,[status(thm)],[f_2444_1]) ).
fof(f_2444_3,plain,
! [U_9555] :
( c_Complete__Lattice_OSup__class_OSup(U_9555,c_Orderings_Obot__class_Obot(tc_fun(U_9555,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_9555)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9555) ),
inference(definitional_conversion,[status(esa)],[f_2444_2]) ).
cnf(f_2444_4,plain,
( c_Complete__Lattice_OSup__class_OSup(U_9555,c_Orderings_Obot__class_Obot(tc_fun(U_9555,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_9555)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9555) ),
inference(clausify,[status(thm)],[f_2444_3]) ).
fof(f_2445_1,plain,
! [V_a_2,T_c] :
( c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = V_a_2
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__singleton]) ).
fof(f_2445_2,plain,
! [U_9557,U_9556] :
( c_Complete__Lattice_OSup__class_OSup(U_9556,hAPP(hAPP(c_Set_Oinsert(U_9556),U_9557),c_Orderings_Obot__class_Obot(tc_fun(U_9556,tc_HOL_Obool)))) = U_9557
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9556) ),
inference(variable_rename,[status(thm)],[f_2445_1]) ).
fof(f_2445_3,plain,
! [U_9556,U_9557] :
( c_Complete__Lattice_OSup__class_OSup(U_9556,hAPP(hAPP(c_Set_Oinsert(U_9556),U_9557),c_Orderings_Obot__class_Obot(tc_fun(U_9556,tc_HOL_Obool)))) = U_9557
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9556) ),
inference(definitional_conversion,[status(esa)],[f_2445_2]) ).
cnf(f_2445_4,plain,
( c_Complete__Lattice_OSup__class_OSup(U_9556,hAPP(hAPP(c_Set_Oinsert(U_9556),U_9557),c_Orderings_Obot__class_Obot(tc_fun(U_9556,tc_HOL_Obool)))) = U_9557
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9556) ),
inference(clausify,[status(thm)],[f_2445_3]) ).
fof(f_2446_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_2446_2,plain,
! [U_9558] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9558)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_9558 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_9558 = 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_9558)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_2446_1]) ).
fof(f_2446_3,plain,
( ! [U_9560] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9560)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_9560 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_9559] :
( U_9559 = 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_9559)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_2446_2]) ).
fof(f_2446_4,plain,
( ! [U_9560] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9560)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_9560 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_9559] :
( U_9559 = 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_9559)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_2446_3]) ).
cnf(f_2446_5,plain,
( U_9559 = 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_9559)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2446_4]) ).
cnf(f_2446_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9560)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_9560 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2446_4]) ).
fof(f_2447_1,plain,
! [V_A_2,V_a_2,T_c] :
( c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__insert]) ).
fof(f_2447_2,plain,
! [U_9563,U_9562,U_9561] :
( c_Complete__Lattice_OSup__class_OSup(U_9561,hAPP(hAPP(c_Set_Oinsert(U_9561),U_9562),U_9563)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9561),U_9562),c_Complete__Lattice_OSup__class_OSup(U_9561,U_9563))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9561) ),
inference(variable_rename,[status(thm)],[f_2447_1]) ).
fof(f_2447_3,plain,
! [U_9561,U_9562,U_9563] :
( c_Complete__Lattice_OSup__class_OSup(U_9561,hAPP(hAPP(c_Set_Oinsert(U_9561),U_9562),U_9563)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9561),U_9562),c_Complete__Lattice_OSup__class_OSup(U_9561,U_9563))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9561) ),
inference(definitional_conversion,[status(esa)],[f_2447_2]) ).
cnf(f_2447_4,plain,
( c_Complete__Lattice_OSup__class_OSup(U_9561,hAPP(hAPP(c_Set_Oinsert(U_9561),U_9562),U_9563)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9561),U_9562),c_Complete__Lattice_OSup__class_OSup(U_9561,U_9563))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9561) ),
inference(clausify,[status(thm)],[f_2447_3]) ).
fof(f_2448_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_2448_2,plain,
! [U_9564] :
( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9564) = U_9564
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9564),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9564) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9564)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9564),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_2448_1]) ).
fof(f_2448_3,plain,
( ! [U_9566] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9566) = U_9566
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9566),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_9565] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9565) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9565)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9565),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_2448_2]) ).
fof(f_2448_4,plain,
( ! [U_9566] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9566) = U_9566
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9566),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_9565] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9565) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9565)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9565),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_2448_3]) ).
cnf(f_2448_5,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9565) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_9565)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9565),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2448_4]) ).
cnf(f_2448_6,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9566) = U_9566
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9566),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2448_4]) ).
fof(f_2449_1,plain,
! [T_c] :
( c_Complete__Lattice_OSup__class_OSup(T_c,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_c)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__UNIV]) ).
fof(f_2449_2,plain,
! [U_9567] :
( c_Complete__Lattice_OSup__class_OSup(U_9567,c_Orderings_Otop__class_Otop(tc_fun(U_9567,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_9567)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9567) ),
inference(variable_rename,[status(thm)],[f_2449_1]) ).
fof(f_2449_3,plain,
! [U_9567] :
( c_Complete__Lattice_OSup__class_OSup(U_9567,c_Orderings_Otop__class_Otop(tc_fun(U_9567,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_9567)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9567) ),
inference(definitional_conversion,[status(esa)],[f_2449_2]) ).
cnf(f_2449_4,plain,
( c_Complete__Lattice_OSup__class_OSup(U_9567,c_Orderings_Otop__class_Otop(tc_fun(U_9567,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_9567)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9567) ),
inference(clausify,[status(thm)],[f_2449_3]) ).
fof(f_2450_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_2450_2,plain,
! [U_9569,U_9568] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9568),U_9569))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9568))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9569))),
inference(variable_rename,[status(thm)],[f_2450_1]) ).
fof(f_2450_3,plain,
! [U_9568,U_9569] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_9568),U_9569))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9568))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9569))),
inference(definitional_conversion,[status(esa)],[f_2450_2]) ).
cnf(f_2450_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_9568),U_9569))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9568))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9569))),
inference(clausify,[status(thm)],[f_2450_3]) ).
fof(f_2451_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_2451_2,plain,
! [U_9571,U_9570] : 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_9570)),U_9571))),
inference(variable_rename,[status(thm)],[f_2451_1]) ).
fof(f_2451_3,plain,
! [U_9570,U_9571] : 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_9570)),U_9571))),
inference(definitional_conversion,[status(esa)],[f_2451_2]) ).
cnf(f_2451_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_9570)),U_9571))),
inference(clausify,[status(thm)],[f_2451_3]) ).
fof(f_2452_1,plain,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I8_J]) ).
fof(f_2452_2,plain,
! [U_9575,U_9574,U_9573,U_9572] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9572,tc_fun(U_9573,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9572,tc_HOL_Obool),U_9574)),U_9575) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9572,tc_HOL_Obool),tc_fun(U_9573,tc_HOL_Obool)),U_9574),hAPP(hAPP(c_COMBC(tc_fun(U_9572,tc_HOL_Obool),tc_fun(U_9572,tc_fun(U_9573,tc_HOL_Obool)),tc_fun(U_9573,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9572,tc_fun(U_9573,tc_HOL_Obool))),U_9575)),
inference(variable_rename,[status(thm)],[f_2452_1]) ).
fof(f_2452_3,plain,
! [U_9572,U_9573,U_9574,U_9575] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9572,tc_fun(U_9573,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9572,tc_HOL_Obool),U_9574)),U_9575) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9572,tc_HOL_Obool),tc_fun(U_9573,tc_HOL_Obool)),U_9574),hAPP(hAPP(c_COMBC(tc_fun(U_9572,tc_HOL_Obool),tc_fun(U_9572,tc_fun(U_9573,tc_HOL_Obool)),tc_fun(U_9573,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9572,tc_fun(U_9573,tc_HOL_Obool))),U_9575)),
inference(definitional_conversion,[status(esa)],[f_2452_2]) ).
cnf(f_2452_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9572,tc_fun(U_9573,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9572,tc_HOL_Obool),U_9574)),U_9575) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9572,tc_HOL_Obool),tc_fun(U_9573,tc_HOL_Obool)),U_9574),hAPP(hAPP(c_COMBC(tc_fun(U_9572,tc_HOL_Obool),tc_fun(U_9572,tc_fun(U_9573,tc_HOL_Obool)),tc_fun(U_9573,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9572,tc_fun(U_9573,tc_HOL_Obool))),U_9575)),
inference(clausify,[status(thm)],[f_2452_3]) ).
fof(f_2453_1,plain,
! [V_B_2,V_A_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_d,tc_HOL_Obool),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I8_J]) ).
fof(f_2453_2,plain,
! [U_9579,U_9578,U_9577,U_9576] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9576,tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),U_9578),hAPP(hAPP(c_COMBC(tc_fun(U_9576,tc_HOL_Obool),tc_fun(U_9576,tc_fun(U_9577,tc_HOL_Obool)),tc_fun(U_9577,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9576,tc_fun(U_9577,tc_HOL_Obool))),U_9579)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9576,tc_fun(U_9577,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9576,tc_HOL_Obool),U_9578)),U_9579),
inference(variable_rename,[status(thm)],[f_2453_1]) ).
fof(f_2453_3,plain,
! [U_9576,U_9577,U_9578,U_9579] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9576,tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),U_9578),hAPP(hAPP(c_COMBC(tc_fun(U_9576,tc_HOL_Obool),tc_fun(U_9576,tc_fun(U_9577,tc_HOL_Obool)),tc_fun(U_9577,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9576,tc_fun(U_9577,tc_HOL_Obool))),U_9579)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9576,tc_fun(U_9577,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9576,tc_HOL_Obool),U_9578)),U_9579),
inference(definitional_conversion,[status(esa)],[f_2453_2]) ).
cnf(f_2453_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9576,tc_HOL_Obool),tc_fun(U_9577,tc_HOL_Obool)),U_9578),hAPP(hAPP(c_COMBC(tc_fun(U_9576,tc_HOL_Obool),tc_fun(U_9576,tc_fun(U_9577,tc_HOL_Obool)),tc_fun(U_9577,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9576,tc_fun(U_9577,tc_HOL_Obool))),U_9579)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9576,tc_fun(U_9577,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9576,tc_HOL_Obool),U_9578)),U_9579),
inference(clausify,[status(thm)],[f_2453_3]) ).
fof(f_2454_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_Un__eq__Union]) ).
fof(f_2454_2,plain,
! [U_9582,U_9581,U_9580] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9580,tc_HOL_Obool)),U_9581),U_9582) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9580,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9580,tc_HOL_Obool)),U_9581),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9580,tc_HOL_Obool)),U_9582),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9580,tc_HOL_Obool),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_2454_1]) ).
fof(f_2454_3,plain,
! [U_9580,U_9581,U_9582] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9580,tc_HOL_Obool)),U_9581),U_9582) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9580,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9580,tc_HOL_Obool)),U_9581),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9580,tc_HOL_Obool)),U_9582),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9580,tc_HOL_Obool),tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_2454_2]) ).
cnf(f_2454_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9580,tc_HOL_Obool)),U_9581),U_9582) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9580,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9580,tc_HOL_Obool)),U_9581),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9580,tc_HOL_Obool)),U_9582),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9580,tc_HOL_Obool),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2454_3]) ).
fof(f_2455_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_d,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_d),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)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(c_Set_Oimage(T_d,tc_fun(T_c,tc_HOL_Obool),V_B_2),V_C_2))),
inference(fof_nnf,[status(thm)],[fact_Un__Union__image]) ).
fof(f_2455_2,plain,
! [U_9587,U_9586,U_9585,U_9584,U_9583] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9583,tc_fun(U_9584,tc_HOL_Obool)),U_9585),hAPP(hAPP(c_COMBS(U_9583,tc_fun(U_9584,tc_HOL_Obool),tc_fun(U_9584,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9584,tc_HOL_Obool),tc_fun(tc_fun(U_9584,tc_HOL_Obool),tc_fun(U_9584,tc_HOL_Obool)),U_9583),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9584,tc_HOL_Obool))),U_9586)),U_9587)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9584,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9584,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9583,tc_fun(U_9584,tc_HOL_Obool),U_9586),U_9585))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9584,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9583,tc_fun(U_9584,tc_HOL_Obool),U_9587),U_9585))),
inference(variable_rename,[status(thm)],[f_2455_1]) ).
fof(f_2455_3,plain,
! [U_9583,U_9584,U_9585,U_9586,U_9587] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9583,tc_fun(U_9584,tc_HOL_Obool)),U_9585),hAPP(hAPP(c_COMBS(U_9583,tc_fun(U_9584,tc_HOL_Obool),tc_fun(U_9584,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9584,tc_HOL_Obool),tc_fun(tc_fun(U_9584,tc_HOL_Obool),tc_fun(U_9584,tc_HOL_Obool)),U_9583),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9584,tc_HOL_Obool))),U_9586)),U_9587)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9584,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9584,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9583,tc_fun(U_9584,tc_HOL_Obool),U_9586),U_9585))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9584,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9583,tc_fun(U_9584,tc_HOL_Obool),U_9587),U_9585))),
inference(definitional_conversion,[status(esa)],[f_2455_2]) ).
cnf(f_2455_4,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9583,tc_fun(U_9584,tc_HOL_Obool)),U_9585),hAPP(hAPP(c_COMBS(U_9583,tc_fun(U_9584,tc_HOL_Obool),tc_fun(U_9584,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9584,tc_HOL_Obool),tc_fun(tc_fun(U_9584,tc_HOL_Obool),tc_fun(U_9584,tc_HOL_Obool)),U_9583),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9584,tc_HOL_Obool))),U_9586)),U_9587)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9584,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9584,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9583,tc_fun(U_9584,tc_HOL_Obool),U_9586),U_9585))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9584,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9583,tc_fun(U_9584,tc_HOL_Obool),U_9587),U_9585))),
inference(clausify,[status(thm)],[f_2455_3]) ).
fof(f_2456_1,plain,
! [V_B_2,V_A_2,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Union__Int__subset]) ).
fof(f_2456_2,plain,
! [U_9590,U_9589,U_9588] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9588,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9588,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_9588,tc_HOL_Obool),tc_HOL_Obool)),U_9589),U_9590))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9588,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9588,tc_HOL_Obool),U_9589)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9588,tc_HOL_Obool),U_9590)))),
inference(variable_rename,[status(thm)],[f_2456_1]) ).
fof(f_2456_3,plain,
! [U_9588,U_9589,U_9590] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9588,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9588,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_9588,tc_HOL_Obool),tc_HOL_Obool)),U_9589),U_9590))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9588,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9588,tc_HOL_Obool),U_9589)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9588,tc_HOL_Obool),U_9590)))),
inference(definitional_conversion,[status(esa)],[f_2456_2]) ).
cnf(f_2456_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9588,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9588,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_9588,tc_HOL_Obool),tc_HOL_Obool)),U_9589),U_9590))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9588,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9588,tc_HOL_Obool),U_9589)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9588,tc_HOL_Obool),U_9590)))),
inference(clausify,[status(thm)],[f_2456_3]) ).
fof(f_2457_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_2457_2,plain,
! [U_9592,U_9591] :
( ( 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_9591)),U_9592)))
| ( U_9592 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_9591 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( U_9592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_9591 != 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_9591)),U_9592))) ) ),
inference(variable_rename,[status(thm)],[f_2457_1]) ).
fof(f_2457_3,plain,
( ! [U_9596,U_9594] :
( 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_9594)),U_9596)))
| ( U_9596 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_9594 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_9595,U_9593] :
( U_9595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_9593 != 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_9593)),U_9595))) ) ),
inference(miniscope,[status(thm)],[f_2457_2]) ).
fof(f_2457_4,plain,
( ! [U_9596,U_9594] :
( U_9596 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP666(U_9596,U_9594) )
& ! [U_9596,U_9594] :
( U_9594 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP666(U_9596,U_9594) )
& ! [U_9596,U_9594] :
( 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_9594)),U_9596)))
| sP666(U_9596,U_9594) )
& ! [U_9595,U_9593] :
( U_9595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_9593 != 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_9593)),U_9595))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP666])],[f_2457_3]) ).
cnf(f_2457_5,plain,
( U_9595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_9593 != 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_9593)),U_9595))) ),
inference(clausify,[status(thm)],[f_2457_4]) ).
cnf(f_2457_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_9594)),U_9596)))
| sP666(U_9596,U_9594) ),
inference(clausify,[status(thm)],[f_2457_4]) ).
cnf(f_2457_7,plain,
( U_9594 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP666(U_9596,U_9594) ),
inference(clausify,[status(thm)],[f_2457_4]) ).
cnf(f_2457_8,plain,
( U_9596 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP666(U_9596,U_9594) ),
inference(clausify,[status(thm)],[f_2457_4]) ).
fof(f_2458_1,plain,
! [V_b_2,V_a_2,T_c] :
( c_Complete__Lattice_OSup__class_OSup(T_c,hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_a_2),V_b_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__binary]) ).
fof(f_2458_2,plain,
! [U_9599,U_9598,U_9597] :
( c_Complete__Lattice_OSup__class_OSup(U_9597,hAPP(hAPP(c_Set_Oinsert(U_9597),U_9598),hAPP(hAPP(c_Set_Oinsert(U_9597),U_9599),c_Orderings_Obot__class_Obot(tc_fun(U_9597,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9597),U_9598),U_9599)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9597) ),
inference(variable_rename,[status(thm)],[f_2458_1]) ).
fof(f_2458_3,plain,
! [U_9597,U_9598,U_9599] :
( c_Complete__Lattice_OSup__class_OSup(U_9597,hAPP(hAPP(c_Set_Oinsert(U_9597),U_9598),hAPP(hAPP(c_Set_Oinsert(U_9597),U_9599),c_Orderings_Obot__class_Obot(tc_fun(U_9597,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9597),U_9598),U_9599)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9597) ),
inference(definitional_conversion,[status(esa)],[f_2458_2]) ).
cnf(f_2458_4,plain,
( c_Complete__Lattice_OSup__class_OSup(U_9597,hAPP(hAPP(c_Set_Oinsert(U_9597),U_9598),hAPP(hAPP(c_Set_Oinsert(U_9597),U_9599),c_Orderings_Obot__class_Obot(tc_fun(U_9597,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9597),U_9598),U_9599)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9597) ),
inference(clausify,[status(thm)],[f_2458_3]) ).
fof(f_2459_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup]) ).
fof(f_2459_2,plain,
! [U_9602,U_9601,U_9600] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9600),U_9602),c_Complete__Lattice_OSup__class_OSup(U_9600,U_9601)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9600,U_9600,c_Lattices_Osemilattice__sup__class_Osup(U_9600)),U_9602),U_9601)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9600),U_9601))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9600) ),
inference(variable_rename,[status(thm)],[f_2459_1]) ).
fof(f_2459_3,plain,
! [U_9600,U_9601,U_9602] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9600),U_9602),c_Complete__Lattice_OSup__class_OSup(U_9600,U_9601)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9600,U_9600,c_Lattices_Osemilattice__sup__class_Osup(U_9600)),U_9602),U_9601)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9600),U_9601))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9600) ),
inference(definitional_conversion,[status(esa)],[f_2459_2]) ).
cnf(f_2459_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9600),U_9602),c_Complete__Lattice_OSup__class_OSup(U_9600,U_9601)) = hAPP(hAPP(c_Finite__Set_Ofold(U_9600,U_9600,c_Lattices_Osemilattice__sup__class_Osup(U_9600)),U_9602),U_9601)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9600),U_9601))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9600) ),
inference(clausify,[status(thm)],[f_2459_3]) ).
fof(f_2460_1,plain,
! [V_A_2,T_c] :
( c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_c,V_A_2)
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup]) ).
fof(f_2460_2,plain,
! [U_9604,U_9603] :
( c_Big__Operators_Olattice__class_OSup__fin(U_9603,U_9604) = c_Complete__Lattice_OSup__class_OSup(U_9603,U_9604)
| U_9604 = c_Orderings_Obot__class_Obot(tc_fun(U_9603,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),U_9604))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9603) ),
inference(variable_rename,[status(thm)],[f_2460_1]) ).
fof(f_2460_3,plain,
! [U_9603,U_9604] :
( c_Big__Operators_Olattice__class_OSup__fin(U_9603,U_9604) = c_Complete__Lattice_OSup__class_OSup(U_9603,U_9604)
| U_9604 = c_Orderings_Obot__class_Obot(tc_fun(U_9603,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),U_9604))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9603) ),
inference(definitional_conversion,[status(esa)],[f_2460_2]) ).
cnf(f_2460_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_9603,U_9604) = c_Complete__Lattice_OSup__class_OSup(U_9603,U_9604)
| U_9604 = c_Orderings_Obot__class_Obot(tc_fun(U_9603,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),U_9604))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9603) ),
inference(clausify,[status(thm)],[f_2460_3]) ).
fof(f_2461_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_2461_2,plain,
! [U_9606,U_9605] : c_Nitpick_Oint__lcm(U_9605,U_9606) = 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_9605)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9606)))),
inference(variable_rename,[status(thm)],[f_2461_1]) ).
fof(f_2461_3,plain,
! [U_9605,U_9606] : c_Nitpick_Oint__lcm(U_9605,U_9606) = 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_9605)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9606)))),
inference(definitional_conversion,[status(esa)],[f_2461_2]) ).
cnf(f_2461_4,plain,
c_Nitpick_Oint__lcm(U_9605,U_9606) = 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_9605)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9606)))),
inference(clausify,[status(thm)],[f_2461_3]) ).
fof(f_2462_1,plain,
! [V_f_2,T_d,T_c,V_S_2] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_S_2))
| ? [B_A] :
( ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,B_A)
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_A),V_S_2)) )
| V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__Inter]) ).
fof(f_2462_2,plain,
! [U_9611,U_9610,U_9609,U_9608] :
( c_Fun_Oinj__on(U_9609,U_9610,U_9611,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9609,tc_HOL_Obool),U_9608))
| ? [U_9607] :
( ~ c_Fun_Oinj__on(U_9609,U_9610,U_9611,U_9607)
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9609,tc_HOL_Obool)),U_9607),U_9608)) )
| U_9608 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9609,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_2462_1]) ).
fof(f_2462_3,plain,
! [U_9611,U_9610,U_9609,U_9608] :
( c_Fun_Oinj__on(U_9609,U_9610,U_9611,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9609,tc_HOL_Obool),U_9608))
| ( ~ c_Fun_Oinj__on(U_9609,U_9610,U_9611,sK232(U_9611,U_9610,U_9609,U_9608))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9609,tc_HOL_Obool)),sK232(U_9611,U_9610,U_9609,U_9608)),U_9608)) )
| U_9608 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9609,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_9607,sK232(U_9611,U_9610,U_9609,U_9608))],[f_2462_2]) ).
fof(f_2462_4,plain,
( ! [U_9608,U_9609,U_9610,U_9611] :
( ~ c_Fun_Oinj__on(U_9609,U_9610,U_9611,sK232(U_9611,U_9610,U_9609,U_9608))
| ~ sP667(U_9608,U_9609,U_9610,U_9611) )
& ! [U_9608,U_9609,U_9610,U_9611] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9609,tc_HOL_Obool)),sK232(U_9611,U_9610,U_9609,U_9608)),U_9608))
| ~ sP667(U_9608,U_9609,U_9610,U_9611) )
& ! [U_9608,U_9609,U_9610,U_9611] :
( c_Fun_Oinj__on(U_9609,U_9610,U_9611,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9609,tc_HOL_Obool),U_9608))
| sP667(U_9608,U_9609,U_9610,U_9611)
| U_9608 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9609,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP667])],[f_2462_3]) ).
cnf(f_2462_5,plain,
( c_Fun_Oinj__on(U_9609,U_9610,U_9611,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9609,tc_HOL_Obool),U_9608))
| sP667(U_9608,U_9609,U_9610,U_9611)
| U_9608 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9609,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2462_4]) ).
cnf(f_2462_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9609,tc_HOL_Obool)),sK232(U_9611,U_9610,U_9609,U_9608)),U_9608))
| ~ sP667(U_9608,U_9609,U_9610,U_9611) ),
inference(clausify,[status(thm)],[f_2462_4]) ).
cnf(f_2462_7,plain,
( ~ c_Fun_Oinj__on(U_9609,U_9610,U_9611,sK232(U_9611,U_9610,U_9609,U_9608))
| ~ sP667(U_9608,U_9609,U_9610,U_9611) ),
inference(clausify,[status(thm)],[f_2462_4]) ).
fof(f_2463_1,plain,
! [V_B_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))
| ? [B_X] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_X),V_B_2))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_X),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Inter__subset]) ).
fof(f_2463_2,plain,
! [U_9615,U_9614,U_9613] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9613,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9613,tc_HOL_Obool),U_9614)),U_9615))
| U_9614 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9613,tc_HOL_Obool),tc_HOL_Obool))
| ? [U_9612] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9613,tc_HOL_Obool)),U_9612),U_9615))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9613,tc_HOL_Obool)),U_9612),U_9614)) ) ),
inference(variable_rename,[status(thm)],[f_2463_1]) ).
fof(f_2463_3,plain,
! [U_9615,U_9614,U_9613] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9613,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9613,tc_HOL_Obool),U_9614)),U_9615))
| U_9614 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9613,tc_HOL_Obool),tc_HOL_Obool))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9613,tc_HOL_Obool)),sK233(U_9615,U_9614,U_9613)),U_9615))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9613,tc_HOL_Obool)),sK233(U_9615,U_9614,U_9613)),U_9614)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_9612,sK233(U_9615,U_9614,U_9613))],[f_2463_2]) ).
fof(f_2463_4,plain,
( ! [U_9613,U_9614,U_9615] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9613,tc_HOL_Obool)),sK233(U_9615,U_9614,U_9613)),U_9615))
| ~ sP668(U_9613,U_9614,U_9615) )
& ! [U_9613,U_9614,U_9615] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9613,tc_HOL_Obool)),sK233(U_9615,U_9614,U_9613)),U_9614))
| ~ sP668(U_9613,U_9614,U_9615) )
& ! [U_9613,U_9614,U_9615] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9613,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9613,tc_HOL_Obool),U_9614)),U_9615))
| U_9614 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9613,tc_HOL_Obool),tc_HOL_Obool))
| sP668(U_9613,U_9614,U_9615) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP668])],[f_2463_3]) ).
cnf(f_2463_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9613,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9613,tc_HOL_Obool),U_9614)),U_9615))
| U_9614 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9613,tc_HOL_Obool),tc_HOL_Obool))
| sP668(U_9613,U_9614,U_9615) ),
inference(clausify,[status(thm)],[f_2463_4]) ).
cnf(f_2463_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9613,tc_HOL_Obool)),sK233(U_9615,U_9614,U_9613)),U_9614))
| ~ sP668(U_9613,U_9614,U_9615) ),
inference(clausify,[status(thm)],[f_2463_4]) ).
cnf(f_2463_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9613,tc_HOL_Obool)),sK233(U_9615,U_9614,U_9613)),U_9615))
| ~ sP668(U_9613,U_9614,U_9615) ),
inference(clausify,[status(thm)],[f_2463_4]) ).
fof(f_2464_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_2464_2,plain,
! [U_9620,U_9619,U_9618] :
( ? [U_9617] :
( hAPP(U_9619,U_9617) = U_9620
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9617),U_9618)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9620),hAPP(U_9619,U_9618)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_9619,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_9620))
| ? [U_9616] :
( ~ 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_9619,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9616),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_9619,U_9616)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9616),U_9618)) ) ),
inference(variable_rename,[status(thm)],[f_2464_1]) ).
fof(f_2464_3,plain,
! [U_9620,U_9619,U_9618] :
( ? [U_9617] :
( hAPP(U_9619,U_9617) = U_9620
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9617),U_9618)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9620),hAPP(U_9619,U_9618)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_9619,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_9620))
| ( ~ 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_9619,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK234(U_9620,U_9619,U_9618)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_9619,sK234(U_9620,U_9619,U_9618))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK234(U_9620,U_9619,U_9618)),U_9618)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_9616,sK234(U_9620,U_9619,U_9618))],[f_2464_2]) ).
fof(f_2464_4,plain,
! [U_9620,U_9619,U_9618] :
( ( hAPP(U_9619,sK235(U_9620,U_9619,U_9618)) = U_9620
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK235(U_9620,U_9619,U_9618)),U_9618)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9620),hAPP(U_9619,U_9618)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_9619,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_9620))
| ( ~ 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_9619,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK234(U_9620,U_9619,U_9618)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_9619,sK234(U_9620,U_9619,U_9618))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK234(U_9620,U_9619,U_9618)),U_9618)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_9617,sK235(U_9620,U_9619,U_9618))],[f_2464_3]) ).
fof(f_2464_5,plain,
( ! [U_9618,U_9619,U_9620] :
( hAPP(U_9619,sK235(U_9620,U_9619,U_9618)) = U_9620
| ~ sP670(U_9618,U_9619,U_9620) )
& ! [U_9618,U_9619,U_9620] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK235(U_9620,U_9619,U_9618)),U_9618))
| ~ sP670(U_9618,U_9619,U_9620) )
& ! [U_9618,U_9619,U_9620] :
( ~ 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_9619,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK234(U_9620,U_9619,U_9618)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_9619,sK234(U_9620,U_9619,U_9618))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ sP669(U_9618,U_9619,U_9620) )
& ! [U_9618,U_9619,U_9620] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK234(U_9620,U_9619,U_9618)),U_9618))
| ~ sP669(U_9618,U_9619,U_9620) )
& ! [U_9618,U_9619,U_9620] :
( sP670(U_9618,U_9619,U_9620)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9620),hAPP(U_9619,U_9618)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_9619,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_9620))
| sP669(U_9618,U_9619,U_9620) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP669,sP670])],[f_2464_4]) ).
cnf(f_2464_6,plain,
( sP670(U_9618,U_9619,U_9620)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9620),hAPP(U_9619,U_9618)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_9619,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_9620))
| sP669(U_9618,U_9619,U_9620) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
cnf(f_2464_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK234(U_9620,U_9619,U_9618)),U_9618))
| ~ sP669(U_9618,U_9619,U_9620) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
cnf(f_2464_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_9619,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK234(U_9620,U_9619,U_9618)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_9619,sK234(U_9620,U_9619,U_9618))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ sP669(U_9618,U_9619,U_9620) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
cnf(f_2464_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK235(U_9620,U_9619,U_9618)),U_9618))
| ~ sP670(U_9618,U_9619,U_9620) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
cnf(f_2464_10,plain,
( hAPP(U_9619,sK235(U_9620,U_9619,U_9618)) = U_9620
| ~ sP670(U_9618,U_9619,U_9620) ),
inference(clausify,[status(thm)],[f_2464_5]) ).
fof(f_2465_1,plain,
! [V_S_2,T_c] : 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_c,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_c,tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_Union__def]) ).
fof(f_2465_2,plain,
! [U_9622,U_9621] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9621,tc_HOL_Obool),U_9622) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9621,tc_HOL_Obool),tc_fun(U_9621,tc_HOL_Obool)),U_9622),c_COMBI(tc_fun(U_9621,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2465_1]) ).
fof(f_2465_3,plain,
! [U_9622,U_9621] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9621,tc_HOL_Obool),U_9622) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9621,tc_HOL_Obool),tc_fun(U_9621,tc_HOL_Obool)),U_9622),c_COMBI(tc_fun(U_9621,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_2465_2]) ).
cnf(f_2465_4,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9621,tc_HOL_Obool),U_9622) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9621,tc_HOL_Obool),tc_fun(U_9621,tc_HOL_Obool)),U_9622),c_COMBI(tc_fun(U_9621,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2465_3]) ).
fof(f_2466_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_2466_2,plain,
! [U_9624,U_9623] : c_Nitpick_Onat__lcm(U_9623,U_9624) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9623),U_9624)),c_Nitpick_Onat__gcd(U_9623,U_9624)),
inference(variable_rename,[status(thm)],[f_2466_1]) ).
fof(f_2466_3,plain,
! [U_9624,U_9623] : c_Nitpick_Onat__lcm(U_9623,U_9624) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9623),U_9624)),c_Nitpick_Onat__gcd(U_9623,U_9624)),
inference(definitional_conversion,[status(esa)],[f_2466_2]) ).
cnf(f_2466_4,plain,
c_Nitpick_Onat__lcm(U_9623,U_9624) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9623),U_9624)),c_Nitpick_Onat__gcd(U_9623,U_9624)),
inference(clausify,[status(thm)],[f_2466_3]) ).
fof(f_2467_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)))
| ? [B_M] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),B_M))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_M),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Union]) ).
fof(f_2467_2,plain,
! [U_9627,U_9626] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9626),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9626,tc_HOL_Obool),U_9627)))
| ? [U_9625] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9626),U_9625))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9626,tc_HOL_Obool)),U_9625),U_9627)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9626,tc_HOL_Obool)),U_9627)) ),
inference(variable_rename,[status(thm)],[f_2467_1]) ).
fof(f_2467_3,plain,
! [U_9627,U_9626] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9626),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9626,tc_HOL_Obool),U_9627)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9626),sK236(U_9627,U_9626)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9626,tc_HOL_Obool)),sK236(U_9627,U_9626)),U_9627)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9626,tc_HOL_Obool)),U_9627)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_9625,sK236(U_9627,U_9626))],[f_2467_2]) ).
fof(f_2467_4,plain,
( ! [U_9626,U_9627] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9626),sK236(U_9627,U_9626)))
| ~ sP671(U_9626,U_9627) )
& ! [U_9626,U_9627] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9626,tc_HOL_Obool)),sK236(U_9627,U_9626)),U_9627))
| ~ sP671(U_9626,U_9627) )
& ! [U_9626,U_9627] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9626),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9626,tc_HOL_Obool),U_9627)))
| sP671(U_9626,U_9627)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9626,tc_HOL_Obool)),U_9627)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP671])],[f_2467_3]) ).
cnf(f_2467_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9626),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9626,tc_HOL_Obool),U_9627)))
| sP671(U_9626,U_9627)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9626,tc_HOL_Obool)),U_9627)) ),
inference(clausify,[status(thm)],[f_2467_4]) ).
cnf(f_2467_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9626,tc_HOL_Obool)),sK236(U_9627,U_9626)),U_9627))
| ~ sP671(U_9626,U_9627) ),
inference(clausify,[status(thm)],[f_2467_4]) ).
cnf(f_2467_7,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9626),sK236(U_9627,U_9626)))
| ~ sP671(U_9626,U_9627) ),
inference(clausify,[status(thm)],[f_2467_4]) ).
fof(f_2468_1,plain,
! [V_F_2,V_x_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ? [B_x] :
( ? [B_xa] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),B_x),B_xa) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& B_x != B_xa
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_x_2),V_F_2))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),V_x_2),V_F_2))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_x_2),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__partition]) ).
fof(f_2468_2,plain,
! [U_9632,U_9631,U_9630] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9630,tc_HOL_Obool)),U_9631),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9630,tc_HOL_Obool),U_9632)) = c_Orderings_Obot__class_Obot(tc_fun(U_9630,tc_HOL_Obool))
| ? [U_9629] :
( ? [U_9628] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9630,tc_HOL_Obool)),U_9629),U_9628) != c_Orderings_Obot__class_Obot(tc_fun(U_9630,tc_HOL_Obool))
& U_9629 != U_9628
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),U_9628),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),U_9629),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632)) ),
inference(variable_rename,[status(thm)],[f_2468_1]) ).
fof(f_2468_3,plain,
! [U_9632,U_9631,U_9630] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9630,tc_HOL_Obool)),U_9631),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9630,tc_HOL_Obool),U_9632)) = c_Orderings_Obot__class_Obot(tc_fun(U_9630,tc_HOL_Obool))
| ( ? [U_9628] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9630,tc_HOL_Obool)),sK237(U_9632,U_9631,U_9630)),U_9628) != c_Orderings_Obot__class_Obot(tc_fun(U_9630,tc_HOL_Obool))
& sK237(U_9632,U_9631,U_9630) != U_9628
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),U_9628),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),sK237(U_9632,U_9631,U_9630)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_9629,sK237(U_9632,U_9631,U_9630))],[f_2468_2]) ).
fof(f_2468_4,plain,
! [U_9632,U_9631,U_9630] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9630,tc_HOL_Obool)),U_9631),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9630,tc_HOL_Obool),U_9632)) = c_Orderings_Obot__class_Obot(tc_fun(U_9630,tc_HOL_Obool))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9630,tc_HOL_Obool)),sK237(U_9632,U_9631,U_9630)),sK238(U_9632,U_9631,U_9630)) != c_Orderings_Obot__class_Obot(tc_fun(U_9630,tc_HOL_Obool))
& sK237(U_9632,U_9631,U_9630) != sK238(U_9632,U_9631,U_9630)
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),sK238(U_9632,U_9631,U_9630)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),sK237(U_9632,U_9631,U_9630)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_9628,sK238(U_9632,U_9631,U_9630))],[f_2468_3]) ).
fof(f_2468_5,plain,
( ! [U_9630,U_9631,U_9632] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9630,tc_HOL_Obool)),sK237(U_9632,U_9631,U_9630)),sK238(U_9632,U_9631,U_9630)) != c_Orderings_Obot__class_Obot(tc_fun(U_9630,tc_HOL_Obool))
| ~ sP672(U_9630,U_9631,U_9632) )
& ! [U_9630,U_9631,U_9632] :
( sK237(U_9632,U_9631,U_9630) != sK238(U_9632,U_9631,U_9630)
| ~ sP672(U_9630,U_9631,U_9632) )
& ! [U_9630,U_9631,U_9632] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),sK238(U_9632,U_9631,U_9630)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632)))
| ~ sP672(U_9630,U_9631,U_9632) )
& ! [U_9630,U_9631,U_9632] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),sK237(U_9632,U_9631,U_9630)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632)))
| ~ sP672(U_9630,U_9631,U_9632) )
& ! [U_9630,U_9631,U_9632] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9630,tc_HOL_Obool)),U_9631),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9630,tc_HOL_Obool),U_9632)) = c_Orderings_Obot__class_Obot(tc_fun(U_9630,tc_HOL_Obool))
| sP672(U_9630,U_9631,U_9632)
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP672])],[f_2468_4]) ).
cnf(f_2468_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9630,tc_HOL_Obool)),U_9631),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9630,tc_HOL_Obool),U_9632)) = c_Orderings_Obot__class_Obot(tc_fun(U_9630,tc_HOL_Obool))
| sP672(U_9630,U_9631,U_9632)
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632)) ),
inference(clausify,[status(thm)],[f_2468_5]) ).
cnf(f_2468_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),sK237(U_9632,U_9631,U_9630)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632)))
| ~ sP672(U_9630,U_9631,U_9632) ),
inference(clausify,[status(thm)],[f_2468_5]) ).
cnf(f_2468_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9630,tc_HOL_Obool)),sK238(U_9632,U_9631,U_9630)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9630,tc_HOL_Obool)),U_9631),U_9632)))
| ~ sP672(U_9630,U_9631,U_9632) ),
inference(clausify,[status(thm)],[f_2468_5]) ).
cnf(f_2468_9,plain,
( sK237(U_9632,U_9631,U_9630) != sK238(U_9632,U_9631,U_9630)
| ~ sP672(U_9630,U_9631,U_9632) ),
inference(clausify,[status(thm)],[f_2468_5]) ).
cnf(f_2468_10,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9630,tc_HOL_Obool)),sK237(U_9632,U_9631,U_9630)),sK238(U_9632,U_9631,U_9630)) != c_Orderings_Obot__class_Obot(tc_fun(U_9630,tc_HOL_Obool))
| ~ sP672(U_9630,U_9631,U_9632) ),
inference(clausify,[status(thm)],[f_2468_5]) ).
fof(f_2469_1,plain,
! [V_k_2,V_C_2,T_c] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_c,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2))
| ? [B_c1] :
( ? [B_c2] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),B_c1),B_c2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& B_c1 != B_c2
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_c2),V_C_2)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_c1),V_C_2)) )
| ? [B_c] :
( hAPP(c_Finite__Set_Ocard(T_c),B_c) != V_k_2
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_c),V_C_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_C_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__partition]) ).
fof(f_2469_2,plain,
! [U_9638,U_9637,U_9636] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9638),hAPP(c_Finite__Set_Ocard(tc_fun(U_9636,tc_HOL_Obool)),U_9637)) = hAPP(c_Finite__Set_Ocard(U_9636),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9637))
| ? [U_9635] :
( ? [U_9634] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9636,tc_HOL_Obool)),U_9635),U_9634) != c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool))
& U_9635 != U_9634
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),U_9634),U_9637)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),U_9635),U_9637)) )
| ? [U_9633] :
( hAPP(c_Finite__Set_Ocard(U_9636),U_9633) != U_9638
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),U_9633),U_9637)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9636),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9637)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9636,tc_HOL_Obool)),U_9637)) ),
inference(variable_rename,[status(thm)],[f_2469_1]) ).
fof(f_2469_3,plain,
! [U_9638,U_9637,U_9636] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9638),hAPP(c_Finite__Set_Ocard(tc_fun(U_9636,tc_HOL_Obool)),U_9637)) = hAPP(c_Finite__Set_Ocard(U_9636),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9637))
| ? [U_9635] :
( ? [U_9634] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9636,tc_HOL_Obool)),U_9635),U_9634) != c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool))
& U_9635 != U_9634
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),U_9634),U_9637)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),U_9635),U_9637)) )
| ( hAPP(c_Finite__Set_Ocard(U_9636),sK239(U_9638,U_9637,U_9636)) != U_9638
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),sK239(U_9638,U_9637,U_9636)),U_9637)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9636),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9637)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9636,tc_HOL_Obool)),U_9637)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_9633,sK239(U_9638,U_9637,U_9636))],[f_2469_2]) ).
fof(f_2469_4,plain,
! [U_9638,U_9637,U_9636] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9638),hAPP(c_Finite__Set_Ocard(tc_fun(U_9636,tc_HOL_Obool)),U_9637)) = hAPP(c_Finite__Set_Ocard(U_9636),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9637))
| ( ? [U_9634] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9636,tc_HOL_Obool)),sK240(U_9638,U_9637,U_9636)),U_9634) != c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool))
& sK240(U_9638,U_9637,U_9636) != U_9634
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),U_9634),U_9637)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),sK240(U_9638,U_9637,U_9636)),U_9637)) )
| ( hAPP(c_Finite__Set_Ocard(U_9636),sK239(U_9638,U_9637,U_9636)) != U_9638
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),sK239(U_9638,U_9637,U_9636)),U_9637)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9636),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9637)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9636,tc_HOL_Obool)),U_9637)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_9635,sK240(U_9638,U_9637,U_9636))],[f_2469_3]) ).
fof(f_2469_5,plain,
! [U_9638,U_9637,U_9636] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9638),hAPP(c_Finite__Set_Ocard(tc_fun(U_9636,tc_HOL_Obool)),U_9637)) = hAPP(c_Finite__Set_Ocard(U_9636),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9637))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9636,tc_HOL_Obool)),sK240(U_9638,U_9637,U_9636)),sK241(U_9638,U_9637,U_9636)) != c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool))
& sK240(U_9638,U_9637,U_9636) != sK241(U_9638,U_9637,U_9636)
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),sK241(U_9638,U_9637,U_9636)),U_9637))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),sK240(U_9638,U_9637,U_9636)),U_9637)) )
| ( hAPP(c_Finite__Set_Ocard(U_9636),sK239(U_9638,U_9637,U_9636)) != U_9638
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),sK239(U_9638,U_9637,U_9636)),U_9637)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9636),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9637)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9636,tc_HOL_Obool)),U_9637)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_9634,sK241(U_9638,U_9637,U_9636))],[f_2469_4]) ).
fof(f_2469_6,plain,
( ! [U_9636,U_9637,U_9638] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9636,tc_HOL_Obool)),sK240(U_9638,U_9637,U_9636)),sK241(U_9638,U_9637,U_9636)) != c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool))
| ~ sP674(U_9636,U_9637,U_9638) )
& ! [U_9636,U_9637,U_9638] :
( sK240(U_9638,U_9637,U_9636) != sK241(U_9638,U_9637,U_9636)
| ~ sP674(U_9636,U_9637,U_9638) )
& ! [U_9636,U_9637,U_9638] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),sK241(U_9638,U_9637,U_9636)),U_9637))
| ~ sP674(U_9636,U_9637,U_9638) )
& ! [U_9636,U_9637,U_9638] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),sK240(U_9638,U_9637,U_9636)),U_9637))
| ~ sP674(U_9636,U_9637,U_9638) )
& ! [U_9636,U_9637,U_9638] :
( hAPP(c_Finite__Set_Ocard(U_9636),sK239(U_9638,U_9637,U_9636)) != U_9638
| ~ sP673(U_9636,U_9637,U_9638) )
& ! [U_9636,U_9637,U_9638] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),sK239(U_9638,U_9637,U_9636)),U_9637))
| ~ sP673(U_9636,U_9637,U_9638) )
& ! [U_9636,U_9637,U_9638] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9638),hAPP(c_Finite__Set_Ocard(tc_fun(U_9636,tc_HOL_Obool)),U_9637)) = hAPP(c_Finite__Set_Ocard(U_9636),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9637))
| sP674(U_9636,U_9637,U_9638)
| sP673(U_9636,U_9637,U_9638)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9636),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9637)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9636,tc_HOL_Obool)),U_9637)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP673,sP674])],[f_2469_5]) ).
cnf(f_2469_7,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9638),hAPP(c_Finite__Set_Ocard(tc_fun(U_9636,tc_HOL_Obool)),U_9637)) = hAPP(c_Finite__Set_Ocard(U_9636),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9637))
| sP674(U_9636,U_9637,U_9638)
| sP673(U_9636,U_9637,U_9638)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9636),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9636,tc_HOL_Obool),U_9637)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9636,tc_HOL_Obool)),U_9637)) ),
inference(clausify,[status(thm)],[f_2469_6]) ).
cnf(f_2469_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),sK239(U_9638,U_9637,U_9636)),U_9637))
| ~ sP673(U_9636,U_9637,U_9638) ),
inference(clausify,[status(thm)],[f_2469_6]) ).
cnf(f_2469_9,plain,
( hAPP(c_Finite__Set_Ocard(U_9636),sK239(U_9638,U_9637,U_9636)) != U_9638
| ~ sP673(U_9636,U_9637,U_9638) ),
inference(clausify,[status(thm)],[f_2469_6]) ).
cnf(f_2469_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),sK240(U_9638,U_9637,U_9636)),U_9637))
| ~ sP674(U_9636,U_9637,U_9638) ),
inference(clausify,[status(thm)],[f_2469_6]) ).
cnf(f_2469_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9636,tc_HOL_Obool)),sK241(U_9638,U_9637,U_9636)),U_9637))
| ~ sP674(U_9636,U_9637,U_9638) ),
inference(clausify,[status(thm)],[f_2469_6]) ).
cnf(f_2469_12,plain,
( sK240(U_9638,U_9637,U_9636) != sK241(U_9638,U_9637,U_9636)
| ~ sP674(U_9636,U_9637,U_9638) ),
inference(clausify,[status(thm)],[f_2469_6]) ).
cnf(f_2469_13,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9636,tc_HOL_Obool)),sK240(U_9638,U_9637,U_9636)),sK241(U_9638,U_9637,U_9636)) != c_Orderings_Obot__class_Obot(tc_fun(U_9636,tc_HOL_Obool))
| ~ sP674(U_9636,U_9637,U_9638) ),
inference(clausify,[status(thm)],[f_2469_6]) ).
fof(f_2470_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_2470_2,plain,
! [U_9640,U_9639] :
( ( c_Nitpick_Onat__gcd(U_9640,U_9639) = c_Nitpick_Onat__gcd(U_9639,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9640,U_9639))
| U_9639 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nitpick_Onat__gcd(U_9640,U_9639) = U_9640
| U_9639 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_2470_1]) ).
fof(f_2470_3,plain,
( ! [U_9644,U_9642] :
( c_Nitpick_Onat__gcd(U_9644,U_9642) = c_Nitpick_Onat__gcd(U_9642,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9644,U_9642))
| U_9642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_9643,U_9641] :
( c_Nitpick_Onat__gcd(U_9643,U_9641) = U_9643
| U_9641 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_2470_2]) ).
fof(f_2470_4,plain,
( ! [U_9642,U_9644] :
( c_Nitpick_Onat__gcd(U_9644,U_9642) = c_Nitpick_Onat__gcd(U_9642,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9644,U_9642))
| U_9642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_9641,U_9643] :
( c_Nitpick_Onat__gcd(U_9643,U_9641) = U_9643
| U_9641 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_2470_3]) ).
cnf(f_2470_5,plain,
( c_Nitpick_Onat__gcd(U_9643,U_9641) = U_9643
| U_9641 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2470_4]) ).
cnf(f_2470_6,plain,
( c_Nitpick_Onat__gcd(U_9644,U_9642) = c_Nitpick_Onat__gcd(U_9642,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_9644,U_9642))
| U_9642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2470_4]) ).
fof(f_2471_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_2471_2,plain,
! [U_9646,U_9645] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_9645),U_9646) = 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_9645)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9646)))),
inference(variable_rename,[status(thm)],[f_2471_1]) ).
fof(f_2471_3,plain,
! [U_9645,U_9646] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_9645),U_9646) = 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_9645)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9646)))),
inference(definitional_conversion,[status(esa)],[f_2471_2]) ).
cnf(f_2471_4,plain,
hAPP(hAPP(c_Nitpick_Oint__gcd,U_9645),U_9646) = 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_9645)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_9646)))),
inference(clausify,[status(thm)],[f_2471_3]) ).
fof(f_2472_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_2472_2,plain,
! [U_9651,U_9650,U_9649] :
( ? [U_9648] :
( hAPP(U_9650,U_9648) = U_9651
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9648),U_9649)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9651),hAPP(U_9650,U_9649)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_9650,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_9651))
| ? [U_9647] :
( ~ 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_9650,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9647),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_9650,U_9647)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9647),U_9649)) ) ),
inference(variable_rename,[status(thm)],[f_2472_1]) ).
fof(f_2472_3,plain,
! [U_9651,U_9650,U_9649] :
( ? [U_9648] :
( hAPP(U_9650,U_9648) = U_9651
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9648),U_9649)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9651),hAPP(U_9650,U_9649)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_9650,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_9651))
| ( ~ 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_9650,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK242(U_9651,U_9650,U_9649)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_9650,sK242(U_9651,U_9650,U_9649))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK242(U_9651,U_9650,U_9649)),U_9649)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_9647,sK242(U_9651,U_9650,U_9649))],[f_2472_2]) ).
fof(f_2472_4,plain,
! [U_9651,U_9650,U_9649] :
( ( hAPP(U_9650,sK243(U_9651,U_9650,U_9649)) = U_9651
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK243(U_9651,U_9650,U_9649)),U_9649)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9651),hAPP(U_9650,U_9649)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_9650,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_9651))
| ( ~ 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_9650,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK242(U_9651,U_9650,U_9649)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_9650,sK242(U_9651,U_9650,U_9649))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK242(U_9651,U_9650,U_9649)),U_9649)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_9648,sK243(U_9651,U_9650,U_9649))],[f_2472_3]) ).
fof(f_2472_5,plain,
( ! [U_9649,U_9650,U_9651] :
( hAPP(U_9650,sK243(U_9651,U_9650,U_9649)) = U_9651
| ~ sP676(U_9649,U_9650,U_9651) )
& ! [U_9649,U_9650,U_9651] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK243(U_9651,U_9650,U_9649)),U_9649))
| ~ sP676(U_9649,U_9650,U_9651) )
& ! [U_9649,U_9650,U_9651] :
( ~ 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_9650,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK242(U_9651,U_9650,U_9649)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_9650,sK242(U_9651,U_9650,U_9649))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ sP675(U_9649,U_9650,U_9651) )
& ! [U_9649,U_9650,U_9651] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK242(U_9651,U_9650,U_9649)),U_9649))
| ~ sP675(U_9649,U_9650,U_9651) )
& ! [U_9649,U_9650,U_9651] :
( sP676(U_9649,U_9650,U_9651)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9651),hAPP(U_9650,U_9649)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_9650,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_9651))
| sP675(U_9649,U_9650,U_9651) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP675,sP676])],[f_2472_4]) ).
cnf(f_2472_6,plain,
( sP676(U_9649,U_9650,U_9651)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9651),hAPP(U_9650,U_9649)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_9650,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_9651))
| sP675(U_9649,U_9650,U_9651) ),
inference(clausify,[status(thm)],[f_2472_5]) ).
cnf(f_2472_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK242(U_9651,U_9650,U_9649)),U_9649))
| ~ sP675(U_9649,U_9650,U_9651) ),
inference(clausify,[status(thm)],[f_2472_5]) ).
cnf(f_2472_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_9650,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK242(U_9651,U_9650,U_9649)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_9650,sK242(U_9651,U_9650,U_9649))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ sP675(U_9649,U_9650,U_9651) ),
inference(clausify,[status(thm)],[f_2472_5]) ).
cnf(f_2472_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK243(U_9651,U_9650,U_9649)),U_9649))
| ~ sP676(U_9649,U_9650,U_9651) ),
inference(clausify,[status(thm)],[f_2472_5]) ).
cnf(f_2472_10,plain,
( hAPP(U_9650,sK243(U_9651,U_9650,U_9649)) = U_9651
| ~ sP676(U_9649,U_9650,U_9651) ),
inference(clausify,[status(thm)],[f_2472_5]) ).
fof(f_2473_1,plain,
! [V_f_2,V_S_2,T_c] :
( 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_c,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_c),B_x),V_S_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) ),
inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat]) ).
fof(f_2473_2,plain,
! [U_9655,U_9654,U_9653] :
( 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_9653,tc_Nat_Onat),U_9655),U_9654)))
| ? [U_9652] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9655,U_9652)))
& hBOOL(hAPP(hAPP(c_member(U_9653),U_9652),U_9654)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9653),U_9654)) ),
inference(variable_rename,[status(thm)],[f_2473_1]) ).
fof(f_2473_3,plain,
! [U_9655,U_9654,U_9653] :
( 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_9653,tc_Nat_Onat),U_9655),U_9654)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9655,sK244(U_9655,U_9654,U_9653))))
& hBOOL(hAPP(hAPP(c_member(U_9653),sK244(U_9655,U_9654,U_9653)),U_9654)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9653),U_9654)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_9652,sK244(U_9655,U_9654,U_9653))],[f_2473_2]) ).
fof(f_2473_4,plain,
( ! [U_9655,U_9653,U_9654] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9655,sK244(U_9655,U_9654,U_9653))))
| ~ sP677(U_9655,U_9653,U_9654) )
& ! [U_9655,U_9653,U_9654] :
( hBOOL(hAPP(hAPP(c_member(U_9653),sK244(U_9655,U_9654,U_9653)),U_9654))
| ~ sP677(U_9655,U_9653,U_9654) )
& ! [U_9655,U_9653,U_9654] :
( 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_9653,tc_Nat_Onat),U_9655),U_9654)))
| sP677(U_9655,U_9653,U_9654)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9653),U_9654)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP677])],[f_2473_3]) ).
cnf(f_2473_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_9653,tc_Nat_Onat),U_9655),U_9654)))
| sP677(U_9655,U_9653,U_9654)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9653),U_9654)) ),
inference(clausify,[status(thm)],[f_2473_4]) ).
cnf(f_2473_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9653),sK244(U_9655,U_9654,U_9653)),U_9654))
| ~ sP677(U_9655,U_9653,U_9654) ),
inference(clausify,[status(thm)],[f_2473_4]) ).
cnf(f_2473_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9655,sK244(U_9655,U_9654,U_9653))))
| ~ sP677(U_9655,U_9653,U_9654) ),
inference(clausify,[status(thm)],[f_2473_4]) ).
fof(f_2474_1,plain,
! [V_A_2,V_f_2,T_e,T_d,T_c,V_I_2] :
( c_Fun_Oinj__on(T_d,T_e,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_HOL_Obool)),V_I_2),V_A_2))
| ? [B_i] :
( ~ c_Fun_Oinj__on(T_d,T_e,V_f_2,hAPP(V_A_2,B_i))
& hBOOL(hAPP(hAPP(c_member(T_c),B_i),V_I_2)) )
| V_I_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__INTER]) ).
fof(f_2474_2,plain,
! [U_9662,U_9661,U_9660,U_9659,U_9658,U_9657] :
( c_Fun_Oinj__on(U_9659,U_9660,U_9661,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9658,tc_fun(U_9659,tc_HOL_Obool)),U_9657),U_9662))
| ? [U_9656] :
( ~ c_Fun_Oinj__on(U_9659,U_9660,U_9661,hAPP(U_9662,U_9656))
& hBOOL(hAPP(hAPP(c_member(U_9658),U_9656),U_9657)) )
| U_9657 = c_Orderings_Obot__class_Obot(tc_fun(U_9658,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_2474_1]) ).
fof(f_2474_3,plain,
! [U_9662,U_9661,U_9660,U_9659,U_9658,U_9657] :
( c_Fun_Oinj__on(U_9659,U_9660,U_9661,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9658,tc_fun(U_9659,tc_HOL_Obool)),U_9657),U_9662))
| ( ~ c_Fun_Oinj__on(U_9659,U_9660,U_9661,hAPP(U_9662,sK245(U_9662,U_9661,U_9660,U_9659,U_9658,U_9657)))
& hBOOL(hAPP(hAPP(c_member(U_9658),sK245(U_9662,U_9661,U_9660,U_9659,U_9658,U_9657)),U_9657)) )
| U_9657 = c_Orderings_Obot__class_Obot(tc_fun(U_9658,tc_HOL_Obool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_9656,sK245(U_9662,U_9661,U_9660,U_9659,U_9658,U_9657))],[f_2474_2]) ).
fof(f_2474_4,plain,
( ! [U_9657,U_9658,U_9659,U_9660,U_9661,U_9662] :
( ~ c_Fun_Oinj__on(U_9659,U_9660,U_9661,hAPP(U_9662,sK245(U_9662,U_9661,U_9660,U_9659,U_9658,U_9657)))
| ~ sP678(U_9657,U_9658,U_9659,U_9660,U_9661,U_9662) )
& ! [U_9657,U_9658,U_9659,U_9660,U_9661,U_9662] :
( hBOOL(hAPP(hAPP(c_member(U_9658),sK245(U_9662,U_9661,U_9660,U_9659,U_9658,U_9657)),U_9657))
| ~ sP678(U_9657,U_9658,U_9659,U_9660,U_9661,U_9662) )
& ! [U_9657,U_9658,U_9659,U_9660,U_9661,U_9662] :
( c_Fun_Oinj__on(U_9659,U_9660,U_9661,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9658,tc_fun(U_9659,tc_HOL_Obool)),U_9657),U_9662))
| sP678(U_9657,U_9658,U_9659,U_9660,U_9661,U_9662)
| U_9657 = c_Orderings_Obot__class_Obot(tc_fun(U_9658,tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP678])],[f_2474_3]) ).
cnf(f_2474_5,plain,
( c_Fun_Oinj__on(U_9659,U_9660,U_9661,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9658,tc_fun(U_9659,tc_HOL_Obool)),U_9657),U_9662))
| sP678(U_9657,U_9658,U_9659,U_9660,U_9661,U_9662)
| U_9657 = c_Orderings_Obot__class_Obot(tc_fun(U_9658,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2474_4]) ).
cnf(f_2474_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9658),sK245(U_9662,U_9661,U_9660,U_9659,U_9658,U_9657)),U_9657))
| ~ sP678(U_9657,U_9658,U_9659,U_9660,U_9661,U_9662) ),
inference(clausify,[status(thm)],[f_2474_4]) ).
cnf(f_2474_7,plain,
( ~ c_Fun_Oinj__on(U_9659,U_9660,U_9661,hAPP(U_9662,sK245(U_9662,U_9661,U_9660,U_9659,U_9658,U_9657)))
| ~ sP678(U_9657,U_9658,U_9659,U_9660,U_9661,U_9662) ),
inference(clausify,[status(thm)],[f_2474_4]) ).
fof(f_2475_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_d,T_c] :
( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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_d),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_c,T_d,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_2475_2,plain,
! [U_9671,U_9670,U_9669,U_9668,U_9667,U_9666,U_9665,U_9664] :
( hAPP(U_9669,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9665,tc_HOL_Obool)),U_9670),U_9671)) = hAPP(hAPP(U_9666,hAPP(U_9669,U_9670)),hAPP(U_9669,U_9671))
| ? [U_9663] :
( hAPP(U_9668,U_9663) != U_9667
& hBOOL(hAPP(hAPP(c_member(U_9665),U_9663),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9665,tc_HOL_Obool)),U_9670),U_9671))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9665),U_9671))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9665),U_9670))
| ~ c_Finite__Set_Ofolding__image__simple(U_9664,U_9665,U_9666,U_9667,U_9668,U_9669) ),
inference(variable_rename,[status(thm)],[f_2475_1]) ).
fof(f_2475_3,plain,
! [U_9671,U_9670,U_9669,U_9668,U_9667,U_9666,U_9665] :
( ! [U_9664] : ~ c_Finite__Set_Ofolding__image__simple(U_9664,U_9665,U_9666,U_9667,U_9668,U_9669)
| hAPP(U_9669,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9665,tc_HOL_Obool)),U_9670),U_9671)) = hAPP(hAPP(U_9666,hAPP(U_9669,U_9670)),hAPP(U_9669,U_9671))
| ? [U_9663] :
( hAPP(U_9668,U_9663) != U_9667
& hBOOL(hAPP(hAPP(c_member(U_9665),U_9663),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9665,tc_HOL_Obool)),U_9670),U_9671))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9665),U_9671))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9665),U_9670)) ),
inference(miniscope,[status(thm)],[f_2475_2]) ).
fof(f_2475_4,plain,
! [U_9671,U_9670,U_9669,U_9668,U_9667,U_9666,U_9665] :
( ! [U_9664] : ~ c_Finite__Set_Ofolding__image__simple(U_9664,U_9665,U_9666,U_9667,U_9668,U_9669)
| hAPP(U_9669,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9665,tc_HOL_Obool)),U_9670),U_9671)) = hAPP(hAPP(U_9666,hAPP(U_9669,U_9670)),hAPP(U_9669,U_9671))
| ( hAPP(U_9668,sK246(U_9671,U_9670,U_9669,U_9668,U_9667,U_9666,U_9665)) != U_9667
& hBOOL(hAPP(hAPP(c_member(U_9665),sK246(U_9671,U_9670,U_9669,U_9668,U_9667,U_9666,U_9665)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9665,tc_HOL_Obool)),U_9670),U_9671))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9665),U_9671))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9665),U_9670)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_9663,sK246(U_9671,U_9670,U_9669,U_9668,U_9667,U_9666,U_9665))],[f_2475_3]) ).
fof(f_2475_5,plain,
( ! [U_9665,U_9666,U_9667,U_9668,U_9669,U_9670,U_9671] :
( hAPP(U_9668,sK246(U_9671,U_9670,U_9669,U_9668,U_9667,U_9666,U_9665)) != U_9667
| ~ sP679(U_9665,U_9666,U_9667,U_9668,U_9669,U_9670,U_9671) )
& ! [U_9665,U_9666,U_9667,U_9668,U_9669,U_9670,U_9671] :
( hBOOL(hAPP(hAPP(c_member(U_9665),sK246(U_9671,U_9670,U_9669,U_9668,U_9667,U_9666,U_9665)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9665,tc_HOL_Obool)),U_9670),U_9671)))
| ~ sP679(U_9665,U_9666,U_9667,U_9668,U_9669,U_9670,U_9671) )
& ! [U_9664,U_9665,U_9666,U_9667,U_9668,U_9669,U_9670,U_9671] :
( ~ c_Finite__Set_Ofolding__image__simple(U_9664,U_9665,U_9666,U_9667,U_9668,U_9669)
| hAPP(U_9669,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9665,tc_HOL_Obool)),U_9670),U_9671)) = hAPP(hAPP(U_9666,hAPP(U_9669,U_9670)),hAPP(U_9669,U_9671))
| sP679(U_9665,U_9666,U_9667,U_9668,U_9669,U_9670,U_9671)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9665),U_9671))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9665),U_9670)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP679])],[f_2475_4]) ).
cnf(f_2475_6,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_9664,U_9665,U_9666,U_9667,U_9668,U_9669)
| hAPP(U_9669,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9665,tc_HOL_Obool)),U_9670),U_9671)) = hAPP(hAPP(U_9666,hAPP(U_9669,U_9670)),hAPP(U_9669,U_9671))
| sP679(U_9665,U_9666,U_9667,U_9668,U_9669,U_9670,U_9671)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9665),U_9671))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9665),U_9670)) ),
inference(clausify,[status(thm)],[f_2475_5]) ).
cnf(f_2475_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_9665),sK246(U_9671,U_9670,U_9669,U_9668,U_9667,U_9666,U_9665)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9665,tc_HOL_Obool)),U_9670),U_9671)))
| ~ sP679(U_9665,U_9666,U_9667,U_9668,U_9669,U_9670,U_9671) ),
inference(clausify,[status(thm)],[f_2475_5]) ).
cnf(f_2475_8,plain,
( hAPP(U_9668,sK246(U_9671,U_9670,U_9669,U_9668,U_9667,U_9666,U_9665)) != U_9667
| ~ sP679(U_9665,U_9666,U_9667,U_9668,U_9669,U_9670,U_9671) ),
inference(clausify,[status(thm)],[f_2475_5]) ).
fof(f_2476_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_2476_2,plain,
! [U_9673,U_9672] :
( 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_9672))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9673)))) = 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_9672))),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_9673)))))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9672)) ),
inference(variable_rename,[status(thm)],[f_2476_1]) ).
fof(f_2476_3,plain,
! [U_9673,U_9672] :
( 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_9672))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9673)))) = 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_9672))),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_9673)))))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9672)) ),
inference(definitional_conversion,[status(esa)],[f_2476_2]) ).
cnf(f_2476_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_9672))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9673)))) = 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_9672))),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_9673)))))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9672)) ),
inference(clausify,[status(thm)],[f_2476_3]) ).
fof(f_2477_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_2477_2,plain,
! [U_9675,U_9674] :
( 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_9674))),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_9675))))) != 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_9674)) ),
inference(variable_rename,[status(thm)],[f_2477_1]) ).
fof(f_2477_3,plain,
! [U_9674,U_9675] :
( 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_9674))),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_9675))))) != 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_9674)) ),
inference(definitional_conversion,[status(esa)],[f_2477_2]) ).
cnf(f_2477_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_9674))),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_9675))))) != 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_9674)) ),
inference(clausify,[status(thm)],[f_2477_3]) ).
fof(f_2478_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_2478_2,plain,
! [U_9677,U_9676] :
( 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_9676))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9677))))) = 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_9676))),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_9677)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9676)) ),
inference(variable_rename,[status(thm)],[f_2478_1]) ).
fof(f_2478_3,plain,
! [U_9676,U_9677] :
( 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_9676))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9677))))) = 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_9676))),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_9677)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9676)) ),
inference(definitional_conversion,[status(esa)],[f_2478_2]) ).
cnf(f_2478_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_9676))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9677))))) = 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_9676))),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_9677)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_9676)) ),
inference(clausify,[status(thm)],[f_2478_3]) ).
fof(f_2479_1,plain,
! [T_c,V_a_2,V_Pa_2] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))
| ~ hBOOL(hAPP(V_Pa_2,V_a_2)) ),
inference(fof_nnf,[status(thm)],[fact_CollectI]) ).
fof(f_2479_2,plain,
! [U_9680,U_9679,U_9678] :
( hBOOL(hAPP(hAPP(c_member(U_9680),U_9679),hAPP(c_Set_OCollect(U_9680),U_9678)))
| ~ hBOOL(hAPP(U_9678,U_9679)) ),
inference(variable_rename,[status(thm)],[f_2479_1]) ).
fof(f_2479_3,plain,
! [U_9678,U_9679,U_9680] :
( hBOOL(hAPP(hAPP(c_member(U_9680),U_9679),hAPP(c_Set_OCollect(U_9680),U_9678)))
| ~ hBOOL(hAPP(U_9678,U_9679)) ),
inference(definitional_conversion,[status(esa)],[f_2479_2]) ).
cnf(f_2479_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9680),U_9679),hAPP(c_Set_OCollect(U_9680),U_9678)))
| ~ hBOOL(hAPP(U_9678,U_9679)) ),
inference(clausify,[status(thm)],[f_2479_3]) ).
fof(f_2480_1,plain,
! [V_Qa_2,V_Pa_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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),V_Pa_2)),V_Qa_2))))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Qa_2)))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI]) ).
fof(f_2480_2,plain,
! [U_9683,U_9682,U_9681] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9681),hAPP(c_Set_OCollect(U_9681),hAPP(hAPP(c_COMBS(U_9681,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9681),c_fconj),U_9682)),U_9683))))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9681),hAPP(c_Set_OCollect(U_9681),U_9683)))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9681),hAPP(c_Set_OCollect(U_9681),U_9682))) ) ),
inference(variable_rename,[status(thm)],[f_2480_1]) ).
fof(f_2480_3,plain,
( ! [U_9681,U_9682,U_9683] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9681),hAPP(c_Set_OCollect(U_9681),U_9683)))
| ~ sP680(U_9681,U_9682,U_9683) )
& ! [U_9681,U_9682,U_9683] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9681),hAPP(c_Set_OCollect(U_9681),U_9682)))
| ~ sP680(U_9681,U_9682,U_9683) )
& ! [U_9681,U_9682,U_9683] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9681),hAPP(c_Set_OCollect(U_9681),hAPP(hAPP(c_COMBS(U_9681,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9681),c_fconj),U_9682)),U_9683))))
| sP680(U_9681,U_9682,U_9683) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP680])],[f_2480_2]) ).
cnf(f_2480_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9681),hAPP(c_Set_OCollect(U_9681),hAPP(hAPP(c_COMBS(U_9681,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9681),c_fconj),U_9682)),U_9683))))
| sP680(U_9681,U_9682,U_9683) ),
inference(clausify,[status(thm)],[f_2480_3]) ).
cnf(f_2480_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9681),hAPP(c_Set_OCollect(U_9681),U_9682)))
| ~ sP680(U_9681,U_9682,U_9683) ),
inference(clausify,[status(thm)],[f_2480_3]) ).
cnf(f_2480_6,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9681),hAPP(c_Set_OCollect(U_9681),U_9683)))
| ~ sP680(U_9681,U_9682,U_9683) ),
inference(clausify,[status(thm)],[f_2480_3]) ).
fof(f_2481_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_2481_2,plain,
! [U_9684] : 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_9684)))),
inference(variable_rename,[status(thm)],[f_2481_1]) ).
fof(f_2481_3,plain,
! [U_9684] : 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_9684)))),
inference(definitional_conversion,[status(esa)],[f_2481_2]) ).
cnf(f_2481_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_9684)))),
inference(clausify,[status(thm)],[f_2481_3]) ).
fof(f_2482_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_2482_2,plain,
! [U_9685] : 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_9685)))),
inference(variable_rename,[status(thm)],[f_2482_1]) ).
fof(f_2482_3,plain,
! [U_9685] : 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_9685)))),
inference(definitional_conversion,[status(esa)],[f_2482_2]) ).
cnf(f_2482_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_9685)))),
inference(clausify,[status(thm)],[f_2482_3]) ).
fof(f_2483_1,plain,
! [V_Qa_2,V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),V_Pa_2)),hAPP(c_Set_OCollect(T_c),V_Qa_2)),
inference(fof_nnf,[status(thm)],[fact_Collect__disj__eq]) ).
fof(f_2483_2,plain,
! [U_9688,U_9687,U_9686] : hAPP(c_Set_OCollect(U_9686),hAPP(hAPP(c_COMBS(U_9686,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9686),c_fdisj),U_9687)),U_9688)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9686,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9686),U_9687)),hAPP(c_Set_OCollect(U_9686),U_9688)),
inference(variable_rename,[status(thm)],[f_2483_1]) ).
fof(f_2483_3,plain,
! [U_9686,U_9687,U_9688] : hAPP(c_Set_OCollect(U_9686),hAPP(hAPP(c_COMBS(U_9686,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9686),c_fdisj),U_9687)),U_9688)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9686,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9686),U_9687)),hAPP(c_Set_OCollect(U_9686),U_9688)),
inference(definitional_conversion,[status(esa)],[f_2483_2]) ).
cnf(f_2483_4,plain,
hAPP(c_Set_OCollect(U_9686),hAPP(hAPP(c_COMBS(U_9686,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9686),c_fdisj),U_9687)),U_9688)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9686,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9686),U_9687)),hAPP(c_Set_OCollect(U_9686),U_9688)),
inference(clausify,[status(thm)],[f_2483_3]) ).
fof(f_2484_1,plain,
! [V_Qa_2,V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(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),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),V_Pa_2)),hAPP(c_Set_OCollect(T_c),V_Qa_2)),
inference(fof_nnf,[status(thm)],[fact_Collect__conj__eq]) ).
fof(f_2484_2,plain,
! [U_9691,U_9690,U_9689] : hAPP(c_Set_OCollect(U_9689),hAPP(hAPP(c_COMBS(U_9689,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9689),c_fconj),U_9690)),U_9691)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9689,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9689),U_9690)),hAPP(c_Set_OCollect(U_9689),U_9691)),
inference(variable_rename,[status(thm)],[f_2484_1]) ).
fof(f_2484_3,plain,
! [U_9689,U_9690,U_9691] : hAPP(c_Set_OCollect(U_9689),hAPP(hAPP(c_COMBS(U_9689,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9689),c_fconj),U_9690)),U_9691)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9689,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9689),U_9690)),hAPP(c_Set_OCollect(U_9689),U_9691)),
inference(definitional_conversion,[status(esa)],[f_2484_2]) ).
cnf(f_2484_4,plain,
hAPP(c_Set_OCollect(U_9689),hAPP(hAPP(c_COMBS(U_9689,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9689),c_fconj),U_9690)),U_9691)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9689,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9689),U_9690)),hAPP(c_Set_OCollect(U_9689),U_9691)),
inference(clausify,[status(thm)],[f_2484_3]) ).
fof(f_2485_1,plain,
! [V_Pa_2,V_a_2,T_c] :
( hBOOL(hAPP(V_Pa_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),V_Pa_2))) ),
inference(fof_nnf,[status(thm)],[fact_CollectE]) ).
fof(f_2485_2,plain,
! [U_9694,U_9693,U_9692] :
( hBOOL(hAPP(U_9694,U_9693))
| ~ hBOOL(hAPP(hAPP(c_member(U_9692),U_9693),hAPP(c_Set_OCollect(U_9692),U_9694))) ),
inference(variable_rename,[status(thm)],[f_2485_1]) ).
fof(f_2485_3,plain,
! [U_9694,U_9693] :
( ! [U_9692] : ~ hBOOL(hAPP(hAPP(c_member(U_9692),U_9693),hAPP(c_Set_OCollect(U_9692),U_9694)))
| hBOOL(hAPP(U_9694,U_9693)) ),
inference(miniscope,[status(thm)],[f_2485_2]) ).
fof(f_2485_4,plain,
! [U_9692,U_9693,U_9694] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9692),U_9693),hAPP(c_Set_OCollect(U_9692),U_9694)))
| hBOOL(hAPP(U_9694,U_9693)) ),
inference(definitional_conversion,[status(esa)],[f_2485_3]) ).
cnf(f_2485_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9692),U_9693),hAPP(c_Set_OCollect(U_9692),U_9694)))
| hBOOL(hAPP(U_9694,U_9693)) ),
inference(clausify,[status(thm)],[f_2485_4]) ).
fof(f_2486_1,plain,
! [V_Pa_2,V_a_2,T_c] :
( hBOOL(hAPP(V_Pa_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),V_Pa_2))) ),
inference(fof_nnf,[status(thm)],[fact_CollectD]) ).
fof(f_2486_2,plain,
! [U_9697,U_9696,U_9695] :
( hBOOL(hAPP(U_9697,U_9696))
| ~ hBOOL(hAPP(hAPP(c_member(U_9695),U_9696),hAPP(c_Set_OCollect(U_9695),U_9697))) ),
inference(variable_rename,[status(thm)],[f_2486_1]) ).
fof(f_2486_3,plain,
! [U_9697,U_9696] :
( ! [U_9695] : ~ hBOOL(hAPP(hAPP(c_member(U_9695),U_9696),hAPP(c_Set_OCollect(U_9695),U_9697)))
| hBOOL(hAPP(U_9697,U_9696)) ),
inference(miniscope,[status(thm)],[f_2486_2]) ).
fof(f_2486_4,plain,
! [U_9695,U_9696,U_9697] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9695),U_9696),hAPP(c_Set_OCollect(U_9695),U_9697)))
| hBOOL(hAPP(U_9697,U_9696)) ),
inference(definitional_conversion,[status(esa)],[f_2486_3]) ).
cnf(f_2486_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9695),U_9696),hAPP(c_Set_OCollect(U_9695),U_9697)))
| hBOOL(hAPP(U_9697,U_9696)) ),
inference(clausify,[status(thm)],[f_2486_4]) ).
fof(f_2487_1,plain,
! [V_Pa_2,V_a_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),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_c),V_a_2),hAPP(c_Set_OCollect(T_c),V_Pa_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq]) ).
fof(f_2487_2,plain,
! [U_9700,U_9699,U_9698] :
( ( hBOOL(hAPP(hAPP(c_member(U_9698),U_9699),hAPP(c_Set_OCollect(U_9698),U_9700)))
| ~ hBOOL(hAPP(U_9700,U_9699)) )
& ( hBOOL(hAPP(U_9700,U_9699))
| ~ hBOOL(hAPP(hAPP(c_member(U_9698),U_9699),hAPP(c_Set_OCollect(U_9698),U_9700))) ) ),
inference(variable_rename,[status(thm)],[f_2487_1]) ).
fof(f_2487_3,plain,
( ! [U_9706,U_9704] :
( ! [U_9702] : hBOOL(hAPP(hAPP(c_member(U_9702),U_9704),hAPP(c_Set_OCollect(U_9702),U_9706)))
| ~ hBOOL(hAPP(U_9706,U_9704)) )
& ! [U_9705,U_9703] :
( ! [U_9701] : ~ hBOOL(hAPP(hAPP(c_member(U_9701),U_9703),hAPP(c_Set_OCollect(U_9701),U_9705)))
| hBOOL(hAPP(U_9705,U_9703)) ) ),
inference(miniscope,[status(thm)],[f_2487_2]) ).
fof(f_2487_4,plain,
( ! [U_9702,U_9704,U_9706] :
( hBOOL(hAPP(hAPP(c_member(U_9702),U_9704),hAPP(c_Set_OCollect(U_9702),U_9706)))
| ~ hBOOL(hAPP(U_9706,U_9704)) )
& ! [U_9705,U_9701,U_9703] :
( ~ hBOOL(hAPP(hAPP(c_member(U_9701),U_9703),hAPP(c_Set_OCollect(U_9701),U_9705)))
| hBOOL(hAPP(U_9705,U_9703)) ) ),
inference(definitional_conversion,[status(esa)],[f_2487_3]) ).
cnf(f_2487_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9701),U_9703),hAPP(c_Set_OCollect(U_9701),U_9705)))
| hBOOL(hAPP(U_9705,U_9703)) ),
inference(clausify,[status(thm)],[f_2487_4]) ).
cnf(f_2487_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9702),U_9704),hAPP(c_Set_OCollect(U_9702),U_9706)))
| ~ hBOOL(hAPP(U_9706,U_9704)) ),
inference(clausify,[status(thm)],[f_2487_4]) ).
fof(f_2488_1,plain,
! [V_A_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Collect__mem__eq]) ).
fof(f_2488_2,plain,
! [U_9708,U_9707] : hAPP(c_Set_OCollect(U_9707),hAPP(hAPP(c_COMBC(U_9707,tc_fun(U_9707,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9707)),U_9708)) = U_9708,
inference(variable_rename,[status(thm)],[f_2488_1]) ).
fof(f_2488_3,plain,
! [U_9707,U_9708] : hAPP(c_Set_OCollect(U_9707),hAPP(hAPP(c_COMBC(U_9707,tc_fun(U_9707,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9707)),U_9708)) = U_9708,
inference(definitional_conversion,[status(esa)],[f_2488_2]) ).
cnf(f_2488_4,plain,
hAPP(c_Set_OCollect(U_9707),hAPP(hAPP(c_COMBC(U_9707,tc_fun(U_9707,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9707)),U_9708)) = U_9708,
inference(clausify,[status(thm)],[f_2488_3]) ).
fof(f_2489_1,plain,
! [T_c] : c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_c),hAPP(c_COMBK(tc_HOL_Obool,T_c),c_fFalse)),
inference(fof_nnf,[status(thm)],[fact_empty__def]) ).
fof(f_2489_2,plain,
! [U_9709] : c_Orderings_Obot__class_Obot(tc_fun(U_9709,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9709),hAPP(c_COMBK(tc_HOL_Obool,U_9709),c_fFalse)),
inference(variable_rename,[status(thm)],[f_2489_1]) ).
fof(f_2489_3,plain,
! [U_9709] : c_Orderings_Obot__class_Obot(tc_fun(U_9709,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9709),hAPP(c_COMBK(tc_HOL_Obool,U_9709),c_fFalse)),
inference(definitional_conversion,[status(esa)],[f_2489_2]) ).
cnf(f_2489_4,plain,
c_Orderings_Obot__class_Obot(tc_fun(U_9709,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9709),hAPP(c_COMBK(tc_HOL_Obool,U_9709),c_fFalse)),
inference(clausify,[status(thm)],[f_2489_3]) ).
fof(f_2490_1,plain,
! [V_Pa_2,T_c] :
( ( c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_c),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_c,tc_HOL_Obool)) != hAPP(c_Set_OCollect(T_c),V_Pa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_empty__Collect__eq]) ).
fof(f_2490_2,plain,
! [U_9713,U_9712] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_9712,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9712),U_9713)
| ? [U_9711] : hBOOL(hAPP(U_9713,U_9711)) )
& ( ! [U_9710] : ~ hBOOL(hAPP(U_9713,U_9710))
| c_Orderings_Obot__class_Obot(tc_fun(U_9712,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_9712),U_9713) ) ),
inference(variable_rename,[status(thm)],[f_2490_1]) ).
fof(f_2490_3,plain,
( ! [U_9717] :
( ! [U_9715] : c_Orderings_Obot__class_Obot(tc_fun(U_9715,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9715),U_9717)
| ? [U_9711] : hBOOL(hAPP(U_9717,U_9711)) )
& ! [U_9716] :
( ! [U_9714] : c_Orderings_Obot__class_Obot(tc_fun(U_9714,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_9714),U_9716)
| ! [U_9710] : ~ hBOOL(hAPP(U_9716,U_9710)) ) ),
inference(miniscope,[status(thm)],[f_2490_2]) ).
fof(f_2490_4,plain,
( ! [U_9717] :
( ! [U_9715] : c_Orderings_Obot__class_Obot(tc_fun(U_9715,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9715),U_9717)
| hBOOL(hAPP(U_9717,sK247(U_9717))) )
& ! [U_9716] :
( ! [U_9714] : c_Orderings_Obot__class_Obot(tc_fun(U_9714,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_9714),U_9716)
| ! [U_9710] : ~ hBOOL(hAPP(U_9716,U_9710)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_9711,sK247(U_9717))],[f_2490_3]) ).
fof(f_2490_5,plain,
( ! [U_9715,U_9717] :
( c_Orderings_Obot__class_Obot(tc_fun(U_9715,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9715),U_9717)
| hBOOL(hAPP(U_9717,sK247(U_9717))) )
& ! [U_9710,U_9714,U_9716] :
( c_Orderings_Obot__class_Obot(tc_fun(U_9714,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_9714),U_9716)
| ~ hBOOL(hAPP(U_9716,U_9710)) ) ),
inference(definitional_conversion,[status(esa)],[f_2490_4]) ).
cnf(f_2490_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_9714,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_9714),U_9716)
| ~ hBOOL(hAPP(U_9716,U_9710)) ),
inference(clausify,[status(thm)],[f_2490_5]) ).
cnf(f_2490_7,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_9715,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9715),U_9717)
| hBOOL(hAPP(U_9717,sK247(U_9717))) ),
inference(clausify,[status(thm)],[f_2490_5]) ).
fof(f_2491_1,plain,
! [V_Pa_2,T_c] :
( ( hAPP(c_Set_OCollect(T_c),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,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_c),V_Pa_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__empty__eq]) ).
fof(f_2491_2,plain,
! [U_9721,U_9720] :
( ( hAPP(c_Set_OCollect(U_9720),U_9721) = c_Orderings_Obot__class_Obot(tc_fun(U_9720,tc_HOL_Obool))
| ? [U_9719] : hBOOL(hAPP(U_9721,U_9719)) )
& ( ! [U_9718] : ~ hBOOL(hAPP(U_9721,U_9718))
| hAPP(c_Set_OCollect(U_9720),U_9721) != c_Orderings_Obot__class_Obot(tc_fun(U_9720,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2491_1]) ).
fof(f_2491_3,plain,
( ! [U_9725] :
( ! [U_9723] : hAPP(c_Set_OCollect(U_9723),U_9725) = c_Orderings_Obot__class_Obot(tc_fun(U_9723,tc_HOL_Obool))
| ? [U_9719] : hBOOL(hAPP(U_9725,U_9719)) )
& ! [U_9724] :
( ! [U_9722] : hAPP(c_Set_OCollect(U_9722),U_9724) != c_Orderings_Obot__class_Obot(tc_fun(U_9722,tc_HOL_Obool))
| ! [U_9718] : ~ hBOOL(hAPP(U_9724,U_9718)) ) ),
inference(miniscope,[status(thm)],[f_2491_2]) ).
fof(f_2491_4,plain,
( ! [U_9725] :
( ! [U_9723] : hAPP(c_Set_OCollect(U_9723),U_9725) = c_Orderings_Obot__class_Obot(tc_fun(U_9723,tc_HOL_Obool))
| hBOOL(hAPP(U_9725,sK248(U_9725))) )
& ! [U_9724] :
( ! [U_9722] : hAPP(c_Set_OCollect(U_9722),U_9724) != c_Orderings_Obot__class_Obot(tc_fun(U_9722,tc_HOL_Obool))
| ! [U_9718] : ~ hBOOL(hAPP(U_9724,U_9718)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_9719,sK248(U_9725))],[f_2491_3]) ).
fof(f_2491_5,plain,
( ! [U_9723,U_9725] :
( hAPP(c_Set_OCollect(U_9723),U_9725) = c_Orderings_Obot__class_Obot(tc_fun(U_9723,tc_HOL_Obool))
| hBOOL(hAPP(U_9725,sK248(U_9725))) )
& ! [U_9724,U_9718,U_9722] :
( hAPP(c_Set_OCollect(U_9722),U_9724) != c_Orderings_Obot__class_Obot(tc_fun(U_9722,tc_HOL_Obool))
| ~ hBOOL(hAPP(U_9724,U_9718)) ) ),
inference(definitional_conversion,[status(esa)],[f_2491_4]) ).
cnf(f_2491_6,plain,
( hAPP(c_Set_OCollect(U_9722),U_9724) != c_Orderings_Obot__class_Obot(tc_fun(U_9722,tc_HOL_Obool))
| ~ hBOOL(hAPP(U_9724,U_9718)) ),
inference(clausify,[status(thm)],[f_2491_5]) ).
cnf(f_2491_7,plain,
( hAPP(c_Set_OCollect(U_9723),U_9725) = c_Orderings_Obot__class_Obot(tc_fun(U_9723,tc_HOL_Obool))
| hBOOL(hAPP(U_9725,sK248(U_9725))) ),
inference(clausify,[status(thm)],[f_2491_5]) ).
fof(f_2492_1,plain,
! [V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),V_Pa_2) = V_Pa_2,
inference(fof_nnf,[status(thm)],[fact_Collect__def]) ).
fof(f_2492_2,plain,
! [U_9727,U_9726] : hAPP(c_Set_OCollect(U_9726),U_9727) = U_9727,
inference(variable_rename,[status(thm)],[f_2492_1]) ).
fof(f_2492_3,plain,
! [U_9726,U_9727] : hAPP(c_Set_OCollect(U_9726),U_9727) = U_9727,
inference(definitional_conversion,[status(esa)],[f_2492_2]) ).
cnf(f_2492_4,plain,
hAPP(c_Set_OCollect(U_9726),U_9727) = U_9727,
inference(clausify,[status(thm)],[f_2492_3]) ).
fof(f_2493_1,plain,
! [T_c] : c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_c),hAPP(c_COMBK(tc_HOL_Obool,T_c),c_fTrue)),
inference(fof_nnf,[status(thm)],[fact_UNIV__def]) ).
fof(f_2493_2,plain,
! [U_9728] : c_Orderings_Otop__class_Otop(tc_fun(U_9728,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9728),hAPP(c_COMBK(tc_HOL_Obool,U_9728),c_fTrue)),
inference(variable_rename,[status(thm)],[f_2493_1]) ).
fof(f_2493_3,plain,
! [U_9728] : c_Orderings_Otop__class_Otop(tc_fun(U_9728,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9728),hAPP(c_COMBK(tc_HOL_Obool,U_9728),c_fTrue)),
inference(definitional_conversion,[status(esa)],[f_2493_2]) ).
cnf(f_2493_4,plain,
c_Orderings_Otop__class_Otop(tc_fun(U_9728,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9728),hAPP(c_COMBK(tc_HOL_Obool,U_9728),c_fTrue)),
inference(clausify,[status(thm)],[f_2493_3]) ).
fof(f_2494_1,plain,
! [V_Pa_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(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_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)),
inference(fof_nnf,[status(thm)],[fact_insert__Collect]) ).
fof(f_2494_2,plain,
! [U_9731,U_9730,U_9729] : hAPP(hAPP(c_Set_Oinsert(U_9729),U_9730),hAPP(c_Set_OCollect(U_9729),U_9731)) = hAPP(c_Set_OCollect(U_9729),hAPP(hAPP(c_COMBS(U_9729,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9729),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9729),c_fNot),hAPP(hAPP(c_COMBC(U_9729,U_9729,tc_HOL_Obool),c_fequal),U_9730)))),U_9731)),
inference(variable_rename,[status(thm)],[f_2494_1]) ).
fof(f_2494_3,plain,
! [U_9729,U_9730,U_9731] : hAPP(hAPP(c_Set_Oinsert(U_9729),U_9730),hAPP(c_Set_OCollect(U_9729),U_9731)) = hAPP(c_Set_OCollect(U_9729),hAPP(hAPP(c_COMBS(U_9729,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9729),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9729),c_fNot),hAPP(hAPP(c_COMBC(U_9729,U_9729,tc_HOL_Obool),c_fequal),U_9730)))),U_9731)),
inference(definitional_conversion,[status(esa)],[f_2494_2]) ).
cnf(f_2494_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_9729),U_9730),hAPP(c_Set_OCollect(U_9729),U_9731)) = hAPP(c_Set_OCollect(U_9729),hAPP(hAPP(c_COMBS(U_9729,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9729),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9729),c_fNot),hAPP(hAPP(c_COMBC(U_9729,U_9729,tc_HOL_Obool),c_fequal),U_9730)))),U_9731)),
inference(clausify,[status(thm)],[f_2494_3]) ).
fof(f_2495_1,plain,
! [V_Qa_2,V_Pa_2,T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),V_Pa_2)),V_Qa_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Qa_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Qa_2)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),V_Pa_2)),V_Qa_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI]) ).
fof(f_2495_2,plain,
! [U_9734,U_9733,U_9732] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),hAPP(hAPP(c_COMBS(U_9732,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9732),c_fdisj),U_9733)),U_9734))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),U_9734)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),U_9733))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),U_9734)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),U_9733))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),hAPP(hAPP(c_COMBS(U_9732,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9732),c_fdisj),U_9733)),U_9734)))) ) ),
inference(variable_rename,[status(thm)],[f_2495_1]) ).
fof(f_2495_3,plain,
( ! [U_9740,U_9738,U_9736] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9736),hAPP(c_Set_OCollect(U_9736),hAPP(hAPP(c_COMBS(U_9736,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9736),c_fdisj),U_9738)),U_9740))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9736),hAPP(c_Set_OCollect(U_9736),U_9740)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9736),hAPP(c_Set_OCollect(U_9736),U_9738))) )
& ! [U_9739,U_9737,U_9735] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9735),hAPP(c_Set_OCollect(U_9735),U_9739)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_9735),hAPP(c_Set_OCollect(U_9735),U_9737))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9735),hAPP(c_Set_OCollect(U_9735),hAPP(hAPP(c_COMBS(U_9735,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9735),c_fdisj),U_9737)),U_9739)))) ) ),
inference(miniscope,[status(thm)],[f_2495_2]) ).
fof(f_2495_4,plain,
( ! [U_9737,U_9735,U_9739] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9735),hAPP(c_Set_OCollect(U_9735),U_9739)))
| ~ sP681(U_9737,U_9735,U_9739) )
& ! [U_9737,U_9735,U_9739] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9735),hAPP(c_Set_OCollect(U_9735),U_9737)))
| ~ sP681(U_9737,U_9735,U_9739) )
& ! [U_9738,U_9740,U_9736] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9736),hAPP(c_Set_OCollect(U_9736),hAPP(hAPP(c_COMBS(U_9736,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9736),c_fdisj),U_9738)),U_9740))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9736),hAPP(c_Set_OCollect(U_9736),U_9740)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9736),hAPP(c_Set_OCollect(U_9736),U_9738))) )
& ! [U_9737,U_9735,U_9739] :
( sP681(U_9737,U_9735,U_9739)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9735),hAPP(c_Set_OCollect(U_9735),hAPP(hAPP(c_COMBS(U_9735,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9735),c_fdisj),U_9737)),U_9739)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP681])],[f_2495_3]) ).
cnf(f_2495_5,plain,
( sP681(U_9737,U_9735,U_9739)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9735),hAPP(c_Set_OCollect(U_9735),hAPP(hAPP(c_COMBS(U_9735,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9735),c_fdisj),U_9737)),U_9739)))) ),
inference(clausify,[status(thm)],[f_2495_4]) ).
cnf(f_2495_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9736),hAPP(c_Set_OCollect(U_9736),hAPP(hAPP(c_COMBS(U_9736,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9736),c_fdisj),U_9738)),U_9740))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9736),hAPP(c_Set_OCollect(U_9736),U_9740)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9736),hAPP(c_Set_OCollect(U_9736),U_9738))) ),
inference(clausify,[status(thm)],[f_2495_4]) ).
cnf(f_2495_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9735),hAPP(c_Set_OCollect(U_9735),U_9737)))
| ~ sP681(U_9737,U_9735,U_9739) ),
inference(clausify,[status(thm)],[f_2495_4]) ).
cnf(f_2495_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9735),hAPP(c_Set_OCollect(U_9735),U_9739)))
| ~ sP681(U_9737,U_9735,U_9739) ),
inference(clausify,[status(thm)],[f_2495_4]) ).
fof(f_2496_1,plain,
! [V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),V_Pa_2)),
inference(fof_nnf,[status(thm)],[fact_Collect__neg__eq]) ).
fof(f_2496_2,plain,
! [U_9742,U_9741] : hAPP(c_Set_OCollect(U_9741),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9741),c_fNot),U_9742)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9741,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9741),U_9742)),
inference(variable_rename,[status(thm)],[f_2496_1]) ).
fof(f_2496_3,plain,
! [U_9741,U_9742] : hAPP(c_Set_OCollect(U_9741),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9741),c_fNot),U_9742)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9741,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9741),U_9742)),
inference(definitional_conversion,[status(esa)],[f_2496_2]) ).
cnf(f_2496_4,plain,
hAPP(c_Set_OCollect(U_9741),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9741),c_fNot),U_9742)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9741,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9741),U_9742)),
inference(clausify,[status(thm)],[f_2496_3]) ).
fof(f_2497_1,plain,
! [V_Pa_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),hAPP(c_Set_OCollect(T_d),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_d,tc_HOL_Obool,T_c),V_Pa_2),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(f_2497_2,plain,
! [U_9746,U_9745,U_9744,U_9743] : hAPP(c_Set_Ovimage(U_9743,U_9744,U_9745),hAPP(c_Set_OCollect(U_9744),U_9746)) = hAPP(c_Set_OCollect(U_9743),hAPP(hAPP(c_COMBB(U_9744,tc_HOL_Obool,U_9743),U_9746),U_9745)),
inference(variable_rename,[status(thm)],[f_2497_1]) ).
fof(f_2497_3,plain,
! [U_9743,U_9744,U_9745,U_9746] : hAPP(c_Set_Ovimage(U_9743,U_9744,U_9745),hAPP(c_Set_OCollect(U_9744),U_9746)) = hAPP(c_Set_OCollect(U_9743),hAPP(hAPP(c_COMBB(U_9744,tc_HOL_Obool,U_9743),U_9746),U_9745)),
inference(definitional_conversion,[status(esa)],[f_2497_2]) ).
cnf(f_2497_4,plain,
hAPP(c_Set_Ovimage(U_9743,U_9744,U_9745),hAPP(c_Set_OCollect(U_9744),U_9746)) = hAPP(c_Set_OCollect(U_9743),hAPP(hAPP(c_COMBB(U_9744,tc_HOL_Obool,U_9743),U_9746),U_9745)),
inference(clausify,[status(thm)],[f_2497_3]) ).
fof(f_2498_1,plain,
! [V_B_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),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_insert__compr]) ).
fof(f_2498_2,plain,
! [U_9749,U_9748,U_9747] : hAPP(hAPP(c_Set_Oinsert(U_9747),U_9748),U_9749) = hAPP(c_Set_OCollect(U_9747),hAPP(hAPP(c_COMBS(U_9747,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9747),c_fdisj),hAPP(hAPP(c_COMBC(U_9747,U_9747,tc_HOL_Obool),c_fequal),U_9748))),hAPP(hAPP(c_COMBC(U_9747,tc_fun(U_9747,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9747)),U_9749))),
inference(variable_rename,[status(thm)],[f_2498_1]) ).
fof(f_2498_3,plain,
! [U_9747,U_9748,U_9749] : hAPP(hAPP(c_Set_Oinsert(U_9747),U_9748),U_9749) = hAPP(c_Set_OCollect(U_9747),hAPP(hAPP(c_COMBS(U_9747,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9747),c_fdisj),hAPP(hAPP(c_COMBC(U_9747,U_9747,tc_HOL_Obool),c_fequal),U_9748))),hAPP(hAPP(c_COMBC(U_9747,tc_fun(U_9747,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9747)),U_9749))),
inference(definitional_conversion,[status(esa)],[f_2498_2]) ).
cnf(f_2498_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_9747),U_9748),U_9749) = hAPP(c_Set_OCollect(U_9747),hAPP(hAPP(c_COMBS(U_9747,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9747),c_fdisj),hAPP(hAPP(c_COMBC(U_9747,U_9747,tc_HOL_Obool),c_fequal),U_9748))),hAPP(hAPP(c_COMBC(U_9747,tc_fun(U_9747,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9747)),U_9749))),
inference(clausify,[status(thm)],[f_2498_3]) ).
fof(f_2499_1,plain,
! [V_B_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),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_insert__compr__raw]) ).
fof(f_2499_2,plain,
! [U_9752,U_9751,U_9750] : hAPP(hAPP(c_Set_Oinsert(U_9750),U_9751),U_9752) = hAPP(c_Set_OCollect(U_9750),hAPP(hAPP(c_COMBS(U_9750,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9750),c_fdisj),hAPP(hAPP(c_COMBC(U_9750,U_9750,tc_HOL_Obool),c_fequal),U_9751))),hAPP(hAPP(c_COMBC(U_9750,tc_fun(U_9750,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9750)),U_9752))),
inference(variable_rename,[status(thm)],[f_2499_1]) ).
fof(f_2499_3,plain,
! [U_9750,U_9751,U_9752] : hAPP(hAPP(c_Set_Oinsert(U_9750),U_9751),U_9752) = hAPP(c_Set_OCollect(U_9750),hAPP(hAPP(c_COMBS(U_9750,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9750),c_fdisj),hAPP(hAPP(c_COMBC(U_9750,U_9750,tc_HOL_Obool),c_fequal),U_9751))),hAPP(hAPP(c_COMBC(U_9750,tc_fun(U_9750,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9750)),U_9752))),
inference(definitional_conversion,[status(esa)],[f_2499_2]) ).
cnf(f_2499_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_9750),U_9751),U_9752) = hAPP(c_Set_OCollect(U_9750),hAPP(hAPP(c_COMBS(U_9750,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9750),c_fdisj),hAPP(hAPP(c_COMBC(U_9750,U_9750,tc_HOL_Obool),c_fequal),U_9751))),hAPP(hAPP(c_COMBC(U_9750,tc_fun(U_9750,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9750)),U_9752))),
inference(clausify,[status(thm)],[f_2499_3]) ).
fof(f_2500_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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_fdisj),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_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Un__def]) ).
fof(f_2500_2,plain,
! [U_9755,U_9754,U_9753] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9753,tc_HOL_Obool)),U_9754),U_9755) = hAPP(c_Set_OCollect(U_9753),hAPP(hAPP(c_COMBS(U_9753,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9753),c_fdisj),hAPP(hAPP(c_COMBC(U_9753,tc_fun(U_9753,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9753)),U_9754))),hAPP(hAPP(c_COMBC(U_9753,tc_fun(U_9753,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9753)),U_9755))),
inference(variable_rename,[status(thm)],[f_2500_1]) ).
fof(f_2500_3,plain,
! [U_9753,U_9754,U_9755] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9753,tc_HOL_Obool)),U_9754),U_9755) = hAPP(c_Set_OCollect(U_9753),hAPP(hAPP(c_COMBS(U_9753,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9753),c_fdisj),hAPP(hAPP(c_COMBC(U_9753,tc_fun(U_9753,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9753)),U_9754))),hAPP(hAPP(c_COMBC(U_9753,tc_fun(U_9753,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9753)),U_9755))),
inference(definitional_conversion,[status(esa)],[f_2500_2]) ).
cnf(f_2500_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9753,tc_HOL_Obool)),U_9754),U_9755) = hAPP(c_Set_OCollect(U_9753),hAPP(hAPP(c_COMBS(U_9753,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9753),c_fdisj),hAPP(hAPP(c_COMBC(U_9753,tc_fun(U_9753,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9753)),U_9754))),hAPP(hAPP(c_COMBC(U_9753,tc_fun(U_9753,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9753)),U_9755))),
inference(clausify,[status(thm)],[f_2500_3]) ).
fof(f_2501_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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(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_Int__def]) ).
fof(f_2501_2,plain,
! [U_9758,U_9757,U_9756] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9756,tc_HOL_Obool)),U_9757),U_9758) = hAPP(c_Set_OCollect(U_9756),hAPP(hAPP(c_COMBS(U_9756,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9756),c_fconj),hAPP(hAPP(c_COMBC(U_9756,tc_fun(U_9756,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9756)),U_9757))),hAPP(hAPP(c_COMBC(U_9756,tc_fun(U_9756,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9756)),U_9758))),
inference(variable_rename,[status(thm)],[f_2501_1]) ).
fof(f_2501_3,plain,
! [U_9756,U_9757,U_9758] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9756,tc_HOL_Obool)),U_9757),U_9758) = hAPP(c_Set_OCollect(U_9756),hAPP(hAPP(c_COMBS(U_9756,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9756),c_fconj),hAPP(hAPP(c_COMBC(U_9756,tc_fun(U_9756,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9756)),U_9757))),hAPP(hAPP(c_COMBC(U_9756,tc_fun(U_9756,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9756)),U_9758))),
inference(definitional_conversion,[status(esa)],[f_2501_2]) ).
cnf(f_2501_4,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9756,tc_HOL_Obool)),U_9757),U_9758) = hAPP(c_Set_OCollect(U_9756),hAPP(hAPP(c_COMBS(U_9756,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9756),c_fconj),hAPP(hAPP(c_COMBC(U_9756,tc_fun(U_9756,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9756)),U_9757))),hAPP(hAPP(c_COMBC(U_9756,tc_fun(U_9756,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9756)),U_9758))),
inference(clausify,[status(thm)],[f_2501_3]) ).
fof(f_2502_1,plain,
! [V_Pa_2,V_A_2,V_x_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_c),V_Pa_2))))
| ~ hBOOL(hAPP(V_Pa_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) )
& ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__Collect]) ).
fof(f_2502_2,plain,
! [U_9762,U_9761,U_9760,U_9759] :
( ( hBOOL(hAPP(hAPP(c_member(U_9759),U_9760),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9759,tc_HOL_Obool)),U_9761),hAPP(c_Set_OCollect(U_9759),U_9762))))
| ~ hBOOL(hAPP(U_9762,U_9760))
| ~ hBOOL(hAPP(hAPP(c_member(U_9759),U_9760),U_9761)) )
& ( ( hBOOL(hAPP(U_9762,U_9760))
& hBOOL(hAPP(hAPP(c_member(U_9759),U_9760),U_9761)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9759),U_9760),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9759,tc_HOL_Obool)),U_9761),hAPP(c_Set_OCollect(U_9759),U_9762)))) ) ),
inference(variable_rename,[status(thm)],[f_2502_1]) ).
fof(f_2502_3,plain,
( ! [U_9770,U_9768,U_9766,U_9764] :
( hBOOL(hAPP(hAPP(c_member(U_9764),U_9766),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9764,tc_HOL_Obool)),U_9768),hAPP(c_Set_OCollect(U_9764),U_9770))))
| ~ hBOOL(hAPP(U_9770,U_9766))
| ~ hBOOL(hAPP(hAPP(c_member(U_9764),U_9766),U_9768)) )
& ! [U_9769,U_9767,U_9765,U_9763] :
( ( hBOOL(hAPP(U_9769,U_9765))
& hBOOL(hAPP(hAPP(c_member(U_9763),U_9765),U_9767)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9763),U_9765),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9763,tc_HOL_Obool)),U_9767),hAPP(c_Set_OCollect(U_9763),U_9769)))) ) ),
inference(miniscope,[status(thm)],[f_2502_2]) ).
fof(f_2502_4,plain,
( ! [U_9765,U_9763,U_9769,U_9767] :
( hBOOL(hAPP(U_9769,U_9765))
| ~ sP682(U_9765,U_9763,U_9769,U_9767) )
& ! [U_9765,U_9763,U_9769,U_9767] :
( hBOOL(hAPP(hAPP(c_member(U_9763),U_9765),U_9767))
| ~ sP682(U_9765,U_9763,U_9769,U_9767) )
& ! [U_9768,U_9766,U_9764,U_9770] :
( hBOOL(hAPP(hAPP(c_member(U_9764),U_9766),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9764,tc_HOL_Obool)),U_9768),hAPP(c_Set_OCollect(U_9764),U_9770))))
| ~ hBOOL(hAPP(U_9770,U_9766))
| ~ hBOOL(hAPP(hAPP(c_member(U_9764),U_9766),U_9768)) )
& ! [U_9765,U_9763,U_9769,U_9767] :
( sP682(U_9765,U_9763,U_9769,U_9767)
| ~ hBOOL(hAPP(hAPP(c_member(U_9763),U_9765),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9763,tc_HOL_Obool)),U_9767),hAPP(c_Set_OCollect(U_9763),U_9769)))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP682])],[f_2502_3]) ).
cnf(f_2502_5,plain,
( sP682(U_9765,U_9763,U_9769,U_9767)
| ~ hBOOL(hAPP(hAPP(c_member(U_9763),U_9765),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9763,tc_HOL_Obool)),U_9767),hAPP(c_Set_OCollect(U_9763),U_9769)))) ),
inference(clausify,[status(thm)],[f_2502_4]) ).
cnf(f_2502_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9764),U_9766),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9764,tc_HOL_Obool)),U_9768),hAPP(c_Set_OCollect(U_9764),U_9770))))
| ~ hBOOL(hAPP(U_9770,U_9766))
| ~ hBOOL(hAPP(hAPP(c_member(U_9764),U_9766),U_9768)) ),
inference(clausify,[status(thm)],[f_2502_4]) ).
cnf(f_2502_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_9763),U_9765),U_9767))
| ~ sP682(U_9765,U_9763,U_9769,U_9767) ),
inference(clausify,[status(thm)],[f_2502_4]) ).
cnf(f_2502_8,plain,
( hBOOL(hAPP(U_9769,U_9765))
| ~ sP682(U_9765,U_9763,U_9769,U_9767) ),
inference(clausify,[status(thm)],[f_2502_4]) ).
fof(f_2503_1,plain,
! [V_a_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(c_fequal,V_a_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_singleton__conv2]) ).
fof(f_2503_2,plain,
! [U_9772,U_9771] : hAPP(c_Set_OCollect(U_9771),hAPP(c_fequal,U_9772)) = hAPP(hAPP(c_Set_Oinsert(U_9771),U_9772),c_Orderings_Obot__class_Obot(tc_fun(U_9771,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2503_1]) ).
fof(f_2503_3,plain,
! [U_9772,U_9771] : hAPP(c_Set_OCollect(U_9771),hAPP(c_fequal,U_9772)) = hAPP(hAPP(c_Set_Oinsert(U_9771),U_9772),c_Orderings_Obot__class_Obot(tc_fun(U_9771,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_2503_2]) ).
cnf(f_2503_4,plain,
hAPP(c_Set_OCollect(U_9771),hAPP(c_fequal,U_9772)) = hAPP(hAPP(c_Set_Oinsert(U_9771),U_9772),c_Orderings_Obot__class_Obot(tc_fun(U_9771,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2503_3]) ).
fof(f_2504_1,plain,
! [V_a_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_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_singleton__conv]) ).
fof(f_2504_2,plain,
! [U_9774,U_9773] : hAPP(c_Set_OCollect(U_9773),hAPP(hAPP(c_COMBC(U_9773,U_9773,tc_HOL_Obool),c_fequal),U_9774)) = hAPP(hAPP(c_Set_Oinsert(U_9773),U_9774),c_Orderings_Obot__class_Obot(tc_fun(U_9773,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2504_1]) ).
fof(f_2504_3,plain,
! [U_9773,U_9774] : hAPP(c_Set_OCollect(U_9773),hAPP(hAPP(c_COMBC(U_9773,U_9773,tc_HOL_Obool),c_fequal),U_9774)) = hAPP(hAPP(c_Set_Oinsert(U_9773),U_9774),c_Orderings_Obot__class_Obot(tc_fun(U_9773,tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_2504_2]) ).
cnf(f_2504_4,plain,
hAPP(c_Set_OCollect(U_9773),hAPP(hAPP(c_COMBC(U_9773,U_9773,tc_HOL_Obool),c_fequal),U_9774)) = hAPP(hAPP(c_Set_Oinsert(U_9773),U_9774),c_Orderings_Obot__class_Obot(tc_fun(U_9773,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2504_3]) ).
fof(f_2505_1,plain,
! [T_c,V_a_2,V_Pa_2] :
( ( hAPP(c_Set_OCollect(T_c),hAPP(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(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| hBOOL(hAPP(V_Pa_2,V_a_2)) )
& ( hAPP(c_Set_OCollect(T_c),hAPP(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(c_fequal,V_a_2))),V_Pa_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(V_Pa_2,V_a_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__conv__if2]) ).
fof(f_2505_2,plain,
! [U_9777,U_9776,U_9775] :
( ( hAPP(c_Set_OCollect(U_9777),hAPP(hAPP(c_COMBS(U_9777,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9777),c_fconj),hAPP(c_fequal,U_9776))),U_9775)) = c_Orderings_Obot__class_Obot(tc_fun(U_9777,tc_HOL_Obool))
| hBOOL(hAPP(U_9775,U_9776)) )
& ( hAPP(c_Set_OCollect(U_9777),hAPP(hAPP(c_COMBS(U_9777,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9777),c_fconj),hAPP(c_fequal,U_9776))),U_9775)) = hAPP(hAPP(c_Set_Oinsert(U_9777),U_9776),c_Orderings_Obot__class_Obot(tc_fun(U_9777,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9775,U_9776)) ) ),
inference(variable_rename,[status(thm)],[f_2505_1]) ).
fof(f_2505_3,plain,
( ! [U_9783,U_9781,U_9779] :
( hAPP(c_Set_OCollect(U_9783),hAPP(hAPP(c_COMBS(U_9783,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9783),c_fconj),hAPP(c_fequal,U_9781))),U_9779)) = c_Orderings_Obot__class_Obot(tc_fun(U_9783,tc_HOL_Obool))
| hBOOL(hAPP(U_9779,U_9781)) )
& ! [U_9782,U_9780,U_9778] :
( hAPP(c_Set_OCollect(U_9782),hAPP(hAPP(c_COMBS(U_9782,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9782),c_fconj),hAPP(c_fequal,U_9780))),U_9778)) = hAPP(hAPP(c_Set_Oinsert(U_9782),U_9780),c_Orderings_Obot__class_Obot(tc_fun(U_9782,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9778,U_9780)) ) ),
inference(miniscope,[status(thm)],[f_2505_2]) ).
fof(f_2505_4,plain,
( ! [U_9779,U_9781,U_9783] :
( hAPP(c_Set_OCollect(U_9783),hAPP(hAPP(c_COMBS(U_9783,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9783),c_fconj),hAPP(c_fequal,U_9781))),U_9779)) = c_Orderings_Obot__class_Obot(tc_fun(U_9783,tc_HOL_Obool))
| hBOOL(hAPP(U_9779,U_9781)) )
& ! [U_9780,U_9782,U_9778] :
( hAPP(c_Set_OCollect(U_9782),hAPP(hAPP(c_COMBS(U_9782,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9782),c_fconj),hAPP(c_fequal,U_9780))),U_9778)) = hAPP(hAPP(c_Set_Oinsert(U_9782),U_9780),c_Orderings_Obot__class_Obot(tc_fun(U_9782,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9778,U_9780)) ) ),
inference(definitional_conversion,[status(esa)],[f_2505_3]) ).
cnf(f_2505_5,plain,
( hAPP(c_Set_OCollect(U_9782),hAPP(hAPP(c_COMBS(U_9782,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9782),c_fconj),hAPP(c_fequal,U_9780))),U_9778)) = hAPP(hAPP(c_Set_Oinsert(U_9782),U_9780),c_Orderings_Obot__class_Obot(tc_fun(U_9782,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9778,U_9780)) ),
inference(clausify,[status(thm)],[f_2505_4]) ).
cnf(f_2505_6,plain,
( hAPP(c_Set_OCollect(U_9783),hAPP(hAPP(c_COMBS(U_9783,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9783),c_fconj),hAPP(c_fequal,U_9781))),U_9779)) = c_Orderings_Obot__class_Obot(tc_fun(U_9783,tc_HOL_Obool))
| hBOOL(hAPP(U_9779,U_9781)) ),
inference(clausify,[status(thm)],[f_2505_4]) ).
fof(f_2506_1,plain,
! [T_c,V_a_2,V_Pa_2] :
( ( hAPP(c_Set_OCollect(T_c),hAPP(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,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| hBOOL(hAPP(V_Pa_2,V_a_2)) )
& ( hAPP(c_Set_OCollect(T_c),hAPP(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,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_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(V_Pa_2,V_a_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__conv__if]) ).
fof(f_2506_2,plain,
! [U_9786,U_9785,U_9784] :
( ( hAPP(c_Set_OCollect(U_9786),hAPP(hAPP(c_COMBS(U_9786,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9786),c_fconj),hAPP(hAPP(c_COMBC(U_9786,U_9786,tc_HOL_Obool),c_fequal),U_9785))),U_9784)) = c_Orderings_Obot__class_Obot(tc_fun(U_9786,tc_HOL_Obool))
| hBOOL(hAPP(U_9784,U_9785)) )
& ( hAPP(c_Set_OCollect(U_9786),hAPP(hAPP(c_COMBS(U_9786,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9786),c_fconj),hAPP(hAPP(c_COMBC(U_9786,U_9786,tc_HOL_Obool),c_fequal),U_9785))),U_9784)) = hAPP(hAPP(c_Set_Oinsert(U_9786),U_9785),c_Orderings_Obot__class_Obot(tc_fun(U_9786,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9784,U_9785)) ) ),
inference(variable_rename,[status(thm)],[f_2506_1]) ).
fof(f_2506_3,plain,
( ! [U_9792,U_9790,U_9788] :
( hAPP(c_Set_OCollect(U_9792),hAPP(hAPP(c_COMBS(U_9792,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9792),c_fconj),hAPP(hAPP(c_COMBC(U_9792,U_9792,tc_HOL_Obool),c_fequal),U_9790))),U_9788)) = c_Orderings_Obot__class_Obot(tc_fun(U_9792,tc_HOL_Obool))
| hBOOL(hAPP(U_9788,U_9790)) )
& ! [U_9791,U_9789,U_9787] :
( hAPP(c_Set_OCollect(U_9791),hAPP(hAPP(c_COMBS(U_9791,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9791),c_fconj),hAPP(hAPP(c_COMBC(U_9791,U_9791,tc_HOL_Obool),c_fequal),U_9789))),U_9787)) = hAPP(hAPP(c_Set_Oinsert(U_9791),U_9789),c_Orderings_Obot__class_Obot(tc_fun(U_9791,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9787,U_9789)) ) ),
inference(miniscope,[status(thm)],[f_2506_2]) ).
fof(f_2506_4,plain,
( ! [U_9790,U_9788,U_9792] :
( hAPP(c_Set_OCollect(U_9792),hAPP(hAPP(c_COMBS(U_9792,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9792),c_fconj),hAPP(hAPP(c_COMBC(U_9792,U_9792,tc_HOL_Obool),c_fequal),U_9790))),U_9788)) = c_Orderings_Obot__class_Obot(tc_fun(U_9792,tc_HOL_Obool))
| hBOOL(hAPP(U_9788,U_9790)) )
& ! [U_9789,U_9791,U_9787] :
( hAPP(c_Set_OCollect(U_9791),hAPP(hAPP(c_COMBS(U_9791,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9791),c_fconj),hAPP(hAPP(c_COMBC(U_9791,U_9791,tc_HOL_Obool),c_fequal),U_9789))),U_9787)) = hAPP(hAPP(c_Set_Oinsert(U_9791),U_9789),c_Orderings_Obot__class_Obot(tc_fun(U_9791,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9787,U_9789)) ) ),
inference(definitional_conversion,[status(esa)],[f_2506_3]) ).
cnf(f_2506_5,plain,
( hAPP(c_Set_OCollect(U_9791),hAPP(hAPP(c_COMBS(U_9791,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9791),c_fconj),hAPP(hAPP(c_COMBC(U_9791,U_9791,tc_HOL_Obool),c_fequal),U_9789))),U_9787)) = hAPP(hAPP(c_Set_Oinsert(U_9791),U_9789),c_Orderings_Obot__class_Obot(tc_fun(U_9791,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_9787,U_9789)) ),
inference(clausify,[status(thm)],[f_2506_4]) ).
cnf(f_2506_6,plain,
( hAPP(c_Set_OCollect(U_9792),hAPP(hAPP(c_COMBS(U_9792,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9792),c_fconj),hAPP(hAPP(c_COMBC(U_9792,U_9792,tc_HOL_Obool),c_fequal),U_9790))),U_9788)) = c_Orderings_Obot__class_Obot(tc_fun(U_9792,tc_HOL_Obool))
| hBOOL(hAPP(U_9788,U_9790)) ),
inference(clausify,[status(thm)],[f_2506_4]) ).
fof(f_2507_1,plain,
! [V_B_2,V_A_2,T_c] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(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_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),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_set__diff__eq]) ).
fof(f_2507_2,plain,
! [U_9795,U_9794,U_9793] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9793,tc_HOL_Obool)),U_9794),U_9795) = hAPP(c_Set_OCollect(U_9793),hAPP(hAPP(c_COMBS(U_9793,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9793),c_fconj),hAPP(hAPP(c_COMBC(U_9793,tc_fun(U_9793,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9793)),U_9794))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9793),c_fNot),hAPP(hAPP(c_COMBC(U_9793,tc_fun(U_9793,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9793)),U_9795)))),
inference(variable_rename,[status(thm)],[f_2507_1]) ).
fof(f_2507_3,plain,
! [U_9793,U_9794,U_9795] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9793,tc_HOL_Obool)),U_9794),U_9795) = hAPP(c_Set_OCollect(U_9793),hAPP(hAPP(c_COMBS(U_9793,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9793),c_fconj),hAPP(hAPP(c_COMBC(U_9793,tc_fun(U_9793,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9793)),U_9794))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9793),c_fNot),hAPP(hAPP(c_COMBC(U_9793,tc_fun(U_9793,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9793)),U_9795)))),
inference(definitional_conversion,[status(esa)],[f_2507_2]) ).
cnf(f_2507_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9793,tc_HOL_Obool)),U_9794),U_9795) = hAPP(c_Set_OCollect(U_9793),hAPP(hAPP(c_COMBS(U_9793,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9793),c_fconj),hAPP(hAPP(c_COMBC(U_9793,tc_fun(U_9793,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9793)),U_9794))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9793),c_fNot),hAPP(hAPP(c_COMBC(U_9793,tc_fun(U_9793,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9793)),U_9795)))),
inference(clausify,[status(thm)],[f_2507_3]) ).
fof(f_2508_1,plain,
! [V_Pa_2,T_c] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))))
| ~ 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_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2)))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__not]) ).
fof(f_2508_2,plain,
! [U_9797,U_9796] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),hAPP(c_Set_OCollect(U_9796),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9796),c_fNot),U_9797))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),c_Orderings_Otop__class_Otop(tc_fun(U_9796,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),c_Orderings_Otop__class_Otop(tc_fun(U_9796,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),hAPP(c_Set_OCollect(U_9796),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9796),c_fNot),U_9797)))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),hAPP(c_Set_OCollect(U_9796),U_9797))) ),
inference(variable_rename,[status(thm)],[f_2508_1]) ).
fof(f_2508_3,plain,
( ! [U_9796,U_9797] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),hAPP(c_Set_OCollect(U_9796),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9796),c_fNot),U_9797))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),c_Orderings_Otop__class_Otop(tc_fun(U_9796,tc_HOL_Obool))))
| ~ sP683(U_9796,U_9797) )
& ! [U_9796,U_9797] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),c_Orderings_Otop__class_Otop(tc_fun(U_9796,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),hAPP(c_Set_OCollect(U_9796),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9796),c_fNot),U_9797))))
| ~ sP683(U_9796,U_9797) )
& ! [U_9796,U_9797] :
( sP683(U_9796,U_9797)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),hAPP(c_Set_OCollect(U_9796),U_9797))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP683])],[f_2508_2]) ).
cnf(f_2508_4,plain,
( sP683(U_9796,U_9797)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),hAPP(c_Set_OCollect(U_9796),U_9797))) ),
inference(clausify,[status(thm)],[f_2508_3]) ).
cnf(f_2508_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),c_Orderings_Otop__class_Otop(tc_fun(U_9796,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),hAPP(c_Set_OCollect(U_9796),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9796),c_fNot),U_9797))))
| ~ sP683(U_9796,U_9797) ),
inference(clausify,[status(thm)],[f_2508_3]) ).
cnf(f_2508_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),hAPP(c_Set_OCollect(U_9796),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9796),c_fNot),U_9797))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9796),c_Orderings_Otop__class_Otop(tc_fun(U_9796,tc_HOL_Obool))))
| ~ sP683(U_9796,U_9797) ),
inference(clausify,[status(thm)],[f_2508_3]) ).
fof(f_2509_1,plain,
! [V_B_2,V_a_2,T_c] : hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2),
inference(fof_nnf,[status(thm)],[fact_insert__def]) ).
fof(f_2509_2,plain,
! [U_9800,U_9799,U_9798] : hAPP(hAPP(c_Set_Oinsert(U_9798),U_9799),U_9800) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9798,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9798),hAPP(hAPP(c_COMBC(U_9798,U_9798,tc_HOL_Obool),c_fequal),U_9799))),U_9800),
inference(variable_rename,[status(thm)],[f_2509_1]) ).
fof(f_2509_3,plain,
! [U_9799,U_9798,U_9800] : hAPP(hAPP(c_Set_Oinsert(U_9798),U_9799),U_9800) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9798,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9798),hAPP(hAPP(c_COMBC(U_9798,U_9798,tc_HOL_Obool),c_fequal),U_9799))),U_9800),
inference(definitional_conversion,[status(esa)],[f_2509_2]) ).
cnf(f_2509_4,plain,
hAPP(hAPP(c_Set_Oinsert(U_9798),U_9799),U_9800) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9798,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9798),hAPP(hAPP(c_COMBC(U_9798,U_9798,tc_HOL_Obool),c_fequal),U_9799))),U_9800),
inference(clausify,[status(thm)],[f_2509_3]) ).
fof(f_2510_1,plain,
! [V_A_2,T_c] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2))),
inference(fof_nnf,[status(thm)],[fact_Compl__eq]) ).
fof(f_2510_2,plain,
! [U_9802,U_9801] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9801,tc_HOL_Obool)),U_9802) = hAPP(c_Set_OCollect(U_9801),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9801),c_fNot),hAPP(hAPP(c_COMBC(U_9801,tc_fun(U_9801,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9801)),U_9802))),
inference(variable_rename,[status(thm)],[f_2510_1]) ).
fof(f_2510_3,plain,
! [U_9801,U_9802] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9801,tc_HOL_Obool)),U_9802) = hAPP(c_Set_OCollect(U_9801),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9801),c_fNot),hAPP(hAPP(c_COMBC(U_9801,tc_fun(U_9801,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9801)),U_9802))),
inference(definitional_conversion,[status(esa)],[f_2510_2]) ).
cnf(f_2510_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9801,tc_HOL_Obool)),U_9802) = hAPP(c_Set_OCollect(U_9801),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9801),c_fNot),hAPP(hAPP(c_COMBC(U_9801,tc_fun(U_9801,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9801)),U_9802))),
inference(clausify,[status(thm)],[f_2510_3]) ).
fof(f_2511_1,plain,
! [V_B_2,V_f_2,T_d,T_c] : hAPP(c_Set_Ovimage(T_c,T_d,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(T_d)),V_f_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__def]) ).
fof(f_2511_2,plain,
! [U_9806,U_9805,U_9804,U_9803] : hAPP(c_Set_Ovimage(U_9803,U_9804,U_9805),U_9806) = hAPP(c_Set_OCollect(U_9803),hAPP(hAPP(c_COMBC(U_9803,tc_fun(U_9804,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_9804,tc_fun(tc_fun(U_9804,tc_HOL_Obool),tc_HOL_Obool),U_9803),c_member(U_9804)),U_9805)),U_9806)),
inference(variable_rename,[status(thm)],[f_2511_1]) ).
fof(f_2511_3,plain,
! [U_9803,U_9804,U_9805,U_9806] : hAPP(c_Set_Ovimage(U_9803,U_9804,U_9805),U_9806) = hAPP(c_Set_OCollect(U_9803),hAPP(hAPP(c_COMBC(U_9803,tc_fun(U_9804,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_9804,tc_fun(tc_fun(U_9804,tc_HOL_Obool),tc_HOL_Obool),U_9803),c_member(U_9804)),U_9805)),U_9806)),
inference(definitional_conversion,[status(esa)],[f_2511_2]) ).
cnf(f_2511_4,plain,
hAPP(c_Set_Ovimage(U_9803,U_9804,U_9805),U_9806) = hAPP(c_Set_OCollect(U_9803),hAPP(hAPP(c_COMBC(U_9803,tc_fun(U_9804,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_9804,tc_fun(tc_fun(U_9804,tc_HOL_Obool),tc_HOL_Obool),U_9803),c_member(U_9804)),U_9805)),U_9806)),
inference(clausify,[status(thm)],[f_2511_3]) ).
fof(f_2512_1,plain,
! [V_Qa_2,V_Pa_2,T_c] : hAPP(c_Set_OCollect(T_c),hAPP(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),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_c),V_Pa_2))),hAPP(c_Set_OCollect(T_c),V_Qa_2)),
inference(fof_nnf,[status(thm)],[fact_Collect__imp__eq]) ).
fof(f_2512_2,plain,
! [U_9809,U_9808,U_9807] : hAPP(c_Set_OCollect(U_9807),hAPP(hAPP(c_COMBS(U_9807,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9807),c_fimplies),U_9808)),U_9809)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9807,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9807,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9807),U_9808))),hAPP(c_Set_OCollect(U_9807),U_9809)),
inference(variable_rename,[status(thm)],[f_2512_1]) ).
fof(f_2512_3,plain,
! [U_9807,U_9808,U_9809] : hAPP(c_Set_OCollect(U_9807),hAPP(hAPP(c_COMBS(U_9807,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9807),c_fimplies),U_9808)),U_9809)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9807,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9807,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9807),U_9808))),hAPP(c_Set_OCollect(U_9807),U_9809)),
inference(definitional_conversion,[status(esa)],[f_2512_2]) ).
cnf(f_2512_4,plain,
hAPP(c_Set_OCollect(U_9807),hAPP(hAPP(c_COMBS(U_9807,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9807),c_fimplies),U_9808)),U_9809)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9807,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9807,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9807),U_9808))),hAPP(c_Set_OCollect(U_9807),U_9809)),
inference(clausify,[status(thm)],[f_2512_3]) ).
fof(f_2513_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_2513_2,plain,
! [U_9811,U_9810] : 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_9810)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9811))))),
inference(variable_rename,[status(thm)],[f_2513_1]) ).
fof(f_2513_3,plain,
! [U_9810,U_9811] : 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_9810)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9811))))),
inference(definitional_conversion,[status(esa)],[f_2513_2]) ).
cnf(f_2513_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_9810)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9811))))),
inference(clausify,[status(thm)],[f_2513_3]) ).
fof(f_2514_1,plain,
! [V_R_2,V_f_2,V_T_2,T_d,V_S_2,T_c,T_e] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_d,tc_HOL_Obool),T_e),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_e),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_e),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_OCollect(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_e),hAPP(hAPP(c_COMBS(T_d,tc_fun(T_c,tc_HOL_Obool),T_e),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_e),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_e),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_e)),hAPP(c_COMBC(T_c,T_d,T_e),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),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_S_2)))),hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),V_R_2))))),V_T_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_e) ),
inference(fof_nnf,[status(thm)],[fact_setsum__setsum__restrict]) ).
fof(f_2514_2,plain,
! [U_9818,U_9817,U_9816,U_9815,U_9814,U_9813,U_9812] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9813,U_9812),hAPP(hAPP(c_COMBS(U_9813,tc_fun(U_9815,tc_HOL_Obool),U_9812),hAPP(hAPP(c_COMBB(tc_fun(U_9815,U_9812),tc_fun(tc_fun(U_9815,tc_HOL_Obool),U_9812),U_9813),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9815,U_9812)),U_9817)),hAPP(hAPP(c_COMBB(tc_fun(U_9815,tc_HOL_Obool),tc_fun(U_9815,tc_HOL_Obool),U_9813),c_Set_OCollect(U_9815)),hAPP(hAPP(c_COMBB(tc_fun(U_9815,tc_HOL_Obool),tc_fun(U_9815,tc_HOL_Obool),U_9813),hAPP(c_COMBS(U_9815,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9815),c_fconj),hAPP(hAPP(c_COMBC(U_9815,tc_fun(U_9815,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9815)),U_9816)))),U_9818)))),U_9814) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9815,U_9812),hAPP(hAPP(c_COMBS(U_9815,tc_fun(U_9813,tc_HOL_Obool),U_9812),hAPP(hAPP(c_COMBB(tc_fun(U_9813,U_9812),tc_fun(tc_fun(U_9813,tc_HOL_Obool),U_9812),U_9815),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9813,U_9812)),hAPP(c_COMBC(U_9813,U_9815,U_9812),U_9817))),hAPP(hAPP(c_COMBB(tc_fun(U_9813,tc_HOL_Obool),tc_fun(U_9813,tc_HOL_Obool),U_9815),c_Set_OCollect(U_9813)),hAPP(hAPP(c_COMBB(tc_fun(U_9813,tc_HOL_Obool),tc_fun(U_9813,tc_HOL_Obool),U_9815),hAPP(c_COMBS(U_9813,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9813),c_fconj),hAPP(hAPP(c_COMBC(U_9813,tc_fun(U_9813,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9813)),U_9814)))),hAPP(c_COMBC(U_9813,U_9815,tc_HOL_Obool),U_9818))))),U_9816)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9815),U_9816))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9813),U_9814))
| ~ class_Groups_Ocomm__monoid__add(U_9812) ),
inference(variable_rename,[status(thm)],[f_2514_1]) ).
fof(f_2514_3,plain,
! [U_9812,U_9813,U_9814,U_9815,U_9816,U_9817,U_9818] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9813,U_9812),hAPP(hAPP(c_COMBS(U_9813,tc_fun(U_9815,tc_HOL_Obool),U_9812),hAPP(hAPP(c_COMBB(tc_fun(U_9815,U_9812),tc_fun(tc_fun(U_9815,tc_HOL_Obool),U_9812),U_9813),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9815,U_9812)),U_9817)),hAPP(hAPP(c_COMBB(tc_fun(U_9815,tc_HOL_Obool),tc_fun(U_9815,tc_HOL_Obool),U_9813),c_Set_OCollect(U_9815)),hAPP(hAPP(c_COMBB(tc_fun(U_9815,tc_HOL_Obool),tc_fun(U_9815,tc_HOL_Obool),U_9813),hAPP(c_COMBS(U_9815,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9815),c_fconj),hAPP(hAPP(c_COMBC(U_9815,tc_fun(U_9815,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9815)),U_9816)))),U_9818)))),U_9814) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9815,U_9812),hAPP(hAPP(c_COMBS(U_9815,tc_fun(U_9813,tc_HOL_Obool),U_9812),hAPP(hAPP(c_COMBB(tc_fun(U_9813,U_9812),tc_fun(tc_fun(U_9813,tc_HOL_Obool),U_9812),U_9815),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9813,U_9812)),hAPP(c_COMBC(U_9813,U_9815,U_9812),U_9817))),hAPP(hAPP(c_COMBB(tc_fun(U_9813,tc_HOL_Obool),tc_fun(U_9813,tc_HOL_Obool),U_9815),c_Set_OCollect(U_9813)),hAPP(hAPP(c_COMBB(tc_fun(U_9813,tc_HOL_Obool),tc_fun(U_9813,tc_HOL_Obool),U_9815),hAPP(c_COMBS(U_9813,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9813),c_fconj),hAPP(hAPP(c_COMBC(U_9813,tc_fun(U_9813,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9813)),U_9814)))),hAPP(c_COMBC(U_9813,U_9815,tc_HOL_Obool),U_9818))))),U_9816)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9815),U_9816))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9813),U_9814))
| ~ class_Groups_Ocomm__monoid__add(U_9812) ),
inference(definitional_conversion,[status(esa)],[f_2514_2]) ).
cnf(f_2514_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9813,U_9812),hAPP(hAPP(c_COMBS(U_9813,tc_fun(U_9815,tc_HOL_Obool),U_9812),hAPP(hAPP(c_COMBB(tc_fun(U_9815,U_9812),tc_fun(tc_fun(U_9815,tc_HOL_Obool),U_9812),U_9813),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9815,U_9812)),U_9817)),hAPP(hAPP(c_COMBB(tc_fun(U_9815,tc_HOL_Obool),tc_fun(U_9815,tc_HOL_Obool),U_9813),c_Set_OCollect(U_9815)),hAPP(hAPP(c_COMBB(tc_fun(U_9815,tc_HOL_Obool),tc_fun(U_9815,tc_HOL_Obool),U_9813),hAPP(c_COMBS(U_9815,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9815),c_fconj),hAPP(hAPP(c_COMBC(U_9815,tc_fun(U_9815,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9815)),U_9816)))),U_9818)))),U_9814) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9815,U_9812),hAPP(hAPP(c_COMBS(U_9815,tc_fun(U_9813,tc_HOL_Obool),U_9812),hAPP(hAPP(c_COMBB(tc_fun(U_9813,U_9812),tc_fun(tc_fun(U_9813,tc_HOL_Obool),U_9812),U_9815),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9813,U_9812)),hAPP(c_COMBC(U_9813,U_9815,U_9812),U_9817))),hAPP(hAPP(c_COMBB(tc_fun(U_9813,tc_HOL_Obool),tc_fun(U_9813,tc_HOL_Obool),U_9815),c_Set_OCollect(U_9813)),hAPP(hAPP(c_COMBB(tc_fun(U_9813,tc_HOL_Obool),tc_fun(U_9813,tc_HOL_Obool),U_9815),hAPP(c_COMBS(U_9813,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9813),c_fconj),hAPP(hAPP(c_COMBC(U_9813,tc_fun(U_9813,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9813)),U_9814)))),hAPP(c_COMBC(U_9813,U_9815,tc_HOL_Obool),U_9818))))),U_9816)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9815),U_9816))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9813),U_9814))
| ~ class_Groups_Ocomm__monoid__add(U_9812) ),
inference(clausify,[status(thm)],[f_2514_3]) ).
fof(f_2515_1,plain,
! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_c,T_d] : hAPP(c_Set_Oimage(T_d,T_c,hAPP(hAPP(c_COMBS(T_d,T_c,T_c),hAPP(hAPP(c_COMBS(T_d,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_d),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_d),V_Pa_2)))),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d),c_fNot),V_Pa_2))))),
inference(fof_nnf,[status(thm)],[fact_if__image__distrib]) ).
fof(f_2515_2,plain,
! [U_9824,U_9823,U_9822,U_9821,U_9820,U_9819] : hAPP(c_Set_Oimage(U_9819,U_9820,hAPP(hAPP(c_COMBS(U_9819,U_9820,U_9820),hAPP(hAPP(c_COMBS(U_9819,U_9820,tc_fun(U_9820,U_9820)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9820,tc_fun(U_9820,U_9820)),U_9819),c_If(U_9820)),U_9821)),U_9822)),U_9823)),U_9824) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9820,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9819,U_9820,U_9822),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9819,tc_HOL_Obool)),U_9824),hAPP(c_Set_OCollect(U_9819),U_9821)))),hAPP(c_Set_Oimage(U_9819,U_9820,U_9823),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9819,tc_HOL_Obool)),U_9824),hAPP(c_Set_OCollect(U_9819),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9819),c_fNot),U_9821))))),
inference(variable_rename,[status(thm)],[f_2515_1]) ).
fof(f_2515_3,plain,
! [U_9819,U_9820,U_9821,U_9822,U_9823,U_9824] : hAPP(c_Set_Oimage(U_9819,U_9820,hAPP(hAPP(c_COMBS(U_9819,U_9820,U_9820),hAPP(hAPP(c_COMBS(U_9819,U_9820,tc_fun(U_9820,U_9820)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9820,tc_fun(U_9820,U_9820)),U_9819),c_If(U_9820)),U_9821)),U_9822)),U_9823)),U_9824) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9820,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9819,U_9820,U_9822),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9819,tc_HOL_Obool)),U_9824),hAPP(c_Set_OCollect(U_9819),U_9821)))),hAPP(c_Set_Oimage(U_9819,U_9820,U_9823),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9819,tc_HOL_Obool)),U_9824),hAPP(c_Set_OCollect(U_9819),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9819),c_fNot),U_9821))))),
inference(definitional_conversion,[status(esa)],[f_2515_2]) ).
cnf(f_2515_4,plain,
hAPP(c_Set_Oimage(U_9819,U_9820,hAPP(hAPP(c_COMBS(U_9819,U_9820,U_9820),hAPP(hAPP(c_COMBS(U_9819,U_9820,tc_fun(U_9820,U_9820)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9820,tc_fun(U_9820,U_9820)),U_9819),c_If(U_9820)),U_9821)),U_9822)),U_9823)),U_9824) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9820,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9819,U_9820,U_9822),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9819,tc_HOL_Obool)),U_9824),hAPP(c_Set_OCollect(U_9819),U_9821)))),hAPP(c_Set_Oimage(U_9819,U_9820,U_9823),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9819,tc_HOL_Obool)),U_9824),hAPP(c_Set_OCollect(U_9819),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9819),c_fNot),U_9821))))),
inference(clausify,[status(thm)],[f_2515_3]) ).
fof(f_2516_1,plain,
! [V_n_2,V_f_2,T_c,V_A_2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| V_A_2 != hAPP(c_Set_Oimage(tc_Nat_Onat,T_c,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_2516_2,plain,
! [U_9828,U_9827,U_9826,U_9825] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9826),U_9825))
| U_9825 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9826,U_9827),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_9828))) ),
inference(variable_rename,[status(thm)],[f_2516_1]) ).
fof(f_2516_3,plain,
! [U_9828,U_9827,U_9825,U_9826] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9826),U_9825))
| U_9825 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9826,U_9827),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_9828))) ),
inference(definitional_conversion,[status(esa)],[f_2516_2]) ).
cnf(f_2516_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9826),U_9825))
| U_9825 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9826,U_9827),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_9828))) ),
inference(clausify,[status(thm)],[f_2516_3]) ).
fof(f_2517_1,plain,
! [V_B_2,V_f_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(c_Set_OCollect(T_c),hAPP(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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBC(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_d))),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set_H]) ).
fof(f_2517_2,plain,
! [U_9833,U_9832,U_9831,U_9830,U_9829] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9830,U_9829),U_9832),hAPP(c_Set_OCollect(U_9830),hAPP(hAPP(c_COMBS(U_9830,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9830),c_fconj),hAPP(hAPP(c_COMBC(U_9830,tc_fun(U_9830,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9830)),U_9831))),hAPP(hAPP(c_COMBC(U_9830,tc_fun(U_9830,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9830)),U_9833)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9830,U_9829),hAPP(hAPP(c_COMBC(U_9830,U_9829,U_9829),hAPP(hAPP(c_COMBS(U_9830,U_9829,tc_fun(U_9829,U_9829)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9829,tc_fun(U_9829,U_9829)),U_9830),c_If(U_9829)),hAPP(hAPP(c_COMBC(U_9830,tc_fun(U_9830,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9830)),U_9833))),U_9832)),c_Groups_Ozero__class_Ozero(U_9829))),U_9831)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9830),U_9831))
| ~ class_Groups_Ocomm__monoid__add(U_9829) ),
inference(variable_rename,[status(thm)],[f_2517_1]) ).
fof(f_2517_3,plain,
! [U_9829,U_9830,U_9831,U_9832,U_9833] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9830,U_9829),U_9832),hAPP(c_Set_OCollect(U_9830),hAPP(hAPP(c_COMBS(U_9830,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9830),c_fconj),hAPP(hAPP(c_COMBC(U_9830,tc_fun(U_9830,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9830)),U_9831))),hAPP(hAPP(c_COMBC(U_9830,tc_fun(U_9830,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9830)),U_9833)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9830,U_9829),hAPP(hAPP(c_COMBC(U_9830,U_9829,U_9829),hAPP(hAPP(c_COMBS(U_9830,U_9829,tc_fun(U_9829,U_9829)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9829,tc_fun(U_9829,U_9829)),U_9830),c_If(U_9829)),hAPP(hAPP(c_COMBC(U_9830,tc_fun(U_9830,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9830)),U_9833))),U_9832)),c_Groups_Ozero__class_Ozero(U_9829))),U_9831)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9830),U_9831))
| ~ class_Groups_Ocomm__monoid__add(U_9829) ),
inference(definitional_conversion,[status(esa)],[f_2517_2]) ).
cnf(f_2517_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9830,U_9829),U_9832),hAPP(c_Set_OCollect(U_9830),hAPP(hAPP(c_COMBS(U_9830,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9830),c_fconj),hAPP(hAPP(c_COMBC(U_9830,tc_fun(U_9830,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9830)),U_9831))),hAPP(hAPP(c_COMBC(U_9830,tc_fun(U_9830,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9830)),U_9833)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9830,U_9829),hAPP(hAPP(c_COMBC(U_9830,U_9829,U_9829),hAPP(hAPP(c_COMBS(U_9830,U_9829,tc_fun(U_9829,U_9829)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9829,tc_fun(U_9829,U_9829)),U_9830),c_If(U_9829)),hAPP(hAPP(c_COMBC(U_9830,tc_fun(U_9830,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9830)),U_9833))),U_9832)),c_Groups_Ozero__class_Ozero(U_9829))),U_9831)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9830),U_9831))
| ~ class_Groups_Ocomm__monoid__add(U_9829) ),
inference(clausify,[status(thm)],[f_2517_3]) ).
fof(f_2518_1,plain,
! [V_f_2,T_e,V_g_2,V_S_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_e,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_e),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),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_S_2)))),hAPP(c_COMBC(T_c,T_e,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_e,tc_HOL_Obool),T_c),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_c,T_e,V_f_2),V_S_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__image__gen]) ).
fof(f_2518_2,plain,
! [U_9839,U_9838,U_9837,U_9836,U_9835,U_9834] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9835,U_9834),U_9837),U_9836) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9838,U_9834),hAPP(hAPP(c_COMBB(tc_fun(U_9835,tc_HOL_Obool),U_9834,U_9838),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9835,U_9834),U_9837)),hAPP(hAPP(c_COMBB(tc_fun(U_9835,tc_HOL_Obool),tc_fun(U_9835,tc_HOL_Obool),U_9838),c_Set_OCollect(U_9835)),hAPP(hAPP(c_COMBB(tc_fun(U_9835,tc_HOL_Obool),tc_fun(U_9835,tc_HOL_Obool),U_9838),hAPP(c_COMBS(U_9835,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9835),c_fconj),hAPP(hAPP(c_COMBC(U_9835,tc_fun(U_9835,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9835)),U_9836)))),hAPP(c_COMBC(U_9835,U_9838,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_9838,tc_fun(U_9838,tc_HOL_Obool),U_9835),c_fequal),U_9839)))))),hAPP(c_Set_Oimage(U_9835,U_9838,U_9839),U_9836))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9835),U_9836))
| ~ class_Groups_Ocomm__monoid__add(U_9834) ),
inference(variable_rename,[status(thm)],[f_2518_1]) ).
fof(f_2518_3,plain,
! [U_9835,U_9834,U_9836,U_9837,U_9838,U_9839] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9835,U_9834),U_9837),U_9836) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9838,U_9834),hAPP(hAPP(c_COMBB(tc_fun(U_9835,tc_HOL_Obool),U_9834,U_9838),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9835,U_9834),U_9837)),hAPP(hAPP(c_COMBB(tc_fun(U_9835,tc_HOL_Obool),tc_fun(U_9835,tc_HOL_Obool),U_9838),c_Set_OCollect(U_9835)),hAPP(hAPP(c_COMBB(tc_fun(U_9835,tc_HOL_Obool),tc_fun(U_9835,tc_HOL_Obool),U_9838),hAPP(c_COMBS(U_9835,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9835),c_fconj),hAPP(hAPP(c_COMBC(U_9835,tc_fun(U_9835,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9835)),U_9836)))),hAPP(c_COMBC(U_9835,U_9838,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_9838,tc_fun(U_9838,tc_HOL_Obool),U_9835),c_fequal),U_9839)))))),hAPP(c_Set_Oimage(U_9835,U_9838,U_9839),U_9836))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9835),U_9836))
| ~ class_Groups_Ocomm__monoid__add(U_9834) ),
inference(definitional_conversion,[status(esa)],[f_2518_2]) ).
cnf(f_2518_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9835,U_9834),U_9837),U_9836) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9838,U_9834),hAPP(hAPP(c_COMBB(tc_fun(U_9835,tc_HOL_Obool),U_9834,U_9838),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9835,U_9834),U_9837)),hAPP(hAPP(c_COMBB(tc_fun(U_9835,tc_HOL_Obool),tc_fun(U_9835,tc_HOL_Obool),U_9838),c_Set_OCollect(U_9835)),hAPP(hAPP(c_COMBB(tc_fun(U_9835,tc_HOL_Obool),tc_fun(U_9835,tc_HOL_Obool),U_9838),hAPP(c_COMBS(U_9835,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9835),c_fconj),hAPP(hAPP(c_COMBC(U_9835,tc_fun(U_9835,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9835)),U_9836)))),hAPP(c_COMBC(U_9835,U_9838,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_9838,tc_fun(U_9838,tc_HOL_Obool),U_9835),c_fequal),U_9839)))))),hAPP(c_Set_Oimage(U_9835,U_9838,U_9839),U_9836))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9835),U_9836))
| ~ class_Groups_Ocomm__monoid__add(U_9834) ),
inference(clausify,[status(thm)],[f_2518_3]) ).
fof(f_2519_1,plain,
! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_c,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,T_d),hAPP(hAPP(c_COMBS(T_c,T_d,tc_fun(T_d,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_d,tc_fun(T_d,T_d)),T_c),c_If(T_d)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_Set_OCollect(T_c),V_Pa_2)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__cases]) ).
fof(f_2519_2,plain,
! [U_9845,U_9844,U_9843,U_9842,U_9841,U_9840] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9841,U_9840),hAPP(hAPP(c_COMBS(U_9841,U_9840,U_9840),hAPP(hAPP(c_COMBS(U_9841,U_9840,tc_fun(U_9840,U_9840)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9840,tc_fun(U_9840,U_9840)),U_9841),c_If(U_9840)),U_9843)),U_9844)),U_9845)),U_9842) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9840),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9841,U_9840),U_9844),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9841,tc_HOL_Obool)),U_9842),hAPP(c_Set_OCollect(U_9841),U_9843)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9841,U_9840),U_9845),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9841,tc_HOL_Obool)),U_9842),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9841,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9841),U_9843)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9841),U_9842))
| ~ class_Groups_Ocomm__monoid__add(U_9840) ),
inference(variable_rename,[status(thm)],[f_2519_1]) ).
fof(f_2519_3,plain,
! [U_9840,U_9841,U_9842,U_9843,U_9844,U_9845] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9841,U_9840),hAPP(hAPP(c_COMBS(U_9841,U_9840,U_9840),hAPP(hAPP(c_COMBS(U_9841,U_9840,tc_fun(U_9840,U_9840)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9840,tc_fun(U_9840,U_9840)),U_9841),c_If(U_9840)),U_9843)),U_9844)),U_9845)),U_9842) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9840),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9841,U_9840),U_9844),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9841,tc_HOL_Obool)),U_9842),hAPP(c_Set_OCollect(U_9841),U_9843)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9841,U_9840),U_9845),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9841,tc_HOL_Obool)),U_9842),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9841,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9841),U_9843)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9841),U_9842))
| ~ class_Groups_Ocomm__monoid__add(U_9840) ),
inference(definitional_conversion,[status(esa)],[f_2519_2]) ).
cnf(f_2519_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9841,U_9840),hAPP(hAPP(c_COMBS(U_9841,U_9840,U_9840),hAPP(hAPP(c_COMBS(U_9841,U_9840,tc_fun(U_9840,U_9840)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9840,tc_fun(U_9840,U_9840)),U_9841),c_If(U_9840)),U_9843)),U_9844)),U_9845)),U_9842) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9840),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9841,U_9840),U_9844),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9841,tc_HOL_Obool)),U_9842),hAPP(c_Set_OCollect(U_9841),U_9843)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9841,U_9840),U_9845),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9841,tc_HOL_Obool)),U_9842),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9841,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9841),U_9843)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9841),U_9842))
| ~ class_Groups_Ocomm__monoid__add(U_9840) ),
inference(clausify,[status(thm)],[f_2519_3]) ).
fof(f_2520_1,plain,
! [V_k_2,V_R_2,V_T_2,T_d,V_S_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_Nat_Onat,T_c),c_Finite__Set_Ocard(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_OCollect(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),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_d),V_T_2))
| ? [B_x] :
( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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_S_2))),hAPP(hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),V_R_2),B_x)))) != V_k_2
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_T_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__multicount]) ).
fof(f_2520_2,plain,
! [U_9852,U_9851,U_9850,U_9849,U_9848,U_9847] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9847,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_HOL_Obool),tc_Nat_Onat,U_9847),c_Finite__Set_Ocard(U_9849)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool),U_9847),c_Set_OCollect(U_9849)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool),U_9847),hAPP(c_COMBS(U_9849,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9849),c_fconj),hAPP(hAPP(c_COMBC(U_9849,tc_fun(U_9849,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9849)),U_9850)))),U_9851)))),U_9848) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9852),hAPP(c_Finite__Set_Ocard(U_9849),U_9850))
| ? [U_9846] :
( hAPP(c_Finite__Set_Ocard(U_9847),hAPP(c_Set_OCollect(U_9847),hAPP(hAPP(c_COMBS(U_9847,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9847),c_fconj),hAPP(hAPP(c_COMBC(U_9847,tc_fun(U_9847,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9847)),U_9848))),hAPP(hAPP(c_COMBC(U_9847,U_9849,tc_HOL_Obool),U_9851),U_9846)))) != U_9852
& hBOOL(hAPP(hAPP(c_member(U_9849),U_9846),U_9850)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9849),U_9850))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9847),U_9848)) ),
inference(variable_rename,[status(thm)],[f_2520_1]) ).
fof(f_2520_3,plain,
! [U_9852,U_9851,U_9850,U_9849,U_9848,U_9847] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9847,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_HOL_Obool),tc_Nat_Onat,U_9847),c_Finite__Set_Ocard(U_9849)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool),U_9847),c_Set_OCollect(U_9849)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool),U_9847),hAPP(c_COMBS(U_9849,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9849),c_fconj),hAPP(hAPP(c_COMBC(U_9849,tc_fun(U_9849,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9849)),U_9850)))),U_9851)))),U_9848) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9852),hAPP(c_Finite__Set_Ocard(U_9849),U_9850))
| ( hAPP(c_Finite__Set_Ocard(U_9847),hAPP(c_Set_OCollect(U_9847),hAPP(hAPP(c_COMBS(U_9847,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9847),c_fconj),hAPP(hAPP(c_COMBC(U_9847,tc_fun(U_9847,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9847)),U_9848))),hAPP(hAPP(c_COMBC(U_9847,U_9849,tc_HOL_Obool),U_9851),sK249(U_9852,U_9851,U_9850,U_9849,U_9848,U_9847))))) != U_9852
& hBOOL(hAPP(hAPP(c_member(U_9849),sK249(U_9852,U_9851,U_9850,U_9849,U_9848,U_9847)),U_9850)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9849),U_9850))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9847),U_9848)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_9846,sK249(U_9852,U_9851,U_9850,U_9849,U_9848,U_9847))],[f_2520_2]) ).
fof(f_2520_4,plain,
( ! [U_9847,U_9848,U_9849,U_9850,U_9851,U_9852] :
( hAPP(c_Finite__Set_Ocard(U_9847),hAPP(c_Set_OCollect(U_9847),hAPP(hAPP(c_COMBS(U_9847,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9847),c_fconj),hAPP(hAPP(c_COMBC(U_9847,tc_fun(U_9847,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9847)),U_9848))),hAPP(hAPP(c_COMBC(U_9847,U_9849,tc_HOL_Obool),U_9851),sK249(U_9852,U_9851,U_9850,U_9849,U_9848,U_9847))))) != U_9852
| ~ sP684(U_9847,U_9848,U_9849,U_9850,U_9851,U_9852) )
& ! [U_9847,U_9848,U_9849,U_9850,U_9851,U_9852] :
( hBOOL(hAPP(hAPP(c_member(U_9849),sK249(U_9852,U_9851,U_9850,U_9849,U_9848,U_9847)),U_9850))
| ~ sP684(U_9847,U_9848,U_9849,U_9850,U_9851,U_9852) )
& ! [U_9847,U_9848,U_9849,U_9850,U_9851,U_9852] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9847,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_HOL_Obool),tc_Nat_Onat,U_9847),c_Finite__Set_Ocard(U_9849)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool),U_9847),c_Set_OCollect(U_9849)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool),U_9847),hAPP(c_COMBS(U_9849,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9849),c_fconj),hAPP(hAPP(c_COMBC(U_9849,tc_fun(U_9849,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9849)),U_9850)))),U_9851)))),U_9848) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9852),hAPP(c_Finite__Set_Ocard(U_9849),U_9850))
| sP684(U_9847,U_9848,U_9849,U_9850,U_9851,U_9852)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9849),U_9850))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9847),U_9848)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP684])],[f_2520_3]) ).
cnf(f_2520_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9847,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_HOL_Obool),tc_Nat_Onat,U_9847),c_Finite__Set_Ocard(U_9849)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool),U_9847),c_Set_OCollect(U_9849)),hAPP(hAPP(c_COMBB(tc_fun(U_9849,tc_HOL_Obool),tc_fun(U_9849,tc_HOL_Obool),U_9847),hAPP(c_COMBS(U_9849,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9849),c_fconj),hAPP(hAPP(c_COMBC(U_9849,tc_fun(U_9849,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9849)),U_9850)))),U_9851)))),U_9848) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9852),hAPP(c_Finite__Set_Ocard(U_9849),U_9850))
| sP684(U_9847,U_9848,U_9849,U_9850,U_9851,U_9852)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9849),U_9850))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9847),U_9848)) ),
inference(clausify,[status(thm)],[f_2520_4]) ).
cnf(f_2520_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9849),sK249(U_9852,U_9851,U_9850,U_9849,U_9848,U_9847)),U_9850))
| ~ sP684(U_9847,U_9848,U_9849,U_9850,U_9851,U_9852) ),
inference(clausify,[status(thm)],[f_2520_4]) ).
cnf(f_2520_7,plain,
( hAPP(c_Finite__Set_Ocard(U_9847),hAPP(c_Set_OCollect(U_9847),hAPP(hAPP(c_COMBS(U_9847,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9847),c_fconj),hAPP(hAPP(c_COMBC(U_9847,tc_fun(U_9847,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9847)),U_9848))),hAPP(hAPP(c_COMBC(U_9847,U_9849,tc_HOL_Obool),U_9851),sK249(U_9852,U_9851,U_9850,U_9849,U_9848,U_9847))))) != U_9852
| ~ sP684(U_9847,U_9848,U_9849,U_9850,U_9851,U_9852) ),
inference(clausify,[status(thm)],[f_2520_4]) ).
fof(f_2521_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib]) ).
fof(f_2521_2,plain,
! [U_9855,U_9854,U_9853] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9853),U_9855),c_Big__Operators_Olattice_OInf__fin(U_9853,c_Orderings_Oord__class_Omin(U_9853),U_9854)) = c_Big__Operators_Olattice_OInf__fin(U_9853,c_Orderings_Oord__class_Omin(U_9853),hAPP(c_Set_OCollect(U_9853),hAPP(hAPP(c_COMBB(tc_fun(U_9853,tc_HOL_Obool),tc_HOL_Obool,U_9853),c_HOL_OEx(U_9853)),hAPP(hAPP(c_COMBC(U_9853,tc_fun(U_9853,tc_HOL_Obool),tc_fun(U_9853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9853,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9853,tc_HOL_Obool),tc_fun(U_9853,tc_HOL_Obool)),U_9853),c_COMBS(U_9853,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9853,tc_HOL_Obool),tc_fun(U_9853,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9853),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9853),c_fconj)),hAPP(hAPP(c_COMBC(U_9853,tc_fun(U_9853,U_9853),tc_fun(U_9853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9853,tc_HOL_Obool),tc_fun(tc_fun(U_9853,U_9853),tc_fun(U_9853,tc_HOL_Obool)),U_9853),c_COMBB(U_9853,tc_HOL_Obool,U_9853)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_9853),U_9855))))),hAPP(hAPP(c_COMBC(U_9853,tc_fun(U_9853,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9853)),U_9854)))))
| U_9854 = c_Orderings_Obot__class_Obot(tc_fun(U_9853,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9853),U_9854))
| ~ class_Orderings_Olinorder(U_9853) ),
inference(variable_rename,[status(thm)],[f_2521_1]) ).
fof(f_2521_3,plain,
! [U_9853,U_9854,U_9855] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9853),U_9855),c_Big__Operators_Olattice_OInf__fin(U_9853,c_Orderings_Oord__class_Omin(U_9853),U_9854)) = c_Big__Operators_Olattice_OInf__fin(U_9853,c_Orderings_Oord__class_Omin(U_9853),hAPP(c_Set_OCollect(U_9853),hAPP(hAPP(c_COMBB(tc_fun(U_9853,tc_HOL_Obool),tc_HOL_Obool,U_9853),c_HOL_OEx(U_9853)),hAPP(hAPP(c_COMBC(U_9853,tc_fun(U_9853,tc_HOL_Obool),tc_fun(U_9853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9853,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9853,tc_HOL_Obool),tc_fun(U_9853,tc_HOL_Obool)),U_9853),c_COMBS(U_9853,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9853,tc_HOL_Obool),tc_fun(U_9853,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9853),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9853),c_fconj)),hAPP(hAPP(c_COMBC(U_9853,tc_fun(U_9853,U_9853),tc_fun(U_9853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9853,tc_HOL_Obool),tc_fun(tc_fun(U_9853,U_9853),tc_fun(U_9853,tc_HOL_Obool)),U_9853),c_COMBB(U_9853,tc_HOL_Obool,U_9853)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_9853),U_9855))))),hAPP(hAPP(c_COMBC(U_9853,tc_fun(U_9853,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9853)),U_9854)))))
| U_9854 = c_Orderings_Obot__class_Obot(tc_fun(U_9853,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9853),U_9854))
| ~ class_Orderings_Olinorder(U_9853) ),
inference(definitional_conversion,[status(esa)],[f_2521_2]) ).
cnf(f_2521_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9853),U_9855),c_Big__Operators_Olattice_OInf__fin(U_9853,c_Orderings_Oord__class_Omin(U_9853),U_9854)) = c_Big__Operators_Olattice_OInf__fin(U_9853,c_Orderings_Oord__class_Omin(U_9853),hAPP(c_Set_OCollect(U_9853),hAPP(hAPP(c_COMBB(tc_fun(U_9853,tc_HOL_Obool),tc_HOL_Obool,U_9853),c_HOL_OEx(U_9853)),hAPP(hAPP(c_COMBC(U_9853,tc_fun(U_9853,tc_HOL_Obool),tc_fun(U_9853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9853,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9853,tc_HOL_Obool),tc_fun(U_9853,tc_HOL_Obool)),U_9853),c_COMBS(U_9853,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9853,tc_HOL_Obool),tc_fun(U_9853,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9853),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9853),c_fconj)),hAPP(hAPP(c_COMBC(U_9853,tc_fun(U_9853,U_9853),tc_fun(U_9853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9853,tc_HOL_Obool),tc_fun(tc_fun(U_9853,U_9853),tc_fun(U_9853,tc_HOL_Obool)),U_9853),c_COMBB(U_9853,tc_HOL_Obool,U_9853)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_9853),U_9855))))),hAPP(hAPP(c_COMBC(U_9853,tc_fun(U_9853,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9853)),U_9854)))))
| U_9854 = c_Orderings_Obot__class_Obot(tc_fun(U_9853,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9853),U_9854))
| ~ class_Orderings_Olinorder(U_9853) ),
inference(clausify,[status(thm)],[f_2521_3]) ).
fof(f_2522_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup1__distrib]) ).
fof(f_2522_2,plain,
! [U_9858,U_9857,U_9856] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9856),U_9858),c_Big__Operators_Olattice_OSup__fin(U_9856,c_Orderings_Oord__class_Omax(U_9856),U_9857)) = c_Big__Operators_Olattice_OSup__fin(U_9856,c_Orderings_Oord__class_Omax(U_9856),hAPP(c_Set_OCollect(U_9856),hAPP(hAPP(c_COMBB(tc_fun(U_9856,tc_HOL_Obool),tc_HOL_Obool,U_9856),c_HOL_OEx(U_9856)),hAPP(hAPP(c_COMBC(U_9856,tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9856,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_HOL_Obool)),U_9856),c_COMBS(U_9856,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9856),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9856),c_fconj)),hAPP(hAPP(c_COMBC(U_9856,tc_fun(U_9856,U_9856),tc_fun(U_9856,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9856,tc_HOL_Obool),tc_fun(tc_fun(U_9856,U_9856),tc_fun(U_9856,tc_HOL_Obool)),U_9856),c_COMBB(U_9856,tc_HOL_Obool,U_9856)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_9856),U_9858))))),hAPP(hAPP(c_COMBC(U_9856,tc_fun(U_9856,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9856)),U_9857)))))
| U_9857 = c_Orderings_Obot__class_Obot(tc_fun(U_9856,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9856),U_9857))
| ~ class_Orderings_Olinorder(U_9856) ),
inference(variable_rename,[status(thm)],[f_2522_1]) ).
fof(f_2522_3,plain,
! [U_9856,U_9857,U_9858] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9856),U_9858),c_Big__Operators_Olattice_OSup__fin(U_9856,c_Orderings_Oord__class_Omax(U_9856),U_9857)) = c_Big__Operators_Olattice_OSup__fin(U_9856,c_Orderings_Oord__class_Omax(U_9856),hAPP(c_Set_OCollect(U_9856),hAPP(hAPP(c_COMBB(tc_fun(U_9856,tc_HOL_Obool),tc_HOL_Obool,U_9856),c_HOL_OEx(U_9856)),hAPP(hAPP(c_COMBC(U_9856,tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9856,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_HOL_Obool)),U_9856),c_COMBS(U_9856,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9856),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9856),c_fconj)),hAPP(hAPP(c_COMBC(U_9856,tc_fun(U_9856,U_9856),tc_fun(U_9856,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9856,tc_HOL_Obool),tc_fun(tc_fun(U_9856,U_9856),tc_fun(U_9856,tc_HOL_Obool)),U_9856),c_COMBB(U_9856,tc_HOL_Obool,U_9856)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_9856),U_9858))))),hAPP(hAPP(c_COMBC(U_9856,tc_fun(U_9856,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9856)),U_9857)))))
| U_9857 = c_Orderings_Obot__class_Obot(tc_fun(U_9856,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9856),U_9857))
| ~ class_Orderings_Olinorder(U_9856) ),
inference(definitional_conversion,[status(esa)],[f_2522_2]) ).
cnf(f_2522_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9856),U_9858),c_Big__Operators_Olattice_OSup__fin(U_9856,c_Orderings_Oord__class_Omax(U_9856),U_9857)) = c_Big__Operators_Olattice_OSup__fin(U_9856,c_Orderings_Oord__class_Omax(U_9856),hAPP(c_Set_OCollect(U_9856),hAPP(hAPP(c_COMBB(tc_fun(U_9856,tc_HOL_Obool),tc_HOL_Obool,U_9856),c_HOL_OEx(U_9856)),hAPP(hAPP(c_COMBC(U_9856,tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9856,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_HOL_Obool)),U_9856),c_COMBS(U_9856,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9856),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9856),c_fconj)),hAPP(hAPP(c_COMBC(U_9856,tc_fun(U_9856,U_9856),tc_fun(U_9856,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9856,tc_HOL_Obool),tc_fun(tc_fun(U_9856,U_9856),tc_fun(U_9856,tc_HOL_Obool)),U_9856),c_COMBB(U_9856,tc_HOL_Obool,U_9856)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_9856),U_9858))))),hAPP(hAPP(c_COMBC(U_9856,tc_fun(U_9856,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9856)),U_9857)))))
| U_9857 = c_Orderings_Obot__class_Obot(tc_fun(U_9856,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9856),U_9857))
| ~ class_Orderings_Olinorder(U_9856) ),
inference(clausify,[status(thm)],[f_2522_3]) ).
fof(f_2523_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_c,c_Orderings_Oord__class_Omin(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBS(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_c),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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal))),c_Orderings_Oord__class_Omax(T_c)))))),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),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_c),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib]) ).
fof(f_2523_2,plain,
! [U_9861,U_9860,U_9859] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9859),c_Big__Operators_Olattice_OInf__fin(U_9859,c_Orderings_Oord__class_Omin(U_9859),U_9860)),c_Big__Operators_Olattice_OInf__fin(U_9859,c_Orderings_Oord__class_Omin(U_9859),U_9861)) = c_Big__Operators_Olattice_OInf__fin(U_9859,c_Orderings_Oord__class_Omin(U_9859),hAPP(c_Set_OCollect(U_9859),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_HOL_Obool,U_9859),c_HOL_OEx(U_9859)),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool)),tc_fun(U_9859,tc_HOL_Obool),U_9859),hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_HOL_Obool,U_9859),c_HOL_OEx(U_9859))),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool)),tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool))),tc_fun(tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool)),tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool))),U_9859),c_COMBS(U_9859,tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_fun(U_9859,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9859,tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool))),U_9859),hAPP(c_COMBB(tc_fun(U_9859,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool)),U_9859),c_COMBS(U_9859,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool)),tc_fun(U_9859,tc_fun(U_9859,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9859),hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9859),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9859),c_fconj))),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_fun(U_9859,U_9859)),tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9859,U_9859),tc_fun(U_9859,tc_HOL_Obool)),tc_fun(tc_fun(U_9859,tc_fun(U_9859,U_9859)),tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool))),U_9859),c_COMBB(tc_fun(U_9859,U_9859),tc_fun(U_9859,tc_HOL_Obool),U_9859)),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_fun(tc_fun(U_9859,U_9859),tc_fun(U_9859,tc_HOL_Obool)),U_9859),c_COMBB(U_9859,tc_HOL_Obool,U_9859)),c_fequal))),c_Orderings_Oord__class_Omax(U_9859)))))),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool)),U_9859),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9859)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9859),c_fconj),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9859)),U_9860)))),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9859)),U_9861)))))))
| U_9861 = c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9859),U_9861))
| U_9860 = c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9859),U_9860))
| ~ class_Orderings_Olinorder(U_9859) ),
inference(variable_rename,[status(thm)],[f_2523_1]) ).
fof(f_2523_3,plain,
! [U_9859,U_9860,U_9861] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9859),c_Big__Operators_Olattice_OInf__fin(U_9859,c_Orderings_Oord__class_Omin(U_9859),U_9860)),c_Big__Operators_Olattice_OInf__fin(U_9859,c_Orderings_Oord__class_Omin(U_9859),U_9861)) = c_Big__Operators_Olattice_OInf__fin(U_9859,c_Orderings_Oord__class_Omin(U_9859),hAPP(c_Set_OCollect(U_9859),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_HOL_Obool,U_9859),c_HOL_OEx(U_9859)),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool)),tc_fun(U_9859,tc_HOL_Obool),U_9859),hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_HOL_Obool,U_9859),c_HOL_OEx(U_9859))),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool)),tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool))),tc_fun(tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool)),tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool))),U_9859),c_COMBS(U_9859,tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_fun(U_9859,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9859,tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool))),U_9859),hAPP(c_COMBB(tc_fun(U_9859,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool)),U_9859),c_COMBS(U_9859,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool)),tc_fun(U_9859,tc_fun(U_9859,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9859),hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9859),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9859),c_fconj))),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_fun(U_9859,U_9859)),tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9859,U_9859),tc_fun(U_9859,tc_HOL_Obool)),tc_fun(tc_fun(U_9859,tc_fun(U_9859,U_9859)),tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool))),U_9859),c_COMBB(tc_fun(U_9859,U_9859),tc_fun(U_9859,tc_HOL_Obool),U_9859)),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_fun(tc_fun(U_9859,U_9859),tc_fun(U_9859,tc_HOL_Obool)),U_9859),c_COMBB(U_9859,tc_HOL_Obool,U_9859)),c_fequal))),c_Orderings_Oord__class_Omax(U_9859)))))),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool)),U_9859),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9859)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9859),c_fconj),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9859)),U_9860)))),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9859)),U_9861)))))))
| U_9861 = c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9859),U_9861))
| U_9860 = c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9859),U_9860))
| ~ class_Orderings_Olinorder(U_9859) ),
inference(definitional_conversion,[status(esa)],[f_2523_2]) ).
cnf(f_2523_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9859),c_Big__Operators_Olattice_OInf__fin(U_9859,c_Orderings_Oord__class_Omin(U_9859),U_9860)),c_Big__Operators_Olattice_OInf__fin(U_9859,c_Orderings_Oord__class_Omin(U_9859),U_9861)) = c_Big__Operators_Olattice_OInf__fin(U_9859,c_Orderings_Oord__class_Omin(U_9859),hAPP(c_Set_OCollect(U_9859),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_HOL_Obool,U_9859),c_HOL_OEx(U_9859)),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool)),tc_fun(U_9859,tc_HOL_Obool),U_9859),hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_HOL_Obool,U_9859),c_HOL_OEx(U_9859))),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool)),tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool))),tc_fun(tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool)),tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool))),U_9859),c_COMBS(U_9859,tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_fun(U_9859,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9859,tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool))),U_9859),hAPP(c_COMBB(tc_fun(U_9859,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool)),U_9859),c_COMBS(U_9859,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool)),tc_fun(U_9859,tc_fun(U_9859,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9859),hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9859),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9859),c_fconj))),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_fun(U_9859,U_9859)),tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9859,U_9859),tc_fun(U_9859,tc_HOL_Obool)),tc_fun(tc_fun(U_9859,tc_fun(U_9859,U_9859)),tc_fun(U_9859,tc_fun(U_9859,tc_HOL_Obool))),U_9859),c_COMBB(tc_fun(U_9859,U_9859),tc_fun(U_9859,tc_HOL_Obool),U_9859)),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_fun(tc_fun(U_9859,U_9859),tc_fun(U_9859,tc_HOL_Obool)),U_9859),c_COMBB(U_9859,tc_HOL_Obool,U_9859)),c_fequal))),c_Orderings_Oord__class_Omax(U_9859)))))),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool)),U_9859),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9859)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9859),c_fconj),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9859)),U_9860)))),hAPP(hAPP(c_COMBC(U_9859,tc_fun(U_9859,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9859)),U_9861)))))))
| U_9861 = c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9859),U_9861))
| U_9860 = c_Orderings_Obot__class_Obot(tc_fun(U_9859,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9859),U_9860))
| ~ class_Orderings_Olinorder(U_9859) ),
inference(clausify,[status(thm)],[f_2523_3]) ).
fof(f_2524_1,plain,
! [V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),V_A_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets]) ).
fof(f_2524_2,plain,
! [U_9863,U_9862] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9862,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_9862,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_9862,tc_HOL_Obool),tc_fun(U_9862,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_9862,tc_HOL_Obool))),U_9863))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9862),U_9863)) ),
inference(variable_rename,[status(thm)],[f_2524_1]) ).
fof(f_2524_3,plain,
! [U_9863,U_9862] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9862,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_9862,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_9862,tc_HOL_Obool),tc_fun(U_9862,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_9862,tc_HOL_Obool))),U_9863))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9862),U_9863)) ),
inference(definitional_conversion,[status(esa)],[f_2524_2]) ).
cnf(f_2524_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9862,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_9862,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_9862,tc_HOL_Obool),tc_fun(U_9862,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_9862,tc_HOL_Obool))),U_9863))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9862),U_9863)) ),
inference(clausify,[status(thm)],[f_2524_3]) ).
fof(f_2525_1,plain,
! [V_A_2,T_c] : hAPP(c_Set_OPow(T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBS(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_c))))),
inference(fof_nnf,[status(thm)],[fact_Pow__Compl]) ).
fof(f_2525_2,plain,
! [U_9865,U_9864] : hAPP(c_Set_OPow(U_9864),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9864,tc_HOL_Obool)),U_9865)) = hAPP(c_Set_OCollect(tc_fun(U_9864,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_9864,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_9864,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9864,tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_9864,tc_HOL_Obool)),c_COMBS(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_9864,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_9864,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_9864,tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_fun(U_9864,tc_HOL_Obool)),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_fun(U_9864,tc_HOL_Obool)),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_9864,tc_HOL_Obool)),c_COMBB(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_9864,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9864,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_9864,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_9864,tc_HOL_Obool)),U_9865)),c_Set_OPow(U_9864))))),
inference(variable_rename,[status(thm)],[f_2525_1]) ).
fof(f_2525_3,plain,
! [U_9864,U_9865] : hAPP(c_Set_OPow(U_9864),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9864,tc_HOL_Obool)),U_9865)) = hAPP(c_Set_OCollect(tc_fun(U_9864,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_9864,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_9864,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9864,tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_9864,tc_HOL_Obool)),c_COMBS(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_9864,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_9864,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_9864,tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_fun(U_9864,tc_HOL_Obool)),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_fun(U_9864,tc_HOL_Obool)),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_9864,tc_HOL_Obool)),c_COMBB(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_9864,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9864,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_9864,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_9864,tc_HOL_Obool)),U_9865)),c_Set_OPow(U_9864))))),
inference(definitional_conversion,[status(esa)],[f_2525_2]) ).
cnf(f_2525_4,plain,
hAPP(c_Set_OPow(U_9864),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9864,tc_HOL_Obool)),U_9865)) = hAPP(c_Set_OCollect(tc_fun(U_9864,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_9864,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_9864,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9864,tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_9864,tc_HOL_Obool)),c_COMBS(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_9864,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_9864,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_9864,tc_HOL_Obool),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_fun(U_9864,tc_HOL_Obool)),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_fun(U_9864,tc_HOL_Obool)),tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_9864,tc_HOL_Obool)),c_COMBB(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_9864,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9864,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9864,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_9864,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_9864,tc_HOL_Obool)),U_9865)),c_Set_OPow(U_9864))))),
inference(clausify,[status(thm)],[f_2525_3]) ).
fof(f_2526_1,plain,
! [V_A_2,T_c] : hAPP(c_Set_OPow(T_c),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Pow__def]) ).
fof(f_2526_2,plain,
! [U_9867,U_9866] : hAPP(c_Set_OPow(U_9866),U_9867) = hAPP(c_Set_OCollect(tc_fun(U_9866,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_9866,tc_HOL_Obool),tc_fun(U_9866,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_9866,tc_HOL_Obool))),U_9867)),
inference(variable_rename,[status(thm)],[f_2526_1]) ).
fof(f_2526_3,plain,
! [U_9866,U_9867] : hAPP(c_Set_OPow(U_9866),U_9867) = hAPP(c_Set_OCollect(tc_fun(U_9866,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_9866,tc_HOL_Obool),tc_fun(U_9866,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_9866,tc_HOL_Obool))),U_9867)),
inference(definitional_conversion,[status(esa)],[f_2526_2]) ).
cnf(f_2526_4,plain,
hAPP(c_Set_OPow(U_9866),U_9867) = hAPP(c_Set_OCollect(tc_fun(U_9866,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_9866,tc_HOL_Obool),tc_fun(U_9866,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_9866,tc_HOL_Obool))),U_9867)),
inference(clausify,[status(thm)],[f_2526_3]) ).
fof(f_2527_1,plain,
! [V_f_2,T_d,V_Pa_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_d),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_d),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_c,T_d),tc_fun(T_c,tc_HOL_Obool)),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)),V_f_2)))),V_Pa_2)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__image__set]) ).
fof(f_2527_2,plain,
! [U_9871,U_9870,U_9869,U_9868] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9870),hAPP(c_Set_OCollect(U_9870),hAPP(hAPP(c_COMBB(tc_fun(U_9868,tc_HOL_Obool),tc_HOL_Obool,U_9870),c_HOL_OEx(U_9868)),hAPP(hAPP(c_COMBC(U_9870,tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9868,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9868,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9868,tc_HOL_Obool)),U_9870),c_COMBS(U_9868,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9868,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9870),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9868),c_fconj)),hAPP(hAPP(c_COMBC(U_9870,tc_fun(U_9868,U_9870),tc_fun(U_9868,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9870,tc_HOL_Obool),tc_fun(tc_fun(U_9868,U_9870),tc_fun(U_9868,tc_HOL_Obool)),U_9870),c_COMBB(U_9870,tc_HOL_Obool,U_9868)),c_fequal)),U_9871)))),U_9869)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9868),hAPP(c_Set_OCollect(U_9868),U_9869))) ),
inference(variable_rename,[status(thm)],[f_2527_1]) ).
fof(f_2527_3,plain,
! [U_9868,U_9869,U_9870,U_9871] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9870),hAPP(c_Set_OCollect(U_9870),hAPP(hAPP(c_COMBB(tc_fun(U_9868,tc_HOL_Obool),tc_HOL_Obool,U_9870),c_HOL_OEx(U_9868)),hAPP(hAPP(c_COMBC(U_9870,tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9868,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9868,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9868,tc_HOL_Obool)),U_9870),c_COMBS(U_9868,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9868,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9870),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9868),c_fconj)),hAPP(hAPP(c_COMBC(U_9870,tc_fun(U_9868,U_9870),tc_fun(U_9868,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9870,tc_HOL_Obool),tc_fun(tc_fun(U_9868,U_9870),tc_fun(U_9868,tc_HOL_Obool)),U_9870),c_COMBB(U_9870,tc_HOL_Obool,U_9868)),c_fequal)),U_9871)))),U_9869)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9868),hAPP(c_Set_OCollect(U_9868),U_9869))) ),
inference(definitional_conversion,[status(esa)],[f_2527_2]) ).
cnf(f_2527_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9870),hAPP(c_Set_OCollect(U_9870),hAPP(hAPP(c_COMBB(tc_fun(U_9868,tc_HOL_Obool),tc_HOL_Obool,U_9870),c_HOL_OEx(U_9868)),hAPP(hAPP(c_COMBC(U_9870,tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9868,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9868,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9868,tc_HOL_Obool)),U_9870),c_COMBS(U_9868,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9868,tc_HOL_Obool),tc_fun(U_9868,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9870),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9868),c_fconj)),hAPP(hAPP(c_COMBC(U_9870,tc_fun(U_9868,U_9870),tc_fun(U_9868,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9870,tc_HOL_Obool),tc_fun(tc_fun(U_9868,U_9870),tc_fun(U_9868,tc_HOL_Obool)),U_9870),c_COMBB(U_9870,tc_HOL_Obool,U_9868)),c_fequal)),U_9871)))),U_9869)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9868),hAPP(c_Set_OCollect(U_9868),U_9869))) ),
inference(clausify,[status(thm)],[f_2527_3]) ).
fof(f_2528_1,plain,
! [V_Qa_2,T_d,V_Pa_2,T_c] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),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),V_Pa_2))),V_Qa_2)))))
| ? [B_y] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBC(T_d,T_c,tc_HOL_Obool),V_Qa_2),B_y))))
& hBOOL(hAPP(V_Pa_2,B_y)) ) )
& ( ! [B_y] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBC(T_d,T_c,tc_HOL_Obool),V_Qa_2),B_y))))
| ~ hBOOL(hAPP(V_Pa_2,B_y)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),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),V_Pa_2))),V_Qa_2))))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),V_Pa_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__bounded__ex]) ).
fof(f_2528_2,plain,
! [U_9877,U_9876,U_9875,U_9874] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_HOL_Obool,U_9876),c_HOL_OEx(U_9874)),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_fun(U_9874,tc_HOL_Obool),U_9876),hAPP(c_COMBS(U_9874,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9874),c_fconj),U_9875))),U_9877)))))
| ? [U_9873] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBC(U_9876,U_9874,tc_HOL_Obool),U_9877),U_9873))))
& hBOOL(hAPP(U_9875,U_9873)) ) )
& ( ! [U_9872] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBC(U_9876,U_9874,tc_HOL_Obool),U_9877),U_9872))))
| ~ hBOOL(hAPP(U_9875,U_9872)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_HOL_Obool,U_9876),c_HOL_OEx(U_9874)),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_fun(U_9874,tc_HOL_Obool),U_9876),hAPP(c_COMBS(U_9874,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9874),c_fconj),U_9875))),U_9877))))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9874),hAPP(c_Set_OCollect(U_9874),U_9875))) ),
inference(variable_rename,[status(thm)],[f_2528_1]) ).
fof(f_2528_3,plain,
! [U_9877,U_9876,U_9875,U_9874] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_HOL_Obool,U_9876),c_HOL_OEx(U_9874)),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_fun(U_9874,tc_HOL_Obool),U_9876),hAPP(c_COMBS(U_9874,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9874),c_fconj),U_9875))),U_9877)))))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBC(U_9876,U_9874,tc_HOL_Obool),U_9877),sK250(U_9877,U_9876,U_9875,U_9874)))))
& hBOOL(hAPP(U_9875,sK250(U_9877,U_9876,U_9875,U_9874))) ) )
& ( ! [U_9872] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBC(U_9876,U_9874,tc_HOL_Obool),U_9877),U_9872))))
| ~ hBOOL(hAPP(U_9875,U_9872)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_HOL_Obool,U_9876),c_HOL_OEx(U_9874)),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_fun(U_9874,tc_HOL_Obool),U_9876),hAPP(c_COMBS(U_9874,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9874),c_fconj),U_9875))),U_9877))))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9874),hAPP(c_Set_OCollect(U_9874),U_9875))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_9873,sK250(U_9877,U_9876,U_9875,U_9874))],[f_2528_2]) ).
fof(f_2528_4,plain,
( ! [U_9874,U_9875,U_9876,U_9877] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBC(U_9876,U_9874,tc_HOL_Obool),U_9877),sK250(U_9877,U_9876,U_9875,U_9874)))))
| ~ sP685(U_9874,U_9875,U_9876,U_9877) )
& ! [U_9874,U_9875,U_9876,U_9877] :
( hBOOL(hAPP(U_9875,sK250(U_9877,U_9876,U_9875,U_9874)))
| ~ sP685(U_9874,U_9875,U_9876,U_9877) )
& ! [U_9872,U_9874,U_9875,U_9876,U_9877] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_HOL_Obool,U_9876),c_HOL_OEx(U_9874)),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_fun(U_9874,tc_HOL_Obool),U_9876),hAPP(c_COMBS(U_9874,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9874),c_fconj),U_9875))),U_9877)))))
| sP685(U_9874,U_9875,U_9876,U_9877)
| ~ sP686(U_9872,U_9874,U_9875,U_9876,U_9877) )
& ! [U_9872,U_9874,U_9875,U_9876,U_9877] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBC(U_9876,U_9874,tc_HOL_Obool),U_9877),U_9872))))
| ~ hBOOL(hAPP(U_9875,U_9872))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_HOL_Obool,U_9876),c_HOL_OEx(U_9874)),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_fun(U_9874,tc_HOL_Obool),U_9876),hAPP(c_COMBS(U_9874,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9874),c_fconj),U_9875))),U_9877)))))
| ~ sP686(U_9872,U_9874,U_9875,U_9876,U_9877) )
& ! [U_9872,U_9874,U_9875,U_9876,U_9877] :
( sP686(U_9872,U_9874,U_9875,U_9876,U_9877)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9874),hAPP(c_Set_OCollect(U_9874),U_9875))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP685,sP686])],[f_2528_3]) ).
cnf(f_2528_5,plain,
( sP686(U_9872,U_9874,U_9875,U_9876,U_9877)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9874),hAPP(c_Set_OCollect(U_9874),U_9875))) ),
inference(clausify,[status(thm)],[f_2528_4]) ).
cnf(f_2528_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBC(U_9876,U_9874,tc_HOL_Obool),U_9877),U_9872))))
| ~ hBOOL(hAPP(U_9875,U_9872))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_HOL_Obool,U_9876),c_HOL_OEx(U_9874)),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_fun(U_9874,tc_HOL_Obool),U_9876),hAPP(c_COMBS(U_9874,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9874),c_fconj),U_9875))),U_9877)))))
| ~ sP686(U_9872,U_9874,U_9875,U_9876,U_9877) ),
inference(clausify,[status(thm)],[f_2528_4]) ).
cnf(f_2528_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_HOL_Obool,U_9876),c_HOL_OEx(U_9874)),hAPP(hAPP(c_COMBB(tc_fun(U_9874,tc_HOL_Obool),tc_fun(U_9874,tc_HOL_Obool),U_9876),hAPP(c_COMBS(U_9874,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9874),c_fconj),U_9875))),U_9877)))))
| sP685(U_9874,U_9875,U_9876,U_9877)
| ~ sP686(U_9872,U_9874,U_9875,U_9876,U_9877) ),
inference(clausify,[status(thm)],[f_2528_4]) ).
cnf(f_2528_8,plain,
( hBOOL(hAPP(U_9875,sK250(U_9877,U_9876,U_9875,U_9874)))
| ~ sP685(U_9874,U_9875,U_9876,U_9877) ),
inference(clausify,[status(thm)],[f_2528_4]) ).
cnf(f_2528_9,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9876),hAPP(c_Set_OCollect(U_9876),hAPP(hAPP(c_COMBC(U_9876,U_9874,tc_HOL_Obool),U_9877),sK250(U_9877,U_9876,U_9875,U_9874)))))
| ~ sP685(U_9874,U_9875,U_9876,U_9877) ),
inference(clausify,[status(thm)],[f_2528_4]) ).
fof(f_2529_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_2529_2,plain,
! [U_9878] : 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_9878))),
inference(variable_rename,[status(thm)],[f_2529_1]) ).
fof(f_2529_3,plain,
! [U_9878] : 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_9878))),
inference(definitional_conversion,[status(esa)],[f_2529_2]) ).
cnf(f_2529_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_9878))),
inference(clausify,[status(thm)],[f_2529_3]) ).
fof(f_2530_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_2530_2,plain,
! [U_9879] : 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_9879)) = 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_9879),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_2530_1]) ).
fof(f_2530_3,plain,
! [U_9879] : 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_9879)) = 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_9879),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(definitional_conversion,[status(esa)],[f_2530_2]) ).
cnf(f_2530_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_9879)) = 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_9879),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_2530_3]) ).
fof(f_2531_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_2531_2,plain,
! [U_9880] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_9880) = 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_9880),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_2531_1]) ).
fof(f_2531_3,plain,
! [U_9880] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_9880) = 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_9880),c_Int_Onat)))),
inference(definitional_conversion,[status(esa)],[f_2531_2]) ).
cnf(f_2531_4,plain,
hAPP(c_Set_OCollect(tc_Nat_Onat),U_9880) = 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_9880),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_2531_3]) ).
fof(f_2532_1,plain,
! [V_k_2,V_N_2,T_c] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_c,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_c),V_k_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_N_2)))))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
| ~ class_Groups_Olinordered__ab__semigroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_add__Min__commute]) ).
fof(f_2532_2,plain,
! [U_9883,U_9882,U_9881] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9881),U_9883),c_Big__Operators_Olinorder__class_OMin(U_9881,U_9882)) = c_Big__Operators_Olinorder__class_OMin(U_9881,hAPP(c_Set_OCollect(U_9881),hAPP(hAPP(c_COMBB(tc_fun(U_9881,tc_HOL_Obool),tc_HOL_Obool,U_9881),c_HOL_OEx(U_9881)),hAPP(hAPP(c_COMBC(U_9881,tc_fun(U_9881,tc_HOL_Obool),tc_fun(U_9881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9881,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9881,tc_HOL_Obool),tc_fun(U_9881,tc_HOL_Obool)),U_9881),c_COMBS(U_9881,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9881,tc_HOL_Obool),tc_fun(U_9881,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9881),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9881),c_fconj)),hAPP(hAPP(c_COMBC(U_9881,tc_fun(U_9881,U_9881),tc_fun(U_9881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9881,tc_HOL_Obool),tc_fun(tc_fun(U_9881,U_9881),tc_fun(U_9881,tc_HOL_Obool)),U_9881),c_COMBB(U_9881,tc_HOL_Obool,U_9881)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_9881),U_9883))))),hAPP(hAPP(c_COMBC(U_9881,tc_fun(U_9881,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9881)),U_9882)))))
| U_9882 = c_Orderings_Obot__class_Obot(tc_fun(U_9881,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9881),U_9882))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_9881) ),
inference(variable_rename,[status(thm)],[f_2532_1]) ).
fof(f_2532_3,plain,
! [U_9881,U_9882,U_9883] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9881),U_9883),c_Big__Operators_Olinorder__class_OMin(U_9881,U_9882)) = c_Big__Operators_Olinorder__class_OMin(U_9881,hAPP(c_Set_OCollect(U_9881),hAPP(hAPP(c_COMBB(tc_fun(U_9881,tc_HOL_Obool),tc_HOL_Obool,U_9881),c_HOL_OEx(U_9881)),hAPP(hAPP(c_COMBC(U_9881,tc_fun(U_9881,tc_HOL_Obool),tc_fun(U_9881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9881,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9881,tc_HOL_Obool),tc_fun(U_9881,tc_HOL_Obool)),U_9881),c_COMBS(U_9881,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9881,tc_HOL_Obool),tc_fun(U_9881,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9881),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9881),c_fconj)),hAPP(hAPP(c_COMBC(U_9881,tc_fun(U_9881,U_9881),tc_fun(U_9881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9881,tc_HOL_Obool),tc_fun(tc_fun(U_9881,U_9881),tc_fun(U_9881,tc_HOL_Obool)),U_9881),c_COMBB(U_9881,tc_HOL_Obool,U_9881)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_9881),U_9883))))),hAPP(hAPP(c_COMBC(U_9881,tc_fun(U_9881,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9881)),U_9882)))))
| U_9882 = c_Orderings_Obot__class_Obot(tc_fun(U_9881,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9881),U_9882))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_9881) ),
inference(definitional_conversion,[status(esa)],[f_2532_2]) ).
cnf(f_2532_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9881),U_9883),c_Big__Operators_Olinorder__class_OMin(U_9881,U_9882)) = c_Big__Operators_Olinorder__class_OMin(U_9881,hAPP(c_Set_OCollect(U_9881),hAPP(hAPP(c_COMBB(tc_fun(U_9881,tc_HOL_Obool),tc_HOL_Obool,U_9881),c_HOL_OEx(U_9881)),hAPP(hAPP(c_COMBC(U_9881,tc_fun(U_9881,tc_HOL_Obool),tc_fun(U_9881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9881,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9881,tc_HOL_Obool),tc_fun(U_9881,tc_HOL_Obool)),U_9881),c_COMBS(U_9881,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9881,tc_HOL_Obool),tc_fun(U_9881,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9881),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9881),c_fconj)),hAPP(hAPP(c_COMBC(U_9881,tc_fun(U_9881,U_9881),tc_fun(U_9881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9881,tc_HOL_Obool),tc_fun(tc_fun(U_9881,U_9881),tc_fun(U_9881,tc_HOL_Obool)),U_9881),c_COMBB(U_9881,tc_HOL_Obool,U_9881)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_9881),U_9883))))),hAPP(hAPP(c_COMBC(U_9881,tc_fun(U_9881,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9881)),U_9882)))))
| U_9882 = c_Orderings_Obot__class_Obot(tc_fun(U_9881,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9881),U_9882))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_9881) ),
inference(clausify,[status(thm)],[f_2532_3]) ).
fof(f_2533_1,plain,
! [V_k_2,V_N_2,T_c] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_c,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_c),V_k_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_N_2)))))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_N_2))
| ~ class_Groups_Olinordered__ab__semigroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_add__Max__commute]) ).
fof(f_2533_2,plain,
! [U_9886,U_9885,U_9884] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9884),U_9886),c_Big__Operators_Olinorder__class_OMax(U_9884,U_9885)) = c_Big__Operators_Olinorder__class_OMax(U_9884,hAPP(c_Set_OCollect(U_9884),hAPP(hAPP(c_COMBB(tc_fun(U_9884,tc_HOL_Obool),tc_HOL_Obool,U_9884),c_HOL_OEx(U_9884)),hAPP(hAPP(c_COMBC(U_9884,tc_fun(U_9884,tc_HOL_Obool),tc_fun(U_9884,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9884,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9884,tc_HOL_Obool),tc_fun(U_9884,tc_HOL_Obool)),U_9884),c_COMBS(U_9884,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9884,tc_HOL_Obool),tc_fun(U_9884,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9884),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9884),c_fconj)),hAPP(hAPP(c_COMBC(U_9884,tc_fun(U_9884,U_9884),tc_fun(U_9884,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9884,tc_HOL_Obool),tc_fun(tc_fun(U_9884,U_9884),tc_fun(U_9884,tc_HOL_Obool)),U_9884),c_COMBB(U_9884,tc_HOL_Obool,U_9884)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_9884),U_9886))))),hAPP(hAPP(c_COMBC(U_9884,tc_fun(U_9884,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9884)),U_9885)))))
| U_9885 = c_Orderings_Obot__class_Obot(tc_fun(U_9884,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9884),U_9885))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_9884) ),
inference(variable_rename,[status(thm)],[f_2533_1]) ).
fof(f_2533_3,plain,
! [U_9884,U_9885,U_9886] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9884),U_9886),c_Big__Operators_Olinorder__class_OMax(U_9884,U_9885)) = c_Big__Operators_Olinorder__class_OMax(U_9884,hAPP(c_Set_OCollect(U_9884),hAPP(hAPP(c_COMBB(tc_fun(U_9884,tc_HOL_Obool),tc_HOL_Obool,U_9884),c_HOL_OEx(U_9884)),hAPP(hAPP(c_COMBC(U_9884,tc_fun(U_9884,tc_HOL_Obool),tc_fun(U_9884,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9884,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9884,tc_HOL_Obool),tc_fun(U_9884,tc_HOL_Obool)),U_9884),c_COMBS(U_9884,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9884,tc_HOL_Obool),tc_fun(U_9884,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9884),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9884),c_fconj)),hAPP(hAPP(c_COMBC(U_9884,tc_fun(U_9884,U_9884),tc_fun(U_9884,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9884,tc_HOL_Obool),tc_fun(tc_fun(U_9884,U_9884),tc_fun(U_9884,tc_HOL_Obool)),U_9884),c_COMBB(U_9884,tc_HOL_Obool,U_9884)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_9884),U_9886))))),hAPP(hAPP(c_COMBC(U_9884,tc_fun(U_9884,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9884)),U_9885)))))
| U_9885 = c_Orderings_Obot__class_Obot(tc_fun(U_9884,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9884),U_9885))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_9884) ),
inference(definitional_conversion,[status(esa)],[f_2533_2]) ).
cnf(f_2533_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9884),U_9886),c_Big__Operators_Olinorder__class_OMax(U_9884,U_9885)) = c_Big__Operators_Olinorder__class_OMax(U_9884,hAPP(c_Set_OCollect(U_9884),hAPP(hAPP(c_COMBB(tc_fun(U_9884,tc_HOL_Obool),tc_HOL_Obool,U_9884),c_HOL_OEx(U_9884)),hAPP(hAPP(c_COMBC(U_9884,tc_fun(U_9884,tc_HOL_Obool),tc_fun(U_9884,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9884,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9884,tc_HOL_Obool),tc_fun(U_9884,tc_HOL_Obool)),U_9884),c_COMBS(U_9884,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9884,tc_HOL_Obool),tc_fun(U_9884,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9884),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9884),c_fconj)),hAPP(hAPP(c_COMBC(U_9884,tc_fun(U_9884,U_9884),tc_fun(U_9884,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9884,tc_HOL_Obool),tc_fun(tc_fun(U_9884,U_9884),tc_fun(U_9884,tc_HOL_Obool)),U_9884),c_COMBB(U_9884,tc_HOL_Obool,U_9884)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_9884),U_9886))))),hAPP(hAPP(c_COMBC(U_9884,tc_fun(U_9884,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9884)),U_9885)))))
| U_9885 = c_Orderings_Obot__class_Obot(tc_fun(U_9884,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9884),U_9885))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_9884) ),
inference(clausify,[status(thm)],[f_2533_3]) ).
fof(f_2534_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBS(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_c),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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_c)))))),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),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_c),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Odistrib__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sup__Inf2__distrib]) ).
fof(f_2534_2,plain,
! [U_9889,U_9888,U_9887] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9887),c_Big__Operators_Olattice__class_OInf__fin(U_9887,U_9888)),c_Big__Operators_Olattice__class_OInf__fin(U_9887,U_9889)) = c_Big__Operators_Olattice__class_OInf__fin(U_9887,hAPP(c_Set_OCollect(U_9887),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_HOL_Obool),tc_HOL_Obool,U_9887),c_HOL_OEx(U_9887)),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool)),tc_fun(U_9887,tc_HOL_Obool),U_9887),hAPP(c_COMBB(tc_fun(U_9887,tc_HOL_Obool),tc_HOL_Obool,U_9887),c_HOL_OEx(U_9887))),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool)),tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_fun(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool))),tc_fun(tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool)),tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool))),U_9887),c_COMBS(U_9887,tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_fun(U_9887,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9887,tc_fun(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool))),U_9887),hAPP(c_COMBB(tc_fun(U_9887,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool)),U_9887),c_COMBS(U_9887,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool)),tc_fun(U_9887,tc_fun(U_9887,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9887),hAPP(c_COMBB(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9887),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9887),c_fconj))),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_fun(U_9887,U_9887)),tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9887,U_9887),tc_fun(U_9887,tc_HOL_Obool)),tc_fun(tc_fun(U_9887,tc_fun(U_9887,U_9887)),tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool))),U_9887),c_COMBB(tc_fun(U_9887,U_9887),tc_fun(U_9887,tc_HOL_Obool),U_9887)),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_HOL_Obool),tc_fun(tc_fun(U_9887,U_9887),tc_fun(U_9887,tc_HOL_Obool)),U_9887),c_COMBB(U_9887,tc_HOL_Obool,U_9887)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_9887)))))),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool)),U_9887),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9887)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9887),c_fconj),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9887)),U_9888)))),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9887)),U_9889)))))))
| U_9889 = c_Orderings_Obot__class_Obot(tc_fun(U_9887,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9887),U_9889))
| U_9888 = c_Orderings_Obot__class_Obot(tc_fun(U_9887,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9887),U_9888))
| ~ class_Lattices_Odistrib__lattice(U_9887) ),
inference(variable_rename,[status(thm)],[f_2534_1]) ).
fof(f_2534_3,plain,
! [U_9887,U_9888,U_9889] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9887),c_Big__Operators_Olattice__class_OInf__fin(U_9887,U_9888)),c_Big__Operators_Olattice__class_OInf__fin(U_9887,U_9889)) = c_Big__Operators_Olattice__class_OInf__fin(U_9887,hAPP(c_Set_OCollect(U_9887),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_HOL_Obool),tc_HOL_Obool,U_9887),c_HOL_OEx(U_9887)),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool)),tc_fun(U_9887,tc_HOL_Obool),U_9887),hAPP(c_COMBB(tc_fun(U_9887,tc_HOL_Obool),tc_HOL_Obool,U_9887),c_HOL_OEx(U_9887))),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool)),tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_fun(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool))),tc_fun(tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool)),tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool))),U_9887),c_COMBS(U_9887,tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_fun(U_9887,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9887,tc_fun(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool))),U_9887),hAPP(c_COMBB(tc_fun(U_9887,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool)),U_9887),c_COMBS(U_9887,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool)),tc_fun(U_9887,tc_fun(U_9887,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9887),hAPP(c_COMBB(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9887),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9887),c_fconj))),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_fun(U_9887,U_9887)),tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9887,U_9887),tc_fun(U_9887,tc_HOL_Obool)),tc_fun(tc_fun(U_9887,tc_fun(U_9887,U_9887)),tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool))),U_9887),c_COMBB(tc_fun(U_9887,U_9887),tc_fun(U_9887,tc_HOL_Obool),U_9887)),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_HOL_Obool),tc_fun(tc_fun(U_9887,U_9887),tc_fun(U_9887,tc_HOL_Obool)),U_9887),c_COMBB(U_9887,tc_HOL_Obool,U_9887)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_9887)))))),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool)),U_9887),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9887)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9887),c_fconj),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9887)),U_9888)))),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9887)),U_9889)))))))
| U_9889 = c_Orderings_Obot__class_Obot(tc_fun(U_9887,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9887),U_9889))
| U_9888 = c_Orderings_Obot__class_Obot(tc_fun(U_9887,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9887),U_9888))
| ~ class_Lattices_Odistrib__lattice(U_9887) ),
inference(definitional_conversion,[status(esa)],[f_2534_2]) ).
cnf(f_2534_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9887),c_Big__Operators_Olattice__class_OInf__fin(U_9887,U_9888)),c_Big__Operators_Olattice__class_OInf__fin(U_9887,U_9889)) = c_Big__Operators_Olattice__class_OInf__fin(U_9887,hAPP(c_Set_OCollect(U_9887),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_HOL_Obool),tc_HOL_Obool,U_9887),c_HOL_OEx(U_9887)),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool)),tc_fun(U_9887,tc_HOL_Obool),U_9887),hAPP(c_COMBB(tc_fun(U_9887,tc_HOL_Obool),tc_HOL_Obool,U_9887),c_HOL_OEx(U_9887))),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool)),tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_fun(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool))),tc_fun(tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool)),tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool))),U_9887),c_COMBS(U_9887,tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_fun(U_9887,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9887,tc_fun(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool))),U_9887),hAPP(c_COMBB(tc_fun(U_9887,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool)),U_9887),c_COMBS(U_9887,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool)),tc_fun(U_9887,tc_fun(U_9887,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9887),hAPP(c_COMBB(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9887),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9887),c_fconj))),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_fun(U_9887,U_9887)),tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9887,U_9887),tc_fun(U_9887,tc_HOL_Obool)),tc_fun(tc_fun(U_9887,tc_fun(U_9887,U_9887)),tc_fun(U_9887,tc_fun(U_9887,tc_HOL_Obool))),U_9887),c_COMBB(tc_fun(U_9887,U_9887),tc_fun(U_9887,tc_HOL_Obool),U_9887)),hAPP(hAPP(c_COMBB(tc_fun(U_9887,tc_HOL_Obool),tc_fun(tc_fun(U_9887,U_9887),tc_fun(U_9887,tc_HOL_Obool)),U_9887),c_COMBB(U_9887,tc_HOL_Obool,U_9887)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_9887)))))),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9887,tc_HOL_Obool),tc_fun(U_9887,tc_HOL_Obool)),U_9887),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9887)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9887),c_fconj),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9887)),U_9888)))),hAPP(hAPP(c_COMBC(U_9887,tc_fun(U_9887,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9887)),U_9889)))))))
| U_9889 = c_Orderings_Obot__class_Obot(tc_fun(U_9887,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9887),U_9889))
| U_9888 = c_Orderings_Obot__class_Obot(tc_fun(U_9887,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9887),U_9888))
| ~ class_Lattices_Odistrib__lattice(U_9887) ),
inference(clausify,[status(thm)],[f_2534_3]) ).
fof(f_2535_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Odistrib__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib]) ).
fof(f_2535_2,plain,
! [U_9892,U_9891,U_9890] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9890),U_9892),c_Big__Operators_Olattice__class_OInf__fin(U_9890,U_9891)) = c_Big__Operators_Olattice__class_OInf__fin(U_9890,hAPP(c_Set_OCollect(U_9890),hAPP(hAPP(c_COMBB(tc_fun(U_9890,tc_HOL_Obool),tc_HOL_Obool,U_9890),c_HOL_OEx(U_9890)),hAPP(hAPP(c_COMBC(U_9890,tc_fun(U_9890,tc_HOL_Obool),tc_fun(U_9890,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9890,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9890,tc_HOL_Obool),tc_fun(U_9890,tc_HOL_Obool)),U_9890),c_COMBS(U_9890,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9890,tc_HOL_Obool),tc_fun(U_9890,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9890),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9890),c_fconj)),hAPP(hAPP(c_COMBC(U_9890,tc_fun(U_9890,U_9890),tc_fun(U_9890,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9890,tc_HOL_Obool),tc_fun(tc_fun(U_9890,U_9890),tc_fun(U_9890,tc_HOL_Obool)),U_9890),c_COMBB(U_9890,tc_HOL_Obool,U_9890)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9890),U_9892))))),hAPP(hAPP(c_COMBC(U_9890,tc_fun(U_9890,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9890)),U_9891)))))
| U_9891 = c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9890),U_9891))
| ~ class_Lattices_Odistrib__lattice(U_9890) ),
inference(variable_rename,[status(thm)],[f_2535_1]) ).
fof(f_2535_3,plain,
! [U_9891,U_9890,U_9892] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9890),U_9892),c_Big__Operators_Olattice__class_OInf__fin(U_9890,U_9891)) = c_Big__Operators_Olattice__class_OInf__fin(U_9890,hAPP(c_Set_OCollect(U_9890),hAPP(hAPP(c_COMBB(tc_fun(U_9890,tc_HOL_Obool),tc_HOL_Obool,U_9890),c_HOL_OEx(U_9890)),hAPP(hAPP(c_COMBC(U_9890,tc_fun(U_9890,tc_HOL_Obool),tc_fun(U_9890,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9890,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9890,tc_HOL_Obool),tc_fun(U_9890,tc_HOL_Obool)),U_9890),c_COMBS(U_9890,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9890,tc_HOL_Obool),tc_fun(U_9890,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9890),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9890),c_fconj)),hAPP(hAPP(c_COMBC(U_9890,tc_fun(U_9890,U_9890),tc_fun(U_9890,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9890,tc_HOL_Obool),tc_fun(tc_fun(U_9890,U_9890),tc_fun(U_9890,tc_HOL_Obool)),U_9890),c_COMBB(U_9890,tc_HOL_Obool,U_9890)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9890),U_9892))))),hAPP(hAPP(c_COMBC(U_9890,tc_fun(U_9890,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9890)),U_9891)))))
| U_9891 = c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9890),U_9891))
| ~ class_Lattices_Odistrib__lattice(U_9890) ),
inference(definitional_conversion,[status(esa)],[f_2535_2]) ).
cnf(f_2535_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9890),U_9892),c_Big__Operators_Olattice__class_OInf__fin(U_9890,U_9891)) = c_Big__Operators_Olattice__class_OInf__fin(U_9890,hAPP(c_Set_OCollect(U_9890),hAPP(hAPP(c_COMBB(tc_fun(U_9890,tc_HOL_Obool),tc_HOL_Obool,U_9890),c_HOL_OEx(U_9890)),hAPP(hAPP(c_COMBC(U_9890,tc_fun(U_9890,tc_HOL_Obool),tc_fun(U_9890,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9890,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9890,tc_HOL_Obool),tc_fun(U_9890,tc_HOL_Obool)),U_9890),c_COMBS(U_9890,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9890,tc_HOL_Obool),tc_fun(U_9890,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9890),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9890),c_fconj)),hAPP(hAPP(c_COMBC(U_9890,tc_fun(U_9890,U_9890),tc_fun(U_9890,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9890,tc_HOL_Obool),tc_fun(tc_fun(U_9890,U_9890),tc_fun(U_9890,tc_HOL_Obool)),U_9890),c_COMBB(U_9890,tc_HOL_Obool,U_9890)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9890),U_9892))))),hAPP(hAPP(c_COMBC(U_9890,tc_fun(U_9890,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9890)),U_9891)))))
| U_9891 = c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9890),U_9891))
| ~ class_Lattices_Odistrib__lattice(U_9890) ),
inference(clausify,[status(thm)],[f_2535_3]) ).
fof(f_2536_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBS(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_c),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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_c)))))),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),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_c),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Odistrib__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inf__Sup2__distrib]) ).
fof(f_2536_2,plain,
! [U_9895,U_9894,U_9893] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9893),c_Big__Operators_Olattice__class_OSup__fin(U_9893,U_9894)),c_Big__Operators_Olattice__class_OSup__fin(U_9893,U_9895)) = c_Big__Operators_Olattice__class_OSup__fin(U_9893,hAPP(c_Set_OCollect(U_9893),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_HOL_Obool),tc_HOL_Obool,U_9893),c_HOL_OEx(U_9893)),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool)),tc_fun(U_9893,tc_HOL_Obool),U_9893),hAPP(c_COMBB(tc_fun(U_9893,tc_HOL_Obool),tc_HOL_Obool,U_9893),c_HOL_OEx(U_9893))),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool)),tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_fun(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool))),tc_fun(tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool)),tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool))),U_9893),c_COMBS(U_9893,tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_fun(U_9893,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9893,tc_fun(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool))),U_9893),hAPP(c_COMBB(tc_fun(U_9893,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool)),U_9893),c_COMBS(U_9893,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool)),tc_fun(U_9893,tc_fun(U_9893,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9893),hAPP(c_COMBB(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9893),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9893),c_fconj))),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_fun(U_9893,U_9893)),tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9893,U_9893),tc_fun(U_9893,tc_HOL_Obool)),tc_fun(tc_fun(U_9893,tc_fun(U_9893,U_9893)),tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool))),U_9893),c_COMBB(tc_fun(U_9893,U_9893),tc_fun(U_9893,tc_HOL_Obool),U_9893)),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_HOL_Obool),tc_fun(tc_fun(U_9893,U_9893),tc_fun(U_9893,tc_HOL_Obool)),U_9893),c_COMBB(U_9893,tc_HOL_Obool,U_9893)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_9893)))))),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool)),U_9893),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9893)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9893),c_fconj),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9893)),U_9894)))),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9893)),U_9895)))))))
| U_9895 = c_Orderings_Obot__class_Obot(tc_fun(U_9893,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9893),U_9895))
| U_9894 = c_Orderings_Obot__class_Obot(tc_fun(U_9893,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9893),U_9894))
| ~ class_Lattices_Odistrib__lattice(U_9893) ),
inference(variable_rename,[status(thm)],[f_2536_1]) ).
fof(f_2536_3,plain,
! [U_9893,U_9894,U_9895] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9893),c_Big__Operators_Olattice__class_OSup__fin(U_9893,U_9894)),c_Big__Operators_Olattice__class_OSup__fin(U_9893,U_9895)) = c_Big__Operators_Olattice__class_OSup__fin(U_9893,hAPP(c_Set_OCollect(U_9893),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_HOL_Obool),tc_HOL_Obool,U_9893),c_HOL_OEx(U_9893)),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool)),tc_fun(U_9893,tc_HOL_Obool),U_9893),hAPP(c_COMBB(tc_fun(U_9893,tc_HOL_Obool),tc_HOL_Obool,U_9893),c_HOL_OEx(U_9893))),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool)),tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_fun(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool))),tc_fun(tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool)),tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool))),U_9893),c_COMBS(U_9893,tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_fun(U_9893,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9893,tc_fun(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool))),U_9893),hAPP(c_COMBB(tc_fun(U_9893,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool)),U_9893),c_COMBS(U_9893,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool)),tc_fun(U_9893,tc_fun(U_9893,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9893),hAPP(c_COMBB(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9893),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9893),c_fconj))),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_fun(U_9893,U_9893)),tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9893,U_9893),tc_fun(U_9893,tc_HOL_Obool)),tc_fun(tc_fun(U_9893,tc_fun(U_9893,U_9893)),tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool))),U_9893),c_COMBB(tc_fun(U_9893,U_9893),tc_fun(U_9893,tc_HOL_Obool),U_9893)),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_HOL_Obool),tc_fun(tc_fun(U_9893,U_9893),tc_fun(U_9893,tc_HOL_Obool)),U_9893),c_COMBB(U_9893,tc_HOL_Obool,U_9893)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_9893)))))),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool)),U_9893),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9893)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9893),c_fconj),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9893)),U_9894)))),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9893)),U_9895)))))))
| U_9895 = c_Orderings_Obot__class_Obot(tc_fun(U_9893,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9893),U_9895))
| U_9894 = c_Orderings_Obot__class_Obot(tc_fun(U_9893,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9893),U_9894))
| ~ class_Lattices_Odistrib__lattice(U_9893) ),
inference(definitional_conversion,[status(esa)],[f_2536_2]) ).
cnf(f_2536_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9893),c_Big__Operators_Olattice__class_OSup__fin(U_9893,U_9894)),c_Big__Operators_Olattice__class_OSup__fin(U_9893,U_9895)) = c_Big__Operators_Olattice__class_OSup__fin(U_9893,hAPP(c_Set_OCollect(U_9893),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_HOL_Obool),tc_HOL_Obool,U_9893),c_HOL_OEx(U_9893)),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool)),tc_fun(U_9893,tc_HOL_Obool),U_9893),hAPP(c_COMBB(tc_fun(U_9893,tc_HOL_Obool),tc_HOL_Obool,U_9893),c_HOL_OEx(U_9893))),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool)),tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_fun(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool))),tc_fun(tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool)),tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool))),U_9893),c_COMBS(U_9893,tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_fun(U_9893,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9893,tc_fun(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool))),U_9893),hAPP(c_COMBB(tc_fun(U_9893,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool)),U_9893),c_COMBS(U_9893,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool)),tc_fun(U_9893,tc_fun(U_9893,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9893),hAPP(c_COMBB(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9893),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9893),c_fconj))),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_fun(U_9893,U_9893)),tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9893,U_9893),tc_fun(U_9893,tc_HOL_Obool)),tc_fun(tc_fun(U_9893,tc_fun(U_9893,U_9893)),tc_fun(U_9893,tc_fun(U_9893,tc_HOL_Obool))),U_9893),c_COMBB(tc_fun(U_9893,U_9893),tc_fun(U_9893,tc_HOL_Obool),U_9893)),hAPP(hAPP(c_COMBB(tc_fun(U_9893,tc_HOL_Obool),tc_fun(tc_fun(U_9893,U_9893),tc_fun(U_9893,tc_HOL_Obool)),U_9893),c_COMBB(U_9893,tc_HOL_Obool,U_9893)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_9893)))))),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9893,tc_HOL_Obool),tc_fun(U_9893,tc_HOL_Obool)),U_9893),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9893)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9893),c_fconj),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9893)),U_9894)))),hAPP(hAPP(c_COMBC(U_9893,tc_fun(U_9893,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9893)),U_9895)))))))
| U_9895 = c_Orderings_Obot__class_Obot(tc_fun(U_9893,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9893),U_9895))
| U_9894 = c_Orderings_Obot__class_Obot(tc_fun(U_9893,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9893),U_9894))
| ~ class_Lattices_Odistrib__lattice(U_9893) ),
inference(clausify,[status(thm)],[f_2536_3]) ).
fof(f_2537_1,plain,
! [V_x_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_c,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_c,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_x_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Odistrib__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib]) ).
fof(f_2537_2,plain,
! [U_9898,U_9897,U_9896] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9896),U_9898),c_Big__Operators_Olattice__class_OSup__fin(U_9896,U_9897)) = c_Big__Operators_Olattice__class_OSup__fin(U_9896,hAPP(c_Set_OCollect(U_9896),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_HOL_Obool),tc_HOL_Obool,U_9896),c_HOL_OEx(U_9896)),hAPP(hAPP(c_COMBC(U_9896,tc_fun(U_9896,tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9896,tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),U_9896),c_COMBS(U_9896,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_HOL_Obool),tc_fun(U_9896,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9896),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9896),c_fconj)),hAPP(hAPP(c_COMBC(U_9896,tc_fun(U_9896,U_9896),tc_fun(U_9896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_HOL_Obool),tc_fun(tc_fun(U_9896,U_9896),tc_fun(U_9896,tc_HOL_Obool)),U_9896),c_COMBB(U_9896,tc_HOL_Obool,U_9896)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9896),U_9898))))),hAPP(hAPP(c_COMBC(U_9896,tc_fun(U_9896,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9896)),U_9897)))))
| U_9897 = c_Orderings_Obot__class_Obot(tc_fun(U_9896,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9896),U_9897))
| ~ class_Lattices_Odistrib__lattice(U_9896) ),
inference(variable_rename,[status(thm)],[f_2537_1]) ).
fof(f_2537_3,plain,
! [U_9896,U_9897,U_9898] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9896),U_9898),c_Big__Operators_Olattice__class_OSup__fin(U_9896,U_9897)) = c_Big__Operators_Olattice__class_OSup__fin(U_9896,hAPP(c_Set_OCollect(U_9896),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_HOL_Obool),tc_HOL_Obool,U_9896),c_HOL_OEx(U_9896)),hAPP(hAPP(c_COMBC(U_9896,tc_fun(U_9896,tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9896,tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),U_9896),c_COMBS(U_9896,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_HOL_Obool),tc_fun(U_9896,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9896),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9896),c_fconj)),hAPP(hAPP(c_COMBC(U_9896,tc_fun(U_9896,U_9896),tc_fun(U_9896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_HOL_Obool),tc_fun(tc_fun(U_9896,U_9896),tc_fun(U_9896,tc_HOL_Obool)),U_9896),c_COMBB(U_9896,tc_HOL_Obool,U_9896)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9896),U_9898))))),hAPP(hAPP(c_COMBC(U_9896,tc_fun(U_9896,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9896)),U_9897)))))
| U_9897 = c_Orderings_Obot__class_Obot(tc_fun(U_9896,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9896),U_9897))
| ~ class_Lattices_Odistrib__lattice(U_9896) ),
inference(definitional_conversion,[status(esa)],[f_2537_2]) ).
cnf(f_2537_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9896),U_9898),c_Big__Operators_Olattice__class_OSup__fin(U_9896,U_9897)) = c_Big__Operators_Olattice__class_OSup__fin(U_9896,hAPP(c_Set_OCollect(U_9896),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_HOL_Obool),tc_HOL_Obool,U_9896),c_HOL_OEx(U_9896)),hAPP(hAPP(c_COMBC(U_9896,tc_fun(U_9896,tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9896,tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),U_9896),c_COMBS(U_9896,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_HOL_Obool),tc_fun(U_9896,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9896),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9896),c_fconj)),hAPP(hAPP(c_COMBC(U_9896,tc_fun(U_9896,U_9896),tc_fun(U_9896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_HOL_Obool),tc_fun(tc_fun(U_9896,U_9896),tc_fun(U_9896,tc_HOL_Obool)),U_9896),c_COMBB(U_9896,tc_HOL_Obool,U_9896)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9896),U_9898))))),hAPP(hAPP(c_COMBC(U_9896,tc_fun(U_9896,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9896)),U_9897)))))
| U_9897 = c_Orderings_Obot__class_Obot(tc_fun(U_9896,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9896),U_9897))
| ~ class_Lattices_Odistrib__lattice(U_9896) ),
inference(clausify,[status(thm)],[f_2537_3]) ).
fof(f_2538_1,plain,
! [V_B_2,V_A_2,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_c,c_Orderings_Oord__class_Omax(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBS(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_c),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_c),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_c),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_c)),c_fequal))),c_Orderings_Oord__class_Omin(T_c)))))),hAPP(hAPP(c_COMBC(T_c,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_c),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_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(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),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_c),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup2__distrib]) ).
fof(f_2538_2,plain,
! [U_9901,U_9900,U_9899] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9899),c_Big__Operators_Olattice_OSup__fin(U_9899,c_Orderings_Oord__class_Omax(U_9899),U_9900)),c_Big__Operators_Olattice_OSup__fin(U_9899,c_Orderings_Oord__class_Omax(U_9899),U_9901)) = c_Big__Operators_Olattice_OSup__fin(U_9899,c_Orderings_Oord__class_Omax(U_9899),hAPP(c_Set_OCollect(U_9899),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_HOL_Obool),tc_HOL_Obool,U_9899),c_HOL_OEx(U_9899)),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool)),tc_fun(U_9899,tc_HOL_Obool),U_9899),hAPP(c_COMBB(tc_fun(U_9899,tc_HOL_Obool),tc_HOL_Obool,U_9899),c_HOL_OEx(U_9899))),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool)),tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_fun(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool))),tc_fun(tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool)),tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool))),U_9899),c_COMBS(U_9899,tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_fun(U_9899,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9899,tc_fun(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool))),U_9899),hAPP(c_COMBB(tc_fun(U_9899,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool)),U_9899),c_COMBS(U_9899,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool)),tc_fun(U_9899,tc_fun(U_9899,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9899),hAPP(c_COMBB(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9899),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9899),c_fconj))),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_fun(U_9899,U_9899)),tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9899,U_9899),tc_fun(U_9899,tc_HOL_Obool)),tc_fun(tc_fun(U_9899,tc_fun(U_9899,U_9899)),tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool))),U_9899),c_COMBB(tc_fun(U_9899,U_9899),tc_fun(U_9899,tc_HOL_Obool),U_9899)),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_HOL_Obool),tc_fun(tc_fun(U_9899,U_9899),tc_fun(U_9899,tc_HOL_Obool)),U_9899),c_COMBB(U_9899,tc_HOL_Obool,U_9899)),c_fequal))),c_Orderings_Oord__class_Omin(U_9899)))))),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool)),U_9899),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9899)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9899),c_fconj),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9899)),U_9900)))),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9899)),U_9901)))))))
| U_9901 = c_Orderings_Obot__class_Obot(tc_fun(U_9899,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),U_9901))
| U_9900 = c_Orderings_Obot__class_Obot(tc_fun(U_9899,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),U_9900))
| ~ class_Orderings_Olinorder(U_9899) ),
inference(variable_rename,[status(thm)],[f_2538_1]) ).
fof(f_2538_3,plain,
! [U_9899,U_9900,U_9901] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9899),c_Big__Operators_Olattice_OSup__fin(U_9899,c_Orderings_Oord__class_Omax(U_9899),U_9900)),c_Big__Operators_Olattice_OSup__fin(U_9899,c_Orderings_Oord__class_Omax(U_9899),U_9901)) = c_Big__Operators_Olattice_OSup__fin(U_9899,c_Orderings_Oord__class_Omax(U_9899),hAPP(c_Set_OCollect(U_9899),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_HOL_Obool),tc_HOL_Obool,U_9899),c_HOL_OEx(U_9899)),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool)),tc_fun(U_9899,tc_HOL_Obool),U_9899),hAPP(c_COMBB(tc_fun(U_9899,tc_HOL_Obool),tc_HOL_Obool,U_9899),c_HOL_OEx(U_9899))),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool)),tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_fun(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool))),tc_fun(tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool)),tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool))),U_9899),c_COMBS(U_9899,tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_fun(U_9899,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9899,tc_fun(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool))),U_9899),hAPP(c_COMBB(tc_fun(U_9899,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool)),U_9899),c_COMBS(U_9899,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool)),tc_fun(U_9899,tc_fun(U_9899,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9899),hAPP(c_COMBB(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9899),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9899),c_fconj))),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_fun(U_9899,U_9899)),tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9899,U_9899),tc_fun(U_9899,tc_HOL_Obool)),tc_fun(tc_fun(U_9899,tc_fun(U_9899,U_9899)),tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool))),U_9899),c_COMBB(tc_fun(U_9899,U_9899),tc_fun(U_9899,tc_HOL_Obool),U_9899)),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_HOL_Obool),tc_fun(tc_fun(U_9899,U_9899),tc_fun(U_9899,tc_HOL_Obool)),U_9899),c_COMBB(U_9899,tc_HOL_Obool,U_9899)),c_fequal))),c_Orderings_Oord__class_Omin(U_9899)))))),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool)),U_9899),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9899)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9899),c_fconj),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9899)),U_9900)))),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9899)),U_9901)))))))
| U_9901 = c_Orderings_Obot__class_Obot(tc_fun(U_9899,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),U_9901))
| U_9900 = c_Orderings_Obot__class_Obot(tc_fun(U_9899,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),U_9900))
| ~ class_Orderings_Olinorder(U_9899) ),
inference(definitional_conversion,[status(esa)],[f_2538_2]) ).
cnf(f_2538_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9899),c_Big__Operators_Olattice_OSup__fin(U_9899,c_Orderings_Oord__class_Omax(U_9899),U_9900)),c_Big__Operators_Olattice_OSup__fin(U_9899,c_Orderings_Oord__class_Omax(U_9899),U_9901)) = c_Big__Operators_Olattice_OSup__fin(U_9899,c_Orderings_Oord__class_Omax(U_9899),hAPP(c_Set_OCollect(U_9899),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_HOL_Obool),tc_HOL_Obool,U_9899),c_HOL_OEx(U_9899)),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool)),tc_fun(U_9899,tc_HOL_Obool),U_9899),hAPP(c_COMBB(tc_fun(U_9899,tc_HOL_Obool),tc_HOL_Obool,U_9899),c_HOL_OEx(U_9899))),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool)),tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_fun(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool))),tc_fun(tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool)),tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool))),U_9899),c_COMBS(U_9899,tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_fun(U_9899,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9899,tc_fun(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool))),U_9899),hAPP(c_COMBB(tc_fun(U_9899,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool)),U_9899),c_COMBS(U_9899,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool)),tc_fun(U_9899,tc_fun(U_9899,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9899),hAPP(c_COMBB(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9899),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9899),c_fconj))),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_fun(U_9899,U_9899)),tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9899,U_9899),tc_fun(U_9899,tc_HOL_Obool)),tc_fun(tc_fun(U_9899,tc_fun(U_9899,U_9899)),tc_fun(U_9899,tc_fun(U_9899,tc_HOL_Obool))),U_9899),c_COMBB(tc_fun(U_9899,U_9899),tc_fun(U_9899,tc_HOL_Obool),U_9899)),hAPP(hAPP(c_COMBB(tc_fun(U_9899,tc_HOL_Obool),tc_fun(tc_fun(U_9899,U_9899),tc_fun(U_9899,tc_HOL_Obool)),U_9899),c_COMBB(U_9899,tc_HOL_Obool,U_9899)),c_fequal))),c_Orderings_Oord__class_Omin(U_9899)))))),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9899,tc_HOL_Obool),tc_fun(U_9899,tc_HOL_Obool)),U_9899),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9899)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9899),c_fconj),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9899)),U_9900)))),hAPP(hAPP(c_COMBC(U_9899,tc_fun(U_9899,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9899)),U_9901)))))))
| U_9901 = c_Orderings_Obot__class_Obot(tc_fun(U_9899,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),U_9901))
| U_9900 = c_Orderings_Obot__class_Obot(tc_fun(U_9899,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9899),U_9900))
| ~ class_Orderings_Olinorder(U_9899) ),
inference(clausify,[status(thm)],[f_2538_3]) ).
fof(f_2539_1,plain,
! [V_k_2,V_R_2,V_t_2,T_d,V_s_2,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_Nat_Onat,T_c),c_Finite__Set_Ocard(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),c_Set_OCollect(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,tc_Nat_Onat),V_k_2),V_t_2)
| ? [B_x] :
( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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_s_2))),hAPP(hAPP(c_COMBC(T_c,T_d,tc_HOL_Obool),V_R_2),B_x)))) != hAPP(V_k_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_t_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),V_t_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_s_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__multicount__gen]) ).
fof(f_2539_2,plain,
! [U_9908,U_9907,U_9906,U_9905,U_9904,U_9903] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9903,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_Nat_Onat,U_9903),c_Finite__Set_Ocard(U_9905)),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_fun(U_9905,tc_HOL_Obool),U_9903),c_Set_OCollect(U_9905)),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_fun(U_9905,tc_HOL_Obool),U_9903),hAPP(c_COMBS(U_9905,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9905),c_fconj),hAPP(hAPP(c_COMBC(U_9905,tc_fun(U_9905,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9905)),U_9906)))),U_9907)))),U_9904) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9905,tc_Nat_Onat),U_9908),U_9906)
| ? [U_9902] :
( hAPP(c_Finite__Set_Ocard(U_9903),hAPP(c_Set_OCollect(U_9903),hAPP(hAPP(c_COMBS(U_9903,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9903),c_fconj),hAPP(hAPP(c_COMBC(U_9903,tc_fun(U_9903,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9903)),U_9904))),hAPP(hAPP(c_COMBC(U_9903,U_9905,tc_HOL_Obool),U_9907),U_9902)))) != hAPP(U_9908,U_9902)
& hBOOL(hAPP(hAPP(c_member(U_9905),U_9902),U_9906)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9905),U_9906))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9903),U_9904)) ),
inference(variable_rename,[status(thm)],[f_2539_1]) ).
fof(f_2539_3,plain,
! [U_9908,U_9907,U_9906,U_9905,U_9904,U_9903] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9903,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_Nat_Onat,U_9903),c_Finite__Set_Ocard(U_9905)),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_fun(U_9905,tc_HOL_Obool),U_9903),c_Set_OCollect(U_9905)),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_fun(U_9905,tc_HOL_Obool),U_9903),hAPP(c_COMBS(U_9905,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9905),c_fconj),hAPP(hAPP(c_COMBC(U_9905,tc_fun(U_9905,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9905)),U_9906)))),U_9907)))),U_9904) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9905,tc_Nat_Onat),U_9908),U_9906)
| ( hAPP(c_Finite__Set_Ocard(U_9903),hAPP(c_Set_OCollect(U_9903),hAPP(hAPP(c_COMBS(U_9903,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9903),c_fconj),hAPP(hAPP(c_COMBC(U_9903,tc_fun(U_9903,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9903)),U_9904))),hAPP(hAPP(c_COMBC(U_9903,U_9905,tc_HOL_Obool),U_9907),sK251(U_9908,U_9907,U_9906,U_9905,U_9904,U_9903))))) != hAPP(U_9908,sK251(U_9908,U_9907,U_9906,U_9905,U_9904,U_9903))
& hBOOL(hAPP(hAPP(c_member(U_9905),sK251(U_9908,U_9907,U_9906,U_9905,U_9904,U_9903)),U_9906)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9905),U_9906))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9903),U_9904)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_9902,sK251(U_9908,U_9907,U_9906,U_9905,U_9904,U_9903))],[f_2539_2]) ).
fof(f_2539_4,plain,
( ! [U_9903,U_9905,U_9904,U_9906,U_9907,U_9908] :
( hAPP(c_Finite__Set_Ocard(U_9903),hAPP(c_Set_OCollect(U_9903),hAPP(hAPP(c_COMBS(U_9903,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9903),c_fconj),hAPP(hAPP(c_COMBC(U_9903,tc_fun(U_9903,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9903)),U_9904))),hAPP(hAPP(c_COMBC(U_9903,U_9905,tc_HOL_Obool),U_9907),sK251(U_9908,U_9907,U_9906,U_9905,U_9904,U_9903))))) != hAPP(U_9908,sK251(U_9908,U_9907,U_9906,U_9905,U_9904,U_9903))
| ~ sP687(U_9903,U_9905,U_9904,U_9906,U_9907,U_9908) )
& ! [U_9903,U_9905,U_9904,U_9906,U_9907,U_9908] :
( hBOOL(hAPP(hAPP(c_member(U_9905),sK251(U_9908,U_9907,U_9906,U_9905,U_9904,U_9903)),U_9906))
| ~ sP687(U_9903,U_9905,U_9904,U_9906,U_9907,U_9908) )
& ! [U_9903,U_9905,U_9904,U_9906,U_9907,U_9908] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9903,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_Nat_Onat,U_9903),c_Finite__Set_Ocard(U_9905)),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_fun(U_9905,tc_HOL_Obool),U_9903),c_Set_OCollect(U_9905)),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_fun(U_9905,tc_HOL_Obool),U_9903),hAPP(c_COMBS(U_9905,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9905),c_fconj),hAPP(hAPP(c_COMBC(U_9905,tc_fun(U_9905,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9905)),U_9906)))),U_9907)))),U_9904) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9905,tc_Nat_Onat),U_9908),U_9906)
| sP687(U_9903,U_9905,U_9904,U_9906,U_9907,U_9908)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9905),U_9906))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9903),U_9904)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP687])],[f_2539_3]) ).
cnf(f_2539_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9903,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_Nat_Onat,U_9903),c_Finite__Set_Ocard(U_9905)),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_fun(U_9905,tc_HOL_Obool),U_9903),c_Set_OCollect(U_9905)),hAPP(hAPP(c_COMBB(tc_fun(U_9905,tc_HOL_Obool),tc_fun(U_9905,tc_HOL_Obool),U_9903),hAPP(c_COMBS(U_9905,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9905),c_fconj),hAPP(hAPP(c_COMBC(U_9905,tc_fun(U_9905,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9905)),U_9906)))),U_9907)))),U_9904) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9905,tc_Nat_Onat),U_9908),U_9906)
| sP687(U_9903,U_9905,U_9904,U_9906,U_9907,U_9908)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9905),U_9906))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9903),U_9904)) ),
inference(clausify,[status(thm)],[f_2539_4]) ).
cnf(f_2539_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9905),sK251(U_9908,U_9907,U_9906,U_9905,U_9904,U_9903)),U_9906))
| ~ sP687(U_9903,U_9905,U_9904,U_9906,U_9907,U_9908) ),
inference(clausify,[status(thm)],[f_2539_4]) ).
cnf(f_2539_7,plain,
( hAPP(c_Finite__Set_Ocard(U_9903),hAPP(c_Set_OCollect(U_9903),hAPP(hAPP(c_COMBS(U_9903,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9903),c_fconj),hAPP(hAPP(c_COMBC(U_9903,tc_fun(U_9903,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9903)),U_9904))),hAPP(hAPP(c_COMBC(U_9903,U_9905,tc_HOL_Obool),U_9907),sK251(U_9908,U_9907,U_9906,U_9905,U_9904,U_9903))))) != hAPP(U_9908,sK251(U_9908,U_9907,U_9906,U_9905,U_9904,U_9903))
| ~ sP687(U_9903,U_9905,U_9904,U_9906,U_9907,U_9908) ),
inference(clausify,[status(thm)],[f_2539_4]) ).
fof(f_2540_1,plain,
! [V_A_2,T_c] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ! [B_n,B_f] : V_A_2 != hAPP(c_Set_Oimage(tc_Nat_Onat,T_c,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))) )
& ( ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_c,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)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__conv__nat__seg__image]) ).
fof(f_2540_2,plain,
! [U_9914,U_9913] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9913),U_9914))
| ! [U_9912,U_9911] : U_9914 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9913,U_9911),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_9912))) )
& ( ? [U_9910,U_9909] : U_9914 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_9913,U_9909),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_9910)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9913),U_9914)) ) ),
inference(variable_rename,[status(thm)],[f_2540_1]) ).
fof(f_2540_3,plain,
( ! [U_9918,U_9916] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9916),U_9918))
| ! [U_9912,U_9911] : U_9918 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9916,U_9911),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_9912))) )
& ! [U_9917,U_9915] :
( ? [U_9910,U_9909] : U_9917 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_9915,U_9909),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_9910)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9915),U_9917)) ) ),
inference(miniscope,[status(thm)],[f_2540_2]) ).
fof(f_2540_4,plain,
( ! [U_9918,U_9916] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9916),U_9918))
| ! [U_9912,U_9911] : U_9918 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9916,U_9911),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_9912))) )
& ! [U_9917,U_9915] :
( ? [U_9909] : U_9917 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_9915,U_9909),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)),sK252(U_9917,U_9915))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9915),U_9917)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_9910,sK252(U_9917,U_9915))],[f_2540_3]) ).
fof(f_2540_5,plain,
( ! [U_9918,U_9916] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9916),U_9918))
| ! [U_9912,U_9911] : U_9918 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9916,U_9911),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_9912))) )
& ! [U_9917,U_9915] :
( U_9917 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_9915,sK253(U_9917,U_9915)),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)),sK252(U_9917,U_9915))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9915),U_9917)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_9909,sK253(U_9917,U_9915))],[f_2540_4]) ).
fof(f_2540_6,plain,
( ! [U_9918,U_9911,U_9912,U_9916] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9916),U_9918))
| U_9918 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9916,U_9911),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_9912))) )
& ! [U_9915,U_9917] :
( U_9917 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_9915,sK253(U_9917,U_9915)),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)),sK252(U_9917,U_9915))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9915),U_9917)) ) ),
inference(definitional_conversion,[status(esa)],[f_2540_5]) ).
cnf(f_2540_7,plain,
( U_9917 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_9915,sK253(U_9917,U_9915)),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)),sK252(U_9917,U_9915))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9915),U_9917)) ),
inference(clausify,[status(thm)],[f_2540_6]) ).
cnf(f_2540_8,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9916),U_9918))
| U_9918 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9916,U_9911),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_9912))) ),
inference(clausify,[status(thm)],[f_2540_6]) ).
fof(f_2541_1,plain,
! [V_f_2,T_d,V_A_2,T_c] :
( ? [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(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(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_f_2,B_x))))))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_pigeonhole__infinite]) ).
fof(f_2541_2,plain,
! [U_9923,U_9922,U_9921,U_9920] :
( ? [U_9919] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9920),hAPP(c_Set_OCollect(U_9920),hAPP(hAPP(c_COMBS(U_9920,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9920),c_fconj),hAPP(hAPP(c_COMBC(U_9920,tc_fun(U_9920,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9920)),U_9921))),hAPP(hAPP(c_COMBC(U_9920,U_9922,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_9922,tc_fun(U_9922,tc_HOL_Obool),U_9920),c_fequal),U_9923)),hAPP(U_9923,U_9919))))))
& hBOOL(hAPP(hAPP(c_member(U_9920),U_9919),U_9921)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9922),hAPP(c_Set_Oimage(U_9920,U_9922,U_9923),U_9921)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_9920),U_9921)) ),
inference(variable_rename,[status(thm)],[f_2541_1]) ).
fof(f_2541_3,plain,
! [U_9923,U_9922,U_9921,U_9920] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9920),hAPP(c_Set_OCollect(U_9920),hAPP(hAPP(c_COMBS(U_9920,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9920),c_fconj),hAPP(hAPP(c_COMBC(U_9920,tc_fun(U_9920,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9920)),U_9921))),hAPP(hAPP(c_COMBC(U_9920,U_9922,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_9922,tc_fun(U_9922,tc_HOL_Obool),U_9920),c_fequal),U_9923)),hAPP(U_9923,sK254(U_9923,U_9922,U_9921,U_9920)))))))
& hBOOL(hAPP(hAPP(c_member(U_9920),sK254(U_9923,U_9922,U_9921,U_9920)),U_9921)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9922),hAPP(c_Set_Oimage(U_9920,U_9922,U_9923),U_9921)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_9920),U_9921)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_9919,sK254(U_9923,U_9922,U_9921,U_9920))],[f_2541_2]) ).
fof(f_2541_4,plain,
( ! [U_9920,U_9921,U_9922,U_9923] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9920),hAPP(c_Set_OCollect(U_9920),hAPP(hAPP(c_COMBS(U_9920,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9920),c_fconj),hAPP(hAPP(c_COMBC(U_9920,tc_fun(U_9920,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9920)),U_9921))),hAPP(hAPP(c_COMBC(U_9920,U_9922,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_9922,tc_fun(U_9922,tc_HOL_Obool),U_9920),c_fequal),U_9923)),hAPP(U_9923,sK254(U_9923,U_9922,U_9921,U_9920)))))))
| ~ sP688(U_9920,U_9921,U_9922,U_9923) )
& ! [U_9920,U_9921,U_9922,U_9923] :
( hBOOL(hAPP(hAPP(c_member(U_9920),sK254(U_9923,U_9922,U_9921,U_9920)),U_9921))
| ~ sP688(U_9920,U_9921,U_9922,U_9923) )
& ! [U_9920,U_9921,U_9922,U_9923] :
( sP688(U_9920,U_9921,U_9922,U_9923)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9922),hAPP(c_Set_Oimage(U_9920,U_9922,U_9923),U_9921)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_9920),U_9921)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP688])],[f_2541_3]) ).
cnf(f_2541_5,plain,
( sP688(U_9920,U_9921,U_9922,U_9923)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9922),hAPP(c_Set_Oimage(U_9920,U_9922,U_9923),U_9921)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_9920),U_9921)) ),
inference(clausify,[status(thm)],[f_2541_4]) ).
cnf(f_2541_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9920),sK254(U_9923,U_9922,U_9921,U_9920)),U_9921))
| ~ sP688(U_9920,U_9921,U_9922,U_9923) ),
inference(clausify,[status(thm)],[f_2541_4]) ).
cnf(f_2541_7,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9920),hAPP(c_Set_OCollect(U_9920),hAPP(hAPP(c_COMBS(U_9920,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9920),c_fconj),hAPP(hAPP(c_COMBC(U_9920,tc_fun(U_9920,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9920)),U_9921))),hAPP(hAPP(c_COMBC(U_9920,U_9922,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_9922,tc_fun(U_9922,tc_HOL_Obool),U_9920),c_fequal),U_9923)),hAPP(U_9923,sK254(U_9923,U_9922,U_9921,U_9920)))))))
| ~ sP688(U_9920,U_9921,U_9922,U_9923) ),
inference(clausify,[status(thm)],[f_2541_4]) ).
fof(f_2542_1,plain,
! [V_r_2,V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2)
| ~ c_Fun_Oinj__on(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),T_c),c_Equiv__Relations_Oquotient(T_c)),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))))),V_r_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__quotient__disjoint]) ).
fof(f_2542_2,plain,
! [U_9926,U_9925,U_9924] :
( hAPP(c_Finite__Set_Ocard(tc_fun(U_9924,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9924),U_9925),U_9926)) = hAPP(c_Finite__Set_Ocard(U_9924),U_9925)
| ~ c_Fun_Oinj__on(U_9924,tc_fun(tc_fun(U_9924,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_9924,tc_fun(tc_prod(U_9924,U_9924),tc_HOL_Obool),tc_fun(tc_fun(U_9924,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9924,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_9924,U_9924),tc_HOL_Obool),tc_fun(tc_fun(U_9924,tc_HOL_Obool),tc_HOL_Obool)),U_9924),c_Equiv__Relations_Oquotient(U_9924)),hAPP(hAPP(c_COMBC(U_9924,tc_fun(U_9924,tc_HOL_Obool),tc_fun(U_9924,tc_HOL_Obool)),c_Set_Oinsert(U_9924)),c_Orderings_Obot__class_Obot(tc_fun(U_9924,tc_HOL_Obool))))),U_9926),U_9925)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9924),U_9925)) ),
inference(variable_rename,[status(thm)],[f_2542_1]) ).
fof(f_2542_3,plain,
! [U_9924,U_9925,U_9926] :
( hAPP(c_Finite__Set_Ocard(tc_fun(U_9924,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9924),U_9925),U_9926)) = hAPP(c_Finite__Set_Ocard(U_9924),U_9925)
| ~ c_Fun_Oinj__on(U_9924,tc_fun(tc_fun(U_9924,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_9924,tc_fun(tc_prod(U_9924,U_9924),tc_HOL_Obool),tc_fun(tc_fun(U_9924,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9924,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_9924,U_9924),tc_HOL_Obool),tc_fun(tc_fun(U_9924,tc_HOL_Obool),tc_HOL_Obool)),U_9924),c_Equiv__Relations_Oquotient(U_9924)),hAPP(hAPP(c_COMBC(U_9924,tc_fun(U_9924,tc_HOL_Obool),tc_fun(U_9924,tc_HOL_Obool)),c_Set_Oinsert(U_9924)),c_Orderings_Obot__class_Obot(tc_fun(U_9924,tc_HOL_Obool))))),U_9926),U_9925)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9924),U_9925)) ),
inference(definitional_conversion,[status(esa)],[f_2542_2]) ).
cnf(f_2542_4,plain,
( hAPP(c_Finite__Set_Ocard(tc_fun(U_9924,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9924),U_9925),U_9926)) = hAPP(c_Finite__Set_Ocard(U_9924),U_9925)
| ~ c_Fun_Oinj__on(U_9924,tc_fun(tc_fun(U_9924,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_9924,tc_fun(tc_prod(U_9924,U_9924),tc_HOL_Obool),tc_fun(tc_fun(U_9924,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9924,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_9924,U_9924),tc_HOL_Obool),tc_fun(tc_fun(U_9924,tc_HOL_Obool),tc_HOL_Obool)),U_9924),c_Equiv__Relations_Oquotient(U_9924)),hAPP(hAPP(c_COMBC(U_9924,tc_fun(U_9924,tc_HOL_Obool),tc_fun(U_9924,tc_HOL_Obool)),c_Set_Oinsert(U_9924)),c_Orderings_Obot__class_Obot(tc_fun(U_9924,tc_HOL_Obool))))),U_9926),U_9925)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9924),U_9925)) ),
inference(clausify,[status(thm)],[f_2542_3]) ).
fof(f_2543_1,plain,
! [V_r_2,V_A_2,T_c] :
( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),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(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_quotient__is__empty]) ).
fof(f_2543_2,plain,
! [U_9929,U_9928,U_9927] :
( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9927),U_9928),U_9929) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9927,tc_HOL_Obool),tc_HOL_Obool))
| U_9928 != c_Orderings_Obot__class_Obot(tc_fun(U_9927,tc_HOL_Obool)) )
& ( U_9928 = c_Orderings_Obot__class_Obot(tc_fun(U_9927,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9927),U_9928),U_9929) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9927,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2543_1]) ).
fof(f_2543_3,plain,
( ! [U_9935,U_9933,U_9931] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9931),U_9933),U_9935) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool))
| U_9933 != c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool)) )
& ! [U_9934,U_9932,U_9930] :
( U_9932 = c_Orderings_Obot__class_Obot(tc_fun(U_9930,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9930),U_9932),U_9934) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9930,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2543_2]) ).
fof(f_2543_4,plain,
( ! [U_9933,U_9935,U_9931] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9931),U_9933),U_9935) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool))
| U_9933 != c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool)) )
& ! [U_9932,U_9930,U_9934] :
( U_9932 = c_Orderings_Obot__class_Obot(tc_fun(U_9930,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9930),U_9932),U_9934) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9930,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(definitional_conversion,[status(esa)],[f_2543_3]) ).
cnf(f_2543_5,plain,
( U_9932 = c_Orderings_Obot__class_Obot(tc_fun(U_9930,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9930),U_9932),U_9934) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9930,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2543_4]) ).
cnf(f_2543_6,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9931),U_9933),U_9935) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool))
| U_9933 != c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2543_4]) ).
fof(f_2544_1,plain,
! [V_r_2,V_A_2,T_c] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_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(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2]) ).
fof(f_2544_2,plain,
! [U_9938,U_9937,U_9936] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9936,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9936),U_9937),U_9938)
| U_9937 != c_Orderings_Obot__class_Obot(tc_fun(U_9936,tc_HOL_Obool)) )
& ( U_9937 = c_Orderings_Obot__class_Obot(tc_fun(U_9936,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9936,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9936),U_9937),U_9938) ) ),
inference(variable_rename,[status(thm)],[f_2544_1]) ).
fof(f_2544_3,plain,
( ! [U_9944,U_9942,U_9940] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9940,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9940),U_9942),U_9944)
| U_9942 != c_Orderings_Obot__class_Obot(tc_fun(U_9940,tc_HOL_Obool)) )
& ! [U_9943,U_9941,U_9939] :
( U_9941 = c_Orderings_Obot__class_Obot(tc_fun(U_9939,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9939,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9939),U_9941),U_9943) ) ),
inference(miniscope,[status(thm)],[f_2544_2]) ).
fof(f_2544_4,plain,
( ! [U_9940,U_9942,U_9944] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9940,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9940),U_9942),U_9944)
| U_9942 != c_Orderings_Obot__class_Obot(tc_fun(U_9940,tc_HOL_Obool)) )
& ! [U_9941,U_9943,U_9939] :
( U_9941 = c_Orderings_Obot__class_Obot(tc_fun(U_9939,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9939,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9939),U_9941),U_9943) ) ),
inference(definitional_conversion,[status(esa)],[f_2544_3]) ).
cnf(f_2544_5,plain,
( U_9941 = c_Orderings_Obot__class_Obot(tc_fun(U_9939,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9939,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9939),U_9941),U_9943) ),
inference(clausify,[status(thm)],[f_2544_4]) ).
cnf(f_2544_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9940,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9940),U_9942),U_9944)
| U_9942 != c_Orderings_Obot__class_Obot(tc_fun(U_9940,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2544_4]) ).
fof(f_2545_1,plain,
! [V_r_2,T_c] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_quotient__empty]) ).
fof(f_2545_2,plain,
! [U_9946,U_9945] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9945),c_Orderings_Obot__class_Obot(tc_fun(U_9945,tc_HOL_Obool))),U_9946) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9945,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2545_1]) ).
fof(f_2545_3,plain,
! [U_9946,U_9945] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9945),c_Orderings_Obot__class_Obot(tc_fun(U_9945,tc_HOL_Obool))),U_9946) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9945,tc_HOL_Obool),tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_2545_2]) ).
cnf(f_2545_4,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9945),c_Orderings_Obot__class_Obot(tc_fun(U_9945,tc_HOL_Obool))),U_9946) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9945,tc_HOL_Obool),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2545_3]) ).
fof(f_2546_1,plain,
! [V_a_2,V_A_2,V_r_2,T_c] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ c_Fun_Oinj__on(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),T_c),c_Equiv__Relations_Oquotient(T_c)),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))))),V_r_2),V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_quotient__diff1]) ).
fof(f_2546_2,plain,
! [U_9950,U_9949,U_9948,U_9947] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9947),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9947,tc_HOL_Obool)),U_9949),hAPP(hAPP(c_Set_Oinsert(U_9947),U_9950),c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool))))),U_9948) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_9947,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9947),U_9949),U_9948)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9947),hAPP(hAPP(c_Set_Oinsert(U_9947),U_9950),c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool)))),U_9948))
| ~ hBOOL(hAPP(hAPP(c_member(U_9947),U_9950),U_9949))
| ~ c_Fun_Oinj__on(U_9947,tc_fun(tc_fun(U_9947,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_9947,tc_fun(tc_prod(U_9947,U_9947),tc_HOL_Obool),tc_fun(tc_fun(U_9947,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9947,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_9947,U_9947),tc_HOL_Obool),tc_fun(tc_fun(U_9947,tc_HOL_Obool),tc_HOL_Obool)),U_9947),c_Equiv__Relations_Oquotient(U_9947)),hAPP(hAPP(c_COMBC(U_9947,tc_fun(U_9947,tc_HOL_Obool),tc_fun(U_9947,tc_HOL_Obool)),c_Set_Oinsert(U_9947)),c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool))))),U_9948),U_9949) ),
inference(variable_rename,[status(thm)],[f_2546_1]) ).
fof(f_2546_3,plain,
! [U_9947,U_9948,U_9949,U_9950] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9947),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9947,tc_HOL_Obool)),U_9949),hAPP(hAPP(c_Set_Oinsert(U_9947),U_9950),c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool))))),U_9948) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_9947,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9947),U_9949),U_9948)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9947),hAPP(hAPP(c_Set_Oinsert(U_9947),U_9950),c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool)))),U_9948))
| ~ hBOOL(hAPP(hAPP(c_member(U_9947),U_9950),U_9949))
| ~ c_Fun_Oinj__on(U_9947,tc_fun(tc_fun(U_9947,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_9947,tc_fun(tc_prod(U_9947,U_9947),tc_HOL_Obool),tc_fun(tc_fun(U_9947,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9947,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_9947,U_9947),tc_HOL_Obool),tc_fun(tc_fun(U_9947,tc_HOL_Obool),tc_HOL_Obool)),U_9947),c_Equiv__Relations_Oquotient(U_9947)),hAPP(hAPP(c_COMBC(U_9947,tc_fun(U_9947,tc_HOL_Obool),tc_fun(U_9947,tc_HOL_Obool)),c_Set_Oinsert(U_9947)),c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool))))),U_9948),U_9949) ),
inference(definitional_conversion,[status(esa)],[f_2546_2]) ).
cnf(f_2546_4,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9947),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9947,tc_HOL_Obool)),U_9949),hAPP(hAPP(c_Set_Oinsert(U_9947),U_9950),c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool))))),U_9948) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_9947,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9947),U_9949),U_9948)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9947),hAPP(hAPP(c_Set_Oinsert(U_9947),U_9950),c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool)))),U_9948))
| ~ hBOOL(hAPP(hAPP(c_member(U_9947),U_9950),U_9949))
| ~ c_Fun_Oinj__on(U_9947,tc_fun(tc_fun(U_9947,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_9947,tc_fun(tc_prod(U_9947,U_9947),tc_HOL_Obool),tc_fun(tc_fun(U_9947,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9947,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_9947,U_9947),tc_HOL_Obool),tc_fun(tc_fun(U_9947,tc_HOL_Obool),tc_HOL_Obool)),U_9947),c_Equiv__Relations_Oquotient(U_9947)),hAPP(hAPP(c_COMBC(U_9947,tc_fun(U_9947,tc_HOL_Obool),tc_fun(U_9947,tc_HOL_Obool)),c_Set_Oinsert(U_9947)),c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool))))),U_9948),U_9949) ),
inference(clausify,[status(thm)],[f_2546_3]) ).
fof(f_2547_1,plain,
! [V_r_2,V_A_2,T_c] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_c,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)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_quotient__def]) ).
fof(f_2547_2,plain,
! [U_9953,U_9952,U_9951] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9951),U_9952),U_9953) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9951,tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool)),U_9952),hAPP(hAPP(c_COMBC(U_9951,tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9951,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool)),U_9951),c_Set_Oinsert(tc_fun(U_9951,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9951,tc_HOL_Obool),tc_fun(U_9951,tc_HOL_Obool),U_9951),c_Relation_OImage(U_9951,U_9951,U_9953)),hAPP(hAPP(c_COMBC(U_9951,tc_fun(U_9951,tc_HOL_Obool),tc_fun(U_9951,tc_HOL_Obool)),c_Set_Oinsert(U_9951)),c_Orderings_Obot__class_Obot(tc_fun(U_9951,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2547_1]) ).
fof(f_2547_3,plain,
! [U_9951,U_9952,U_9953] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9951),U_9952),U_9953) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9951,tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool)),U_9952),hAPP(hAPP(c_COMBC(U_9951,tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9951,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool)),U_9951),c_Set_Oinsert(tc_fun(U_9951,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9951,tc_HOL_Obool),tc_fun(U_9951,tc_HOL_Obool),U_9951),c_Relation_OImage(U_9951,U_9951,U_9953)),hAPP(hAPP(c_COMBC(U_9951,tc_fun(U_9951,tc_HOL_Obool),tc_fun(U_9951,tc_HOL_Obool)),c_Set_Oinsert(U_9951)),c_Orderings_Obot__class_Obot(tc_fun(U_9951,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool)))),
inference(definitional_conversion,[status(esa)],[f_2547_2]) ).
cnf(f_2547_4,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9951),U_9952),U_9953) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9951,tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool)),U_9952),hAPP(hAPP(c_COMBC(U_9951,tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9951,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool)),U_9951),c_Set_Oinsert(tc_fun(U_9951,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9951,tc_HOL_Obool),tc_fun(U_9951,tc_HOL_Obool),U_9951),c_Relation_OImage(U_9951,U_9951,U_9953)),hAPP(hAPP(c_COMBC(U_9951,tc_fun(U_9951,tc_HOL_Obool),tc_fun(U_9951,tc_HOL_Obool)),c_Set_Oinsert(U_9951)),c_Orderings_Obot__class_Obot(tc_fun(U_9951,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9951,tc_HOL_Obool),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2547_3]) ).
fof(f_2548_1,plain,
! [V_r_2,V_x_2,T_c] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_singleton__quotient]) ).
fof(f_2548_2,plain,
! [U_9956,U_9955,U_9954] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9954),hAPP(hAPP(c_Set_Oinsert(U_9954),U_9955),c_Orderings_Obot__class_Obot(tc_fun(U_9954,tc_HOL_Obool)))),U_9956) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9954,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9954,U_9954,U_9956),hAPP(hAPP(c_Set_Oinsert(U_9954),U_9955),c_Orderings_Obot__class_Obot(tc_fun(U_9954,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9954,tc_HOL_Obool),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2548_1]) ).
fof(f_2548_3,plain,
! [U_9954,U_9955,U_9956] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9954),hAPP(hAPP(c_Set_Oinsert(U_9954),U_9955),c_Orderings_Obot__class_Obot(tc_fun(U_9954,tc_HOL_Obool)))),U_9956) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9954,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9954,U_9954,U_9956),hAPP(hAPP(c_Set_Oinsert(U_9954),U_9955),c_Orderings_Obot__class_Obot(tc_fun(U_9954,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9954,tc_HOL_Obool),tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_2548_2]) ).
cnf(f_2548_4,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9954),hAPP(hAPP(c_Set_Oinsert(U_9954),U_9955),c_Orderings_Obot__class_Obot(tc_fun(U_9954,tc_HOL_Obool)))),U_9956) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9954,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9954,U_9954,U_9956),hAPP(hAPP(c_Set_Oinsert(U_9954),U_9955),c_Orderings_Obot__class_Obot(tc_fun(U_9954,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9954,tc_HOL_Obool),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2548_3]) ).
fof(f_2549_1,plain,
! [V_B_2,T_d,V_A_2,T_c] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)))
| ? [B_a] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(V_B_2,B_a)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_a),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__UN__I]) ).
fof(f_2549_2,plain,
! [U_9961,U_9960,U_9959,U_9958] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9960),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9958,tc_fun(U_9960,tc_HOL_Obool)),U_9959),U_9961)))
| ? [U_9957] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9960),hAPP(U_9961,U_9957)))
& hBOOL(hAPP(hAPP(c_member(U_9958),U_9957),U_9959)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9958),U_9959)) ),
inference(variable_rename,[status(thm)],[f_2549_1]) ).
fof(f_2549_3,plain,
! [U_9961,U_9960,U_9959,U_9958] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9960),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9958,tc_fun(U_9960,tc_HOL_Obool)),U_9959),U_9961)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9960),hAPP(U_9961,sK255(U_9961,U_9960,U_9959,U_9958))))
& hBOOL(hAPP(hAPP(c_member(U_9958),sK255(U_9961,U_9960,U_9959,U_9958)),U_9959)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9958),U_9959)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_9957,sK255(U_9961,U_9960,U_9959,U_9958))],[f_2549_2]) ).
fof(f_2549_4,plain,
( ! [U_9958,U_9959,U_9960,U_9961] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9960),hAPP(U_9961,sK255(U_9961,U_9960,U_9959,U_9958))))
| ~ sP689(U_9958,U_9959,U_9960,U_9961) )
& ! [U_9958,U_9959,U_9960,U_9961] :
( hBOOL(hAPP(hAPP(c_member(U_9958),sK255(U_9961,U_9960,U_9959,U_9958)),U_9959))
| ~ sP689(U_9958,U_9959,U_9960,U_9961) )
& ! [U_9958,U_9959,U_9960,U_9961] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9960),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9958,tc_fun(U_9960,tc_HOL_Obool)),U_9959),U_9961)))
| sP689(U_9958,U_9959,U_9960,U_9961)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9958),U_9959)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP689])],[f_2549_3]) ).
cnf(f_2549_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9960),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9958,tc_fun(U_9960,tc_HOL_Obool)),U_9959),U_9961)))
| sP689(U_9958,U_9959,U_9960,U_9961)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9958),U_9959)) ),
inference(clausify,[status(thm)],[f_2549_4]) ).
cnf(f_2549_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9958),sK255(U_9961,U_9960,U_9959,U_9958)),U_9959))
| ~ sP689(U_9958,U_9959,U_9960,U_9961) ),
inference(clausify,[status(thm)],[f_2549_4]) ).
cnf(f_2549_7,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9960),hAPP(U_9961,sK255(U_9961,U_9960,U_9959,U_9958))))
| ~ sP689(U_9958,U_9959,U_9960,U_9961) ),
inference(clausify,[status(thm)],[f_2549_4]) ).
fof(f_2550_1,plain,
! [V_k_2,V_N_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_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2)
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__diff__nat]) ).
fof(f_2550_2,plain,
! [U_9964,U_9963] :
( 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)),U_9964),U_9963)
| ? [U_9962] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9964),U_9962))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9962),U_9963)) ) ),
inference(variable_rename,[status(thm)],[f_2550_1]) ).
fof(f_2550_3,plain,
! [U_9964,U_9963] :
( 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)),U_9964),U_9963)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9964),sK256(U_9964,U_9963)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK256(U_9964,U_9963)),U_9963)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_9962,sK256(U_9964,U_9963))],[f_2550_2]) ).
fof(f_2550_4,plain,
( ! [U_9963,U_9964] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9964),sK256(U_9964,U_9963)))
| ~ sP690(U_9963,U_9964) )
& ! [U_9963,U_9964] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK256(U_9964,U_9963)),U_9963))
| ~ sP690(U_9963,U_9964) )
& ! [U_9963,U_9964] :
( 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)),U_9964),U_9963)
| sP690(U_9963,U_9964) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP690])],[f_2550_3]) ).
cnf(f_2550_5,plain,
( 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)),U_9964),U_9963)
| sP690(U_9963,U_9964) ),
inference(clausify,[status(thm)],[f_2550_4]) ).
cnf(f_2550_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK256(U_9964,U_9963)),U_9963))
| ~ sP690(U_9963,U_9964) ),
inference(clausify,[status(thm)],[f_2550_4]) ).
cnf(f_2550_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9964),sK256(U_9964,U_9963)))
| ~ sP690(U_9963,U_9964) ),
inference(clausify,[status(thm)],[f_2550_4]) ).
fof(f_2551_1,plain,
! [V_r_2,V_A_2,V_x_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_quotientI]) ).
fof(f_2551_2,plain,
! [U_9968,U_9967,U_9966,U_9965] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9965,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9965,U_9965,U_9968),hAPP(hAPP(c_Set_Oinsert(U_9965),U_9966),c_Orderings_Obot__class_Obot(tc_fun(U_9965,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9965),U_9967),U_9968)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9965),U_9966),U_9967)) ),
inference(variable_rename,[status(thm)],[f_2551_1]) ).
fof(f_2551_3,plain,
! [U_9965,U_9966,U_9967,U_9968] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9965,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9965,U_9965,U_9968),hAPP(hAPP(c_Set_Oinsert(U_9965),U_9966),c_Orderings_Obot__class_Obot(tc_fun(U_9965,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9965),U_9967),U_9968)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9965),U_9966),U_9967)) ),
inference(definitional_conversion,[status(esa)],[f_2551_2]) ).
cnf(f_2551_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9965,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9965,U_9965,U_9968),hAPP(hAPP(c_Set_Oinsert(U_9965),U_9966),c_Orderings_Obot__class_Obot(tc_fun(U_9965,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9965),U_9967),U_9968)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9965),U_9966),U_9967)) ),
inference(clausify,[status(thm)],[f_2551_3]) ).
fof(f_2552_1,plain,
! [V_B_2,V_r_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Relation_OImage(T_d,T_c,V_r_2)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),c_Set_Oinsert(T_d)),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_Image__eq__UN]) ).
fof(f_2552_2,plain,
! [U_9972,U_9971,U_9970,U_9969] : hAPP(c_Relation_OImage(U_9969,U_9970,U_9971),U_9972) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9969,tc_fun(U_9970,tc_HOL_Obool)),U_9972),hAPP(hAPP(c_COMBB(tc_fun(U_9969,tc_HOL_Obool),tc_fun(U_9970,tc_HOL_Obool),U_9969),c_Relation_OImage(U_9969,U_9970,U_9971)),hAPP(hAPP(c_COMBC(U_9969,tc_fun(U_9969,tc_HOL_Obool),tc_fun(U_9969,tc_HOL_Obool)),c_Set_Oinsert(U_9969)),c_Orderings_Obot__class_Obot(tc_fun(U_9969,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_2552_1]) ).
fof(f_2552_3,plain,
! [U_9969,U_9970,U_9971,U_9972] : hAPP(c_Relation_OImage(U_9969,U_9970,U_9971),U_9972) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9969,tc_fun(U_9970,tc_HOL_Obool)),U_9972),hAPP(hAPP(c_COMBB(tc_fun(U_9969,tc_HOL_Obool),tc_fun(U_9970,tc_HOL_Obool),U_9969),c_Relation_OImage(U_9969,U_9970,U_9971)),hAPP(hAPP(c_COMBC(U_9969,tc_fun(U_9969,tc_HOL_Obool),tc_fun(U_9969,tc_HOL_Obool)),c_Set_Oinsert(U_9969)),c_Orderings_Obot__class_Obot(tc_fun(U_9969,tc_HOL_Obool))))),
inference(definitional_conversion,[status(esa)],[f_2552_2]) ).
cnf(f_2552_4,plain,
hAPP(c_Relation_OImage(U_9969,U_9970,U_9971),U_9972) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9969,tc_fun(U_9970,tc_HOL_Obool)),U_9972),hAPP(hAPP(c_COMBB(tc_fun(U_9969,tc_HOL_Obool),tc_fun(U_9970,tc_HOL_Obool),U_9969),c_Relation_OImage(U_9969,U_9970,U_9971)),hAPP(hAPP(c_COMBC(U_9969,tc_fun(U_9969,tc_HOL_Obool),tc_fun(U_9969,tc_HOL_Obool)),c_Set_Oinsert(U_9969)),c_Orderings_Obot__class_Obot(tc_fun(U_9969,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2552_3]) ).
fof(f_2553_1,plain,
! [V_B_2,V_A_2,T_e,V_r_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Relation_OImage(T_d,T_c,V_r_2)),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Image__INT__subset]) ).
fof(f_2553_2,plain,
! [U_9978,U_9977,U_9976,U_9975,U_9974,U_9973] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9973,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9974,U_9973,U_9975),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9976,tc_fun(U_9974,tc_HOL_Obool)),U_9977),U_9978))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9976,tc_fun(U_9973,tc_HOL_Obool)),U_9977),hAPP(hAPP(c_COMBB(tc_fun(U_9974,tc_HOL_Obool),tc_fun(U_9973,tc_HOL_Obool),U_9976),c_Relation_OImage(U_9974,U_9973,U_9975)),U_9978)))),
inference(variable_rename,[status(thm)],[f_2553_1]) ).
fof(f_2553_3,plain,
! [U_9973,U_9974,U_9975,U_9976,U_9977,U_9978] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9973,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9974,U_9973,U_9975),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9976,tc_fun(U_9974,tc_HOL_Obool)),U_9977),U_9978))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9976,tc_fun(U_9973,tc_HOL_Obool)),U_9977),hAPP(hAPP(c_COMBB(tc_fun(U_9974,tc_HOL_Obool),tc_fun(U_9973,tc_HOL_Obool),U_9976),c_Relation_OImage(U_9974,U_9973,U_9975)),U_9978)))),
inference(definitional_conversion,[status(esa)],[f_2553_2]) ).
cnf(f_2553_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9973,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9974,U_9973,U_9975),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9976,tc_fun(U_9974,tc_HOL_Obool)),U_9977),U_9978))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9976,tc_fun(U_9973,tc_HOL_Obool)),U_9977),hAPP(hAPP(c_COMBB(tc_fun(U_9974,tc_HOL_Obool),tc_fun(U_9973,tc_HOL_Obool),U_9976),c_Relation_OImage(U_9974,U_9973,U_9975)),U_9978)))),
inference(clausify,[status(thm)],[f_2553_3]) ).
fof(f_2554_1,plain,
! [V_B_2,V_A_2,V_R_2,T_d,T_c] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,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_Relation_OImage(T_d,T_c,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Image__Int__subset]) ).
fof(f_2554_2,plain,
! [U_9983,U_9982,U_9981,U_9980,U_9979] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9979,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9980,U_9979,U_9981),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9980,tc_HOL_Obool)),U_9982),U_9983))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9979,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9980,U_9979,U_9981),U_9982)),hAPP(c_Relation_OImage(U_9980,U_9979,U_9981),U_9983)))),
inference(variable_rename,[status(thm)],[f_2554_1]) ).
fof(f_2554_3,plain,
! [U_9979,U_9980,U_9981,U_9982,U_9983] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9979,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9980,U_9979,U_9981),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9980,tc_HOL_Obool)),U_9982),U_9983))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9979,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9980,U_9979,U_9981),U_9982)),hAPP(c_Relation_OImage(U_9980,U_9979,U_9981),U_9983)))),
inference(definitional_conversion,[status(esa)],[f_2554_2]) ).
cnf(f_2554_4,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9979,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9980,U_9979,U_9981),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9980,tc_HOL_Obool)),U_9982),U_9983))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9979,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9980,U_9979,U_9981),U_9982)),hAPP(c_Relation_OImage(U_9980,U_9979,U_9981),U_9983)))),
inference(clausify,[status(thm)],[f_2554_3]) ).
fof(f_2555_1,plain,
! [V_B_2,V_A_2,T_e,V_r_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_e),c_Relation_OImage(T_d,T_c,V_r_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Image__UN]) ).
fof(f_2555_2,plain,
! [U_9989,U_9988,U_9987,U_9986,U_9985,U_9984] : hAPP(c_Relation_OImage(U_9984,U_9985,U_9986),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9987,tc_fun(U_9984,tc_HOL_Obool)),U_9988),U_9989)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9987,tc_fun(U_9985,tc_HOL_Obool)),U_9988),hAPP(hAPP(c_COMBB(tc_fun(U_9984,tc_HOL_Obool),tc_fun(U_9985,tc_HOL_Obool),U_9987),c_Relation_OImage(U_9984,U_9985,U_9986)),U_9989)),
inference(variable_rename,[status(thm)],[f_2555_1]) ).
fof(f_2555_3,plain,
! [U_9984,U_9985,U_9986,U_9987,U_9988,U_9989] : hAPP(c_Relation_OImage(U_9984,U_9985,U_9986),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9987,tc_fun(U_9984,tc_HOL_Obool)),U_9988),U_9989)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9987,tc_fun(U_9985,tc_HOL_Obool)),U_9988),hAPP(hAPP(c_COMBB(tc_fun(U_9984,tc_HOL_Obool),tc_fun(U_9985,tc_HOL_Obool),U_9987),c_Relation_OImage(U_9984,U_9985,U_9986)),U_9989)),
inference(definitional_conversion,[status(esa)],[f_2555_2]) ).
cnf(f_2555_4,plain,
hAPP(c_Relation_OImage(U_9984,U_9985,U_9986),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9987,tc_fun(U_9984,tc_HOL_Obool)),U_9988),U_9989)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9987,tc_fun(U_9985,tc_HOL_Obool)),U_9988),hAPP(hAPP(c_COMBB(tc_fun(U_9984,tc_HOL_Obool),tc_fun(U_9985,tc_HOL_Obool),U_9987),c_Relation_OImage(U_9984,U_9985,U_9986)),U_9989)),
inference(clausify,[status(thm)],[f_2555_3]) ).
fof(f_2556_1,plain,
! [V_R_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Image__empty]) ).
fof(f_2556_2,plain,
! [U_9992,U_9991,U_9990] : hAPP(c_Relation_OImage(U_9990,U_9991,U_9992),c_Orderings_Obot__class_Obot(tc_fun(U_9990,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9991,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2556_1]) ).
fof(f_2556_3,plain,
! [U_9992,U_9991,U_9990] : hAPP(c_Relation_OImage(U_9990,U_9991,U_9992),c_Orderings_Obot__class_Obot(tc_fun(U_9990,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9991,tc_HOL_Obool)),
inference(definitional_conversion,[status(esa)],[f_2556_2]) ).
cnf(f_2556_4,plain,
hAPP(c_Relation_OImage(U_9990,U_9991,U_9992),c_Orderings_Obot__class_Obot(tc_fun(U_9990,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9991,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2556_3]) ).
fof(f_2557_1,plain,
! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_d,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_c,T_d,V_r_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_Image__mono]) ).
fof(f_2557_2,plain,
! [U_9998,U_9997,U_9996,U_9995,U_9994,U_9993] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9994,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9993,U_9994,U_9995),U_9997)),hAPP(c_Relation_OImage(U_9993,U_9994,U_9996),U_9998)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9993,tc_HOL_Obool)),U_9997),U_9998))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9993,U_9994),tc_HOL_Obool)),U_9995),U_9996)) ),
inference(variable_rename,[status(thm)],[f_2557_1]) ).
fof(f_2557_3,plain,
! [U_9993,U_9994,U_9995,U_9996,U_9997,U_9998] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9994,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9993,U_9994,U_9995),U_9997)),hAPP(c_Relation_OImage(U_9993,U_9994,U_9996),U_9998)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9993,tc_HOL_Obool)),U_9997),U_9998))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9993,U_9994),tc_HOL_Obool)),U_9995),U_9996)) ),
inference(definitional_conversion,[status(esa)],[f_2557_2]) ).
cnf(f_2557_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9994,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9993,U_9994,U_9995),U_9997)),hAPP(c_Relation_OImage(U_9993,U_9994,U_9996),U_9998)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9993,tc_HOL_Obool)),U_9997),U_9998))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9993,U_9994),tc_HOL_Obool)),U_9995),U_9996)) ),
inference(clausify,[status(thm)],[f_2557_3]) ).
fof(f_2558_1,plain,
! [V_B_2,V_A_2,V_R_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_d,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(c_Relation_OImage(T_d,T_c,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Image__Un]) ).
fof(f_2558_2,plain,
! [U_10003,U_10002,U_10001,U_10000,U_9999] : hAPP(c_Relation_OImage(U_9999,U_10000,U_10001),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9999,tc_HOL_Obool)),U_10002),U_10003)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10000,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9999,U_10000,U_10001),U_10002)),hAPP(c_Relation_OImage(U_9999,U_10000,U_10001),U_10003)),
inference(variable_rename,[status(thm)],[f_2558_1]) ).
fof(f_2558_3,plain,
! [U_9999,U_10000,U_10001,U_10002,U_10003] : hAPP(c_Relation_OImage(U_9999,U_10000,U_10001),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9999,tc_HOL_Obool)),U_10002),U_10003)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10000,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9999,U_10000,U_10001),U_10002)),hAPP(c_Relation_OImage(U_9999,U_10000,U_10001),U_10003)),
inference(definitional_conversion,[status(esa)],[f_2558_2]) ).
cnf(f_2558_4,plain,
hAPP(c_Relation_OImage(U_9999,U_10000,U_10001),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9999,tc_HOL_Obool)),U_10002),U_10003)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10000,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9999,U_10000,U_10001),U_10002)),hAPP(c_Relation_OImage(U_9999,U_10000,U_10001),U_10003)),
inference(clausify,[status(thm)],[f_2558_3]) ).
fof(f_2559_1,plain,
! [V_A_2,V_S_2,V_R_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_c,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_d,T_c,V_S_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Un__Image]) ).
fof(f_2559_2,plain,
! [U_10008,U_10007,U_10006,U_10005,U_10004] : hAPP(c_Relation_OImage(U_10004,U_10005,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10004,U_10005),tc_HOL_Obool)),U_10006),U_10007)),U_10008) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10005,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10004,U_10005,U_10006),U_10008)),hAPP(c_Relation_OImage(U_10004,U_10005,U_10007),U_10008)),
inference(variable_rename,[status(thm)],[f_2559_1]) ).
fof(f_2559_3,plain,
! [U_10006,U_10007,U_10008,U_10004,U_10005] : hAPP(c_Relation_OImage(U_10004,U_10005,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10004,U_10005),tc_HOL_Obool)),U_10006),U_10007)),U_10008) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10005,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10004,U_10005,U_10006),U_10008)),hAPP(c_Relation_OImage(U_10004,U_10005,U_10007),U_10008)),
inference(definitional_conversion,[status(esa)],[f_2559_2]) ).
cnf(f_2559_4,plain,
hAPP(c_Relation_OImage(U_10004,U_10005,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10004,U_10005),tc_HOL_Obool)),U_10006),U_10007)),U_10008) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10005,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10004,U_10005,U_10006),U_10008)),hAPP(c_Relation_OImage(U_10004,U_10005,U_10007),U_10008)),
inference(clausify,[status(thm)],[f_2559_3]) ).
fof(f_2560_1,plain,
! [V_r_2,V_A_2,V_X_2,T_c] :
( ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
& V_X_2 = hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_quotientE]) ).
fof(f_2560_2,plain,
! [U_10013,U_10012,U_10011,U_10010] :
( ? [U_10009] :
( hBOOL(hAPP(hAPP(c_member(U_10010),U_10009),U_10012))
& U_10011 = hAPP(c_Relation_OImage(U_10010,U_10010,U_10013),hAPP(hAPP(c_Set_Oinsert(U_10010),U_10009),c_Orderings_Obot__class_Obot(tc_fun(U_10010,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10010,tc_HOL_Obool)),U_10011),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10010),U_10012),U_10013))) ),
inference(variable_rename,[status(thm)],[f_2560_1]) ).
fof(f_2560_3,plain,
! [U_10013,U_10012,U_10011,U_10010] :
( ( hBOOL(hAPP(hAPP(c_member(U_10010),sK257(U_10013,U_10012,U_10011,U_10010)),U_10012))
& U_10011 = hAPP(c_Relation_OImage(U_10010,U_10010,U_10013),hAPP(hAPP(c_Set_Oinsert(U_10010),sK257(U_10013,U_10012,U_10011,U_10010)),c_Orderings_Obot__class_Obot(tc_fun(U_10010,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10010,tc_HOL_Obool)),U_10011),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10010),U_10012),U_10013))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_10009,sK257(U_10013,U_10012,U_10011,U_10010))],[f_2560_2]) ).
fof(f_2560_4,plain,
( ! [U_10010,U_10011,U_10012,U_10013] :
( hBOOL(hAPP(hAPP(c_member(U_10010),sK257(U_10013,U_10012,U_10011,U_10010)),U_10012))
| ~ sP691(U_10010,U_10011,U_10012,U_10013) )
& ! [U_10010,U_10011,U_10012,U_10013] :
( U_10011 = hAPP(c_Relation_OImage(U_10010,U_10010,U_10013),hAPP(hAPP(c_Set_Oinsert(U_10010),sK257(U_10013,U_10012,U_10011,U_10010)),c_Orderings_Obot__class_Obot(tc_fun(U_10010,tc_HOL_Obool))))
| ~ sP691(U_10010,U_10011,U_10012,U_10013) )
& ! [U_10010,U_10011,U_10012,U_10013] :
( sP691(U_10010,U_10011,U_10012,U_10013)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10010,tc_HOL_Obool)),U_10011),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10010),U_10012),U_10013))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP691])],[f_2560_3]) ).
cnf(f_2560_5,plain,
( sP691(U_10010,U_10011,U_10012,U_10013)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10010,tc_HOL_Obool)),U_10011),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10010),U_10012),U_10013))) ),
inference(clausify,[status(thm)],[f_2560_4]) ).
cnf(f_2560_6,plain,
( U_10011 = hAPP(c_Relation_OImage(U_10010,U_10010,U_10013),hAPP(hAPP(c_Set_Oinsert(U_10010),sK257(U_10013,U_10012,U_10011,U_10010)),c_Orderings_Obot__class_Obot(tc_fun(U_10010,tc_HOL_Obool))))
| ~ sP691(U_10010,U_10011,U_10012,U_10013) ),
inference(clausify,[status(thm)],[f_2560_4]) ).
cnf(f_2560_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_10010),sK257(U_10013,U_10012,U_10011,U_10010)),U_10012))
| ~ sP691(U_10010,U_10011,U_10012,U_10013) ),
inference(clausify,[status(thm)],[f_2560_4]) ).
fof(f_2561_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_2561_2,plain,
! [U_10015,U_10014] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10015)),hAPP(c_Int_Onat,U_10014)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10015),U_10014)),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_10014)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10015)),hAPP(c_Int_Onat,U_10014)) = hAPP(c_Int_Onat,U_10015)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10014)) ) ),
inference(variable_rename,[status(thm)],[f_2561_1]) ).
fof(f_2561_3,plain,
( ! [U_10019,U_10017] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10019)),hAPP(c_Int_Onat,U_10017)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10019),U_10017)),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_10017)) )
& ! [U_10018,U_10016] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10018)),hAPP(c_Int_Onat,U_10016)) = hAPP(c_Int_Onat,U_10018)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10016)) ) ),
inference(miniscope,[status(thm)],[f_2561_2]) ).
fof(f_2561_4,plain,
( ! [U_10019,U_10017] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10019)),hAPP(c_Int_Onat,U_10017)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10019),U_10017)),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_10017)) )
& ! [U_10018,U_10016] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10018)),hAPP(c_Int_Onat,U_10016)) = hAPP(c_Int_Onat,U_10018)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10016)) ) ),
inference(definitional_conversion,[status(esa)],[f_2561_3]) ).
cnf(f_2561_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10018)),hAPP(c_Int_Onat,U_10016)) = hAPP(c_Int_Onat,U_10018)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10016)) ),
inference(clausify,[status(thm)],[f_2561_4]) ).
cnf(f_2561_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10019)),hAPP(c_Int_Onat,U_10017)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10019),U_10017)),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_10017)) ),
inference(clausify,[status(thm)],[f_2561_4]) ).
fof(f_2562_1,plain,
! [V_n_2,V_A_2,V_f_2,T_c] :
( ? [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_c),B_x),V_A_2)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,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_2562_2,plain,
! [U_10024,U_10023,U_10022,U_10021] :
( ? [U_10020] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10022,U_10020)))
& hBOOL(hAPP(hAPP(c_member(U_10021),U_10020),U_10023)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10021,tc_Nat_Onat),U_10022),U_10023) != hAPP(c_Nat_OSuc,U_10024) ),
inference(variable_rename,[status(thm)],[f_2562_1]) ).
fof(f_2562_3,plain,
! [U_10024,U_10023,U_10022,U_10021] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10022,sK258(U_10024,U_10023,U_10022,U_10021))))
& hBOOL(hAPP(hAPP(c_member(U_10021),sK258(U_10024,U_10023,U_10022,U_10021)),U_10023)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10021,tc_Nat_Onat),U_10022),U_10023) != hAPP(c_Nat_OSuc,U_10024) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_10020,sK258(U_10024,U_10023,U_10022,U_10021))],[f_2562_2]) ).
fof(f_2562_4,plain,
( ! [U_10021,U_10022,U_10023,U_10024] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10022,sK258(U_10024,U_10023,U_10022,U_10021))))
| ~ sP692(U_10021,U_10022,U_10023,U_10024) )
& ! [U_10021,U_10022,U_10023,U_10024] :
( hBOOL(hAPP(hAPP(c_member(U_10021),sK258(U_10024,U_10023,U_10022,U_10021)),U_10023))
| ~ sP692(U_10021,U_10022,U_10023,U_10024) )
& ! [U_10021,U_10022,U_10023,U_10024] :
( sP692(U_10021,U_10022,U_10023,U_10024)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10021,tc_Nat_Onat),U_10022),U_10023) != hAPP(c_Nat_OSuc,U_10024) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP692])],[f_2562_3]) ).
cnf(f_2562_5,plain,
( sP692(U_10021,U_10022,U_10023,U_10024)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10021,tc_Nat_Onat),U_10022),U_10023) != hAPP(c_Nat_OSuc,U_10024) ),
inference(clausify,[status(thm)],[f_2562_4]) ).
cnf(f_2562_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10021),sK258(U_10024,U_10023,U_10022,U_10021)),U_10023))
| ~ sP692(U_10021,U_10022,U_10023,U_10024) ),
inference(clausify,[status(thm)],[f_2562_4]) ).
cnf(f_2562_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10022,sK258(U_10024,U_10023,U_10022,U_10021))))
| ~ sP692(U_10021,U_10022,U_10023,U_10024) ),
inference(clausify,[status(thm)],[f_2562_4]) ).
fof(f_2563_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_2563_2,plain,
! [U_10028,U_10027,U_10026] :
( ? [U_10025] : U_10026 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10027),U_10025))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10028),U_10026))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10026,U_10027) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10028,U_10027) ),
inference(variable_rename,[status(thm)],[f_2563_1]) ).
fof(f_2563_3,plain,
! [U_10028,U_10027,U_10026] :
( U_10026 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10027),sK259(U_10028,U_10027,U_10026)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10028),U_10026))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10026,U_10027) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10028,U_10027) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_10025,sK259(U_10028,U_10027,U_10026))],[f_2563_2]) ).
fof(f_2563_4,plain,
! [U_10027,U_10026,U_10028] :
( U_10026 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10027),sK259(U_10028,U_10027,U_10026)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10028),U_10026))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10026,U_10027) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10028,U_10027) ),
inference(definitional_conversion,[status(esa)],[f_2563_3]) ).
cnf(f_2563_5,plain,
( U_10026 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10027),sK259(U_10028,U_10027,U_10026)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10028),U_10026))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10026,U_10027) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10028,U_10027) ),
inference(clausify,[status(thm)],[f_2563_4]) ).
fof(f_2564_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_2564_2,plain,
! [U_10029] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10029))),
inference(variable_rename,[status(thm)],[f_2564_1]) ).
fof(f_2564_3,plain,
! [U_10029] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10029))),
inference(definitional_conversion,[status(esa)],[f_2564_2]) ).
cnf(f_2564_4,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10029))),
inference(clausify,[status(thm)],[f_2564_3]) ).
fof(f_2565_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_2565_2,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_2565_1]) ).
cnf(f_2565_3,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_2565_2]) ).
fof(f_2566_1,plain,
! [V_B_2,T_c,V_A_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_A_2),V_B_2))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_less__by__empty]) ).
fof(f_2566_2,plain,
! [U_10032,U_10031,U_10030] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10031,U_10031),tc_HOL_Obool)),U_10030),U_10032))
| U_10030 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10031,U_10031),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_2566_1]) ).
fof(f_2566_3,plain,
! [U_10030,U_10031,U_10032] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10031,U_10031),tc_HOL_Obool)),U_10030),U_10032))
| U_10030 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10031,U_10031),tc_HOL_Obool)) ),
inference(definitional_conversion,[status(esa)],[f_2566_2]) ).
cnf(f_2566_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10031,U_10031),tc_HOL_Obool)),U_10030),U_10032))
| U_10030 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10031,U_10031),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2566_3]) ).
fof(f_2567_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_2567_2,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_2567_1]) ).
cnf(f_2567_3,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_2567_2]) ).
fof(f_2568_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_2568_2,plain,
! [U_10033] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10033))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10033)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10033))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10033)) ) ),
inference(variable_rename,[status(thm)],[f_2568_1]) ).
fof(f_2568_3,plain,
( ! [U_10035] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10035)) )
& ! [U_10034] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10034))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10034)) ) ),
inference(miniscope,[status(thm)],[f_2568_2]) ).
fof(f_2568_4,plain,
( ! [U_10035] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10035)) )
& ! [U_10034] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10034))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10034)) ) ),
inference(definitional_conversion,[status(esa)],[f_2568_3]) ).
cnf(f_2568_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10034))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10034)) ),
inference(clausify,[status(thm)],[f_2568_4]) ).
cnf(f_2568_6,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10035)) ),
inference(clausify,[status(thm)],[f_2568_4]) ).
fof(f_2569_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_2569_2,plain,
! [U_10036] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10036))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10036),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10036),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10036)) ) ),
inference(variable_rename,[status(thm)],[f_2569_1]) ).
fof(f_2569_3,plain,
( ! [U_10038] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10038),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_10037] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10037),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10037)) ) ),
inference(miniscope,[status(thm)],[f_2569_2]) ).
fof(f_2569_4,plain,
( ! [U_10038] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10038),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_10037] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10037),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10037)) ) ),
inference(definitional_conversion,[status(esa)],[f_2569_3]) ).
cnf(f_2569_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10037),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10037)) ),
inference(clausify,[status(thm)],[f_2569_4]) ).
cnf(f_2569_6,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10038),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2569_4]) ).
fof(f_2570_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_2570_2,plain,
! [U_10039] :
( hAPP(c_Int_Onat,U_10039) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10039)) ),
inference(variable_rename,[status(thm)],[f_2570_1]) ).
fof(f_2570_3,plain,
! [U_10039] :
( hAPP(c_Int_Onat,U_10039) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10039)) ),
inference(definitional_conversion,[status(esa)],[f_2570_2]) ).
cnf(f_2570_4,plain,
( hAPP(c_Int_Onat,U_10039) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10039)) ),
inference(clausify,[status(thm)],[f_2570_3]) ).
fof(f_2571_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_2571_2,plain,
! [U_10040] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_10040)) = U_10040
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10040)) ),
inference(variable_rename,[status(thm)],[f_2571_1]) ).
fof(f_2571_3,plain,
! [U_10040] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_10040)) = U_10040
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10040)) ),
inference(definitional_conversion,[status(esa)],[f_2571_2]) ).
cnf(f_2571_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_10040)) = U_10040
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10040)) ),
inference(clausify,[status(thm)],[f_2571_3]) ).
fof(f_2572_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_2572_2,plain,
! [U_10041] : 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_10041))))),
inference(variable_rename,[status(thm)],[f_2572_1]) ).
fof(f_2572_3,plain,
! [U_10041] : 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_10041))))),
inference(definitional_conversion,[status(esa)],[f_2572_2]) ).
cnf(f_2572_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_10041))))),
inference(clausify,[status(thm)],[f_2572_3]) ).
fof(f_2573_1,plain,
! [V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com1_2)),c_Com_Ocom_Ocom__size(V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_com_Osize_I5_J]) ).
fof(f_2573_2,plain,
! [U_10044,U_10043,U_10042] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_10042,U_10043,U_10044)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_10043)),c_Com_Ocom_Ocom__size(U_10044))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2573_1]) ).
fof(f_2573_3,plain,
! [U_10042,U_10043,U_10044] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_10042,U_10043,U_10044)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_10043)),c_Com_Ocom_Ocom__size(U_10044))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_2573_2]) ).
cnf(f_2573_4,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_10042,U_10043,U_10044)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_10043)),c_Com_Ocom_Ocom__size(U_10044))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2573_3]) ).
fof(f_2574_1,plain,
! [V_com2_2,V_com1_2,V_fun_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1_2)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_com_Osize_I13_J]) ).
fof(f_2574_2,plain,
! [U_10047,U_10046,U_10045] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_10045,U_10046,U_10047)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_10046)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_10047))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2574_1]) ).
fof(f_2574_3,plain,
! [U_10045,U_10046,U_10047] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_10045,U_10046,U_10047)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_10046)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_10047))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_2574_2]) ).
cnf(f_2574_4,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_10045,U_10046,U_10047)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_10046)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_10047))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2574_3]) ).
fof(f_2575_1,plain,
! [V_f_2,V_S_2,T_c,T_d] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_f_2),c_Groups_Oone__class_Oone(T_d)),V_S_2) = c_Groups_Oone__class_Oone(T_d)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_d)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_S_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__1]) ).
fof(f_2575_2,plain,
! [U_10052,U_10051,U_10050,U_10049] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10049,U_10050,c_Groups_Otimes__class_Otimes(U_10049)),U_10052),c_Groups_Oone__class_Oone(U_10049)),U_10051) = c_Groups_Oone__class_Oone(U_10049)
| ? [U_10048] :
( hAPP(U_10052,U_10048) != c_Groups_Oone__class_Oone(U_10049)
& hBOOL(hAPP(hAPP(c_member(U_10050),U_10048),U_10051)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10050),U_10051))
| ~ class_Groups_Ocomm__monoid__mult(U_10049) ),
inference(variable_rename,[status(thm)],[f_2575_1]) ).
fof(f_2575_3,plain,
! [U_10052,U_10051,U_10050,U_10049] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10049,U_10050,c_Groups_Otimes__class_Otimes(U_10049)),U_10052),c_Groups_Oone__class_Oone(U_10049)),U_10051) = c_Groups_Oone__class_Oone(U_10049)
| ( hAPP(U_10052,sK260(U_10052,U_10051,U_10050,U_10049)) != c_Groups_Oone__class_Oone(U_10049)
& hBOOL(hAPP(hAPP(c_member(U_10050),sK260(U_10052,U_10051,U_10050,U_10049)),U_10051)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10050),U_10051))
| ~ class_Groups_Ocomm__monoid__mult(U_10049) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_10048,sK260(U_10052,U_10051,U_10050,U_10049))],[f_2575_2]) ).
fof(f_2575_4,plain,
( ! [U_10049,U_10050,U_10051,U_10052] :
( hAPP(U_10052,sK260(U_10052,U_10051,U_10050,U_10049)) != c_Groups_Oone__class_Oone(U_10049)
| ~ sP693(U_10049,U_10050,U_10051,U_10052) )
& ! [U_10049,U_10050,U_10051,U_10052] :
( hBOOL(hAPP(hAPP(c_member(U_10050),sK260(U_10052,U_10051,U_10050,U_10049)),U_10051))
| ~ sP693(U_10049,U_10050,U_10051,U_10052) )
& ! [U_10049,U_10050,U_10051,U_10052] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10049,U_10050,c_Groups_Otimes__class_Otimes(U_10049)),U_10052),c_Groups_Oone__class_Oone(U_10049)),U_10051) = c_Groups_Oone__class_Oone(U_10049)
| sP693(U_10049,U_10050,U_10051,U_10052)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10050),U_10051))
| ~ class_Groups_Ocomm__monoid__mult(U_10049) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP693])],[f_2575_3]) ).
cnf(f_2575_5,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10049,U_10050,c_Groups_Otimes__class_Otimes(U_10049)),U_10052),c_Groups_Oone__class_Oone(U_10049)),U_10051) = c_Groups_Oone__class_Oone(U_10049)
| sP693(U_10049,U_10050,U_10051,U_10052)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10050),U_10051))
| ~ class_Groups_Ocomm__monoid__mult(U_10049) ),
inference(clausify,[status(thm)],[f_2575_4]) ).
cnf(f_2575_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10050),sK260(U_10052,U_10051,U_10050,U_10049)),U_10051))
| ~ sP693(U_10049,U_10050,U_10051,U_10052) ),
inference(clausify,[status(thm)],[f_2575_4]) ).
cnf(f_2575_7,plain,
( hAPP(U_10052,sK260(U_10052,U_10051,U_10050,U_10049)) != c_Groups_Oone__class_Oone(U_10049)
| ~ sP693(U_10049,U_10050,U_10051,U_10052) ),
inference(clausify,[status(thm)],[f_2575_4]) ).
fof(f_2576_1,plain,
! [V_A_2,T_c] :
( hAPP(c_Finite__Set_Ocard(T_c),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_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oneutral]) ).
fof(f_2576_2,plain,
! [U_10055,U_10054] :
( hAPP(c_Finite__Set_Ocard(U_10054),U_10055) = 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_10053] : hBOOL(hAPP(hAPP(c_member(U_10054),U_10053),U_10055)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10054),U_10055)) ),
inference(variable_rename,[status(thm)],[f_2576_1]) ).
fof(f_2576_3,plain,
! [U_10055,U_10054] :
( hAPP(c_Finite__Set_Ocard(U_10054),U_10055) = 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_10054),sK261(U_10055,U_10054)),U_10055)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10054),U_10055)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_10053,sK261(U_10055,U_10054))],[f_2576_2]) ).
fof(f_2576_4,plain,
( ! [U_10055,U_10054] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP694(U_10055,U_10054) )
& ! [U_10055,U_10054] :
( hBOOL(hAPP(hAPP(c_member(U_10054),sK261(U_10055,U_10054)),U_10055))
| ~ sP694(U_10055,U_10054) )
& ! [U_10055,U_10054] :
( hAPP(c_Finite__Set_Ocard(U_10054),U_10055) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP694(U_10055,U_10054)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10054),U_10055)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP694])],[f_2576_3]) ).
cnf(f_2576_5,plain,
( hAPP(c_Finite__Set_Ocard(U_10054),U_10055) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP694(U_10055,U_10054)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10054),U_10055)) ),
inference(clausify,[status(thm)],[f_2576_4]) ).
cnf(f_2576_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10054),sK261(U_10055,U_10054)),U_10055))
| ~ sP694(U_10055,U_10054) ),
inference(clausify,[status(thm)],[f_2576_4]) ).
cnf(f_2576_7,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP694(U_10055,U_10054) ),
inference(clausify,[status(thm)],[f_2576_4]) ).
fof(f_2577_1,plain,
! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
( ( c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) = c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2)
| V_com2_2 != V_com2_H_2
| V_com1_2 != V_com1_H_2
| V_fun_2 != V_fun_H_2 )
& ( ( V_com2_2 = V_com2_H_2
& V_com1_2 = V_com1_H_2
& V_fun_2 = V_fun_H_2 )
| c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I4_J]) ).
fof(f_2577_2,plain,
! [U_10061,U_10060,U_10059,U_10058,U_10057,U_10056] :
( ( c_Com_Ocom_OCond(U_10056,U_10057,U_10058) = c_Com_Ocom_OCond(U_10059,U_10060,U_10061)
| U_10058 != U_10061
| U_10057 != U_10060
| U_10056 != U_10059 )
& ( ( U_10058 = U_10061
& U_10057 = U_10060
& U_10056 = U_10059 )
| c_Com_Ocom_OCond(U_10056,U_10057,U_10058) != c_Com_Ocom_OCond(U_10059,U_10060,U_10061) ) ),
inference(variable_rename,[status(thm)],[f_2577_1]) ).
fof(f_2577_3,plain,
( ! [U_10073,U_10071,U_10069,U_10067,U_10065,U_10063] :
( c_Com_Ocom_OCond(U_10063,U_10065,U_10067) = c_Com_Ocom_OCond(U_10069,U_10071,U_10073)
| U_10067 != U_10073
| U_10065 != U_10071
| U_10063 != U_10069 )
& ! [U_10072,U_10070,U_10068,U_10066,U_10064,U_10062] :
( ( U_10066 = U_10072
& U_10064 = U_10070
& U_10062 = U_10068 )
| c_Com_Ocom_OCond(U_10062,U_10064,U_10066) != c_Com_Ocom_OCond(U_10068,U_10070,U_10072) ) ),
inference(miniscope,[status(thm)],[f_2577_2]) ).
fof(f_2577_4,plain,
( ! [U_10068,U_10070,U_10066,U_10062,U_10064,U_10072] :
( U_10066 = U_10072
| ~ sP695(U_10068,U_10070,U_10066,U_10062,U_10064,U_10072) )
& ! [U_10068,U_10070,U_10066,U_10062,U_10064,U_10072] :
( U_10064 = U_10070
| ~ sP695(U_10068,U_10070,U_10066,U_10062,U_10064,U_10072) )
& ! [U_10068,U_10070,U_10066,U_10062,U_10064,U_10072] :
( U_10062 = U_10068
| ~ sP695(U_10068,U_10070,U_10066,U_10062,U_10064,U_10072) )
& ! [U_10071,U_10069,U_10067,U_10065,U_10063,U_10073] :
( c_Com_Ocom_OCond(U_10063,U_10065,U_10067) = c_Com_Ocom_OCond(U_10069,U_10071,U_10073)
| U_10067 != U_10073
| U_10065 != U_10071
| U_10063 != U_10069 )
& ! [U_10068,U_10070,U_10066,U_10062,U_10064,U_10072] :
( sP695(U_10068,U_10070,U_10066,U_10062,U_10064,U_10072)
| c_Com_Ocom_OCond(U_10062,U_10064,U_10066) != c_Com_Ocom_OCond(U_10068,U_10070,U_10072) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP695])],[f_2577_3]) ).
cnf(f_2577_5,plain,
( sP695(U_10068,U_10070,U_10066,U_10062,U_10064,U_10072)
| c_Com_Ocom_OCond(U_10062,U_10064,U_10066) != c_Com_Ocom_OCond(U_10068,U_10070,U_10072) ),
inference(clausify,[status(thm)],[f_2577_4]) ).
cnf(f_2577_6,plain,
( c_Com_Ocom_OCond(U_10063,U_10065,U_10067) = c_Com_Ocom_OCond(U_10069,U_10071,U_10073)
| U_10067 != U_10073
| U_10065 != U_10071
| U_10063 != U_10069 ),
inference(clausify,[status(thm)],[f_2577_4]) ).
cnf(f_2577_7,plain,
( U_10062 = U_10068
| ~ sP695(U_10068,U_10070,U_10066,U_10062,U_10064,U_10072) ),
inference(clausify,[status(thm)],[f_2577_4]) ).
cnf(f_2577_8,plain,
( U_10064 = U_10070
| ~ sP695(U_10068,U_10070,U_10066,U_10062,U_10064,U_10072) ),
inference(clausify,[status(thm)],[f_2577_4]) ).
cnf(f_2577_9,plain,
( U_10066 = U_10072
| ~ sP695(U_10068,U_10070,U_10066,U_10062,U_10064,U_10072) ),
inference(clausify,[status(thm)],[f_2577_4]) ).
fof(f_2578_1,plain,
! [V_com_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I52_J]) ).
fof(f_2578_2,plain,
! [U_10078,U_10077,U_10076,U_10075,U_10074] : c_Com_Ocom_OCond(U_10074,U_10075,U_10076) != c_Com_Ocom_OWhile(U_10077,U_10078),
inference(variable_rename,[status(thm)],[f_2578_1]) ).
fof(f_2578_3,plain,
! [U_10078,U_10077,U_10075,U_10074,U_10076] : c_Com_Ocom_OCond(U_10074,U_10075,U_10076) != c_Com_Ocom_OWhile(U_10077,U_10078),
inference(definitional_conversion,[status(esa)],[f_2578_2]) ).
cnf(f_2578_4,plain,
c_Com_Ocom_OCond(U_10074,U_10075,U_10076) != c_Com_Ocom_OWhile(U_10077,U_10078),
inference(clausify,[status(thm)],[f_2578_3]) ).
fof(f_2579_1,plain,
! [V_com2_2,V_com1_2,V_fun_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I53_J]) ).
fof(f_2579_2,plain,
! [U_10083,U_10082,U_10081,U_10080,U_10079] : c_Com_Ocom_OWhile(U_10079,U_10080) != c_Com_Ocom_OCond(U_10081,U_10082,U_10083),
inference(variable_rename,[status(thm)],[f_2579_1]) ).
fof(f_2579_3,plain,
! [U_10079,U_10081,U_10080,U_10083,U_10082] : c_Com_Ocom_OWhile(U_10079,U_10080) != c_Com_Ocom_OCond(U_10081,U_10082,U_10083),
inference(definitional_conversion,[status(esa)],[f_2579_2]) ).
cnf(f_2579_4,plain,
c_Com_Ocom_OWhile(U_10079,U_10080) != c_Com_Ocom_OCond(U_10081,U_10082,U_10083),
inference(clausify,[status(thm)],[f_2579_3]) ).
fof(f_2580_1,plain,
! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I45_J]) ).
fof(f_2580_2,plain,
! [U_10088,U_10087,U_10086,U_10085,U_10084] : c_Com_Ocom_OCond(U_10084,U_10085,U_10086) != c_Com_Ocom_OSemi(U_10087,U_10088),
inference(variable_rename,[status(thm)],[f_2580_1]) ).
fof(f_2580_3,plain,
! [U_10085,U_10087,U_10084,U_10086,U_10088] : c_Com_Ocom_OCond(U_10084,U_10085,U_10086) != c_Com_Ocom_OSemi(U_10087,U_10088),
inference(definitional_conversion,[status(esa)],[f_2580_2]) ).
cnf(f_2580_4,plain,
c_Com_Ocom_OCond(U_10084,U_10085,U_10086) != c_Com_Ocom_OSemi(U_10087,U_10088),
inference(clausify,[status(thm)],[f_2580_3]) ).
fof(f_2581_1,plain,
! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I44_J]) ).
fof(f_2581_2,plain,
! [U_10093,U_10092,U_10091,U_10090,U_10089] : c_Com_Ocom_OSemi(U_10089,U_10090) != c_Com_Ocom_OCond(U_10091,U_10092,U_10093),
inference(variable_rename,[status(thm)],[f_2581_1]) ).
fof(f_2581_3,plain,
! [U_10089,U_10090,U_10091,U_10092,U_10093] : c_Com_Ocom_OSemi(U_10089,U_10090) != c_Com_Ocom_OCond(U_10091,U_10092,U_10093),
inference(definitional_conversion,[status(esa)],[f_2581_2]) ).
cnf(f_2581_4,plain,
c_Com_Ocom_OSemi(U_10089,U_10090) != c_Com_Ocom_OCond(U_10091,U_10092,U_10093),
inference(clausify,[status(thm)],[f_2581_3]) ).
fof(f_2582_1,plain,
! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSKIP,
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I15_J]) ).
fof(f_2582_2,plain,
! [U_10096,U_10095,U_10094] : c_Com_Ocom_OCond(U_10094,U_10095,U_10096) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[f_2582_1]) ).
fof(f_2582_3,plain,
! [U_10095,U_10094,U_10096] : c_Com_Ocom_OCond(U_10094,U_10095,U_10096) != c_Com_Ocom_OSKIP,
inference(definitional_conversion,[status(esa)],[f_2582_2]) ).
cnf(f_2582_4,plain,
c_Com_Ocom_OCond(U_10094,U_10095,U_10096) != c_Com_Ocom_OSKIP,
inference(clausify,[status(thm)],[f_2582_3]) ).
fof(f_2583_1,plain,
! [V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I14_J]) ).
fof(f_2583_2,plain,
! [U_10099,U_10098,U_10097] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_10097,U_10098,U_10099),
inference(variable_rename,[status(thm)],[f_2583_1]) ).
fof(f_2583_3,plain,
! [U_10097,U_10098,U_10099] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_10097,U_10098,U_10099),
inference(definitional_conversion,[status(esa)],[f_2583_2]) ).
cnf(f_2583_4,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_10097,U_10098,U_10099),
inference(clausify,[status(thm)],[f_2583_3]) ).
fof(f_2584_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_2584_2,plain,
! [U_10103,U_10102,U_10101] :
( hBOOL(hAPP(U_10102,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10103),U_10101))
| ~ hBOOL(hAPP(U_10102,U_10103))
| ? [U_10100] :
( ~ hBOOL(hAPP(U_10102,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10100),U_10101)))
& hBOOL(hAPP(U_10102,U_10100))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10100),U_10101)) ) ),
inference(variable_rename,[status(thm)],[f_2584_1]) ).
fof(f_2584_3,plain,
! [U_10103,U_10102,U_10101] :
( hBOOL(hAPP(U_10102,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10103),U_10101))
| ~ hBOOL(hAPP(U_10102,U_10103))
| ( ~ hBOOL(hAPP(U_10102,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK262(U_10103,U_10102,U_10101)),U_10101)))
& hBOOL(hAPP(U_10102,sK262(U_10103,U_10102,U_10101)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK262(U_10103,U_10102,U_10101)),U_10101)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_10100,sK262(U_10103,U_10102,U_10101))],[f_2584_2]) ).
fof(f_2584_4,plain,
( ! [U_10101,U_10102,U_10103] :
( ~ hBOOL(hAPP(U_10102,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK262(U_10103,U_10102,U_10101)),U_10101)))
| ~ sP696(U_10101,U_10102,U_10103) )
& ! [U_10101,U_10102,U_10103] :
( hBOOL(hAPP(U_10102,sK262(U_10103,U_10102,U_10101)))
| ~ sP696(U_10101,U_10102,U_10103) )
& ! [U_10101,U_10102,U_10103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK262(U_10103,U_10102,U_10101)),U_10101))
| ~ sP696(U_10101,U_10102,U_10103) )
& ! [U_10101,U_10102,U_10103] :
( hBOOL(hAPP(U_10102,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10103),U_10101))
| ~ hBOOL(hAPP(U_10102,U_10103))
| sP696(U_10101,U_10102,U_10103) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP696])],[f_2584_3]) ).
cnf(f_2584_5,plain,
( hBOOL(hAPP(U_10102,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10103),U_10101))
| ~ hBOOL(hAPP(U_10102,U_10103))
| sP696(U_10101,U_10102,U_10103) ),
inference(clausify,[status(thm)],[f_2584_4]) ).
cnf(f_2584_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK262(U_10103,U_10102,U_10101)),U_10101))
| ~ sP696(U_10101,U_10102,U_10103) ),
inference(clausify,[status(thm)],[f_2584_4]) ).
cnf(f_2584_7,plain,
( hBOOL(hAPP(U_10102,sK262(U_10103,U_10102,U_10101)))
| ~ sP696(U_10101,U_10102,U_10103) ),
inference(clausify,[status(thm)],[f_2584_4]) ).
cnf(f_2584_8,plain,
( ~ hBOOL(hAPP(U_10102,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK262(U_10103,U_10102,U_10101)),U_10101)))
| ~ sP696(U_10101,U_10102,U_10103) ),
inference(clausify,[status(thm)],[f_2584_4]) ).
fof(f_2585_1,plain,
! [V_A_2,V_C_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,tc_HOL_Obool),V_C_2)))
| ? [B_X] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_A_2),B_X))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),B_X),V_C_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_InterI]) ).
fof(f_2585_2,plain,
! [U_10107,U_10106,U_10105] :
( hBOOL(hAPP(hAPP(c_member(U_10105),U_10107),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10105,tc_HOL_Obool),U_10106)))
| ? [U_10104] :
( ~ hBOOL(hAPP(hAPP(c_member(U_10105),U_10107),U_10104))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_10105,tc_HOL_Obool)),U_10104),U_10106)) ) ),
inference(variable_rename,[status(thm)],[f_2585_1]) ).
fof(f_2585_3,plain,
! [U_10107,U_10106,U_10105] :
( hBOOL(hAPP(hAPP(c_member(U_10105),U_10107),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10105,tc_HOL_Obool),U_10106)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_10105),U_10107),sK263(U_10107,U_10106,U_10105)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_10105,tc_HOL_Obool)),sK263(U_10107,U_10106,U_10105)),U_10106)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_10104,sK263(U_10107,U_10106,U_10105))],[f_2585_2]) ).
fof(f_2585_4,plain,
( ! [U_10106,U_10107,U_10105] :
( ~ hBOOL(hAPP(hAPP(c_member(U_10105),U_10107),sK263(U_10107,U_10106,U_10105)))
| ~ sP697(U_10106,U_10107,U_10105) )
& ! [U_10106,U_10107,U_10105] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10105,tc_HOL_Obool)),sK263(U_10107,U_10106,U_10105)),U_10106))
| ~ sP697(U_10106,U_10107,U_10105) )
& ! [U_10106,U_10107,U_10105] :
( hBOOL(hAPP(hAPP(c_member(U_10105),U_10107),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10105,tc_HOL_Obool),U_10106)))
| sP697(U_10106,U_10107,U_10105) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP697])],[f_2585_3]) ).
cnf(f_2585_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_10105),U_10107),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10105,tc_HOL_Obool),U_10106)))
| sP697(U_10106,U_10107,U_10105) ),
inference(clausify,[status(thm)],[f_2585_4]) ).
cnf(f_2585_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10105,tc_HOL_Obool)),sK263(U_10107,U_10106,U_10105)),U_10106))
| ~ sP697(U_10106,U_10107,U_10105) ),
inference(clausify,[status(thm)],[f_2585_4]) ).
cnf(f_2585_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_10105),U_10107),sK263(U_10107,U_10106,U_10105)))
| ~ sP697(U_10106,U_10107,U_10105) ),
inference(clausify,[status(thm)],[f_2585_4]) ).
fof(f_2586_1,plain,
! [V_z_2,V_h_2,V_g_2,V_A_2,T_c,T_d] :
( 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),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),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_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__cong]) ).
fof(f_2586_2,plain,
! [U_10114,U_10113,U_10112,U_10111,U_10110,U_10109] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10109,U_10110,c_Groups_Otimes__class_Otimes(U_10109)),U_10112),U_10114),U_10111) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10109,U_10110,c_Groups_Otimes__class_Otimes(U_10109)),U_10113),U_10114),U_10111)
| ? [U_10108] :
( hAPP(U_10112,U_10108) != hAPP(U_10113,U_10108)
& hBOOL(hAPP(hAPP(c_member(U_10110),U_10108),U_10111)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10110),U_10111))
| ~ class_Groups_Oab__semigroup__mult(U_10109) ),
inference(variable_rename,[status(thm)],[f_2586_1]) ).
fof(f_2586_3,plain,
! [U_10114,U_10113,U_10112,U_10111,U_10110,U_10109] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10109,U_10110,c_Groups_Otimes__class_Otimes(U_10109)),U_10112),U_10114),U_10111) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10109,U_10110,c_Groups_Otimes__class_Otimes(U_10109)),U_10113),U_10114),U_10111)
| ( hAPP(U_10112,sK264(U_10114,U_10113,U_10112,U_10111,U_10110,U_10109)) != hAPP(U_10113,sK264(U_10114,U_10113,U_10112,U_10111,U_10110,U_10109))
& hBOOL(hAPP(hAPP(c_member(U_10110),sK264(U_10114,U_10113,U_10112,U_10111,U_10110,U_10109)),U_10111)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10110),U_10111))
| ~ class_Groups_Oab__semigroup__mult(U_10109) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_10108,sK264(U_10114,U_10113,U_10112,U_10111,U_10110,U_10109))],[f_2586_2]) ).
fof(f_2586_4,plain,
( ! [U_10109,U_10110,U_10111,U_10112,U_10113,U_10114] :
( hAPP(U_10112,sK264(U_10114,U_10113,U_10112,U_10111,U_10110,U_10109)) != hAPP(U_10113,sK264(U_10114,U_10113,U_10112,U_10111,U_10110,U_10109))
| ~ sP698(U_10109,U_10110,U_10111,U_10112,U_10113,U_10114) )
& ! [U_10109,U_10110,U_10111,U_10112,U_10113,U_10114] :
( hBOOL(hAPP(hAPP(c_member(U_10110),sK264(U_10114,U_10113,U_10112,U_10111,U_10110,U_10109)),U_10111))
| ~ sP698(U_10109,U_10110,U_10111,U_10112,U_10113,U_10114) )
& ! [U_10109,U_10110,U_10111,U_10112,U_10113,U_10114] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10109,U_10110,c_Groups_Otimes__class_Otimes(U_10109)),U_10112),U_10114),U_10111) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10109,U_10110,c_Groups_Otimes__class_Otimes(U_10109)),U_10113),U_10114),U_10111)
| sP698(U_10109,U_10110,U_10111,U_10112,U_10113,U_10114)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10110),U_10111))
| ~ class_Groups_Oab__semigroup__mult(U_10109) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP698])],[f_2586_3]) ).
cnf(f_2586_5,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10109,U_10110,c_Groups_Otimes__class_Otimes(U_10109)),U_10112),U_10114),U_10111) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10109,U_10110,c_Groups_Otimes__class_Otimes(U_10109)),U_10113),U_10114),U_10111)
| sP698(U_10109,U_10110,U_10111,U_10112,U_10113,U_10114)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10110),U_10111))
| ~ class_Groups_Oab__semigroup__mult(U_10109) ),
inference(clausify,[status(thm)],[f_2586_4]) ).
cnf(f_2586_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10110),sK264(U_10114,U_10113,U_10112,U_10111,U_10110,U_10109)),U_10111))
| ~ sP698(U_10109,U_10110,U_10111,U_10112,U_10113,U_10114) ),
inference(clausify,[status(thm)],[f_2586_4]) ).
cnf(f_2586_7,plain,
( hAPP(U_10112,sK264(U_10114,U_10113,U_10112,U_10111,U_10110,U_10109)) != hAPP(U_10113,sK264(U_10114,U_10113,U_10112,U_10111,U_10110,U_10109))
| ~ sP698(U_10109,U_10110,U_10111,U_10112,U_10113,U_10114) ),
inference(clausify,[status(thm)],[f_2586_4]) ).
fof(f_2587_1,plain,
! [V_c_2,V_b_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_c_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inf__le__fold__inf]) ).
fof(f_2587_2,plain,
! [U_10119,U_10118,U_10117,U_10116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10116),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10116),U_10118),U_10119)),hAPP(hAPP(c_Finite__Set_Ofold(U_10116,U_10116,c_Lattices_Osemilattice__inf__class_Oinf(U_10116)),U_10119),U_10117)))
| ? [U_10115] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10116),U_10118),U_10115))
& hBOOL(hAPP(hAPP(c_member(U_10116),U_10115),U_10117)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10116),U_10117))
| ~ class_Lattices_Osemilattice__inf(U_10116) ),
inference(variable_rename,[status(thm)],[f_2587_1]) ).
fof(f_2587_3,plain,
! [U_10119,U_10118,U_10117,U_10116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10116),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10116),U_10118),U_10119)),hAPP(hAPP(c_Finite__Set_Ofold(U_10116,U_10116,c_Lattices_Osemilattice__inf__class_Oinf(U_10116)),U_10119),U_10117)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10116),U_10118),sK265(U_10119,U_10118,U_10117,U_10116)))
& hBOOL(hAPP(hAPP(c_member(U_10116),sK265(U_10119,U_10118,U_10117,U_10116)),U_10117)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10116),U_10117))
| ~ class_Lattices_Osemilattice__inf(U_10116) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_10115,sK265(U_10119,U_10118,U_10117,U_10116))],[f_2587_2]) ).
fof(f_2587_4,plain,
( ! [U_10116,U_10118,U_10117,U_10119] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10116),U_10118),sK265(U_10119,U_10118,U_10117,U_10116)))
| ~ sP699(U_10116,U_10118,U_10117,U_10119) )
& ! [U_10116,U_10118,U_10117,U_10119] :
( hBOOL(hAPP(hAPP(c_member(U_10116),sK265(U_10119,U_10118,U_10117,U_10116)),U_10117))
| ~ sP699(U_10116,U_10118,U_10117,U_10119) )
& ! [U_10116,U_10118,U_10117,U_10119] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10116),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10116),U_10118),U_10119)),hAPP(hAPP(c_Finite__Set_Ofold(U_10116,U_10116,c_Lattices_Osemilattice__inf__class_Oinf(U_10116)),U_10119),U_10117)))
| sP699(U_10116,U_10118,U_10117,U_10119)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10116),U_10117))
| ~ class_Lattices_Osemilattice__inf(U_10116) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP699])],[f_2587_3]) ).
cnf(f_2587_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10116),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10116),U_10118),U_10119)),hAPP(hAPP(c_Finite__Set_Ofold(U_10116,U_10116,c_Lattices_Osemilattice__inf__class_Oinf(U_10116)),U_10119),U_10117)))
| sP699(U_10116,U_10118,U_10117,U_10119)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10116),U_10117))
| ~ class_Lattices_Osemilattice__inf(U_10116) ),
inference(clausify,[status(thm)],[f_2587_4]) ).
cnf(f_2587_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10116),sK265(U_10119,U_10118,U_10117,U_10116)),U_10117))
| ~ sP699(U_10116,U_10118,U_10117,U_10119) ),
inference(clausify,[status(thm)],[f_2587_4]) ).
cnf(f_2587_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10116),U_10118),sK265(U_10119,U_10118,U_10117,U_10116)))
| ~ sP699(U_10116,U_10118,U_10117,U_10119) ),
inference(clausify,[status(thm)],[f_2587_4]) ).
fof(f_2588_1,plain,
! [V_c_2,V_b_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_c,c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_b_2),V_c_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ class_Lattices_Osemilattice__sup(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__sup__le__sup]) ).
fof(f_2588_2,plain,
! [U_10124,U_10123,U_10122,U_10121] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10121),hAPP(hAPP(c_Finite__Set_Ofold(U_10121,U_10121,c_Lattices_Osemilattice__sup__class_Osup(U_10121)),U_10124),U_10122)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10121),U_10123),U_10124)))
| ? [U_10120] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10121),U_10120),U_10123))
& hBOOL(hAPP(hAPP(c_member(U_10121),U_10120),U_10122)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10121),U_10122))
| ~ class_Lattices_Osemilattice__sup(U_10121) ),
inference(variable_rename,[status(thm)],[f_2588_1]) ).
fof(f_2588_3,plain,
! [U_10124,U_10123,U_10122,U_10121] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10121),hAPP(hAPP(c_Finite__Set_Ofold(U_10121,U_10121,c_Lattices_Osemilattice__sup__class_Osup(U_10121)),U_10124),U_10122)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10121),U_10123),U_10124)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10121),sK266(U_10124,U_10123,U_10122,U_10121)),U_10123))
& hBOOL(hAPP(hAPP(c_member(U_10121),sK266(U_10124,U_10123,U_10122,U_10121)),U_10122)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10121),U_10122))
| ~ class_Lattices_Osemilattice__sup(U_10121) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_10120,sK266(U_10124,U_10123,U_10122,U_10121))],[f_2588_2]) ).
fof(f_2588_4,plain,
( ! [U_10121,U_10122,U_10123,U_10124] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10121),sK266(U_10124,U_10123,U_10122,U_10121)),U_10123))
| ~ sP700(U_10121,U_10122,U_10123,U_10124) )
& ! [U_10121,U_10122,U_10123,U_10124] :
( hBOOL(hAPP(hAPP(c_member(U_10121),sK266(U_10124,U_10123,U_10122,U_10121)),U_10122))
| ~ sP700(U_10121,U_10122,U_10123,U_10124) )
& ! [U_10121,U_10122,U_10123,U_10124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10121),hAPP(hAPP(c_Finite__Set_Ofold(U_10121,U_10121,c_Lattices_Osemilattice__sup__class_Osup(U_10121)),U_10124),U_10122)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10121),U_10123),U_10124)))
| sP700(U_10121,U_10122,U_10123,U_10124)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10121),U_10122))
| ~ class_Lattices_Osemilattice__sup(U_10121) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP700])],[f_2588_3]) ).
cnf(f_2588_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10121),hAPP(hAPP(c_Finite__Set_Ofold(U_10121,U_10121,c_Lattices_Osemilattice__sup__class_Osup(U_10121)),U_10124),U_10122)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10121),U_10123),U_10124)))
| sP700(U_10121,U_10122,U_10123,U_10124)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10121),U_10122))
| ~ class_Lattices_Osemilattice__sup(U_10121) ),
inference(clausify,[status(thm)],[f_2588_4]) ).
cnf(f_2588_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10121),sK266(U_10124,U_10123,U_10122,U_10121)),U_10122))
| ~ sP700(U_10121,U_10122,U_10123,U_10124) ),
inference(clausify,[status(thm)],[f_2588_4]) ).
cnf(f_2588_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10121),sK266(U_10124,U_10123,U_10122,U_10121)),U_10123))
| ~ sP700(U_10121,U_10122,U_10123,U_10124) ),
inference(clausify,[status(thm)],[f_2588_4]) ).
fof(f_2589_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_2589_2,plain,
! [U_10125] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10125) = 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_10125)),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_10125))) ),
inference(variable_rename,[status(thm)],[f_2589_1]) ).
fof(f_2589_3,plain,
! [U_10125] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10125) = 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_10125)),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_10125))) ),
inference(definitional_conversion,[status(esa)],[f_2589_2]) ).
cnf(f_2589_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10125) = 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_10125)),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_10125))) ),
inference(clausify,[status(thm)],[f_2589_3]) ).
fof(f_2590_1,plain,
! [V_Y_2,V_X_2,V_r_2,V_A_2,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_X_2 = V_Y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_quotient__disj]) ).
fof(f_2590_2,plain,
! [U_10130,U_10129,U_10128,U_10127,U_10126] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10126,tc_HOL_Obool)),U_10129),U_10130) = c_Orderings_Obot__class_Obot(tc_fun(U_10126,tc_HOL_Obool))
| U_10129 = U_10130
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10126,tc_HOL_Obool)),U_10130),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10126),U_10127),U_10128)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10126,tc_HOL_Obool)),U_10129),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10126),U_10127),U_10128)))
| ~ c_Equiv__Relations_Oequiv(U_10126,U_10127,U_10128) ),
inference(variable_rename,[status(thm)],[f_2590_1]) ).
fof(f_2590_3,plain,
! [U_10126,U_10127,U_10128,U_10129,U_10130] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10126,tc_HOL_Obool)),U_10129),U_10130) = c_Orderings_Obot__class_Obot(tc_fun(U_10126,tc_HOL_Obool))
| U_10129 = U_10130
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10126,tc_HOL_Obool)),U_10130),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10126),U_10127),U_10128)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10126,tc_HOL_Obool)),U_10129),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10126),U_10127),U_10128)))
| ~ c_Equiv__Relations_Oequiv(U_10126,U_10127,U_10128) ),
inference(definitional_conversion,[status(esa)],[f_2590_2]) ).
cnf(f_2590_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10126,tc_HOL_Obool)),U_10129),U_10130) = c_Orderings_Obot__class_Obot(tc_fun(U_10126,tc_HOL_Obool))
| U_10129 = U_10130
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10126,tc_HOL_Obool)),U_10130),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10126),U_10127),U_10128)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10126,tc_HOL_Obool)),U_10129),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10126),U_10127),U_10128)))
| ~ c_Equiv__Relations_Oequiv(U_10126,U_10127,U_10128) ),
inference(clausify,[status(thm)],[f_2590_3]) ).
fof(f_2591_1,plain,
! [V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_com_Osize_I3_J]) ).
fof(f_2591_2,plain,
! [U_10133,U_10132,U_10131] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_10131,U_10132,U_10133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_10133)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2591_1]) ).
fof(f_2591_3,plain,
! [U_10133,U_10132,U_10131] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_10131,U_10132,U_10133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_10133)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_2591_2]) ).
cnf(f_2591_4,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_10131,U_10132,U_10133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_10133)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2591_3]) ).
fof(f_2592_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_2592_2,plain,
! [U_10135,U_10134] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10134),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10135)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10134),U_10135)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10135))) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10134),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10135)) = c_Groups_Ozero__class_Ozero(U_10134)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10135))) ) )
| ~ class_Int_Onumber__ring(U_10134) ),
inference(variable_rename,[status(thm)],[f_2592_1]) ).
fof(f_2592_3,plain,
( ! [U_10134,U_10135] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10134),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10135)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10134),U_10135)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10135)))
| ~ sP701(U_10134,U_10135) )
& ! [U_10134,U_10135] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10134),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10135)) = c_Groups_Ozero__class_Ozero(U_10134)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10135)))
| ~ sP701(U_10134,U_10135) )
& ! [U_10134,U_10135] :
( sP701(U_10134,U_10135)
| ~ class_Int_Onumber__ring(U_10134) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP701])],[f_2592_2]) ).
cnf(f_2592_4,plain,
( sP701(U_10134,U_10135)
| ~ class_Int_Onumber__ring(U_10134) ),
inference(clausify,[status(thm)],[f_2592_3]) ).
cnf(f_2592_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10134),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10135)) = c_Groups_Ozero__class_Ozero(U_10134)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10135)))
| ~ sP701(U_10134,U_10135) ),
inference(clausify,[status(thm)],[f_2592_3]) ).
cnf(f_2592_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10134),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10135)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10134),U_10135)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10135)))
| ~ sP701(U_10134,U_10135) ),
inference(clausify,[status(thm)],[f_2592_3]) ).
fof(f_2593_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_2593_2,plain,
! [U_10137,U_10136] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10137)) = c_Groups_Ozero__class_Ozero(U_10136)
| 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_10137))) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10137)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10136),U_10137)
| ~ 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_10137))) ) )
| ~ class_Int_Onumber__ring(U_10136) ),
inference(variable_rename,[status(thm)],[f_2593_1]) ).
fof(f_2593_3,plain,
( ! [U_10136,U_10137] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10137)) = c_Groups_Ozero__class_Ozero(U_10136)
| 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_10137)))
| ~ sP702(U_10136,U_10137) )
& ! [U_10136,U_10137] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10137)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10136),U_10137)
| ~ 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_10137)))
| ~ sP702(U_10136,U_10137) )
& ! [U_10136,U_10137] :
( sP702(U_10136,U_10137)
| ~ class_Int_Onumber__ring(U_10136) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP702])],[f_2593_2]) ).
cnf(f_2593_4,plain,
( sP702(U_10136,U_10137)
| ~ class_Int_Onumber__ring(U_10136) ),
inference(clausify,[status(thm)],[f_2593_3]) ).
cnf(f_2593_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10137)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10136),U_10137)
| ~ 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_10137)))
| ~ sP702(U_10136,U_10137) ),
inference(clausify,[status(thm)],[f_2593_3]) ).
cnf(f_2593_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10136),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10137)) = c_Groups_Ozero__class_Ozero(U_10136)
| 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_10137)))
| ~ sP702(U_10136,U_10137) ),
inference(clausify,[status(thm)],[f_2593_3]) ).
fof(f_2594_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_2594_2,plain,
! [U_10139,U_10138] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10138),U_10139) = hAPP(c_Int_Oring__1__class_Oof__int(U_10138),U_10139)
| ~ class_Int_Onumber__ring(U_10138) ),
inference(variable_rename,[status(thm)],[f_2594_1]) ).
fof(f_2594_3,plain,
! [U_10138,U_10139] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10138),U_10139) = hAPP(c_Int_Oring__1__class_Oof__int(U_10138),U_10139)
| ~ class_Int_Onumber__ring(U_10138) ),
inference(definitional_conversion,[status(esa)],[f_2594_2]) ).
cnf(f_2594_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10138),U_10139) = hAPP(c_Int_Oring__1__class_Oof__int(U_10138),U_10139)
| ~ class_Int_Onumber__ring(U_10138) ),
inference(clausify,[status(thm)],[f_2594_3]) ).
fof(f_2595_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_2595_2,plain,
! [U_10141,U_10140] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_10140),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10141)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10140),U_10141)
| ~ class_Int_Onumber__ring(U_10140) ),
inference(variable_rename,[status(thm)],[f_2595_1]) ).
fof(f_2595_3,plain,
! [U_10140,U_10141] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_10140),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10141)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10140),U_10141)
| ~ class_Int_Onumber__ring(U_10140) ),
inference(definitional_conversion,[status(esa)],[f_2595_2]) ).
cnf(f_2595_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_10140),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10141)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10140),U_10141)
| ~ class_Int_Onumber__ring(U_10140) ),
inference(clausify,[status(thm)],[f_2595_3]) ).
fof(f_2596_1,plain,
! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
( ( c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) = c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2)
| V_com_2 != V_com_H_2
| V_fun_2 != V_fun_H_2
| V_loc_2 != V_loc_H_2 )
& ( ( V_com_2 = V_com_H_2
& V_fun_2 = V_fun_H_2
& V_loc_2 = V_loc_H_2 )
| c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I2_J]) ).
fof(f_2596_2,plain,
! [U_10147,U_10146,U_10145,U_10144,U_10143,U_10142] :
( ( c_Com_Ocom_OLocal(U_10142,U_10143,U_10144) = c_Com_Ocom_OLocal(U_10145,U_10146,U_10147)
| U_10144 != U_10147
| U_10143 != U_10146
| U_10142 != U_10145 )
& ( ( U_10144 = U_10147
& U_10143 = U_10146
& U_10142 = U_10145 )
| c_Com_Ocom_OLocal(U_10142,U_10143,U_10144) != c_Com_Ocom_OLocal(U_10145,U_10146,U_10147) ) ),
inference(variable_rename,[status(thm)],[f_2596_1]) ).
fof(f_2596_3,plain,
( ! [U_10159,U_10157,U_10155,U_10153,U_10151,U_10149] :
( c_Com_Ocom_OLocal(U_10149,U_10151,U_10153) = c_Com_Ocom_OLocal(U_10155,U_10157,U_10159)
| U_10153 != U_10159
| U_10151 != U_10157
| U_10149 != U_10155 )
& ! [U_10158,U_10156,U_10154,U_10152,U_10150,U_10148] :
( ( U_10152 = U_10158
& U_10150 = U_10156
& U_10148 = U_10154 )
| c_Com_Ocom_OLocal(U_10148,U_10150,U_10152) != c_Com_Ocom_OLocal(U_10154,U_10156,U_10158) ) ),
inference(miniscope,[status(thm)],[f_2596_2]) ).
fof(f_2596_4,plain,
( ! [U_10158,U_10152,U_10148,U_10154,U_10150,U_10156] :
( U_10152 = U_10158
| ~ sP703(U_10158,U_10152,U_10148,U_10154,U_10150,U_10156) )
& ! [U_10158,U_10152,U_10148,U_10154,U_10150,U_10156] :
( U_10150 = U_10156
| ~ sP703(U_10158,U_10152,U_10148,U_10154,U_10150,U_10156) )
& ! [U_10158,U_10152,U_10148,U_10154,U_10150,U_10156] :
( U_10148 = U_10154
| ~ sP703(U_10158,U_10152,U_10148,U_10154,U_10150,U_10156) )
& ! [U_10153,U_10151,U_10155,U_10149,U_10157,U_10159] :
( c_Com_Ocom_OLocal(U_10149,U_10151,U_10153) = c_Com_Ocom_OLocal(U_10155,U_10157,U_10159)
| U_10153 != U_10159
| U_10151 != U_10157
| U_10149 != U_10155 )
& ! [U_10158,U_10152,U_10148,U_10154,U_10150,U_10156] :
( sP703(U_10158,U_10152,U_10148,U_10154,U_10150,U_10156)
| c_Com_Ocom_OLocal(U_10148,U_10150,U_10152) != c_Com_Ocom_OLocal(U_10154,U_10156,U_10158) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP703])],[f_2596_3]) ).
cnf(f_2596_5,plain,
( sP703(U_10158,U_10152,U_10148,U_10154,U_10150,U_10156)
| c_Com_Ocom_OLocal(U_10148,U_10150,U_10152) != c_Com_Ocom_OLocal(U_10154,U_10156,U_10158) ),
inference(clausify,[status(thm)],[f_2596_4]) ).
cnf(f_2596_6,plain,
( c_Com_Ocom_OLocal(U_10149,U_10151,U_10153) = c_Com_Ocom_OLocal(U_10155,U_10157,U_10159)
| U_10153 != U_10159
| U_10151 != U_10157
| U_10149 != U_10155 ),
inference(clausify,[status(thm)],[f_2596_4]) ).
cnf(f_2596_7,plain,
( U_10148 = U_10154
| ~ sP703(U_10158,U_10152,U_10148,U_10154,U_10150,U_10156) ),
inference(clausify,[status(thm)],[f_2596_4]) ).
cnf(f_2596_8,plain,
( U_10150 = U_10156
| ~ sP703(U_10158,U_10152,U_10148,U_10154,U_10150,U_10156) ),
inference(clausify,[status(thm)],[f_2596_4]) ).
cnf(f_2596_9,plain,
( U_10152 = U_10158
| ~ sP703(U_10158,U_10152,U_10148,U_10154,U_10150,U_10156) ),
inference(clausify,[status(thm)],[f_2596_4]) ).
fof(f_2597_1,plain,
! [V_x_2,V_w_2,T_c] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = V_x_2
| V_x_2 != hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) )
& ( V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)
| hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) != V_x_2 ) )
| ~ class_Int_Onumber(T_c) ),
inference(fof_nnf,[status(thm)],[fact_number__of__reorient]) ).
fof(f_2597_2,plain,
! [U_10162,U_10161,U_10160] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_10160),U_10161) = U_10162
| U_10162 != hAPP(c_Int_Onumber__class_Onumber__of(U_10160),U_10161) )
& ( U_10162 = hAPP(c_Int_Onumber__class_Onumber__of(U_10160),U_10161)
| hAPP(c_Int_Onumber__class_Onumber__of(U_10160),U_10161) != U_10162 ) )
| ~ class_Int_Onumber(U_10160) ),
inference(variable_rename,[status(thm)],[f_2597_1]) ).
fof(f_2597_3,plain,
( ! [U_10160,U_10161,U_10162] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10160),U_10161) = U_10162
| U_10162 != hAPP(c_Int_Onumber__class_Onumber__of(U_10160),U_10161)
| ~ sP704(U_10160,U_10161,U_10162) )
& ! [U_10160,U_10161,U_10162] :
( U_10162 = hAPP(c_Int_Onumber__class_Onumber__of(U_10160),U_10161)
| hAPP(c_Int_Onumber__class_Onumber__of(U_10160),U_10161) != U_10162
| ~ sP704(U_10160,U_10161,U_10162) )
& ! [U_10160,U_10161,U_10162] :
( sP704(U_10160,U_10161,U_10162)
| ~ class_Int_Onumber(U_10160) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP704])],[f_2597_2]) ).
cnf(f_2597_4,plain,
( sP704(U_10160,U_10161,U_10162)
| ~ class_Int_Onumber(U_10160) ),
inference(clausify,[status(thm)],[f_2597_3]) ).
cnf(f_2597_5,plain,
( U_10162 = hAPP(c_Int_Onumber__class_Onumber__of(U_10160),U_10161)
| hAPP(c_Int_Onumber__class_Onumber__of(U_10160),U_10161) != U_10162
| ~ sP704(U_10160,U_10161,U_10162) ),
inference(clausify,[status(thm)],[f_2597_3]) ).
cnf(f_2597_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10160),U_10161) = U_10162
| U_10162 != hAPP(c_Int_Onumber__class_Onumber__of(U_10160),U_10161)
| ~ sP704(U_10160,U_10161,U_10162) ),
inference(clausify,[status(thm)],[f_2597_3]) ).
fof(f_2598_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2) ) )
| ~ class_Int_Oring__char__0(T_c)
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of]) ).
fof(f_2598_2,plain,
! [U_10165,U_10164,U_10163] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_10163),U_10164) = hAPP(c_Int_Onumber__class_Onumber__of(U_10163),U_10165)
| U_10164 != U_10165 )
& ( U_10164 = U_10165
| hAPP(c_Int_Onumber__class_Onumber__of(U_10163),U_10164) != hAPP(c_Int_Onumber__class_Onumber__of(U_10163),U_10165) ) )
| ~ class_Int_Oring__char__0(U_10163)
| ~ class_Int_Onumber__ring(U_10163) ),
inference(variable_rename,[status(thm)],[f_2598_1]) ).
fof(f_2598_3,plain,
( ! [U_10164,U_10163,U_10165] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10163),U_10164) = hAPP(c_Int_Onumber__class_Onumber__of(U_10163),U_10165)
| U_10164 != U_10165
| ~ sP705(U_10164,U_10163,U_10165) )
& ! [U_10164,U_10163,U_10165] :
( U_10164 = U_10165
| hAPP(c_Int_Onumber__class_Onumber__of(U_10163),U_10164) != hAPP(c_Int_Onumber__class_Onumber__of(U_10163),U_10165)
| ~ sP705(U_10164,U_10163,U_10165) )
& ! [U_10164,U_10163,U_10165] :
( sP705(U_10164,U_10163,U_10165)
| ~ class_Int_Oring__char__0(U_10163)
| ~ class_Int_Onumber__ring(U_10163) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP705])],[f_2598_2]) ).
cnf(f_2598_4,plain,
( sP705(U_10164,U_10163,U_10165)
| ~ class_Int_Oring__char__0(U_10163)
| ~ class_Int_Onumber__ring(U_10163) ),
inference(clausify,[status(thm)],[f_2598_3]) ).
cnf(f_2598_5,plain,
( U_10164 = U_10165
| hAPP(c_Int_Onumber__class_Onumber__of(U_10163),U_10164) != hAPP(c_Int_Onumber__class_Onumber__of(U_10163),U_10165)
| ~ sP705(U_10164,U_10163,U_10165) ),
inference(clausify,[status(thm)],[f_2598_3]) ).
cnf(f_2598_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10163),U_10164) = hAPP(c_Int_Onumber__class_Onumber__of(U_10163),U_10165)
| U_10164 != U_10165
| ~ sP705(U_10164,U_10163,U_10165) ),
inference(clausify,[status(thm)],[f_2598_3]) ).
fof(f_2599_1,plain,
! [V_com_2,V_fun_2,V_loc_2,V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I39_J]) ).
fof(f_2599_2,plain,
! [U_10170,U_10169,U_10168,U_10167,U_10166] : c_Com_Ocom_OWhile(U_10166,U_10167) != c_Com_Ocom_OLocal(U_10168,U_10169,U_10170),
inference(variable_rename,[status(thm)],[f_2599_1]) ).
fof(f_2599_3,plain,
! [U_10167,U_10170,U_10168,U_10169,U_10166] : c_Com_Ocom_OWhile(U_10166,U_10167) != c_Com_Ocom_OLocal(U_10168,U_10169,U_10170),
inference(definitional_conversion,[status(esa)],[f_2599_2]) ).
cnf(f_2599_4,plain,
c_Com_Ocom_OWhile(U_10166,U_10167) != c_Com_Ocom_OLocal(U_10168,U_10169,U_10170),
inference(clausify,[status(thm)],[f_2599_3]) ).
fof(f_2600_1,plain,
! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I38_J]) ).
fof(f_2600_2,plain,
! [U_10175,U_10174,U_10173,U_10172,U_10171] : c_Com_Ocom_OLocal(U_10171,U_10172,U_10173) != c_Com_Ocom_OWhile(U_10174,U_10175),
inference(variable_rename,[status(thm)],[f_2600_1]) ).
fof(f_2600_3,plain,
! [U_10171,U_10173,U_10172,U_10174,U_10175] : c_Com_Ocom_OLocal(U_10171,U_10172,U_10173) != c_Com_Ocom_OWhile(U_10174,U_10175),
inference(definitional_conversion,[status(esa)],[f_2600_2]) ).
cnf(f_2600_4,plain,
c_Com_Ocom_OLocal(U_10171,U_10172,U_10173) != c_Com_Ocom_OWhile(U_10174,U_10175),
inference(clausify,[status(thm)],[f_2600_3]) ).
fof(f_2601_1,plain,
! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I37_J]) ).
fof(f_2601_2,plain,
! [U_10181,U_10180,U_10179,U_10178,U_10177,U_10176] : c_Com_Ocom_OCond(U_10176,U_10177,U_10178) != c_Com_Ocom_OLocal(U_10179,U_10180,U_10181),
inference(variable_rename,[status(thm)],[f_2601_1]) ).
fof(f_2601_3,plain,
! [U_10177,U_10176,U_10178,U_10179,U_10180,U_10181] : c_Com_Ocom_OCond(U_10176,U_10177,U_10178) != c_Com_Ocom_OLocal(U_10179,U_10180,U_10181),
inference(definitional_conversion,[status(esa)],[f_2601_2]) ).
cnf(f_2601_4,plain,
c_Com_Ocom_OCond(U_10176,U_10177,U_10178) != c_Com_Ocom_OLocal(U_10179,U_10180,U_10181),
inference(clausify,[status(thm)],[f_2601_3]) ).
fof(f_2602_1,plain,
! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I36_J]) ).
fof(f_2602_2,plain,
! [U_10187,U_10186,U_10185,U_10184,U_10183,U_10182] : c_Com_Ocom_OLocal(U_10182,U_10183,U_10184) != c_Com_Ocom_OCond(U_10185,U_10186,U_10187),
inference(variable_rename,[status(thm)],[f_2602_1]) ).
fof(f_2602_3,plain,
! [U_10183,U_10182,U_10184,U_10185,U_10186,U_10187] : c_Com_Ocom_OLocal(U_10182,U_10183,U_10184) != c_Com_Ocom_OCond(U_10185,U_10186,U_10187),
inference(definitional_conversion,[status(esa)],[f_2602_2]) ).
cnf(f_2602_4,plain,
c_Com_Ocom_OLocal(U_10182,U_10183,U_10184) != c_Com_Ocom_OCond(U_10185,U_10186,U_10187),
inference(clausify,[status(thm)],[f_2602_3]) ).
fof(f_2603_1,plain,
! [V_com2_H_2,V_com1_H_2,V_com_2,V_fun_2,V_loc_2] : c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) != c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I34_J]) ).
fof(f_2603_2,plain,
! [U_10192,U_10191,U_10190,U_10189,U_10188] : c_Com_Ocom_OLocal(U_10188,U_10189,U_10190) != c_Com_Ocom_OSemi(U_10191,U_10192),
inference(variable_rename,[status(thm)],[f_2603_1]) ).
fof(f_2603_3,plain,
! [U_10189,U_10188,U_10190,U_10191,U_10192] : c_Com_Ocom_OLocal(U_10188,U_10189,U_10190) != c_Com_Ocom_OSemi(U_10191,U_10192),
inference(definitional_conversion,[status(esa)],[f_2603_2]) ).
cnf(f_2603_4,plain,
c_Com_Ocom_OLocal(U_10188,U_10189,U_10190) != c_Com_Ocom_OSemi(U_10191,U_10192),
inference(clausify,[status(thm)],[f_2603_3]) ).
fof(f_2604_1,plain,
! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2] : c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I35_J]) ).
fof(f_2604_2,plain,
! [U_10197,U_10196,U_10195,U_10194,U_10193] : c_Com_Ocom_OSemi(U_10193,U_10194) != c_Com_Ocom_OLocal(U_10195,U_10196,U_10197),
inference(variable_rename,[status(thm)],[f_2604_1]) ).
fof(f_2604_3,plain,
! [U_10193,U_10194,U_10195,U_10196,U_10197] : c_Com_Ocom_OSemi(U_10193,U_10194) != c_Com_Ocom_OLocal(U_10195,U_10196,U_10197),
inference(definitional_conversion,[status(esa)],[f_2604_2]) ).
cnf(f_2604_4,plain,
c_Com_Ocom_OSemi(U_10193,U_10194) != c_Com_Ocom_OLocal(U_10195,U_10196,U_10197),
inference(clausify,[status(thm)],[f_2604_3]) ).
fof(f_2605_1,plain,
! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP,
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I11_J]) ).
fof(f_2605_2,plain,
! [U_10200,U_10199,U_10198] : c_Com_Ocom_OLocal(U_10198,U_10199,U_10200) != c_Com_Ocom_OSKIP,
inference(variable_rename,[status(thm)],[f_2605_1]) ).
fof(f_2605_3,plain,
! [U_10199,U_10198,U_10200] : c_Com_Ocom_OLocal(U_10198,U_10199,U_10200) != c_Com_Ocom_OSKIP,
inference(definitional_conversion,[status(esa)],[f_2605_2]) ).
cnf(f_2605_4,plain,
c_Com_Ocom_OLocal(U_10198,U_10199,U_10200) != c_Com_Ocom_OSKIP,
inference(clausify,[status(thm)],[f_2605_3]) ).
fof(f_2606_1,plain,
! [V_com_H_2,V_fun_H_2,V_loc_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(V_loc_H_2,V_fun_H_2,V_com_H_2),
inference(fof_nnf,[status(thm)],[fact_com_Osimps_I10_J]) ).
fof(f_2606_2,plain,
! [U_10203,U_10202,U_10201] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_10201,U_10202,U_10203),
inference(variable_rename,[status(thm)],[f_2606_1]) ).
fof(f_2606_3,plain,
! [U_10201,U_10202,U_10203] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_10201,U_10202,U_10203),
inference(definitional_conversion,[status(esa)],[f_2606_2]) ).
cnf(f_2606_4,plain,
c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_10201,U_10202,U_10203),
inference(clausify,[status(thm)],[f_2606_3]) ).
fof(f_2607_1,plain,
! [V_w_2,V_v_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) )
| ~ class_Orderings_Olinorder(T_c)
| ~ class_Int_Onumber(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of__eq__not__less]) ).
fof(f_2607_2,plain,
! [U_10206,U_10205,U_10204] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10204),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10205)),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10206)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10204),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10206)),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10205))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10204),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10206)),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10205)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10204),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10205)),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10206))) ) )
| ~ class_Orderings_Olinorder(U_10204)
| ~ class_Int_Onumber(U_10204) ),
inference(variable_rename,[status(thm)],[f_2607_1]) ).
fof(f_2607_3,plain,
( ! [U_10204,U_10205,U_10206] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10204),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10205)),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10206)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10204),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10206)),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10205)))
| ~ sP706(U_10204,U_10205,U_10206) )
& ! [U_10204,U_10205,U_10206] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10204),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10206)),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10205)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10204),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10205)),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10206)))
| ~ sP706(U_10204,U_10205,U_10206) )
& ! [U_10204,U_10205,U_10206] :
( sP706(U_10204,U_10205,U_10206)
| ~ class_Orderings_Olinorder(U_10204)
| ~ class_Int_Onumber(U_10204) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP706])],[f_2607_2]) ).
cnf(f_2607_4,plain,
( sP706(U_10204,U_10205,U_10206)
| ~ class_Orderings_Olinorder(U_10204)
| ~ class_Int_Onumber(U_10204) ),
inference(clausify,[status(thm)],[f_2607_3]) ).
cnf(f_2607_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10204),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10206)),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10205)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10204),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10205)),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10206)))
| ~ sP706(U_10204,U_10205,U_10206) ),
inference(clausify,[status(thm)],[f_2607_3]) ).
cnf(f_2607_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10204),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10205)),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10206)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10204),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10206)),hAPP(c_Int_Onumber__class_Onumber__of(U_10204),U_10205)))
| ~ sP706(U_10204,U_10205,U_10206) ),
inference(clausify,[status(thm)],[f_2607_3]) ).
fof(f_2608_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_2608_2,plain,
! [U_10210,U_10209,U_10208,U_10207] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10207),hAPP(c_Int_Onumber__class_Onumber__of(U_10207),U_10208)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10207),U_10209),U_10210)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10207),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10207),hAPP(c_Int_Onumber__class_Onumber__of(U_10207),U_10208)),U_10209)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10207),hAPP(c_Int_Onumber__class_Onumber__of(U_10207),U_10208)),U_10210))
| ~ class_Rings_Osemiring(U_10207)
| ~ class_Int_Onumber(U_10207) ),
inference(variable_rename,[status(thm)],[f_2608_1]) ).
fof(f_2608_3,plain,
! [U_10208,U_10207,U_10209,U_10210] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10207),hAPP(c_Int_Onumber__class_Onumber__of(U_10207),U_10208)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10207),U_10209),U_10210)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10207),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10207),hAPP(c_Int_Onumber__class_Onumber__of(U_10207),U_10208)),U_10209)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10207),hAPP(c_Int_Onumber__class_Onumber__of(U_10207),U_10208)),U_10210))
| ~ class_Rings_Osemiring(U_10207)
| ~ class_Int_Onumber(U_10207) ),
inference(definitional_conversion,[status(esa)],[f_2608_2]) ).
cnf(f_2608_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10207),hAPP(c_Int_Onumber__class_Onumber__of(U_10207),U_10208)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10207),U_10209),U_10210)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10207),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10207),hAPP(c_Int_Onumber__class_Onumber__of(U_10207),U_10208)),U_10209)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10207),hAPP(c_Int_Onumber__class_Onumber__of(U_10207),U_10208)),U_10210))
| ~ class_Rings_Osemiring(U_10207)
| ~ class_Int_Onumber(U_10207) ),
inference(clausify,[status(thm)],[f_2608_3]) ).
fof(f_2609_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_2609_2,plain,
! [U_10214,U_10213,U_10212,U_10211] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10211),U_10212),U_10213)),hAPP(c_Int_Onumber__class_Onumber__of(U_10211),U_10214)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10211),U_10212),hAPP(c_Int_Onumber__class_Onumber__of(U_10211),U_10214))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10211),U_10213),hAPP(c_Int_Onumber__class_Onumber__of(U_10211),U_10214)))
| ~ class_Rings_Osemiring(U_10211)
| ~ class_Int_Onumber(U_10211) ),
inference(variable_rename,[status(thm)],[f_2609_1]) ).
fof(f_2609_3,plain,
! [U_10212,U_10211,U_10213,U_10214] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10211),U_10212),U_10213)),hAPP(c_Int_Onumber__class_Onumber__of(U_10211),U_10214)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10211),U_10212),hAPP(c_Int_Onumber__class_Onumber__of(U_10211),U_10214))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10211),U_10213),hAPP(c_Int_Onumber__class_Onumber__of(U_10211),U_10214)))
| ~ class_Rings_Osemiring(U_10211)
| ~ class_Int_Onumber(U_10211) ),
inference(definitional_conversion,[status(esa)],[f_2609_2]) ).
cnf(f_2609_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10211),U_10212),U_10213)),hAPP(c_Int_Onumber__class_Onumber__of(U_10211),U_10214)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10211),U_10212),hAPP(c_Int_Onumber__class_Onumber__of(U_10211),U_10214))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10211),U_10213),hAPP(c_Int_Onumber__class_Onumber__of(U_10211),U_10214)))
| ~ class_Rings_Osemiring(U_10211)
| ~ class_Int_Onumber(U_10211) ),
inference(clausify,[status(thm)],[f_2609_3]) ).
fof(f_2610_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_2610_2,plain,
! [U_10218,U_10217,U_10216,U_10215] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10215),hAPP(c_Int_Onumber__class_Onumber__of(U_10215),U_10216)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10215),U_10217),U_10218)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10215),hAPP(c_Int_Onumber__class_Onumber__of(U_10215),U_10216)),U_10217)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10215),hAPP(c_Int_Onumber__class_Onumber__of(U_10215),U_10216)),U_10218))
| ~ class_Rings_Oring(U_10215)
| ~ class_Int_Onumber(U_10215) ),
inference(variable_rename,[status(thm)],[f_2610_1]) ).
fof(f_2610_3,plain,
! [U_10215,U_10216,U_10217,U_10218] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10215),hAPP(c_Int_Onumber__class_Onumber__of(U_10215),U_10216)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10215),U_10217),U_10218)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10215),hAPP(c_Int_Onumber__class_Onumber__of(U_10215),U_10216)),U_10217)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10215),hAPP(c_Int_Onumber__class_Onumber__of(U_10215),U_10216)),U_10218))
| ~ class_Rings_Oring(U_10215)
| ~ class_Int_Onumber(U_10215) ),
inference(definitional_conversion,[status(esa)],[f_2610_2]) ).
cnf(f_2610_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10215),hAPP(c_Int_Onumber__class_Onumber__of(U_10215),U_10216)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10215),U_10217),U_10218)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10215),hAPP(c_Int_Onumber__class_Onumber__of(U_10215),U_10216)),U_10217)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10215),hAPP(c_Int_Onumber__class_Onumber__of(U_10215),U_10216)),U_10218))
| ~ class_Rings_Oring(U_10215)
| ~ class_Int_Onumber(U_10215) ),
inference(clausify,[status(thm)],[f_2610_3]) ).
fof(f_2611_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_2611_2,plain,
! [U_10222,U_10221,U_10220,U_10219] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10219),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10219),U_10220),U_10221)),hAPP(c_Int_Onumber__class_Onumber__of(U_10219),U_10222)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10219),U_10220),hAPP(c_Int_Onumber__class_Onumber__of(U_10219),U_10222))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10219),U_10221),hAPP(c_Int_Onumber__class_Onumber__of(U_10219),U_10222)))
| ~ class_Rings_Oring(U_10219)
| ~ class_Int_Onumber(U_10219) ),
inference(variable_rename,[status(thm)],[f_2611_1]) ).
fof(f_2611_3,plain,
! [U_10220,U_10219,U_10221,U_10222] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10219),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10219),U_10220),U_10221)),hAPP(c_Int_Onumber__class_Onumber__of(U_10219),U_10222)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10219),U_10220),hAPP(c_Int_Onumber__class_Onumber__of(U_10219),U_10222))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10219),U_10221),hAPP(c_Int_Onumber__class_Onumber__of(U_10219),U_10222)))
| ~ class_Rings_Oring(U_10219)
| ~ class_Int_Onumber(U_10219) ),
inference(definitional_conversion,[status(esa)],[f_2611_2]) ).
cnf(f_2611_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10219),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10219),U_10220),U_10221)),hAPP(c_Int_Onumber__class_Onumber__of(U_10219),U_10222)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10219),U_10220),hAPP(c_Int_Onumber__class_Onumber__of(U_10219),U_10222))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10219),U_10221),hAPP(c_Int_Onumber__class_Onumber__of(U_10219),U_10222)))
| ~ class_Rings_Oring(U_10219)
| ~ class_Int_Onumber(U_10219) ),
inference(clausify,[status(thm)],[f_2611_3]) ).
fof(f_2612_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2))) ) )
| ~ class_Rings_Olinordered__idom(T_c)
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of]) ).
fof(f_2612_2,plain,
! [U_10225,U_10224,U_10223] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10223),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10224)),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10224),U_10225)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10224),U_10225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10223),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10224)),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10225))) ) )
| ~ class_Rings_Olinordered__idom(U_10223)
| ~ class_Int_Onumber__ring(U_10223) ),
inference(variable_rename,[status(thm)],[f_2612_1]) ).
fof(f_2612_3,plain,
( ! [U_10223,U_10224,U_10225] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10223),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10224)),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10224),U_10225))
| ~ sP707(U_10223,U_10224,U_10225) )
& ! [U_10223,U_10224,U_10225] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10224),U_10225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10223),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10224)),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10225)))
| ~ sP707(U_10223,U_10224,U_10225) )
& ! [U_10223,U_10224,U_10225] :
( sP707(U_10223,U_10224,U_10225)
| ~ class_Rings_Olinordered__idom(U_10223)
| ~ class_Int_Onumber__ring(U_10223) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP707])],[f_2612_2]) ).
cnf(f_2612_4,plain,
( sP707(U_10223,U_10224,U_10225)
| ~ class_Rings_Olinordered__idom(U_10223)
| ~ class_Int_Onumber__ring(U_10223) ),
inference(clausify,[status(thm)],[f_2612_3]) ).
cnf(f_2612_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10224),U_10225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10223),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10224)),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10225)))
| ~ sP707(U_10223,U_10224,U_10225) ),
inference(clausify,[status(thm)],[f_2612_3]) ).
cnf(f_2612_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10223),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10224)),hAPP(c_Int_Onumber__class_Onumber__of(U_10223),U_10225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10224),U_10225))
| ~ sP707(U_10223,U_10224,U_10225) ),
inference(clausify,[status(thm)],[f_2612_3]) ).
fof(f_2613_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2))) ) )
| ~ class_Rings_Olinordered__idom(T_c)
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__number__of]) ).
fof(f_2613_2,plain,
! [U_10228,U_10227,U_10226] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10226),hAPP(c_Int_Onumber__class_Onumber__of(U_10226),U_10227)),hAPP(c_Int_Onumber__class_Onumber__of(U_10226),U_10228)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10227),U_10228)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10227),U_10228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10226),hAPP(c_Int_Onumber__class_Onumber__of(U_10226),U_10227)),hAPP(c_Int_Onumber__class_Onumber__of(U_10226),U_10228))) ) )
| ~ class_Rings_Olinordered__idom(U_10226)
| ~ class_Int_Onumber__ring(U_10226) ),
inference(variable_rename,[status(thm)],[f_2613_1]) ).
fof(f_2613_3,plain,
( ! [U_10227,U_10228,U_10226] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10226),hAPP(c_Int_Onumber__class_Onumber__of(U_10226),U_10227)),hAPP(c_Int_Onumber__class_Onumber__of(U_10226),U_10228)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10227),U_10228))
| ~ sP708(U_10227,U_10228,U_10226) )
& ! [U_10227,U_10228,U_10226] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10227),U_10228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10226),hAPP(c_Int_Onumber__class_Onumber__of(U_10226),U_10227)),hAPP(c_Int_Onumber__class_Onumber__of(U_10226),U_10228)))
| ~ sP708(U_10227,U_10228,U_10226) )
& ! [U_10227,U_10228,U_10226] :
( sP708(U_10227,U_10228,U_10226)
| ~ class_Rings_Olinordered__idom(U_10226)
| ~ class_Int_Onumber__ring(U_10226) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP708])],[f_2613_2]) ).
cnf(f_2613_4,plain,
( sP708(U_10227,U_10228,U_10226)
| ~ class_Rings_Olinordered__idom(U_10226)
| ~ class_Int_Onumber__ring(U_10226) ),
inference(clausify,[status(thm)],[f_2613_3]) ).
cnf(f_2613_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10227),U_10228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10226),hAPP(c_Int_Onumber__class_Onumber__of(U_10226),U_10227)),hAPP(c_Int_Onumber__class_Onumber__of(U_10226),U_10228)))
| ~ sP708(U_10227,U_10228,U_10226) ),
inference(clausify,[status(thm)],[f_2613_3]) ).
cnf(f_2613_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10226),hAPP(c_Int_Onumber__class_Onumber__of(U_10226),U_10227)),hAPP(c_Int_Onumber__class_Onumber__of(U_10226),U_10228)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10227),U_10228))
| ~ sP708(U_10227,U_10228,U_10226) ),
inference(clausify,[status(thm)],[f_2613_3]) ).
fof(f_2614_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_2614_2,plain,
! [U_10231,U_10230,U_10229] :
( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10229),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10229),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231))) )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10229),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10229),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231))) ) )
| ~ class_Orderings_Oord(U_10229)
| ~ class_Int_Onumber(U_10229) ),
inference(variable_rename,[status(thm)],[f_2614_1]) ).
fof(f_2614_3,plain,
( ! [U_10229,U_10230,U_10231] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10229),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10229),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)))
| ~ sP709(U_10229,U_10230,U_10231) )
& ! [U_10229,U_10230,U_10231] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10229),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10229),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)))
| ~ sP709(U_10229,U_10230,U_10231) )
& ! [U_10229,U_10230,U_10231] :
( sP709(U_10229,U_10230,U_10231)
| ~ class_Orderings_Oord(U_10229)
| ~ class_Int_Onumber(U_10229) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP709])],[f_2614_2]) ).
cnf(f_2614_4,plain,
( sP709(U_10229,U_10230,U_10231)
| ~ class_Orderings_Oord(U_10229)
| ~ class_Int_Onumber(U_10229) ),
inference(clausify,[status(thm)],[f_2614_3]) ).
cnf(f_2614_5,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10229),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10229),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)))
| ~ sP709(U_10229,U_10230,U_10231) ),
inference(clausify,[status(thm)],[f_2614_3]) ).
cnf(f_2614_6,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10229),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10229),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10230)),hAPP(c_Int_Onumber__class_Onumber__of(U_10229),U_10231)))
| ~ sP709(U_10229,U_10230,U_10231) ),
inference(clausify,[status(thm)],[f_2614_3]) ).
fof(f_2615_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_2615_2,plain,
! [U_10234,U_10233,U_10232] :
( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10232),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10232),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234))) )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10232),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10232),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234))) ) )
| ~ class_Orderings_Oord(U_10232)
| ~ class_Int_Onumber(U_10232) ),
inference(variable_rename,[status(thm)],[f_2615_1]) ).
fof(f_2615_3,plain,
( ! [U_10233,U_10234,U_10232] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10232),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10232),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)))
| ~ sP710(U_10233,U_10234,U_10232) )
& ! [U_10233,U_10234,U_10232] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10232),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10232),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)))
| ~ sP710(U_10233,U_10234,U_10232) )
& ! [U_10233,U_10234,U_10232] :
( sP710(U_10233,U_10234,U_10232)
| ~ class_Orderings_Oord(U_10232)
| ~ class_Int_Onumber(U_10232) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP710])],[f_2615_2]) ).
cnf(f_2615_4,plain,
( sP710(U_10233,U_10234,U_10232)
| ~ class_Orderings_Oord(U_10232)
| ~ class_Int_Onumber(U_10232) ),
inference(clausify,[status(thm)],[f_2615_3]) ).
cnf(f_2615_5,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10232),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10232),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)))
| ~ sP710(U_10233,U_10234,U_10232) ),
inference(clausify,[status(thm)],[f_2615_3]) ).
cnf(f_2615_6,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10232),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10232),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10233)),hAPP(c_Int_Onumber__class_Onumber__of(U_10232),U_10234)))
| ~ sP710(U_10233,U_10234,U_10232) ),
inference(clausify,[status(thm)],[f_2615_3]) ).
fof(f_2616_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_2616_2,plain,
! [U_10238,U_10237,U_10236,U_10235] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10235),hAPP(c_Int_Onumber__class_Onumber__of(U_10235),U_10236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10235),hAPP(c_Int_Onumber__class_Onumber__of(U_10235),U_10237)),U_10238)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10235),hAPP(c_Int_Onumber__class_Onumber__of(U_10235),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10236),U_10237))),U_10238)
| ~ class_Int_Onumber__ring(U_10235) ),
inference(variable_rename,[status(thm)],[f_2616_1]) ).
fof(f_2616_3,plain,
! [U_10237,U_10236,U_10235,U_10238] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10235),hAPP(c_Int_Onumber__class_Onumber__of(U_10235),U_10236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10235),hAPP(c_Int_Onumber__class_Onumber__of(U_10235),U_10237)),U_10238)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10235),hAPP(c_Int_Onumber__class_Onumber__of(U_10235),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10236),U_10237))),U_10238)
| ~ class_Int_Onumber__ring(U_10235) ),
inference(definitional_conversion,[status(esa)],[f_2616_2]) ).
cnf(f_2616_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10235),hAPP(c_Int_Onumber__class_Onumber__of(U_10235),U_10236)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10235),hAPP(c_Int_Onumber__class_Onumber__of(U_10235),U_10237)),U_10238)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10235),hAPP(c_Int_Onumber__class_Onumber__of(U_10235),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10236),U_10237))),U_10238)
| ~ class_Int_Onumber__ring(U_10235) ),
inference(clausify,[status(thm)],[f_2616_3]) ).
fof(f_2617_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_2617_2,plain,
! [U_10241,U_10240,U_10239] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10239),hAPP(c_Int_Onumber__class_Onumber__of(U_10239),U_10240)),hAPP(c_Int_Onumber__class_Onumber__of(U_10239),U_10241)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10239),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10240),U_10241))
| ~ class_Int_Onumber__ring(U_10239) ),
inference(variable_rename,[status(thm)],[f_2617_1]) ).
fof(f_2617_3,plain,
! [U_10239,U_10240,U_10241] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10239),hAPP(c_Int_Onumber__class_Onumber__of(U_10239),U_10240)),hAPP(c_Int_Onumber__class_Onumber__of(U_10239),U_10241)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10239),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10240),U_10241))
| ~ class_Int_Onumber__ring(U_10239) ),
inference(definitional_conversion,[status(esa)],[f_2617_2]) ).
cnf(f_2617_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10239),hAPP(c_Int_Onumber__class_Onumber__of(U_10239),U_10240)),hAPP(c_Int_Onumber__class_Onumber__of(U_10239),U_10241)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10239),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10240),U_10241))
| ~ class_Int_Onumber__ring(U_10239) ),
inference(clausify,[status(thm)],[f_2617_3]) ).
fof(f_2618_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_2618_2,plain,
! [U_10244,U_10243,U_10242] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10242),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10243),U_10244)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10242),hAPP(c_Int_Onumber__class_Onumber__of(U_10242),U_10243)),hAPP(c_Int_Onumber__class_Onumber__of(U_10242),U_10244))
| ~ class_Int_Onumber__ring(U_10242) ),
inference(variable_rename,[status(thm)],[f_2618_1]) ).
fof(f_2618_3,plain,
! [U_10242,U_10243,U_10244] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10242),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10243),U_10244)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10242),hAPP(c_Int_Onumber__class_Onumber__of(U_10242),U_10243)),hAPP(c_Int_Onumber__class_Onumber__of(U_10242),U_10244))
| ~ class_Int_Onumber__ring(U_10242) ),
inference(definitional_conversion,[status(esa)],[f_2618_2]) ).
cnf(f_2618_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10242),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10243),U_10244)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10242),hAPP(c_Int_Onumber__class_Onumber__of(U_10242),U_10243)),hAPP(c_Int_Onumber__class_Onumber__of(U_10242),U_10244))
| ~ class_Int_Onumber__ring(U_10242) ),
inference(clausify,[status(thm)],[f_2618_3]) ).
fof(f_2619_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_2619_2,plain,
! [U_10248,U_10247,U_10246,U_10245] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10245),hAPP(c_Int_Onumber__class_Onumber__of(U_10245),U_10246)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10245),hAPP(c_Int_Onumber__class_Onumber__of(U_10245),U_10247)),U_10248)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10245),hAPP(c_Int_Onumber__class_Onumber__of(U_10245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10246),U_10247))),U_10248)
| ~ class_Int_Onumber__ring(U_10245) ),
inference(variable_rename,[status(thm)],[f_2619_1]) ).
fof(f_2619_3,plain,
! [U_10245,U_10246,U_10247,U_10248] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10245),hAPP(c_Int_Onumber__class_Onumber__of(U_10245),U_10246)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10245),hAPP(c_Int_Onumber__class_Onumber__of(U_10245),U_10247)),U_10248)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10245),hAPP(c_Int_Onumber__class_Onumber__of(U_10245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10246),U_10247))),U_10248)
| ~ class_Int_Onumber__ring(U_10245) ),
inference(definitional_conversion,[status(esa)],[f_2619_2]) ).
cnf(f_2619_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10245),hAPP(c_Int_Onumber__class_Onumber__of(U_10245),U_10246)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10245),hAPP(c_Int_Onumber__class_Onumber__of(U_10245),U_10247)),U_10248)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10245),hAPP(c_Int_Onumber__class_Onumber__of(U_10245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10246),U_10247))),U_10248)
| ~ class_Int_Onumber__ring(U_10245) ),
inference(clausify,[status(thm)],[f_2619_3]) ).
fof(f_2620_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_2620_2,plain,
! [U_10251,U_10250,U_10249] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10249),hAPP(c_Int_Onumber__class_Onumber__of(U_10249),U_10250)),hAPP(c_Int_Onumber__class_Onumber__of(U_10249),U_10251)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10249),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10250),U_10251))
| ~ class_Int_Onumber__ring(U_10249) ),
inference(variable_rename,[status(thm)],[f_2620_1]) ).
fof(f_2620_3,plain,
! [U_10249,U_10250,U_10251] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10249),hAPP(c_Int_Onumber__class_Onumber__of(U_10249),U_10250)),hAPP(c_Int_Onumber__class_Onumber__of(U_10249),U_10251)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10249),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10250),U_10251))
| ~ class_Int_Onumber__ring(U_10249) ),
inference(definitional_conversion,[status(esa)],[f_2620_2]) ).
cnf(f_2620_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10249),hAPP(c_Int_Onumber__class_Onumber__of(U_10249),U_10250)),hAPP(c_Int_Onumber__class_Onumber__of(U_10249),U_10251)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10249),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10250),U_10251))
| ~ class_Int_Onumber__ring(U_10249) ),
inference(clausify,[status(thm)],[f_2620_3]) ).
fof(f_2621_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_2621_2,plain,
! [U_10254,U_10253,U_10252] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10253),U_10254)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10252),hAPP(c_Int_Onumber__class_Onumber__of(U_10252),U_10253)),hAPP(c_Int_Onumber__class_Onumber__of(U_10252),U_10254))
| ~ class_Int_Onumber__ring(U_10252) ),
inference(variable_rename,[status(thm)],[f_2621_1]) ).
fof(f_2621_3,plain,
! [U_10252,U_10253,U_10254] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10253),U_10254)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10252),hAPP(c_Int_Onumber__class_Onumber__of(U_10252),U_10253)),hAPP(c_Int_Onumber__class_Onumber__of(U_10252),U_10254))
| ~ class_Int_Onumber__ring(U_10252) ),
inference(definitional_conversion,[status(esa)],[f_2621_2]) ).
cnf(f_2621_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10253),U_10254)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10252),hAPP(c_Int_Onumber__class_Onumber__of(U_10252),U_10253)),hAPP(c_Int_Onumber__class_Onumber__of(U_10252),U_10254))
| ~ class_Int_Onumber__ring(U_10252) ),
inference(clausify,[status(thm)],[f_2621_3]) ).
fof(f_2622_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_2622_2,plain,
! [U_10257,U_10256,U_10255] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10255),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10256),U_10257)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10255),hAPP(c_Int_Onumber__class_Onumber__of(U_10255),U_10256)),hAPP(c_Int_Onumber__class_Onumber__of(U_10255),U_10257))
| ~ class_Int_Onumber__ring(U_10255) ),
inference(variable_rename,[status(thm)],[f_2622_1]) ).
fof(f_2622_3,plain,
! [U_10255,U_10256,U_10257] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10255),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10256),U_10257)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10255),hAPP(c_Int_Onumber__class_Onumber__of(U_10255),U_10256)),hAPP(c_Int_Onumber__class_Onumber__of(U_10255),U_10257))
| ~ class_Int_Onumber__ring(U_10255) ),
inference(definitional_conversion,[status(esa)],[f_2622_2]) ).
cnf(f_2622_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10255),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10256),U_10257)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10255),hAPP(c_Int_Onumber__class_Onumber__of(U_10255),U_10256)),hAPP(c_Int_Onumber__class_Onumber__of(U_10255),U_10257))
| ~ class_Int_Onumber__ring(U_10255) ),
inference(clausify,[status(thm)],[f_2622_3]) ).
fof(f_2623_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_2623_2,plain,
! [U_10259,U_10258] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_10258),hAPP(c_Int_Onumber__class_Onumber__of(U_10258),U_10259)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10258),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10259))
| ~ class_Int_Onumber__ring(U_10258) ),
inference(variable_rename,[status(thm)],[f_2623_1]) ).
fof(f_2623_3,plain,
! [U_10258,U_10259] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_10258),hAPP(c_Int_Onumber__class_Onumber__of(U_10258),U_10259)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10258),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10259))
| ~ class_Int_Onumber__ring(U_10258) ),
inference(definitional_conversion,[status(esa)],[f_2623_2]) ).
cnf(f_2623_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_10258),hAPP(c_Int_Onumber__class_Onumber__of(U_10258),U_10259)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10258),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10259))
| ~ class_Int_Onumber__ring(U_10258) ),
inference(clausify,[status(thm)],[f_2623_3]) ).
fof(f_2624_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_2624_2,plain,
! [U_10261,U_10260] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10260),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10261)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10260),hAPP(c_Int_Onumber__class_Onumber__of(U_10260),U_10261))
| ~ class_Int_Onumber__ring(U_10260) ),
inference(variable_rename,[status(thm)],[f_2624_1]) ).
fof(f_2624_3,plain,
! [U_10260,U_10261] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10260),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10261)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10260),hAPP(c_Int_Onumber__class_Onumber__of(U_10260),U_10261))
| ~ class_Int_Onumber__ring(U_10260) ),
inference(definitional_conversion,[status(esa)],[f_2624_2]) ).
cnf(f_2624_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10260),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10261)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10260),hAPP(c_Int_Onumber__class_Onumber__of(U_10260),U_10261))
| ~ class_Int_Onumber__ring(U_10260) ),
inference(clausify,[status(thm)],[f_2624_3]) ).
fof(f_2625_1,plain,
! [V_w_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Int_Oring__1__class_OInts(T_c)))
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Ints__number__of]) ).
fof(f_2625_2,plain,
! [U_10263,U_10262] :
( hBOOL(hAPP(hAPP(c_member(U_10262),hAPP(c_Int_Onumber__class_Onumber__of(U_10262),U_10263)),c_Int_Oring__1__class_OInts(U_10262)))
| ~ class_Int_Onumber__ring(U_10262) ),
inference(variable_rename,[status(thm)],[f_2625_1]) ).
fof(f_2625_3,plain,
! [U_10262,U_10263] :
( hBOOL(hAPP(hAPP(c_member(U_10262),hAPP(c_Int_Onumber__class_Onumber__of(U_10262),U_10263)),c_Int_Oring__1__class_OInts(U_10262)))
| ~ class_Int_Onumber__ring(U_10262) ),
inference(definitional_conversion,[status(esa)],[f_2625_2]) ).
cnf(f_2625_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10262),hAPP(c_Int_Onumber__class_Onumber__of(U_10262),U_10263)),c_Int_Oring__1__class_OInts(U_10262)))
| ~ class_Int_Onumber__ring(U_10262) ),
inference(clausify,[status(thm)],[f_2625_3]) ).
fof(f_2626_1,plain,
! [V_r_2,V_A_2,T_c] :
( c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)) = V_A_2
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_Union__quotient]) ).
fof(f_2626_2,plain,
! [U_10266,U_10265,U_10264] :
( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10264,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10264),U_10265),U_10266)) = U_10265
| ~ c_Equiv__Relations_Oequiv(U_10264,U_10265,U_10266) ),
inference(variable_rename,[status(thm)],[f_2626_1]) ).
fof(f_2626_3,plain,
! [U_10264,U_10265,U_10266] :
( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10264,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10264),U_10265),U_10266)) = U_10265
| ~ c_Equiv__Relations_Oequiv(U_10264,U_10265,U_10266) ),
inference(definitional_conversion,[status(esa)],[f_2626_2]) ).
cnf(f_2626_4,plain,
( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10264,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10264),U_10265),U_10266)) = U_10265
| ~ c_Equiv__Relations_Oequiv(U_10264,U_10265,U_10266) ),
inference(clausify,[status(thm)],[f_2626_3]) ).
fof(f_2627_1,plain,
! [V_a_2,V_w_2,V_b_2,T_c] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) = V_a_2
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_c)
& hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c) )
| ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))
& hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))
| hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) != V_a_2 ) )
| ~ class_Int_Onumber(T_c)
| ~ class_Fields_Ofield__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1]) ).
fof(f_2627_2,plain,
! [U_10270,U_10269,U_10268,U_10267] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10267),U_10268),hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269)) = U_10270
| ( U_10270 != c_Groups_Ozero__class_Ozero(U_10267)
& hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269) = c_Groups_Ozero__class_Ozero(U_10267) )
| ( U_10268 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10267),U_10270),hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269))
& hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269) != c_Groups_Ozero__class_Ozero(U_10267) ) )
& ( ( ( U_10270 = c_Groups_Ozero__class_Ozero(U_10267)
| hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269) != c_Groups_Ozero__class_Ozero(U_10267) )
& ( U_10268 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10267),U_10270),hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269))
| hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269) = c_Groups_Ozero__class_Ozero(U_10267) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10267),U_10268),hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269)) != U_10270 ) )
| ~ class_Int_Onumber(U_10267)
| ~ class_Fields_Ofield__inverse__zero(U_10267) ),
inference(variable_rename,[status(thm)],[f_2627_1]) ).
fof(f_2627_3,plain,
( ! [U_10267,U_10269,U_10270] :
( U_10270 != c_Groups_Ozero__class_Ozero(U_10267)
| ~ sP713(U_10267,U_10269,U_10270) )
& ! [U_10267,U_10269,U_10270] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269) = c_Groups_Ozero__class_Ozero(U_10267)
| ~ sP713(U_10267,U_10269,U_10270) )
& ! [U_10267,U_10268,U_10269,U_10270] :
( U_10268 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10267),U_10270),hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269))
| ~ sP712(U_10267,U_10268,U_10269,U_10270) )
& ! [U_10267,U_10268,U_10269,U_10270] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269) != c_Groups_Ozero__class_Ozero(U_10267)
| ~ sP712(U_10267,U_10268,U_10269,U_10270) )
& ! [U_10267,U_10268,U_10269,U_10270] :
( U_10270 = c_Groups_Ozero__class_Ozero(U_10267)
| hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269) != c_Groups_Ozero__class_Ozero(U_10267)
| ~ sP711(U_10267,U_10268,U_10269,U_10270) )
& ! [U_10267,U_10268,U_10269,U_10270] :
( U_10268 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10267),U_10270),hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269))
| hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269) = c_Groups_Ozero__class_Ozero(U_10267)
| ~ sP711(U_10267,U_10268,U_10269,U_10270) )
& ! [U_10267,U_10268,U_10269,U_10270] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10267),U_10268),hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269)) = U_10270
| sP713(U_10267,U_10269,U_10270)
| sP712(U_10267,U_10268,U_10269,U_10270)
| ~ sP714(U_10267,U_10268,U_10269,U_10270) )
& ! [U_10267,U_10268,U_10269,U_10270] :
( sP711(U_10267,U_10268,U_10269,U_10270)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10267),U_10268),hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269)) != U_10270
| ~ sP714(U_10267,U_10268,U_10269,U_10270) )
& ! [U_10267,U_10268,U_10269,U_10270] :
( sP714(U_10267,U_10268,U_10269,U_10270)
| ~ class_Int_Onumber(U_10267)
| ~ class_Fields_Ofield__inverse__zero(U_10267) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP711,sP712,sP713,sP714])],[f_2627_2]) ).
cnf(f_2627_4,plain,
( sP714(U_10267,U_10268,U_10269,U_10270)
| ~ class_Int_Onumber(U_10267)
| ~ class_Fields_Ofield__inverse__zero(U_10267) ),
inference(clausify,[status(thm)],[f_2627_3]) ).
cnf(f_2627_5,plain,
( sP711(U_10267,U_10268,U_10269,U_10270)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10267),U_10268),hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269)) != U_10270
| ~ sP714(U_10267,U_10268,U_10269,U_10270) ),
inference(clausify,[status(thm)],[f_2627_3]) ).
cnf(f_2627_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10267),U_10268),hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269)) = U_10270
| sP713(U_10267,U_10269,U_10270)
| sP712(U_10267,U_10268,U_10269,U_10270)
| ~ sP714(U_10267,U_10268,U_10269,U_10270) ),
inference(clausify,[status(thm)],[f_2627_3]) ).
cnf(f_2627_7,plain,
( U_10268 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10267),U_10270),hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269))
| hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269) = c_Groups_Ozero__class_Ozero(U_10267)
| ~ sP711(U_10267,U_10268,U_10269,U_10270) ),
inference(clausify,[status(thm)],[f_2627_3]) ).
cnf(f_2627_8,plain,
( U_10270 = c_Groups_Ozero__class_Ozero(U_10267)
| hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269) != c_Groups_Ozero__class_Ozero(U_10267)
| ~ sP711(U_10267,U_10268,U_10269,U_10270) ),
inference(clausify,[status(thm)],[f_2627_3]) ).
cnf(f_2627_9,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269) != c_Groups_Ozero__class_Ozero(U_10267)
| ~ sP712(U_10267,U_10268,U_10269,U_10270) ),
inference(clausify,[status(thm)],[f_2627_3]) ).
cnf(f_2627_10,plain,
( U_10268 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10267),U_10270),hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269))
| ~ sP712(U_10267,U_10268,U_10269,U_10270) ),
inference(clausify,[status(thm)],[f_2627_3]) ).
cnf(f_2627_11,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10267),U_10269) = c_Groups_Ozero__class_Ozero(U_10267)
| ~ sP713(U_10267,U_10269,U_10270) ),
inference(clausify,[status(thm)],[f_2627_3]) ).
cnf(f_2627_12,plain,
( U_10270 != c_Groups_Ozero__class_Ozero(U_10267)
| ~ sP713(U_10267,U_10269,U_10270) ),
inference(clausify,[status(thm)],[f_2627_3]) ).
fof(f_2628_1,plain,
! [V_w_2,V_c_2,V_b_2,T_c] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)
| ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) != c_Groups_Ozero__class_Ozero(T_c)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_c) )
| ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)
& V_c_2 != c_Groups_Ozero__class_Ozero(T_c) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)
| V_c_2 = c_Groups_Ozero__class_Ozero(T_c) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) ) )
| ~ class_Int_Onumber(T_c)
| ~ class_Fields_Ofield__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of]) ).
fof(f_2628_2,plain,
! [U_10274,U_10273,U_10272,U_10271] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10271),U_10272),U_10273) = hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274)
| ( hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274) != c_Groups_Ozero__class_Ozero(U_10271)
& U_10273 = c_Groups_Ozero__class_Ozero(U_10271) )
| ( U_10272 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10271),hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274)),U_10273)
& U_10273 != c_Groups_Ozero__class_Ozero(U_10271) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274) = c_Groups_Ozero__class_Ozero(U_10271)
| U_10273 != c_Groups_Ozero__class_Ozero(U_10271) )
& ( U_10272 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10271),hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274)),U_10273)
| U_10273 = c_Groups_Ozero__class_Ozero(U_10271) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10271),U_10272),U_10273) != hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274) ) )
| ~ class_Int_Onumber(U_10271)
| ~ class_Fields_Ofield__inverse__zero(U_10271) ),
inference(variable_rename,[status(thm)],[f_2628_1]) ).
fof(f_2628_3,plain,
( ! [U_10271,U_10273,U_10274] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274) != c_Groups_Ozero__class_Ozero(U_10271)
| ~ sP717(U_10271,U_10273,U_10274) )
& ! [U_10271,U_10273,U_10274] :
( U_10273 = c_Groups_Ozero__class_Ozero(U_10271)
| ~ sP717(U_10271,U_10273,U_10274) )
& ! [U_10271,U_10272,U_10273,U_10274] :
( U_10272 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10271),hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274)),U_10273)
| ~ sP716(U_10271,U_10272,U_10273,U_10274) )
& ! [U_10271,U_10272,U_10273,U_10274] :
( U_10273 != c_Groups_Ozero__class_Ozero(U_10271)
| ~ sP716(U_10271,U_10272,U_10273,U_10274) )
& ! [U_10271,U_10272,U_10273,U_10274] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274) = c_Groups_Ozero__class_Ozero(U_10271)
| U_10273 != c_Groups_Ozero__class_Ozero(U_10271)
| ~ sP715(U_10271,U_10272,U_10273,U_10274) )
& ! [U_10271,U_10272,U_10273,U_10274] :
( U_10272 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10271),hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274)),U_10273)
| U_10273 = c_Groups_Ozero__class_Ozero(U_10271)
| ~ sP715(U_10271,U_10272,U_10273,U_10274) )
& ! [U_10271,U_10272,U_10273,U_10274] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10271),U_10272),U_10273) = hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274)
| sP717(U_10271,U_10273,U_10274)
| sP716(U_10271,U_10272,U_10273,U_10274)
| ~ sP718(U_10271,U_10272,U_10273,U_10274) )
& ! [U_10271,U_10272,U_10273,U_10274] :
( sP715(U_10271,U_10272,U_10273,U_10274)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10271),U_10272),U_10273) != hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274)
| ~ sP718(U_10271,U_10272,U_10273,U_10274) )
& ! [U_10271,U_10272,U_10273,U_10274] :
( sP718(U_10271,U_10272,U_10273,U_10274)
| ~ class_Int_Onumber(U_10271)
| ~ class_Fields_Ofield__inverse__zero(U_10271) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP715,sP716,sP717,sP718])],[f_2628_2]) ).
cnf(f_2628_4,plain,
( sP718(U_10271,U_10272,U_10273,U_10274)
| ~ class_Int_Onumber(U_10271)
| ~ class_Fields_Ofield__inverse__zero(U_10271) ),
inference(clausify,[status(thm)],[f_2628_3]) ).
cnf(f_2628_5,plain,
( sP715(U_10271,U_10272,U_10273,U_10274)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10271),U_10272),U_10273) != hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274)
| ~ sP718(U_10271,U_10272,U_10273,U_10274) ),
inference(clausify,[status(thm)],[f_2628_3]) ).
cnf(f_2628_6,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10271),U_10272),U_10273) = hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274)
| sP717(U_10271,U_10273,U_10274)
| sP716(U_10271,U_10272,U_10273,U_10274)
| ~ sP718(U_10271,U_10272,U_10273,U_10274) ),
inference(clausify,[status(thm)],[f_2628_3]) ).
cnf(f_2628_7,plain,
( U_10272 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10271),hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274)),U_10273)
| U_10273 = c_Groups_Ozero__class_Ozero(U_10271)
| ~ sP715(U_10271,U_10272,U_10273,U_10274) ),
inference(clausify,[status(thm)],[f_2628_3]) ).
cnf(f_2628_8,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274) = c_Groups_Ozero__class_Ozero(U_10271)
| U_10273 != c_Groups_Ozero__class_Ozero(U_10271)
| ~ sP715(U_10271,U_10272,U_10273,U_10274) ),
inference(clausify,[status(thm)],[f_2628_3]) ).
cnf(f_2628_9,plain,
( U_10273 != c_Groups_Ozero__class_Ozero(U_10271)
| ~ sP716(U_10271,U_10272,U_10273,U_10274) ),
inference(clausify,[status(thm)],[f_2628_3]) ).
cnf(f_2628_10,plain,
( U_10272 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10271),hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274)),U_10273)
| ~ sP716(U_10271,U_10272,U_10273,U_10274) ),
inference(clausify,[status(thm)],[f_2628_3]) ).
cnf(f_2628_11,plain,
( U_10273 = c_Groups_Ozero__class_Ozero(U_10271)
| ~ sP717(U_10271,U_10273,U_10274) ),
inference(clausify,[status(thm)],[f_2628_3]) ).
cnf(f_2628_12,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10271),U_10274) != c_Groups_Ozero__class_Ozero(U_10271)
| ~ sP717(U_10271,U_10273,U_10274) ),
inference(clausify,[status(thm)],[f_2628_3]) ).
fof(f_2629_1,plain,
! [V_c_2,V_b_2,V_w_2,T_c] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)
| ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) != c_Groups_Ozero__class_Ozero(T_c)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_c) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2) != V_b_2
& V_c_2 != c_Groups_Ozero__class_Ozero(T_c) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2) = V_b_2
| V_c_2 = c_Groups_Ozero__class_Ozero(T_c) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2) ) )
| ~ class_Int_Onumber(T_c)
| ~ class_Fields_Ofield__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of]) ).
fof(f_2629_2,plain,
! [U_10278,U_10277,U_10276,U_10275] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10275),U_10277),U_10278)
| ( hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276) != c_Groups_Ozero__class_Ozero(U_10275)
& U_10278 = c_Groups_Ozero__class_Ozero(U_10275) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10275),hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276)),U_10278) != U_10277
& U_10278 != c_Groups_Ozero__class_Ozero(U_10275) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276) = c_Groups_Ozero__class_Ozero(U_10275)
| U_10278 != c_Groups_Ozero__class_Ozero(U_10275) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10275),hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276)),U_10278) = U_10277
| U_10278 = c_Groups_Ozero__class_Ozero(U_10275) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10275),U_10277),U_10278) ) )
| ~ class_Int_Onumber(U_10275)
| ~ class_Fields_Ofield__inverse__zero(U_10275) ),
inference(variable_rename,[status(thm)],[f_2629_1]) ).
fof(f_2629_3,plain,
( ! [U_10275,U_10276,U_10278] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276) != c_Groups_Ozero__class_Ozero(U_10275)
| ~ sP721(U_10275,U_10276,U_10278) )
& ! [U_10275,U_10276,U_10278] :
( U_10278 = c_Groups_Ozero__class_Ozero(U_10275)
| ~ sP721(U_10275,U_10276,U_10278) )
& ! [U_10275,U_10276,U_10277,U_10278] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10275),hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276)),U_10278) != U_10277
| ~ sP720(U_10275,U_10276,U_10277,U_10278) )
& ! [U_10275,U_10276,U_10277,U_10278] :
( U_10278 != c_Groups_Ozero__class_Ozero(U_10275)
| ~ sP720(U_10275,U_10276,U_10277,U_10278) )
& ! [U_10275,U_10276,U_10277,U_10278] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276) = c_Groups_Ozero__class_Ozero(U_10275)
| U_10278 != c_Groups_Ozero__class_Ozero(U_10275)
| ~ sP719(U_10275,U_10276,U_10277,U_10278) )
& ! [U_10275,U_10276,U_10277,U_10278] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10275),hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276)),U_10278) = U_10277
| U_10278 = c_Groups_Ozero__class_Ozero(U_10275)
| ~ sP719(U_10275,U_10276,U_10277,U_10278) )
& ! [U_10275,U_10276,U_10277,U_10278] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10275),U_10277),U_10278)
| sP721(U_10275,U_10276,U_10278)
| sP720(U_10275,U_10276,U_10277,U_10278)
| ~ sP722(U_10275,U_10276,U_10277,U_10278) )
& ! [U_10275,U_10276,U_10277,U_10278] :
( sP719(U_10275,U_10276,U_10277,U_10278)
| hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10275),U_10277),U_10278)
| ~ sP722(U_10275,U_10276,U_10277,U_10278) )
& ! [U_10275,U_10276,U_10277,U_10278] :
( sP722(U_10275,U_10276,U_10277,U_10278)
| ~ class_Int_Onumber(U_10275)
| ~ class_Fields_Ofield__inverse__zero(U_10275) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP719,sP720,sP721,sP722])],[f_2629_2]) ).
cnf(f_2629_4,plain,
( sP722(U_10275,U_10276,U_10277,U_10278)
| ~ class_Int_Onumber(U_10275)
| ~ class_Fields_Ofield__inverse__zero(U_10275) ),
inference(clausify,[status(thm)],[f_2629_3]) ).
cnf(f_2629_5,plain,
( sP719(U_10275,U_10276,U_10277,U_10278)
| hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10275),U_10277),U_10278)
| ~ sP722(U_10275,U_10276,U_10277,U_10278) ),
inference(clausify,[status(thm)],[f_2629_3]) ).
cnf(f_2629_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10275),U_10277),U_10278)
| sP721(U_10275,U_10276,U_10278)
| sP720(U_10275,U_10276,U_10277,U_10278)
| ~ sP722(U_10275,U_10276,U_10277,U_10278) ),
inference(clausify,[status(thm)],[f_2629_3]) ).
cnf(f_2629_7,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10275),hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276)),U_10278) = U_10277
| U_10278 = c_Groups_Ozero__class_Ozero(U_10275)
| ~ sP719(U_10275,U_10276,U_10277,U_10278) ),
inference(clausify,[status(thm)],[f_2629_3]) ).
cnf(f_2629_8,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276) = c_Groups_Ozero__class_Ozero(U_10275)
| U_10278 != c_Groups_Ozero__class_Ozero(U_10275)
| ~ sP719(U_10275,U_10276,U_10277,U_10278) ),
inference(clausify,[status(thm)],[f_2629_3]) ).
cnf(f_2629_9,plain,
( U_10278 != c_Groups_Ozero__class_Ozero(U_10275)
| ~ sP720(U_10275,U_10276,U_10277,U_10278) ),
inference(clausify,[status(thm)],[f_2629_3]) ).
cnf(f_2629_10,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10275),hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276)),U_10278) != U_10277
| ~ sP720(U_10275,U_10276,U_10277,U_10278) ),
inference(clausify,[status(thm)],[f_2629_3]) ).
cnf(f_2629_11,plain,
( U_10278 = c_Groups_Ozero__class_Ozero(U_10275)
| ~ sP721(U_10275,U_10276,U_10278) ),
inference(clausify,[status(thm)],[f_2629_3]) ).
cnf(f_2629_12,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10275),U_10276) != c_Groups_Ozero__class_Ozero(U_10275)
| ~ sP721(U_10275,U_10276,U_10278) ),
inference(clausify,[status(thm)],[f_2629_3]) ).
fof(f_2630_1,plain,
! [V_w_2,V_b_2,V_a_2,T_c] :
( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_c)
& hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) != V_b_2
& hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) != c_Groups_Ozero__class_Ozero(T_c) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) = V_b_2
| hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2) = c_Groups_Ozero__class_Ozero(T_c) ) )
| V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) ) )
| ~ class_Int_Onumber(T_c)
| ~ class_Fields_Ofield__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1]) ).
fof(f_2630_2,plain,
! [U_10282,U_10281,U_10280,U_10279] :
( ( ( U_10280 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10279),U_10281),hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282))
| ( U_10280 != c_Groups_Ozero__class_Ozero(U_10279)
& hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282) = c_Groups_Ozero__class_Ozero(U_10279) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10279),U_10280),hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282)) != U_10281
& hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282) != c_Groups_Ozero__class_Ozero(U_10279) ) )
& ( ( ( U_10280 = c_Groups_Ozero__class_Ozero(U_10279)
| hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282) != c_Groups_Ozero__class_Ozero(U_10279) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10279),U_10280),hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282)) = U_10281
| hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282) = c_Groups_Ozero__class_Ozero(U_10279) ) )
| U_10280 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10279),U_10281),hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282)) ) )
| ~ class_Int_Onumber(U_10279)
| ~ class_Fields_Ofield__inverse__zero(U_10279) ),
inference(variable_rename,[status(thm)],[f_2630_1]) ).
fof(f_2630_3,plain,
( ! [U_10282,U_10279,U_10280] :
( U_10280 != c_Groups_Ozero__class_Ozero(U_10279)
| ~ sP725(U_10282,U_10279,U_10280) )
& ! [U_10282,U_10279,U_10280] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282) = c_Groups_Ozero__class_Ozero(U_10279)
| ~ sP725(U_10282,U_10279,U_10280) )
& ! [U_10282,U_10281,U_10279,U_10280] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10279),U_10280),hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282)) != U_10281
| ~ sP724(U_10282,U_10281,U_10279,U_10280) )
& ! [U_10282,U_10281,U_10279,U_10280] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282) != c_Groups_Ozero__class_Ozero(U_10279)
| ~ sP724(U_10282,U_10281,U_10279,U_10280) )
& ! [U_10282,U_10281,U_10279,U_10280] :
( U_10280 = c_Groups_Ozero__class_Ozero(U_10279)
| hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282) != c_Groups_Ozero__class_Ozero(U_10279)
| ~ sP723(U_10282,U_10281,U_10279,U_10280) )
& ! [U_10282,U_10281,U_10279,U_10280] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10279),U_10280),hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282)) = U_10281
| hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282) = c_Groups_Ozero__class_Ozero(U_10279)
| ~ sP723(U_10282,U_10281,U_10279,U_10280) )
& ! [U_10282,U_10281,U_10279,U_10280] :
( U_10280 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10279),U_10281),hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282))
| sP725(U_10282,U_10279,U_10280)
| sP724(U_10282,U_10281,U_10279,U_10280)
| ~ sP726(U_10282,U_10281,U_10279,U_10280) )
& ! [U_10282,U_10281,U_10279,U_10280] :
( sP723(U_10282,U_10281,U_10279,U_10280)
| U_10280 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10279),U_10281),hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282))
| ~ sP726(U_10282,U_10281,U_10279,U_10280) )
& ! [U_10282,U_10281,U_10279,U_10280] :
( sP726(U_10282,U_10281,U_10279,U_10280)
| ~ class_Int_Onumber(U_10279)
| ~ class_Fields_Ofield__inverse__zero(U_10279) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP723,sP724,sP725,sP726])],[f_2630_2]) ).
cnf(f_2630_4,plain,
( sP726(U_10282,U_10281,U_10279,U_10280)
| ~ class_Int_Onumber(U_10279)
| ~ class_Fields_Ofield__inverse__zero(U_10279) ),
inference(clausify,[status(thm)],[f_2630_3]) ).
cnf(f_2630_5,plain,
( sP723(U_10282,U_10281,U_10279,U_10280)
| U_10280 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10279),U_10281),hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282))
| ~ sP726(U_10282,U_10281,U_10279,U_10280) ),
inference(clausify,[status(thm)],[f_2630_3]) ).
cnf(f_2630_6,plain,
( U_10280 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10279),U_10281),hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282))
| sP725(U_10282,U_10279,U_10280)
| sP724(U_10282,U_10281,U_10279,U_10280)
| ~ sP726(U_10282,U_10281,U_10279,U_10280) ),
inference(clausify,[status(thm)],[f_2630_3]) ).
cnf(f_2630_7,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10279),U_10280),hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282)) = U_10281
| hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282) = c_Groups_Ozero__class_Ozero(U_10279)
| ~ sP723(U_10282,U_10281,U_10279,U_10280) ),
inference(clausify,[status(thm)],[f_2630_3]) ).
cnf(f_2630_8,plain,
( U_10280 = c_Groups_Ozero__class_Ozero(U_10279)
| hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282) != c_Groups_Ozero__class_Ozero(U_10279)
| ~ sP723(U_10282,U_10281,U_10279,U_10280) ),
inference(clausify,[status(thm)],[f_2630_3]) ).
cnf(f_2630_9,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282) != c_Groups_Ozero__class_Ozero(U_10279)
| ~ sP724(U_10282,U_10281,U_10279,U_10280) ),
inference(clausify,[status(thm)],[f_2630_3]) ).
cnf(f_2630_10,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10279),U_10280),hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282)) != U_10281
| ~ sP724(U_10282,U_10281,U_10279,U_10280) ),
inference(clausify,[status(thm)],[f_2630_3]) ).
cnf(f_2630_11,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10279),U_10282) = c_Groups_Ozero__class_Ozero(U_10279)
| ~ sP725(U_10282,U_10279,U_10280) ),
inference(clausify,[status(thm)],[f_2630_3]) ).
cnf(f_2630_12,plain,
( U_10280 != c_Groups_Ozero__class_Ozero(U_10279)
| ~ sP725(U_10282,U_10279,U_10280) ),
inference(clausify,[status(thm)],[f_2630_3]) ).
fof(f_2631_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_2631_2,plain,
! [U_10286,U_10285,U_10284,U_10283] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10283),hAPP(c_Int_Onumber__class_Onumber__of(U_10283),U_10284)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10283),hAPP(c_Int_Onumber__class_Onumber__of(U_10283),U_10285)),U_10286)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10283),hAPP(c_Int_Onumber__class_Onumber__of(U_10283),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10284),U_10285))),U_10286)
| ~ class_Int_Onumber__ring(U_10283) ),
inference(variable_rename,[status(thm)],[f_2631_1]) ).
fof(f_2631_3,plain,
! [U_10286,U_10283,U_10285,U_10284] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10283),hAPP(c_Int_Onumber__class_Onumber__of(U_10283),U_10284)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10283),hAPP(c_Int_Onumber__class_Onumber__of(U_10283),U_10285)),U_10286)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10283),hAPP(c_Int_Onumber__class_Onumber__of(U_10283),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10284),U_10285))),U_10286)
| ~ class_Int_Onumber__ring(U_10283) ),
inference(definitional_conversion,[status(esa)],[f_2631_2]) ).
cnf(f_2631_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10283),hAPP(c_Int_Onumber__class_Onumber__of(U_10283),U_10284)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10283),hAPP(c_Int_Onumber__class_Onumber__of(U_10283),U_10285)),U_10286)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10283),hAPP(c_Int_Onumber__class_Onumber__of(U_10283),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10284),U_10285))),U_10286)
| ~ class_Int_Onumber__ring(U_10283) ),
inference(clausify,[status(thm)],[f_2631_3]) ).
fof(f_2632_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_2632_2,plain,
! [U_10289,U_10288,U_10287] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10287),hAPP(c_Groups_Ouminus__class_Ouminus(U_10287),hAPP(c_Int_Onumber__class_Onumber__of(U_10287),U_10288))),U_10289) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10287),hAPP(c_Int_Onumber__class_Onumber__of(U_10287),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10288))),U_10289)
| ~ class_Int_Onumber__ring(U_10287) ),
inference(variable_rename,[status(thm)],[f_2632_1]) ).
fof(f_2632_3,plain,
! [U_10287,U_10288,U_10289] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10287),hAPP(c_Groups_Ouminus__class_Ouminus(U_10287),hAPP(c_Int_Onumber__class_Onumber__of(U_10287),U_10288))),U_10289) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10287),hAPP(c_Int_Onumber__class_Onumber__of(U_10287),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10288))),U_10289)
| ~ class_Int_Onumber__ring(U_10287) ),
inference(definitional_conversion,[status(esa)],[f_2632_2]) ).
cnf(f_2632_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10287),hAPP(c_Groups_Ouminus__class_Ouminus(U_10287),hAPP(c_Int_Onumber__class_Onumber__of(U_10287),U_10288))),U_10289) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10287),hAPP(c_Int_Onumber__class_Onumber__of(U_10287),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10288))),U_10289)
| ~ class_Int_Onumber__ring(U_10287) ),
inference(clausify,[status(thm)],[f_2632_3]) ).
fof(f_2633_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_2633_2,plain,
! [U_10292,U_10291,U_10290] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10290),hAPP(c_Int_Onumber__class_Onumber__of(U_10290),U_10291)),hAPP(c_Int_Onumber__class_Onumber__of(U_10290),U_10292)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10290),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10291),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10292)))
| ~ class_Int_Onumber__ring(U_10290) ),
inference(variable_rename,[status(thm)],[f_2633_1]) ).
fof(f_2633_3,plain,
! [U_10290,U_10291,U_10292] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10290),hAPP(c_Int_Onumber__class_Onumber__of(U_10290),U_10291)),hAPP(c_Int_Onumber__class_Onumber__of(U_10290),U_10292)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10290),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10291),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10292)))
| ~ class_Int_Onumber__ring(U_10290) ),
inference(definitional_conversion,[status(esa)],[f_2633_2]) ).
cnf(f_2633_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10290),hAPP(c_Int_Onumber__class_Onumber__of(U_10290),U_10291)),hAPP(c_Int_Onumber__class_Onumber__of(U_10290),U_10292)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10290),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10291),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10292)))
| ~ class_Int_Onumber__ring(U_10290) ),
inference(clausify,[status(thm)],[f_2633_3]) ).
fof(f_2634_1,plain,
! [V_a_2,V_w_2,V_b_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_a_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_a_2)) ) )
| ~ class_Int_Onumber(T_c)
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of1]) ).
fof(f_2634_2,plain,
! [U_10296,U_10295,U_10294,U_10293] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10293),U_10294),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))),U_10296))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),U_10296))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)),c_Groups_Ozero__class_Ozero(U_10293))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10293),U_10296),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))),U_10294))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)),c_Groups_Ozero__class_Ozero(U_10293))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),U_10294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10293),U_10296),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),U_10296))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)),c_Groups_Ozero__class_Ozero(U_10293))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10293),U_10296),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))),U_10294))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)),c_Groups_Ozero__class_Ozero(U_10293))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),U_10294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10293),U_10296),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10293),U_10294),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))),U_10296)) ) )
| ~ class_Int_Onumber(U_10293)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10293) ),
inference(variable_rename,[status(thm)],[f_2634_1]) ).
fof(f_2634_3,plain,
( ! [U_10293,U_10295,U_10296] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),U_10296))
| ~ sP731(U_10293,U_10295,U_10296) )
& ! [U_10293,U_10295,U_10296] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)),c_Groups_Ozero__class_Ozero(U_10293)))
| ~ sP731(U_10293,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10293),U_10296),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))),U_10294))
| ~ sP730(U_10293,U_10294,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)),c_Groups_Ozero__class_Ozero(U_10293)))
| ~ sP730(U_10293,U_10294,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( sP731(U_10293,U_10295,U_10296)
| sP730(U_10293,U_10294,U_10295,U_10296)
| ~ sP732(U_10293,U_10294,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)))
| ~ sP732(U_10293,U_10294,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),U_10294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10293),U_10296),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))))
| ~ sP729(U_10293,U_10294,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)))
| ~ sP729(U_10293,U_10294,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),U_10296))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)),c_Groups_Ozero__class_Ozero(U_10293)))
| ~ sP727(U_10293,U_10294,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10293),U_10296),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))),U_10294))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)),c_Groups_Ozero__class_Ozero(U_10293)))
| ~ sP727(U_10293,U_10294,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( sP727(U_10293,U_10294,U_10295,U_10296)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)))
| ~ sP728(U_10293,U_10294,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),U_10294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10293),U_10296),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)))
| ~ sP728(U_10293,U_10294,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10293),U_10294),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))),U_10296))
| sP732(U_10293,U_10294,U_10295,U_10296)
| sP729(U_10293,U_10294,U_10295,U_10296)
| ~ sP733(U_10293,U_10294,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( sP728(U_10293,U_10294,U_10295,U_10296)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10293),U_10294),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))),U_10296))
| ~ sP733(U_10293,U_10294,U_10295,U_10296) )
& ! [U_10293,U_10294,U_10295,U_10296] :
( sP733(U_10293,U_10294,U_10295,U_10296)
| ~ class_Int_Onumber(U_10293)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10293) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP727,sP728,sP729,sP730,sP731,sP732,sP733])],[f_2634_2]) ).
cnf(f_2634_4,plain,
( sP733(U_10293,U_10294,U_10295,U_10296)
| ~ class_Int_Onumber(U_10293)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10293) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_5,plain,
( sP728(U_10293,U_10294,U_10295,U_10296)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10293),U_10294),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))),U_10296))
| ~ sP733(U_10293,U_10294,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10293),U_10294),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))),U_10296))
| sP732(U_10293,U_10294,U_10295,U_10296)
| sP729(U_10293,U_10294,U_10295,U_10296)
| ~ sP733(U_10293,U_10294,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),U_10294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10293),U_10296),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)))
| ~ sP728(U_10293,U_10294,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_8,plain,
( sP727(U_10293,U_10294,U_10295,U_10296)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)))
| ~ sP728(U_10293,U_10294,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10293),U_10296),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))),U_10294))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)),c_Groups_Ozero__class_Ozero(U_10293)))
| ~ sP727(U_10293,U_10294,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),U_10296))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)),c_Groups_Ozero__class_Ozero(U_10293)))
| ~ sP727(U_10293,U_10294,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)))
| ~ sP729(U_10293,U_10294,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),U_10294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10293),U_10296),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))))
| ~ sP729(U_10293,U_10294,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)))
| ~ sP732(U_10293,U_10294,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_14,plain,
( sP731(U_10293,U_10295,U_10296)
| sP730(U_10293,U_10294,U_10295,U_10296)
| ~ sP732(U_10293,U_10294,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)),c_Groups_Ozero__class_Ozero(U_10293)))
| ~ sP730(U_10293,U_10294,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10293),U_10296),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295))),U_10294))
| ~ sP730(U_10293,U_10294,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),hAPP(c_Int_Onumber__class_Onumber__of(U_10293),U_10295)),c_Groups_Ozero__class_Ozero(U_10293)))
| ~ sP731(U_10293,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
cnf(f_2634_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10293),c_Groups_Ozero__class_Ozero(U_10293)),U_10296))
| ~ sP731(U_10293,U_10295,U_10296) ),
inference(clausify,[status(thm)],[f_2634_3]) ).
fof(f_2635_1,plain,
! [V_w_2,V_c_2,V_b_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) )
| ~ class_Int_Onumber(T_c)
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of]) ).
fof(f_2635_2,plain,
! [U_10300,U_10299,U_10298,U_10297] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10297),U_10298),U_10299)),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10299),c_Groups_Ozero__class_Ozero(U_10297))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10297),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)),U_10299)),U_10298))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10299),c_Groups_Ozero__class_Ozero(U_10297))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),U_10299)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10297),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)),U_10299)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),U_10299)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10299),c_Groups_Ozero__class_Ozero(U_10297))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10297),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)),U_10299)),U_10298))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10299),c_Groups_Ozero__class_Ozero(U_10297))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),U_10299)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10297),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)),U_10299)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),U_10299)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10297),U_10298),U_10299)),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300))) ) )
| ~ class_Int_Onumber(U_10297)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10297) ),
inference(variable_rename,[status(thm)],[f_2635_1]) ).
fof(f_2635_3,plain,
( ! [U_10300,U_10299,U_10297] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)))
| ~ sP738(U_10300,U_10299,U_10297) )
& ! [U_10300,U_10299,U_10297] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10299),c_Groups_Ozero__class_Ozero(U_10297)))
| ~ sP738(U_10300,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10297),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)),U_10299)),U_10298))
| ~ sP737(U_10300,U_10298,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10299),c_Groups_Ozero__class_Ozero(U_10297)))
| ~ sP737(U_10300,U_10298,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( sP738(U_10300,U_10299,U_10297)
| sP737(U_10300,U_10298,U_10299,U_10297)
| ~ sP739(U_10300,U_10298,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),U_10299))
| ~ sP739(U_10300,U_10298,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10297),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)),U_10299)))
| ~ sP736(U_10300,U_10298,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),U_10299))
| ~ sP736(U_10300,U_10298,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10299),c_Groups_Ozero__class_Ozero(U_10297)))
| ~ sP734(U_10300,U_10298,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10297),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)),U_10299)),U_10298))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10299),c_Groups_Ozero__class_Ozero(U_10297)))
| ~ sP734(U_10300,U_10298,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( sP734(U_10300,U_10298,U_10299,U_10297)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),U_10299))
| ~ sP735(U_10300,U_10298,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10297),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)),U_10299)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),U_10299))
| ~ sP735(U_10300,U_10298,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10297),U_10298),U_10299)),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)))
| sP739(U_10300,U_10298,U_10299,U_10297)
| sP736(U_10300,U_10298,U_10299,U_10297)
| ~ sP740(U_10300,U_10298,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( sP735(U_10300,U_10298,U_10299,U_10297)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10297),U_10298),U_10299)),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)))
| ~ sP740(U_10300,U_10298,U_10299,U_10297) )
& ! [U_10300,U_10298,U_10299,U_10297] :
( sP740(U_10300,U_10298,U_10299,U_10297)
| ~ class_Int_Onumber(U_10297)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10297) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP734,sP735,sP736,sP737,sP738,sP739,sP740])],[f_2635_2]) ).
cnf(f_2635_4,plain,
( sP740(U_10300,U_10298,U_10299,U_10297)
| ~ class_Int_Onumber(U_10297)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_5,plain,
( sP735(U_10300,U_10298,U_10299,U_10297)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10297),U_10298),U_10299)),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)))
| ~ sP740(U_10300,U_10298,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10297),U_10298),U_10299)),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)))
| sP739(U_10300,U_10298,U_10299,U_10297)
| sP736(U_10300,U_10298,U_10299,U_10297)
| ~ sP740(U_10300,U_10298,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10297),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)),U_10299)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),U_10299))
| ~ sP735(U_10300,U_10298,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_8,plain,
( sP734(U_10300,U_10298,U_10299,U_10297)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),U_10299))
| ~ sP735(U_10300,U_10298,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10297),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)),U_10299)),U_10298))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10299),c_Groups_Ozero__class_Ozero(U_10297)))
| ~ sP734(U_10300,U_10298,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10299),c_Groups_Ozero__class_Ozero(U_10297)))
| ~ sP734(U_10300,U_10298,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),U_10299))
| ~ sP736(U_10300,U_10298,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10297),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)),U_10299)))
| ~ sP736(U_10300,U_10298,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),U_10299))
| ~ sP739(U_10300,U_10298,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_14,plain,
( sP738(U_10300,U_10299,U_10297)
| sP737(U_10300,U_10298,U_10299,U_10297)
| ~ sP739(U_10300,U_10298,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10299),c_Groups_Ozero__class_Ozero(U_10297)))
| ~ sP737(U_10300,U_10298,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10297),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)),U_10299)),U_10298))
| ~ sP737(U_10300,U_10298,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),U_10299),c_Groups_Ozero__class_Ozero(U_10297)))
| ~ sP738(U_10300,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
cnf(f_2635_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10297),c_Groups_Ozero__class_Ozero(U_10297)),hAPP(c_Int_Onumber__class_Onumber__of(U_10297),U_10300)))
| ~ sP738(U_10300,U_10299,U_10297) ),
inference(clausify,[status(thm)],[f_2635_3]) ).
fof(f_2636_1,plain,
! [V_c_2,V_b_2,V_w_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) ) )
| ~ class_Int_Onumber(T_c)
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of]) ).
fof(f_2636_2,plain,
! [U_10304,U_10303,U_10302,U_10301] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10301),U_10303),U_10304)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),c_Groups_Ozero__class_Ozero(U_10301)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10304),c_Groups_Ozero__class_Ozero(U_10301))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),U_10304)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10304),c_Groups_Ozero__class_Ozero(U_10301))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),c_Groups_Ozero__class_Ozero(U_10301)),U_10304)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),U_10304)),U_10303))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),c_Groups_Ozero__class_Ozero(U_10301)),U_10304)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),c_Groups_Ozero__class_Ozero(U_10301)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10304),c_Groups_Ozero__class_Ozero(U_10301))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),U_10304)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10304),c_Groups_Ozero__class_Ozero(U_10301))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),c_Groups_Ozero__class_Ozero(U_10301)),U_10304)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),U_10304)),U_10303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),c_Groups_Ozero__class_Ozero(U_10301)),U_10304)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10301),U_10303),U_10304))) ) )
| ~ class_Int_Onumber(U_10301)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10301) ),
inference(variable_rename,[status(thm)],[f_2636_1]) ).
fof(f_2636_3,plain,
( ! [U_10304,U_10302,U_10301] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),c_Groups_Ozero__class_Ozero(U_10301)))
| ~ sP745(U_10304,U_10302,U_10301) )
& ! [U_10304,U_10302,U_10301] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10304),c_Groups_Ozero__class_Ozero(U_10301)))
| ~ sP745(U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),U_10304)))
| ~ sP744(U_10303,U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10304),c_Groups_Ozero__class_Ozero(U_10301)))
| ~ sP744(U_10303,U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( sP745(U_10304,U_10302,U_10301)
| sP744(U_10303,U_10304,U_10302,U_10301)
| ~ sP746(U_10303,U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),c_Groups_Ozero__class_Ozero(U_10301)),U_10304))
| ~ sP746(U_10303,U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),U_10304)),U_10303))
| ~ sP743(U_10303,U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),c_Groups_Ozero__class_Ozero(U_10301)),U_10304))
| ~ sP743(U_10303,U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),c_Groups_Ozero__class_Ozero(U_10301)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10304),c_Groups_Ozero__class_Ozero(U_10301)))
| ~ sP741(U_10303,U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),U_10304)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10304),c_Groups_Ozero__class_Ozero(U_10301)))
| ~ sP741(U_10303,U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( sP741(U_10303,U_10304,U_10302,U_10301)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),c_Groups_Ozero__class_Ozero(U_10301)),U_10304))
| ~ sP742(U_10303,U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),U_10304)),U_10303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),c_Groups_Ozero__class_Ozero(U_10301)),U_10304))
| ~ sP742(U_10303,U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10301),U_10303),U_10304)))
| sP746(U_10303,U_10304,U_10302,U_10301)
| sP743(U_10303,U_10304,U_10302,U_10301)
| ~ sP747(U_10303,U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( sP742(U_10303,U_10304,U_10302,U_10301)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10301),U_10303),U_10304)))
| ~ sP747(U_10303,U_10304,U_10302,U_10301) )
& ! [U_10303,U_10304,U_10302,U_10301] :
( sP747(U_10303,U_10304,U_10302,U_10301)
| ~ class_Int_Onumber(U_10301)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10301) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP741,sP742,sP743,sP744,sP745,sP746,sP747])],[f_2636_2]) ).
cnf(f_2636_4,plain,
( sP747(U_10303,U_10304,U_10302,U_10301)
| ~ class_Int_Onumber(U_10301)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_5,plain,
( sP742(U_10303,U_10304,U_10302,U_10301)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10301),U_10303),U_10304)))
| ~ sP747(U_10303,U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10301),U_10303),U_10304)))
| sP746(U_10303,U_10304,U_10302,U_10301)
| sP743(U_10303,U_10304,U_10302,U_10301)
| ~ sP747(U_10303,U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),U_10304)),U_10303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),c_Groups_Ozero__class_Ozero(U_10301)),U_10304))
| ~ sP742(U_10303,U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_8,plain,
( sP741(U_10303,U_10304,U_10302,U_10301)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),c_Groups_Ozero__class_Ozero(U_10301)),U_10304))
| ~ sP742(U_10303,U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),U_10304)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10304),c_Groups_Ozero__class_Ozero(U_10301)))
| ~ sP741(U_10303,U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),c_Groups_Ozero__class_Ozero(U_10301)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10304),c_Groups_Ozero__class_Ozero(U_10301)))
| ~ sP741(U_10303,U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),c_Groups_Ozero__class_Ozero(U_10301)),U_10304))
| ~ sP743(U_10303,U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),U_10304)),U_10303))
| ~ sP743(U_10303,U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),c_Groups_Ozero__class_Ozero(U_10301)),U_10304))
| ~ sP746(U_10303,U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_14,plain,
( sP745(U_10304,U_10302,U_10301)
| sP744(U_10303,U_10304,U_10302,U_10301)
| ~ sP746(U_10303,U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10304),c_Groups_Ozero__class_Ozero(U_10301)))
| ~ sP744(U_10303,U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),U_10304)))
| ~ sP744(U_10303,U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),U_10304),c_Groups_Ozero__class_Ozero(U_10301)))
| ~ sP745(U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
cnf(f_2636_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10301),hAPP(c_Int_Onumber__class_Onumber__of(U_10301),U_10302)),c_Groups_Ozero__class_Ozero(U_10301)))
| ~ sP745(U_10304,U_10302,U_10301) ),
inference(clausify,[status(thm)],[f_2636_3]) ).
fof(f_2637_1,plain,
! [V_w_2,V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))) ) )
| ~ class_Int_Onumber(T_c)
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of1]) ).
fof(f_2637_2,plain,
! [U_10308,U_10307,U_10306,U_10305] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10306),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10305),U_10307),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10306),c_Groups_Ozero__class_Ozero(U_10305)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)),c_Groups_Ozero__class_Ozero(U_10305))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10305),U_10306),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)),c_Groups_Ozero__class_Ozero(U_10305))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),c_Groups_Ozero__class_Ozero(U_10305)),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10305),U_10306),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))),U_10307))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),c_Groups_Ozero__class_Ozero(U_10305)),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10306),c_Groups_Ozero__class_Ozero(U_10305)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)),c_Groups_Ozero__class_Ozero(U_10305))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10305),U_10306),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)),c_Groups_Ozero__class_Ozero(U_10305))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),c_Groups_Ozero__class_Ozero(U_10305)),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10305),U_10306),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))),U_10307))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),c_Groups_Ozero__class_Ozero(U_10305)),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10306),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10305),U_10307),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)))) ) )
| ~ class_Int_Onumber(U_10305)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10305) ),
inference(variable_rename,[status(thm)],[f_2637_1]) ).
fof(f_2637_3,plain,
( ! [U_10306,U_10308,U_10305] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10306),c_Groups_Ozero__class_Ozero(U_10305)))
| ~ sP752(U_10306,U_10308,U_10305) )
& ! [U_10306,U_10308,U_10305] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)),c_Groups_Ozero__class_Ozero(U_10305)))
| ~ sP752(U_10306,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10305),U_10306),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))))
| ~ sP751(U_10306,U_10307,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)),c_Groups_Ozero__class_Ozero(U_10305)))
| ~ sP751(U_10306,U_10307,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( sP752(U_10306,U_10308,U_10305)
| sP751(U_10306,U_10307,U_10308,U_10305)
| ~ sP753(U_10306,U_10307,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),c_Groups_Ozero__class_Ozero(U_10305)),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)))
| ~ sP753(U_10306,U_10307,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10305),U_10306),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))),U_10307))
| ~ sP750(U_10306,U_10307,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),c_Groups_Ozero__class_Ozero(U_10305)),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)))
| ~ sP750(U_10306,U_10307,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10306),c_Groups_Ozero__class_Ozero(U_10305)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)),c_Groups_Ozero__class_Ozero(U_10305)))
| ~ sP748(U_10306,U_10307,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10305),U_10306),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)),c_Groups_Ozero__class_Ozero(U_10305)))
| ~ sP748(U_10306,U_10307,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( sP748(U_10306,U_10307,U_10308,U_10305)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),c_Groups_Ozero__class_Ozero(U_10305)),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)))
| ~ sP749(U_10306,U_10307,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10305),U_10306),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))),U_10307))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),c_Groups_Ozero__class_Ozero(U_10305)),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)))
| ~ sP749(U_10306,U_10307,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10306),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10305),U_10307),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))))
| sP753(U_10306,U_10307,U_10308,U_10305)
| sP750(U_10306,U_10307,U_10308,U_10305)
| ~ sP754(U_10306,U_10307,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( sP749(U_10306,U_10307,U_10308,U_10305)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10306),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10305),U_10307),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))))
| ~ sP754(U_10306,U_10307,U_10308,U_10305) )
& ! [U_10306,U_10307,U_10308,U_10305] :
( sP754(U_10306,U_10307,U_10308,U_10305)
| ~ class_Int_Onumber(U_10305)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10305) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP748,sP749,sP750,sP751,sP752,sP753,sP754])],[f_2637_2]) ).
cnf(f_2637_4,plain,
( sP754(U_10306,U_10307,U_10308,U_10305)
| ~ class_Int_Onumber(U_10305)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_5,plain,
( sP749(U_10306,U_10307,U_10308,U_10305)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10306),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10305),U_10307),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))))
| ~ sP754(U_10306,U_10307,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10306),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10305),U_10307),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))))
| sP753(U_10306,U_10307,U_10308,U_10305)
| sP750(U_10306,U_10307,U_10308,U_10305)
| ~ sP754(U_10306,U_10307,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10305),U_10306),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))),U_10307))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),c_Groups_Ozero__class_Ozero(U_10305)),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)))
| ~ sP749(U_10306,U_10307,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_8,plain,
( sP748(U_10306,U_10307,U_10308,U_10305)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),c_Groups_Ozero__class_Ozero(U_10305)),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)))
| ~ sP749(U_10306,U_10307,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10305),U_10306),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)),c_Groups_Ozero__class_Ozero(U_10305)))
| ~ sP748(U_10306,U_10307,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10306),c_Groups_Ozero__class_Ozero(U_10305)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)),c_Groups_Ozero__class_Ozero(U_10305)))
| ~ sP748(U_10306,U_10307,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),c_Groups_Ozero__class_Ozero(U_10305)),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)))
| ~ sP750(U_10306,U_10307,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10305),U_10306),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))),U_10307))
| ~ sP750(U_10306,U_10307,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),c_Groups_Ozero__class_Ozero(U_10305)),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)))
| ~ sP753(U_10306,U_10307,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_14,plain,
( sP752(U_10306,U_10308,U_10305)
| sP751(U_10306,U_10307,U_10308,U_10305)
| ~ sP753(U_10306,U_10307,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)),c_Groups_Ozero__class_Ozero(U_10305)))
| ~ sP751(U_10306,U_10307,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10305),U_10306),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308))))
| ~ sP751(U_10306,U_10307,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),hAPP(c_Int_Onumber__class_Onumber__of(U_10305),U_10308)),c_Groups_Ozero__class_Ozero(U_10305)))
| ~ sP752(U_10306,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
cnf(f_2637_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10305),U_10306),c_Groups_Ozero__class_Ozero(U_10305)))
| ~ sP752(U_10306,U_10308,U_10305) ),
inference(clausify,[status(thm)],[f_2637_3]) ).
fof(f_2638_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_2638_2,plain,
! [U_10310,U_10309] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)),c_Groups_Ozero__class_Ozero(U_10309))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)),c_Groups_Ozero__class_Ozero(U_10309))) ) )
| ~ class_Rings_Olinordered__idom(U_10309)
| ~ class_Int_Onumber__ring(U_10309) ),
inference(variable_rename,[status(thm)],[f_2638_1]) ).
fof(f_2638_3,plain,
( ! [U_10310,U_10309] :
( hAPP(c_Groups_Oabs__class_Oabs(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)),c_Groups_Ozero__class_Ozero(U_10309)))
| ~ sP755(U_10310,U_10309) )
& ! [U_10310,U_10309] :
( hAPP(c_Groups_Oabs__class_Oabs(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)),c_Groups_Ozero__class_Ozero(U_10309)))
| ~ sP755(U_10310,U_10309) )
& ! [U_10310,U_10309] :
( sP755(U_10310,U_10309)
| ~ class_Rings_Olinordered__idom(U_10309)
| ~ class_Int_Onumber__ring(U_10309) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP755])],[f_2638_2]) ).
cnf(f_2638_4,plain,
( sP755(U_10310,U_10309)
| ~ class_Rings_Olinordered__idom(U_10309)
| ~ class_Int_Onumber__ring(U_10309) ),
inference(clausify,[status(thm)],[f_2638_3]) ).
cnf(f_2638_5,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)),c_Groups_Ozero__class_Ozero(U_10309)))
| ~ sP755(U_10310,U_10309) ),
inference(clausify,[status(thm)],[f_2638_3]) ).
cnf(f_2638_6,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10309),hAPP(c_Int_Onumber__class_Onumber__of(U_10309),U_10310)),c_Groups_Ozero__class_Ozero(U_10309)))
| ~ sP755(U_10310,U_10309) ),
inference(clausify,[status(thm)],[f_2638_3]) ).
fof(f_2639_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_2639_2,plain,
! [U_10314,U_10313,U_10312,U_10311] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10311),hAPP(c_Int_Onumber__class_Onumber__of(U_10311),U_10312)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10311),U_10313),hAPP(c_Int_Onumber__class_Onumber__of(U_10311),U_10314))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10311),hAPP(c_Int_Onumber__class_Onumber__of(U_10311),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10312),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10314)))),U_10313)
| ~ class_Int_Onumber__ring(U_10311) ),
inference(variable_rename,[status(thm)],[f_2639_1]) ).
fof(f_2639_3,plain,
! [U_10313,U_10314,U_10312,U_10311] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10311),hAPP(c_Int_Onumber__class_Onumber__of(U_10311),U_10312)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10311),U_10313),hAPP(c_Int_Onumber__class_Onumber__of(U_10311),U_10314))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10311),hAPP(c_Int_Onumber__class_Onumber__of(U_10311),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10312),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10314)))),U_10313)
| ~ class_Int_Onumber__ring(U_10311) ),
inference(definitional_conversion,[status(esa)],[f_2639_2]) ).
cnf(f_2639_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10311),hAPP(c_Int_Onumber__class_Onumber__of(U_10311),U_10312)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10311),U_10313),hAPP(c_Int_Onumber__class_Onumber__of(U_10311),U_10314))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10311),hAPP(c_Int_Onumber__class_Onumber__of(U_10311),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10312),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10314)))),U_10313)
| ~ class_Int_Onumber__ring(U_10311) ),
inference(clausify,[status(thm)],[f_2639_3]) ).
fof(f_2640_1,plain,
! [V_w_2,V_b_2,V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),c_Groups_Ozero__class_Ozero(T_c)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))) ) )
| ~ class_Int_Onumber(T_c)
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of1]) ).
fof(f_2640_2,plain,
! [U_10318,U_10317,U_10316,U_10315] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10316),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10315),U_10317),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10316),c_Groups_Ozero__class_Ozero(U_10315)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)),c_Groups_Ozero__class_Ozero(U_10315))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10315),U_10316),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)),c_Groups_Ozero__class_Ozero(U_10315))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),c_Groups_Ozero__class_Ozero(U_10315)),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10315),U_10316),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))),U_10317))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),c_Groups_Ozero__class_Ozero(U_10315)),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10316),c_Groups_Ozero__class_Ozero(U_10315)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)),c_Groups_Ozero__class_Ozero(U_10315))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10315),U_10316),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)),c_Groups_Ozero__class_Ozero(U_10315))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),c_Groups_Ozero__class_Ozero(U_10315)),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10315),U_10316),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))),U_10317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),c_Groups_Ozero__class_Ozero(U_10315)),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10316),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10315),U_10317),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)))) ) )
| ~ class_Int_Onumber(U_10315)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10315) ),
inference(variable_rename,[status(thm)],[f_2640_1]) ).
fof(f_2640_3,plain,
( ! [U_10316,U_10315,U_10318] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10316),c_Groups_Ozero__class_Ozero(U_10315)))
| ~ sP760(U_10316,U_10315,U_10318) )
& ! [U_10316,U_10315,U_10318] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)),c_Groups_Ozero__class_Ozero(U_10315)))
| ~ sP760(U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10315),U_10316),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))))
| ~ sP759(U_10317,U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)),c_Groups_Ozero__class_Ozero(U_10315)))
| ~ sP759(U_10317,U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( sP760(U_10316,U_10315,U_10318)
| sP759(U_10317,U_10316,U_10315,U_10318)
| ~ sP761(U_10317,U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),c_Groups_Ozero__class_Ozero(U_10315)),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)))
| ~ sP761(U_10317,U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10315),U_10316),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))),U_10317))
| ~ sP758(U_10317,U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),c_Groups_Ozero__class_Ozero(U_10315)),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)))
| ~ sP758(U_10317,U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10316),c_Groups_Ozero__class_Ozero(U_10315)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)),c_Groups_Ozero__class_Ozero(U_10315)))
| ~ sP756(U_10317,U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10315),U_10316),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)),c_Groups_Ozero__class_Ozero(U_10315)))
| ~ sP756(U_10317,U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( sP756(U_10317,U_10316,U_10315,U_10318)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),c_Groups_Ozero__class_Ozero(U_10315)),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)))
| ~ sP757(U_10317,U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10315),U_10316),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))),U_10317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),c_Groups_Ozero__class_Ozero(U_10315)),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)))
| ~ sP757(U_10317,U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10316),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10315),U_10317),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))))
| sP761(U_10317,U_10316,U_10315,U_10318)
| sP758(U_10317,U_10316,U_10315,U_10318)
| ~ sP762(U_10317,U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( sP757(U_10317,U_10316,U_10315,U_10318)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10316),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10315),U_10317),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))))
| ~ sP762(U_10317,U_10316,U_10315,U_10318) )
& ! [U_10317,U_10316,U_10315,U_10318] :
( sP762(U_10317,U_10316,U_10315,U_10318)
| ~ class_Int_Onumber(U_10315)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10315) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP756,sP757,sP758,sP759,sP760,sP761,sP762])],[f_2640_2]) ).
cnf(f_2640_4,plain,
( sP762(U_10317,U_10316,U_10315,U_10318)
| ~ class_Int_Onumber(U_10315)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10315) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_5,plain,
( sP757(U_10317,U_10316,U_10315,U_10318)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10316),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10315),U_10317),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))))
| ~ sP762(U_10317,U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10316),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10315),U_10317),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))))
| sP761(U_10317,U_10316,U_10315,U_10318)
| sP758(U_10317,U_10316,U_10315,U_10318)
| ~ sP762(U_10317,U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10315),U_10316),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))),U_10317))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),c_Groups_Ozero__class_Ozero(U_10315)),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)))
| ~ sP757(U_10317,U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_8,plain,
( sP756(U_10317,U_10316,U_10315,U_10318)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),c_Groups_Ozero__class_Ozero(U_10315)),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)))
| ~ sP757(U_10317,U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10315),U_10316),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)),c_Groups_Ozero__class_Ozero(U_10315)))
| ~ sP756(U_10317,U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10316),c_Groups_Ozero__class_Ozero(U_10315)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)),c_Groups_Ozero__class_Ozero(U_10315)))
| ~ sP756(U_10317,U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),c_Groups_Ozero__class_Ozero(U_10315)),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)))
| ~ sP758(U_10317,U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10315),U_10316),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))),U_10317))
| ~ sP758(U_10317,U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),c_Groups_Ozero__class_Ozero(U_10315)),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)))
| ~ sP761(U_10317,U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_14,plain,
( sP760(U_10316,U_10315,U_10318)
| sP759(U_10317,U_10316,U_10315,U_10318)
| ~ sP761(U_10317,U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)),c_Groups_Ozero__class_Ozero(U_10315)))
| ~ sP759(U_10317,U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10315),U_10316),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318))))
| ~ sP759(U_10317,U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10315),hAPP(c_Int_Onumber__class_Onumber__of(U_10315),U_10318)),c_Groups_Ozero__class_Ozero(U_10315)))
| ~ sP760(U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
cnf(f_2640_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10315),U_10316),c_Groups_Ozero__class_Ozero(U_10315)))
| ~ sP760(U_10316,U_10315,U_10318) ),
inference(clausify,[status(thm)],[f_2640_3]) ).
fof(f_2641_1,plain,
! [V_c_2,V_b_2,V_w_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2))) ) )
| ~ class_Int_Onumber(T_c)
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of]) ).
fof(f_2641_2,plain,
! [U_10322,U_10321,U_10320,U_10319] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10319),U_10321),U_10322)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),c_Groups_Ozero__class_Ozero(U_10319)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),U_10322),c_Groups_Ozero__class_Ozero(U_10319))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),U_10321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),U_10322)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),U_10322),c_Groups_Ozero__class_Ozero(U_10319))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),c_Groups_Ozero__class_Ozero(U_10319)),U_10322)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),U_10322)),U_10321))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),c_Groups_Ozero__class_Ozero(U_10319)),U_10322)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),c_Groups_Ozero__class_Ozero(U_10319)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),U_10322),c_Groups_Ozero__class_Ozero(U_10319))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),U_10321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),U_10322)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),U_10322),c_Groups_Ozero__class_Ozero(U_10319))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),c_Groups_Ozero__class_Ozero(U_10319)),U_10322)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),U_10322)),U_10321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),c_Groups_Ozero__class_Ozero(U_10319)),U_10322)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10319),U_10321),U_10322))) ) )
| ~ class_Int_Onumber(U_10319)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10319) ),
inference(variable_rename,[status(thm)],[f_2641_1]) ).
fof(f_2641_3,plain,
( ! [U_10320,U_10322,U_10319] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),c_Groups_Ozero__class_Ozero(U_10319)))
| ~ sP767(U_10320,U_10322,U_10319) )
& ! [U_10320,U_10322,U_10319] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),U_10322),c_Groups_Ozero__class_Ozero(U_10319)))
| ~ sP767(U_10320,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),U_10321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),U_10322)))
| ~ sP766(U_10320,U_10321,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),U_10322),c_Groups_Ozero__class_Ozero(U_10319)))
| ~ sP766(U_10320,U_10321,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( sP767(U_10320,U_10322,U_10319)
| sP766(U_10320,U_10321,U_10322,U_10319)
| ~ sP768(U_10320,U_10321,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),c_Groups_Ozero__class_Ozero(U_10319)),U_10322))
| ~ sP768(U_10320,U_10321,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),U_10322)),U_10321))
| ~ sP765(U_10320,U_10321,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),c_Groups_Ozero__class_Ozero(U_10319)),U_10322))
| ~ sP765(U_10320,U_10321,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),c_Groups_Ozero__class_Ozero(U_10319)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),U_10322),c_Groups_Ozero__class_Ozero(U_10319)))
| ~ sP763(U_10320,U_10321,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),U_10321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),U_10322)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),U_10322),c_Groups_Ozero__class_Ozero(U_10319)))
| ~ sP763(U_10320,U_10321,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( sP763(U_10320,U_10321,U_10322,U_10319)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),c_Groups_Ozero__class_Ozero(U_10319)),U_10322))
| ~ sP764(U_10320,U_10321,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),U_10322)),U_10321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),c_Groups_Ozero__class_Ozero(U_10319)),U_10322))
| ~ sP764(U_10320,U_10321,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10319),U_10321),U_10322)))
| sP768(U_10320,U_10321,U_10322,U_10319)
| sP765(U_10320,U_10321,U_10322,U_10319)
| ~ sP769(U_10320,U_10321,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( sP764(U_10320,U_10321,U_10322,U_10319)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10319),U_10321),U_10322)))
| ~ sP769(U_10320,U_10321,U_10322,U_10319) )
& ! [U_10320,U_10321,U_10322,U_10319] :
( sP769(U_10320,U_10321,U_10322,U_10319)
| ~ class_Int_Onumber(U_10319)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10319) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP763,sP764,sP765,sP766,sP767,sP768,sP769])],[f_2641_2]) ).
cnf(f_2641_4,plain,
( sP769(U_10320,U_10321,U_10322,U_10319)
| ~ class_Int_Onumber(U_10319)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_5,plain,
( sP764(U_10320,U_10321,U_10322,U_10319)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10319),U_10321),U_10322)))
| ~ sP769(U_10320,U_10321,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10319),U_10321),U_10322)))
| sP768(U_10320,U_10321,U_10322,U_10319)
| sP765(U_10320,U_10321,U_10322,U_10319)
| ~ sP769(U_10320,U_10321,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),U_10322)),U_10321))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),c_Groups_Ozero__class_Ozero(U_10319)),U_10322))
| ~ sP764(U_10320,U_10321,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_8,plain,
( sP763(U_10320,U_10321,U_10322,U_10319)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),c_Groups_Ozero__class_Ozero(U_10319)),U_10322))
| ~ sP764(U_10320,U_10321,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),U_10321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),U_10322)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),U_10322),c_Groups_Ozero__class_Ozero(U_10319)))
| ~ sP763(U_10320,U_10321,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),c_Groups_Ozero__class_Ozero(U_10319)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),U_10322),c_Groups_Ozero__class_Ozero(U_10319)))
| ~ sP763(U_10320,U_10321,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),c_Groups_Ozero__class_Ozero(U_10319)),U_10322))
| ~ sP765(U_10320,U_10321,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),U_10322)),U_10321))
| ~ sP765(U_10320,U_10321,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),c_Groups_Ozero__class_Ozero(U_10319)),U_10322))
| ~ sP768(U_10320,U_10321,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_14,plain,
( sP767(U_10320,U_10322,U_10319)
| sP766(U_10320,U_10321,U_10322,U_10319)
| ~ sP768(U_10320,U_10321,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),U_10322),c_Groups_Ozero__class_Ozero(U_10319)))
| ~ sP766(U_10320,U_10321,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),U_10321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),U_10322)))
| ~ sP766(U_10320,U_10321,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10319),U_10322),c_Groups_Ozero__class_Ozero(U_10319)))
| ~ sP767(U_10320,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10319),hAPP(c_Int_Onumber__class_Onumber__of(U_10319),U_10320)),c_Groups_Ozero__class_Ozero(U_10319)))
| ~ sP767(U_10320,U_10322,U_10319) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
fof(f_2642_1,plain,
! [V_w_2,V_c_2,V_b_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),V_c_2),c_Groups_Ozero__class_Ozero(T_c))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) )
| ~ class_Int_Onumber(T_c)
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of]) ).
fof(f_2642_2,plain,
! [U_10326,U_10325,U_10324,U_10323] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10323),U_10324),U_10325)),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),U_10325),c_Groups_Ozero__class_Ozero(U_10323))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10323),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)),U_10325)),U_10324))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),U_10325),c_Groups_Ozero__class_Ozero(U_10323))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),U_10325)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),U_10324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10323),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)),U_10325)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),U_10325)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),U_10325),c_Groups_Ozero__class_Ozero(U_10323))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10323),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)),U_10325)),U_10324))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),U_10325),c_Groups_Ozero__class_Ozero(U_10323))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),U_10325)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),U_10324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10323),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)),U_10325)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),U_10325)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10323),U_10324),U_10325)),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326))) ) )
| ~ class_Int_Onumber(U_10323)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10323) ),
inference(variable_rename,[status(thm)],[f_2642_1]) ).
fof(f_2642_3,plain,
( ! [U_10325,U_10326,U_10323] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)))
| ~ sP774(U_10325,U_10326,U_10323) )
& ! [U_10325,U_10326,U_10323] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),U_10325),c_Groups_Ozero__class_Ozero(U_10323)))
| ~ sP774(U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10323),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)),U_10325)),U_10324))
| ~ sP773(U_10324,U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),U_10325),c_Groups_Ozero__class_Ozero(U_10323)))
| ~ sP773(U_10324,U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( sP774(U_10325,U_10326,U_10323)
| sP773(U_10324,U_10325,U_10326,U_10323)
| ~ sP775(U_10324,U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),U_10325))
| ~ sP775(U_10324,U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),U_10324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10323),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)),U_10325)))
| ~ sP772(U_10324,U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),U_10325))
| ~ sP772(U_10324,U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),U_10325),c_Groups_Ozero__class_Ozero(U_10323)))
| ~ sP770(U_10324,U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10323),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)),U_10325)),U_10324))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),U_10325),c_Groups_Ozero__class_Ozero(U_10323)))
| ~ sP770(U_10324,U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( sP770(U_10324,U_10325,U_10326,U_10323)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),U_10325))
| ~ sP771(U_10324,U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),U_10324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10323),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)),U_10325)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),U_10325))
| ~ sP771(U_10324,U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10323),U_10324),U_10325)),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)))
| sP775(U_10324,U_10325,U_10326,U_10323)
| sP772(U_10324,U_10325,U_10326,U_10323)
| ~ sP776(U_10324,U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( sP771(U_10324,U_10325,U_10326,U_10323)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10323),U_10324),U_10325)),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)))
| ~ sP776(U_10324,U_10325,U_10326,U_10323) )
& ! [U_10324,U_10325,U_10326,U_10323] :
( sP776(U_10324,U_10325,U_10326,U_10323)
| ~ class_Int_Onumber(U_10323)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10323) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP770,sP771,sP772,sP773,sP774,sP775,sP776])],[f_2642_2]) ).
cnf(f_2642_4,plain,
( sP776(U_10324,U_10325,U_10326,U_10323)
| ~ class_Int_Onumber(U_10323)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_5,plain,
( sP771(U_10324,U_10325,U_10326,U_10323)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10323),U_10324),U_10325)),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)))
| ~ sP776(U_10324,U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10323),U_10324),U_10325)),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)))
| sP775(U_10324,U_10325,U_10326,U_10323)
| sP772(U_10324,U_10325,U_10326,U_10323)
| ~ sP776(U_10324,U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),U_10324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10323),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)),U_10325)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),U_10325))
| ~ sP771(U_10324,U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_8,plain,
( sP770(U_10324,U_10325,U_10326,U_10323)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),U_10325))
| ~ sP771(U_10324,U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10323),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)),U_10325)),U_10324))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),U_10325),c_Groups_Ozero__class_Ozero(U_10323)))
| ~ sP770(U_10324,U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),U_10325),c_Groups_Ozero__class_Ozero(U_10323)))
| ~ sP770(U_10324,U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),U_10325))
| ~ sP772(U_10324,U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),U_10324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10323),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)),U_10325)))
| ~ sP772(U_10324,U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),U_10325))
| ~ sP775(U_10324,U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_14,plain,
( sP774(U_10325,U_10326,U_10323)
| sP773(U_10324,U_10325,U_10326,U_10323)
| ~ sP775(U_10324,U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),U_10325),c_Groups_Ozero__class_Ozero(U_10323)))
| ~ sP773(U_10324,U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10323),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)),U_10325)),U_10324))
| ~ sP773(U_10324,U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10323),U_10325),c_Groups_Ozero__class_Ozero(U_10323)))
| ~ sP774(U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10323),c_Groups_Ozero__class_Ozero(U_10323)),hAPP(c_Int_Onumber__class_Onumber__of(U_10323),U_10326)))
| ~ sP774(U_10325,U_10326,U_10323) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
fof(f_2643_1,plain,
! [V_a_2,V_w_2,V_b_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_a_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_a_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))),V_a_2)) ) )
| ~ class_Int_Onumber(T_c)
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of1]) ).
fof(f_2643_2,plain,
! [U_10330,U_10329,U_10328,U_10327] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10327),U_10328),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))),U_10330))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),U_10330))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)),c_Groups_Ozero__class_Ozero(U_10327))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10327),U_10330),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))),U_10328))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)),c_Groups_Ozero__class_Ozero(U_10327))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),U_10328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10327),U_10330),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),U_10330))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)),c_Groups_Ozero__class_Ozero(U_10327))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10327),U_10330),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))),U_10328))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)),c_Groups_Ozero__class_Ozero(U_10327))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),U_10328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10327),U_10330),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10327),U_10328),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))),U_10330)) ) )
| ~ class_Int_Onumber(U_10327)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10327) ),
inference(variable_rename,[status(thm)],[f_2643_1]) ).
fof(f_2643_3,plain,
( ! [U_10329,U_10330,U_10327] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),U_10330))
| ~ sP781(U_10329,U_10330,U_10327) )
& ! [U_10329,U_10330,U_10327] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)),c_Groups_Ozero__class_Ozero(U_10327)))
| ~ sP781(U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10327),U_10330),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))),U_10328))
| ~ sP780(U_10328,U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)),c_Groups_Ozero__class_Ozero(U_10327)))
| ~ sP780(U_10328,U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( sP781(U_10329,U_10330,U_10327)
| sP780(U_10328,U_10329,U_10330,U_10327)
| ~ sP782(U_10328,U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)))
| ~ sP782(U_10328,U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),U_10328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10327),U_10330),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))))
| ~ sP779(U_10328,U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)))
| ~ sP779(U_10328,U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),U_10330))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)),c_Groups_Ozero__class_Ozero(U_10327)))
| ~ sP777(U_10328,U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10327),U_10330),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))),U_10328))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)),c_Groups_Ozero__class_Ozero(U_10327)))
| ~ sP777(U_10328,U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( sP777(U_10328,U_10329,U_10330,U_10327)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)))
| ~ sP778(U_10328,U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),U_10328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10327),U_10330),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)))
| ~ sP778(U_10328,U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10327),U_10328),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))),U_10330))
| sP782(U_10328,U_10329,U_10330,U_10327)
| sP779(U_10328,U_10329,U_10330,U_10327)
| ~ sP783(U_10328,U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( sP778(U_10328,U_10329,U_10330,U_10327)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10327),U_10328),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))),U_10330))
| ~ sP783(U_10328,U_10329,U_10330,U_10327) )
& ! [U_10328,U_10329,U_10330,U_10327] :
( sP783(U_10328,U_10329,U_10330,U_10327)
| ~ class_Int_Onumber(U_10327)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10327) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP777,sP778,sP779,sP780,sP781,sP782,sP783])],[f_2643_2]) ).
cnf(f_2643_4,plain,
( sP783(U_10328,U_10329,U_10330,U_10327)
| ~ class_Int_Onumber(U_10327)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_5,plain,
( sP778(U_10328,U_10329,U_10330,U_10327)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10327),U_10328),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))),U_10330))
| ~ sP783(U_10328,U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10327),U_10328),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))),U_10330))
| sP782(U_10328,U_10329,U_10330,U_10327)
| sP779(U_10328,U_10329,U_10330,U_10327)
| ~ sP783(U_10328,U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),U_10328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10327),U_10330),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)))
| ~ sP778(U_10328,U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_8,plain,
( sP777(U_10328,U_10329,U_10330,U_10327)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)))
| ~ sP778(U_10328,U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10327),U_10330),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))),U_10328))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)),c_Groups_Ozero__class_Ozero(U_10327)))
| ~ sP777(U_10328,U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_10,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),U_10330))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)),c_Groups_Ozero__class_Ozero(U_10327)))
| ~ sP777(U_10328,U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)))
| ~ sP779(U_10328,U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),U_10328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10327),U_10330),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))))
| ~ sP779(U_10328,U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)))
| ~ sP782(U_10328,U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_14,plain,
( sP781(U_10329,U_10330,U_10327)
| sP780(U_10328,U_10329,U_10330,U_10327)
| ~ sP782(U_10328,U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_15,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)),c_Groups_Ozero__class_Ozero(U_10327)))
| ~ sP780(U_10328,U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10327),U_10330),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329))),U_10328))
| ~ sP780(U_10328,U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10327),hAPP(c_Int_Onumber__class_Onumber__of(U_10327),U_10329)),c_Groups_Ozero__class_Ozero(U_10327)))
| ~ sP781(U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
cnf(f_2643_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10327),c_Groups_Ozero__class_Ozero(U_10327)),U_10330))
| ~ sP781(U_10329,U_10330,U_10327) ),
inference(clausify,[status(thm)],[f_2643_3]) ).
fof(f_2644_1,plain,
! [V_a_2,V_r_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Relation_OImage(T_c,T_c,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(T_c),V_a_2),V_A_2))
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_equiv__class__self]) ).
fof(f_2644_2,plain,
! [U_10334,U_10333,U_10332,U_10331] :
( hBOOL(hAPP(hAPP(c_member(U_10331),U_10334),hAPP(c_Relation_OImage(U_10331,U_10331,U_10333),hAPP(hAPP(c_Set_Oinsert(U_10331),U_10334),c_Orderings_Obot__class_Obot(tc_fun(U_10331,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10331),U_10334),U_10332))
| ~ c_Equiv__Relations_Oequiv(U_10331,U_10332,U_10333) ),
inference(variable_rename,[status(thm)],[f_2644_1]) ).
fof(f_2644_3,plain,
! [U_10333,U_10331,U_10332,U_10334] :
( hBOOL(hAPP(hAPP(c_member(U_10331),U_10334),hAPP(c_Relation_OImage(U_10331,U_10331,U_10333),hAPP(hAPP(c_Set_Oinsert(U_10331),U_10334),c_Orderings_Obot__class_Obot(tc_fun(U_10331,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10331),U_10334),U_10332))
| ~ c_Equiv__Relations_Oequiv(U_10331,U_10332,U_10333) ),
inference(definitional_conversion,[status(esa)],[f_2644_2]) ).
cnf(f_2644_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10331),U_10334),hAPP(c_Relation_OImage(U_10331,U_10331,U_10333),hAPP(hAPP(c_Set_Oinsert(U_10331),U_10334),c_Orderings_Obot__class_Obot(tc_fun(U_10331,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10331),U_10334),U_10332))
| ~ c_Equiv__Relations_Oequiv(U_10331,U_10332,U_10333) ),
inference(clausify,[status(thm)],[f_2644_3]) ).
fof(f_2645_1,plain,
! [V_com_2,V_fun_2,V_loc_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_com_Osize_I11_J]) ).
fof(f_2645_2,plain,
! [U_10337,U_10336,U_10335] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_10335,U_10336,U_10337)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_10337)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2645_1]) ).
fof(f_2645_3,plain,
! [U_10335,U_10337,U_10336] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_10335,U_10336,U_10337)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_10337)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definitional_conversion,[status(esa)],[f_2645_2]) ).
cnf(f_2645_4,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_10335,U_10336,U_10337)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_10337)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2645_3]) ).
fof(f_2646_1,plain,
! [V_a_2,V_f_2,T_d,V_r_2,V_A_2,T_c] :
( hAPP(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_r_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) = hAPP(V_f_2,V_a_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ c_Equiv__Relations_Ocongruent(T_c,tc_fun(T_d,tc_HOL_Obool),V_r_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_UN__equiv__class]) ).
fof(f_2646_2,plain,
! [U_10343,U_10342,U_10341,U_10340,U_10339,U_10338] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10338,tc_fun(U_10341,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10338,U_10338,U_10340),hAPP(hAPP(c_Set_Oinsert(U_10338),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))))),U_10342) = hAPP(U_10342,U_10343)
| ~ hBOOL(hAPP(hAPP(c_member(U_10338),U_10343),U_10339))
| ~ c_Equiv__Relations_Ocongruent(U_10338,tc_fun(U_10341,tc_HOL_Obool),U_10340,U_10342)
| ~ c_Equiv__Relations_Oequiv(U_10338,U_10339,U_10340) ),
inference(variable_rename,[status(thm)],[f_2646_1]) ).
fof(f_2646_3,plain,
! [U_10340,U_10338,U_10339,U_10341,U_10342,U_10343] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10338,tc_fun(U_10341,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10338,U_10338,U_10340),hAPP(hAPP(c_Set_Oinsert(U_10338),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))))),U_10342) = hAPP(U_10342,U_10343)
| ~ hBOOL(hAPP(hAPP(c_member(U_10338),U_10343),U_10339))
| ~ c_Equiv__Relations_Ocongruent(U_10338,tc_fun(U_10341,tc_HOL_Obool),U_10340,U_10342)
| ~ c_Equiv__Relations_Oequiv(U_10338,U_10339,U_10340) ),
inference(definitional_conversion,[status(esa)],[f_2646_2]) ).
cnf(f_2646_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10338,tc_fun(U_10341,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10338,U_10338,U_10340),hAPP(hAPP(c_Set_Oinsert(U_10338),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))))),U_10342) = hAPP(U_10342,U_10343)
| ~ hBOOL(hAPP(hAPP(c_member(U_10338),U_10343),U_10339))
| ~ c_Equiv__Relations_Ocongruent(U_10338,tc_fun(U_10341,tc_HOL_Obool),U_10340,U_10342)
| ~ c_Equiv__Relations_Oequiv(U_10338,U_10339,U_10340) ),
inference(clausify,[status(thm)],[f_2646_3]) ).
fof(f_2647_1,plain,
! [V_a2_2,V_a1_2,V_f_2,T_e,V_r2_2,V_A2_2,T_d,V_r1_2,V_A1_2,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_e,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_d,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_d),V_a2_2),V_A2_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a1_2),V_A1_2))
| ~ c_Equiv__Relations_Ocongruent2(T_c,T_d,tc_fun(T_e,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_d,V_A2_2,V_r2_2)
| ~ c_Equiv__Relations_Oequiv(T_c,V_A1_2,V_r1_2) ),
inference(fof_nnf,[status(thm)],[fact_UN__equiv__class2]) ).
fof(f_2647_2,plain,
! [U_10353,U_10352,U_10351,U_10350,U_10349,U_10348,U_10347,U_10346,U_10345,U_10344] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10344,tc_fun(U_10350,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10344,U_10344,U_10346),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10352),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_10347,tc_fun(U_10350,tc_HOL_Obool)),tc_fun(U_10350,tc_HOL_Obool),U_10344),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10347,tc_fun(U_10350,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10347,U_10347,U_10349),hAPP(hAPP(c_Set_Oinsert(U_10347),U_10353),c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool)))))),U_10351)) = hAPP(hAPP(U_10351,U_10352),U_10353)
| ~ hBOOL(hAPP(hAPP(c_member(U_10347),U_10353),U_10348))
| ~ hBOOL(hAPP(hAPP(c_member(U_10344),U_10352),U_10345))
| ~ c_Equiv__Relations_Ocongruent2(U_10344,U_10347,tc_fun(U_10350,tc_HOL_Obool),U_10346,U_10349,U_10351)
| ~ c_Equiv__Relations_Oequiv(U_10347,U_10348,U_10349)
| ~ c_Equiv__Relations_Oequiv(U_10344,U_10345,U_10346) ),
inference(variable_rename,[status(thm)],[f_2647_1]) ).
fof(f_2647_3,plain,
! [U_10346,U_10344,U_10345,U_10347,U_10348,U_10349,U_10350,U_10351,U_10352,U_10353] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10344,tc_fun(U_10350,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10344,U_10344,U_10346),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10352),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_10347,tc_fun(U_10350,tc_HOL_Obool)),tc_fun(U_10350,tc_HOL_Obool),U_10344),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10347,tc_fun(U_10350,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10347,U_10347,U_10349),hAPP(hAPP(c_Set_Oinsert(U_10347),U_10353),c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool)))))),U_10351)) = hAPP(hAPP(U_10351,U_10352),U_10353)
| ~ hBOOL(hAPP(hAPP(c_member(U_10347),U_10353),U_10348))
| ~ hBOOL(hAPP(hAPP(c_member(U_10344),U_10352),U_10345))
| ~ c_Equiv__Relations_Ocongruent2(U_10344,U_10347,tc_fun(U_10350,tc_HOL_Obool),U_10346,U_10349,U_10351)
| ~ c_Equiv__Relations_Oequiv(U_10347,U_10348,U_10349)
| ~ c_Equiv__Relations_Oequiv(U_10344,U_10345,U_10346) ),
inference(definitional_conversion,[status(esa)],[f_2647_2]) ).
cnf(f_2647_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10344,tc_fun(U_10350,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10344,U_10344,U_10346),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10352),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_10347,tc_fun(U_10350,tc_HOL_Obool)),tc_fun(U_10350,tc_HOL_Obool),U_10344),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10347,tc_fun(U_10350,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10347,U_10347,U_10349),hAPP(hAPP(c_Set_Oinsert(U_10347),U_10353),c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool)))))),U_10351)) = hAPP(hAPP(U_10351,U_10352),U_10353)
| ~ hBOOL(hAPP(hAPP(c_member(U_10347),U_10353),U_10348))
| ~ hBOOL(hAPP(hAPP(c_member(U_10344),U_10352),U_10345))
| ~ c_Equiv__Relations_Ocongruent2(U_10344,U_10347,tc_fun(U_10350,tc_HOL_Obool),U_10346,U_10349,U_10351)
| ~ c_Equiv__Relations_Oequiv(U_10347,U_10348,U_10349)
| ~ c_Equiv__Relations_Oequiv(U_10344,U_10345,U_10346) ),
inference(clausify,[status(thm)],[f_2647_3]) ).
fof(f_2648_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_2648_2,plain,
! [U_10354] :
( ( 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_10354)) = 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_10354)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10354))) )
& ( 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_10354)) = 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_10354))) ) ),
inference(variable_rename,[status(thm)],[f_2648_1]) ).
fof(f_2648_3,plain,
( ! [U_10356] :
( 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_10356)) = 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_10356)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10356))) )
& ! [U_10355] :
( 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_10355)) = 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_10355))) ) ),
inference(miniscope,[status(thm)],[f_2648_2]) ).
fof(f_2648_4,plain,
( ! [U_10356] :
( 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_10356)) = 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_10356)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10356))) )
& ! [U_10355] :
( 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_10355)) = 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_10355))) ) ),
inference(definitional_conversion,[status(esa)],[f_2648_3]) ).
cnf(f_2648_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_10355)) = 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_10355))) ),
inference(clausify,[status(thm)],[f_2648_4]) ).
cnf(f_2648_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_10356)) = 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_10356)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10356))) ),
inference(clausify,[status(thm)],[f_2648_4]) ).
fof(f_2649_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_2649_2,plain,
! [U_10357] : 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_10357)) = 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_10357))),
inference(variable_rename,[status(thm)],[f_2649_1]) ).
fof(f_2649_3,plain,
! [U_10357] : 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_10357)) = 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_10357))),
inference(definitional_conversion,[status(esa)],[f_2649_2]) ).
cnf(f_2649_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_10357)) = 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_10357))),
inference(clausify,[status(thm)],[f_2649_3]) ).
fof(f_2650_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_2650_2,plain,
! [U_10359,U_10358] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10358)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10359)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10358),U_10359)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10358),U_10359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10358)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10359))) ) ),
inference(variable_rename,[status(thm)],[f_2650_1]) ).
fof(f_2650_3,plain,
( ! [U_10363,U_10361] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10361)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10363)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10361),U_10363)) )
& ! [U_10362,U_10360] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10360),U_10362))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10360)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10362))) ) ),
inference(miniscope,[status(thm)],[f_2650_2]) ).
fof(f_2650_4,plain,
( ! [U_10363,U_10361] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10361)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10363)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10361),U_10363)) )
& ! [U_10362,U_10360] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10360),U_10362))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10360)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10362))) ) ),
inference(definitional_conversion,[status(esa)],[f_2650_3]) ).
cnf(f_2650_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10360),U_10362))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10360)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10362))) ),
inference(clausify,[status(thm)],[f_2650_4]) ).
cnf(f_2650_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_10361)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10363)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10361),U_10363)) ),
inference(clausify,[status(thm)],[f_2650_4]) ).
fof(f_2651_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_2651_2,plain,
! [U_10364] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10364)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10364)),
inference(variable_rename,[status(thm)],[f_2651_1]) ).
fof(f_2651_3,plain,
! [U_10364] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10364)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10364)),
inference(definitional_conversion,[status(esa)],[f_2651_2]) ).
cnf(f_2651_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10364)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10364)),
inference(clausify,[status(thm)],[f_2651_3]) ).
fof(f_2652_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_2652_2,plain,
! [U_10365] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10365) = U_10365,
inference(variable_rename,[status(thm)],[f_2652_1]) ).
fof(f_2652_3,plain,
! [U_10365] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10365) = U_10365,
inference(definitional_conversion,[status(esa)],[f_2652_2]) ).
cnf(f_2652_4,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10365) = U_10365,
inference(clausify,[status(thm)],[f_2652_3]) ).
fof(f_2653_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_2653_2,plain,
! [U_10367,U_10366] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10366)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10367)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10366),U_10367)),
inference(variable_rename,[status(thm)],[f_2653_1]) ).
fof(f_2653_3,plain,
! [U_10366,U_10367] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10366)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10367)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10366),U_10367)),
inference(definitional_conversion,[status(esa)],[f_2653_2]) ).
cnf(f_2653_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10366)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10367)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10366),U_10367)),
inference(clausify,[status(thm)],[f_2653_3]) ).
fof(f_2654_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_2654_2,plain,
! [U_10369,U_10368] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10368)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10369)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10368),U_10369)),
inference(variable_rename,[status(thm)],[f_2654_1]) ).
fof(f_2654_3,plain,
! [U_10368,U_10369] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10368)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10369)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10368),U_10369)),
inference(definitional_conversion,[status(esa)],[f_2654_2]) ).
cnf(f_2654_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10368)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10369)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10368),U_10369)),
inference(clausify,[status(thm)],[f_2654_3]) ).
fof(f_2655_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_2655_2,plain,
! [U_10371,U_10370] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10370)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10371)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10370),U_10371)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10370),U_10371))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10370)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10371))) ) ),
inference(variable_rename,[status(thm)],[f_2655_1]) ).
fof(f_2655_3,plain,
( ! [U_10375,U_10373] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10373)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10375)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10373),U_10375)) )
& ! [U_10374,U_10372] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10372),U_10374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10372)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10374))) ) ),
inference(miniscope,[status(thm)],[f_2655_2]) ).
fof(f_2655_4,plain,
( ! [U_10373,U_10375] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10373)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10375)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10373),U_10375)) )
& ! [U_10374,U_10372] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10372),U_10374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10372)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10374))) ) ),
inference(definitional_conversion,[status(esa)],[f_2655_3]) ).
cnf(f_2655_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10372),U_10374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10372)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10374))) ),
inference(clausify,[status(thm)],[f_2655_4]) ).
cnf(f_2655_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10373)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10375)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10373),U_10375)) ),
inference(clausify,[status(thm)],[f_2655_4]) ).
fof(f_2656_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_2656_2,plain,
! [U_10376] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_10376),
inference(variable_rename,[status(thm)],[f_2656_1]) ).
fof(f_2656_3,plain,
! [U_10376] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_10376),
inference(definitional_conversion,[status(esa)],[f_2656_2]) ).
cnf(f_2656_4,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10376) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_10376),
inference(clausify,[status(thm)],[f_2656_3]) ).
fof(f_2657_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_2657_2,plain,
! [U_10377] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10377) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10377)),
inference(variable_rename,[status(thm)],[f_2657_1]) ).
fof(f_2657_3,plain,
! [U_10377] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10377) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10377)),
inference(definitional_conversion,[status(esa)],[f_2657_2]) ).
cnf(f_2657_4,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10377) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10377)),
inference(clausify,[status(thm)],[f_2657_3]) ).
fof(f_2658_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_2658_2,plain,
! [U_10378] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10378)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10378),
inference(variable_rename,[status(thm)],[f_2658_1]) ).
fof(f_2658_3,plain,
! [U_10378] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10378)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10378),
inference(definitional_conversion,[status(esa)],[f_2658_2]) ).
cnf(f_2658_4,plain,
hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10378)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10378),
inference(clausify,[status(thm)],[f_2658_3]) ).
fof(f_2659_1,plain,
! [V_a_2,V_f_2,V_r2_2,T_e,T_d,V_r1_2,V_A_2,T_c] :
( c_Equiv__Relations_Ocongruent(T_d,T_e,V_r2_2,hAPP(V_f_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ c_Equiv__Relations_Ocongruent2(T_c,T_d,T_e,V_r1_2,V_r2_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r1_2) ),
inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent]) ).
fof(f_2659_2,plain,
! [U_10386,U_10385,U_10384,U_10383,U_10382,U_10381,U_10380,U_10379] :
( c_Equiv__Relations_Ocongruent(U_10382,U_10383,U_10384,hAPP(U_10385,U_10386))
| ~ hBOOL(hAPP(hAPP(c_member(U_10379),U_10386),U_10380))
| ~ c_Equiv__Relations_Ocongruent2(U_10379,U_10382,U_10383,U_10381,U_10384,U_10385)
| ~ c_Equiv__Relations_Oequiv(U_10379,U_10380,U_10381) ),
inference(variable_rename,[status(thm)],[f_2659_1]) ).
fof(f_2659_3,plain,
! [U_10379,U_10380,U_10381,U_10382,U_10383,U_10384,U_10385,U_10386] :
( c_Equiv__Relations_Ocongruent(U_10382,U_10383,U_10384,hAPP(U_10385,U_10386))
| ~ hBOOL(hAPP(hAPP(c_member(U_10379),U_10386),U_10380))
| ~ c_Equiv__Relations_Ocongruent2(U_10379,U_10382,U_10383,U_10381,U_10384,U_10385)
| ~ c_Equiv__Relations_Oequiv(U_10379,U_10380,U_10381) ),
inference(definitional_conversion,[status(esa)],[f_2659_2]) ).
cnf(f_2659_4,plain,
( c_Equiv__Relations_Ocongruent(U_10382,U_10383,U_10384,hAPP(U_10385,U_10386))
| ~ hBOOL(hAPP(hAPP(c_member(U_10379),U_10386),U_10380))
| ~ c_Equiv__Relations_Ocongruent2(U_10379,U_10382,U_10383,U_10381,U_10384,U_10385)
| ~ c_Equiv__Relations_Oequiv(U_10379,U_10380,U_10381) ),
inference(clausify,[status(thm)],[f_2659_3]) ).
fof(f_2660_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_2660_2,plain,
! [U_10388,U_10387] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10387)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10388)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10387),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10388))),
inference(variable_rename,[status(thm)],[f_2660_1]) ).
fof(f_2660_3,plain,
! [U_10387,U_10388] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10387)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10388)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10387),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10388))),
inference(definitional_conversion,[status(esa)],[f_2660_2]) ).
cnf(f_2660_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10387)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10388)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10387),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10388))),
inference(clausify,[status(thm)],[f_2660_3]) ).
fof(f_2661_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_2661_2,plain,
! [U_10389] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10389) = 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_10389))) ),
inference(variable_rename,[status(thm)],[f_2661_1]) ).
fof(f_2661_3,plain,
! [U_10389] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10389) = 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_10389))) ),
inference(definitional_conversion,[status(esa)],[f_2661_2]) ).
cnf(f_2661_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10389) = 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_10389))) ),
inference(clausify,[status(thm)],[f_2661_3]) ).
fof(f_2662_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_2662_2,plain,
! [U_10391,U_10390] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10390) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10391)
| ~ 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_10391)))
| U_10390 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10391)) )
& ( ( 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_10391)))
& U_10390 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10391)) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10390) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10391) ) ),
inference(variable_rename,[status(thm)],[f_2662_1]) ).
fof(f_2662_3,plain,
( ! [U_10395,U_10393] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10393) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10395)
| ~ 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_10395)))
| U_10393 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10395)) )
& ! [U_10394,U_10392] :
( ( 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_10394)))
& U_10392 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10394)) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10392) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10394) ) ),
inference(miniscope,[status(thm)],[f_2662_2]) ).
fof(f_2662_4,plain,
( ! [U_10394,U_10392] :
( 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_10394)))
| ~ sP784(U_10394,U_10392) )
& ! [U_10394,U_10392] :
( U_10392 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10394))
| ~ sP784(U_10394,U_10392) )
& ! [U_10393,U_10395] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10393) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10395)
| ~ 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_10395)))
| U_10393 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10395)) )
& ! [U_10394,U_10392] :
( sP784(U_10394,U_10392)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10392) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10394) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP784])],[f_2662_3]) ).
cnf(f_2662_5,plain,
( sP784(U_10394,U_10392)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10392) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10394) ),
inference(clausify,[status(thm)],[f_2662_4]) ).
cnf(f_2662_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10393) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10395)
| ~ 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_10395)))
| U_10393 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10395)) ),
inference(clausify,[status(thm)],[f_2662_4]) ).
cnf(f_2662_7,plain,
( U_10392 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10394))
| ~ sP784(U_10394,U_10392) ),
inference(clausify,[status(thm)],[f_2662_4]) ).
cnf(f_2662_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_10394)))
| ~ sP784(U_10394,U_10392) ),
inference(clausify,[status(thm)],[f_2662_4]) ).
fof(f_2663_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_2663_2,plain,
! [U_10397,U_10396] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10396) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10397)
| ( ( ( U_10396 != U_10397
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397))) )
| ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10396) != 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_10397))) ) )
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10396))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397)),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_10396))) ) )
& ( ( ( ( ( U_10396 = U_10397
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10396) = 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_10397))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10396))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10397)),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_10396))) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10396) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10397) ) ),
inference(variable_rename,[status(thm)],[f_2663_1]) ).
fof(f_2663_3,plain,
( ! [U_10401,U_10399] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10399) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10401)
| ( ( ( U_10399 != U_10401
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10401))) )
| ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10399) != 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_10401))) ) )
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10399))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10401)),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_10399))) ) )
& ! [U_10400,U_10398] :
( ( ( ( ( U_10398 = U_10400
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10400))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10398) = 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_10400))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10398))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10400)),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_10398))) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10398) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10400) ) ),
inference(miniscope,[status(thm)],[f_2663_2]) ).
fof(f_2663_4,plain,
( ! [U_10401,U_10399] :
( U_10399 != U_10401
| ~ sP789(U_10401,U_10399) )
& ! [U_10401,U_10399] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10401)))
| ~ sP789(U_10401,U_10399) )
& ! [U_10401,U_10399] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10399) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP788(U_10401,U_10399) )
& ! [U_10401,U_10399] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10401)))
| ~ sP788(U_10401,U_10399) )
& ! [U_10401,U_10399] :
( sP789(U_10401,U_10399)
| sP788(U_10401,U_10399)
| ~ sP790(U_10401,U_10399) )
& ! [U_10401,U_10399] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10399)))
| ~ sP790(U_10401,U_10399) )
& ! [U_10401,U_10399] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10401)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP787(U_10401,U_10399) )
& ! [U_10401,U_10399] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10399)))
| ~ sP787(U_10401,U_10399) )
& ! [U_10398,U_10400] :
( U_10398 = U_10400
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10400)))
| ~ sP785(U_10398,U_10400) )
& ! [U_10398,U_10400] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10398) = 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_10400)))
| ~ sP785(U_10398,U_10400) )
& ! [U_10398,U_10400] :
( sP785(U_10398,U_10400)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10398)))
| ~ sP786(U_10398,U_10400) )
& ! [U_10398,U_10400] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10400)),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_10398)))
| ~ sP786(U_10398,U_10400) )
& ! [U_10401,U_10399] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10399) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10401)
| sP790(U_10401,U_10399)
| sP787(U_10401,U_10399) )
& ! [U_10398,U_10400] :
( sP786(U_10398,U_10400)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10398) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10400) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP785,sP786,sP787,sP788,sP789,sP790])],[f_2663_3]) ).
cnf(f_2663_5,plain,
( sP786(U_10398,U_10400)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10398) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10400) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10399) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10401)
| sP790(U_10401,U_10399)
| sP787(U_10401,U_10399) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_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_10400)),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_10398)))
| ~ sP786(U_10398,U_10400) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_8,plain,
( sP785(U_10398,U_10400)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10398)))
| ~ sP786(U_10398,U_10400) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_9,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10398) = 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_10400)))
| ~ sP785(U_10398,U_10400) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_10,plain,
( U_10398 = U_10400
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10400)))
| ~ sP785(U_10398,U_10400) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_11,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10399)))
| ~ sP787(U_10401,U_10399) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_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_10401)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP787(U_10401,U_10399) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_13,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10399)))
| ~ sP790(U_10401,U_10399) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_14,plain,
( sP789(U_10401,U_10399)
| sP788(U_10401,U_10399)
| ~ sP790(U_10401,U_10399) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_15,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10401)))
| ~ sP788(U_10401,U_10399) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_16,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10399) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP788(U_10401,U_10399) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_17,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10401)))
| ~ sP789(U_10401,U_10399) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
cnf(f_2663_18,plain,
( U_10399 != U_10401
| ~ sP789(U_10401,U_10399) ),
inference(clausify,[status(thm)],[f_2663_4]) ).
fof(f_2664_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_2664_2,plain,
! [U_10404,U_10403,U_10402] :
( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10402)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10403)),U_10404)) = 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_10402),U_10403))),U_10404)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10403))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10402)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10403)),U_10404)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10402)),U_10404)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10403))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10402))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10402)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10403)),U_10404)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10403)),U_10404)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10402))) ) ),
inference(variable_rename,[status(thm)],[f_2664_1]) ).
fof(f_2664_3,plain,
( ! [U_10410,U_10408,U_10406] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10406)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10408)),U_10410)) = 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_10406),U_10408))),U_10410)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10408))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10406)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10408)),U_10410)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10406)),U_10410)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10408))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10406))) )
& ! [U_10409,U_10407,U_10405] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10405)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10407)),U_10409)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10407)),U_10409)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10405))) ) ),
inference(miniscope,[status(thm)],[f_2664_2]) ).
fof(f_2664_4,plain,
( ! [U_10406,U_10408,U_10410] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10406)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10408)),U_10410)) = 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_10406),U_10408))),U_10410)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10408)))
| ~ sP791(U_10406,U_10408,U_10410) )
& ! [U_10406,U_10408,U_10410] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10406)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10408)),U_10410)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10406)),U_10410)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10408)))
| ~ sP791(U_10406,U_10408,U_10410) )
& ! [U_10406,U_10408,U_10410] :
( sP791(U_10406,U_10408,U_10410)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10406))) )
& ! [U_10407,U_10409,U_10405] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10405)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10407)),U_10409)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10407)),U_10409)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10405))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP791])],[f_2664_3]) ).
cnf(f_2664_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10405)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10407)),U_10409)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10407)),U_10409)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10405))) ),
inference(clausify,[status(thm)],[f_2664_4]) ).
cnf(f_2664_6,plain,
( sP791(U_10406,U_10408,U_10410)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10406))) ),
inference(clausify,[status(thm)],[f_2664_4]) ).
cnf(f_2664_7,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10406)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10408)),U_10410)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10406)),U_10410)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10408)))
| ~ sP791(U_10406,U_10408,U_10410) ),
inference(clausify,[status(thm)],[f_2664_4]) ).
cnf(f_2664_8,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10406)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10408)),U_10410)) = 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_10406),U_10408))),U_10410)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10408)))
| ~ sP791(U_10406,U_10408,U_10410) ),
inference(clausify,[status(thm)],[f_2664_4]) ).
fof(f_2665_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_2665_2,plain,
! [U_10411] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10411)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10411)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10411))) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10411)) = 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_10411))) ) ),
inference(variable_rename,[status(thm)],[f_2665_1]) ).
fof(f_2665_3,plain,
( ! [U_10413] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10413)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10413)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10413))) )
& ! [U_10412] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10412)) = 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_10412))) ) ),
inference(miniscope,[status(thm)],[f_2665_2]) ).
fof(f_2665_4,plain,
( ! [U_10413] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10413)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10413)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10413))) )
& ! [U_10412] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10412)) = 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_10412))) ) ),
inference(definitional_conversion,[status(esa)],[f_2665_3]) ).
cnf(f_2665_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10412)) = 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_10412))) ),
inference(clausify,[status(thm)],[f_2665_4]) ).
cnf(f_2665_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10413)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10413)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10413))) ),
inference(clausify,[status(thm)],[f_2665_4]) ).
fof(f_2666_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_2666_2,plain,
! [U_10415,U_10414] :
( ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10414),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10415)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10414),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10415)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10415))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10414),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10415)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10414)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10415))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10414))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10414),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10415)) = 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_10414))) ) ),
inference(variable_rename,[status(thm)],[f_2666_1]) ).
fof(f_2666_3,plain,
( ! [U_10419,U_10417] :
( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10417),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10419)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10417),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10419)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10419))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10417),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10419)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10417)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10419))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10417))) )
& ! [U_10418,U_10416] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10416),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10418)) = 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_10416))) ) ),
inference(miniscope,[status(thm)],[f_2666_2]) ).
fof(f_2666_4,plain,
( ! [U_10417,U_10419] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10417),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10419)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10417),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10419)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10419)))
| ~ sP792(U_10417,U_10419) )
& ! [U_10417,U_10419] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10417),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10419)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10417)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10419)))
| ~ sP792(U_10417,U_10419) )
& ! [U_10417,U_10419] :
( sP792(U_10417,U_10419)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10417))) )
& ! [U_10418,U_10416] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10416),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10418)) = 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_10416))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP792])],[f_2666_3]) ).
cnf(f_2666_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10416),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10418)) = 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_10416))) ),
inference(clausify,[status(thm)],[f_2666_4]) ).
cnf(f_2666_6,plain,
( sP792(U_10417,U_10419)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10417))) ),
inference(clausify,[status(thm)],[f_2666_4]) ).
cnf(f_2666_7,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10417),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10419)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10417)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10419)))
| ~ sP792(U_10417,U_10419) ),
inference(clausify,[status(thm)],[f_2666_4]) ).
cnf(f_2666_8,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10417),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10419)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10417),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10419)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10419)))
| ~ sP792(U_10417,U_10419) ),
inference(clausify,[status(thm)],[f_2666_4]) ).
fof(f_2667_1,plain,
! [V_a_2,V_f_2,T_e,V_r2_2,V_A2_2,T_d,V_r1_2,V_A1_2,T_c] :
( c_Equiv__Relations_Ocongruent(T_c,tc_fun(T_e,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_d,T_d,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))),V_f_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),V_a_2),V_A2_2))
| ~ c_Equiv__Relations_Ocongruent2(T_c,T_d,tc_fun(T_e,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_d,V_A2_2,V_r2_2)
| ~ c_Equiv__Relations_Oequiv(T_c,V_A1_2,V_r1_2) ),
inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent__UN]) ).
fof(f_2667_2,plain,
! [U_10428,U_10427,U_10426,U_10425,U_10424,U_10423,U_10422,U_10421,U_10420] :
( c_Equiv__Relations_Ocongruent(U_10420,tc_fun(U_10426,tc_HOL_Obool),U_10422,hAPP(hAPP(c_COMBB(tc_fun(U_10423,tc_fun(U_10426,tc_HOL_Obool)),tc_fun(U_10426,tc_HOL_Obool),U_10420),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10423,tc_fun(U_10426,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10423,U_10423,U_10425),hAPP(hAPP(c_Set_Oinsert(U_10423),U_10428),c_Orderings_Obot__class_Obot(tc_fun(U_10423,tc_HOL_Obool)))))),U_10427))
| ~ hBOOL(hAPP(hAPP(c_member(U_10423),U_10428),U_10424))
| ~ c_Equiv__Relations_Ocongruent2(U_10420,U_10423,tc_fun(U_10426,tc_HOL_Obool),U_10422,U_10425,U_10427)
| ~ c_Equiv__Relations_Oequiv(U_10423,U_10424,U_10425)
| ~ c_Equiv__Relations_Oequiv(U_10420,U_10421,U_10422) ),
inference(variable_rename,[status(thm)],[f_2667_1]) ).
fof(f_2667_3,plain,
! [U_10426,U_10428,U_10420,U_10421,U_10427,U_10423,U_10422,U_10424,U_10425] :
( c_Equiv__Relations_Ocongruent(U_10420,tc_fun(U_10426,tc_HOL_Obool),U_10422,hAPP(hAPP(c_COMBB(tc_fun(U_10423,tc_fun(U_10426,tc_HOL_Obool)),tc_fun(U_10426,tc_HOL_Obool),U_10420),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10423,tc_fun(U_10426,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10423,U_10423,U_10425),hAPP(hAPP(c_Set_Oinsert(U_10423),U_10428),c_Orderings_Obot__class_Obot(tc_fun(U_10423,tc_HOL_Obool)))))),U_10427))
| ~ hBOOL(hAPP(hAPP(c_member(U_10423),U_10428),U_10424))
| ~ c_Equiv__Relations_Ocongruent2(U_10420,U_10423,tc_fun(U_10426,tc_HOL_Obool),U_10422,U_10425,U_10427)
| ~ c_Equiv__Relations_Oequiv(U_10423,U_10424,U_10425)
| ~ c_Equiv__Relations_Oequiv(U_10420,U_10421,U_10422) ),
inference(definitional_conversion,[status(esa)],[f_2667_2]) ).
cnf(f_2667_4,plain,
( c_Equiv__Relations_Ocongruent(U_10420,tc_fun(U_10426,tc_HOL_Obool),U_10422,hAPP(hAPP(c_COMBB(tc_fun(U_10423,tc_fun(U_10426,tc_HOL_Obool)),tc_fun(U_10426,tc_HOL_Obool),U_10420),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10423,tc_fun(U_10426,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10423,U_10423,U_10425),hAPP(hAPP(c_Set_Oinsert(U_10423),U_10428),c_Orderings_Obot__class_Obot(tc_fun(U_10423,tc_HOL_Obool)))))),U_10427))
| ~ hBOOL(hAPP(hAPP(c_member(U_10423),U_10428),U_10424))
| ~ c_Equiv__Relations_Ocongruent2(U_10420,U_10423,tc_fun(U_10426,tc_HOL_Obool),U_10422,U_10425,U_10427)
| ~ c_Equiv__Relations_Oequiv(U_10423,U_10424,U_10425)
| ~ c_Equiv__Relations_Oequiv(U_10420,U_10421,U_10422) ),
inference(clausify,[status(thm)],[f_2667_3]) ).
fof(f_2668_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_2668_2,plain,
! [U_10430,U_10429] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10429)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10430)) = 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_10429)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10430)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10429))) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10429)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10430)) = 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_10429))) ) ),
inference(variable_rename,[status(thm)],[f_2668_1]) ).
fof(f_2668_3,plain,
( ! [U_10434,U_10432] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10432)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10434)) = 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_10432)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10434)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10432))) )
& ! [U_10433,U_10431] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10431)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10433)) = 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_10431))) ) ),
inference(miniscope,[status(thm)],[f_2668_2]) ).
fof(f_2668_4,plain,
( ! [U_10434,U_10432] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10432)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10434)) = 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_10432)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10434)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10432))) )
& ! [U_10433,U_10431] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10431)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10433)) = 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_10431))) ) ),
inference(definitional_conversion,[status(esa)],[f_2668_3]) ).
cnf(f_2668_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10431)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10433)) = 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_10431))) ),
inference(clausify,[status(thm)],[f_2668_4]) ).
cnf(f_2668_6,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10432)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10434)) = 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_10432)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10434)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10432))) ),
inference(clausify,[status(thm)],[f_2668_4]) ).
fof(f_2669_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_2669_2,plain,
! [U_10436,U_10435] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10435)),U_10436) = 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_10435)),U_10436))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10435))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10435)),U_10436) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10436)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10435))) ) ),
inference(variable_rename,[status(thm)],[f_2669_1]) ).
fof(f_2669_3,plain,
( ! [U_10440,U_10438] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10438)),U_10440) = 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_10438)),U_10440))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10438))) )
& ! [U_10439,U_10437] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10437)),U_10439) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10439)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10437))) ) ),
inference(miniscope,[status(thm)],[f_2669_2]) ).
fof(f_2669_4,plain,
( ! [U_10438,U_10440] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10438)),U_10440) = 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_10438)),U_10440))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10438))) )
& ! [U_10439,U_10437] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10437)),U_10439) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10439)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10437))) ) ),
inference(definitional_conversion,[status(esa)],[f_2669_3]) ).
cnf(f_2669_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10437)),U_10439) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10439)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10437))) ),
inference(clausify,[status(thm)],[f_2669_4]) ).
cnf(f_2669_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10438)),U_10440) = 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_10438)),U_10440))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10438))) ),
inference(clausify,[status(thm)],[f_2669_4]) ).
fof(f_2670_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_2670_2,plain,
! [U_10442,U_10441] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10441)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10442)) = 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_10441)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10442)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10441))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10441)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10442)) = 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_10442))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10441))) ) ),
inference(variable_rename,[status(thm)],[f_2670_1]) ).
fof(f_2670_3,plain,
( ! [U_10446,U_10444] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10444)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10446)) = 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_10444)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10446)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10444))) )
& ! [U_10445,U_10443] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10443)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10445)) = 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_10445))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10443))) ) ),
inference(miniscope,[status(thm)],[f_2670_2]) ).
fof(f_2670_4,plain,
( ! [U_10444,U_10446] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10444)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10446)) = 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_10444)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10446)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10444))) )
& ! [U_10445,U_10443] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10443)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10445)) = 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_10445))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10443))) ) ),
inference(definitional_conversion,[status(esa)],[f_2670_3]) ).
cnf(f_2670_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10443)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10445)) = 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_10445))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10443))) ),
inference(clausify,[status(thm)],[f_2670_4]) ).
cnf(f_2670_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10444)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10446)) = 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_10444)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10446)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10444))) ),
inference(clausify,[status(thm)],[f_2670_4]) ).
fof(f_2671_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_2671_2,plain,
! [U_10448,U_10447] :
( ( 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_10447)),U_10448)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10447))),U_10448)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10447))) )
& ( 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_10447)),U_10448)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_10448)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10447))) ) ),
inference(variable_rename,[status(thm)],[f_2671_1]) ).
fof(f_2671_3,plain,
( ! [U_10452,U_10450] :
( 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_10450)),U_10452)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10450))),U_10452)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10450))) )
& ! [U_10451,U_10449] :
( 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_10449)),U_10451)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_10451)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10449))) ) ),
inference(miniscope,[status(thm)],[f_2671_2]) ).
fof(f_2671_4,plain,
( ! [U_10452,U_10450] :
( 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_10450)),U_10452)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10450))),U_10452)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10450))) )
& ! [U_10449,U_10451] :
( 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_10449)),U_10451)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_10451)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10449))) ) ),
inference(definitional_conversion,[status(esa)],[f_2671_3]) ).
cnf(f_2671_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_10449)),U_10451)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_10451)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10449))) ),
inference(clausify,[status(thm)],[f_2671_4]) ).
cnf(f_2671_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_10450)),U_10452)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10450))),U_10452)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10450))) ),
inference(clausify,[status(thm)],[f_2671_4]) ).
fof(f_2672_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_2672_2,plain,
! [U_10454,U_10453] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10454)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10453)) = 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_10454),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10453)))),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_10453),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10454)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10453)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10454)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10453),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2672_1]) ).
fof(f_2672_3,plain,
( ! [U_10458,U_10456] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10458)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10456)) = 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_10458),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10456)))),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_10456),c_Int_OPls)) )
& ! [U_10457,U_10455] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10457)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10455)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10457)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10455),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2672_2]) ).
fof(f_2672_4,plain,
( ! [U_10456,U_10458] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10458)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10456)) = 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_10458),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10456)))),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_10456),c_Int_OPls)) )
& ! [U_10457,U_10455] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10457)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10455)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10457)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10455),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2672_3]) ).
cnf(f_2672_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10457)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10455)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10457)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10455),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2672_4]) ).
cnf(f_2672_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10458)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10456)) = 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_10458),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10456)))),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_10456),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2672_4]) ).
fof(f_2673_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_2673_2,plain,
! [U_10460,U_10459] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10459)),hAPP(c_Nat_OSuc,U_10460)) = 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_10459))),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_10460)))),
inference(variable_rename,[status(thm)],[f_2673_1]) ).
fof(f_2673_3,plain,
! [U_10460,U_10459] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10459)),hAPP(c_Nat_OSuc,U_10460)) = 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_10459))),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_10460)))),
inference(definitional_conversion,[status(esa)],[f_2673_2]) ).
cnf(f_2673_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10459)),hAPP(c_Nat_OSuc,U_10460)) = 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_10459))),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_10460)))),
inference(clausify,[status(thm)],[f_2673_3]) ).
fof(f_2674_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_2674_2,plain,
! [U_10462,U_10461] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10461)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10462)) = 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_10462))),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_10461)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_2674_1]) ).
fof(f_2674_3,plain,
! [U_10461,U_10462] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10461)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10462)) = 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_10462))),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_10461)),c_Int_Onat)))),
inference(definitional_conversion,[status(esa)],[f_2674_2]) ).
cnf(f_2674_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10461)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10462)) = 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_10462))),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_10461)),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_2674_3]) ).
fof(f_2675_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_2675_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_2675_1]) ).
cnf(f_2675_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_2675_2]) ).
fof(f_2676_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_2676_2,plain,
! [U_10463] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10463),c_Int_OPls) = U_10463,
inference(variable_rename,[status(thm)],[f_2676_1]) ).
fof(f_2676_3,plain,
! [U_10463] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10463),c_Int_OPls) = U_10463,
inference(definitional_conversion,[status(esa)],[f_2676_2]) ).
cnf(f_2676_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10463),c_Int_OPls) = U_10463,
inference(clausify,[status(thm)],[f_2676_3]) ).
fof(f_2677_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_2677_2,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_2677_1]) ).
cnf(f_2677_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_2677_2]) ).
fof(f_2678_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_2678_2,plain,
! [U_10464] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10464),c_Int_OPls) = U_10464,
inference(variable_rename,[status(thm)],[f_2678_1]) ).
fof(f_2678_3,plain,
! [U_10464] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10464),c_Int_OPls) = U_10464,
inference(definitional_conversion,[status(esa)],[f_2678_2]) ).
cnf(f_2678_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10464),c_Int_OPls) = U_10464,
inference(clausify,[status(thm)],[f_2678_3]) ).
fof(f_2679_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_2679_2,plain,
! [U_10465] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_10465) = U_10465,
inference(variable_rename,[status(thm)],[f_2679_1]) ).
fof(f_2679_3,plain,
! [U_10465] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_10465) = U_10465,
inference(definitional_conversion,[status(esa)],[f_2679_2]) ).
cnf(f_2679_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_10465) = U_10465,
inference(clausify,[status(thm)],[f_2679_3]) ).
fof(f_2680_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_2680_2,plain,
! [U_10466] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_10466) = c_Int_OPls,
inference(variable_rename,[status(thm)],[f_2680_1]) ).
fof(f_2680_3,plain,
! [U_10466] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_10466) = c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_2680_2]) ).
cnf(f_2680_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_10466) = c_Int_OPls,
inference(clausify,[status(thm)],[f_2680_3]) ).
fof(f_2681_1,plain,
! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
inference(fof_nnf,[status(thm)],[fact_succ__pred]) ).
fof(f_2681_2,plain,
! [U_10467] : c_Int_Osucc(c_Int_Opred(U_10467)) = U_10467,
inference(variable_rename,[status(thm)],[f_2681_1]) ).
fof(f_2681_3,plain,
! [U_10467] : c_Int_Osucc(c_Int_Opred(U_10467)) = U_10467,
inference(definitional_conversion,[status(esa)],[f_2681_2]) ).
cnf(f_2681_4,plain,
c_Int_Osucc(c_Int_Opred(U_10467)) = U_10467,
inference(clausify,[status(thm)],[f_2681_3]) ).
fof(f_2682_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_2682_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_2682_1]) ).
cnf(f_2682_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(clausify,[status(thm)],[f_2682_2]) ).
fof(f_2683_1,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).
fof(f_2683_2,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_2683_1]) ).
cnf(f_2683_3,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_2683_2]) ).
fof(f_2684_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_2684_2,plain,
! [U_10468] :
( c_Groups_Ozero__class_Ozero(U_10468) = hAPP(c_Int_Onumber__class_Onumber__of(U_10468),c_Int_OPls)
| ~ class_Int_Onumber__ring(U_10468) ),
inference(variable_rename,[status(thm)],[f_2684_1]) ).
fof(f_2684_3,plain,
! [U_10468] :
( c_Groups_Ozero__class_Ozero(U_10468) = hAPP(c_Int_Onumber__class_Onumber__of(U_10468),c_Int_OPls)
| ~ class_Int_Onumber__ring(U_10468) ),
inference(definitional_conversion,[status(esa)],[f_2684_2]) ).
cnf(f_2684_4,plain,
( c_Groups_Ozero__class_Ozero(U_10468) = hAPP(c_Int_Onumber__class_Onumber__of(U_10468),c_Int_OPls)
| ~ class_Int_Onumber__ring(U_10468) ),
inference(clausify,[status(thm)],[f_2684_3]) ).
fof(f_2685_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_2685_2,plain,
! [U_10469] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10469),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_10469)
| ~ class_Int_Onumber__ring(U_10469) ),
inference(variable_rename,[status(thm)],[f_2685_1]) ).
fof(f_2685_3,plain,
! [U_10469] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10469),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_10469)
| ~ class_Int_Onumber__ring(U_10469) ),
inference(definitional_conversion,[status(esa)],[f_2685_2]) ).
cnf(f_2685_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10469),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_10469)
| ~ class_Int_Onumber__ring(U_10469) ),
inference(clausify,[status(thm)],[f_2685_3]) ).
fof(f_2686_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_2686_2,plain,
! [U_10471,U_10470] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10470),hAPP(c_Int_Onumber__class_Onumber__of(U_10470),c_Int_OPls)),U_10471) = U_10471
| ~ class_Int_Onumber__ring(U_10470) ),
inference(variable_rename,[status(thm)],[f_2686_1]) ).
fof(f_2686_3,plain,
! [U_10470,U_10471] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10470),hAPP(c_Int_Onumber__class_Onumber__of(U_10470),c_Int_OPls)),U_10471) = U_10471
| ~ class_Int_Onumber__ring(U_10470) ),
inference(definitional_conversion,[status(esa)],[f_2686_2]) ).
cnf(f_2686_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10470),hAPP(c_Int_Onumber__class_Onumber__of(U_10470),c_Int_OPls)),U_10471) = U_10471
| ~ class_Int_Onumber__ring(U_10470) ),
inference(clausify,[status(thm)],[f_2686_3]) ).
fof(f_2687_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_2687_2,plain,
! [U_10473,U_10472] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10472),U_10473),hAPP(c_Int_Onumber__class_Onumber__of(U_10472),c_Int_OPls)) = U_10473
| ~ class_Int_Onumber__ring(U_10472) ),
inference(variable_rename,[status(thm)],[f_2687_1]) ).
fof(f_2687_3,plain,
! [U_10472,U_10473] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10472),U_10473),hAPP(c_Int_Onumber__class_Onumber__of(U_10472),c_Int_OPls)) = U_10473
| ~ class_Int_Onumber__ring(U_10472) ),
inference(definitional_conversion,[status(esa)],[f_2687_2]) ).
cnf(f_2687_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10472),U_10473),hAPP(c_Int_Onumber__class_Onumber__of(U_10472),c_Int_OPls)) = U_10473
| ~ class_Int_Onumber__ring(U_10472) ),
inference(clausify,[status(thm)],[f_2687_3]) ).
fof(f_2688_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_2688_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_2688_1]) ).
cnf(f_2688_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_2688_2]) ).
fof(f_2689_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_2689_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_2689_1]) ).
cnf(f_2689_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_2689_2]) ).
fof(f_2690_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_2690_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_2690_1]) ).
cnf(f_2690_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_2690_2]) ).
fof(f_2691_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_2691_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_2691_1]) ).
cnf(f_2691_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_2691_2]) ).
fof(f_2692_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_2692_2,plain,
! [U_10475,U_10474] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10475)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10474)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10475),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_10474)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10474)) ),
inference(variable_rename,[status(thm)],[f_2692_1]) ).
fof(f_2692_3,plain,
! [U_10474,U_10475] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10475)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10474)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10475),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_10474)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10474)) ),
inference(definitional_conversion,[status(esa)],[f_2692_2]) ).
cnf(f_2692_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10475)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10474)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10475),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_10474)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10474)) ),
inference(clausify,[status(thm)],[f_2692_3]) ).
fof(f_2693_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_2693_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_2693_1]) ).
cnf(f_2693_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_2693_2]) ).
fof(f_2694_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_2694_2,plain,
! [U_10476] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10476)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10476))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10476),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10476)),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_10476),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2694_1]) ).
fof(f_2694_3,plain,
( ! [U_10478] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10478)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10478))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10478),c_Int_OPls)) )
& ! [U_10477] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10477)),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_10477),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2694_2]) ).
fof(f_2694_4,plain,
( ! [U_10478] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10478)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10478))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10478),c_Int_OPls)) )
& ! [U_10477] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10477)),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_10477),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2694_3]) ).
cnf(f_2694_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10477)),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_10477),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2694_4]) ).
cnf(f_2694_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10478)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10478))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10478),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2694_4]) ).
fof(f_2695_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_2695_2,plain,
! [U_10479] :
( ( 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_10479)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10479))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10479),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_10479)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10479),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2695_1]) ).
fof(f_2695_3,plain,
( ! [U_10481] :
( 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_10481)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10481))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10481),c_Int_OPls)) )
& ! [U_10480] :
( 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_10480)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10480),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2695_2]) ).
fof(f_2695_4,plain,
( ! [U_10481] :
( 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_10481)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10481))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10481),c_Int_OPls)) )
& ! [U_10480] :
( 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_10480)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10480),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2695_3]) ).
cnf(f_2695_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_10480)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10480),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2695_4]) ).
cnf(f_2695_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_10481)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10481))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10481),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2695_4]) ).
fof(f_2696_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_2696_2,plain,
! [U_10483,U_10482] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10482),U_10483))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_10482)),U_10483)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_10482)),U_10483))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10482),U_10483)) ) ),
inference(variable_rename,[status(thm)],[f_2696_1]) ).
fof(f_2696_3,plain,
( ! [U_10487,U_10485] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10485),U_10487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_10485)),U_10487)) )
& ! [U_10486,U_10484] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_10484)),U_10486))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10484),U_10486)) ) ),
inference(miniscope,[status(thm)],[f_2696_2]) ).
fof(f_2696_4,plain,
( ! [U_10487,U_10485] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10485),U_10487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_10485)),U_10487)) )
& ! [U_10484,U_10486] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_10484)),U_10486))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10484),U_10486)) ) ),
inference(definitional_conversion,[status(esa)],[f_2696_3]) ).
cnf(f_2696_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_10484)),U_10486))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10484),U_10486)) ),
inference(clausify,[status(thm)],[f_2696_4]) ).
cnf(f_2696_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10485),U_10487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_10485)),U_10487)) ),
inference(clausify,[status(thm)],[f_2696_4]) ).
fof(f_2697_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_2697_2,plain,
! [U_10488] : c_Int_Opred(U_10488) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10488),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[f_2697_1]) ).
fof(f_2697_3,plain,
! [U_10488] : c_Int_Opred(U_10488) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10488),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_2697_2]) ).
cnf(f_2697_4,plain,
c_Int_Opred(U_10488) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10488),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_2697_3]) ).
fof(f_2698_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_2698_2,plain,
! [U_10489] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10489)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_10489))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10489),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10489)),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_10489),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2698_1]) ).
fof(f_2698_3,plain,
( ! [U_10491] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10491)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_10491))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10491),c_Int_OPls)) )
& ! [U_10490] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10490)),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_10490),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2698_2]) ).
fof(f_2698_4,plain,
( ! [U_10491] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10491)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_10491))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10491),c_Int_OPls)) )
& ! [U_10490] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10490)),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_10490),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2698_3]) ).
cnf(f_2698_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10490)),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_10490),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2698_4]) ).
cnf(f_2698_6,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10491)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_10491))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10491),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2698_4]) ).
fof(f_2699_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_2699_2,plain,
! [U_10493,U_10492] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10492),U_10493),hAPP(c_Int_Onumber__class_Onumber__of(U_10492),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_10492)
| ~ class_Int_Onumber__ring(U_10492)
| ~ class_Fields_Ofield__inverse__zero(U_10492) ),
inference(variable_rename,[status(thm)],[f_2699_1]) ).
fof(f_2699_3,plain,
! [U_10492,U_10493] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10492),U_10493),hAPP(c_Int_Onumber__class_Onumber__of(U_10492),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_10492)
| ~ class_Int_Onumber__ring(U_10492)
| ~ class_Fields_Ofield__inverse__zero(U_10492) ),
inference(definitional_conversion,[status(esa)],[f_2699_2]) ).
cnf(f_2699_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10492),U_10493),hAPP(c_Int_Onumber__class_Onumber__of(U_10492),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_10492)
| ~ class_Int_Onumber__ring(U_10492)
| ~ class_Fields_Ofield__inverse__zero(U_10492) ),
inference(clausify,[status(thm)],[f_2699_3]) ).
fof(f_2700_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_2700_2,plain,
! [U_10494] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10494),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10494),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10494) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_2700_1]) ).
fof(f_2700_3,plain,
( ! [U_10496] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10496) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10496),c_Int_OPls)) )
& ! [U_10495] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10495),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10495) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_2700_2]) ).
fof(f_2700_4,plain,
( ! [U_10496] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10496) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10496),c_Int_OPls)) )
& ! [U_10495] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10495),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10495) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_2700_3]) ).
cnf(f_2700_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10495),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10495) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2700_4]) ).
cnf(f_2700_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10496) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10496),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2700_4]) ).
fof(f_2701_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_2701_2,plain,
! [U_10497] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10497)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10497),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10497),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10497) ) ),
inference(variable_rename,[status(thm)],[f_2701_1]) ).
fof(f_2701_3,plain,
( ! [U_10499] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10499)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10499),c_Int_OPls)) )
& ! [U_10498] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10498),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10498) ) ),
inference(miniscope,[status(thm)],[f_2701_2]) ).
fof(f_2701_4,plain,
( ! [U_10499] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10499)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10499),c_Int_OPls)) )
& ! [U_10498] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10498),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10498) ) ),
inference(definitional_conversion,[status(esa)],[f_2701_3]) ).
cnf(f_2701_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10498),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10498) ),
inference(clausify,[status(thm)],[f_2701_4]) ).
cnf(f_2701_6,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10499)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10499),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2701_4]) ).
fof(f_2702_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_2702_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_2702_1]) ).
cnf(f_2702_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_2702_2]) ).
fof(f_2703_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_2703_2,plain,
! [U_10501,U_10500] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10500)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10501)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10500),U_10501))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10501))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10500),U_10501)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10500),U_10501))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10501))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10500),U_10501)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10500)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10501))) ) ),
inference(variable_rename,[status(thm)],[f_2703_1]) ).
fof(f_2703_3,plain,
( ! [U_10505,U_10503] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10503)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10505)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10503),U_10505))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10505))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10503),U_10505)) ) )
& ! [U_10504,U_10502] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10502),U_10504))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10502),U_10504)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10502)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10504))) ) ),
inference(miniscope,[status(thm)],[f_2703_2]) ).
fof(f_2703_4,plain,
( ! [U_10503,U_10505] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10505))
| ~ sP794(U_10503,U_10505) )
& ! [U_10503,U_10505] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10503),U_10505))
| ~ sP794(U_10503,U_10505) )
& ! [U_10504,U_10502] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10502),U_10504))
| ~ sP793(U_10504,U_10502) )
& ! [U_10504,U_10502] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10502),U_10504))
| ~ sP793(U_10504,U_10502) )
& ! [U_10503,U_10505] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10503)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10505)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10503),U_10505))
| sP794(U_10503,U_10505) )
& ! [U_10504,U_10502] :
( sP793(U_10504,U_10502)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10502)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10504))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP793,sP794])],[f_2703_3]) ).
cnf(f_2703_5,plain,
( sP793(U_10504,U_10502)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10502)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10504))) ),
inference(clausify,[status(thm)],[f_2703_4]) ).
cnf(f_2703_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10503)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10505)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10503),U_10505))
| sP794(U_10503,U_10505) ),
inference(clausify,[status(thm)],[f_2703_4]) ).
cnf(f_2703_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10502),U_10504))
| ~ sP793(U_10504,U_10502) ),
inference(clausify,[status(thm)],[f_2703_4]) ).
cnf(f_2703_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10502),U_10504))
| ~ sP793(U_10504,U_10502) ),
inference(clausify,[status(thm)],[f_2703_4]) ).
cnf(f_2703_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10503),U_10505))
| ~ sP794(U_10503,U_10505) ),
inference(clausify,[status(thm)],[f_2703_4]) ).
cnf(f_2703_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10505))
| ~ sP794(U_10503,U_10505) ),
inference(clausify,[status(thm)],[f_2703_4]) ).
fof(f_2704_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_2704_2,plain,
! [U_10507,U_10506] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10506)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10507)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10506),c_Int_OPls))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10506),U_10507)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10506),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10506),U_10507))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10506)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10507))) ) ),
inference(variable_rename,[status(thm)],[f_2704_1]) ).
fof(f_2704_3,plain,
( ! [U_10511,U_10509] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10509)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10511)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10509),c_Int_OPls))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10509),U_10511)) ) )
& ! [U_10510,U_10508] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10508),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10508),U_10510))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10508)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10510))) ) ),
inference(miniscope,[status(thm)],[f_2704_2]) ).
fof(f_2704_4,plain,
( ! [U_10511,U_10509] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10509),c_Int_OPls))
| ~ sP795(U_10511,U_10509) )
& ! [U_10511,U_10509] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10509),U_10511))
| ~ sP795(U_10511,U_10509) )
& ! [U_10511,U_10509] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10509)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10511)))
| sP795(U_10511,U_10509) )
& ! [U_10510,U_10508] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10508),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10508),U_10510))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10508)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10510))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP795])],[f_2704_3]) ).
cnf(f_2704_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10508),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10508),U_10510))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10508)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10510))) ),
inference(clausify,[status(thm)],[f_2704_4]) ).
cnf(f_2704_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_10509)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10511)))
| sP795(U_10511,U_10509) ),
inference(clausify,[status(thm)],[f_2704_4]) ).
cnf(f_2704_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10509),U_10511))
| ~ sP795(U_10511,U_10509) ),
inference(clausify,[status(thm)],[f_2704_4]) ).
cnf(f_2704_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10509),c_Int_OPls))
| ~ sP795(U_10511,U_10509) ),
inference(clausify,[status(thm)],[f_2704_4]) ).
fof(f_2705_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_2705_2,plain,
! [U_10512] : c_Int_Osucc(U_10512) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10512),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[f_2705_1]) ).
fof(f_2705_3,plain,
! [U_10512] : c_Int_Osucc(U_10512) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10512),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_2705_2]) ).
cnf(f_2705_4,plain,
c_Int_Osucc(U_10512) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10512),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_2705_3]) ).
fof(f_2706_1,plain,
! [V_y_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2))) ) )
| ~ class_Rings_Olinordered__idom(T_c)
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I1_J]) ).
fof(f_2706_2,plain,
! [U_10514,U_10513] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10513),c_Groups_Ozero__class_Ozero(U_10513)),hAPP(c_Int_Onumber__class_Onumber__of(U_10513),U_10514)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10514)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10514))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10513),c_Groups_Ozero__class_Ozero(U_10513)),hAPP(c_Int_Onumber__class_Onumber__of(U_10513),U_10514))) ) )
| ~ class_Rings_Olinordered__idom(U_10513)
| ~ class_Int_Onumber__ring(U_10513) ),
inference(variable_rename,[status(thm)],[f_2706_1]) ).
fof(f_2706_3,plain,
( ! [U_10513,U_10514] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10513),c_Groups_Ozero__class_Ozero(U_10513)),hAPP(c_Int_Onumber__class_Onumber__of(U_10513),U_10514)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10514))
| ~ sP796(U_10513,U_10514) )
& ! [U_10513,U_10514] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10514))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10513),c_Groups_Ozero__class_Ozero(U_10513)),hAPP(c_Int_Onumber__class_Onumber__of(U_10513),U_10514)))
| ~ sP796(U_10513,U_10514) )
& ! [U_10513,U_10514] :
( sP796(U_10513,U_10514)
| ~ class_Rings_Olinordered__idom(U_10513)
| ~ class_Int_Onumber__ring(U_10513) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP796])],[f_2706_2]) ).
cnf(f_2706_4,plain,
( sP796(U_10513,U_10514)
| ~ class_Rings_Olinordered__idom(U_10513)
| ~ class_Int_Onumber__ring(U_10513) ),
inference(clausify,[status(thm)],[f_2706_3]) ).
cnf(f_2706_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10514))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10513),c_Groups_Ozero__class_Ozero(U_10513)),hAPP(c_Int_Onumber__class_Onumber__of(U_10513),U_10514)))
| ~ sP796(U_10513,U_10514) ),
inference(clausify,[status(thm)],[f_2706_3]) ).
cnf(f_2706_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10513),c_Groups_Ozero__class_Ozero(U_10513)),hAPP(c_Int_Onumber__class_Onumber__of(U_10513),U_10514)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10514))
| ~ sP796(U_10513,U_10514) ),
inference(clausify,[status(thm)],[f_2706_3]) ).
fof(f_2707_1,plain,
! [V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ 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_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Rings_Olinordered__idom(T_c)
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I3_J]) ).
fof(f_2707_2,plain,
! [U_10516,U_10515] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10515),hAPP(c_Int_Onumber__class_Onumber__of(U_10515),U_10516)),c_Groups_Ozero__class_Ozero(U_10515)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10516),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10516),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10515),hAPP(c_Int_Onumber__class_Onumber__of(U_10515),U_10516)),c_Groups_Ozero__class_Ozero(U_10515))) ) )
| ~ class_Rings_Olinordered__idom(U_10515)
| ~ class_Int_Onumber__ring(U_10515) ),
inference(variable_rename,[status(thm)],[f_2707_1]) ).
fof(f_2707_3,plain,
( ! [U_10515,U_10516] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10515),hAPP(c_Int_Onumber__class_Onumber__of(U_10515),U_10516)),c_Groups_Ozero__class_Ozero(U_10515)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10516),c_Int_OPls))
| ~ sP797(U_10515,U_10516) )
& ! [U_10515,U_10516] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10516),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10515),hAPP(c_Int_Onumber__class_Onumber__of(U_10515),U_10516)),c_Groups_Ozero__class_Ozero(U_10515)))
| ~ sP797(U_10515,U_10516) )
& ! [U_10515,U_10516] :
( sP797(U_10515,U_10516)
| ~ class_Rings_Olinordered__idom(U_10515)
| ~ class_Int_Onumber__ring(U_10515) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP797])],[f_2707_2]) ).
cnf(f_2707_4,plain,
( sP797(U_10515,U_10516)
| ~ class_Rings_Olinordered__idom(U_10515)
| ~ class_Int_Onumber__ring(U_10515) ),
inference(clausify,[status(thm)],[f_2707_3]) ).
cnf(f_2707_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10516),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10515),hAPP(c_Int_Onumber__class_Onumber__of(U_10515),U_10516)),c_Groups_Ozero__class_Ozero(U_10515)))
| ~ sP797(U_10515,U_10516) ),
inference(clausify,[status(thm)],[f_2707_3]) ).
cnf(f_2707_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10515),hAPP(c_Int_Onumber__class_Onumber__of(U_10515),U_10516)),c_Groups_Ozero__class_Ozero(U_10515)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10516),c_Int_OPls))
| ~ sP797(U_10515,U_10516) ),
inference(clausify,[status(thm)],[f_2707_3]) ).
fof(f_2708_1,plain,
! [V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Ozero__class_Ozero(T_c)))
| ~ 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_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Ozero__class_Ozero(T_c))) ) )
| ~ class_Rings_Olinordered__idom(T_c)
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I3_J]) ).
fof(f_2708_2,plain,
! [U_10518,U_10517] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10517),hAPP(c_Int_Onumber__class_Onumber__of(U_10517),U_10518)),c_Groups_Ozero__class_Ozero(U_10517)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10518),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10518),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10517),hAPP(c_Int_Onumber__class_Onumber__of(U_10517),U_10518)),c_Groups_Ozero__class_Ozero(U_10517))) ) )
| ~ class_Rings_Olinordered__idom(U_10517)
| ~ class_Int_Onumber__ring(U_10517) ),
inference(variable_rename,[status(thm)],[f_2708_1]) ).
fof(f_2708_3,plain,
( ! [U_10517,U_10518] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10517),hAPP(c_Int_Onumber__class_Onumber__of(U_10517),U_10518)),c_Groups_Ozero__class_Ozero(U_10517)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10518),c_Int_OPls))
| ~ sP798(U_10517,U_10518) )
& ! [U_10517,U_10518] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10518),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10517),hAPP(c_Int_Onumber__class_Onumber__of(U_10517),U_10518)),c_Groups_Ozero__class_Ozero(U_10517)))
| ~ sP798(U_10517,U_10518) )
& ! [U_10517,U_10518] :
( sP798(U_10517,U_10518)
| ~ class_Rings_Olinordered__idom(U_10517)
| ~ class_Int_Onumber__ring(U_10517) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP798])],[f_2708_2]) ).
cnf(f_2708_4,plain,
( sP798(U_10517,U_10518)
| ~ class_Rings_Olinordered__idom(U_10517)
| ~ class_Int_Onumber__ring(U_10517) ),
inference(clausify,[status(thm)],[f_2708_3]) ).
cnf(f_2708_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10518),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10517),hAPP(c_Int_Onumber__class_Onumber__of(U_10517),U_10518)),c_Groups_Ozero__class_Ozero(U_10517)))
| ~ sP798(U_10517,U_10518) ),
inference(clausify,[status(thm)],[f_2708_3]) ).
cnf(f_2708_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10517),hAPP(c_Int_Onumber__class_Onumber__of(U_10517),U_10518)),c_Groups_Ozero__class_Ozero(U_10517)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10518),c_Int_OPls))
| ~ sP798(U_10517,U_10518) ),
inference(clausify,[status(thm)],[f_2708_3]) ).
fof(f_2709_1,plain,
! [V_y_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2))) ) )
| ~ class_Rings_Olinordered__idom(T_c)
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I1_J]) ).
fof(f_2709_2,plain,
! [U_10520,U_10519] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10519),c_Groups_Ozero__class_Ozero(U_10519)),hAPP(c_Int_Onumber__class_Onumber__of(U_10519),U_10520)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10520)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10519),c_Groups_Ozero__class_Ozero(U_10519)),hAPP(c_Int_Onumber__class_Onumber__of(U_10519),U_10520))) ) )
| ~ class_Rings_Olinordered__idom(U_10519)
| ~ class_Int_Onumber__ring(U_10519) ),
inference(variable_rename,[status(thm)],[f_2709_1]) ).
fof(f_2709_3,plain,
( ! [U_10519,U_10520] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10519),c_Groups_Ozero__class_Ozero(U_10519)),hAPP(c_Int_Onumber__class_Onumber__of(U_10519),U_10520)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10520))
| ~ sP799(U_10519,U_10520) )
& ! [U_10519,U_10520] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10519),c_Groups_Ozero__class_Ozero(U_10519)),hAPP(c_Int_Onumber__class_Onumber__of(U_10519),U_10520)))
| ~ sP799(U_10519,U_10520) )
& ! [U_10519,U_10520] :
( sP799(U_10519,U_10520)
| ~ class_Rings_Olinordered__idom(U_10519)
| ~ class_Int_Onumber__ring(U_10519) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP799])],[f_2709_2]) ).
cnf(f_2709_4,plain,
( sP799(U_10519,U_10520)
| ~ class_Rings_Olinordered__idom(U_10519)
| ~ class_Int_Onumber__ring(U_10519) ),
inference(clausify,[status(thm)],[f_2709_3]) ).
cnf(f_2709_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10519),c_Groups_Ozero__class_Ozero(U_10519)),hAPP(c_Int_Onumber__class_Onumber__of(U_10519),U_10520)))
| ~ sP799(U_10519,U_10520) ),
inference(clausify,[status(thm)],[f_2709_3]) ).
cnf(f_2709_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10519),c_Groups_Ozero__class_Ozero(U_10519)),hAPP(c_Int_Onumber__class_Onumber__of(U_10519),U_10520)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10520))
| ~ sP799(U_10519,U_10520) ),
inference(clausify,[status(thm)],[f_2709_3]) ).
fof(f_2710_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_2710_2,plain,
! [U_10521] :
( ( 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_10521)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10521)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10521))
| ~ 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_10521))) ) ),
inference(variable_rename,[status(thm)],[f_2710_1]) ).
fof(f_2710_3,plain,
( ! [U_10523] :
( 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_10523)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10523)) )
& ! [U_10522] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10522))
| ~ 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_10522))) ) ),
inference(miniscope,[status(thm)],[f_2710_2]) ).
fof(f_2710_4,plain,
( ! [U_10523] :
( 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_10523)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10523)) )
& ! [U_10522] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10522))
| ~ 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_10522))) ) ),
inference(definitional_conversion,[status(esa)],[f_2710_3]) ).
cnf(f_2710_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10522))
| ~ 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_10522))) ),
inference(clausify,[status(thm)],[f_2710_4]) ).
cnf(f_2710_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_10523)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10523)) ),
inference(clausify,[status(thm)],[f_2710_4]) ).
fof(f_2711_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_2711_2,plain,
! [U_10525,U_10524] :
( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10524)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10525)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10524),U_10525))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10525),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10524)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10525)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10524)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10525),c_Int_OPls)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10524),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10524)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10525)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10525)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10524),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2711_1]) ).
fof(f_2711_3,plain,
( ! [U_10529,U_10527] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10527)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10529)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10527),U_10529))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10529),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10527)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10529)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10527)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10529),c_Int_OPls)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10527),c_Int_OPls)) )
& ! [U_10528,U_10526] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10526)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10528)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10528)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10526),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2711_2]) ).
fof(f_2711_4,plain,
( ! [U_10527,U_10529] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10527)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10529)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10527),U_10529))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10529),c_Int_OPls))
| ~ sP800(U_10527,U_10529) )
& ! [U_10527,U_10529] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10527)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10529)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10527)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10529),c_Int_OPls))
| ~ sP800(U_10527,U_10529) )
& ! [U_10527,U_10529] :
( sP800(U_10527,U_10529)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10527),c_Int_OPls)) )
& ! [U_10528,U_10526] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10526)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10528)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10528)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10526),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP800])],[f_2711_3]) ).
cnf(f_2711_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10526)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10528)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10528)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10526),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2711_4]) ).
cnf(f_2711_6,plain,
( sP800(U_10527,U_10529)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10527),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2711_4]) ).
cnf(f_2711_7,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10527)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10529)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10527)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10529),c_Int_OPls))
| ~ sP800(U_10527,U_10529) ),
inference(clausify,[status(thm)],[f_2711_4]) ).
cnf(f_2711_8,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10527)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10529)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10527),U_10529))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10529),c_Int_OPls))
| ~ sP800(U_10527,U_10529) ),
inference(clausify,[status(thm)],[f_2711_4]) ).
fof(f_2712_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_2712_2,plain,
! [U_10531,U_10530] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10530),c_Int_Osucc(U_10531)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10530),c_Groups_Oone__class_Oone(U_10530)),hAPP(c_Int_Onumber__class_Onumber__of(U_10530),U_10531))
| ~ class_Int_Onumber__ring(U_10530) ),
inference(variable_rename,[status(thm)],[f_2712_1]) ).
fof(f_2712_3,plain,
! [U_10531,U_10530] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10530),c_Int_Osucc(U_10531)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10530),c_Groups_Oone__class_Oone(U_10530)),hAPP(c_Int_Onumber__class_Onumber__of(U_10530),U_10531))
| ~ class_Int_Onumber__ring(U_10530) ),
inference(definitional_conversion,[status(esa)],[f_2712_2]) ).
cnf(f_2712_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10530),c_Int_Osucc(U_10531)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10530),c_Groups_Oone__class_Oone(U_10530)),hAPP(c_Int_Onumber__class_Onumber__of(U_10530),U_10531))
| ~ class_Int_Onumber__ring(U_10530) ),
inference(clausify,[status(thm)],[f_2712_3]) ).
fof(f_2713_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_2713_2,plain,
! [U_10533,U_10532] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10532),c_Int_Opred(U_10533)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10532),hAPP(c_Groups_Ouminus__class_Ouminus(U_10532),c_Groups_Oone__class_Oone(U_10532))),hAPP(c_Int_Onumber__class_Onumber__of(U_10532),U_10533))
| ~ class_Int_Onumber__ring(U_10532) ),
inference(variable_rename,[status(thm)],[f_2713_1]) ).
fof(f_2713_3,plain,
! [U_10532,U_10533] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10532),c_Int_Opred(U_10533)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10532),hAPP(c_Groups_Ouminus__class_Ouminus(U_10532),c_Groups_Oone__class_Oone(U_10532))),hAPP(c_Int_Onumber__class_Onumber__of(U_10532),U_10533))
| ~ class_Int_Onumber__ring(U_10532) ),
inference(definitional_conversion,[status(esa)],[f_2713_2]) ).
cnf(f_2713_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10532),c_Int_Opred(U_10533)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10532),hAPP(c_Groups_Ouminus__class_Ouminus(U_10532),c_Groups_Oone__class_Oone(U_10532))),hAPP(c_Int_Onumber__class_Onumber__of(U_10532),U_10533))
| ~ class_Int_Onumber__ring(U_10532) ),
inference(clausify,[status(thm)],[f_2713_3]) ).
fof(f_2714_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_2714_2,plain,
! [U_10535,U_10534] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10534)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10535)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10534),U_10535))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10534),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10534)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10535)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10534),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2714_1]) ).
fof(f_2714_3,plain,
( ! [U_10539,U_10537] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10537)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10539)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10537),U_10539))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10537),c_Int_OPls)) )
& ! [U_10538,U_10536] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10536)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10538)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10536),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2714_2]) ).
fof(f_2714_4,plain,
( ! [U_10537,U_10539] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10537)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10539)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10537),U_10539))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10537),c_Int_OPls)) )
& ! [U_10538,U_10536] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10536)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10538)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10536),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2714_3]) ).
cnf(f_2714_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10536)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10538)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10536),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2714_4]) ).
cnf(f_2714_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10537)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10539)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10537),U_10539))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10537),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2714_4]) ).
fof(f_2715_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_2715_2,plain,
! [U_10542,U_10541,U_10540] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10541)),U_10542)) = 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_10540),U_10541))),U_10542)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10540),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10540)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10541)),U_10542)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10540),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2715_1]) ).
fof(f_2715_3,plain,
( ! [U_10548,U_10546,U_10544] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10544)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10546)),U_10548)) = 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_10544),U_10546))),U_10548)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10544),c_Int_OPls)) )
& ! [U_10547,U_10545,U_10543] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10543)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10545)),U_10547)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10543),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2715_2]) ).
fof(f_2715_4,plain,
( ! [U_10544,U_10546,U_10548] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10544)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10546)),U_10548)) = 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_10544),U_10546))),U_10548)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10544),c_Int_OPls)) )
& ! [U_10545,U_10543,U_10547] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10543)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10545)),U_10547)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10543),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2715_3]) ).
cnf(f_2715_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10543)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10545)),U_10547)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10543),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2715_4]) ).
cnf(f_2715_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10544)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10546)),U_10548)) = 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_10544),U_10546))),U_10548)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10544),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2715_4]) ).
fof(f_2716_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_2716_2,plain,
! [U_10549] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10549))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10549) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10549) = 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_10549)))) ) ),
inference(variable_rename,[status(thm)],[f_2716_1]) ).
fof(f_2716_3,plain,
( ! [U_10551] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10551))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10551) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_10550] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10550) = 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_10550)))) ) ),
inference(miniscope,[status(thm)],[f_2716_2]) ).
fof(f_2716_4,plain,
( ! [U_10551] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10551))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10551) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_10550] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10550) = 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_10550)))) ) ),
inference(definitional_conversion,[status(esa)],[f_2716_3]) ).
cnf(f_2716_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10550) = 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_10550)))) ),
inference(clausify,[status(thm)],[f_2716_4]) ).
cnf(f_2716_6,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10551))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10551) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2716_4]) ).
fof(f_2717_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_2717_2,plain,
! [U_10553,U_10552] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10552) = hAPP(c_Nat_OSuc,U_10553)
| ~ 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_10552))),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_10553))))) )
& ( 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_10552))),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_10553)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10552) != hAPP(c_Nat_OSuc,U_10553) ) ),
inference(variable_rename,[status(thm)],[f_2717_1]) ).
fof(f_2717_3,plain,
( ! [U_10557,U_10555] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10555) = hAPP(c_Nat_OSuc,U_10557)
| ~ 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_10555))),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_10557))))) )
& ! [U_10556,U_10554] :
( 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_10554))),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_10556)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10554) != hAPP(c_Nat_OSuc,U_10556) ) ),
inference(miniscope,[status(thm)],[f_2717_2]) ).
fof(f_2717_4,plain,
( ! [U_10555,U_10557] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10555) = hAPP(c_Nat_OSuc,U_10557)
| ~ 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_10555))),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_10557))))) )
& ! [U_10556,U_10554] :
( 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_10554))),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_10556)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10554) != hAPP(c_Nat_OSuc,U_10556) ) ),
inference(definitional_conversion,[status(esa)],[f_2717_3]) ).
cnf(f_2717_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_10554))),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_10556)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10554) != hAPP(c_Nat_OSuc,U_10556) ),
inference(clausify,[status(thm)],[f_2717_4]) ).
cnf(f_2717_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10555) = hAPP(c_Nat_OSuc,U_10557)
| ~ 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_10555))),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_10557))))) ),
inference(clausify,[status(thm)],[f_2717_4]) ).
fof(f_2718_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_2718_2,plain,
! [U_10559,U_10558] :
( ( hAPP(c_Nat_OSuc,U_10558) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10559)
| ~ 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_10559))),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_10558))))) )
& ( 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_10559))),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_10558)))))
| hAPP(c_Nat_OSuc,U_10558) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10559) ) ),
inference(variable_rename,[status(thm)],[f_2718_1]) ).
fof(f_2718_3,plain,
( ! [U_10563,U_10561] :
( hAPP(c_Nat_OSuc,U_10561) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10563)
| ~ 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_10563))),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_10561))))) )
& ! [U_10562,U_10560] :
( 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_10562))),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_10560)))))
| hAPP(c_Nat_OSuc,U_10560) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10562) ) ),
inference(miniscope,[status(thm)],[f_2718_2]) ).
fof(f_2718_4,plain,
( ! [U_10563,U_10561] :
( hAPP(c_Nat_OSuc,U_10561) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10563)
| ~ 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_10563))),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_10561))))) )
& ! [U_10562,U_10560] :
( 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_10562))),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_10560)))))
| hAPP(c_Nat_OSuc,U_10560) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10562) ) ),
inference(definitional_conversion,[status(esa)],[f_2718_3]) ).
cnf(f_2718_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_10562))),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_10560)))))
| hAPP(c_Nat_OSuc,U_10560) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10562) ),
inference(clausify,[status(thm)],[f_2718_4]) ).
cnf(f_2718_6,plain,
( hAPP(c_Nat_OSuc,U_10561) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10563)
| ~ 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_10563))),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_10561))))) ),
inference(clausify,[status(thm)],[f_2718_4]) ).
fof(f_2719_1,plain,
! [V_v_2,V_f_2,V_a_2,T_c] : c_Nat_Onat_Onat__case(T_c,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_c),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_c)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,tc_Int_Oint),V_f_2),c_Int_Onat))),
inference(fof_nnf,[status(thm)],[fact_nat__case__number__of]) ).
fof(f_2719_2,plain,
! [U_10567,U_10566,U_10565,U_10564] : c_Nat_Onat_Onat__case(U_10564,U_10565,U_10566,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10567)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10564),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10567))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10564,U_10564),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10564,tc_fun(U_10564,U_10564)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10564,tc_fun(U_10564,U_10564)),tc_Int_Oint),c_If(U_10564)),c_Nat__Numeral_Oneg)),U_10565)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10564,tc_Int_Oint),U_10566),c_Int_Onat))),
inference(variable_rename,[status(thm)],[f_2719_1]) ).
fof(f_2719_3,plain,
! [U_10564,U_10565,U_10566,U_10567] : c_Nat_Onat_Onat__case(U_10564,U_10565,U_10566,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10567)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10564),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10567))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10564,U_10564),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10564,tc_fun(U_10564,U_10564)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10564,tc_fun(U_10564,U_10564)),tc_Int_Oint),c_If(U_10564)),c_Nat__Numeral_Oneg)),U_10565)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10564,tc_Int_Oint),U_10566),c_Int_Onat))),
inference(definitional_conversion,[status(esa)],[f_2719_2]) ).
cnf(f_2719_4,plain,
c_Nat_Onat_Onat__case(U_10564,U_10565,U_10566,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10567)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10564),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10567))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10564,U_10564),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10564,tc_fun(U_10564,U_10564)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10564,tc_fun(U_10564,U_10564)),tc_Int_Oint),c_If(U_10564)),c_Nat__Numeral_Oneg)),U_10565)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10564,tc_Int_Oint),U_10566),c_Int_Onat))),
inference(clausify,[status(thm)],[f_2719_3]) ).
fof(f_2720_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_2720_2,plain,
! [U_10569,U_10568] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10568)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10569)))
| ~ 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_10569))),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_10568)),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_10569))),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_10568)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10568)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10569))) ) ),
inference(variable_rename,[status(thm)],[f_2720_1]) ).
fof(f_2720_3,plain,
( ! [U_10573,U_10571] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10571)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10573)))
| ~ 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_10573))),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_10571)),c_Int_Onat))))) )
& ! [U_10572,U_10570] :
( 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_10572))),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_10570)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10570)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10572))) ) ),
inference(miniscope,[status(thm)],[f_2720_2]) ).
fof(f_2720_4,plain,
( ! [U_10571,U_10573] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10571)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10573)))
| ~ 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_10573))),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_10571)),c_Int_Onat))))) )
& ! [U_10570,U_10572] :
( 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_10572))),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_10570)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10570)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10572))) ) ),
inference(definitional_conversion,[status(esa)],[f_2720_3]) ).
cnf(f_2720_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_10572))),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_10570)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10570)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10572))) ),
inference(clausify,[status(thm)],[f_2720_4]) ).
cnf(f_2720_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10571)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10573)))
| ~ 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_10573))),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_10571)),c_Int_Onat))))) ),
inference(clausify,[status(thm)],[f_2720_4]) ).
fof(f_2721_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_2721_2,plain,
! [U_10575,U_10574] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10574)),hAPP(c_Nat_OSuc,U_10575)))
| ~ 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_10574))),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_10575)))) )
& ( 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_10574))),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_10575))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10574)),hAPP(c_Nat_OSuc,U_10575))) ) ),
inference(variable_rename,[status(thm)],[f_2721_1]) ).
fof(f_2721_3,plain,
( ! [U_10579,U_10577] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10577)),hAPP(c_Nat_OSuc,U_10579)))
| ~ 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_10577))),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_10579)))) )
& ! [U_10578,U_10576] :
( 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_10576))),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_10578))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10576)),hAPP(c_Nat_OSuc,U_10578))) ) ),
inference(miniscope,[status(thm)],[f_2721_2]) ).
fof(f_2721_4,plain,
( ! [U_10577,U_10579] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10577)),hAPP(c_Nat_OSuc,U_10579)))
| ~ 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_10577))),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_10579)))) )
& ! [U_10578,U_10576] :
( 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_10576))),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_10578))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10576)),hAPP(c_Nat_OSuc,U_10578))) ) ),
inference(definitional_conversion,[status(esa)],[f_2721_3]) ).
cnf(f_2721_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_10576))),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_10578))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10576)),hAPP(c_Nat_OSuc,U_10578))) ),
inference(clausify,[status(thm)],[f_2721_4]) ).
cnf(f_2721_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10577)),hAPP(c_Nat_OSuc,U_10579)))
| ~ 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_10577))),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_10579)))) ),
inference(clausify,[status(thm)],[f_2721_4]) ).
fof(f_2722_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_2722_2,plain,
! [U_10581,U_10580] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10580)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10581)))
| ~ 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_10581))),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_10580)),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_10581))),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_10580)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10580)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10581))) ) ),
inference(variable_rename,[status(thm)],[f_2722_1]) ).
fof(f_2722_3,plain,
( ! [U_10585,U_10583] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10583)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10585)))
| ~ 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_10585))),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_10583)),c_Int_Onat))))) )
& ! [U_10584,U_10582] :
( 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_10584))),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_10582)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10582)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10584))) ) ),
inference(miniscope,[status(thm)],[f_2722_2]) ).
fof(f_2722_4,plain,
( ! [U_10585,U_10583] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10583)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10585)))
| ~ 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_10585))),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_10583)),c_Int_Onat))))) )
& ! [U_10584,U_10582] :
( 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_10584))),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_10582)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10582)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10584))) ) ),
inference(definitional_conversion,[status(esa)],[f_2722_3]) ).
cnf(f_2722_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_10584))),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_10582)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10582)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10584))) ),
inference(clausify,[status(thm)],[f_2722_4]) ).
cnf(f_2722_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10583)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10585)))
| ~ 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_10585))),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_10583)),c_Int_Onat))))) ),
inference(clausify,[status(thm)],[f_2722_4]) ).
fof(f_2723_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_2723_2,plain,
! [U_10587,U_10586] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10586)),hAPP(c_Nat_OSuc,U_10587)))
| ~ 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_10586))),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_10587)))) )
& ( 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_10586))),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_10587))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10586)),hAPP(c_Nat_OSuc,U_10587))) ) ),
inference(variable_rename,[status(thm)],[f_2723_1]) ).
fof(f_2723_3,plain,
( ! [U_10591,U_10589] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10589)),hAPP(c_Nat_OSuc,U_10591)))
| ~ 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_10589))),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_10591)))) )
& ! [U_10590,U_10588] :
( 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_10588))),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_10590))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10588)),hAPP(c_Nat_OSuc,U_10590))) ) ),
inference(miniscope,[status(thm)],[f_2723_2]) ).
fof(f_2723_4,plain,
( ! [U_10591,U_10589] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10589)),hAPP(c_Nat_OSuc,U_10591)))
| ~ 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_10589))),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_10591)))) )
& ! [U_10590,U_10588] :
( 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_10588))),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_10590))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10588)),hAPP(c_Nat_OSuc,U_10590))) ) ),
inference(definitional_conversion,[status(esa)],[f_2723_3]) ).
cnf(f_2723_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_10588))),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_10590))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10588)),hAPP(c_Nat_OSuc,U_10590))) ),
inference(clausify,[status(thm)],[f_2723_4]) ).
cnf(f_2723_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_10589)),hAPP(c_Nat_OSuc,U_10591)))
| ~ 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_10589))),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_10591)))) ),
inference(clausify,[status(thm)],[f_2723_4]) ).
fof(f_2724_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_2724_2,plain,
! [U_10592] :
( ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10592)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10592))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10592))) )
& ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10592)) = 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_10592))) ) ),
inference(variable_rename,[status(thm)],[f_2724_1]) ).
fof(f_2724_3,plain,
( ! [U_10594] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10594)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10594))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10594))) )
& ! [U_10593] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10593)) = 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_10593))) ) ),
inference(miniscope,[status(thm)],[f_2724_2]) ).
fof(f_2724_4,plain,
( ! [U_10594] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10594)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10594))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10594))) )
& ! [U_10593] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10593)) = 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_10593))) ) ),
inference(definitional_conversion,[status(esa)],[f_2724_3]) ).
cnf(f_2724_5,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10593)) = 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_10593))) ),
inference(clausify,[status(thm)],[f_2724_4]) ).
cnf(f_2724_6,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10594)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_10594))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10594))) ),
inference(clausify,[status(thm)],[f_2724_4]) ).
fof(f_2725_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_2725_2,plain,
! [U_10596,U_10595] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10595)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10596)) = 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_10596))),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_10595))),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_10595)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_2725_1]) ).
fof(f_2725_3,plain,
! [U_10595,U_10596] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10595)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10596)) = 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_10596))),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_10595))),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_10595)),c_Int_Onat)))),
inference(definitional_conversion,[status(esa)],[f_2725_2]) ).
cnf(f_2725_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10595)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10596)) = 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_10596))),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_10595))),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_10595)),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_2725_3]) ).
fof(f_2726_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_2726_2,plain,
! [U_10598,U_10597] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10597)),hAPP(c_Nat_OSuc,U_10598)) = 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_10597))),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_10598))),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_10598)))),
inference(variable_rename,[status(thm)],[f_2726_1]) ).
fof(f_2726_3,plain,
! [U_10597,U_10598] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10597)),hAPP(c_Nat_OSuc,U_10598)) = 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_10597))),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_10598))),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_10598)))),
inference(definitional_conversion,[status(esa)],[f_2726_2]) ).
cnf(f_2726_4,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10597)),hAPP(c_Nat_OSuc,U_10598)) = 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_10597))),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_10598))),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_10598)))),
inference(clausify,[status(thm)],[f_2726_3]) ).
fof(f_2727_1,plain,
! [V_n_2,V_v_2,V_f_2,V_a_2,T_c] : c_Nat_Onat_Onat__case(T_c,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_c),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_c)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_c,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,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_2727_2,plain,
! [U_10603,U_10602,U_10601,U_10600,U_10599] : c_Nat_Onat_Onat__case(U_10599,U_10600,U_10601,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10602)),U_10603)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10599),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10602))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10599,U_10599),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10599,tc_fun(U_10599,U_10599)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10599,tc_fun(U_10599,U_10599)),tc_Int_Oint),c_If(U_10599)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_10599,U_10600,U_10601,U_10603))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10599,tc_Int_Oint),U_10601),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_10603)))),
inference(variable_rename,[status(thm)],[f_2727_1]) ).
fof(f_2727_3,plain,
! [U_10600,U_10601,U_10602,U_10603,U_10599] : c_Nat_Onat_Onat__case(U_10599,U_10600,U_10601,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10602)),U_10603)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10599),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10602))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10599,U_10599),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10599,tc_fun(U_10599,U_10599)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10599,tc_fun(U_10599,U_10599)),tc_Int_Oint),c_If(U_10599)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_10599,U_10600,U_10601,U_10603))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10599,tc_Int_Oint),U_10601),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_10603)))),
inference(definitional_conversion,[status(esa)],[f_2727_2]) ).
cnf(f_2727_4,plain,
c_Nat_Onat_Onat__case(U_10599,U_10600,U_10601,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10602)),U_10603)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10599),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10602))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10599,U_10599),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10599,tc_fun(U_10599,U_10599)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10599,tc_fun(U_10599,U_10599)),tc_Int_Oint),c_If(U_10599)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_10599,U_10600,U_10601,U_10603))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10599,tc_Int_Oint),U_10601),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_10603)))),
inference(clausify,[status(thm)],[f_2727_3]) ).
fof(f_2728_1,plain,
! [V_n_2,V_v_2,V_f_2,V_a_2,T_c] : hAPP(c_Nat_Onat_Onat__rec(T_c,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_c),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_c)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_c,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_c,T_c),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_c,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_c,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_2728_2,plain,
! [U_10608,U_10607,U_10606,U_10605,U_10604] : hAPP(c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10607)),U_10608)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10604),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10607))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10604,U_10604),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10604,tc_fun(U_10604,U_10604)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10604,tc_fun(U_10604,U_10604)),tc_Int_Oint),c_If(U_10604)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606),U_10608))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10604,U_10604),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10604,U_10604),tc_Int_Oint),U_10606),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_10608))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10604,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606)),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_10608))))),
inference(variable_rename,[status(thm)],[f_2728_1]) ).
fof(f_2728_3,plain,
! [U_10604,U_10605,U_10606,U_10607,U_10608] : hAPP(c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10607)),U_10608)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10604),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10607))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10604,U_10604),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10604,tc_fun(U_10604,U_10604)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10604,tc_fun(U_10604,U_10604)),tc_Int_Oint),c_If(U_10604)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606),U_10608))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10604,U_10604),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10604,U_10604),tc_Int_Oint),U_10606),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_10608))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10604,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606)),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_10608))))),
inference(definitional_conversion,[status(esa)],[f_2728_2]) ).
cnf(f_2728_4,plain,
hAPP(c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10607)),U_10608)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10604),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10607))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10604,U_10604),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10604,tc_fun(U_10604,U_10604)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10604,tc_fun(U_10604,U_10604)),tc_Int_Oint),c_If(U_10604)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606),U_10608))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10604,U_10604),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10604,U_10604),tc_Int_Oint),U_10606),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_10608))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10604,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10604,U_10605,U_10606)),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_10608))))),
inference(clausify,[status(thm)],[f_2728_3]) ).
fof(f_2729_1,plain,
! [V_v_2,V_f_2,V_a_2,T_c] : hAPP(c_Nat_Onat_Onat__rec(T_c,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_c),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_c)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_c,T_c),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_c,T_c),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_c,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_c,V_a_2,V_f_2)),c_Int_Onat)))),
inference(fof_nnf,[status(thm)],[fact_nat__rec__number__of]) ).
fof(f_2729_2,plain,
! [U_10612,U_10611,U_10610,U_10609] : hAPP(c_Nat_Onat_Onat__rec(U_10609,U_10610,U_10611),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10612)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10609),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10612))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10609,U_10609),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10609,tc_fun(U_10609,U_10609)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10609,tc_fun(U_10609,U_10609)),tc_Int_Oint),c_If(U_10609)),c_Nat__Numeral_Oneg)),U_10610)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10609,U_10609),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10609,U_10609),tc_Int_Oint),U_10611),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10609,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10609,U_10610,U_10611)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_2729_1]) ).
fof(f_2729_3,plain,
! [U_10609,U_10610,U_10611,U_10612] : hAPP(c_Nat_Onat_Onat__rec(U_10609,U_10610,U_10611),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10612)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10609),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10612))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10609,U_10609),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10609,tc_fun(U_10609,U_10609)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10609,tc_fun(U_10609,U_10609)),tc_Int_Oint),c_If(U_10609)),c_Nat__Numeral_Oneg)),U_10610)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10609,U_10609),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10609,U_10609),tc_Int_Oint),U_10611),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10609,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10609,U_10610,U_10611)),c_Int_Onat)))),
inference(definitional_conversion,[status(esa)],[f_2729_2]) ).
cnf(f_2729_4,plain,
hAPP(c_Nat_Onat_Onat__rec(U_10609,U_10610,U_10611),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10612)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10609),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10612))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10609,U_10609),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10609,tc_fun(U_10609,U_10609)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10609,tc_fun(U_10609,U_10609)),tc_Int_Oint),c_If(U_10609)),c_Nat__Numeral_Oneg)),U_10610)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10609,U_10609),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10609,U_10609),tc_Int_Oint),U_10611),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10609,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10609,U_10610,U_10611)),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_2729_3]) ).
fof(f_2730_1,plain,
! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_e,V_r2_2,V_A2_2,T_d,V_r1_2,V_A1_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_e,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),tc_fun(T_e,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_e,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2))
| ? [B_x1] :
( ? [B_x2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x2),V_A2_2)) )
& hBOOL(hAPP(hAPP(c_member(T_c),B_x1),V_A1_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_d),V_A2_2),V_r2_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A1_2),V_r1_2)))
| ~ c_Equiv__Relations_Ocongruent2(T_c,T_d,tc_fun(T_e,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_d,V_A2_2,V_r2_2)
| ~ c_Equiv__Relations_Oequiv(T_c,V_A1_2,V_r1_2) ),
inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type2]) ).
fof(f_2730_2,plain,
! [U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10621,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10615,tc_fun(U_10621,tc_HOL_Obool)),U_10623),hAPP(hAPP(c_COMBB(tc_fun(U_10618,tc_fun(U_10621,tc_HOL_Obool)),tc_fun(U_10621,tc_HOL_Obool),U_10615),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10618,tc_fun(U_10621,tc_HOL_Obool)),U_10624)),U_10622))),U_10625))
| ? [U_10614] :
( ? [U_10613] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10621,tc_HOL_Obool)),hAPP(hAPP(U_10622,U_10614),U_10613)),U_10625))
& hBOOL(hAPP(hAPP(c_member(U_10618),U_10613),U_10619)) )
& hBOOL(hAPP(hAPP(c_member(U_10615),U_10614),U_10616)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10618,tc_HOL_Obool)),U_10624),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10618),U_10619),U_10620)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10615,tc_HOL_Obool)),U_10623),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10615),U_10616),U_10617)))
| ~ c_Equiv__Relations_Ocongruent2(U_10615,U_10618,tc_fun(U_10621,tc_HOL_Obool),U_10617,U_10620,U_10622)
| ~ c_Equiv__Relations_Oequiv(U_10618,U_10619,U_10620)
| ~ c_Equiv__Relations_Oequiv(U_10615,U_10616,U_10617) ),
inference(variable_rename,[status(thm)],[f_2730_1]) ).
fof(f_2730_3,plain,
! [U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10621,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10615,tc_fun(U_10621,tc_HOL_Obool)),U_10623),hAPP(hAPP(c_COMBB(tc_fun(U_10618,tc_fun(U_10621,tc_HOL_Obool)),tc_fun(U_10621,tc_HOL_Obool),U_10615),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10618,tc_fun(U_10621,tc_HOL_Obool)),U_10624)),U_10622))),U_10625))
| ( ? [U_10613] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10621,tc_HOL_Obool)),hAPP(hAPP(U_10622,sK267(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615)),U_10613)),U_10625))
& hBOOL(hAPP(hAPP(c_member(U_10618),U_10613),U_10619)) )
& hBOOL(hAPP(hAPP(c_member(U_10615),sK267(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615)),U_10616)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10618,tc_HOL_Obool)),U_10624),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10618),U_10619),U_10620)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10615,tc_HOL_Obool)),U_10623),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10615),U_10616),U_10617)))
| ~ c_Equiv__Relations_Ocongruent2(U_10615,U_10618,tc_fun(U_10621,tc_HOL_Obool),U_10617,U_10620,U_10622)
| ~ c_Equiv__Relations_Oequiv(U_10618,U_10619,U_10620)
| ~ c_Equiv__Relations_Oequiv(U_10615,U_10616,U_10617) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_10614,sK267(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615))],[f_2730_2]) ).
fof(f_2730_4,plain,
! [U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10621,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10615,tc_fun(U_10621,tc_HOL_Obool)),U_10623),hAPP(hAPP(c_COMBB(tc_fun(U_10618,tc_fun(U_10621,tc_HOL_Obool)),tc_fun(U_10621,tc_HOL_Obool),U_10615),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10618,tc_fun(U_10621,tc_HOL_Obool)),U_10624)),U_10622))),U_10625))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10621,tc_HOL_Obool)),hAPP(hAPP(U_10622,sK267(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615)),sK268(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615))),U_10625))
& hBOOL(hAPP(hAPP(c_member(U_10618),sK268(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615)),U_10619))
& hBOOL(hAPP(hAPP(c_member(U_10615),sK267(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615)),U_10616)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10618,tc_HOL_Obool)),U_10624),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10618),U_10619),U_10620)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10615,tc_HOL_Obool)),U_10623),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10615),U_10616),U_10617)))
| ~ c_Equiv__Relations_Ocongruent2(U_10615,U_10618,tc_fun(U_10621,tc_HOL_Obool),U_10617,U_10620,U_10622)
| ~ c_Equiv__Relations_Oequiv(U_10618,U_10619,U_10620)
| ~ c_Equiv__Relations_Oequiv(U_10615,U_10616,U_10617) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_10613,sK268(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615))],[f_2730_3]) ).
fof(f_2730_5,plain,
( ! [U_10615,U_10616,U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623,U_10624,U_10625] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10621,tc_HOL_Obool)),hAPP(hAPP(U_10622,sK267(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615)),sK268(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615))),U_10625))
| ~ sP801(U_10615,U_10616,U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623,U_10624,U_10625) )
& ! [U_10615,U_10616,U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623,U_10624,U_10625] :
( hBOOL(hAPP(hAPP(c_member(U_10618),sK268(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615)),U_10619))
| ~ sP801(U_10615,U_10616,U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623,U_10624,U_10625) )
& ! [U_10615,U_10616,U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623,U_10624,U_10625] :
( hBOOL(hAPP(hAPP(c_member(U_10615),sK267(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615)),U_10616))
| ~ sP801(U_10615,U_10616,U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623,U_10624,U_10625) )
& ! [U_10615,U_10616,U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623,U_10624,U_10625] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10621,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10615,tc_fun(U_10621,tc_HOL_Obool)),U_10623),hAPP(hAPP(c_COMBB(tc_fun(U_10618,tc_fun(U_10621,tc_HOL_Obool)),tc_fun(U_10621,tc_HOL_Obool),U_10615),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10618,tc_fun(U_10621,tc_HOL_Obool)),U_10624)),U_10622))),U_10625))
| sP801(U_10615,U_10616,U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623,U_10624,U_10625)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10618,tc_HOL_Obool)),U_10624),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10618),U_10619),U_10620)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10615,tc_HOL_Obool)),U_10623),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10615),U_10616),U_10617)))
| ~ c_Equiv__Relations_Ocongruent2(U_10615,U_10618,tc_fun(U_10621,tc_HOL_Obool),U_10617,U_10620,U_10622)
| ~ c_Equiv__Relations_Oequiv(U_10618,U_10619,U_10620)
| ~ c_Equiv__Relations_Oequiv(U_10615,U_10616,U_10617) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP801])],[f_2730_4]) ).
cnf(f_2730_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10621,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10615,tc_fun(U_10621,tc_HOL_Obool)),U_10623),hAPP(hAPP(c_COMBB(tc_fun(U_10618,tc_fun(U_10621,tc_HOL_Obool)),tc_fun(U_10621,tc_HOL_Obool),U_10615),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10618,tc_fun(U_10621,tc_HOL_Obool)),U_10624)),U_10622))),U_10625))
| sP801(U_10615,U_10616,U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623,U_10624,U_10625)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10618,tc_HOL_Obool)),U_10624),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10618),U_10619),U_10620)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10615,tc_HOL_Obool)),U_10623),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10615),U_10616),U_10617)))
| ~ c_Equiv__Relations_Ocongruent2(U_10615,U_10618,tc_fun(U_10621,tc_HOL_Obool),U_10617,U_10620,U_10622)
| ~ c_Equiv__Relations_Oequiv(U_10618,U_10619,U_10620)
| ~ c_Equiv__Relations_Oequiv(U_10615,U_10616,U_10617) ),
inference(clausify,[status(thm)],[f_2730_5]) ).
cnf(f_2730_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_10615),sK267(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615)),U_10616))
| ~ sP801(U_10615,U_10616,U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623,U_10624,U_10625) ),
inference(clausify,[status(thm)],[f_2730_5]) ).
cnf(f_2730_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_10618),sK268(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615)),U_10619))
| ~ sP801(U_10615,U_10616,U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623,U_10624,U_10625) ),
inference(clausify,[status(thm)],[f_2730_5]) ).
cnf(f_2730_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10621,tc_HOL_Obool)),hAPP(hAPP(U_10622,sK267(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615)),sK268(U_10625,U_10624,U_10623,U_10622,U_10621,U_10620,U_10619,U_10618,U_10617,U_10616,U_10615))),U_10625))
| ~ sP801(U_10615,U_10616,U_10617,U_10618,U_10619,U_10620,U_10621,U_10622,U_10623,U_10624,U_10625) ),
inference(clausify,[status(thm)],[f_2730_5]) ).
fof(f_2731_1,plain,
! [V_B_2,V_X_2,V_f_2,T_d,V_r_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
| ~ c_Equiv__Relations_Ocongruent(T_c,tc_fun(T_d,tc_HOL_Obool),V_r_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type]) ).
fof(f_2731_2,plain,
! [U_10633,U_10632,U_10631,U_10630,U_10629,U_10628,U_10627] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10630,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10627,tc_fun(U_10630,tc_HOL_Obool)),U_10632),U_10631)),U_10633))
| ? [U_10626] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10630,tc_HOL_Obool)),hAPP(U_10631,U_10626)),U_10633))
& hBOOL(hAPP(hAPP(c_member(U_10627),U_10626),U_10628)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10627,tc_HOL_Obool)),U_10632),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10627),U_10628),U_10629)))
| ~ c_Equiv__Relations_Ocongruent(U_10627,tc_fun(U_10630,tc_HOL_Obool),U_10629,U_10631)
| ~ c_Equiv__Relations_Oequiv(U_10627,U_10628,U_10629) ),
inference(variable_rename,[status(thm)],[f_2731_1]) ).
fof(f_2731_3,plain,
! [U_10633,U_10632,U_10631,U_10630,U_10629,U_10628,U_10627] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10630,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10627,tc_fun(U_10630,tc_HOL_Obool)),U_10632),U_10631)),U_10633))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10630,tc_HOL_Obool)),hAPP(U_10631,sK269(U_10633,U_10632,U_10631,U_10630,U_10629,U_10628,U_10627))),U_10633))
& hBOOL(hAPP(hAPP(c_member(U_10627),sK269(U_10633,U_10632,U_10631,U_10630,U_10629,U_10628,U_10627)),U_10628)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10627,tc_HOL_Obool)),U_10632),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10627),U_10628),U_10629)))
| ~ c_Equiv__Relations_Ocongruent(U_10627,tc_fun(U_10630,tc_HOL_Obool),U_10629,U_10631)
| ~ c_Equiv__Relations_Oequiv(U_10627,U_10628,U_10629) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_10626,sK269(U_10633,U_10632,U_10631,U_10630,U_10629,U_10628,U_10627))],[f_2731_2]) ).
fof(f_2731_4,plain,
( ! [U_10627,U_10633,U_10630,U_10632,U_10631,U_10628,U_10629] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10630,tc_HOL_Obool)),hAPP(U_10631,sK269(U_10633,U_10632,U_10631,U_10630,U_10629,U_10628,U_10627))),U_10633))
| ~ sP802(U_10627,U_10633,U_10630,U_10632,U_10631,U_10628,U_10629) )
& ! [U_10627,U_10633,U_10630,U_10632,U_10631,U_10628,U_10629] :
( hBOOL(hAPP(hAPP(c_member(U_10627),sK269(U_10633,U_10632,U_10631,U_10630,U_10629,U_10628,U_10627)),U_10628))
| ~ sP802(U_10627,U_10633,U_10630,U_10632,U_10631,U_10628,U_10629) )
& ! [U_10627,U_10633,U_10630,U_10632,U_10631,U_10628,U_10629] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10630,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10627,tc_fun(U_10630,tc_HOL_Obool)),U_10632),U_10631)),U_10633))
| sP802(U_10627,U_10633,U_10630,U_10632,U_10631,U_10628,U_10629)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10627,tc_HOL_Obool)),U_10632),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10627),U_10628),U_10629)))
| ~ c_Equiv__Relations_Ocongruent(U_10627,tc_fun(U_10630,tc_HOL_Obool),U_10629,U_10631)
| ~ c_Equiv__Relations_Oequiv(U_10627,U_10628,U_10629) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP802])],[f_2731_3]) ).
cnf(f_2731_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10630,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10627,tc_fun(U_10630,tc_HOL_Obool)),U_10632),U_10631)),U_10633))
| sP802(U_10627,U_10633,U_10630,U_10632,U_10631,U_10628,U_10629)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10627,tc_HOL_Obool)),U_10632),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10627),U_10628),U_10629)))
| ~ c_Equiv__Relations_Ocongruent(U_10627,tc_fun(U_10630,tc_HOL_Obool),U_10629,U_10631)
| ~ c_Equiv__Relations_Oequiv(U_10627,U_10628,U_10629) ),
inference(clausify,[status(thm)],[f_2731_4]) ).
cnf(f_2731_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10627),sK269(U_10633,U_10632,U_10631,U_10630,U_10629,U_10628,U_10627)),U_10628))
| ~ sP802(U_10627,U_10633,U_10630,U_10632,U_10631,U_10628,U_10629) ),
inference(clausify,[status(thm)],[f_2731_4]) ).
cnf(f_2731_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10630,tc_HOL_Obool)),hAPP(U_10631,sK269(U_10633,U_10632,U_10631,U_10630,U_10629,U_10628,U_10627))),U_10633))
| ~ sP802(U_10627,U_10633,U_10630,U_10632,U_10631,U_10628,U_10629) ),
inference(clausify,[status(thm)],[f_2731_4]) ).
fof(f_2732_1,plain,
! [V_f2_2,V_f1_2,T_c] : hAPP(c_Nat_Onat_Onat__rec(T_c,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_2732_2,plain,
! [U_10636,U_10635,U_10634] : hAPP(c_Nat_Onat_Onat__rec(U_10634,U_10635,U_10636),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10635,
inference(variable_rename,[status(thm)],[f_2732_1]) ).
fof(f_2732_3,plain,
! [U_10635,U_10634,U_10636] : hAPP(c_Nat_Onat_Onat__rec(U_10634,U_10635,U_10636),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10635,
inference(definitional_conversion,[status(esa)],[f_2732_2]) ).
cnf(f_2732_4,plain,
hAPP(c_Nat_Onat_Onat__rec(U_10634,U_10635,U_10636),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10635,
inference(clausify,[status(thm)],[f_2732_3]) ).
fof(f_2733_1,plain,
! [V_nat_2,V_f2_2,V_f1_2,T_c] : hAPP(c_Nat_Onat_Onat__rec(T_c,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_c,V_f1_2,V_f2_2),V_nat_2)),
inference(fof_nnf,[status(thm)],[fact_nat__rec__Suc]) ).
fof(f_2733_2,plain,
! [U_10640,U_10639,U_10638,U_10637] : hAPP(c_Nat_Onat_Onat__rec(U_10637,U_10638,U_10639),hAPP(c_Nat_OSuc,U_10640)) = hAPP(hAPP(U_10639,U_10640),hAPP(c_Nat_Onat_Onat__rec(U_10637,U_10638,U_10639),U_10640)),
inference(variable_rename,[status(thm)],[f_2733_1]) ).
fof(f_2733_3,plain,
! [U_10639,U_10640,U_10637,U_10638] : hAPP(c_Nat_Onat_Onat__rec(U_10637,U_10638,U_10639),hAPP(c_Nat_OSuc,U_10640)) = hAPP(hAPP(U_10639,U_10640),hAPP(c_Nat_Onat_Onat__rec(U_10637,U_10638,U_10639),U_10640)),
inference(definitional_conversion,[status(esa)],[f_2733_2]) ).
cnf(f_2733_4,plain,
hAPP(c_Nat_Onat_Onat__rec(U_10637,U_10638,U_10639),hAPP(c_Nat_OSuc,U_10640)) = hAPP(hAPP(U_10639,U_10640),hAPP(c_Nat_Onat_Onat__rec(U_10637,U_10638,U_10639),U_10640)),
inference(clausify,[status(thm)],[f_2733_3]) ).
fof(f_2734_1,plain,
! [V_x_2,T_c] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) = c_Groups_Ozero__class_Ozero(T_c)
| ~ c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c),V_x_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J]) ).
fof(f_2734_2,plain,
! [U_10642,U_10641] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_10641),U_10642) = c_Groups_Ozero__class_Ozero(U_10641)
| ~ c_Int_Oiszero(U_10641,hAPP(c_Int_Onumber__class_Onumber__of(U_10641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10642),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
& ( c_Int_Oiszero(U_10641,hAPP(c_Int_Onumber__class_Onumber__of(U_10641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10642),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_10641),U_10642) != c_Groups_Ozero__class_Ozero(U_10641) ) )
| ~ class_Int_Onumber__ring(U_10641) ),
inference(variable_rename,[status(thm)],[f_2734_1]) ).
fof(f_2734_3,plain,
( ! [U_10642,U_10641] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10641),U_10642) = c_Groups_Ozero__class_Ozero(U_10641)
| ~ c_Int_Oiszero(U_10641,hAPP(c_Int_Onumber__class_Onumber__of(U_10641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10642),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| ~ sP803(U_10642,U_10641) )
& ! [U_10642,U_10641] :
( c_Int_Oiszero(U_10641,hAPP(c_Int_Onumber__class_Onumber__of(U_10641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10642),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_10641),U_10642) != c_Groups_Ozero__class_Ozero(U_10641)
| ~ sP803(U_10642,U_10641) )
& ! [U_10642,U_10641] :
( sP803(U_10642,U_10641)
| ~ class_Int_Onumber__ring(U_10641) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP803])],[f_2734_2]) ).
cnf(f_2734_4,plain,
( sP803(U_10642,U_10641)
| ~ class_Int_Onumber__ring(U_10641) ),
inference(clausify,[status(thm)],[f_2734_3]) ).
cnf(f_2734_5,plain,
( c_Int_Oiszero(U_10641,hAPP(c_Int_Onumber__class_Onumber__of(U_10641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10642),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_10641),U_10642) != c_Groups_Ozero__class_Ozero(U_10641)
| ~ sP803(U_10642,U_10641) ),
inference(clausify,[status(thm)],[f_2734_3]) ).
cnf(f_2734_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10641),U_10642) = c_Groups_Ozero__class_Ozero(U_10641)
| ~ c_Int_Oiszero(U_10641,hAPP(c_Int_Onumber__class_Onumber__of(U_10641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10642),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| ~ sP803(U_10642,U_10641) ),
inference(clausify,[status(thm)],[f_2734_3]) ).
fof(f_2735_1,plain,
! [V_y_2,T_c] :
( ( ( c_Groups_Ozero__class_Ozero(T_c) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2)
| ~ c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c) != hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2) ) )
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J]) ).
fof(f_2735_2,plain,
! [U_10644,U_10643] :
( ( ( c_Groups_Ozero__class_Ozero(U_10643) = hAPP(c_Int_Onumber__class_Onumber__of(U_10643),U_10644)
| ~ c_Int_Oiszero(U_10643,hAPP(c_Int_Onumber__class_Onumber__of(U_10643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10644)))) )
& ( c_Int_Oiszero(U_10643,hAPP(c_Int_Onumber__class_Onumber__of(U_10643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10644))))
| c_Groups_Ozero__class_Ozero(U_10643) != hAPP(c_Int_Onumber__class_Onumber__of(U_10643),U_10644) ) )
| ~ class_Int_Onumber__ring(U_10643) ),
inference(variable_rename,[status(thm)],[f_2735_1]) ).
fof(f_2735_3,plain,
( ! [U_10644,U_10643] :
( c_Groups_Ozero__class_Ozero(U_10643) = hAPP(c_Int_Onumber__class_Onumber__of(U_10643),U_10644)
| ~ c_Int_Oiszero(U_10643,hAPP(c_Int_Onumber__class_Onumber__of(U_10643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10644))))
| ~ sP804(U_10644,U_10643) )
& ! [U_10644,U_10643] :
( c_Int_Oiszero(U_10643,hAPP(c_Int_Onumber__class_Onumber__of(U_10643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10644))))
| c_Groups_Ozero__class_Ozero(U_10643) != hAPP(c_Int_Onumber__class_Onumber__of(U_10643),U_10644)
| ~ sP804(U_10644,U_10643) )
& ! [U_10644,U_10643] :
( sP804(U_10644,U_10643)
| ~ class_Int_Onumber__ring(U_10643) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP804])],[f_2735_2]) ).
cnf(f_2735_4,plain,
( sP804(U_10644,U_10643)
| ~ class_Int_Onumber__ring(U_10643) ),
inference(clausify,[status(thm)],[f_2735_3]) ).
cnf(f_2735_5,plain,
( c_Int_Oiszero(U_10643,hAPP(c_Int_Onumber__class_Onumber__of(U_10643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10644))))
| c_Groups_Ozero__class_Ozero(U_10643) != hAPP(c_Int_Onumber__class_Onumber__of(U_10643),U_10644)
| ~ sP804(U_10644,U_10643) ),
inference(clausify,[status(thm)],[f_2735_3]) ).
cnf(f_2735_6,plain,
( c_Groups_Ozero__class_Ozero(U_10643) = hAPP(c_Int_Onumber__class_Onumber__of(U_10643),U_10644)
| ~ c_Int_Oiszero(U_10643,hAPP(c_Int_Onumber__class_Onumber__of(U_10643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10644))))
| ~ sP804(U_10644,U_10643) ),
inference(clausify,[status(thm)],[f_2735_3]) ).
fof(f_2736_1,plain,
! [V_v_2,V_w_2,T_c] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c)
| 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_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c,T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_c),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)))),c_COMBI(T_c)))
| ~ 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_c) ),
inference(fof_nnf,[status(thm)],[fact_power__number__of__odd__number__of]) ).
fof(f_2736_2,plain,
! [U_10647,U_10646,U_10645] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10645),hAPP(c_Int_Onumber__class_Onumber__of(U_10645),U_10647)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10646))) = c_Groups_Oone__class_Oone(U_10645)
| 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_10646))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10645),hAPP(c_Int_Onumber__class_Onumber__of(U_10645),U_10647)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10646))) = hAPP(hAPP(c_HOL_OLet(U_10645,U_10645),hAPP(hAPP(c_Power_Opower__class_Opower(U_10645),hAPP(c_Int_Onumber__class_Onumber__of(U_10645),U_10647)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10646))),hAPP(hAPP(c_COMBS(U_10645,U_10645,U_10645),hAPP(hAPP(c_COMBB(U_10645,tc_fun(U_10645,U_10645),U_10645),c_Groups_Otimes__class_Otimes(U_10645)),hAPP(c_Groups_Otimes__class_Otimes(U_10645),hAPP(c_Int_Onumber__class_Onumber__of(U_10645),U_10647)))),c_COMBI(U_10645)))
| ~ 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_10646))) ) )
| ~ class_Int_Onumber__ring(U_10645) ),
inference(variable_rename,[status(thm)],[f_2736_1]) ).
fof(f_2736_3,plain,
( ! [U_10646,U_10645,U_10647] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10645),hAPP(c_Int_Onumber__class_Onumber__of(U_10645),U_10647)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10646))) = c_Groups_Oone__class_Oone(U_10645)
| 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_10646)))
| ~ sP805(U_10646,U_10645,U_10647) )
& ! [U_10646,U_10645,U_10647] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10645),hAPP(c_Int_Onumber__class_Onumber__of(U_10645),U_10647)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10646))) = hAPP(hAPP(c_HOL_OLet(U_10645,U_10645),hAPP(hAPP(c_Power_Opower__class_Opower(U_10645),hAPP(c_Int_Onumber__class_Onumber__of(U_10645),U_10647)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10646))),hAPP(hAPP(c_COMBS(U_10645,U_10645,U_10645),hAPP(hAPP(c_COMBB(U_10645,tc_fun(U_10645,U_10645),U_10645),c_Groups_Otimes__class_Otimes(U_10645)),hAPP(c_Groups_Otimes__class_Otimes(U_10645),hAPP(c_Int_Onumber__class_Onumber__of(U_10645),U_10647)))),c_COMBI(U_10645)))
| ~ 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_10646)))
| ~ sP805(U_10646,U_10645,U_10647) )
& ! [U_10646,U_10645,U_10647] :
( sP805(U_10646,U_10645,U_10647)
| ~ class_Int_Onumber__ring(U_10645) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP805])],[f_2736_2]) ).
cnf(f_2736_4,plain,
( sP805(U_10646,U_10645,U_10647)
| ~ class_Int_Onumber__ring(U_10645) ),
inference(clausify,[status(thm)],[f_2736_3]) ).
cnf(f_2736_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10645),hAPP(c_Int_Onumber__class_Onumber__of(U_10645),U_10647)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10646))) = hAPP(hAPP(c_HOL_OLet(U_10645,U_10645),hAPP(hAPP(c_Power_Opower__class_Opower(U_10645),hAPP(c_Int_Onumber__class_Onumber__of(U_10645),U_10647)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10646))),hAPP(hAPP(c_COMBS(U_10645,U_10645,U_10645),hAPP(hAPP(c_COMBB(U_10645,tc_fun(U_10645,U_10645),U_10645),c_Groups_Otimes__class_Otimes(U_10645)),hAPP(c_Groups_Otimes__class_Otimes(U_10645),hAPP(c_Int_Onumber__class_Onumber__of(U_10645),U_10647)))),c_COMBI(U_10645)))
| ~ 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_10646)))
| ~ sP805(U_10646,U_10645,U_10647) ),
inference(clausify,[status(thm)],[f_2736_3]) ).
cnf(f_2736_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10645),hAPP(c_Int_Onumber__class_Onumber__of(U_10645),U_10647)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10646))) = c_Groups_Oone__class_Oone(U_10645)
| 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_10646)))
| ~ sP805(U_10646,U_10645,U_10647) ),
inference(clausify,[status(thm)],[f_2736_3]) ).
fof(f_2737_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_2737_2,plain,
! [U_10649,U_10648] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10649),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10648))) = 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_10648))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10649),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10648))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10649),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10648))),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_10649))),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_10648))) ) ),
inference(variable_rename,[status(thm)],[f_2737_1]) ).
fof(f_2737_3,plain,
( ! [U_10653,U_10651] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10653),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10651))) = 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_10651))) )
& ! [U_10652,U_10650] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10652),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10650))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10652),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10650))),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_10652))),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_10650))) ) ),
inference(miniscope,[status(thm)],[f_2737_2]) ).
fof(f_2737_4,plain,
( ! [U_10651,U_10653] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10653),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10651))) = 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_10651))) )
& ! [U_10650,U_10652] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10652),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10650))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10652),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10650))),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_10652))),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_10650))) ) ),
inference(definitional_conversion,[status(esa)],[f_2737_3]) ).
cnf(f_2737_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10652),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10650))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10652),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10650))),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_10652))),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_10650))) ),
inference(clausify,[status(thm)],[f_2737_4]) ).
cnf(f_2737_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10653),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10651))) = 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_10651))) ),
inference(clausify,[status(thm)],[f_2737_4]) ).
fof(f_2738_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_2738_2,plain,
! [U_10655,U_10654] :
( ~ c_Int_Oiszero(U_10654,hAPP(c_Int_Onumber__class_Onumber__of(U_10654),c_Int_OBit1(U_10655)))
| ~ class_Int_Oring__char__0(U_10654)
| ~ class_Int_Onumber__ring(U_10654) ),
inference(variable_rename,[status(thm)],[f_2738_1]) ).
fof(f_2738_3,plain,
! [U_10655,U_10654] :
( ~ c_Int_Oiszero(U_10654,hAPP(c_Int_Onumber__class_Onumber__of(U_10654),c_Int_OBit1(U_10655)))
| ~ class_Int_Oring__char__0(U_10654)
| ~ class_Int_Onumber__ring(U_10654) ),
inference(definitional_conversion,[status(esa)],[f_2738_2]) ).
cnf(f_2738_4,plain,
( ~ c_Int_Oiszero(U_10654,hAPP(c_Int_Onumber__class_Onumber__of(U_10654),c_Int_OBit1(U_10655)))
| ~ class_Int_Oring__char__0(U_10654)
| ~ class_Int_Onumber__ring(U_10654) ),
inference(clausify,[status(thm)],[f_2738_3]) ).
fof(f_2739_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_2739_2,plain,
! [U_10657,U_10656] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10656)),c_Int_OBit1(U_10657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10656),U_10657)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10656),U_10657))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10656)),c_Int_OBit1(U_10657))) ) ),
inference(variable_rename,[status(thm)],[f_2739_1]) ).
fof(f_2739_3,plain,
( ! [U_10661,U_10659] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10659)),c_Int_OBit1(U_10661)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10659),U_10661)) )
& ! [U_10660,U_10658] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10658),U_10660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10658)),c_Int_OBit1(U_10660))) ) ),
inference(miniscope,[status(thm)],[f_2739_2]) ).
fof(f_2739_4,plain,
( ! [U_10659,U_10661] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10659)),c_Int_OBit1(U_10661)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10659),U_10661)) )
& ! [U_10660,U_10658] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10658),U_10660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10658)),c_Int_OBit1(U_10660))) ) ),
inference(definitional_conversion,[status(esa)],[f_2739_3]) ).
cnf(f_2739_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10658),U_10660))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10658)),c_Int_OBit1(U_10660))) ),
inference(clausify,[status(thm)],[f_2739_4]) ).
cnf(f_2739_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10659)),c_Int_OBit1(U_10661)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10659),U_10661)) ),
inference(clausify,[status(thm)],[f_2739_4]) ).
fof(f_2740_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_2740_2,plain,
! [U_10663,U_10662] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10662)),c_Int_OBit1(U_10663)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10662),U_10663)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10662),U_10663))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10662)),c_Int_OBit1(U_10663))) ) ),
inference(variable_rename,[status(thm)],[f_2740_1]) ).
fof(f_2740_3,plain,
( ! [U_10667,U_10665] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10665)),c_Int_OBit1(U_10667)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10665),U_10667)) )
& ! [U_10666,U_10664] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10664),U_10666))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10664)),c_Int_OBit1(U_10666))) ) ),
inference(miniscope,[status(thm)],[f_2740_2]) ).
fof(f_2740_4,plain,
( ! [U_10665,U_10667] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10665)),c_Int_OBit1(U_10667)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10665),U_10667)) )
& ! [U_10666,U_10664] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10664),U_10666))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10664)),c_Int_OBit1(U_10666))) ) ),
inference(definitional_conversion,[status(esa)],[f_2740_3]) ).
cnf(f_2740_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10664),U_10666))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10664)),c_Int_OBit1(U_10666))) ),
inference(clausify,[status(thm)],[f_2740_4]) ).
cnf(f_2740_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10665)),c_Int_OBit1(U_10667)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10665),U_10667)) ),
inference(clausify,[status(thm)],[f_2740_4]) ).
fof(f_2741_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_2741_2,plain,
! [U_10669,U_10668] :
( ( c_Int_OBit1(U_10668) = c_Int_OBit1(U_10669)
| U_10668 != U_10669 )
& ( U_10668 = U_10669
| c_Int_OBit1(U_10668) != c_Int_OBit1(U_10669) ) ),
inference(variable_rename,[status(thm)],[f_2741_1]) ).
fof(f_2741_3,plain,
( ! [U_10673,U_10671] :
( c_Int_OBit1(U_10671) = c_Int_OBit1(U_10673)
| U_10671 != U_10673 )
& ! [U_10672,U_10670] :
( U_10670 = U_10672
| c_Int_OBit1(U_10670) != c_Int_OBit1(U_10672) ) ),
inference(miniscope,[status(thm)],[f_2741_2]) ).
fof(f_2741_4,plain,
( ! [U_10671,U_10673] :
( c_Int_OBit1(U_10671) = c_Int_OBit1(U_10673)
| U_10671 != U_10673 )
& ! [U_10670,U_10672] :
( U_10670 = U_10672
| c_Int_OBit1(U_10670) != c_Int_OBit1(U_10672) ) ),
inference(definitional_conversion,[status(esa)],[f_2741_3]) ).
cnf(f_2741_5,plain,
( U_10670 = U_10672
| c_Int_OBit1(U_10670) != c_Int_OBit1(U_10672) ),
inference(clausify,[status(thm)],[f_2741_4]) ).
cnf(f_2741_6,plain,
( c_Int_OBit1(U_10671) = c_Int_OBit1(U_10673)
| U_10671 != U_10673 ),
inference(clausify,[status(thm)],[f_2741_4]) ).
fof(f_2742_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_2742_2,plain,
! [U_10675,U_10674] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10674)),c_Int_OBit1(U_10675)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10674),U_10675)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10674),U_10675))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10674)),c_Int_OBit1(U_10675))) ) ),
inference(variable_rename,[status(thm)],[f_2742_1]) ).
fof(f_2742_3,plain,
( ! [U_10679,U_10677] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10677)),c_Int_OBit1(U_10679)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10677),U_10679)) )
& ! [U_10678,U_10676] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10676),U_10678))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10676)),c_Int_OBit1(U_10678))) ) ),
inference(miniscope,[status(thm)],[f_2742_2]) ).
fof(f_2742_4,plain,
( ! [U_10677,U_10679] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10677)),c_Int_OBit1(U_10679)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10677),U_10679)) )
& ! [U_10678,U_10676] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10676),U_10678))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10676)),c_Int_OBit1(U_10678))) ) ),
inference(definitional_conversion,[status(esa)],[f_2742_3]) ).
cnf(f_2742_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10676),U_10678))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10676)),c_Int_OBit1(U_10678))) ),
inference(clausify,[status(thm)],[f_2742_4]) ).
cnf(f_2742_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10677)),c_Int_OBit1(U_10679)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10677),U_10679)) ),
inference(clausify,[status(thm)],[f_2742_4]) ).
fof(f_2743_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_2743_2,plain,
! [U_10681,U_10680] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10680)),c_Int_OBit1(U_10681)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10680),U_10681)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10680),U_10681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10680)),c_Int_OBit1(U_10681))) ) ),
inference(variable_rename,[status(thm)],[f_2743_1]) ).
fof(f_2743_3,plain,
( ! [U_10685,U_10683] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10683)),c_Int_OBit1(U_10685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10683),U_10685)) )
& ! [U_10684,U_10682] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10682),U_10684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10682)),c_Int_OBit1(U_10684))) ) ),
inference(miniscope,[status(thm)],[f_2743_2]) ).
fof(f_2743_4,plain,
( ! [U_10683,U_10685] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10683)),c_Int_OBit1(U_10685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10683),U_10685)) )
& ! [U_10684,U_10682] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10682),U_10684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10682)),c_Int_OBit1(U_10684))) ) ),
inference(definitional_conversion,[status(esa)],[f_2743_3]) ).
cnf(f_2743_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10682),U_10684))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10682)),c_Int_OBit1(U_10684))) ),
inference(clausify,[status(thm)],[f_2743_4]) ).
cnf(f_2743_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10683)),c_Int_OBit1(U_10685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10683),U_10685)) ),
inference(clausify,[status(thm)],[f_2743_4]) ).
fof(f_2744_1,plain,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).
fof(f_2744_2,plain,
! [U_10686] : c_Int_OBit1(U_10686) != c_Int_OPls,
inference(variable_rename,[status(thm)],[f_2744_1]) ).
fof(f_2744_3,plain,
! [U_10686] : c_Int_OBit1(U_10686) != c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_2744_2]) ).
cnf(f_2744_4,plain,
c_Int_OBit1(U_10686) != c_Int_OPls,
inference(clausify,[status(thm)],[f_2744_3]) ).
fof(f_2745_1,plain,
! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).
fof(f_2745_2,plain,
! [U_10687] : c_Int_OPls != c_Int_OBit1(U_10687),
inference(variable_rename,[status(thm)],[f_2745_1]) ).
fof(f_2745_3,plain,
! [U_10687] : c_Int_OPls != c_Int_OBit1(U_10687),
inference(definitional_conversion,[status(esa)],[f_2745_2]) ).
cnf(f_2745_4,plain,
c_Int_OPls != c_Int_OBit1(U_10687),
inference(clausify,[status(thm)],[f_2745_3]) ).
fof(f_2746_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_2746_2,plain,
! [U_10688] :
( ~ c_Int_Oiszero(U_10688,hAPP(c_Int_Onumber__class_Onumber__of(U_10688),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_10688) ),
inference(variable_rename,[status(thm)],[f_2746_1]) ).
fof(f_2746_3,plain,
! [U_10688] :
( ~ c_Int_Oiszero(U_10688,hAPP(c_Int_Onumber__class_Onumber__of(U_10688),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_10688) ),
inference(definitional_conversion,[status(esa)],[f_2746_2]) ).
cnf(f_2746_4,plain,
( ~ c_Int_Oiszero(U_10688,hAPP(c_Int_Onumber__class_Onumber__of(U_10688),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_10688) ),
inference(clausify,[status(thm)],[f_2746_3]) ).
fof(f_2747_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_2747_2,plain,
! [U_10689] :
( c_Int_Oiszero(U_10689,c_Groups_Ozero__class_Ozero(U_10689))
| ~ class_Rings_Osemiring__1(U_10689) ),
inference(variable_rename,[status(thm)],[f_2747_1]) ).
fof(f_2747_3,plain,
! [U_10689] :
( c_Int_Oiszero(U_10689,c_Groups_Ozero__class_Ozero(U_10689))
| ~ class_Rings_Osemiring__1(U_10689) ),
inference(definitional_conversion,[status(esa)],[f_2747_2]) ).
cnf(f_2747_4,plain,
( c_Int_Oiszero(U_10689,c_Groups_Ozero__class_Ozero(U_10689))
| ~ class_Rings_Osemiring__1(U_10689) ),
inference(clausify,[status(thm)],[f_2747_3]) ).
fof(f_2748_1,plain,
! [V_z_2,T_c] :
( ( ( c_Int_Oiszero(T_c,V_z_2)
| V_z_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_z_2 = c_Groups_Ozero__class_Ozero(T_c)
| ~ c_Int_Oiszero(T_c,V_z_2) ) )
| ~ class_Rings_Osemiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_iszero__def]) ).
fof(f_2748_2,plain,
! [U_10691,U_10690] :
( ( ( c_Int_Oiszero(U_10690,U_10691)
| U_10691 != c_Groups_Ozero__class_Ozero(U_10690) )
& ( U_10691 = c_Groups_Ozero__class_Ozero(U_10690)
| ~ c_Int_Oiszero(U_10690,U_10691) ) )
| ~ class_Rings_Osemiring__1(U_10690) ),
inference(variable_rename,[status(thm)],[f_2748_1]) ).
fof(f_2748_3,plain,
( ! [U_10690,U_10691] :
( c_Int_Oiszero(U_10690,U_10691)
| U_10691 != c_Groups_Ozero__class_Ozero(U_10690)
| ~ sP806(U_10690,U_10691) )
& ! [U_10690,U_10691] :
( U_10691 = c_Groups_Ozero__class_Ozero(U_10690)
| ~ c_Int_Oiszero(U_10690,U_10691)
| ~ sP806(U_10690,U_10691) )
& ! [U_10690,U_10691] :
( sP806(U_10690,U_10691)
| ~ class_Rings_Osemiring__1(U_10690) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP806])],[f_2748_2]) ).
cnf(f_2748_4,plain,
( sP806(U_10690,U_10691)
| ~ class_Rings_Osemiring__1(U_10690) ),
inference(clausify,[status(thm)],[f_2748_3]) ).
cnf(f_2748_5,plain,
( U_10691 = c_Groups_Ozero__class_Ozero(U_10690)
| ~ c_Int_Oiszero(U_10690,U_10691)
| ~ sP806(U_10690,U_10691) ),
inference(clausify,[status(thm)],[f_2748_3]) ).
cnf(f_2748_6,plain,
( c_Int_Oiszero(U_10690,U_10691)
| U_10691 != c_Groups_Ozero__class_Ozero(U_10690)
| ~ sP806(U_10690,U_10691) ),
inference(clausify,[status(thm)],[f_2748_3]) ).
fof(f_2749_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_2749_2,plain,
! [U_10692] :
( ~ c_Int_Oiszero(U_10692,c_Groups_Oone__class_Oone(U_10692))
| ~ class_Rings_Osemiring__1(U_10692) ),
inference(variable_rename,[status(thm)],[f_2749_1]) ).
fof(f_2749_3,plain,
! [U_10692] :
( ~ c_Int_Oiszero(U_10692,c_Groups_Oone__class_Oone(U_10692))
| ~ class_Rings_Osemiring__1(U_10692) ),
inference(definitional_conversion,[status(esa)],[f_2749_2]) ).
cnf(f_2749_4,plain,
( ~ c_Int_Oiszero(U_10692,c_Groups_Oone__class_Oone(U_10692))
| ~ class_Rings_Osemiring__1(U_10692) ),
inference(clausify,[status(thm)],[f_2749_3]) ).
fof(f_2750_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_2750_2,plain,
! [U_10693] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10693)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10693),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10693),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10693)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_2750_1]) ).
fof(f_2750_3,plain,
( ! [U_10695] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10695)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10695),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_10694] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10694),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10694)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_2750_2]) ).
fof(f_2750_4,plain,
( ! [U_10695] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10695)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10695),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_10694] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10694),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10694)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_2750_3]) ).
cnf(f_2750_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10694),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10694)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2750_4]) ).
cnf(f_2750_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10695)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10695),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2750_4]) ).
fof(f_2751_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_2751_2,plain,
! [U_10696] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10696)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10696)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10696))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10696))) ) ),
inference(variable_rename,[status(thm)],[f_2751_1]) ).
fof(f_2751_3,plain,
( ! [U_10698] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10698)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10698)) )
& ! [U_10697] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10697))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10697))) ) ),
inference(miniscope,[status(thm)],[f_2751_2]) ).
fof(f_2751_4,plain,
( ! [U_10698] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10698)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10698)) )
& ! [U_10697] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10697))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10697))) ) ),
inference(definitional_conversion,[status(esa)],[f_2751_3]) ).
cnf(f_2751_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10697))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10697))) ),
inference(clausify,[status(thm)],[f_2751_4]) ).
cnf(f_2751_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10698)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10698)) ),
inference(clausify,[status(thm)],[f_2751_4]) ).
fof(f_2752_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_2752_2,plain,
! [U_10699] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10699)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10699),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10699),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10699)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2752_1]) ).
fof(f_2752_3,plain,
( ! [U_10701] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10701)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10701),c_Int_OPls)) )
& ! [U_10700] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10700),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10700)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2752_2]) ).
fof(f_2752_4,plain,
( ! [U_10701] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10701)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10701),c_Int_OPls)) )
& ! [U_10700] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10700),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10700)),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2752_3]) ).
cnf(f_2752_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10700),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10700)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2752_4]) ).
cnf(f_2752_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10701)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10701),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2752_4]) ).
fof(f_2753_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_2753_2,plain,
! [U_10702] : c_Int_OBit1(U_10702) = 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_10702)),U_10702),
inference(variable_rename,[status(thm)],[f_2753_1]) ).
fof(f_2753_3,plain,
! [U_10702] : c_Int_OBit1(U_10702) = 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_10702)),U_10702),
inference(definitional_conversion,[status(esa)],[f_2753_2]) ).
cnf(f_2753_4,plain,
c_Int_OBit1(U_10702) = 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_10702)),U_10702),
inference(clausify,[status(thm)],[f_2753_3]) ).
fof(f_2754_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_2754_2,plain,
! [U_10703] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10703))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10703))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10703)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10703)))) ) ),
inference(variable_rename,[status(thm)],[f_2754_1]) ).
fof(f_2754_3,plain,
( ! [U_10705] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10705))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10705))) )
& ! [U_10704] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10704)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10704)))) ) ),
inference(miniscope,[status(thm)],[f_2754_2]) ).
fof(f_2754_4,plain,
( ! [U_10705] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10705))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10705))) )
& ! [U_10704] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10704)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10704)))) ) ),
inference(definitional_conversion,[status(esa)],[f_2754_3]) ).
cnf(f_2754_5,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10704)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10704)))) ),
inference(clausify,[status(thm)],[f_2754_4]) ).
cnf(f_2754_6,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10705))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10705))) ),
inference(clausify,[status(thm)],[f_2754_4]) ).
fof(f_2755_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_2755_2,plain,
! [U_10706] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_10706)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10706))),
inference(variable_rename,[status(thm)],[f_2755_1]) ).
fof(f_2755_3,plain,
! [U_10706] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_10706)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10706))),
inference(definitional_conversion,[status(esa)],[f_2755_2]) ).
cnf(f_2755_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_10706)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10706))),
inference(clausify,[status(thm)],[f_2755_3]) ).
fof(f_2756_1,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_succ__Pls]) ).
fof(f_2756_2,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(definitional_conversion,[status(esa)],[f_2756_1]) ).
cnf(f_2756_3,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(clausify,[status(thm)],[f_2756_2]) ).
fof(f_2757_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_2757_2,plain,
! [U_10708,U_10707] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10707),c_Int_OBit1(U_10708)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10707),c_Groups_Oone__class_Oone(U_10707)),hAPP(c_Int_Onumber__class_Onumber__of(U_10707),U_10708))),hAPP(c_Int_Onumber__class_Onumber__of(U_10707),U_10708))
| ~ class_Int_Onumber__ring(U_10707) ),
inference(variable_rename,[status(thm)],[f_2757_1]) ).
fof(f_2757_3,plain,
! [U_10707,U_10708] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10707),c_Int_OBit1(U_10708)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10707),c_Groups_Oone__class_Oone(U_10707)),hAPP(c_Int_Onumber__class_Onumber__of(U_10707),U_10708))),hAPP(c_Int_Onumber__class_Onumber__of(U_10707),U_10708))
| ~ class_Int_Onumber__ring(U_10707) ),
inference(definitional_conversion,[status(esa)],[f_2757_2]) ).
cnf(f_2757_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10707),c_Int_OBit1(U_10708)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10707),c_Groups_Oone__class_Oone(U_10707)),hAPP(c_Int_Onumber__class_Onumber__of(U_10707),U_10708))),hAPP(c_Int_Onumber__class_Onumber__of(U_10707),U_10708))
| ~ class_Int_Onumber__ring(U_10707) ),
inference(clausify,[status(thm)],[f_2757_3]) ).
fof(f_2758_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_2758_2,plain,
! [U_10710,U_10709] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10709),hAPP(c_Int_Onumber__class_Onumber__of(U_10709),c_Int_OBit1(c_Int_OPls))),U_10710) = U_10710
| ~ class_Int_Onumber__ring(U_10709) ),
inference(variable_rename,[status(thm)],[f_2758_1]) ).
fof(f_2758_3,plain,
! [U_10709,U_10710] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10709),hAPP(c_Int_Onumber__class_Onumber__of(U_10709),c_Int_OBit1(c_Int_OPls))),U_10710) = U_10710
| ~ class_Int_Onumber__ring(U_10709) ),
inference(definitional_conversion,[status(esa)],[f_2758_2]) ).
cnf(f_2758_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10709),hAPP(c_Int_Onumber__class_Onumber__of(U_10709),c_Int_OBit1(c_Int_OPls))),U_10710) = U_10710
| ~ class_Int_Onumber__ring(U_10709) ),
inference(clausify,[status(thm)],[f_2758_3]) ).
fof(f_2759_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_2759_2,plain,
! [U_10712,U_10711] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10711),U_10712),hAPP(c_Int_Onumber__class_Onumber__of(U_10711),c_Int_OBit1(c_Int_OPls))) = U_10712
| ~ class_Int_Onumber__ring(U_10711) ),
inference(variable_rename,[status(thm)],[f_2759_1]) ).
fof(f_2759_3,plain,
! [U_10711,U_10712] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10711),U_10712),hAPP(c_Int_Onumber__class_Onumber__of(U_10711),c_Int_OBit1(c_Int_OPls))) = U_10712
| ~ class_Int_Onumber__ring(U_10711) ),
inference(definitional_conversion,[status(esa)],[f_2759_2]) ).
cnf(f_2759_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10711),U_10712),hAPP(c_Int_Onumber__class_Onumber__of(U_10711),c_Int_OBit1(c_Int_OPls))) = U_10712
| ~ class_Int_Onumber__ring(U_10711) ),
inference(clausify,[status(thm)],[f_2759_3]) ).
fof(f_2760_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_2760_2,plain,
! [U_10713] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10713),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_10713)
| ~ class_Int_Onumber__ring(U_10713) ),
inference(variable_rename,[status(thm)],[f_2760_1]) ).
fof(f_2760_3,plain,
! [U_10713] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10713),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_10713)
| ~ class_Int_Onumber__ring(U_10713) ),
inference(definitional_conversion,[status(esa)],[f_2760_2]) ).
cnf(f_2760_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10713),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_10713)
| ~ class_Int_Onumber__ring(U_10713) ),
inference(clausify,[status(thm)],[f_2760_3]) ).
fof(f_2761_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_2761_2,plain,
! [U_10714] :
( c_Groups_Oone__class_Oone(U_10714) = hAPP(c_Int_Onumber__class_Onumber__of(U_10714),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_10714) ),
inference(variable_rename,[status(thm)],[f_2761_1]) ).
fof(f_2761_3,plain,
! [U_10714] :
( c_Groups_Oone__class_Oone(U_10714) = hAPP(c_Int_Onumber__class_Onumber__of(U_10714),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_10714) ),
inference(definitional_conversion,[status(esa)],[f_2761_2]) ).
cnf(f_2761_4,plain,
( c_Groups_Oone__class_Oone(U_10714) = hAPP(c_Int_Onumber__class_Onumber__of(U_10714),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_10714) ),
inference(clausify,[status(thm)],[f_2761_3]) ).
fof(f_2762_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_2762_2,plain,
! [U_10715] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10715)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10715)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10715))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10715))) ) ),
inference(variable_rename,[status(thm)],[f_2762_1]) ).
fof(f_2762_3,plain,
( ! [U_10717] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10717)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10717)) )
& ! [U_10716] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10716))) ) ),
inference(miniscope,[status(thm)],[f_2762_2]) ).
fof(f_2762_4,plain,
( ! [U_10717] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10717)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10717)) )
& ! [U_10716] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10716))) ) ),
inference(definitional_conversion,[status(esa)],[f_2762_3]) ).
cnf(f_2762_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10716))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10716))) ),
inference(clausify,[status(thm)],[f_2762_4]) ).
cnf(f_2762_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_10717)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10717)) ),
inference(clausify,[status(thm)],[f_2762_4]) ).
fof(f_2763_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_2763_2,plain,
! [U_10718] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10718)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10718),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10718),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10718)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2763_1]) ).
fof(f_2763_3,plain,
( ! [U_10720] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10720)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10720),c_Int_OPls)) )
& ! [U_10719] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10719),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10719)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2763_2]) ).
fof(f_2763_4,plain,
( ! [U_10720] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10720)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10720),c_Int_OPls)) )
& ! [U_10719] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10719),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10719)),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2763_3]) ).
cnf(f_2763_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10719),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10719)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2763_4]) ).
cnf(f_2763_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10720)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10720),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2763_4]) ).
fof(f_2764_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_2764_2,plain,
! [U_10722,U_10721] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10721),U_10722),hAPP(c_Int_Onumber__class_Onumber__of(U_10721),c_Int_OBit1(c_Int_OPls))) = U_10722
| ~ class_Int_Onumber__ring(U_10721)
| ~ class_Fields_Ofield(U_10721) ),
inference(variable_rename,[status(thm)],[f_2764_1]) ).
fof(f_2764_3,plain,
! [U_10721,U_10722] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10721),U_10722),hAPP(c_Int_Onumber__class_Onumber__of(U_10721),c_Int_OBit1(c_Int_OPls))) = U_10722
| ~ class_Int_Onumber__ring(U_10721)
| ~ class_Fields_Ofield(U_10721) ),
inference(definitional_conversion,[status(esa)],[f_2764_2]) ).
cnf(f_2764_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10721),U_10722),hAPP(c_Int_Onumber__class_Onumber__of(U_10721),c_Int_OBit1(c_Int_OPls))) = U_10722
| ~ class_Int_Onumber__ring(U_10721)
| ~ class_Fields_Ofield(U_10721) ),
inference(clausify,[status(thm)],[f_2764_3]) ).
fof(f_2765_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_2765_2,plain,
! [U_10724,U_10723] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10723),U_10724),hAPP(c_Int_Onumber__class_Onumber__of(U_10723),c_Int_OBit1(c_Int_OPls))) = U_10724
| ~ class_Int_Onumber__ring(U_10723)
| ~ class_Fields_Ofield(U_10723) ),
inference(variable_rename,[status(thm)],[f_2765_1]) ).
fof(f_2765_3,plain,
! [U_10723,U_10724] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10723),U_10724),hAPP(c_Int_Onumber__class_Onumber__of(U_10723),c_Int_OBit1(c_Int_OPls))) = U_10724
| ~ class_Int_Onumber__ring(U_10723)
| ~ class_Fields_Ofield(U_10723) ),
inference(definitional_conversion,[status(esa)],[f_2765_2]) ).
cnf(f_2765_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10723),U_10724),hAPP(c_Int_Onumber__class_Onumber__of(U_10723),c_Int_OBit1(c_Int_OPls))) = U_10724
| ~ class_Int_Onumber__ring(U_10723)
| ~ class_Fields_Ofield(U_10723) ),
inference(clausify,[status(thm)],[f_2765_3]) ).
fof(f_2766_1,plain,
! [V_y_2,T_c] :
( ( ( c_Groups_Oone__class_Oone(T_c) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2)
| ~ c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c) != hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2) ) )
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J]) ).
fof(f_2766_2,plain,
! [U_10726,U_10725] :
( ( ( c_Groups_Oone__class_Oone(U_10725) = hAPP(c_Int_Onumber__class_Onumber__of(U_10725),U_10726)
| ~ c_Int_Oiszero(U_10725,hAPP(c_Int_Onumber__class_Onumber__of(U_10725),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_10726)))) )
& ( c_Int_Oiszero(U_10725,hAPP(c_Int_Onumber__class_Onumber__of(U_10725),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_10726))))
| c_Groups_Oone__class_Oone(U_10725) != hAPP(c_Int_Onumber__class_Onumber__of(U_10725),U_10726) ) )
| ~ class_Int_Onumber__ring(U_10725) ),
inference(variable_rename,[status(thm)],[f_2766_1]) ).
fof(f_2766_3,plain,
( ! [U_10725,U_10726] :
( c_Groups_Oone__class_Oone(U_10725) = hAPP(c_Int_Onumber__class_Onumber__of(U_10725),U_10726)
| ~ c_Int_Oiszero(U_10725,hAPP(c_Int_Onumber__class_Onumber__of(U_10725),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_10726))))
| ~ sP807(U_10725,U_10726) )
& ! [U_10725,U_10726] :
( c_Int_Oiszero(U_10725,hAPP(c_Int_Onumber__class_Onumber__of(U_10725),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_10726))))
| c_Groups_Oone__class_Oone(U_10725) != hAPP(c_Int_Onumber__class_Onumber__of(U_10725),U_10726)
| ~ sP807(U_10725,U_10726) )
& ! [U_10725,U_10726] :
( sP807(U_10725,U_10726)
| ~ class_Int_Onumber__ring(U_10725) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP807])],[f_2766_2]) ).
cnf(f_2766_4,plain,
( sP807(U_10725,U_10726)
| ~ class_Int_Onumber__ring(U_10725) ),
inference(clausify,[status(thm)],[f_2766_3]) ).
cnf(f_2766_5,plain,
( c_Int_Oiszero(U_10725,hAPP(c_Int_Onumber__class_Onumber__of(U_10725),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_10726))))
| c_Groups_Oone__class_Oone(U_10725) != hAPP(c_Int_Onumber__class_Onumber__of(U_10725),U_10726)
| ~ sP807(U_10725,U_10726) ),
inference(clausify,[status(thm)],[f_2766_3]) ).
cnf(f_2766_6,plain,
( c_Groups_Oone__class_Oone(U_10725) = hAPP(c_Int_Onumber__class_Onumber__of(U_10725),U_10726)
| ~ c_Int_Oiszero(U_10725,hAPP(c_Int_Onumber__class_Onumber__of(U_10725),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_10726))))
| ~ sP807(U_10725,U_10726) ),
inference(clausify,[status(thm)],[f_2766_3]) ).
fof(f_2767_1,plain,
! [V_x_2,T_c] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) = c_Groups_Oone__class_Oone(T_c)
| ~ c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c),V_x_2) != c_Groups_Oone__class_Oone(T_c) ) )
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J]) ).
fof(f_2767_2,plain,
! [U_10728,U_10727] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_10727),U_10728) = c_Groups_Oone__class_Oone(U_10727)
| ~ c_Int_Oiszero(U_10727,hAPP(c_Int_Onumber__class_Onumber__of(U_10727),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10728),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
& ( c_Int_Oiszero(U_10727,hAPP(c_Int_Onumber__class_Onumber__of(U_10727),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10728),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_10727),U_10728) != c_Groups_Oone__class_Oone(U_10727) ) )
| ~ class_Int_Onumber__ring(U_10727) ),
inference(variable_rename,[status(thm)],[f_2767_1]) ).
fof(f_2767_3,plain,
( ! [U_10728,U_10727] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10727),U_10728) = c_Groups_Oone__class_Oone(U_10727)
| ~ c_Int_Oiszero(U_10727,hAPP(c_Int_Onumber__class_Onumber__of(U_10727),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10728),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| ~ sP808(U_10728,U_10727) )
& ! [U_10728,U_10727] :
( c_Int_Oiszero(U_10727,hAPP(c_Int_Onumber__class_Onumber__of(U_10727),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10728),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_10727),U_10728) != c_Groups_Oone__class_Oone(U_10727)
| ~ sP808(U_10728,U_10727) )
& ! [U_10728,U_10727] :
( sP808(U_10728,U_10727)
| ~ class_Int_Onumber__ring(U_10727) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP808])],[f_2767_2]) ).
cnf(f_2767_4,plain,
( sP808(U_10728,U_10727)
| ~ class_Int_Onumber__ring(U_10727) ),
inference(clausify,[status(thm)],[f_2767_3]) ).
cnf(f_2767_5,plain,
( c_Int_Oiszero(U_10727,hAPP(c_Int_Onumber__class_Onumber__of(U_10727),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10728),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_10727),U_10728) != c_Groups_Oone__class_Oone(U_10727)
| ~ sP808(U_10728,U_10727) ),
inference(clausify,[status(thm)],[f_2767_3]) ).
cnf(f_2767_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10727),U_10728) = c_Groups_Oone__class_Oone(U_10727)
| ~ c_Int_Oiszero(U_10727,hAPP(c_Int_Onumber__class_Onumber__of(U_10727),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10728),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| ~ sP808(U_10728,U_10727) ),
inference(clausify,[status(thm)],[f_2767_3]) ).
fof(f_2768_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_2768_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_2768_1]) ).
cnf(f_2768_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_2768_2]) ).
fof(f_2769_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_2769_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_2769_1]) ).
cnf(f_2769_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_2769_2]) ).
fof(f_2770_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_2770_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_2770_1]) ).
cnf(f_2770_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_2770_2]) ).
fof(f_2771_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_2771_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_2771_1]) ).
cnf(f_2771_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_2771_2]) ).
fof(f_2772_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_2772_2,plain,
! [U_10729] :
( c_Int_Oiszero(U_10729,hAPP(c_Int_Onumber__class_Onumber__of(U_10729),c_Int_OPls))
| ~ class_Int_Onumber__ring(U_10729) ),
inference(variable_rename,[status(thm)],[f_2772_1]) ).
fof(f_2772_3,plain,
! [U_10729] :
( c_Int_Oiszero(U_10729,hAPP(c_Int_Onumber__class_Onumber__of(U_10729),c_Int_OPls))
| ~ class_Int_Onumber__ring(U_10729) ),
inference(definitional_conversion,[status(esa)],[f_2772_2]) ).
cnf(f_2772_4,plain,
( c_Int_Oiszero(U_10729,hAPP(c_Int_Onumber__class_Onumber__of(U_10729),c_Int_OPls))
| ~ class_Int_Onumber__ring(U_10729) ),
inference(clausify,[status(thm)],[f_2772_3]) ).
fof(f_2773_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_2773_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_2773_1]) ).
cnf(f_2773_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_2773_2]) ).
fof(f_2774_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_2774_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_2774_1]) ).
cnf(f_2774_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_2774_2]) ).
fof(f_2775_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_2775_2,plain,
! [U_10731,U_10730] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10730),U_10731),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_10730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10730),U_10731),U_10731)),U_10731)
| ~ class_Groups_Omonoid__mult(U_10730) ),
inference(variable_rename,[status(thm)],[f_2775_1]) ).
fof(f_2775_3,plain,
! [U_10730,U_10731] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10730),U_10731),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_10730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10730),U_10731),U_10731)),U_10731)
| ~ class_Groups_Omonoid__mult(U_10730) ),
inference(definitional_conversion,[status(esa)],[f_2775_2]) ).
cnf(f_2775_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10730),U_10731),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_10730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10730),U_10731),U_10731)),U_10731)
| ~ class_Groups_Omonoid__mult(U_10730) ),
inference(clausify,[status(thm)],[f_2775_3]) ).
fof(f_2776_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_2776_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_2776_1]) ).
cnf(f_2776_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_2776_2]) ).
fof(f_2777_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_2777_2,plain,
! [U_10732] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10732))) = 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_10732),
inference(variable_rename,[status(thm)],[f_2777_1]) ).
fof(f_2777_3,plain,
! [U_10732] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10732))) = 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_10732),
inference(definitional_conversion,[status(esa)],[f_2777_2]) ).
cnf(f_2777_4,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10732))) = 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_10732),
inference(clausify,[status(thm)],[f_2777_3]) ).
fof(f_2778_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_2778_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_2778_1]) ).
cnf(f_2778_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_2778_2]) ).
fof(f_2779_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_2779_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_2779_1]) ).
cnf(f_2779_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_2779_2]) ).
fof(f_2780_1,plain,
! [V_y_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Oone__class_Oone(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c),c_Groups_Oone__class_Oone(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2))) ) )
| ~ class_Rings_Olinordered__idom(T_c)
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I2_J]) ).
fof(f_2780_2,plain,
! [U_10734,U_10733] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10733),c_Groups_Oone__class_Oone(U_10733)),hAPP(c_Int_Onumber__class_Onumber__of(U_10733),U_10734)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10734)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10734))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10733),c_Groups_Oone__class_Oone(U_10733)),hAPP(c_Int_Onumber__class_Onumber__of(U_10733),U_10734))) ) )
| ~ class_Rings_Olinordered__idom(U_10733)
| ~ class_Int_Onumber__ring(U_10733) ),
inference(variable_rename,[status(thm)],[f_2780_1]) ).
fof(f_2780_3,plain,
( ! [U_10733,U_10734] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10733),c_Groups_Oone__class_Oone(U_10733)),hAPP(c_Int_Onumber__class_Onumber__of(U_10733),U_10734)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10734))
| ~ sP809(U_10733,U_10734) )
& ! [U_10733,U_10734] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10734))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10733),c_Groups_Oone__class_Oone(U_10733)),hAPP(c_Int_Onumber__class_Onumber__of(U_10733),U_10734)))
| ~ sP809(U_10733,U_10734) )
& ! [U_10733,U_10734] :
( sP809(U_10733,U_10734)
| ~ class_Rings_Olinordered__idom(U_10733)
| ~ class_Int_Onumber__ring(U_10733) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP809])],[f_2780_2]) ).
cnf(f_2780_4,plain,
( sP809(U_10733,U_10734)
| ~ class_Rings_Olinordered__idom(U_10733)
| ~ class_Int_Onumber__ring(U_10733) ),
inference(clausify,[status(thm)],[f_2780_3]) ).
cnf(f_2780_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10734))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10733),c_Groups_Oone__class_Oone(U_10733)),hAPP(c_Int_Onumber__class_Onumber__of(U_10733),U_10734)))
| ~ sP809(U_10733,U_10734) ),
inference(clausify,[status(thm)],[f_2780_3]) ).
cnf(f_2780_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10733),c_Groups_Oone__class_Oone(U_10733)),hAPP(c_Int_Onumber__class_Onumber__of(U_10733),U_10734)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10734))
| ~ sP809(U_10733,U_10734) ),
inference(clausify,[status(thm)],[f_2780_3]) ).
fof(f_2781_1,plain,
! [V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Oone__class_Oone(T_c)))
| ~ 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_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Oone__class_Oone(T_c))) ) )
| ~ class_Rings_Olinordered__idom(T_c)
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I4_J]) ).
fof(f_2781_2,plain,
! [U_10736,U_10735] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10735),hAPP(c_Int_Onumber__class_Onumber__of(U_10735),U_10736)),c_Groups_Oone__class_Oone(U_10735)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10736),c_Int_OBit1(c_Int_OPls))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10736),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10735),hAPP(c_Int_Onumber__class_Onumber__of(U_10735),U_10736)),c_Groups_Oone__class_Oone(U_10735))) ) )
| ~ class_Rings_Olinordered__idom(U_10735)
| ~ class_Int_Onumber__ring(U_10735) ),
inference(variable_rename,[status(thm)],[f_2781_1]) ).
fof(f_2781_3,plain,
( ! [U_10736,U_10735] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10735),hAPP(c_Int_Onumber__class_Onumber__of(U_10735),U_10736)),c_Groups_Oone__class_Oone(U_10735)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10736),c_Int_OBit1(c_Int_OPls)))
| ~ sP810(U_10736,U_10735) )
& ! [U_10736,U_10735] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10736),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10735),hAPP(c_Int_Onumber__class_Onumber__of(U_10735),U_10736)),c_Groups_Oone__class_Oone(U_10735)))
| ~ sP810(U_10736,U_10735) )
& ! [U_10736,U_10735] :
( sP810(U_10736,U_10735)
| ~ class_Rings_Olinordered__idom(U_10735)
| ~ class_Int_Onumber__ring(U_10735) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP810])],[f_2781_2]) ).
cnf(f_2781_4,plain,
( sP810(U_10736,U_10735)
| ~ class_Rings_Olinordered__idom(U_10735)
| ~ class_Int_Onumber__ring(U_10735) ),
inference(clausify,[status(thm)],[f_2781_3]) ).
cnf(f_2781_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10736),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10735),hAPP(c_Int_Onumber__class_Onumber__of(U_10735),U_10736)),c_Groups_Oone__class_Oone(U_10735)))
| ~ sP810(U_10736,U_10735) ),
inference(clausify,[status(thm)],[f_2781_3]) ).
cnf(f_2781_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10735),hAPP(c_Int_Onumber__class_Onumber__of(U_10735),U_10736)),c_Groups_Oone__class_Oone(U_10735)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10736),c_Int_OBit1(c_Int_OPls)))
| ~ sP810(U_10736,U_10735) ),
inference(clausify,[status(thm)],[f_2781_3]) ).
fof(f_2782_1,plain,
! [V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Oone__class_Oone(T_c)))
| ~ 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_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2)),c_Groups_Oone__class_Oone(T_c))) ) )
| ~ class_Rings_Olinordered__idom(T_c)
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I4_J]) ).
fof(f_2782_2,plain,
! [U_10738,U_10737] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10737),hAPP(c_Int_Onumber__class_Onumber__of(U_10737),U_10738)),c_Groups_Oone__class_Oone(U_10737)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10738),c_Int_OBit1(c_Int_OPls))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10738),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10737),hAPP(c_Int_Onumber__class_Onumber__of(U_10737),U_10738)),c_Groups_Oone__class_Oone(U_10737))) ) )
| ~ class_Rings_Olinordered__idom(U_10737)
| ~ class_Int_Onumber__ring(U_10737) ),
inference(variable_rename,[status(thm)],[f_2782_1]) ).
fof(f_2782_3,plain,
( ! [U_10737,U_10738] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10737),hAPP(c_Int_Onumber__class_Onumber__of(U_10737),U_10738)),c_Groups_Oone__class_Oone(U_10737)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10738),c_Int_OBit1(c_Int_OPls)))
| ~ sP811(U_10737,U_10738) )
& ! [U_10737,U_10738] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10738),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10737),hAPP(c_Int_Onumber__class_Onumber__of(U_10737),U_10738)),c_Groups_Oone__class_Oone(U_10737)))
| ~ sP811(U_10737,U_10738) )
& ! [U_10737,U_10738] :
( sP811(U_10737,U_10738)
| ~ class_Rings_Olinordered__idom(U_10737)
| ~ class_Int_Onumber__ring(U_10737) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP811])],[f_2782_2]) ).
cnf(f_2782_4,plain,
( sP811(U_10737,U_10738)
| ~ class_Rings_Olinordered__idom(U_10737)
| ~ class_Int_Onumber__ring(U_10737) ),
inference(clausify,[status(thm)],[f_2782_3]) ).
cnf(f_2782_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10738),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10737),hAPP(c_Int_Onumber__class_Onumber__of(U_10737),U_10738)),c_Groups_Oone__class_Oone(U_10737)))
| ~ sP811(U_10737,U_10738) ),
inference(clausify,[status(thm)],[f_2782_3]) ).
cnf(f_2782_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10737),hAPP(c_Int_Onumber__class_Onumber__of(U_10737),U_10738)),c_Groups_Oone__class_Oone(U_10737)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10738),c_Int_OBit1(c_Int_OPls)))
| ~ sP811(U_10737,U_10738) ),
inference(clausify,[status(thm)],[f_2782_3]) ).
fof(f_2783_1,plain,
! [V_y_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Oone__class_Oone(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c),c_Groups_Oone__class_Oone(T_c)),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2))) ) )
| ~ class_Rings_Olinordered__idom(T_c)
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I2_J]) ).
fof(f_2783_2,plain,
! [U_10740,U_10739] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10739),c_Groups_Oone__class_Oone(U_10739)),hAPP(c_Int_Onumber__class_Onumber__of(U_10739),U_10740)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10740)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10740))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10739),c_Groups_Oone__class_Oone(U_10739)),hAPP(c_Int_Onumber__class_Onumber__of(U_10739),U_10740))) ) )
| ~ class_Rings_Olinordered__idom(U_10739)
| ~ class_Int_Onumber__ring(U_10739) ),
inference(variable_rename,[status(thm)],[f_2783_1]) ).
fof(f_2783_3,plain,
( ! [U_10740,U_10739] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10739),c_Groups_Oone__class_Oone(U_10739)),hAPP(c_Int_Onumber__class_Onumber__of(U_10739),U_10740)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10740))
| ~ sP812(U_10740,U_10739) )
& ! [U_10740,U_10739] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10740))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10739),c_Groups_Oone__class_Oone(U_10739)),hAPP(c_Int_Onumber__class_Onumber__of(U_10739),U_10740)))
| ~ sP812(U_10740,U_10739) )
& ! [U_10740,U_10739] :
( sP812(U_10740,U_10739)
| ~ class_Rings_Olinordered__idom(U_10739)
| ~ class_Int_Onumber__ring(U_10739) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP812])],[f_2783_2]) ).
cnf(f_2783_4,plain,
( sP812(U_10740,U_10739)
| ~ class_Rings_Olinordered__idom(U_10739)
| ~ class_Int_Onumber__ring(U_10739) ),
inference(clausify,[status(thm)],[f_2783_3]) ).
cnf(f_2783_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10740))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10739),c_Groups_Oone__class_Oone(U_10739)),hAPP(c_Int_Onumber__class_Onumber__of(U_10739),U_10740)))
| ~ sP812(U_10740,U_10739) ),
inference(clausify,[status(thm)],[f_2783_3]) ).
cnf(f_2783_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10739),c_Groups_Oone__class_Oone(U_10739)),hAPP(c_Int_Onumber__class_Onumber__of(U_10739),U_10740)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10740))
| ~ sP812(U_10740,U_10739) ),
inference(clausify,[status(thm)],[f_2783_3]) ).
fof(f_2784_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_2784_2,plain,
! [U_10742,U_10741] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10741),c_Groups_Oone__class_Oone(U_10741)),hAPP(c_Int_Onumber__class_Onumber__of(U_10741),U_10742)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10741),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10742))
| ~ class_Int_Onumber__ring(U_10741) ),
inference(variable_rename,[status(thm)],[f_2784_1]) ).
fof(f_2784_3,plain,
! [U_10742,U_10741] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10741),c_Groups_Oone__class_Oone(U_10741)),hAPP(c_Int_Onumber__class_Onumber__of(U_10741),U_10742)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10741),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10742))
| ~ class_Int_Onumber__ring(U_10741) ),
inference(definitional_conversion,[status(esa)],[f_2784_2]) ).
cnf(f_2784_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10741),c_Groups_Oone__class_Oone(U_10741)),hAPP(c_Int_Onumber__class_Onumber__of(U_10741),U_10742)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10741),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_10742))
| ~ class_Int_Onumber__ring(U_10741) ),
inference(clausify,[status(thm)],[f_2784_3]) ).
fof(f_2785_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_2785_2,plain,
! [U_10744,U_10743] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10743),hAPP(c_Int_Onumber__class_Onumber__of(U_10743),U_10744)),c_Groups_Oone__class_Oone(U_10743)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10744),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_10743) ),
inference(variable_rename,[status(thm)],[f_2785_1]) ).
fof(f_2785_3,plain,
! [U_10743,U_10744] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10743),hAPP(c_Int_Onumber__class_Onumber__of(U_10743),U_10744)),c_Groups_Oone__class_Oone(U_10743)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10744),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_10743) ),
inference(definitional_conversion,[status(esa)],[f_2785_2]) ).
cnf(f_2785_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10743),hAPP(c_Int_Onumber__class_Onumber__of(U_10743),U_10744)),c_Groups_Oone__class_Oone(U_10743)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10744),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_10743) ),
inference(clausify,[status(thm)],[f_2785_3]) ).
fof(f_2786_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_2786_2,plain,
! [U_10746,U_10745] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10746)),U_10745) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10745),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_10745)) ),
inference(variable_rename,[status(thm)],[f_2786_1]) ).
fof(f_2786_3,plain,
! [U_10745,U_10746] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10746)),U_10745) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10745),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_10745)) ),
inference(definitional_conversion,[status(esa)],[f_2786_2]) ).
cnf(f_2786_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10746)),U_10745) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10745),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_10745)) ),
inference(clausify,[status(thm)],[f_2786_3]) ).
fof(f_2787_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_2787_2,plain,
! [U_10748,U_10747] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10747))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10748)) = 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_10747),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10748)),
inference(variable_rename,[status(thm)],[f_2787_1]) ).
fof(f_2787_3,plain,
! [U_10747,U_10748] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10747))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10748)) = 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_10747),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10748)),
inference(definitional_conversion,[status(esa)],[f_2787_2]) ).
cnf(f_2787_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10747))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10748)) = 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_10747),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10748)),
inference(clausify,[status(thm)],[f_2787_3]) ).
fof(f_2788_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_2788_2,plain,
! [U_10750,U_10749] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10749))),U_10750) = 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_10749),U_10750),
inference(variable_rename,[status(thm)],[f_2788_1]) ).
fof(f_2788_3,plain,
! [U_10749,U_10750] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10749))),U_10750) = 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_10749),U_10750),
inference(definitional_conversion,[status(esa)],[f_2788_2]) ).
cnf(f_2788_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10749))),U_10750) = 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_10749),U_10750),
inference(clausify,[status(thm)],[f_2788_3]) ).
fof(f_2789_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_2789_2,plain,
! [U_10752,U_10751] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10751,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10752)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10751,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_10752)),
inference(variable_rename,[status(thm)],[f_2789_1]) ).
fof(f_2789_3,plain,
! [U_10752,U_10751] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10751,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10752)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10751,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_10752)),
inference(definitional_conversion,[status(esa)],[f_2789_2]) ).
cnf(f_2789_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10751,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10752)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10751,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_10752)),
inference(clausify,[status(thm)],[f_2789_3]) ).
fof(f_2790_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_2790_2,plain,
! [U_10754,U_10753] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10753)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10754)) = 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_10753)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10754)),
inference(variable_rename,[status(thm)],[f_2790_1]) ).
fof(f_2790_3,plain,
! [U_10753,U_10754] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10753)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10754)) = 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_10753)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10754)),
inference(definitional_conversion,[status(esa)],[f_2790_2]) ).
cnf(f_2790_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_10753)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10754)) = 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_10753)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10754)),
inference(clausify,[status(thm)],[f_2790_3]) ).
fof(f_2791_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_2791_2,plain,
! [U_10756,U_10755] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10755)))),U_10756) = 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_10755)),U_10756),
inference(variable_rename,[status(thm)],[f_2791_1]) ).
fof(f_2791_3,plain,
! [U_10755,U_10756] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10755)))),U_10756) = 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_10755)),U_10756),
inference(definitional_conversion,[status(esa)],[f_2791_2]) ).
cnf(f_2791_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_10755)))),U_10756) = 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_10755)),U_10756),
inference(clausify,[status(thm)],[f_2791_3]) ).
fof(f_2792_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_2792_2,plain,
! [U_10758,U_10757] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10757),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10758)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10757),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_10758)),
inference(variable_rename,[status(thm)],[f_2792_1]) ).
fof(f_2792_3,plain,
! [U_10757,U_10758] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10757),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10758)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10757),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_10758)),
inference(definitional_conversion,[status(esa)],[f_2792_2]) ).
cnf(f_2792_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10757),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10758)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10757),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_10758)),
inference(clausify,[status(thm)],[f_2792_3]) ).
fof(f_2793_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2)
| ~ c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c),V_x_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_y_2) ) )
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq]) ).
fof(f_2793_2,plain,
! [U_10761,U_10760,U_10759] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_10759),U_10760) = hAPP(c_Int_Onumber__class_Onumber__of(U_10759),U_10761)
| ~ c_Int_Oiszero(U_10759,hAPP(c_Int_Onumber__class_Onumber__of(U_10759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10760),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10761)))) )
& ( c_Int_Oiszero(U_10759,hAPP(c_Int_Onumber__class_Onumber__of(U_10759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10760),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10761))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_10759),U_10760) != hAPP(c_Int_Onumber__class_Onumber__of(U_10759),U_10761) ) )
| ~ class_Int_Onumber__ring(U_10759) ),
inference(variable_rename,[status(thm)],[f_2793_1]) ).
fof(f_2793_3,plain,
( ! [U_10759,U_10760,U_10761] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10759),U_10760) = hAPP(c_Int_Onumber__class_Onumber__of(U_10759),U_10761)
| ~ c_Int_Oiszero(U_10759,hAPP(c_Int_Onumber__class_Onumber__of(U_10759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10760),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10761))))
| ~ sP813(U_10759,U_10760,U_10761) )
& ! [U_10759,U_10760,U_10761] :
( c_Int_Oiszero(U_10759,hAPP(c_Int_Onumber__class_Onumber__of(U_10759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10760),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10761))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_10759),U_10760) != hAPP(c_Int_Onumber__class_Onumber__of(U_10759),U_10761)
| ~ sP813(U_10759,U_10760,U_10761) )
& ! [U_10759,U_10760,U_10761] :
( sP813(U_10759,U_10760,U_10761)
| ~ class_Int_Onumber__ring(U_10759) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP813])],[f_2793_2]) ).
cnf(f_2793_4,plain,
( sP813(U_10759,U_10760,U_10761)
| ~ class_Int_Onumber__ring(U_10759) ),
inference(clausify,[status(thm)],[f_2793_3]) ).
cnf(f_2793_5,plain,
( c_Int_Oiszero(U_10759,hAPP(c_Int_Onumber__class_Onumber__of(U_10759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10760),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10761))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_10759),U_10760) != hAPP(c_Int_Onumber__class_Onumber__of(U_10759),U_10761)
| ~ sP813(U_10759,U_10760,U_10761) ),
inference(clausify,[status(thm)],[f_2793_3]) ).
cnf(f_2793_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10759),U_10760) = hAPP(c_Int_Onumber__class_Onumber__of(U_10759),U_10761)
| ~ c_Int_Oiszero(U_10759,hAPP(c_Int_Onumber__class_Onumber__of(U_10759),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10760),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10761))))
| ~ sP813(U_10759,U_10760,U_10761) ),
inference(clausify,[status(thm)],[f_2793_3]) ).
fof(f_2794_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_2794_2,plain,
! [U_10763,U_10762] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10762),c_Groups_Oone__class_Oone(U_10762)),hAPP(c_Int_Onumber__class_Onumber__of(U_10762),U_10763)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10762),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_10763)))
| ~ class_Int_Onumber__ring(U_10762) ),
inference(variable_rename,[status(thm)],[f_2794_1]) ).
fof(f_2794_3,plain,
! [U_10762,U_10763] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10762),c_Groups_Oone__class_Oone(U_10762)),hAPP(c_Int_Onumber__class_Onumber__of(U_10762),U_10763)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10762),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_10763)))
| ~ class_Int_Onumber__ring(U_10762) ),
inference(definitional_conversion,[status(esa)],[f_2794_2]) ).
cnf(f_2794_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10762),c_Groups_Oone__class_Oone(U_10762)),hAPP(c_Int_Onumber__class_Onumber__of(U_10762),U_10763)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10762),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_10763)))
| ~ class_Int_Onumber__ring(U_10762) ),
inference(clausify,[status(thm)],[f_2794_3]) ).
fof(f_2795_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_2795_2,plain,
! [U_10765,U_10764] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10764),hAPP(c_Int_Onumber__class_Onumber__of(U_10764),U_10765)),c_Groups_Oone__class_Oone(U_10764)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10765),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_10764) ),
inference(variable_rename,[status(thm)],[f_2795_1]) ).
fof(f_2795_3,plain,
! [U_10764,U_10765] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10764),hAPP(c_Int_Onumber__class_Onumber__of(U_10764),U_10765)),c_Groups_Oone__class_Oone(U_10764)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10765),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_10764) ),
inference(definitional_conversion,[status(esa)],[f_2795_2]) ).
cnf(f_2795_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10764),hAPP(c_Int_Onumber__class_Onumber__of(U_10764),U_10765)),c_Groups_Oone__class_Oone(U_10764)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10765),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_10764) ),
inference(clausify,[status(thm)],[f_2795_3]) ).
fof(f_2796_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_2796_2,plain,
! [U_10766] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10766)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10766)),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_10766))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10766)) = 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_10766))) ) ),
inference(variable_rename,[status(thm)],[f_2796_1]) ).
fof(f_2796_3,plain,
( ! [U_10768] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10768)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10768)),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_10768))) )
& ! [U_10767] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10767)) = 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_10767))) ) ),
inference(miniscope,[status(thm)],[f_2796_2]) ).
fof(f_2796_4,plain,
( ! [U_10768] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10768)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10768)),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_10768))) )
& ! [U_10767] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10767)) = 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_10767))) ) ),
inference(definitional_conversion,[status(esa)],[f_2796_3]) ).
cnf(f_2796_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10767)) = 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_10767))) ),
inference(clausify,[status(thm)],[f_2796_4]) ).
cnf(f_2796_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10768)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10768)),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_10768))) ),
inference(clausify,[status(thm)],[f_2796_4]) ).
fof(f_2797_1,plain,
! [V_z_2,V_w_2,T_c] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c)
| 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_c),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_c,T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_c),c_Groups_Otimes__class_Otimes(T_c)),hAPP(c_Groups_Otimes__class_Otimes(T_c),V_z_2))),c_COMBI(T_c)))
| ~ 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_c) ),
inference(fof_nnf,[status(thm)],[fact_power__number__of__odd]) ).
fof(f_2797_2,plain,
! [U_10771,U_10770,U_10769] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10769),U_10771),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10770))) = c_Groups_Oone__class_Oone(U_10769)
| 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_10770))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10769),U_10771),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10770))) = hAPP(hAPP(c_HOL_OLet(U_10769,U_10769),hAPP(hAPP(c_Power_Opower__class_Opower(U_10769),U_10771),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10770))),hAPP(hAPP(c_COMBS(U_10769,U_10769,U_10769),hAPP(hAPP(c_COMBB(U_10769,tc_fun(U_10769,U_10769),U_10769),c_Groups_Otimes__class_Otimes(U_10769)),hAPP(c_Groups_Otimes__class_Otimes(U_10769),U_10771))),c_COMBI(U_10769)))
| ~ 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_10770))) ) )
| ~ class_Int_Onumber__ring(U_10769) ),
inference(variable_rename,[status(thm)],[f_2797_1]) ).
fof(f_2797_3,plain,
( ! [U_10769,U_10770,U_10771] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10769),U_10771),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10770))) = c_Groups_Oone__class_Oone(U_10769)
| 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_10770)))
| ~ sP814(U_10769,U_10770,U_10771) )
& ! [U_10769,U_10770,U_10771] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10769),U_10771),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10770))) = hAPP(hAPP(c_HOL_OLet(U_10769,U_10769),hAPP(hAPP(c_Power_Opower__class_Opower(U_10769),U_10771),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10770))),hAPP(hAPP(c_COMBS(U_10769,U_10769,U_10769),hAPP(hAPP(c_COMBB(U_10769,tc_fun(U_10769,U_10769),U_10769),c_Groups_Otimes__class_Otimes(U_10769)),hAPP(c_Groups_Otimes__class_Otimes(U_10769),U_10771))),c_COMBI(U_10769)))
| ~ 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_10770)))
| ~ sP814(U_10769,U_10770,U_10771) )
& ! [U_10769,U_10770,U_10771] :
( sP814(U_10769,U_10770,U_10771)
| ~ class_Int_Onumber__ring(U_10769) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP814])],[f_2797_2]) ).
cnf(f_2797_4,plain,
( sP814(U_10769,U_10770,U_10771)
| ~ class_Int_Onumber__ring(U_10769) ),
inference(clausify,[status(thm)],[f_2797_3]) ).
cnf(f_2797_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10769),U_10771),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10770))) = hAPP(hAPP(c_HOL_OLet(U_10769,U_10769),hAPP(hAPP(c_Power_Opower__class_Opower(U_10769),U_10771),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10770))),hAPP(hAPP(c_COMBS(U_10769,U_10769,U_10769),hAPP(hAPP(c_COMBB(U_10769,tc_fun(U_10769,U_10769),U_10769),c_Groups_Otimes__class_Otimes(U_10769)),hAPP(c_Groups_Otimes__class_Otimes(U_10769),U_10771))),c_COMBI(U_10769)))
| ~ 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_10770)))
| ~ sP814(U_10769,U_10770,U_10771) ),
inference(clausify,[status(thm)],[f_2797_3]) ).
cnf(f_2797_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10769),U_10771),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10770))) = c_Groups_Oone__class_Oone(U_10769)
| 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_10770)))
| ~ sP814(U_10769,U_10770,U_10771) ),
inference(clausify,[status(thm)],[f_2797_3]) ).
fof(f_2798_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_2798_2,plain,
! [U_10773,U_10772] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10773)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10772))) = 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_10773)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10772)))),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_10772))) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10773)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10772))) = 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_10773),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10772)))),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_10772))) ) ),
inference(variable_rename,[status(thm)],[f_2798_1]) ).
fof(f_2798_3,plain,
( ! [U_10777,U_10775] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10777)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10775))) = 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_10777)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10775)))),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_10775))) )
& ! [U_10776,U_10774] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10776)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10774))) = 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_10776),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10774)))),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_10774))) ) ),
inference(miniscope,[status(thm)],[f_2798_2]) ).
fof(f_2798_4,plain,
( ! [U_10775,U_10777] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10777)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10775))) = 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_10777)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10775)))),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_10775))) )
& ! [U_10776,U_10774] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10776)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10774))) = 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_10776),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10774)))),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_10774))) ) ),
inference(definitional_conversion,[status(esa)],[f_2798_3]) ).
cnf(f_2798_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10776)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10774))) = 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_10776),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10774)))),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_10774))) ),
inference(clausify,[status(thm)],[f_2798_4]) ).
cnf(f_2798_6,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_10777)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10775))) = 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_10777)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10775)))),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_10775))) ),
inference(clausify,[status(thm)],[f_2798_4]) ).
fof(f_2799_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_2799_2,plain,
! [U_10779,U_10778] :
( 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_10779)),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_10778)) = 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_10779),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_10778))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10778),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2799_1]) ).
fof(f_2799_3,plain,
! [U_10779,U_10778] :
( 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_10779)),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_10778)) = 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_10779),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_10778))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10778),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2799_2]) ).
cnf(f_2799_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_10779)),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_10778)) = 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_10779),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_10778))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10778),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2799_3]) ).
fof(f_2800_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_2800_2,plain,
! [U_10782,U_10781,U_10780] : 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_10780)),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_10781))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10782))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10782)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10780),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10780),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_10782),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_10781)))),
inference(variable_rename,[status(thm)],[f_2800_1]) ).
fof(f_2800_3,plain,
! [U_10780,U_10781,U_10782] : 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_10780)),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_10781))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10782))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10782)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10780),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10780),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_10782),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_10781)))),
inference(definitional_conversion,[status(esa)],[f_2800_2]) ).
cnf(f_2800_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_10780)),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_10781))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10782))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10782)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10780),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10780),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_10782),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_10781)))),
inference(clausify,[status(thm)],[f_2800_3]) ).
fof(f_2801_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_2801_2,plain,
! [U_10784,U_10783] :
( 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_10784))),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_10783)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10784),U_10783)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10783)) ),
inference(variable_rename,[status(thm)],[f_2801_1]) ).
fof(f_2801_3,plain,
! [U_10784,U_10783] :
( 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_10784))),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_10783)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10784),U_10783)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10783)) ),
inference(definitional_conversion,[status(esa)],[f_2801_2]) ).
cnf(f_2801_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_10784))),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_10783)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10784),U_10783)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10783)) ),
inference(clausify,[status(thm)],[f_2801_3]) ).
fof(f_2802_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_2802_2,plain,
! [U_10786,U_10785] : c_Int_OBit0(U_10785) != c_Int_OBit1(U_10786),
inference(variable_rename,[status(thm)],[f_2802_1]) ).
fof(f_2802_3,plain,
! [U_10785,U_10786] : c_Int_OBit0(U_10785) != c_Int_OBit1(U_10786),
inference(definitional_conversion,[status(esa)],[f_2802_2]) ).
cnf(f_2802_4,plain,
c_Int_OBit0(U_10785) != c_Int_OBit1(U_10786),
inference(clausify,[status(thm)],[f_2802_3]) ).
fof(f_2803_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_2803_2,plain,
! [U_10788,U_10787] : c_Int_OBit1(U_10787) != c_Int_OBit0(U_10788),
inference(variable_rename,[status(thm)],[f_2803_1]) ).
fof(f_2803_3,plain,
! [U_10787,U_10788] : c_Int_OBit1(U_10787) != c_Int_OBit0(U_10788),
inference(definitional_conversion,[status(esa)],[f_2803_2]) ).
cnf(f_2803_4,plain,
c_Int_OBit1(U_10787) != c_Int_OBit0(U_10788),
inference(clausify,[status(thm)],[f_2803_3]) ).
fof(f_2804_1,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).
fof(f_2804_2,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_2804_1]) ).
cnf(f_2804_3,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_2804_2]) ).
fof(f_2805_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_2805_2,plain,
! [U_10789] :
( ( c_Int_OPls = c_Int_OBit0(U_10789)
| c_Int_OPls != U_10789 )
& ( c_Int_OPls = U_10789
| c_Int_OPls != c_Int_OBit0(U_10789) ) ),
inference(variable_rename,[status(thm)],[f_2805_1]) ).
fof(f_2805_3,plain,
( ! [U_10791] :
( c_Int_OPls = c_Int_OBit0(U_10791)
| c_Int_OPls != U_10791 )
& ! [U_10790] :
( c_Int_OPls = U_10790
| c_Int_OPls != c_Int_OBit0(U_10790) ) ),
inference(miniscope,[status(thm)],[f_2805_2]) ).
fof(f_2805_4,plain,
( ! [U_10791] :
( c_Int_OPls = c_Int_OBit0(U_10791)
| c_Int_OPls != U_10791 )
& ! [U_10790] :
( c_Int_OPls = U_10790
| c_Int_OPls != c_Int_OBit0(U_10790) ) ),
inference(definitional_conversion,[status(esa)],[f_2805_3]) ).
cnf(f_2805_5,plain,
( c_Int_OPls = U_10790
| c_Int_OPls != c_Int_OBit0(U_10790) ),
inference(clausify,[status(thm)],[f_2805_4]) ).
cnf(f_2805_6,plain,
( c_Int_OPls = c_Int_OBit0(U_10791)
| c_Int_OPls != U_10791 ),
inference(clausify,[status(thm)],[f_2805_4]) ).
fof(f_2806_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_2806_2,plain,
! [U_10792] :
( ( c_Int_OBit0(U_10792) = c_Int_OPls
| U_10792 != c_Int_OPls )
& ( U_10792 = c_Int_OPls
| c_Int_OBit0(U_10792) != c_Int_OPls ) ),
inference(variable_rename,[status(thm)],[f_2806_1]) ).
fof(f_2806_3,plain,
( ! [U_10794] :
( c_Int_OBit0(U_10794) = c_Int_OPls
| U_10794 != c_Int_OPls )
& ! [U_10793] :
( U_10793 = c_Int_OPls
| c_Int_OBit0(U_10793) != c_Int_OPls ) ),
inference(miniscope,[status(thm)],[f_2806_2]) ).
fof(f_2806_4,plain,
( ! [U_10794] :
( c_Int_OBit0(U_10794) = c_Int_OPls
| U_10794 != c_Int_OPls )
& ! [U_10793] :
( U_10793 = c_Int_OPls
| c_Int_OBit0(U_10793) != c_Int_OPls ) ),
inference(definitional_conversion,[status(esa)],[f_2806_3]) ).
cnf(f_2806_5,plain,
( U_10793 = c_Int_OPls
| c_Int_OBit0(U_10793) != c_Int_OPls ),
inference(clausify,[status(thm)],[f_2806_4]) ).
cnf(f_2806_6,plain,
( c_Int_OBit0(U_10794) = c_Int_OPls
| U_10794 != c_Int_OPls ),
inference(clausify,[status(thm)],[f_2806_4]) ).
fof(f_2807_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_2807_2,plain,
! [U_10795] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_10795)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10795)),
inference(variable_rename,[status(thm)],[f_2807_1]) ).
fof(f_2807_3,plain,
! [U_10795] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_10795)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10795)),
inference(definitional_conversion,[status(esa)],[f_2807_2]) ).
cnf(f_2807_4,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_10795)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10795)),
inference(clausify,[status(thm)],[f_2807_3]) ).
fof(f_2808_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_2808_2,plain,
! [U_10797,U_10796] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10796)),c_Int_OBit0(U_10797)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10796),U_10797)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10796),U_10797))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10796)),c_Int_OBit0(U_10797))) ) ),
inference(variable_rename,[status(thm)],[f_2808_1]) ).
fof(f_2808_3,plain,
( ! [U_10801,U_10799] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10799)),c_Int_OBit0(U_10801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10799),U_10801)) )
& ! [U_10800,U_10798] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10798),U_10800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10798)),c_Int_OBit0(U_10800))) ) ),
inference(miniscope,[status(thm)],[f_2808_2]) ).
fof(f_2808_4,plain,
( ! [U_10799,U_10801] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10799)),c_Int_OBit0(U_10801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10799),U_10801)) )
& ! [U_10800,U_10798] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10798),U_10800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10798)),c_Int_OBit0(U_10800))) ) ),
inference(definitional_conversion,[status(esa)],[f_2808_3]) ).
cnf(f_2808_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10798),U_10800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10798)),c_Int_OBit0(U_10800))) ),
inference(clausify,[status(thm)],[f_2808_4]) ).
cnf(f_2808_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10799)),c_Int_OBit0(U_10801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10799),U_10801)) ),
inference(clausify,[status(thm)],[f_2808_4]) ).
fof(f_2809_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_2809_2,plain,
! [U_10803,U_10802] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10802)),c_Int_OBit0(U_10803)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10802),U_10803)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10802),U_10803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10802)),c_Int_OBit0(U_10803))) ) ),
inference(variable_rename,[status(thm)],[f_2809_1]) ).
fof(f_2809_3,plain,
( ! [U_10807,U_10805] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10805)),c_Int_OBit0(U_10807)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10805),U_10807)) )
& ! [U_10806,U_10804] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10804),U_10806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10804)),c_Int_OBit0(U_10806))) ) ),
inference(miniscope,[status(thm)],[f_2809_2]) ).
fof(f_2809_4,plain,
( ! [U_10807,U_10805] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10805)),c_Int_OBit0(U_10807)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10805),U_10807)) )
& ! [U_10806,U_10804] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10804),U_10806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10804)),c_Int_OBit0(U_10806))) ) ),
inference(definitional_conversion,[status(esa)],[f_2809_3]) ).
cnf(f_2809_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10804),U_10806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10804)),c_Int_OBit0(U_10806))) ),
inference(clausify,[status(thm)],[f_2809_4]) ).
cnf(f_2809_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10805)),c_Int_OBit0(U_10807)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10805),U_10807)) ),
inference(clausify,[status(thm)],[f_2809_4]) ).
fof(f_2810_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_2810_2,plain,
! [U_10808] : c_Int_OBit0(U_10808) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10808),U_10808),
inference(variable_rename,[status(thm)],[f_2810_1]) ).
fof(f_2810_3,plain,
! [U_10808] : c_Int_OBit0(U_10808) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10808),U_10808),
inference(definitional_conversion,[status(esa)],[f_2810_2]) ).
cnf(f_2810_4,plain,
c_Int_OBit0(U_10808) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10808),U_10808),
inference(clausify,[status(thm)],[f_2810_3]) ).
fof(f_2811_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_2811_2,plain,
! [U_10810,U_10809] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_10809)),c_Int_OBit0(U_10810)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10809),U_10810)),
inference(variable_rename,[status(thm)],[f_2811_1]) ).
fof(f_2811_3,plain,
! [U_10809,U_10810] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_10809)),c_Int_OBit0(U_10810)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10809),U_10810)),
inference(definitional_conversion,[status(esa)],[f_2811_2]) ).
cnf(f_2811_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_10809)),c_Int_OBit0(U_10810)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10809),U_10810)),
inference(clausify,[status(thm)],[f_2811_3]) ).
fof(f_2812_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_2812_2,plain,
! [U_10812,U_10811] :
( ( c_Int_OBit0(U_10811) = c_Int_OBit0(U_10812)
| U_10811 != U_10812 )
& ( U_10811 = U_10812
| c_Int_OBit0(U_10811) != c_Int_OBit0(U_10812) ) ),
inference(variable_rename,[status(thm)],[f_2812_1]) ).
fof(f_2812_3,plain,
( ! [U_10816,U_10814] :
( c_Int_OBit0(U_10814) = c_Int_OBit0(U_10816)
| U_10814 != U_10816 )
& ! [U_10815,U_10813] :
( U_10813 = U_10815
| c_Int_OBit0(U_10813) != c_Int_OBit0(U_10815) ) ),
inference(miniscope,[status(thm)],[f_2812_2]) ).
fof(f_2812_4,plain,
( ! [U_10814,U_10816] :
( c_Int_OBit0(U_10814) = c_Int_OBit0(U_10816)
| U_10814 != U_10816 )
& ! [U_10815,U_10813] :
( U_10813 = U_10815
| c_Int_OBit0(U_10813) != c_Int_OBit0(U_10815) ) ),
inference(definitional_conversion,[status(esa)],[f_2812_3]) ).
cnf(f_2812_5,plain,
( U_10813 = U_10815
| c_Int_OBit0(U_10813) != c_Int_OBit0(U_10815) ),
inference(clausify,[status(thm)],[f_2812_4]) ).
cnf(f_2812_6,plain,
( c_Int_OBit0(U_10814) = c_Int_OBit0(U_10816)
| U_10814 != U_10816 ),
inference(clausify,[status(thm)],[f_2812_4]) ).
fof(f_2813_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_2813_2,plain,
! [U_10818,U_10817] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_10817)),U_10818) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10817),U_10818)),
inference(variable_rename,[status(thm)],[f_2813_1]) ).
fof(f_2813_3,plain,
! [U_10817,U_10818] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_10817)),U_10818) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10817),U_10818)),
inference(definitional_conversion,[status(esa)],[f_2813_2]) ).
cnf(f_2813_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_10817)),U_10818) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10817),U_10818)),
inference(clausify,[status(thm)],[f_2813_3]) ).
fof(f_2814_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_2814_2,plain,
! [U_10820,U_10819] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_10819)),c_Int_OBit0(U_10820)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10819),U_10820)),
inference(variable_rename,[status(thm)],[f_2814_1]) ).
fof(f_2814_3,plain,
! [U_10819,U_10820] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_10819)),c_Int_OBit0(U_10820)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10819),U_10820)),
inference(definitional_conversion,[status(esa)],[f_2814_2]) ).
cnf(f_2814_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_10819)),c_Int_OBit0(U_10820)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10819),U_10820)),
inference(clausify,[status(thm)],[f_2814_3]) ).
fof(f_2815_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_2815_2,plain,
! [U_10822,U_10821] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10821)),c_Int_OBit0(U_10822)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10821),U_10822)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10821),U_10822))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10821)),c_Int_OBit0(U_10822))) ) ),
inference(variable_rename,[status(thm)],[f_2815_1]) ).
fof(f_2815_3,plain,
( ! [U_10826,U_10824] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10824)),c_Int_OBit0(U_10826)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10824),U_10826)) )
& ! [U_10825,U_10823] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10823),U_10825))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10823)),c_Int_OBit0(U_10825))) ) ),
inference(miniscope,[status(thm)],[f_2815_2]) ).
fof(f_2815_4,plain,
( ! [U_10824,U_10826] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10824)),c_Int_OBit0(U_10826)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10824),U_10826)) )
& ! [U_10825,U_10823] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10823),U_10825))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10823)),c_Int_OBit0(U_10825))) ) ),
inference(definitional_conversion,[status(esa)],[f_2815_3]) ).
cnf(f_2815_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10823),U_10825))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10823)),c_Int_OBit0(U_10825))) ),
inference(clausify,[status(thm)],[f_2815_4]) ).
cnf(f_2815_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10824)),c_Int_OBit0(U_10826)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10824),U_10826)) ),
inference(clausify,[status(thm)],[f_2815_4]) ).
fof(f_2816_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_2816_2,plain,
! [U_10828,U_10827] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10827)),c_Int_OBit0(U_10828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10827),U_10828)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10827),U_10828))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10827)),c_Int_OBit0(U_10828))) ) ),
inference(variable_rename,[status(thm)],[f_2816_1]) ).
fof(f_2816_3,plain,
( ! [U_10832,U_10830] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10830)),c_Int_OBit0(U_10832)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10830),U_10832)) )
& ! [U_10831,U_10829] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10829),U_10831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10829)),c_Int_OBit0(U_10831))) ) ),
inference(miniscope,[status(thm)],[f_2816_2]) ).
fof(f_2816_4,plain,
( ! [U_10830,U_10832] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10830)),c_Int_OBit0(U_10832)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10830),U_10832)) )
& ! [U_10831,U_10829] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10829),U_10831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10829)),c_Int_OBit0(U_10831))) ) ),
inference(definitional_conversion,[status(esa)],[f_2816_3]) ).
cnf(f_2816_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10829),U_10831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10829)),c_Int_OBit0(U_10831))) ),
inference(clausify,[status(thm)],[f_2816_4]) ).
cnf(f_2816_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10830)),c_Int_OBit0(U_10832)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10830),U_10832)) ),
inference(clausify,[status(thm)],[f_2816_4]) ).
fof(f_2817_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_2817_2,plain,
! [U_10833] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10833)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10833),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10833),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10833)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_2817_1]) ).
fof(f_2817_3,plain,
( ! [U_10835] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10835)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10835),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_10834] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10834),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10834)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_2817_2]) ).
fof(f_2817_4,plain,
( ! [U_10835] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10835)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10835),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_10834] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10834),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10834)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_2817_3]) ).
cnf(f_2817_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10834),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10834)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2817_4]) ).
cnf(f_2817_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10835)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10835),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2817_4]) ).
fof(f_2818_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_2818_2,plain,
! [U_10836] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10836)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10836)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10836))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10836))) ) ),
inference(variable_rename,[status(thm)],[f_2818_1]) ).
fof(f_2818_3,plain,
( ! [U_10838] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10838)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10838)) )
& ! [U_10837] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10837))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10837))) ) ),
inference(miniscope,[status(thm)],[f_2818_2]) ).
fof(f_2818_4,plain,
( ! [U_10838] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10838)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10838)) )
& ! [U_10837] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10837))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10837))) ) ),
inference(definitional_conversion,[status(esa)],[f_2818_3]) ).
cnf(f_2818_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10837))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10837))) ),
inference(clausify,[status(thm)],[f_2818_4]) ).
cnf(f_2818_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10838)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_10838)) ),
inference(clausify,[status(thm)],[f_2818_4]) ).
fof(f_2819_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_2819_2,plain,
! [U_10839] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10839)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10839),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10839),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10839)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2819_1]) ).
fof(f_2819_3,plain,
( ! [U_10841] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10841)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10841),c_Int_OPls)) )
& ! [U_10840] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10840),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10840)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2819_2]) ).
fof(f_2819_4,plain,
( ! [U_10841] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10841)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10841),c_Int_OPls)) )
& ! [U_10840] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10840),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10840)),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2819_3]) ).
cnf(f_2819_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10840),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10840)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2819_4]) ).
cnf(f_2819_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10841)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10841),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2819_4]) ).
fof(f_2820_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_2820_2,plain,
! [U_10843,U_10842] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10842)),c_Int_OBit1(U_10843)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10842),U_10843)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10842),U_10843))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10842)),c_Int_OBit1(U_10843))) ) ),
inference(variable_rename,[status(thm)],[f_2820_1]) ).
fof(f_2820_3,plain,
( ! [U_10847,U_10845] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10845)),c_Int_OBit1(U_10847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10845),U_10847)) )
& ! [U_10846,U_10844] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10844),U_10846))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10844)),c_Int_OBit1(U_10846))) ) ),
inference(miniscope,[status(thm)],[f_2820_2]) ).
fof(f_2820_4,plain,
( ! [U_10845,U_10847] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10845)),c_Int_OBit1(U_10847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10845),U_10847)) )
& ! [U_10846,U_10844] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10844),U_10846))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10844)),c_Int_OBit1(U_10846))) ) ),
inference(definitional_conversion,[status(esa)],[f_2820_3]) ).
cnf(f_2820_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10844),U_10846))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10844)),c_Int_OBit1(U_10846))) ),
inference(clausify,[status(thm)],[f_2820_4]) ).
cnf(f_2820_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10845)),c_Int_OBit1(U_10847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10845),U_10847)) ),
inference(clausify,[status(thm)],[f_2820_4]) ).
fof(f_2821_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_2821_2,plain,
! [U_10849,U_10848] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10848)),c_Int_OBit1(U_10849)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10848),U_10849)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10848),U_10849))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10848)),c_Int_OBit1(U_10849))) ) ),
inference(variable_rename,[status(thm)],[f_2821_1]) ).
fof(f_2821_3,plain,
( ! [U_10853,U_10851] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10851)),c_Int_OBit1(U_10853)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10851),U_10853)) )
& ! [U_10852,U_10850] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10850),U_10852))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10850)),c_Int_OBit1(U_10852))) ) ),
inference(miniscope,[status(thm)],[f_2821_2]) ).
fof(f_2821_4,plain,
( ! [U_10851,U_10853] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10851)),c_Int_OBit1(U_10853)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10851),U_10853)) )
& ! [U_10852,U_10850] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10850),U_10852))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10850)),c_Int_OBit1(U_10852))) ) ),
inference(definitional_conversion,[status(esa)],[f_2821_3]) ).
cnf(f_2821_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10850),U_10852))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10850)),c_Int_OBit1(U_10852))) ),
inference(clausify,[status(thm)],[f_2821_4]) ).
cnf(f_2821_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_10851)),c_Int_OBit1(U_10853)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10851),U_10853)) ),
inference(clausify,[status(thm)],[f_2821_4]) ).
fof(f_2822_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_2822_2,plain,
! [U_10854] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10854)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10854)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10854))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10854))) ) ),
inference(variable_rename,[status(thm)],[f_2822_1]) ).
fof(f_2822_3,plain,
( ! [U_10856] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10856)) )
& ! [U_10855] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10855))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10855))) ) ),
inference(miniscope,[status(thm)],[f_2822_2]) ).
fof(f_2822_4,plain,
( ! [U_10856] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10856)) )
& ! [U_10855] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10855))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10855))) ) ),
inference(definitional_conversion,[status(esa)],[f_2822_3]) ).
cnf(f_2822_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10855))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10855))) ),
inference(clausify,[status(thm)],[f_2822_4]) ).
cnf(f_2822_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_10856)) ),
inference(clausify,[status(thm)],[f_2822_4]) ).
fof(f_2823_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_2823_2,plain,
! [U_10857] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10857)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10857),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10857),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10857)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_2823_1]) ).
fof(f_2823_3,plain,
( ! [U_10859] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10859)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10859),c_Int_OPls)) )
& ! [U_10858] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10858),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10858)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_2823_2]) ).
fof(f_2823_4,plain,
( ! [U_10859] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10859)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10859),c_Int_OPls)) )
& ! [U_10858] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10858),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10858)),c_Int_OPls)) ) ),
inference(definitional_conversion,[status(esa)],[f_2823_3]) ).
cnf(f_2823_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10858),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10858)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2823_4]) ).
cnf(f_2823_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10859)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10859),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_2823_4]) ).
fof(f_2824_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_2824_2,plain,
! [U_10861,U_10860] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10860)),c_Int_OBit0(U_10861)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10860),U_10861)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10860),U_10861))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10860)),c_Int_OBit0(U_10861))) ) ),
inference(variable_rename,[status(thm)],[f_2824_1]) ).
fof(f_2824_3,plain,
( ! [U_10865,U_10863] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10863)),c_Int_OBit0(U_10865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10863),U_10865)) )
& ! [U_10864,U_10862] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10862),U_10864))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10862)),c_Int_OBit0(U_10864))) ) ),
inference(miniscope,[status(thm)],[f_2824_2]) ).
fof(f_2824_4,plain,
( ! [U_10863,U_10865] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10863)),c_Int_OBit0(U_10865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10863),U_10865)) )
& ! [U_10864,U_10862] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10862),U_10864))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10862)),c_Int_OBit0(U_10864))) ) ),
inference(definitional_conversion,[status(esa)],[f_2824_3]) ).
cnf(f_2824_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10862),U_10864))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10862)),c_Int_OBit0(U_10864))) ),
inference(clausify,[status(thm)],[f_2824_4]) ).
cnf(f_2824_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10863)),c_Int_OBit0(U_10865)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10863),U_10865)) ),
inference(clausify,[status(thm)],[f_2824_4]) ).
fof(f_2825_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_2825_2,plain,
! [U_10867,U_10866] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10866)),c_Int_OBit0(U_10867)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10866),U_10867)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10866),U_10867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10866)),c_Int_OBit0(U_10867))) ) ),
inference(variable_rename,[status(thm)],[f_2825_1]) ).
fof(f_2825_3,plain,
( ! [U_10871,U_10869] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10869)),c_Int_OBit0(U_10871)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10869),U_10871)) )
& ! [U_10870,U_10868] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10868),U_10870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10868)),c_Int_OBit0(U_10870))) ) ),
inference(miniscope,[status(thm)],[f_2825_2]) ).
fof(f_2825_4,plain,
( ! [U_10869,U_10871] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10869)),c_Int_OBit0(U_10871)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10869),U_10871)) )
& ! [U_10870,U_10868] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10868),U_10870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10868)),c_Int_OBit0(U_10870))) ) ),
inference(definitional_conversion,[status(esa)],[f_2825_3]) ).
cnf(f_2825_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10868),U_10870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10868)),c_Int_OBit0(U_10870))) ),
inference(clausify,[status(thm)],[f_2825_4]) ).
cnf(f_2825_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_10869)),c_Int_OBit0(U_10871)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10869),U_10871)) ),
inference(clausify,[status(thm)],[f_2825_4]) ).
fof(f_2826_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_2826_2,plain,
! [U_10873,U_10872] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_10872)),c_Int_OBit1(U_10873)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10872),U_10873)),
inference(variable_rename,[status(thm)],[f_2826_1]) ).
fof(f_2826_3,plain,
! [U_10873,U_10872] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_10872)),c_Int_OBit1(U_10873)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10872),U_10873)),
inference(definitional_conversion,[status(esa)],[f_2826_2]) ).
cnf(f_2826_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_10872)),c_Int_OBit1(U_10873)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10872),U_10873)),
inference(clausify,[status(thm)],[f_2826_3]) ).
fof(f_2827_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_2827_2,plain,
! [U_10875,U_10874] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_10874)),c_Int_OBit0(U_10875)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10874),U_10875)),
inference(variable_rename,[status(thm)],[f_2827_1]) ).
fof(f_2827_3,plain,
! [U_10874,U_10875] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_10874)),c_Int_OBit0(U_10875)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10874),U_10875)),
inference(definitional_conversion,[status(esa)],[f_2827_2]) ).
cnf(f_2827_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_10874)),c_Int_OBit0(U_10875)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10874),U_10875)),
inference(clausify,[status(thm)],[f_2827_3]) ).
fof(f_2828_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_2828_2,plain,
! [U_10876] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10876)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_10876)),
inference(variable_rename,[status(thm)],[f_2828_1]) ).
fof(f_2828_3,plain,
! [U_10876] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10876)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_10876)),
inference(definitional_conversion,[status(esa)],[f_2828_2]) ).
cnf(f_2828_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_10876)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_10876)),
inference(clausify,[status(thm)],[f_2828_3]) ).
fof(f_2829_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_2829_2,plain,
! [U_10878,U_10877] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_10877)),c_Int_OBit1(U_10878)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10877),U_10878)),
inference(variable_rename,[status(thm)],[f_2829_1]) ).
fof(f_2829_3,plain,
! [U_10877,U_10878] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_10877)),c_Int_OBit1(U_10878)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10877),U_10878)),
inference(definitional_conversion,[status(esa)],[f_2829_2]) ).
cnf(f_2829_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_10877)),c_Int_OBit1(U_10878)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10877),U_10878)),
inference(clausify,[status(thm)],[f_2829_3]) ).
fof(f_2830_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_2830_2,plain,
! [U_10880,U_10879] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_10879)),c_Int_OBit0(U_10880)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10879),U_10880)),
inference(variable_rename,[status(thm)],[f_2830_1]) ).
fof(f_2830_3,plain,
! [U_10879,U_10880] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_10879)),c_Int_OBit0(U_10880)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10879),U_10880)),
inference(definitional_conversion,[status(esa)],[f_2830_2]) ).
cnf(f_2830_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_10879)),c_Int_OBit0(U_10880)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10879),U_10880)),
inference(clausify,[status(thm)],[f_2830_3]) ).
fof(f_2831_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_2831_2,plain,
! [U_10882,U_10881] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10881))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10882))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10881)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10882)),
inference(variable_rename,[status(thm)],[f_2831_1]) ).
fof(f_2831_3,plain,
! [U_10881,U_10882] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10881))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10882))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10881)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10882)),
inference(definitional_conversion,[status(esa)],[f_2831_2]) ).
cnf(f_2831_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_10881))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10882))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10881)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10882)),
inference(clausify,[status(thm)],[f_2831_3]) ).
fof(f_2832_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_2832_2,plain,
! [U_10883] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10883))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10883))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10883)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10883)))) ) ),
inference(variable_rename,[status(thm)],[f_2832_1]) ).
fof(f_2832_3,plain,
( ! [U_10885] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10885))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10885))) )
& ! [U_10884] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10884)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10884)))) ) ),
inference(miniscope,[status(thm)],[f_2832_2]) ).
fof(f_2832_4,plain,
( ! [U_10885] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10885))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10885))) )
& ! [U_10884] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10884)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10884)))) ) ),
inference(definitional_conversion,[status(esa)],[f_2832_3]) ).
cnf(f_2832_5,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10884)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10884)))) ),
inference(clausify,[status(thm)],[f_2832_4]) ).
cnf(f_2832_6,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10885))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10885))) ),
inference(clausify,[status(thm)],[f_2832_4]) ).
fof(f_2833_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_2833_2,plain,
! [U_10886] : c_Int_Opred(c_Int_OBit1(U_10886)) = c_Int_OBit0(U_10886),
inference(variable_rename,[status(thm)],[f_2833_1]) ).
fof(f_2833_3,plain,
! [U_10886] : c_Int_Opred(c_Int_OBit1(U_10886)) = c_Int_OBit0(U_10886),
inference(definitional_conversion,[status(esa)],[f_2833_2]) ).
cnf(f_2833_4,plain,
c_Int_Opred(c_Int_OBit1(U_10886)) = c_Int_OBit0(U_10886),
inference(clausify,[status(thm)],[f_2833_3]) ).
fof(f_2834_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_2834_2,plain,
! [U_10887] : c_Int_Opred(c_Int_OBit0(U_10887)) = c_Int_OBit1(c_Int_Opred(U_10887)),
inference(variable_rename,[status(thm)],[f_2834_1]) ).
fof(f_2834_3,plain,
! [U_10887] : c_Int_Opred(c_Int_OBit0(U_10887)) = c_Int_OBit1(c_Int_Opred(U_10887)),
inference(definitional_conversion,[status(esa)],[f_2834_2]) ).
cnf(f_2834_4,plain,
c_Int_Opred(c_Int_OBit0(U_10887)) = c_Int_OBit1(c_Int_Opred(U_10887)),
inference(clausify,[status(thm)],[f_2834_3]) ).
fof(f_2835_1,plain,
! [V_w_2,T_c] :
( ( ( c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),c_Int_OBit0(V_w_2)))
| ~ c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)) )
& ( c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2))
| ~ c_Int_Oiszero(T_c,hAPP(c_Int_Onumber__class_Onumber__of(T_c),c_Int_OBit0(V_w_2))) ) )
| ~ class_Int_Oring__char__0(T_c)
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0]) ).
fof(f_2835_2,plain,
! [U_10889,U_10888] :
( ( ( c_Int_Oiszero(U_10888,hAPP(c_Int_Onumber__class_Onumber__of(U_10888),c_Int_OBit0(U_10889)))
| ~ c_Int_Oiszero(U_10888,hAPP(c_Int_Onumber__class_Onumber__of(U_10888),U_10889)) )
& ( c_Int_Oiszero(U_10888,hAPP(c_Int_Onumber__class_Onumber__of(U_10888),U_10889))
| ~ c_Int_Oiszero(U_10888,hAPP(c_Int_Onumber__class_Onumber__of(U_10888),c_Int_OBit0(U_10889))) ) )
| ~ class_Int_Oring__char__0(U_10888)
| ~ class_Int_Onumber__ring(U_10888) ),
inference(variable_rename,[status(thm)],[f_2835_1]) ).
fof(f_2835_3,plain,
( ! [U_10888,U_10889] :
( c_Int_Oiszero(U_10888,hAPP(c_Int_Onumber__class_Onumber__of(U_10888),c_Int_OBit0(U_10889)))
| ~ c_Int_Oiszero(U_10888,hAPP(c_Int_Onumber__class_Onumber__of(U_10888),U_10889))
| ~ sP815(U_10888,U_10889) )
& ! [U_10888,U_10889] :
( c_Int_Oiszero(U_10888,hAPP(c_Int_Onumber__class_Onumber__of(U_10888),U_10889))
| ~ c_Int_Oiszero(U_10888,hAPP(c_Int_Onumber__class_Onumber__of(U_10888),c_Int_OBit0(U_10889)))
| ~ sP815(U_10888,U_10889) )
& ! [U_10888,U_10889] :
( sP815(U_10888,U_10889)
| ~ class_Int_Oring__char__0(U_10888)
| ~ class_Int_Onumber__ring(U_10888) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP815])],[f_2835_2]) ).
cnf(f_2835_4,plain,
( sP815(U_10888,U_10889)
| ~ class_Int_Oring__char__0(U_10888)
| ~ class_Int_Onumber__ring(U_10888) ),
inference(clausify,[status(thm)],[f_2835_3]) ).
cnf(f_2835_5,plain,
( c_Int_Oiszero(U_10888,hAPP(c_Int_Onumber__class_Onumber__of(U_10888),U_10889))
| ~ c_Int_Oiszero(U_10888,hAPP(c_Int_Onumber__class_Onumber__of(U_10888),c_Int_OBit0(U_10889)))
| ~ sP815(U_10888,U_10889) ),
inference(clausify,[status(thm)],[f_2835_3]) ).
cnf(f_2835_6,plain,
( c_Int_Oiszero(U_10888,hAPP(c_Int_Onumber__class_Onumber__of(U_10888),c_Int_OBit0(U_10889)))
| ~ c_Int_Oiszero(U_10888,hAPP(c_Int_Onumber__class_Onumber__of(U_10888),U_10889))
| ~ sP815(U_10888,U_10889) ),
inference(clausify,[status(thm)],[f_2835_3]) ).
fof(f_2836_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_2836_2,plain,
! [U_10890] : c_Int_Osucc(c_Int_OBit0(U_10890)) = c_Int_OBit1(U_10890),
inference(variable_rename,[status(thm)],[f_2836_1]) ).
fof(f_2836_3,plain,
! [U_10890] : c_Int_Osucc(c_Int_OBit0(U_10890)) = c_Int_OBit1(U_10890),
inference(definitional_conversion,[status(esa)],[f_2836_2]) ).
cnf(f_2836_4,plain,
c_Int_Osucc(c_Int_OBit0(U_10890)) = c_Int_OBit1(U_10890),
inference(clausify,[status(thm)],[f_2836_3]) ).
fof(f_2837_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_2837_2,plain,
! [U_10891] : c_Int_Osucc(c_Int_OBit1(U_10891)) = c_Int_OBit0(c_Int_Osucc(U_10891)),
inference(variable_rename,[status(thm)],[f_2837_1]) ).
fof(f_2837_3,plain,
! [U_10891] : c_Int_Osucc(c_Int_OBit1(U_10891)) = c_Int_OBit0(c_Int_Osucc(U_10891)),
inference(definitional_conversion,[status(esa)],[f_2837_2]) ).
cnf(f_2837_4,plain,
c_Int_Osucc(c_Int_OBit1(U_10891)) = c_Int_OBit0(c_Int_Osucc(U_10891)),
inference(clausify,[status(thm)],[f_2837_3]) ).
fof(f_2838_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_2838_2,plain,
! [U_10892] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10892)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10892)),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_2838_1]) ).
fof(f_2838_3,plain,
! [U_10892] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10892)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10892)),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_2838_2]) ).
cnf(f_2838_4,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10892)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10892)),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_2838_3]) ).
fof(f_2839_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_2839_2,plain,
! [U_10894,U_10893] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10893),c_Int_OBit0(U_10894)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10893),c_Groups_Ozero__class_Ozero(U_10893)),hAPP(c_Int_Onumber__class_Onumber__of(U_10893),U_10894))),hAPP(c_Int_Onumber__class_Onumber__of(U_10893),U_10894))
| ~ class_Int_Onumber__ring(U_10893) ),
inference(variable_rename,[status(thm)],[f_2839_1]) ).
fof(f_2839_3,plain,
! [U_10893,U_10894] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_10893),c_Int_OBit0(U_10894)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10893),c_Groups_Ozero__class_Ozero(U_10893)),hAPP(c_Int_Onumber__class_Onumber__of(U_10893),U_10894))),hAPP(c_Int_Onumber__class_Onumber__of(U_10893),U_10894))
| ~ class_Int_Onumber__ring(U_10893) ),
inference(definitional_conversion,[status(esa)],[f_2839_2]) ).
cnf(f_2839_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_10893),c_Int_OBit0(U_10894)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10893),c_Groups_Ozero__class_Ozero(U_10893)),hAPP(c_Int_Onumber__class_Onumber__of(U_10893),U_10894))),hAPP(c_Int_Onumber__class_Onumber__of(U_10893),U_10894))
| ~ class_Int_Onumber__ring(U_10893) ),
inference(clausify,[status(thm)],[f_2839_3]) ).
fof(f_2840_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_2840_2,plain,
! [U_10896,U_10895] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10895)),c_Int_OBit0(U_10896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10895),U_10896)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10895),U_10896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10895)),c_Int_OBit0(U_10896))) ) ),
inference(variable_rename,[status(thm)],[f_2840_1]) ).
fof(f_2840_3,plain,
( ! [U_10900,U_10898] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10898)),c_Int_OBit0(U_10900)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10898),U_10900)) )
& ! [U_10899,U_10897] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10897),U_10899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10897)),c_Int_OBit0(U_10899))) ) ),
inference(miniscope,[status(thm)],[f_2840_2]) ).
fof(f_2840_4,plain,
( ! [U_10900,U_10898] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10898)),c_Int_OBit0(U_10900)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10898),U_10900)) )
& ! [U_10899,U_10897] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10897),U_10899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10897)),c_Int_OBit0(U_10899))) ) ),
inference(definitional_conversion,[status(esa)],[f_2840_3]) ).
cnf(f_2840_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10897),U_10899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10897)),c_Int_OBit0(U_10899))) ),
inference(clausify,[status(thm)],[f_2840_4]) ).
cnf(f_2840_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10898)),c_Int_OBit0(U_10900)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10898),U_10900)) ),
inference(clausify,[status(thm)],[f_2840_4]) ).
fof(f_2841_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_2841_2,plain,
! [U_10902,U_10901] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10901)),c_Int_OBit0(U_10902)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10901),U_10902)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10901),U_10902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10901)),c_Int_OBit0(U_10902))) ) ),
inference(variable_rename,[status(thm)],[f_2841_1]) ).
fof(f_2841_3,plain,
( ! [U_10906,U_10904] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10904)),c_Int_OBit0(U_10906)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10904),U_10906)) )
& ! [U_10905,U_10903] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10903),U_10905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10903)),c_Int_OBit0(U_10905))) ) ),
inference(miniscope,[status(thm)],[f_2841_2]) ).
fof(f_2841_4,plain,
( ! [U_10904,U_10906] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10904)),c_Int_OBit0(U_10906)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10904),U_10906)) )
& ! [U_10905,U_10903] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10903),U_10905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10903)),c_Int_OBit0(U_10905))) ) ),
inference(definitional_conversion,[status(esa)],[f_2841_3]) ).
cnf(f_2841_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10903),U_10905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10903)),c_Int_OBit0(U_10905))) ),
inference(clausify,[status(thm)],[f_2841_4]) ).
cnf(f_2841_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_10904)),c_Int_OBit0(U_10906)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10904),U_10906)) ),
inference(clausify,[status(thm)],[f_2841_4]) ).
fof(f_2842_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_2842_2,plain,
! [U_10908,U_10907] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10907)),c_Int_OBit1(U_10908)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10907),U_10908)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10907),U_10908))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10907)),c_Int_OBit1(U_10908))) ) ),
inference(variable_rename,[status(thm)],[f_2842_1]) ).
fof(f_2842_3,plain,
( ! [U_10912,U_10910] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10910)),c_Int_OBit1(U_10912)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10910),U_10912)) )
& ! [U_10911,U_10909] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10909),U_10911))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10909)),c_Int_OBit1(U_10911))) ) ),
inference(miniscope,[status(thm)],[f_2842_2]) ).
fof(f_2842_4,plain,
( ! [U_10910,U_10912] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10910)),c_Int_OBit1(U_10912)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10910),U_10912)) )
& ! [U_10911,U_10909] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10909),U_10911))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10909)),c_Int_OBit1(U_10911))) ) ),
inference(definitional_conversion,[status(esa)],[f_2842_3]) ).
cnf(f_2842_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10909),U_10911))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10909)),c_Int_OBit1(U_10911))) ),
inference(clausify,[status(thm)],[f_2842_4]) ).
cnf(f_2842_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10910)),c_Int_OBit1(U_10912)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10910),U_10912)) ),
inference(clausify,[status(thm)],[f_2842_4]) ).
fof(f_2843_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_2843_2,plain,
! [U_10914,U_10913] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10913)),c_Int_OBit1(U_10914)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10913),U_10914)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10913),U_10914))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10913)),c_Int_OBit1(U_10914))) ) ),
inference(variable_rename,[status(thm)],[f_2843_1]) ).
fof(f_2843_3,plain,
( ! [U_10918,U_10916] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10916)),c_Int_OBit1(U_10918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10916),U_10918)) )
& ! [U_10917,U_10915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10915),U_10917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10915)),c_Int_OBit1(U_10917))) ) ),
inference(miniscope,[status(thm)],[f_2843_2]) ).
fof(f_2843_4,plain,
( ! [U_10916,U_10918] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10916)),c_Int_OBit1(U_10918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10916),U_10918)) )
& ! [U_10917,U_10915] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10915),U_10917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10915)),c_Int_OBit1(U_10917))) ) ),
inference(definitional_conversion,[status(esa)],[f_2843_3]) ).
cnf(f_2843_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10915),U_10917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10915)),c_Int_OBit1(U_10917))) ),
inference(clausify,[status(thm)],[f_2843_4]) ).
cnf(f_2843_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_10916)),c_Int_OBit1(U_10918)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10916),U_10918)) ),
inference(clausify,[status(thm)],[f_2843_4]) ).
fof(f_2844_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_2844_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_2844_1]) ).
cnf(f_2844_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_2844_2]) ).
fof(f_2845_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_2845_2,plain,
! [U_10920,U_10919] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_10919)),U_10920) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10919),U_10920))),U_10920),
inference(variable_rename,[status(thm)],[f_2845_1]) ).
fof(f_2845_3,plain,
! [U_10919,U_10920] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_10919)),U_10920) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10919),U_10920))),U_10920),
inference(definitional_conversion,[status(esa)],[f_2845_2]) ).
cnf(f_2845_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_10919)),U_10920) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10919),U_10920))),U_10920),
inference(clausify,[status(thm)],[f_2845_3]) ).
fof(f_2846_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_2846_2,plain,
! [U_10922,U_10921] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_10921)),c_Int_OBit1(U_10922)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_10921)),U_10922)),
inference(variable_rename,[status(thm)],[f_2846_1]) ).
fof(f_2846_3,plain,
! [U_10921,U_10922] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_10921)),c_Int_OBit1(U_10922)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_10921)),U_10922)),
inference(definitional_conversion,[status(esa)],[f_2846_2]) ).
cnf(f_2846_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_10921)),c_Int_OBit1(U_10922)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_10921)),U_10922)),
inference(clausify,[status(thm)],[f_2846_3]) ).
fof(f_2847_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_2847_2,plain,
! [U_10924,U_10923] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_10923)),c_Int_OBit1(U_10924)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10923),c_Int_Osucc(U_10924))),
inference(variable_rename,[status(thm)],[f_2847_1]) ).
fof(f_2847_3,plain,
! [U_10923,U_10924] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_10923)),c_Int_OBit1(U_10924)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10923),c_Int_Osucc(U_10924))),
inference(definitional_conversion,[status(esa)],[f_2847_2]) ).
cnf(f_2847_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_10923)),c_Int_OBit1(U_10924)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10923),c_Int_Osucc(U_10924))),
inference(clausify,[status(thm)],[f_2847_3]) ).
fof(f_2848_1,plain,
! [V_w_2,V_z_2,T_c] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c,T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),c_Groups_Otimes__class_Otimes(T_c)),c_COMBI(T_c)))
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_power__number__of__even]) ).
fof(f_2848_2,plain,
! [U_10927,U_10926,U_10925] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10925),U_10926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10927))) = hAPP(hAPP(c_HOL_OLet(U_10925,U_10925),hAPP(hAPP(c_Power_Opower__class_Opower(U_10925),U_10926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10927))),hAPP(hAPP(c_COMBS(U_10925,U_10925,U_10925),c_Groups_Otimes__class_Otimes(U_10925)),c_COMBI(U_10925)))
| ~ class_Int_Onumber__ring(U_10925) ),
inference(variable_rename,[status(thm)],[f_2848_1]) ).
fof(f_2848_3,plain,
! [U_10925,U_10926,U_10927] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10925),U_10926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10927))) = hAPP(hAPP(c_HOL_OLet(U_10925,U_10925),hAPP(hAPP(c_Power_Opower__class_Opower(U_10925),U_10926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10927))),hAPP(hAPP(c_COMBS(U_10925,U_10925,U_10925),c_Groups_Otimes__class_Otimes(U_10925)),c_COMBI(U_10925)))
| ~ class_Int_Onumber__ring(U_10925) ),
inference(definitional_conversion,[status(esa)],[f_2848_2]) ).
cnf(f_2848_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10925),U_10926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10927))) = hAPP(hAPP(c_HOL_OLet(U_10925,U_10925),hAPP(hAPP(c_Power_Opower__class_Opower(U_10925),U_10926),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10927))),hAPP(hAPP(c_COMBS(U_10925,U_10925,U_10925),c_Groups_Otimes__class_Otimes(U_10925)),c_COMBI(U_10925)))
| ~ class_Int_Onumber__ring(U_10925) ),
inference(clausify,[status(thm)],[f_2848_3]) ).
fof(f_2849_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_2849_2,plain,
! [U_10929,U_10928] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10928),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10929))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10928),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10929))),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_2849_1]) ).
fof(f_2849_3,plain,
! [U_10928,U_10929] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10928),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10929))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10928),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10929))),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_2849_2]) ).
cnf(f_2849_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10928),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10929))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10928),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10929))),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_2849_3]) ).
fof(f_2850_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_2850_2,plain,
! [U_10931,U_10930] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10930),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10930),c_Groups_Oone__class_Oone(U_10930)),c_Groups_Oone__class_Oone(U_10930))),hAPP(c_Int_Onumber__class_Onumber__of(U_10930),U_10931)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10930),c_Int_OBit0(U_10931))
| ~ class_Int_Onumber__ring(U_10930) ),
inference(variable_rename,[status(thm)],[f_2850_1]) ).
fof(f_2850_3,plain,
! [U_10930,U_10931] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10930),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10930),c_Groups_Oone__class_Oone(U_10930)),c_Groups_Oone__class_Oone(U_10930))),hAPP(c_Int_Onumber__class_Onumber__of(U_10930),U_10931)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10930),c_Int_OBit0(U_10931))
| ~ class_Int_Onumber__ring(U_10930) ),
inference(definitional_conversion,[status(esa)],[f_2850_2]) ).
cnf(f_2850_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10930),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10930),c_Groups_Oone__class_Oone(U_10930)),c_Groups_Oone__class_Oone(U_10930))),hAPP(c_Int_Onumber__class_Onumber__of(U_10930),U_10931)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10930),c_Int_OBit0(U_10931))
| ~ class_Int_Onumber__ring(U_10930) ),
inference(clausify,[status(thm)],[f_2850_3]) ).
fof(f_2851_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_2851_2,plain,
! [U_10932] :
( ( 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_10932))))
& 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_10932)))) )
| ~ 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_10932))) ),
inference(variable_rename,[status(thm)],[f_2851_1]) ).
fof(f_2851_3,plain,
( ! [U_10932] :
( 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_10932))))
| ~ sP816(U_10932) )
& ! [U_10932] :
( 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_10932))))
| ~ sP816(U_10932) )
& ! [U_10932] :
( sP816(U_10932)
| ~ 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_10932))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP816])],[f_2851_2]) ).
cnf(f_2851_4,plain,
( sP816(U_10932)
| ~ 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_10932))) ),
inference(clausify,[status(thm)],[f_2851_3]) ).
cnf(f_2851_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_10932))))
| ~ sP816(U_10932) ),
inference(clausify,[status(thm)],[f_2851_3]) ).
cnf(f_2851_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_10932))))
| ~ sP816(U_10932) ),
inference(clausify,[status(thm)],[f_2851_3]) ).
fof(f_2852_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_2852_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_2852_1]) ).
cnf(f_2852_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_2852_2]) ).
fof(f_2853_1,plain,
! [V_w_2,V_v_2,T_c] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),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_c,T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),c_Groups_Otimes__class_Otimes(T_c)),c_COMBI(T_c)))
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_power__number__of__even__number__of]) ).
fof(f_2853_2,plain,
! [U_10935,U_10934,U_10933] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10933),hAPP(c_Int_Onumber__class_Onumber__of(U_10933),U_10934)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10935))) = hAPP(hAPP(c_HOL_OLet(U_10933,U_10933),hAPP(hAPP(c_Power_Opower__class_Opower(U_10933),hAPP(c_Int_Onumber__class_Onumber__of(U_10933),U_10934)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10935))),hAPP(hAPP(c_COMBS(U_10933,U_10933,U_10933),c_Groups_Otimes__class_Otimes(U_10933)),c_COMBI(U_10933)))
| ~ class_Int_Onumber__ring(U_10933) ),
inference(variable_rename,[status(thm)],[f_2853_1]) ).
fof(f_2853_3,plain,
! [U_10933,U_10934,U_10935] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10933),hAPP(c_Int_Onumber__class_Onumber__of(U_10933),U_10934)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10935))) = hAPP(hAPP(c_HOL_OLet(U_10933,U_10933),hAPP(hAPP(c_Power_Opower__class_Opower(U_10933),hAPP(c_Int_Onumber__class_Onumber__of(U_10933),U_10934)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10935))),hAPP(hAPP(c_COMBS(U_10933,U_10933,U_10933),c_Groups_Otimes__class_Otimes(U_10933)),c_COMBI(U_10933)))
| ~ class_Int_Onumber__ring(U_10933) ),
inference(definitional_conversion,[status(esa)],[f_2853_2]) ).
cnf(f_2853_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10933),hAPP(c_Int_Onumber__class_Onumber__of(U_10933),U_10934)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10935))) = hAPP(hAPP(c_HOL_OLet(U_10933,U_10933),hAPP(hAPP(c_Power_Opower__class_Opower(U_10933),hAPP(c_Int_Onumber__class_Onumber__of(U_10933),U_10934)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10935))),hAPP(hAPP(c_COMBS(U_10933,U_10933,U_10933),c_Groups_Otimes__class_Otimes(U_10933)),c_COMBI(U_10933)))
| ~ class_Int_Onumber__ring(U_10933) ),
inference(clausify,[status(thm)],[f_2853_3]) ).
fof(f_2854_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_2854_2,plain,
! [U_10937,U_10936] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10936),hAPP(c_Int_Onumber__class_Onumber__of(U_10936),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10937) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10936),U_10937),U_10937)
| ~ class_Int_Onumber__ring(U_10936) ),
inference(variable_rename,[status(thm)],[f_2854_1]) ).
fof(f_2854_3,plain,
! [U_10937,U_10936] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10936),hAPP(c_Int_Onumber__class_Onumber__of(U_10936),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10937) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10936),U_10937),U_10937)
| ~ class_Int_Onumber__ring(U_10936) ),
inference(definitional_conversion,[status(esa)],[f_2854_2]) ).
cnf(f_2854_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10936),hAPP(c_Int_Onumber__class_Onumber__of(U_10936),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10937) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10936),U_10937),U_10937)
| ~ class_Int_Onumber__ring(U_10936) ),
inference(clausify,[status(thm)],[f_2854_3]) ).
fof(f_2855_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_2855_2,plain,
! [U_10939,U_10938] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10938),U_10939),hAPP(c_Int_Onumber__class_Onumber__of(U_10938),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10938),U_10939),U_10939)
| ~ class_Int_Onumber__ring(U_10938) ),
inference(variable_rename,[status(thm)],[f_2855_1]) ).
fof(f_2855_3,plain,
! [U_10938,U_10939] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10938),U_10939),hAPP(c_Int_Onumber__class_Onumber__of(U_10938),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10938),U_10939),U_10939)
| ~ class_Int_Onumber__ring(U_10938) ),
inference(definitional_conversion,[status(esa)],[f_2855_2]) ).
cnf(f_2855_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10938),U_10939),hAPP(c_Int_Onumber__class_Onumber__of(U_10938),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10938),U_10939),U_10939)
| ~ class_Int_Onumber__ring(U_10938) ),
inference(clausify,[status(thm)],[f_2855_3]) ).
fof(f_2856_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_2856_2,plain,
! [U_10940] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10940),c_Groups_Oone__class_Oone(U_10940)),c_Groups_Oone__class_Oone(U_10940)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10940),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_10940) ),
inference(variable_rename,[status(thm)],[f_2856_1]) ).
fof(f_2856_3,plain,
! [U_10940] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10940),c_Groups_Oone__class_Oone(U_10940)),c_Groups_Oone__class_Oone(U_10940)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10940),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_10940) ),
inference(definitional_conversion,[status(esa)],[f_2856_2]) ).
cnf(f_2856_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10940),c_Groups_Oone__class_Oone(U_10940)),c_Groups_Oone__class_Oone(U_10940)) = hAPP(c_Int_Onumber__class_Onumber__of(U_10940),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_10940) ),
inference(clausify,[status(thm)],[f_2856_3]) ).
fof(f_2857_1,plain,
! [V_a_2,T_c] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_c)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_c) ),
inference(fof_nnf,[status(thm)],[fact_zero__eq__power2]) ).
fof(f_2857_2,plain,
! [U_10942,U_10941] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10941),U_10942),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_10941)
| U_10942 != c_Groups_Ozero__class_Ozero(U_10941) )
& ( U_10942 = c_Groups_Ozero__class_Ozero(U_10941)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_10941),U_10942),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_10941) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_10941) ),
inference(variable_rename,[status(thm)],[f_2857_1]) ).
fof(f_2857_3,plain,
( ! [U_10941,U_10942] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10941),U_10942),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_10941)
| U_10942 != c_Groups_Ozero__class_Ozero(U_10941)
| ~ sP817(U_10941,U_10942) )
& ! [U_10941,U_10942] :
( U_10942 = c_Groups_Ozero__class_Ozero(U_10941)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_10941),U_10942),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_10941)
| ~ sP817(U_10941,U_10942) )
& ! [U_10941,U_10942] :
( sP817(U_10941,U_10942)
| ~ class_Rings_Oring__1__no__zero__divisors(U_10941) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP817])],[f_2857_2]) ).
cnf(f_2857_4,plain,
( sP817(U_10941,U_10942)
| ~ class_Rings_Oring__1__no__zero__divisors(U_10941) ),
inference(clausify,[status(thm)],[f_2857_3]) ).
cnf(f_2857_5,plain,
( U_10942 = c_Groups_Ozero__class_Ozero(U_10941)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_10941),U_10942),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_10941)
| ~ sP817(U_10941,U_10942) ),
inference(clausify,[status(thm)],[f_2857_3]) ).
cnf(f_2857_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10941),U_10942),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_10941)
| U_10942 != c_Groups_Ozero__class_Ozero(U_10941)
| ~ sP817(U_10941,U_10942) ),
inference(clausify,[status(thm)],[f_2857_3]) ).
fof(f_2858_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_2858_2,plain,
! [U_10943] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10943),c_Groups_Ozero__class_Ozero(U_10943)),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_10943)
| ~ class_Rings_Osemiring__1(U_10943) ),
inference(variable_rename,[status(thm)],[f_2858_1]) ).
fof(f_2858_3,plain,
! [U_10943] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10943),c_Groups_Ozero__class_Ozero(U_10943)),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_10943)
| ~ class_Rings_Osemiring__1(U_10943) ),
inference(definitional_conversion,[status(esa)],[f_2858_2]) ).
cnf(f_2858_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10943),c_Groups_Ozero__class_Ozero(U_10943)),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_10943)
| ~ class_Rings_Osemiring__1(U_10943) ),
inference(clausify,[status(thm)],[f_2858_3]) ).
fof(f_2859_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_2859_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_2859_1]) ).
cnf(f_2859_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_2859_2]) ).
fof(f_2860_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_2860_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_2860_1]) ).
cnf(f_2860_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_2860_2]) ).
fof(f_2861_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_2861_2,plain,
! [U_10945,U_10944] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10944),U_10945),U_10945) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10944),U_10945),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_10944) ),
inference(variable_rename,[status(thm)],[f_2861_1]) ).
fof(f_2861_3,plain,
! [U_10944,U_10945] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10944),U_10945),U_10945) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10944),U_10945),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_10944) ),
inference(definitional_conversion,[status(esa)],[f_2861_2]) ).
cnf(f_2861_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10944),U_10945),U_10945) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10944),U_10945),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_10944) ),
inference(clausify,[status(thm)],[f_2861_3]) ).
fof(f_2862_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_2862_2,plain,
! [U_10947,U_10946] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10946),U_10947),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_10946),U_10947),U_10947)
| ~ class_Groups_Omonoid__mult(U_10946) ),
inference(variable_rename,[status(thm)],[f_2862_1]) ).
fof(f_2862_3,plain,
! [U_10946,U_10947] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10946),U_10947),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_10946),U_10947),U_10947)
| ~ class_Groups_Omonoid__mult(U_10946) ),
inference(definitional_conversion,[status(esa)],[f_2862_2]) ).
cnf(f_2862_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10946),U_10947),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_10946),U_10947),U_10947)
| ~ class_Groups_Omonoid__mult(U_10946) ),
inference(clausify,[status(thm)],[f_2862_3]) ).
fof(f_2863_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_2863_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_2863_1]) ).
cnf(f_2863_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_2863_2]) ).
fof(f_2864_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_2864_2,plain,
! [U_10948] : 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_10948) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10948)),
inference(variable_rename,[status(thm)],[f_2864_1]) ).
fof(f_2864_3,plain,
! [U_10948] : 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_10948) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10948)),
inference(definitional_conversion,[status(esa)],[f_2864_2]) ).
cnf(f_2864_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_10948) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10948)),
inference(clausify,[status(thm)],[f_2864_3]) ).
fof(f_2865_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_2865_2,plain,
! [U_10949] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10949),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_10949)),
inference(variable_rename,[status(thm)],[f_2865_1]) ).
fof(f_2865_3,plain,
! [U_10949] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10949),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_10949)),
inference(definitional_conversion,[status(esa)],[f_2865_2]) ).
cnf(f_2865_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10949),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_10949)),
inference(clausify,[status(thm)],[f_2865_3]) ).
fof(f_2866_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_2866_2,plain,
! [U_10950] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10950),c_Groups_Oone__class_Oone(U_10950)),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_10950)
| ~ class_Rings_Osemiring__1(U_10950) ),
inference(variable_rename,[status(thm)],[f_2866_1]) ).
fof(f_2866_3,plain,
! [U_10950] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10950),c_Groups_Oone__class_Oone(U_10950)),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_10950)
| ~ class_Rings_Osemiring__1(U_10950) ),
inference(definitional_conversion,[status(esa)],[f_2866_2]) ).
cnf(f_2866_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10950),c_Groups_Oone__class_Oone(U_10950)),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_10950)
| ~ class_Rings_Osemiring__1(U_10950) ),
inference(clausify,[status(thm)],[f_2866_3]) ).
fof(f_2867_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_2867_2,plain,
! [U_10952,U_10951] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10951),hAPP(c_Groups_Ouminus__class_Ouminus(U_10951),U_10952)),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_10951),U_10952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_10951) ),
inference(variable_rename,[status(thm)],[f_2867_1]) ).
fof(f_2867_3,plain,
! [U_10951,U_10952] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10951),hAPP(c_Groups_Ouminus__class_Ouminus(U_10951),U_10952)),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_10951),U_10952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_10951) ),
inference(definitional_conversion,[status(esa)],[f_2867_2]) ).
cnf(f_2867_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10951),hAPP(c_Groups_Ouminus__class_Ouminus(U_10951),U_10952)),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_10951),U_10952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_10951) ),
inference(clausify,[status(thm)],[f_2867_3]) ).
fof(f_2868_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_2868_2,plain,
! [U_10953] : 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_10953) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10953),U_10953),
inference(variable_rename,[status(thm)],[f_2868_1]) ).
fof(f_2868_3,plain,
! [U_10953] : 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_10953) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10953),U_10953),
inference(definitional_conversion,[status(esa)],[f_2868_2]) ).
cnf(f_2868_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_10953) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10953),U_10953),
inference(clausify,[status(thm)],[f_2868_3]) ).
fof(f_2869_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_2869_2,plain,
! [U_10954] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10954),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_10954),U_10954),
inference(variable_rename,[status(thm)],[f_2869_1]) ).
fof(f_2869_3,plain,
! [U_10954] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10954),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_10954),U_10954),
inference(definitional_conversion,[status(esa)],[f_2869_2]) ).
cnf(f_2869_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10954),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_10954),U_10954),
inference(clausify,[status(thm)],[f_2869_3]) ).
fof(f_2870_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_2870_2,plain,
! [U_10957,U_10956,U_10955] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10955),U_10956),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_10957)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10955),hAPP(hAPP(c_Power_Opower__class_Opower(U_10955),U_10956),U_10957)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_10955) ),
inference(variable_rename,[status(thm)],[f_2870_1]) ).
fof(f_2870_3,plain,
! [U_10955,U_10956,U_10957] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10955),U_10956),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_10957)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10955),hAPP(hAPP(c_Power_Opower__class_Opower(U_10955),U_10956),U_10957)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_10955) ),
inference(definitional_conversion,[status(esa)],[f_2870_2]) ).
cnf(f_2870_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10955),U_10956),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_10957)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10955),hAPP(hAPP(c_Power_Opower__class_Opower(U_10955),U_10956),U_10957)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_10955) ),
inference(clausify,[status(thm)],[f_2870_3]) ).
fof(f_2871_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_2871_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_2871_1]) ).
cnf(f_2871_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_2871_2]) ).
fof(f_2872_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_2872_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_2872_1]) ).
cnf(f_2872_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_2872_2]) ).
fof(f_2873_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_2873_2,plain,
! [U_10959,U_10958] :
( hAPP(c_Groups_Oabs__class_Oabs(U_10958),hAPP(hAPP(c_Power_Opower__class_Opower(U_10958),U_10959),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_10958),U_10959),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_10958) ),
inference(variable_rename,[status(thm)],[f_2873_1]) ).
fof(f_2873_3,plain,
! [U_10958,U_10959] :
( hAPP(c_Groups_Oabs__class_Oabs(U_10958),hAPP(hAPP(c_Power_Opower__class_Opower(U_10958),U_10959),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_10958),U_10959),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_10958) ),
inference(definitional_conversion,[status(esa)],[f_2873_2]) ).
cnf(f_2873_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_10958),hAPP(hAPP(c_Power_Opower__class_Opower(U_10958),U_10959),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_10958),U_10959),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_10958) ),
inference(clausify,[status(thm)],[f_2873_3]) ).
fof(f_2874_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_2874_2,plain,
! [U_10961,U_10960] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10960),hAPP(c_Groups_Oabs__class_Oabs(U_10960),U_10961)),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_10960),U_10961),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_10960) ),
inference(variable_rename,[status(thm)],[f_2874_1]) ).
fof(f_2874_3,plain,
! [U_10960,U_10961] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10960),hAPP(c_Groups_Oabs__class_Oabs(U_10960),U_10961)),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_10960),U_10961),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_10960) ),
inference(definitional_conversion,[status(esa)],[f_2874_2]) ).
cnf(f_2874_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10960),hAPP(c_Groups_Oabs__class_Oabs(U_10960),U_10961)),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_10960),U_10961),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_10960) ),
inference(clausify,[status(thm)],[f_2874_3]) ).
fof(f_2875_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_2875_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_2875_1]) ).
cnf(f_2875_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_2875_2]) ).
fof(f_2876_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_2876_2,plain,
! [U_10962] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10962)),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_10962,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_2876_1]) ).
fof(f_2876_3,plain,
! [U_10962] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10962)),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_10962,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_2876_2]) ).
cnf(f_2876_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10962)),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_10962,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_2876_3]) ).
fof(f_2877_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_2877_2,plain,
! [U_10963] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10963))),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_10963),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_2877_1]) ).
fof(f_2877_3,plain,
! [U_10963] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10963))),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_10963),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_2877_2]) ).
cnf(f_2877_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_10963))),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_10963),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_2877_3]) ).
fof(f_2878_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_2878_2,plain,
! [U_10965,U_10964] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10964)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10965))) = 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_10964),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10965))),
inference(variable_rename,[status(thm)],[f_2878_1]) ).
fof(f_2878_3,plain,
! [U_10964,U_10965] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10964)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10965))) = 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_10964),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10965))),
inference(definitional_conversion,[status(esa)],[f_2878_2]) ).
cnf(f_2878_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10964)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_10965))) = 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_10964),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10965))),
inference(clausify,[status(thm)],[f_2878_3]) ).
fof(f_2879_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_2879_2,plain,
! [U_10966] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10966),U_10966)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_10966,
inference(variable_rename,[status(thm)],[f_2879_1]) ).
fof(f_2879_3,plain,
! [U_10966] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10966),U_10966)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_10966,
inference(definitional_conversion,[status(esa)],[f_2879_2]) ).
cnf(f_2879_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10966),U_10966)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_10966,
inference(clausify,[status(thm)],[f_2879_3]) ).
fof(f_2880_1,plain,
! [V_r_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_r_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_c),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Int_Onumber__ring(T_c)
| ~ class_Fields_Olinordered__field__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff]) ).
fof(f_2880_2,plain,
! [U_10968,U_10967] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10967),c_Groups_Ozero__class_Ozero(U_10967)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10967),U_10968),hAPP(c_Int_Onumber__class_Onumber__of(U_10967),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10967),c_Groups_Ozero__class_Ozero(U_10967)),U_10968)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10967),c_Groups_Ozero__class_Ozero(U_10967)),U_10968))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10967),c_Groups_Ozero__class_Ozero(U_10967)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10967),U_10968),hAPP(c_Int_Onumber__class_Onumber__of(U_10967),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Int_Onumber__ring(U_10967)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10967) ),
inference(variable_rename,[status(thm)],[f_2880_1]) ).
fof(f_2880_3,plain,
( ! [U_10967,U_10968] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10967),c_Groups_Ozero__class_Ozero(U_10967)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10967),U_10968),hAPP(c_Int_Onumber__class_Onumber__of(U_10967),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10967),c_Groups_Ozero__class_Ozero(U_10967)),U_10968))
| ~ sP818(U_10967,U_10968) )
& ! [U_10967,U_10968] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10967),c_Groups_Ozero__class_Ozero(U_10967)),U_10968))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10967),c_Groups_Ozero__class_Ozero(U_10967)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10967),U_10968),hAPP(c_Int_Onumber__class_Onumber__of(U_10967),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ sP818(U_10967,U_10968) )
& ! [U_10967,U_10968] :
( sP818(U_10967,U_10968)
| ~ class_Int_Onumber__ring(U_10967)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10967) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP818])],[f_2880_2]) ).
cnf(f_2880_4,plain,
( sP818(U_10967,U_10968)
| ~ class_Int_Onumber__ring(U_10967)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10967) ),
inference(clausify,[status(thm)],[f_2880_3]) ).
cnf(f_2880_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10967),c_Groups_Ozero__class_Ozero(U_10967)),U_10968))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10967),c_Groups_Ozero__class_Ozero(U_10967)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10967),U_10968),hAPP(c_Int_Onumber__class_Onumber__of(U_10967),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ sP818(U_10967,U_10968) ),
inference(clausify,[status(thm)],[f_2880_3]) ).
cnf(f_2880_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10967),c_Groups_Ozero__class_Ozero(U_10967)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10967),U_10968),hAPP(c_Int_Onumber__class_Onumber__of(U_10967),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10967),c_Groups_Ozero__class_Ozero(U_10967)),U_10968))
| ~ sP818(U_10967,U_10968) ),
inference(clausify,[status(thm)],[f_2880_3]) ).
fof(f_2881_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_2881_2,plain,
! [U_10970,U_10969] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10969),c_Groups_Ozero__class_Ozero(U_10969)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10969),U_10970),hAPP(c_Int_Onumber__class_Onumber__of(U_10969),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10969),c_Groups_Ozero__class_Ozero(U_10969)),U_10970))
| ~ class_Int_Onumber__ring(U_10969)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10969) ),
inference(variable_rename,[status(thm)],[f_2881_1]) ).
fof(f_2881_3,plain,
! [U_10970,U_10969] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10969),c_Groups_Ozero__class_Ozero(U_10969)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10969),U_10970),hAPP(c_Int_Onumber__class_Onumber__of(U_10969),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10969),c_Groups_Ozero__class_Ozero(U_10969)),U_10970))
| ~ class_Int_Onumber__ring(U_10969)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10969) ),
inference(definitional_conversion,[status(esa)],[f_2881_2]) ).
cnf(f_2881_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10969),c_Groups_Ozero__class_Ozero(U_10969)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10969),U_10970),hAPP(c_Int_Onumber__class_Onumber__of(U_10969),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10969),c_Groups_Ozero__class_Ozero(U_10969)),U_10970))
| ~ class_Int_Onumber__ring(U_10969)
| ~ class_Fields_Olinordered__field__inverse__zero(U_10969) ),
inference(clausify,[status(thm)],[f_2881_3]) ).
fof(f_2882_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_2882_2,plain,
! [U_10972,U_10971] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10971),c_Groups_Ozero__class_Ozero(U_10971)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10971),U_10972),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_10971) ),
inference(variable_rename,[status(thm)],[f_2882_1]) ).
fof(f_2882_3,plain,
! [U_10971,U_10972] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10971),c_Groups_Ozero__class_Ozero(U_10971)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10971),U_10972),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_10971) ),
inference(definitional_conversion,[status(esa)],[f_2882_2]) ).
cnf(f_2882_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10971),c_Groups_Ozero__class_Ozero(U_10971)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10971),U_10972),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_10971) ),
inference(clausify,[status(thm)],[f_2882_3]) ).
fof(f_2883_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_2883_2,plain,
! [U_10975,U_10974,U_10973] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),U_10974),U_10975))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),c_Groups_Ozero__class_Ozero(U_10973)),U_10975))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),hAPP(hAPP(c_Power_Opower__class_Opower(U_10973),U_10974),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_10973),U_10975),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_10973) ),
inference(variable_rename,[status(thm)],[f_2883_1]) ).
fof(f_2883_3,plain,
! [U_10973,U_10974,U_10975] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),U_10974),U_10975))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),c_Groups_Ozero__class_Ozero(U_10973)),U_10975))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),hAPP(hAPP(c_Power_Opower__class_Opower(U_10973),U_10974),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_10973),U_10975),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_10973) ),
inference(definitional_conversion,[status(esa)],[f_2883_2]) ).
cnf(f_2883_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),U_10974),U_10975))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),c_Groups_Ozero__class_Ozero(U_10973)),U_10975))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10973),hAPP(hAPP(c_Power_Opower__class_Opower(U_10973),U_10974),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_10973),U_10975),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_10973) ),
inference(clausify,[status(thm)],[f_2883_3]) ).
fof(f_2884_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_2884_2,plain,
! [U_10978,U_10977,U_10976] :
( U_10977 = U_10978
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10976),c_Groups_Ozero__class_Ozero(U_10976)),U_10978))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10976),c_Groups_Ozero__class_Ozero(U_10976)),U_10977))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_10976),U_10977),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_10976),U_10978),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_10976) ),
inference(variable_rename,[status(thm)],[f_2884_1]) ).
fof(f_2884_3,plain,
! [U_10976,U_10977,U_10978] :
( U_10977 = U_10978
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10976),c_Groups_Ozero__class_Ozero(U_10976)),U_10978))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10976),c_Groups_Ozero__class_Ozero(U_10976)),U_10977))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_10976),U_10977),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_10976),U_10978),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_10976) ),
inference(definitional_conversion,[status(esa)],[f_2884_2]) ).
cnf(f_2884_4,plain,
( U_10977 = U_10978
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10976),c_Groups_Ozero__class_Ozero(U_10976)),U_10978))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10976),c_Groups_Ozero__class_Ozero(U_10976)),U_10977))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_10976),U_10977),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_10976),U_10978),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_10976) ),
inference(clausify,[status(thm)],[f_2884_3]) ).
fof(f_2885_1,plain,
! [V_a_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c) )
& ( V_a_2 != c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power2]) ).
fof(f_2885_2,plain,
! [U_10980,U_10979] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10979),c_Groups_Ozero__class_Ozero(U_10979)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10979),U_10980),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| U_10980 = c_Groups_Ozero__class_Ozero(U_10979) )
& ( U_10980 != c_Groups_Ozero__class_Ozero(U_10979)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10979),c_Groups_Ozero__class_Ozero(U_10979)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10979),U_10980),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Rings_Olinordered__idom(U_10979) ),
inference(variable_rename,[status(thm)],[f_2885_1]) ).
fof(f_2885_3,plain,
( ! [U_10980,U_10979] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10979),c_Groups_Ozero__class_Ozero(U_10979)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10979),U_10980),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| U_10980 = c_Groups_Ozero__class_Ozero(U_10979)
| ~ sP819(U_10980,U_10979) )
& ! [U_10980,U_10979] :
( U_10980 != c_Groups_Ozero__class_Ozero(U_10979)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10979),c_Groups_Ozero__class_Ozero(U_10979)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10979),U_10980),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ sP819(U_10980,U_10979) )
& ! [U_10980,U_10979] :
( sP819(U_10980,U_10979)
| ~ class_Rings_Olinordered__idom(U_10979) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP819])],[f_2885_2]) ).
cnf(f_2885_4,plain,
( sP819(U_10980,U_10979)
| ~ class_Rings_Olinordered__idom(U_10979) ),
inference(clausify,[status(thm)],[f_2885_3]) ).
cnf(f_2885_5,plain,
( U_10980 != c_Groups_Ozero__class_Ozero(U_10979)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10979),c_Groups_Ozero__class_Ozero(U_10979)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10979),U_10980),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ sP819(U_10980,U_10979) ),
inference(clausify,[status(thm)],[f_2885_3]) ).
cnf(f_2885_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10979),c_Groups_Ozero__class_Ozero(U_10979)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10979),U_10980),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| U_10980 = c_Groups_Ozero__class_Ozero(U_10979)
| ~ sP819(U_10980,U_10979) ),
inference(clausify,[status(thm)],[f_2885_3]) ).
fof(f_2886_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_2886_2,plain,
! [U_10982,U_10981] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10981),hAPP(hAPP(c_Power_Opower__class_Opower(U_10981),U_10982),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_10981)))
| ~ class_Rings_Olinordered__idom(U_10981) ),
inference(variable_rename,[status(thm)],[f_2886_1]) ).
fof(f_2886_3,plain,
! [U_10981,U_10982] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10981),hAPP(hAPP(c_Power_Opower__class_Opower(U_10981),U_10982),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_10981)))
| ~ class_Rings_Olinordered__idom(U_10981) ),
inference(definitional_conversion,[status(esa)],[f_2886_2]) ).
cnf(f_2886_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10981),hAPP(hAPP(c_Power_Opower__class_Opower(U_10981),U_10982),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_10981)))
| ~ class_Rings_Olinordered__idom(U_10981) ),
inference(clausify,[status(thm)],[f_2886_3]) ).
fof(f_2887_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),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_c)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_c)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_c)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_c) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),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_c) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff]) ).
fof(f_2887_2,plain,
! [U_10985,U_10984,U_10983] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10983),hAPP(hAPP(c_Power_Opower__class_Opower(U_10983),U_10984),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_10983),U_10985),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_10983)
| U_10985 != c_Groups_Ozero__class_Ozero(U_10983)
| U_10984 != c_Groups_Ozero__class_Ozero(U_10983) )
& ( ( U_10985 = c_Groups_Ozero__class_Ozero(U_10983)
& U_10984 = c_Groups_Ozero__class_Ozero(U_10983) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10983),hAPP(hAPP(c_Power_Opower__class_Opower(U_10983),U_10984),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_10983),U_10985),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_10983) ) )
| ~ class_Rings_Olinordered__idom(U_10983) ),
inference(variable_rename,[status(thm)],[f_2887_1]) ).
fof(f_2887_3,plain,
( ! [U_10983,U_10984,U_10985] :
( U_10985 = c_Groups_Ozero__class_Ozero(U_10983)
| ~ sP820(U_10983,U_10984,U_10985) )
& ! [U_10983,U_10984,U_10985] :
( U_10984 = c_Groups_Ozero__class_Ozero(U_10983)
| ~ sP820(U_10983,U_10984,U_10985) )
& ! [U_10983,U_10984,U_10985] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10983),hAPP(hAPP(c_Power_Opower__class_Opower(U_10983),U_10984),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_10983),U_10985),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_10983)
| U_10985 != c_Groups_Ozero__class_Ozero(U_10983)
| U_10984 != c_Groups_Ozero__class_Ozero(U_10983)
| ~ sP821(U_10983,U_10984,U_10985) )
& ! [U_10983,U_10984,U_10985] :
( sP820(U_10983,U_10984,U_10985)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10983),hAPP(hAPP(c_Power_Opower__class_Opower(U_10983),U_10984),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_10983),U_10985),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_10983)
| ~ sP821(U_10983,U_10984,U_10985) )
& ! [U_10983,U_10984,U_10985] :
( sP821(U_10983,U_10984,U_10985)
| ~ class_Rings_Olinordered__idom(U_10983) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP820,sP821])],[f_2887_2]) ).
cnf(f_2887_4,plain,
( sP821(U_10983,U_10984,U_10985)
| ~ class_Rings_Olinordered__idom(U_10983) ),
inference(clausify,[status(thm)],[f_2887_3]) ).
cnf(f_2887_5,plain,
( sP820(U_10983,U_10984,U_10985)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10983),hAPP(hAPP(c_Power_Opower__class_Opower(U_10983),U_10984),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_10983),U_10985),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_10983)
| ~ sP821(U_10983,U_10984,U_10985) ),
inference(clausify,[status(thm)],[f_2887_3]) ).
cnf(f_2887_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10983),hAPP(hAPP(c_Power_Opower__class_Opower(U_10983),U_10984),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_10983),U_10985),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_10983)
| U_10985 != c_Groups_Ozero__class_Ozero(U_10983)
| U_10984 != c_Groups_Ozero__class_Ozero(U_10983)
| ~ sP821(U_10983,U_10984,U_10985) ),
inference(clausify,[status(thm)],[f_2887_3]) ).
cnf(f_2887_7,plain,
( U_10984 = c_Groups_Ozero__class_Ozero(U_10983)
| ~ sP820(U_10983,U_10984,U_10985) ),
inference(clausify,[status(thm)],[f_2887_3]) ).
cnf(f_2887_8,plain,
( U_10985 = c_Groups_Ozero__class_Ozero(U_10983)
| ~ sP820(U_10983,U_10984,U_10985) ),
inference(clausify,[status(thm)],[f_2887_3]) ).
fof(f_2888_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_2888_2,plain,
! [U_10987,U_10986] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10986),hAPP(c_Int_Onumber__class_Onumber__of(U_10986),U_10987)),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_10986),hAPP(c_Int_Onumber__class_Onumber__of(U_10986),U_10987)),hAPP(c_Int_Onumber__class_Onumber__of(U_10986),U_10987))
| ~ class_Int_Onumber(U_10986)
| ~ class_Groups_Omonoid__mult(U_10986) ),
inference(variable_rename,[status(thm)],[f_2888_1]) ).
fof(f_2888_3,plain,
! [U_10986,U_10987] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10986),hAPP(c_Int_Onumber__class_Onumber__of(U_10986),U_10987)),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_10986),hAPP(c_Int_Onumber__class_Onumber__of(U_10986),U_10987)),hAPP(c_Int_Onumber__class_Onumber__of(U_10986),U_10987))
| ~ class_Int_Onumber(U_10986)
| ~ class_Groups_Omonoid__mult(U_10986) ),
inference(definitional_conversion,[status(esa)],[f_2888_2]) ).
cnf(f_2888_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10986),hAPP(c_Int_Onumber__class_Onumber__of(U_10986),U_10987)),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_10986),hAPP(c_Int_Onumber__class_Onumber__of(U_10986),U_10987)),hAPP(c_Int_Onumber__class_Onumber__of(U_10986),U_10987))
| ~ class_Int_Onumber(U_10986)
| ~ class_Groups_Omonoid__mult(U_10986) ),
inference(clausify,[status(thm)],[f_2888_3]) ).
fof(f_2889_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_2889_2,plain,
! [U_10988] :
( U_10988 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_10988 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10988),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_2889_1]) ).
fof(f_2889_3,plain,
! [U_10988] :
( U_10988 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_10988 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10988),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_2889_2]) ).
cnf(f_2889_4,plain,
( U_10988 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_10988 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10988),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(clausify,[status(thm)],[f_2889_3]) ).
fof(f_2890_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_2890_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_2890_1]) ).
cnf(f_2890_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_2890_2]) ).
fof(f_2891_1,plain,
! [V_a_2,T_c] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c)
| ( V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Groups_Oone__class_Oone(T_c))
& V_a_2 != c_Groups_Oone__class_Oone(T_c) ) )
& ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),c_Groups_Oone__class_Oone(T_c))
| V_a_2 = c_Groups_Oone__class_Oone(T_c)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_c) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff]) ).
fof(f_2891_2,plain,
! [U_10990,U_10989] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10989),U_10990),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_10989)
| ( U_10990 != hAPP(c_Groups_Ouminus__class_Ouminus(U_10989),c_Groups_Oone__class_Oone(U_10989))
& U_10990 != c_Groups_Oone__class_Oone(U_10989) ) )
& ( U_10990 = hAPP(c_Groups_Ouminus__class_Ouminus(U_10989),c_Groups_Oone__class_Oone(U_10989))
| U_10990 = c_Groups_Oone__class_Oone(U_10989)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_10989),U_10990),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_10989) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_10989) ),
inference(variable_rename,[status(thm)],[f_2891_1]) ).
fof(f_2891_3,plain,
( ! [U_10989,U_10990] :
( U_10990 != hAPP(c_Groups_Ouminus__class_Ouminus(U_10989),c_Groups_Oone__class_Oone(U_10989))
| ~ sP822(U_10989,U_10990) )
& ! [U_10989,U_10990] :
( U_10990 != c_Groups_Oone__class_Oone(U_10989)
| ~ sP822(U_10989,U_10990) )
& ! [U_10989,U_10990] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10989),U_10990),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_10989)
| sP822(U_10989,U_10990)
| ~ sP823(U_10989,U_10990) )
& ! [U_10989,U_10990] :
( U_10990 = hAPP(c_Groups_Ouminus__class_Ouminus(U_10989),c_Groups_Oone__class_Oone(U_10989))
| U_10990 = c_Groups_Oone__class_Oone(U_10989)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_10989),U_10990),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_10989)
| ~ sP823(U_10989,U_10990) )
& ! [U_10989,U_10990] :
( sP823(U_10989,U_10990)
| ~ class_Rings_Oring__1__no__zero__divisors(U_10989) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP822,sP823])],[f_2891_2]) ).
cnf(f_2891_4,plain,
( sP823(U_10989,U_10990)
| ~ class_Rings_Oring__1__no__zero__divisors(U_10989) ),
inference(clausify,[status(thm)],[f_2891_3]) ).
cnf(f_2891_5,plain,
( U_10990 = hAPP(c_Groups_Ouminus__class_Ouminus(U_10989),c_Groups_Oone__class_Oone(U_10989))
| U_10990 = c_Groups_Oone__class_Oone(U_10989)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_10989),U_10990),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_10989)
| ~ sP823(U_10989,U_10990) ),
inference(clausify,[status(thm)],[f_2891_3]) ).
cnf(f_2891_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10989),U_10990),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_10989)
| sP822(U_10989,U_10990)
| ~ sP823(U_10989,U_10990) ),
inference(clausify,[status(thm)],[f_2891_3]) ).
cnf(f_2891_7,plain,
( U_10990 != c_Groups_Oone__class_Oone(U_10989)
| ~ sP822(U_10989,U_10990) ),
inference(clausify,[status(thm)],[f_2891_3]) ).
cnf(f_2891_8,plain,
( U_10990 != hAPP(c_Groups_Ouminus__class_Ouminus(U_10989),c_Groups_Oone__class_Oone(U_10989))
| ~ sP822(U_10989,U_10990) ),
inference(clausify,[status(thm)],[f_2891_3]) ).
fof(f_2892_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_2892_2,plain,
! [U_10993,U_10992,U_10991] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10991),U_10992),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_10993)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10991),hAPP(hAPP(c_Power_Opower__class_Opower(U_10991),U_10992),U_10993)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10991),U_10992),U_10993))
| ~ class_Rings_Ocomm__semiring__1(U_10991) ),
inference(variable_rename,[status(thm)],[f_2892_1]) ).
fof(f_2892_3,plain,
! [U_10993,U_10991,U_10992] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10991),U_10992),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_10993)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10991),hAPP(hAPP(c_Power_Opower__class_Opower(U_10991),U_10992),U_10993)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10991),U_10992),U_10993))
| ~ class_Rings_Ocomm__semiring__1(U_10991) ),
inference(definitional_conversion,[status(esa)],[f_2892_2]) ).
cnf(f_2892_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10991),U_10992),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_10993)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10991),hAPP(hAPP(c_Power_Opower__class_Opower(U_10991),U_10992),U_10993)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10991),U_10992),U_10993))
| ~ class_Rings_Ocomm__semiring__1(U_10991) ),
inference(clausify,[status(thm)],[f_2892_3]) ).
fof(f_2893_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_2893_2,plain,
! [U_10996,U_10995,U_10994] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10994),hAPP(c_Groups_Ouminus__class_Ouminus(U_10994),U_10995)),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_10996)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10994),U_10995),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_10996))
| ~ class_Rings_Oring__1(U_10994) ),
inference(variable_rename,[status(thm)],[f_2893_1]) ).
fof(f_2893_3,plain,
! [U_10994,U_10996,U_10995] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10994),hAPP(c_Groups_Ouminus__class_Ouminus(U_10994),U_10995)),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_10996)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10994),U_10995),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_10996))
| ~ class_Rings_Oring__1(U_10994) ),
inference(definitional_conversion,[status(esa)],[f_2893_2]) ).
cnf(f_2893_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_10994),hAPP(c_Groups_Ouminus__class_Ouminus(U_10994),U_10995)),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_10996)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10994),U_10995),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_10996))
| ~ class_Rings_Oring__1(U_10994) ),
inference(clausify,[status(thm)],[f_2893_3]) ).
fof(f_2894_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_2894_2,plain,
! [U_10999,U_10998,U_10997] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10997),U_10998),U_10999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10997),c_Groups_Ozero__class_Ozero(U_10997)),U_10999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10997),hAPP(hAPP(c_Power_Opower__class_Opower(U_10997),U_10998),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_10997),U_10999),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_10997) ),
inference(variable_rename,[status(thm)],[f_2894_1]) ).
fof(f_2894_3,plain,
! [U_10997,U_10998,U_10999] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10997),U_10998),U_10999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10997),c_Groups_Ozero__class_Ozero(U_10997)),U_10999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10997),hAPP(hAPP(c_Power_Opower__class_Opower(U_10997),U_10998),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_10997),U_10999),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_10997) ),
inference(definitional_conversion,[status(esa)],[f_2894_2]) ).
cnf(f_2894_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10997),U_10998),U_10999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10997),c_Groups_Ozero__class_Ozero(U_10997)),U_10999))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10997),hAPP(hAPP(c_Power_Opower__class_Opower(U_10997),U_10998),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_10997),U_10999),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_10997) ),
inference(clausify,[status(thm)],[f_2894_3]) ).
fof(f_2895_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_2895_2,plain,
! [U_11002,U_11001,U_11000] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11000),c_Groups_Ozero__class_Ozero(U_11000)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11000),hAPP(hAPP(c_Power_Opower__class_Opower(U_11000),U_11001),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_11000),U_11002),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_11000) ),
inference(variable_rename,[status(thm)],[f_2895_1]) ).
fof(f_2895_3,plain,
! [U_11001,U_11000,U_11002] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11000),c_Groups_Ozero__class_Ozero(U_11000)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11000),hAPP(hAPP(c_Power_Opower__class_Opower(U_11000),U_11001),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_11000),U_11002),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_11000) ),
inference(definitional_conversion,[status(esa)],[f_2895_2]) ).
cnf(f_2895_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11000),c_Groups_Ozero__class_Ozero(U_11000)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11000),hAPP(hAPP(c_Power_Opower__class_Opower(U_11000),U_11001),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_11000),U_11002),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_11000) ),
inference(clausify,[status(thm)],[f_2895_3]) ).
fof(f_2896_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),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_c)))
| V_y_2 != c_Groups_Ozero__class_Ozero(T_c)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_c) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_c)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_c) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),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_c))) ) )
| ~ class_Rings_Olinordered__idom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff]) ).
fof(f_2896_2,plain,
! [U_11005,U_11004,U_11003] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11003),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11003),hAPP(hAPP(c_Power_Opower__class_Opower(U_11003),U_11004),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_11003),U_11005),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_11003)))
| U_11005 != c_Groups_Ozero__class_Ozero(U_11003)
| U_11004 != c_Groups_Ozero__class_Ozero(U_11003) )
& ( ( U_11005 = c_Groups_Ozero__class_Ozero(U_11003)
& U_11004 = c_Groups_Ozero__class_Ozero(U_11003) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11003),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11003),hAPP(hAPP(c_Power_Opower__class_Opower(U_11003),U_11004),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_11003),U_11005),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_11003))) ) )
| ~ class_Rings_Olinordered__idom(U_11003) ),
inference(variable_rename,[status(thm)],[f_2896_1]) ).
fof(f_2896_3,plain,
( ! [U_11003,U_11004,U_11005] :
( U_11005 = c_Groups_Ozero__class_Ozero(U_11003)
| ~ sP824(U_11003,U_11004,U_11005) )
& ! [U_11003,U_11004,U_11005] :
( U_11004 = c_Groups_Ozero__class_Ozero(U_11003)
| ~ sP824(U_11003,U_11004,U_11005) )
& ! [U_11003,U_11004,U_11005] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11003),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11003),hAPP(hAPP(c_Power_Opower__class_Opower(U_11003),U_11004),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_11003),U_11005),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_11003)))
| U_11005 != c_Groups_Ozero__class_Ozero(U_11003)
| U_11004 != c_Groups_Ozero__class_Ozero(U_11003)
| ~ sP825(U_11003,U_11004,U_11005) )
& ! [U_11003,U_11004,U_11005] :
( sP824(U_11003,U_11004,U_11005)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11003),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11003),hAPP(hAPP(c_Power_Opower__class_Opower(U_11003),U_11004),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_11003),U_11005),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_11003)))
| ~ sP825(U_11003,U_11004,U_11005) )
& ! [U_11003,U_11004,U_11005] :
( sP825(U_11003,U_11004,U_11005)
| ~ class_Rings_Olinordered__idom(U_11003) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP824,sP825])],[f_2896_2]) ).
cnf(f_2896_4,plain,
( sP825(U_11003,U_11004,U_11005)
| ~ class_Rings_Olinordered__idom(U_11003) ),
inference(clausify,[status(thm)],[f_2896_3]) ).
cnf(f_2896_5,plain,
( sP824(U_11003,U_11004,U_11005)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11003),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11003),hAPP(hAPP(c_Power_Opower__class_Opower(U_11003),U_11004),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_11003),U_11005),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_11003)))
| ~ sP825(U_11003,U_11004,U_11005) ),
inference(clausify,[status(thm)],[f_2896_3]) ).
cnf(f_2896_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11003),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11003),hAPP(hAPP(c_Power_Opower__class_Opower(U_11003),U_11004),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_11003),U_11005),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_11003)))
| U_11005 != c_Groups_Ozero__class_Ozero(U_11003)
| U_11004 != c_Groups_Ozero__class_Ozero(U_11003)
| ~ sP825(U_11003,U_11004,U_11005) ),
inference(clausify,[status(thm)],[f_2896_3]) ).
cnf(f_2896_7,plain,
( U_11004 = c_Groups_Ozero__class_Ozero(U_11003)
| ~ sP824(U_11003,U_11004,U_11005) ),
inference(clausify,[status(thm)],[f_2896_3]) ).
cnf(f_2896_8,plain,
( U_11005 = c_Groups_Ozero__class_Ozero(U_11003)
| ~ sP824(U_11003,U_11004,U_11005) ),
inference(clausify,[status(thm)],[f_2896_3]) ).
fof(f_2897_1,plain,
! [V_y_2,V_x_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),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_c)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_c) ) )
& ( V_y_2 != c_Groups_Ozero__class_Ozero(T_c)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),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_c),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_c) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff]) ).
fof(f_2897_2,plain,
! [U_11008,U_11007,U_11006] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11006),c_Groups_Ozero__class_Ozero(U_11006)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11006),hAPP(hAPP(c_Power_Opower__class_Opower(U_11006),U_11007),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_11006),U_11008),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ( U_11008 = c_Groups_Ozero__class_Ozero(U_11006)
& U_11007 = c_Groups_Ozero__class_Ozero(U_11006) ) )
& ( U_11008 != c_Groups_Ozero__class_Ozero(U_11006)
| U_11007 != c_Groups_Ozero__class_Ozero(U_11006)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11006),c_Groups_Ozero__class_Ozero(U_11006)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11006),hAPP(hAPP(c_Power_Opower__class_Opower(U_11006),U_11007),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_11006),U_11008),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
| ~ class_Rings_Olinordered__idom(U_11006) ),
inference(variable_rename,[status(thm)],[f_2897_1]) ).
fof(f_2897_3,plain,
( ! [U_11007,U_11006,U_11008] :
( U_11008 = c_Groups_Ozero__class_Ozero(U_11006)
| ~ sP826(U_11007,U_11006,U_11008) )
& ! [U_11007,U_11006,U_11008] :
( U_11007 = c_Groups_Ozero__class_Ozero(U_11006)
| ~ sP826(U_11007,U_11006,U_11008) )
& ! [U_11007,U_11006,U_11008] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11006),c_Groups_Ozero__class_Ozero(U_11006)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11006),hAPP(hAPP(c_Power_Opower__class_Opower(U_11006),U_11007),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_11006),U_11008),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| sP826(U_11007,U_11006,U_11008)
| ~ sP827(U_11007,U_11006,U_11008) )
& ! [U_11007,U_11006,U_11008] :
( U_11008 != c_Groups_Ozero__class_Ozero(U_11006)
| U_11007 != c_Groups_Ozero__class_Ozero(U_11006)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11006),c_Groups_Ozero__class_Ozero(U_11006)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11006),hAPP(hAPP(c_Power_Opower__class_Opower(U_11006),U_11007),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_11006),U_11008),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ sP827(U_11007,U_11006,U_11008) )
& ! [U_11007,U_11006,U_11008] :
( sP827(U_11007,U_11006,U_11008)
| ~ class_Rings_Olinordered__idom(U_11006) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP826,sP827])],[f_2897_2]) ).
cnf(f_2897_4,plain,
( sP827(U_11007,U_11006,U_11008)
| ~ class_Rings_Olinordered__idom(U_11006) ),
inference(clausify,[status(thm)],[f_2897_3]) ).
cnf(f_2897_5,plain,
( U_11008 != c_Groups_Ozero__class_Ozero(U_11006)
| U_11007 != c_Groups_Ozero__class_Ozero(U_11006)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11006),c_Groups_Ozero__class_Ozero(U_11006)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11006),hAPP(hAPP(c_Power_Opower__class_Opower(U_11006),U_11007),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_11006),U_11008),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ sP827(U_11007,U_11006,U_11008) ),
inference(clausify,[status(thm)],[f_2897_3]) ).
cnf(f_2897_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11006),c_Groups_Ozero__class_Ozero(U_11006)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11006),hAPP(hAPP(c_Power_Opower__class_Opower(U_11006),U_11007),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_11006),U_11008),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| sP826(U_11007,U_11006,U_11008)
| ~ sP827(U_11007,U_11006,U_11008) ),
inference(clausify,[status(thm)],[f_2897_3]) ).
cnf(f_2897_7,plain,
( U_11007 = c_Groups_Ozero__class_Ozero(U_11006)
| ~ sP826(U_11007,U_11006,U_11008) ),
inference(clausify,[status(thm)],[f_2897_3]) ).
cnf(f_2897_8,plain,
( U_11008 = c_Groups_Ozero__class_Ozero(U_11006)
| ~ sP826(U_11007,U_11006,U_11008) ),
inference(clausify,[status(thm)],[f_2897_3]) ).
fof(f_2898_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_2898_2,plain,
! [U_11011,U_11010,U_11009] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11009),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11009),hAPP(hAPP(c_Power_Opower__class_Opower(U_11009),U_11010),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_11009),U_11011),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_11009)))
| ~ class_Rings_Olinordered__idom(U_11009) ),
inference(variable_rename,[status(thm)],[f_2898_1]) ).
fof(f_2898_3,plain,
! [U_11010,U_11009,U_11011] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11009),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11009),hAPP(hAPP(c_Power_Opower__class_Opower(U_11009),U_11010),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_11009),U_11011),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_11009)))
| ~ class_Rings_Olinordered__idom(U_11009) ),
inference(definitional_conversion,[status(esa)],[f_2898_2]) ).
cnf(f_2898_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11009),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11009),hAPP(hAPP(c_Power_Opower__class_Opower(U_11009),U_11010),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_11009),U_11011),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_11009)))
| ~ class_Rings_Olinordered__idom(U_11009) ),
inference(clausify,[status(thm)],[f_2898_3]) ).
fof(f_2899_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_2899_2,plain,
! [U_11014,U_11013,U_11012] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11012),U_11013),U_11014)),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_11012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11012),hAPP(hAPP(c_Power_Opower__class_Opower(U_11012),U_11013),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_11012),U_11014),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_11012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11012),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11013)),U_11014))
| ~ class_Int_Onumber__ring(U_11012) ),
inference(variable_rename,[status(thm)],[f_2899_1]) ).
fof(f_2899_3,plain,
! [U_11012,U_11013,U_11014] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11012),U_11013),U_11014)),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_11012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11012),hAPP(hAPP(c_Power_Opower__class_Opower(U_11012),U_11013),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_11012),U_11014),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_11012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11012),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11013)),U_11014))
| ~ class_Int_Onumber__ring(U_11012) ),
inference(definitional_conversion,[status(esa)],[f_2899_2]) ).
cnf(f_2899_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11012),U_11013),U_11014)),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_11012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11012),hAPP(hAPP(c_Power_Opower__class_Opower(U_11012),U_11013),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_11012),U_11014),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_11012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11012),hAPP(c_Int_Onumber__class_Onumber__of(U_11012),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11013)),U_11014))
| ~ class_Int_Onumber__ring(U_11012) ),
inference(clausify,[status(thm)],[f_2899_3]) ).
fof(f_2900_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_2900_2,plain,
! [U_11017,U_11016,U_11015] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11015),c_Groups_Ozero__class_Ozero(U_11015)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11015),U_11016),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_11017))))
| ~ class_Rings_Olinordered__idom(U_11015) ),
inference(variable_rename,[status(thm)],[f_2900_1]) ).
fof(f_2900_3,plain,
! [U_11015,U_11016,U_11017] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11015),c_Groups_Ozero__class_Ozero(U_11015)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11015),U_11016),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_11017))))
| ~ class_Rings_Olinordered__idom(U_11015) ),
inference(definitional_conversion,[status(esa)],[f_2900_2]) ).
cnf(f_2900_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11015),c_Groups_Ozero__class_Ozero(U_11015)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11015),U_11016),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_11017))))
| ~ class_Rings_Olinordered__idom(U_11015) ),
inference(clausify,[status(thm)],[f_2900_3]) ).
fof(f_2901_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_2901_2,plain,
! [U_11020,U_11019,U_11018] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11018),U_11019),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_11020))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11018),U_11019),hAPP(hAPP(c_Power_Opower__class_Opower(U_11018),hAPP(hAPP(c_Power_Opower__class_Opower(U_11018),U_11019),U_11020)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_11018) ),
inference(variable_rename,[status(thm)],[f_2901_1]) ).
fof(f_2901_3,plain,
! [U_11018,U_11019,U_11020] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11018),U_11019),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_11020))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11018),U_11019),hAPP(hAPP(c_Power_Opower__class_Opower(U_11018),hAPP(hAPP(c_Power_Opower__class_Opower(U_11018),U_11019),U_11020)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_11018) ),
inference(definitional_conversion,[status(esa)],[f_2901_2]) ).
cnf(f_2901_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11018),U_11019),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_11020))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11018),U_11019),hAPP(hAPP(c_Power_Opower__class_Opower(U_11018),hAPP(hAPP(c_Power_Opower__class_Opower(U_11018),U_11019),U_11020)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_11018) ),
inference(clausify,[status(thm)],[f_2901_3]) ).
fof(f_2902_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_2902_2,plain,
! [U_11023,U_11022,U_11021] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11021),U_11022),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_11023))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11021),U_11022),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11021),hAPP(hAPP(c_Power_Opower__class_Opower(U_11021),U_11022),U_11023)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11021),U_11022),U_11023)))
| ~ class_Rings_Ocomm__semiring__1(U_11021) ),
inference(variable_rename,[status(thm)],[f_2902_1]) ).
fof(f_2902_3,plain,
! [U_11021,U_11022,U_11023] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11021),U_11022),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_11023))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11021),U_11022),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11021),hAPP(hAPP(c_Power_Opower__class_Opower(U_11021),U_11022),U_11023)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11021),U_11022),U_11023)))
| ~ class_Rings_Ocomm__semiring__1(U_11021) ),
inference(definitional_conversion,[status(esa)],[f_2902_2]) ).
cnf(f_2902_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11021),U_11022),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_11023))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11021),U_11022),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11021),hAPP(hAPP(c_Power_Opower__class_Opower(U_11021),U_11022),U_11023)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11021),U_11022),U_11023)))
| ~ class_Rings_Ocomm__semiring__1(U_11021) ),
inference(clausify,[status(thm)],[f_2902_3]) ).
fof(f_2903_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_2903_2,plain,
! [U_11025,U_11024] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11024),hAPP(c_Groups_Ouminus__class_Ouminus(U_11024),c_Groups_Oone__class_Oone(U_11024))),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_11025)) = c_Groups_Oone__class_Oone(U_11024)
| ~ class_Rings_Oring__1(U_11024) ),
inference(variable_rename,[status(thm)],[f_2903_1]) ).
fof(f_2903_3,plain,
! [U_11024,U_11025] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11024),hAPP(c_Groups_Ouminus__class_Ouminus(U_11024),c_Groups_Oone__class_Oone(U_11024))),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_11025)) = c_Groups_Oone__class_Oone(U_11024)
| ~ class_Rings_Oring__1(U_11024) ),
inference(definitional_conversion,[status(esa)],[f_2903_2]) ).
cnf(f_2903_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11024),hAPP(c_Groups_Ouminus__class_Ouminus(U_11024),c_Groups_Oone__class_Oone(U_11024))),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_11025)) = c_Groups_Oone__class_Oone(U_11024)
| ~ class_Rings_Oring__1(U_11024) ),
inference(clausify,[status(thm)],[f_2903_3]) ).
fof(f_2904_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_2904_2,plain,
! [U_11027,U_11026] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11027))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11026))) = 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_11027)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11026))
| 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_11026))) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11027))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11026))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11027)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11026))
| ~ 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_11026))) ) ),
inference(variable_rename,[status(thm)],[f_2904_1]) ).
fof(f_2904_3,plain,
( ! [U_11031,U_11029] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11031))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11029))) = 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_11031)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11029))
| 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_11029))) )
& ! [U_11030,U_11028] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11030))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11028))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11030)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11028))
| ~ 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_11028))) ) ),
inference(miniscope,[status(thm)],[f_2904_2]) ).
fof(f_2904_4,plain,
( ! [U_11029,U_11031] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11031))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11029))) = 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_11031)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11029))
| 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_11029))) )
& ! [U_11030,U_11028] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_11030))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11028))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11030)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11028))
| ~ 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_11028))) ) ),
inference(definitional_conversion,[status(esa)],[f_2904_3]) ).
cnf(f_2904_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_11030))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11028))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11030)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11028))
| ~ 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_11028))) ),
inference(clausify,[status(thm)],[f_2904_4]) ).
cnf(f_2904_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_11031))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_11029))) = 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_11031)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11029))
| 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_11029))) ),
inference(clausify,[status(thm)],[f_2904_4]) ).
fof(f_2905_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_2905_2,plain,
! [U_11032] :
( ( 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_11032,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_11032,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_11032,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_11032,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_2905_1]) ).
fof(f_2905_3,plain,
( ! [U_11034] :
( 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_11034,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_11034,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_11033] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11033,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_11033,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
inference(miniscope,[status(thm)],[f_2905_2]) ).
fof(f_2905_4,plain,
( ! [U_11034] :
( 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_11034,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_11034,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_11033] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11033,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_11033,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_2905_3]) ).
cnf(f_2905_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11033,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_11033,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(clausify,[status(thm)],[f_2905_4]) ).
cnf(f_2905_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_11034,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_11034,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_2905_4]) ).
fof(f_2906_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_2906_2,plain,
! [U_11035] :
( 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_11035),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_11035)) ),
inference(variable_rename,[status(thm)],[f_2906_1]) ).
fof(f_2906_3,plain,
! [U_11035] :
( 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_11035),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_11035)) ),
inference(definitional_conversion,[status(esa)],[f_2906_2]) ).
cnf(f_2906_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_11035),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_11035)) ),
inference(clausify,[status(thm)],[f_2906_3]) ).
fof(f_2907_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_2907_2,plain,
! [U_11038,U_11037,U_11036] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11036),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11036),U_11037),U_11038)),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_11036),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11036),hAPP(hAPP(c_Power_Opower__class_Opower(U_11036),U_11037),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_11036),U_11038),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_11036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11036),hAPP(c_Int_Onumber__class_Onumber__of(U_11036),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11037)),U_11038))
| ~ class_Int_Onumber__ring(U_11036) ),
inference(variable_rename,[status(thm)],[f_2907_1]) ).
fof(f_2907_3,plain,
! [U_11036,U_11037,U_11038] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11036),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11036),U_11037),U_11038)),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_11036),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11036),hAPP(hAPP(c_Power_Opower__class_Opower(U_11036),U_11037),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_11036),U_11038),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_11036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11036),hAPP(c_Int_Onumber__class_Onumber__of(U_11036),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11037)),U_11038))
| ~ class_Int_Onumber__ring(U_11036) ),
inference(definitional_conversion,[status(esa)],[f_2907_2]) ).
cnf(f_2907_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11036),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11036),U_11037),U_11038)),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_11036),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11036),hAPP(hAPP(c_Power_Opower__class_Opower(U_11036),U_11037),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_11036),U_11038),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_11036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11036),hAPP(c_Int_Onumber__class_Onumber__of(U_11036),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11037)),U_11038))
| ~ class_Int_Onumber__ring(U_11036) ),
inference(clausify,[status(thm)],[f_2907_3]) ).
fof(f_2908_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_2908_2,plain,
! [U_11041,U_11040,U_11039] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11039),c_Groups_Ozero__class_Ozero(U_11039)),U_11040))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11039),c_Groups_Ozero__class_Ozero(U_11039)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11039),U_11040),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_11041)))))
| ~ class_Rings_Olinordered__idom(U_11039) ),
inference(variable_rename,[status(thm)],[f_2908_1]) ).
fof(f_2908_3,plain,
! [U_11039,U_11040,U_11041] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11039),c_Groups_Ozero__class_Ozero(U_11039)),U_11040))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11039),c_Groups_Ozero__class_Ozero(U_11039)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11039),U_11040),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_11041)))))
| ~ class_Rings_Olinordered__idom(U_11039) ),
inference(definitional_conversion,[status(esa)],[f_2908_2]) ).
cnf(f_2908_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11039),c_Groups_Ozero__class_Ozero(U_11039)),U_11040))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11039),c_Groups_Ozero__class_Ozero(U_11039)),hAPP(hAPP(c_Power_Opower__class_Opower(U_11039),U_11040),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_11041)))))
| ~ class_Rings_Olinordered__idom(U_11039) ),
inference(clausify,[status(thm)],[f_2908_3]) ).
fof(f_2909_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_2909_2,plain,
! [U_11044,U_11043,U_11042] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11042),hAPP(hAPP(c_Power_Opower__class_Opower(U_11042),U_11043),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_11044)))),c_Groups_Ozero__class_Ozero(U_11042)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11042),U_11043),c_Groups_Ozero__class_Ozero(U_11042)))
| ~ class_Rings_Olinordered__idom(U_11042) ),
inference(variable_rename,[status(thm)],[f_2909_1]) ).
fof(f_2909_3,plain,
! [U_11042,U_11043,U_11044] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11042),hAPP(hAPP(c_Power_Opower__class_Opower(U_11042),U_11043),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_11044)))),c_Groups_Ozero__class_Ozero(U_11042)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11042),U_11043),c_Groups_Ozero__class_Ozero(U_11042)))
| ~ class_Rings_Olinordered__idom(U_11042) ),
inference(definitional_conversion,[status(esa)],[f_2909_2]) ).
cnf(f_2909_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11042),hAPP(hAPP(c_Power_Opower__class_Opower(U_11042),U_11043),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_11044)))),c_Groups_Ozero__class_Ozero(U_11042)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11042),U_11043),c_Groups_Ozero__class_Ozero(U_11042)))
| ~ class_Rings_Olinordered__idom(U_11042) ),
inference(clausify,[status(thm)],[f_2909_3]) ).
fof(f_2910_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_2910_2,plain,
! [U_11046,U_11045] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11045),hAPP(c_Groups_Ouminus__class_Ouminus(U_11045),c_Groups_Oone__class_Oone(U_11045))),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_11046))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11045),c_Groups_Oone__class_Oone(U_11045))
| ~ class_Rings_Oring__1(U_11045) ),
inference(variable_rename,[status(thm)],[f_2910_1]) ).
fof(f_2910_3,plain,
! [U_11045,U_11046] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11045),hAPP(c_Groups_Ouminus__class_Ouminus(U_11045),c_Groups_Oone__class_Oone(U_11045))),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_11046))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11045),c_Groups_Oone__class_Oone(U_11045))
| ~ class_Rings_Oring__1(U_11045) ),
inference(definitional_conversion,[status(esa)],[f_2910_2]) ).
cnf(f_2910_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11045),hAPP(c_Groups_Ouminus__class_Ouminus(U_11045),c_Groups_Oone__class_Oone(U_11045))),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_11046))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11045),c_Groups_Oone__class_Oone(U_11045))
| ~ class_Rings_Oring__1(U_11045) ),
inference(clausify,[status(thm)],[f_2910_3]) ).
fof(f_2911_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_2911_2,plain,
! [U_11047] :
( 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_11047),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_11047)) ),
inference(variable_rename,[status(thm)],[f_2911_1]) ).
fof(f_2911_3,plain,
! [U_11047] :
( 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_11047),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_11047)) ),
inference(definitional_conversion,[status(esa)],[f_2911_2]) ).
cnf(f_2911_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_11047),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_11047)) ),
inference(clausify,[status(thm)],[f_2911_3]) ).
fof(f_2912_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_2912_2,plain,
! [U_11049,U_11048] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11048),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_11049))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11048),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11048),hAPP(c_Int_Onat,U_11049))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11048),hAPP(c_Int_Onat,U_11049)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11049))
| ~ class_Rings_Osemiring__1(U_11048) ),
inference(variable_rename,[status(thm)],[f_2912_1]) ).
fof(f_2912_3,plain,
! [U_11048,U_11049] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11048),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_11049))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11048),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11048),hAPP(c_Int_Onat,U_11049))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11048),hAPP(c_Int_Onat,U_11049)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11049))
| ~ class_Rings_Osemiring__1(U_11048) ),
inference(definitional_conversion,[status(esa)],[f_2912_2]) ).
cnf(f_2912_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11048),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_11049))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11048),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11048),hAPP(c_Int_Onat,U_11049))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11048),hAPP(c_Int_Onat,U_11049)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11049))
| ~ class_Rings_Osemiring__1(U_11048) ),
inference(clausify,[status(thm)],[f_2912_3]) ).
fof(f_2913_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_2913_2,plain,
! [U_11051,U_11050] :
( 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_11051)),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_11050)) = 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_11051,U_11050)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11050)) ),
inference(variable_rename,[status(thm)],[f_2913_1]) ).
fof(f_2913_3,plain,
! [U_11051,U_11050] :
( 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_11051)),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_11050)) = 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_11051,U_11050)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11050)) ),
inference(definitional_conversion,[status(esa)],[f_2913_2]) ).
cnf(f_2913_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_11051)),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_11050)) = 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_11051,U_11050)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11050)) ),
inference(clausify,[status(thm)],[f_2913_3]) ).
fof(f_2914_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_2914_2,plain,
! [U_11053,U_11052] :
( 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_11053))),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_11052)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11053),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11052)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11052),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_2914_1]) ).
fof(f_2914_3,plain,
! [U_11052,U_11053] :
( 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_11053))),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_11052)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11053),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11052)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11052),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_2914_2]) ).
cnf(f_2914_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_11053))),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_11052)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11053),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11052)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11052),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_2914_3]) ).
fof(f_2915_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_2915_2,plain,
! [U_11054] :
( ( ( ( hAPP(c_Code__Numeral_Oint__of,U_11054) = 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_11054),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_11054,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_11054) = 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_11054),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_11054,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_11054 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hAPP(c_Code__Numeral_Oint__of,U_11054) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11054 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[f_2915_1]) ).
fof(f_2915_3,plain,
( ! [U_11056] :
( ( ( hAPP(c_Code__Numeral_Oint__of,U_11056) = 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_11056),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_11056,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_11056) = 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_11056),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_11056,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_11056 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_11055] :
( hAPP(c_Code__Numeral_Oint__of,U_11055) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11055 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(miniscope,[status(thm)],[f_2915_2]) ).
fof(f_2915_4,plain,
( ! [U_11056] :
( hAPP(c_Code__Numeral_Oint__of,U_11056) = 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_11056),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_11056,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)
| ~ sP828(U_11056) )
& ! [U_11056] :
( hAPP(c_Code__Numeral_Oint__of,U_11056) = 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_11056),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_11056,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)
| ~ sP828(U_11056) )
& ! [U_11056] :
( sP828(U_11056)
| U_11056 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_11055] :
( hAPP(c_Code__Numeral_Oint__of,U_11055) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11055 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP828])],[f_2915_3]) ).
cnf(f_2915_5,plain,
( hAPP(c_Code__Numeral_Oint__of,U_11055) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11055 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2915_4]) ).
cnf(f_2915_6,plain,
( sP828(U_11056)
| U_11056 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2915_4]) ).
cnf(f_2915_7,plain,
( hAPP(c_Code__Numeral_Oint__of,U_11056) = 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_11056),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_11056,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)
| ~ sP828(U_11056) ),
inference(clausify,[status(thm)],[f_2915_4]) ).
cnf(f_2915_8,plain,
( hAPP(c_Code__Numeral_Oint__of,U_11056) = 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_11056),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_11056,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)
| ~ sP828(U_11056) ),
inference(clausify,[status(thm)],[f_2915_4]) ).
fof(f_2916_1,plain,
! [V_k_2,T_c] :
( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_c),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_c),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_c,T_c)),tc_fun(tc_Int_Oint,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_c),T_c),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_c,T_c)),tc_fun(tc_Int_Oint,T_c)),tc_Int_Oint),c_COMBB(tc_fun(T_c,T_c),T_c,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,T_c),T_c),tc_Int_Oint),c_HOL_OLet(T_c,T_c)),c_Int_Oring__1__class_Oof__int(T_c)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_c,T_c),tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,T_c)),tc_Int_Oint),c_COMBS(T_c,T_c,T_c)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_c,T_c),tc_fun(T_c,tc_fun(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_c,T_c)),tc_fun(tc_fun(T_c,T_c),tc_fun(T_c,tc_fun(T_c,T_c))),tc_Int_Oint),c_COMBB(T_c,tc_fun(T_c,T_c),T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),tc_Int_Oint),c_If(T_c)),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_c,T_c,T_c),c_Groups_Oplus__class_Oplus(T_c)),c_COMBI(T_c))))),hAPP(hAPP(c_COMBC(T_c,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_c),c_Groups_Oplus__class_Oplus(T_c)),hAPP(hAPP(c_COMBS(T_c,T_c,T_c),c_Groups_Oplus__class_Oplus(T_c)),c_COMBI(T_c)))),c_Groups_Oone__class_Oone(T_c))))),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_c),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_c),hAPP(c_Int_Oring__1__class_Oof__int(T_c),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_c),V_k_2) = c_Groups_Ozero__class_Ozero(T_c)
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ class_Rings_Oring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__int__num]) ).
fof(f_2916_2,plain,
! [U_11058,U_11057] :
( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_11057),U_11058) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_11057),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_11057,U_11057)),tc_fun(tc_Int_Oint,U_11057)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11057,U_11057),U_11057),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_11057,U_11057)),tc_fun(tc_Int_Oint,U_11057)),tc_Int_Oint),c_COMBB(tc_fun(U_11057,U_11057),U_11057,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_11057,tc_fun(tc_fun(U_11057,U_11057),U_11057),tc_Int_Oint),c_HOL_OLet(U_11057,U_11057)),c_Int_Oring__1__class_Oof__int(U_11057)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_11057,U_11057),tc_fun(U_11057,U_11057)),hAPP(hAPP(c_COMBB(tc_fun(U_11057,tc_fun(U_11057,U_11057)),tc_fun(tc_fun(U_11057,U_11057),tc_fun(U_11057,U_11057)),tc_Int_Oint),c_COMBS(U_11057,U_11057,U_11057)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_11057,U_11057),tc_fun(U_11057,tc_fun(U_11057,U_11057))),hAPP(hAPP(c_COMBB(tc_fun(U_11057,tc_fun(U_11057,U_11057)),tc_fun(tc_fun(U_11057,U_11057),tc_fun(U_11057,tc_fun(U_11057,U_11057))),tc_Int_Oint),c_COMBB(U_11057,tc_fun(U_11057,U_11057),U_11057)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11057,tc_fun(U_11057,U_11057)),tc_Int_Oint),c_If(U_11057)),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_11057,U_11057,U_11057),c_Groups_Oplus__class_Oplus(U_11057)),c_COMBI(U_11057))))),hAPP(hAPP(c_COMBC(U_11057,U_11057,U_11057),hAPP(hAPP(c_COMBB(U_11057,tc_fun(U_11057,U_11057),U_11057),c_Groups_Oplus__class_Oplus(U_11057)),hAPP(hAPP(c_COMBS(U_11057,U_11057,U_11057),c_Groups_Oplus__class_Oplus(U_11057)),c_COMBI(U_11057)))),c_Groups_Oone__class_Oone(U_11057))))),c_Divides_Odivmod__int(U_11058,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_11058),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(U_11057),U_11058) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11057),hAPP(c_Int_Oring__1__class_Oof__int(U_11057),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11058)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11058),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| U_11058 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(U_11057),U_11058) = c_Groups_Ozero__class_Ozero(U_11057)
| U_11058 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ class_Rings_Oring__1(U_11057) ),
inference(variable_rename,[status(thm)],[f_2916_1]) ).
fof(f_2916_3,plain,
( ! [U_11057,U_11058] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_11057),U_11058) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_11057),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_11057,U_11057)),tc_fun(tc_Int_Oint,U_11057)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11057,U_11057),U_11057),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_11057,U_11057)),tc_fun(tc_Int_Oint,U_11057)),tc_Int_Oint),c_COMBB(tc_fun(U_11057,U_11057),U_11057,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_11057,tc_fun(tc_fun(U_11057,U_11057),U_11057),tc_Int_Oint),c_HOL_OLet(U_11057,U_11057)),c_Int_Oring__1__class_Oof__int(U_11057)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_11057,U_11057),tc_fun(U_11057,U_11057)),hAPP(hAPP(c_COMBB(tc_fun(U_11057,tc_fun(U_11057,U_11057)),tc_fun(tc_fun(U_11057,U_11057),tc_fun(U_11057,U_11057)),tc_Int_Oint),c_COMBS(U_11057,U_11057,U_11057)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_11057,U_11057),tc_fun(U_11057,tc_fun(U_11057,U_11057))),hAPP(hAPP(c_COMBB(tc_fun(U_11057,tc_fun(U_11057,U_11057)),tc_fun(tc_fun(U_11057,U_11057),tc_fun(U_11057,tc_fun(U_11057,U_11057))),tc_Int_Oint),c_COMBB(U_11057,tc_fun(U_11057,U_11057),U_11057)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11057,tc_fun(U_11057,U_11057)),tc_Int_Oint),c_If(U_11057)),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_11057,U_11057,U_11057),c_Groups_Oplus__class_Oplus(U_11057)),c_COMBI(U_11057))))),hAPP(hAPP(c_COMBC(U_11057,U_11057,U_11057),hAPP(hAPP(c_COMBB(U_11057,tc_fun(U_11057,U_11057),U_11057),c_Groups_Oplus__class_Oplus(U_11057)),hAPP(hAPP(c_COMBS(U_11057,U_11057,U_11057),c_Groups_Oplus__class_Oplus(U_11057)),c_COMBI(U_11057)))),c_Groups_Oone__class_Oone(U_11057))))),c_Divides_Odivmod__int(U_11058,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_11058),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP829(U_11057,U_11058) )
& ! [U_11057,U_11058] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_11057),U_11058) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11057),hAPP(c_Int_Oring__1__class_Oof__int(U_11057),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11058)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11058),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP829(U_11057,U_11058) )
& ! [U_11057,U_11058] :
( sP829(U_11057,U_11058)
| U_11058 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP830(U_11057,U_11058) )
& ! [U_11057,U_11058] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_11057),U_11058) = c_Groups_Ozero__class_Ozero(U_11057)
| U_11058 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP830(U_11057,U_11058) )
& ! [U_11057,U_11058] :
( sP830(U_11057,U_11058)
| ~ class_Rings_Oring__1(U_11057) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP829,sP830])],[f_2916_2]) ).
cnf(f_2916_4,plain,
( sP830(U_11057,U_11058)
| ~ class_Rings_Oring__1(U_11057) ),
inference(clausify,[status(thm)],[f_2916_3]) ).
cnf(f_2916_5,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_11057),U_11058) = c_Groups_Ozero__class_Ozero(U_11057)
| U_11058 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP830(U_11057,U_11058) ),
inference(clausify,[status(thm)],[f_2916_3]) ).
cnf(f_2916_6,plain,
( sP829(U_11057,U_11058)
| U_11058 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP830(U_11057,U_11058) ),
inference(clausify,[status(thm)],[f_2916_3]) ).
cnf(f_2916_7,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_11057),U_11058) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11057),hAPP(c_Int_Oring__1__class_Oof__int(U_11057),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11058)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11058),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP829(U_11057,U_11058) ),
inference(clausify,[status(thm)],[f_2916_3]) ).
cnf(f_2916_8,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_11057),U_11058) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_11057),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_11057,U_11057)),tc_fun(tc_Int_Oint,U_11057)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11057,U_11057),U_11057),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_11057,U_11057)),tc_fun(tc_Int_Oint,U_11057)),tc_Int_Oint),c_COMBB(tc_fun(U_11057,U_11057),U_11057,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_11057,tc_fun(tc_fun(U_11057,U_11057),U_11057),tc_Int_Oint),c_HOL_OLet(U_11057,U_11057)),c_Int_Oring__1__class_Oof__int(U_11057)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_11057,U_11057),tc_fun(U_11057,U_11057)),hAPP(hAPP(c_COMBB(tc_fun(U_11057,tc_fun(U_11057,U_11057)),tc_fun(tc_fun(U_11057,U_11057),tc_fun(U_11057,U_11057)),tc_Int_Oint),c_COMBS(U_11057,U_11057,U_11057)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_11057,U_11057),tc_fun(U_11057,tc_fun(U_11057,U_11057))),hAPP(hAPP(c_COMBB(tc_fun(U_11057,tc_fun(U_11057,U_11057)),tc_fun(tc_fun(U_11057,U_11057),tc_fun(U_11057,tc_fun(U_11057,U_11057))),tc_Int_Oint),c_COMBB(U_11057,tc_fun(U_11057,U_11057),U_11057)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11057,tc_fun(U_11057,U_11057)),tc_Int_Oint),c_If(U_11057)),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_11057,U_11057,U_11057),c_Groups_Oplus__class_Oplus(U_11057)),c_COMBI(U_11057))))),hAPP(hAPP(c_COMBC(U_11057,U_11057,U_11057),hAPP(hAPP(c_COMBB(U_11057,tc_fun(U_11057,U_11057),U_11057),c_Groups_Oplus__class_Oplus(U_11057)),hAPP(hAPP(c_COMBS(U_11057,U_11057,U_11057),c_Groups_Oplus__class_Oplus(U_11057)),c_COMBI(U_11057)))),c_Groups_Oone__class_Oone(U_11057))))),c_Divides_Odivmod__int(U_11058,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_11058),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP829(U_11057,U_11058) ),
inference(clausify,[status(thm)],[f_2916_3]) ).
fof(f_2917_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_2917_2,plain,
! [U_11060,U_11059] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11059),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),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_11060))) = hAPP(c_Int_Onumber__class_Onumber__of(U_11059),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_11059) ),
inference(variable_rename,[status(thm)],[f_2917_1]) ).
fof(f_2917_3,plain,
! [U_11060,U_11059] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11059),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),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_11060))) = hAPP(c_Int_Onumber__class_Onumber__of(U_11059),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_11059) ),
inference(definitional_conversion,[status(esa)],[f_2917_2]) ).
cnf(f_2917_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11059),hAPP(c_Int_Onumber__class_Onumber__of(U_11059),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_11060))) = hAPP(c_Int_Onumber__class_Onumber__of(U_11059),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_11059) ),
inference(clausify,[status(thm)],[f_2917_3]) ).
fof(f_2918_1,plain,
! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I45_J]) ).
fof(f_2918_2,plain,
! [U_11061] : c_Int_OBit0(U_11061) != c_Int_OMin,
inference(variable_rename,[status(thm)],[f_2918_1]) ).
fof(f_2918_3,plain,
! [U_11061] : c_Int_OBit0(U_11061) != c_Int_OMin,
inference(definitional_conversion,[status(esa)],[f_2918_2]) ).
cnf(f_2918_4,plain,
c_Int_OBit0(U_11061) != c_Int_OMin,
inference(clausify,[status(thm)],[f_2918_3]) ).
fof(f_2919_1,plain,
! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I42_J]) ).
fof(f_2919_2,plain,
! [U_11062] : c_Int_OMin != c_Int_OBit0(U_11062),
inference(variable_rename,[status(thm)],[f_2919_1]) ).
fof(f_2919_3,plain,
! [U_11062] : c_Int_OMin != c_Int_OBit0(U_11062),
inference(definitional_conversion,[status(esa)],[f_2919_2]) ).
cnf(f_2919_4,plain,
c_Int_OMin != c_Int_OBit0(U_11062),
inference(clausify,[status(thm)],[f_2919_3]) ).
fof(f_2920_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_2920_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_2920_1]) ).
cnf(f_2920_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_2920_2]) ).
fof(f_2921_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_2921_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_2921_1]) ).
cnf(f_2921_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_2921_2]) ).
fof(f_2922_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_2922_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_2922_1]) ).
cnf(f_2922_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(clausify,[status(thm)],[f_2922_2]) ).
fof(f_2923_1,plain,
c_Int_OPls != c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I37_J]) ).
fof(f_2923_2,plain,
c_Int_OPls != c_Int_OMin,
inference(definitional_conversion,[status(esa)],[f_2923_1]) ).
cnf(f_2923_3,plain,
c_Int_OPls != c_Int_OMin,
inference(clausify,[status(thm)],[f_2923_2]) ).
fof(f_2924_1,plain,
c_Int_OMin != c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I40_J]) ).
fof(f_2924_2,plain,
c_Int_OMin != c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_2924_1]) ).
cnf(f_2924_3,plain,
c_Int_OMin != c_Int_OPls,
inference(clausify,[status(thm)],[f_2924_2]) ).
fof(f_2925_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_2925_2,plain,
! [U_11063] :
( ( c_Int_OBit1(U_11063) = c_Int_OMin
| U_11063 != c_Int_OMin )
& ( U_11063 = c_Int_OMin
| c_Int_OBit1(U_11063) != c_Int_OMin ) ),
inference(variable_rename,[status(thm)],[f_2925_1]) ).
fof(f_2925_3,plain,
( ! [U_11065] :
( c_Int_OBit1(U_11065) = c_Int_OMin
| U_11065 != c_Int_OMin )
& ! [U_11064] :
( U_11064 = c_Int_OMin
| c_Int_OBit1(U_11064) != c_Int_OMin ) ),
inference(miniscope,[status(thm)],[f_2925_2]) ).
fof(f_2925_4,plain,
( ! [U_11065] :
( c_Int_OBit1(U_11065) = c_Int_OMin
| U_11065 != c_Int_OMin )
& ! [U_11064] :
( U_11064 = c_Int_OMin
| c_Int_OBit1(U_11064) != c_Int_OMin ) ),
inference(definitional_conversion,[status(esa)],[f_2925_3]) ).
cnf(f_2925_5,plain,
( U_11064 = c_Int_OMin
| c_Int_OBit1(U_11064) != c_Int_OMin ),
inference(clausify,[status(thm)],[f_2925_4]) ).
cnf(f_2925_6,plain,
( c_Int_OBit1(U_11065) = c_Int_OMin
| U_11065 != c_Int_OMin ),
inference(clausify,[status(thm)],[f_2925_4]) ).
fof(f_2926_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_2926_2,plain,
! [U_11066] :
( ( c_Int_OMin = c_Int_OBit1(U_11066)
| c_Int_OMin != U_11066 )
& ( c_Int_OMin = U_11066
| c_Int_OMin != c_Int_OBit1(U_11066) ) ),
inference(variable_rename,[status(thm)],[f_2926_1]) ).
fof(f_2926_3,plain,
( ! [U_11068] :
( c_Int_OMin = c_Int_OBit1(U_11068)
| c_Int_OMin != U_11068 )
& ! [U_11067] :
( c_Int_OMin = U_11067
| c_Int_OMin != c_Int_OBit1(U_11067) ) ),
inference(miniscope,[status(thm)],[f_2926_2]) ).
fof(f_2926_4,plain,
( ! [U_11068] :
( c_Int_OMin = c_Int_OBit1(U_11068)
| c_Int_OMin != U_11068 )
& ! [U_11067] :
( c_Int_OMin = U_11067
| c_Int_OMin != c_Int_OBit1(U_11067) ) ),
inference(definitional_conversion,[status(esa)],[f_2926_3]) ).
cnf(f_2926_5,plain,
( c_Int_OMin = U_11067
| c_Int_OMin != c_Int_OBit1(U_11067) ),
inference(clausify,[status(thm)],[f_2926_4]) ).
cnf(f_2926_6,plain,
( c_Int_OMin = c_Int_OBit1(U_11068)
| c_Int_OMin != U_11068 ),
inference(clausify,[status(thm)],[f_2926_4]) ).
fof(f_2927_1,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_Bit1__Min]) ).
fof(f_2927_2,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(definitional_conversion,[status(esa)],[f_2927_1]) ).
cnf(f_2927_3,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(clausify,[status(thm)],[f_2927_2]) ).
fof(f_2928_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_2928_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_2928_1]) ).
cnf(f_2928_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_2928_2]) ).
fof(f_2929_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_2929_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_2929_1]) ).
cnf(f_2929_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_2929_2]) ).
fof(f_2930_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_2930_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_2930_1]) ).
cnf(f_2930_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_2930_2]) ).
fof(f_2931_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_2931_2,plain,
! [U_11069] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11069)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11069),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11069),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11069)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_2931_1]) ).
fof(f_2931_3,plain,
( ! [U_11071] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11071)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11071),c_Int_OMin)) )
& ! [U_11070] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11070),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11070)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_2931_2]) ).
fof(f_2931_4,plain,
( ! [U_11071] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11071)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11071),c_Int_OMin)) )
& ! [U_11070] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11070),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11070)),c_Int_OMin)) ) ),
inference(definitional_conversion,[status(esa)],[f_2931_3]) ).
cnf(f_2931_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11070),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11070)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2931_4]) ).
cnf(f_2931_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_11071)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11071),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2931_4]) ).
fof(f_2932_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_2932_2,plain,
! [U_11072] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11072)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11072)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11072))) ) ),
inference(variable_rename,[status(thm)],[f_2932_1]) ).
fof(f_2932_3,plain,
( ! [U_11074] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11074)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11074)) )
& ! [U_11073] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11073))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11073))) ) ),
inference(miniscope,[status(thm)],[f_2932_2]) ).
fof(f_2932_4,plain,
( ! [U_11074] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11074)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11074)) )
& ! [U_11073] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11073))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11073))) ) ),
inference(definitional_conversion,[status(esa)],[f_2932_3]) ).
cnf(f_2932_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11073))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11073))) ),
inference(clausify,[status(thm)],[f_2932_4]) ).
cnf(f_2932_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11074)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_11074)) ),
inference(clausify,[status(thm)],[f_2932_4]) ).
fof(f_2933_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_2933_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_2933_1]) ).
cnf(f_2933_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(clausify,[status(thm)],[f_2933_2]) ).
fof(f_2934_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_2934_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_2934_1]) ).
cnf(f_2934_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(clausify,[status(thm)],[f_2934_2]) ).
fof(f_2935_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_2935_2,plain,
! [U_11075] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11075)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11075),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11075),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11075)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_2935_1]) ).
fof(f_2935_3,plain,
( ! [U_11077] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11077)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11077),c_Int_OMin)) )
& ! [U_11076] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11076),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11076)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_2935_2]) ).
fof(f_2935_4,plain,
( ! [U_11077] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11077)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11077),c_Int_OMin)) )
& ! [U_11076] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11076),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11076)),c_Int_OMin)) ) ),
inference(definitional_conversion,[status(esa)],[f_2935_3]) ).
cnf(f_2935_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11076),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11076)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2935_4]) ).
cnf(f_2935_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_11077)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11077),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2935_4]) ).
fof(f_2936_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_2936_2,plain,
! [U_11078] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11078)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11078))) ) ),
inference(variable_rename,[status(thm)],[f_2936_1]) ).
fof(f_2936_3,plain,
( ! [U_11080] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11080)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11080)) )
& ! [U_11079] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11079))) ) ),
inference(miniscope,[status(thm)],[f_2936_2]) ).
fof(f_2936_4,plain,
( ! [U_11080] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11080)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11080)) )
& ! [U_11079] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11079))) ) ),
inference(definitional_conversion,[status(esa)],[f_2936_3]) ).
cnf(f_2936_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11079))) ),
inference(clausify,[status(thm)],[f_2936_4]) ).
cnf(f_2936_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11080)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11080)) ),
inference(clausify,[status(thm)],[f_2936_4]) ).
fof(f_2937_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_2937_2,plain,
! [U_11081] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11081)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11081),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11081),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11081)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_2937_1]) ).
fof(f_2937_3,plain,
( ! [U_11083] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11083)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11083),c_Int_OMin)) )
& ! [U_11082] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11082),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11082)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_2937_2]) ).
fof(f_2937_4,plain,
( ! [U_11083] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11083)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11083),c_Int_OMin)) )
& ! [U_11082] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11082),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11082)),c_Int_OMin)) ) ),
inference(definitional_conversion,[status(esa)],[f_2937_3]) ).
cnf(f_2937_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11082),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11082)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2937_4]) ).
cnf(f_2937_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_11083)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11083),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2937_4]) ).
fof(f_2938_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_2938_2,plain,
! [U_11084] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11084)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11084)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11084))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11084))) ) ),
inference(variable_rename,[status(thm)],[f_2938_1]) ).
fof(f_2938_3,plain,
( ! [U_11086] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11086)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11086)) )
& ! [U_11085] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11085))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11085))) ) ),
inference(miniscope,[status(thm)],[f_2938_2]) ).
fof(f_2938_4,plain,
( ! [U_11086] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11086)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11086)) )
& ! [U_11085] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11085))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11085))) ) ),
inference(definitional_conversion,[status(esa)],[f_2938_3]) ).
cnf(f_2938_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11085))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11085))) ),
inference(clausify,[status(thm)],[f_2938_4]) ).
cnf(f_2938_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11086)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11086)) ),
inference(clausify,[status(thm)],[f_2938_4]) ).
fof(f_2939_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_2939_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_2939_1]) ).
cnf(f_2939_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_2939_2]) ).
fof(f_2940_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_2940_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_2940_1]) ).
cnf(f_2940_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_2940_2]) ).
fof(f_2941_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_2941_2,plain,
! [U_11087] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_11087) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11087),
inference(variable_rename,[status(thm)],[f_2941_1]) ).
fof(f_2941_3,plain,
! [U_11087] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_11087) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11087),
inference(definitional_conversion,[status(esa)],[f_2941_2]) ).
cnf(f_2941_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_11087) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11087),
inference(clausify,[status(thm)],[f_2941_3]) ).
fof(f_2942_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_2942_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_2942_1]) ).
cnf(f_2942_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_2942_2]) ).
fof(f_2943_1,plain,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_pred__Pls]) ).
fof(f_2943_2,plain,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
inference(definitional_conversion,[status(esa)],[f_2943_1]) ).
cnf(f_2943_3,plain,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
inference(clausify,[status(thm)],[f_2943_2]) ).
fof(f_2944_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_2944_2,plain,
! [U_11088] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11088),c_Int_OMin) = c_Int_Opred(U_11088),
inference(variable_rename,[status(thm)],[f_2944_1]) ).
fof(f_2944_3,plain,
! [U_11088] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11088),c_Int_OMin) = c_Int_Opred(U_11088),
inference(definitional_conversion,[status(esa)],[f_2944_2]) ).
cnf(f_2944_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11088),c_Int_OMin) = c_Int_Opred(U_11088),
inference(clausify,[status(thm)],[f_2944_3]) ).
fof(f_2945_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_2945_2,plain,
! [U_11089] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_11089) = c_Int_Opred(U_11089),
inference(variable_rename,[status(thm)],[f_2945_1]) ).
fof(f_2945_3,plain,
! [U_11089] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_11089) = c_Int_Opred(U_11089),
inference(definitional_conversion,[status(esa)],[f_2945_2]) ).
cnf(f_2945_4,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_11089) = c_Int_Opred(U_11089),
inference(clausify,[status(thm)],[f_2945_3]) ).
fof(f_2946_1,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(fof_nnf,[status(thm)],[fact_pred__Min]) ).
fof(f_2946_2,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(definitional_conversion,[status(esa)],[f_2946_1]) ).
cnf(f_2946_3,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(clausify,[status(thm)],[f_2946_2]) ).
fof(f_2947_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_2947_2,plain,
! [U_11090] :
( ~ c_Int_Oiszero(U_11090,hAPP(c_Int_Onumber__class_Onumber__of(U_11090),c_Int_OMin))
| ~ class_Int_Onumber__ring(U_11090) ),
inference(variable_rename,[status(thm)],[f_2947_1]) ).
fof(f_2947_3,plain,
! [U_11090] :
( ~ c_Int_Oiszero(U_11090,hAPP(c_Int_Onumber__class_Onumber__of(U_11090),c_Int_OMin))
| ~ class_Int_Onumber__ring(U_11090) ),
inference(definitional_conversion,[status(esa)],[f_2947_2]) ).
cnf(f_2947_4,plain,
( ~ c_Int_Oiszero(U_11090,hAPP(c_Int_Onumber__class_Onumber__of(U_11090),c_Int_OMin))
| ~ class_Int_Onumber__ring(U_11090) ),
inference(clausify,[status(thm)],[f_2947_3]) ).
fof(f_2948_1,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_succ__Min]) ).
fof(f_2948_2,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_2948_1]) ).
cnf(f_2948_3,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(clausify,[status(thm)],[f_2948_2]) ).
fof(f_2949_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_2949_2,plain,
! [U_11091] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11091),c_Int_OMin) = c_Int_Osucc(U_11091),
inference(variable_rename,[status(thm)],[f_2949_1]) ).
fof(f_2949_3,plain,
! [U_11091] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11091),c_Int_OMin) = c_Int_Osucc(U_11091),
inference(definitional_conversion,[status(esa)],[f_2949_2]) ).
cnf(f_2949_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11091),c_Int_OMin) = c_Int_Osucc(U_11091),
inference(clausify,[status(thm)],[f_2949_3]) ).
fof(f_2950_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_2950_2,plain,
! [U_11093,U_11092] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11092),U_11093),hAPP(c_Int_Onumber__class_Onumber__of(U_11092),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11092),U_11093)
| ~ class_Int_Onumber__ring(U_11092) ),
inference(variable_rename,[status(thm)],[f_2950_1]) ).
fof(f_2950_3,plain,
! [U_11092,U_11093] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11092),U_11093),hAPP(c_Int_Onumber__class_Onumber__of(U_11092),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11092),U_11093)
| ~ class_Int_Onumber__ring(U_11092) ),
inference(definitional_conversion,[status(esa)],[f_2950_2]) ).
cnf(f_2950_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11092),U_11093),hAPP(c_Int_Onumber__class_Onumber__of(U_11092),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11092),U_11093)
| ~ class_Int_Onumber__ring(U_11092) ),
inference(clausify,[status(thm)],[f_2950_3]) ).
fof(f_2951_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_2951_2,plain,
! [U_11095,U_11094] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11094),hAPP(c_Int_Onumber__class_Onumber__of(U_11094),c_Int_OMin)),U_11095) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11094),U_11095)
| ~ class_Int_Onumber__ring(U_11094) ),
inference(variable_rename,[status(thm)],[f_2951_1]) ).
fof(f_2951_3,plain,
! [U_11094,U_11095] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11094),hAPP(c_Int_Onumber__class_Onumber__of(U_11094),c_Int_OMin)),U_11095) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11094),U_11095)
| ~ class_Int_Onumber__ring(U_11094) ),
inference(definitional_conversion,[status(esa)],[f_2951_2]) ).
cnf(f_2951_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11094),hAPP(c_Int_Onumber__class_Onumber__of(U_11094),c_Int_OMin)),U_11095) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11094),U_11095)
| ~ class_Int_Onumber__ring(U_11094) ),
inference(clausify,[status(thm)],[f_2951_3]) ).
fof(f_2952_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_2952_2,plain,
! [U_11096] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_11096),c_Groups_Oone__class_Oone(U_11096)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11096),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_11096) ),
inference(variable_rename,[status(thm)],[f_2952_1]) ).
fof(f_2952_3,plain,
! [U_11096] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_11096),c_Groups_Oone__class_Oone(U_11096)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11096),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_11096) ),
inference(definitional_conversion,[status(esa)],[f_2952_2]) ).
cnf(f_2952_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_11096),c_Groups_Oone__class_Oone(U_11096)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11096),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_11096) ),
inference(clausify,[status(thm)],[f_2952_3]) ).
fof(f_2953_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_2953_2,plain,
! [U_11097] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_11097),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11097),c_Groups_Oone__class_Oone(U_11097))
| ~ class_Int_Onumber__ring(U_11097) ),
inference(variable_rename,[status(thm)],[f_2953_1]) ).
fof(f_2953_3,plain,
! [U_11097] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_11097),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11097),c_Groups_Oone__class_Oone(U_11097))
| ~ class_Int_Onumber__ring(U_11097) ),
inference(definitional_conversion,[status(esa)],[f_2953_2]) ).
cnf(f_2953_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_11097),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11097),c_Groups_Oone__class_Oone(U_11097))
| ~ class_Int_Onumber__ring(U_11097) ),
inference(clausify,[status(thm)],[f_2953_3]) ).
fof(f_2954_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_2954_2,plain,
! [U_11098] :
( hAPP(c_Groups_Oabs__class_Oabs(U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11098),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_11098)
| ~ class_Rings_Olinordered__idom(U_11098)
| ~ class_Int_Onumber__ring(U_11098) ),
inference(variable_rename,[status(thm)],[f_2954_1]) ).
fof(f_2954_3,plain,
! [U_11098] :
( hAPP(c_Groups_Oabs__class_Oabs(U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11098),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_11098)
| ~ class_Rings_Olinordered__idom(U_11098)
| ~ class_Int_Onumber__ring(U_11098) ),
inference(definitional_conversion,[status(esa)],[f_2954_2]) ).
cnf(f_2954_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_11098),hAPP(c_Int_Onumber__class_Onumber__of(U_11098),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_11098)
| ~ class_Rings_Olinordered__idom(U_11098)
| ~ class_Int_Onumber__ring(U_11098) ),
inference(clausify,[status(thm)],[f_2954_3]) ).
fof(f_2955_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_2955_2,plain,
! [U_11100,U_11099] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11099),U_11100)
| ~ class_Int_Onumber__ring(U_11099)
| ~ class_Fields_Ofield__inverse__zero(U_11099) ),
inference(variable_rename,[status(thm)],[f_2955_1]) ).
fof(f_2955_3,plain,
! [U_11099,U_11100] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11099),U_11100)
| ~ class_Int_Onumber__ring(U_11099)
| ~ class_Fields_Ofield__inverse__zero(U_11099) ),
inference(definitional_conversion,[status(esa)],[f_2955_2]) ).
cnf(f_2955_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11099),U_11100),hAPP(c_Int_Onumber__class_Onumber__of(U_11099),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11099),U_11100)
| ~ class_Int_Onumber__ring(U_11099)
| ~ class_Fields_Ofield__inverse__zero(U_11099) ),
inference(clausify,[status(thm)],[f_2955_3]) ).
fof(f_2956_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_2956_2,plain,
! [U_11101] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11101)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11101)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11101))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11101))) ) ),
inference(variable_rename,[status(thm)],[f_2956_1]) ).
fof(f_2956_3,plain,
( ! [U_11103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11103)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11103)) )
& ! [U_11102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11102))) ) ),
inference(miniscope,[status(thm)],[f_2956_2]) ).
fof(f_2956_4,plain,
( ! [U_11103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11103)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11103)) )
& ! [U_11102] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11102))) ) ),
inference(definitional_conversion,[status(esa)],[f_2956_3]) ).
cnf(f_2956_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11102))) ),
inference(clausify,[status(thm)],[f_2956_4]) ).
cnf(f_2956_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11103)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_11103)) ),
inference(clausify,[status(thm)],[f_2956_4]) ).
fof(f_2957_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_2957_2,plain,
! [U_11104] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11104)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11104),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11104),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11104)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_2957_1]) ).
fof(f_2957_3,plain,
( ! [U_11106] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11106)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11106),c_Int_OMin)) )
& ! [U_11105] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11105),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11105)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_2957_2]) ).
fof(f_2957_4,plain,
( ! [U_11106] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11106)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11106),c_Int_OMin)) )
& ! [U_11105] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11105),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11105)),c_Int_OMin)) ) ),
inference(definitional_conversion,[status(esa)],[f_2957_3]) ).
cnf(f_2957_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11105),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11105)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2957_4]) ).
cnf(f_2957_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_11106)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11106),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_2957_4]) ).
fof(f_2958_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_2958_2,plain,
! [U_11107] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11107,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_2958_1]) ).
fof(f_2958_3,plain,
! [U_11107] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11107,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_2958_2]) ).
cnf(f_2958_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11107,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_2958_3]) ).
fof(f_2959_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_2959_2,plain,
! [U_11108] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11108)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11108)),
inference(variable_rename,[status(thm)],[f_2959_1]) ).
fof(f_2959_3,plain,
! [U_11108] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11108)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11108)),
inference(definitional_conversion,[status(esa)],[f_2959_2]) ).
cnf(f_2959_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_11108)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11108)),
inference(clausify,[status(thm)],[f_2959_3]) ).
fof(f_2960_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_2960_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_2960_1]) ).
cnf(f_2960_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_2960_2]) ).
fof(f_2961_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_2961_2,plain,
! [U_11110,U_11109] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11109),U_11110) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( U_11110 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_11109 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
& ( U_11110 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_11109 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ( ( U_11110 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& U_11109 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
| ( U_11110 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_11109 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11109),U_11110) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_2961_1]) ).
fof(f_2961_3,plain,
( ! [U_11114,U_11112] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11112),U_11114) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( U_11114 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_11112 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
& ( U_11114 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_11112 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ! [U_11113,U_11111] :
( ( U_11113 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& U_11111 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
| ( U_11113 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_11111 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11111),U_11113) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_2961_2]) ).
fof(f_2961_4,plain,
( ! [U_11112,U_11114] :
( U_11114 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_11112 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ sP833(U_11112,U_11114) )
& ! [U_11112,U_11114] :
( U_11114 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_11112 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP833(U_11112,U_11114) )
& ! [U_11111,U_11113] :
( U_11113 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ sP832(U_11111,U_11113) )
& ! [U_11111,U_11113] :
( U_11111 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ sP832(U_11111,U_11113) )
& ! [U_11111,U_11113] :
( U_11113 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP831(U_11111,U_11113) )
& ! [U_11111,U_11113] :
( U_11111 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP831(U_11111,U_11113) )
& ! [U_11112,U_11114] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11112),U_11114) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| sP833(U_11112,U_11114) )
& ! [U_11111,U_11113] :
( sP832(U_11111,U_11113)
| sP831(U_11111,U_11113)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11111),U_11113) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP831,sP832,sP833])],[f_2961_3]) ).
cnf(f_2961_5,plain,
( sP832(U_11111,U_11113)
| sP831(U_11111,U_11113)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11111),U_11113) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2961_4]) ).
cnf(f_2961_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11112),U_11114) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| sP833(U_11112,U_11114) ),
inference(clausify,[status(thm)],[f_2961_4]) ).
cnf(f_2961_7,plain,
( U_11111 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP831(U_11111,U_11113) ),
inference(clausify,[status(thm)],[f_2961_4]) ).
cnf(f_2961_8,plain,
( U_11113 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP831(U_11111,U_11113) ),
inference(clausify,[status(thm)],[f_2961_4]) ).
cnf(f_2961_9,plain,
( U_11111 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ sP832(U_11111,U_11113) ),
inference(clausify,[status(thm)],[f_2961_4]) ).
cnf(f_2961_10,plain,
( U_11113 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ sP832(U_11111,U_11113) ),
inference(clausify,[status(thm)],[f_2961_4]) ).
cnf(f_2961_11,plain,
( U_11114 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_11112 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP833(U_11112,U_11114) ),
inference(clausify,[status(thm)],[f_2961_4]) ).
cnf(f_2961_12,plain,
( U_11114 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_11112 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| ~ sP833(U_11112,U_11114) ),
inference(clausify,[status(thm)],[f_2961_4]) ).
fof(f_2962_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_2962_2,plain,
! [U_11116,U_11115] :
( U_11115 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_11115 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11115),U_11116) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2962_1]) ).
fof(f_2962_3,plain,
! [U_11116,U_11115] :
( U_11115 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_11115 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11115),U_11116) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_2962_2]) ).
cnf(f_2962_4,plain,
( U_11115 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_11115 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11115),U_11116) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2962_3]) ).
fof(f_2963_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_2963_2,plain,
! [U_11117] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11117)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11117)),
inference(variable_rename,[status(thm)],[f_2963_1]) ).
fof(f_2963_3,plain,
! [U_11117] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11117)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11117)),
inference(definitional_conversion,[status(esa)],[f_2963_2]) ).
cnf(f_2963_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_11117)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11117)),
inference(clausify,[status(thm)],[f_2963_3]) ).
fof(f_2964_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_2964_2,plain,
! [U_11118] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11118)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11118)),
inference(variable_rename,[status(thm)],[f_2964_1]) ).
fof(f_2964_3,plain,
! [U_11118] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11118)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11118)),
inference(definitional_conversion,[status(esa)],[f_2964_2]) ).
cnf(f_2964_4,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_11118)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_11118)),
inference(clausify,[status(thm)],[f_2964_3]) ).
fof(f_2965_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_2965_2,plain,
! [U_11119] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_11119),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11119),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_11119) ),
inference(variable_rename,[status(thm)],[f_2965_1]) ).
fof(f_2965_3,plain,
! [U_11119] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_11119),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11119),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_11119) ),
inference(definitional_conversion,[status(esa)],[f_2965_2]) ).
cnf(f_2965_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_11119),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_11119),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_11119) ),
inference(clausify,[status(thm)],[f_2965_3]) ).
fof(f_2966_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_2966_2,plain,
! [U_11120] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11120),
inference(variable_rename,[status(thm)],[f_2966_1]) ).
fof(f_2966_3,plain,
! [U_11120] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11120),
inference(definitional_conversion,[status(esa)],[f_2966_2]) ).
cnf(f_2966_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11120),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11120),
inference(clausify,[status(thm)],[f_2966_3]) ).
fof(f_2967_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_2967_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_2967_1]) ).
cnf(f_2967_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_2967_2]) ).
fof(f_2968_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_2968_2,plain,
! [U_11122,U_11121] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11121),hAPP(c_Int_Onumber__class_Onumber__of(U_11121),c_Int_OMin)),U_11122) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11121),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11121),c_Groups_Oone__class_Oone(U_11121)),U_11122))
| ~ class_Int_Onumber__ring(U_11121)
| ~ class_Fields_Ofield__inverse__zero(U_11121) ),
inference(variable_rename,[status(thm)],[f_2968_1]) ).
fof(f_2968_3,plain,
! [U_11121,U_11122] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11121),hAPP(c_Int_Onumber__class_Onumber__of(U_11121),c_Int_OMin)),U_11122) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11121),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11121),c_Groups_Oone__class_Oone(U_11121)),U_11122))
| ~ class_Int_Onumber__ring(U_11121)
| ~ class_Fields_Ofield__inverse__zero(U_11121) ),
inference(definitional_conversion,[status(esa)],[f_2968_2]) ).
cnf(f_2968_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11121),hAPP(c_Int_Onumber__class_Onumber__of(U_11121),c_Int_OMin)),U_11122) = hAPP(c_Groups_Ouminus__class_Ouminus(U_11121),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11121),c_Groups_Oone__class_Oone(U_11121)),U_11122))
| ~ class_Int_Onumber__ring(U_11121)
| ~ class_Fields_Ofield__inverse__zero(U_11121) ),
inference(clausify,[status(thm)],[f_2968_3]) ).
fof(f_2969_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_2969_2,plain,
! [U_11124,U_11123] :
( hAPP(c_Groups_Oabs__class_Oabs(U_11123),hAPP(hAPP(c_Power_Opower__class_Opower(U_11123),hAPP(c_Int_Onumber__class_Onumber__of(U_11123),c_Int_OMin)),U_11124)) = c_Groups_Oone__class_Oone(U_11123)
| ~ class_Rings_Olinordered__idom(U_11123)
| ~ class_Int_Onumber__ring(U_11123) ),
inference(variable_rename,[status(thm)],[f_2969_1]) ).
fof(f_2969_3,plain,
! [U_11123,U_11124] :
( hAPP(c_Groups_Oabs__class_Oabs(U_11123),hAPP(hAPP(c_Power_Opower__class_Opower(U_11123),hAPP(c_Int_Onumber__class_Onumber__of(U_11123),c_Int_OMin)),U_11124)) = c_Groups_Oone__class_Oone(U_11123)
| ~ class_Rings_Olinordered__idom(U_11123)
| ~ class_Int_Onumber__ring(U_11123) ),
inference(definitional_conversion,[status(esa)],[f_2969_2]) ).
cnf(f_2969_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_11123),hAPP(hAPP(c_Power_Opower__class_Opower(U_11123),hAPP(c_Int_Onumber__class_Onumber__of(U_11123),c_Int_OMin)),U_11124)) = c_Groups_Oone__class_Oone(U_11123)
| ~ class_Rings_Olinordered__idom(U_11123)
| ~ class_Int_Onumber__ring(U_11123) ),
inference(clausify,[status(thm)],[f_2969_3]) ).
fof(f_2970_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_2970_2,plain,
! [U_11125] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_11125) = 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_11125)) ),
inference(variable_rename,[status(thm)],[f_2970_1]) ).
fof(f_2970_3,plain,
! [U_11125] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_11125) = 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_11125)) ),
inference(definitional_conversion,[status(esa)],[f_2970_2]) ).
cnf(f_2970_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_11125) = 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_11125)) ),
inference(clausify,[status(thm)],[f_2970_3]) ).
fof(f_2971_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_2971_2,plain,
! [U_11127,U_11126] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11126),U_11127) = 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_11126),U_11127)),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_11126)) ),
inference(variable_rename,[status(thm)],[f_2971_1]) ).
fof(f_2971_3,plain,
! [U_11126,U_11127] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11126),U_11127) = 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_11126),U_11127)),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_11126)) ),
inference(definitional_conversion,[status(esa)],[f_2971_2]) ).
cnf(f_2971_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11126),U_11127) = 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_11126),U_11127)),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_11126)) ),
inference(clausify,[status(thm)],[f_2971_3]) ).
fof(f_2972_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_2972_2,plain,
! [U_11128] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_11128) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11128),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_11128)) ),
inference(variable_rename,[status(thm)],[f_2972_1]) ).
fof(f_2972_3,plain,
! [U_11128] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_11128) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11128),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_11128)) ),
inference(definitional_conversion,[status(esa)],[f_2972_2]) ).
cnf(f_2972_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_11128) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11128),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_11128)) ),
inference(clausify,[status(thm)],[f_2972_3]) ).
fof(f_2973_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_2973_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_2973_1]) ).
cnf(f_2973_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_2973_2]) ).
fof(f_2974_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_2974_2,plain,
! [U_11130,U_11129] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11129),hAPP(c_Int_Onumber__class_Onumber__of(U_11129),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_11130)) = c_Groups_Oone__class_Oone(U_11129)
| ~ class_Int_Onumber__ring(U_11129) ),
inference(variable_rename,[status(thm)],[f_2974_1]) ).
fof(f_2974_3,plain,
! [U_11129,U_11130] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11129),hAPP(c_Int_Onumber__class_Onumber__of(U_11129),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_11130)) = c_Groups_Oone__class_Oone(U_11129)
| ~ class_Int_Onumber__ring(U_11129) ),
inference(definitional_conversion,[status(esa)],[f_2974_2]) ).
cnf(f_2974_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11129),hAPP(c_Int_Onumber__class_Onumber__of(U_11129),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_11130)) = c_Groups_Oone__class_Oone(U_11129)
| ~ class_Int_Onumber__ring(U_11129) ),
inference(clausify,[status(thm)],[f_2974_3]) ).
fof(f_2975_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_2975_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_2975_1]) ).
cnf(f_2975_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_2975_2]) ).
fof(f_2976_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_2976_2,plain,
! [U_11131] : c_Int_Oint__ge__less__than(U_11131) = 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_11131)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_2976_1]) ).
fof(f_2976_3,plain,
! [U_11131] : c_Int_Oint__ge__less__than(U_11131) = 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_11131)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(definitional_conversion,[status(esa)],[f_2976_2]) ).
cnf(f_2976_4,plain,
c_Int_Oint__ge__less__than(U_11131) = 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_11131)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_2976_3]) ).
fof(f_2977_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_2977_2,plain,
! [U_11132] : c_Int_Oint__ge__less__than2(U_11132) = 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_11132)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_2977_1]) ).
fof(f_2977_3,plain,
! [U_11132] : c_Int_Oint__ge__less__than2(U_11132) = 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_11132)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(definitional_conversion,[status(esa)],[f_2977_2]) ).
cnf(f_2977_4,plain,
c_Int_Oint__ge__less__than2(U_11132) = 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_11132)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_2977_3]) ).
fof(f_2978_1,plain,
! [T_d,T_c] : c_Fun_Oinj__on(tc_fun(T_c,T_d),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,T_d)),c_Set_OCollect(tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,T_d)),c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool)),hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBC(T_d,T_d,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_c,T_d),tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_inj__graph]) ).
fof(f_2978_2,plain,
! [U_11134,U_11133] : c_Fun_Oinj__on(tc_fun(U_11133,U_11134),tc_fun(tc_prod(U_11133,U_11134),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11133,U_11134),tc_HOL_Obool),tc_fun(tc_prod(U_11133,U_11134),tc_HOL_Obool),tc_fun(U_11133,U_11134)),c_Set_OCollect(tc_prod(U_11133,U_11134))),hAPP(hAPP(c_COMBB(tc_fun(U_11133,tc_fun(U_11134,tc_HOL_Obool)),tc_fun(tc_prod(U_11133,U_11134),tc_HOL_Obool),tc_fun(U_11133,U_11134)),c_Product__Type_Oprod_Oprod__case(U_11133,U_11134,tc_HOL_Obool)),hAPP(c_COMBB(U_11134,tc_fun(U_11134,tc_HOL_Obool),U_11133),hAPP(c_COMBC(U_11134,U_11134,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_11133,U_11134),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2978_1]) ).
fof(f_2978_3,plain,
! [U_11133,U_11134] : c_Fun_Oinj__on(tc_fun(U_11133,U_11134),tc_fun(tc_prod(U_11133,U_11134),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11133,U_11134),tc_HOL_Obool),tc_fun(tc_prod(U_11133,U_11134),tc_HOL_Obool),tc_fun(U_11133,U_11134)),c_Set_OCollect(tc_prod(U_11133,U_11134))),hAPP(hAPP(c_COMBB(tc_fun(U_11133,tc_fun(U_11134,tc_HOL_Obool)),tc_fun(tc_prod(U_11133,U_11134),tc_HOL_Obool),tc_fun(U_11133,U_11134)),c_Product__Type_Oprod_Oprod__case(U_11133,U_11134,tc_HOL_Obool)),hAPP(c_COMBB(U_11134,tc_fun(U_11134,tc_HOL_Obool),U_11133),hAPP(c_COMBC(U_11134,U_11134,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_11133,U_11134),tc_HOL_Obool))),
inference(definitional_conversion,[status(esa)],[f_2978_2]) ).
cnf(f_2978_4,plain,
c_Fun_Oinj__on(tc_fun(U_11133,U_11134),tc_fun(tc_prod(U_11133,U_11134),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11133,U_11134),tc_HOL_Obool),tc_fun(tc_prod(U_11133,U_11134),tc_HOL_Obool),tc_fun(U_11133,U_11134)),c_Set_OCollect(tc_prod(U_11133,U_11134))),hAPP(hAPP(c_COMBB(tc_fun(U_11133,tc_fun(U_11134,tc_HOL_Obool)),tc_fun(tc_prod(U_11133,U_11134),tc_HOL_Obool),tc_fun(U_11133,U_11134)),c_Product__Type_Oprod_Oprod__case(U_11133,U_11134,tc_HOL_Obool)),hAPP(c_COMBB(U_11134,tc_fun(U_11134,tc_HOL_Obool),U_11133),hAPP(c_COMBC(U_11134,U_11134,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_11133,U_11134),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2978_3]) ).
fof(f_2979_1,plain,
! [V_B_2,V_A_2,T_d,T_c] : c_Nitpick_Oprod(T_c,T_d,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_c,T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),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(T_d,tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool),c_member(T_d)),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Oprod__def]) ).
fof(f_2979_2,plain,
! [U_11138,U_11137,U_11136,U_11135] : c_Nitpick_Oprod(U_11135,U_11136,U_11137,U_11138) = hAPP(c_Set_OCollect(tc_prod(U_11135,U_11136)),hAPP(c_Product__Type_Oprod_Oprod__case(U_11135,U_11136,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11135,tc_fun(U_11136,tc_HOL_Obool),tc_fun(U_11136,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11136,tc_HOL_Obool),tc_fun(U_11136,tc_HOL_Obool)),U_11135),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11136)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11135),c_fconj),hAPP(hAPP(c_COMBC(U_11135,tc_fun(U_11135,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11135)),U_11137)))),hAPP(hAPP(c_COMBC(U_11136,tc_fun(U_11136,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11136)),U_11138)))),
inference(variable_rename,[status(thm)],[f_2979_1]) ).
fof(f_2979_3,plain,
! [U_11135,U_11136,U_11137,U_11138] : c_Nitpick_Oprod(U_11135,U_11136,U_11137,U_11138) = hAPP(c_Set_OCollect(tc_prod(U_11135,U_11136)),hAPP(c_Product__Type_Oprod_Oprod__case(U_11135,U_11136,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11135,tc_fun(U_11136,tc_HOL_Obool),tc_fun(U_11136,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11136,tc_HOL_Obool),tc_fun(U_11136,tc_HOL_Obool)),U_11135),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11136)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11135),c_fconj),hAPP(hAPP(c_COMBC(U_11135,tc_fun(U_11135,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11135)),U_11137)))),hAPP(hAPP(c_COMBC(U_11136,tc_fun(U_11136,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11136)),U_11138)))),
inference(definitional_conversion,[status(esa)],[f_2979_2]) ).
cnf(f_2979_4,plain,
c_Nitpick_Oprod(U_11135,U_11136,U_11137,U_11138) = hAPP(c_Set_OCollect(tc_prod(U_11135,U_11136)),hAPP(c_Product__Type_Oprod_Oprod__case(U_11135,U_11136,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11135,tc_fun(U_11136,tc_HOL_Obool),tc_fun(U_11136,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11136,tc_HOL_Obool),tc_fun(U_11136,tc_HOL_Obool)),U_11135),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11136)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11135),c_fconj),hAPP(hAPP(c_COMBC(U_11135,tc_fun(U_11135,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11135)),U_11137)))),hAPP(hAPP(c_COMBC(U_11136,tc_fun(U_11136,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11136)),U_11138)))),
inference(clausify,[status(thm)],[f_2979_3]) ).
fof(f_2980_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_2980_2,plain,
! [U_11140,U_11139] :
( ( c_Code__Numeral_Onat__of__aux(U_11139,U_11140) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_11139),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_11140))
| U_11139 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( c_Code__Numeral_Onat__of__aux(U_11139,U_11140) = U_11140
| U_11139 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[f_2980_1]) ).
fof(f_2980_3,plain,
( ! [U_11144,U_11142] :
( c_Code__Numeral_Onat__of__aux(U_11142,U_11144) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_11142),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_11144))
| U_11142 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_11143,U_11141] :
( c_Code__Numeral_Onat__of__aux(U_11141,U_11143) = U_11143
| U_11141 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(miniscope,[status(thm)],[f_2980_2]) ).
fof(f_2980_4,plain,
( ! [U_11142,U_11144] :
( c_Code__Numeral_Onat__of__aux(U_11142,U_11144) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_11142),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_11144))
| U_11142 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_11143,U_11141] :
( c_Code__Numeral_Onat__of__aux(U_11141,U_11143) = U_11143
| U_11141 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(definitional_conversion,[status(esa)],[f_2980_3]) ).
cnf(f_2980_5,plain,
( c_Code__Numeral_Onat__of__aux(U_11141,U_11143) = U_11143
| U_11141 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2980_4]) ).
cnf(f_2980_6,plain,
( c_Code__Numeral_Onat__of__aux(U_11142,U_11144) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_11142),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_11144))
| U_11142 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_2980_4]) ).
fof(f_2981_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_2981_2,plain,
! [U_11146,U_11145] : c_Divides_Odivmod__int__rel(U_11145,U_11146) = 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_11145))),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_11146)))))),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_11146))),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_11146))))),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_11146)))),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_11146))),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_2981_1]) ).
fof(f_2981_3,plain,
! [U_11145,U_11146] : c_Divides_Odivmod__int__rel(U_11145,U_11146) = 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_11145))),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_11146)))))),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_11146))),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_11146))))),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_11146)))),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_11146))),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_2981_2]) ).
cnf(f_2981_4,plain,
c_Divides_Odivmod__int__rel(U_11145,U_11146) = 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_11145))),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_11146)))))),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_11146))),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_11146))))),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_11146)))),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_11146))),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_2981_3]) ).
fof(f_2982_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_2982_2,plain,
! [U_11148,U_11147] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11148,U_11147),c_Divides_Odivmod__int(U_11148,U_11147)))
| U_11147 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2982_1]) ).
fof(f_2982_3,plain,
! [U_11147,U_11148] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11148,U_11147),c_Divides_Odivmod__int(U_11148,U_11147)))
| U_11147 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_2982_2]) ).
cnf(f_2982_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11148,U_11147),c_Divides_Odivmod__int(U_11148,U_11147)))
| U_11147 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2982_3]) ).
fof(f_2983_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_2983_2,plain,
! [U_11153,U_11152,U_11151,U_11150,U_11149] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11149,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11150),U_11153)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11151),U_11153)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11150),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11151,U_11153))),U_11152))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11153))
| U_11150 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11149,U_11150),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11151),U_11152))) ),
inference(variable_rename,[status(thm)],[f_2983_1]) ).
fof(f_2983_3,plain,
! [U_11149,U_11150,U_11151,U_11152,U_11153] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11149,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11150),U_11153)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11151),U_11153)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11150),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11151,U_11153))),U_11152))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11153))
| U_11150 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11149,U_11150),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11151),U_11152))) ),
inference(definitional_conversion,[status(esa)],[f_2983_2]) ).
cnf(f_2983_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11149,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11150),U_11153)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11151),U_11153)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11150),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11151,U_11153))),U_11152))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11153))
| U_11150 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11149,U_11150),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11151),U_11152))) ),
inference(clausify,[status(thm)],[f_2983_3]) ).
fof(f_2984_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_2984_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_2984_1]) ).
cnf(f_2984_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_2984_2]) ).
fof(f_2985_1,plain,
! [V_w_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Int_Onumber__class_Onumber__of(T_c),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_c)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
| ~ class_Int_Onumber__ring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Nats__number__of]) ).
fof(f_2985_2,plain,
! [U_11155,U_11154] :
( hBOOL(hAPP(hAPP(c_member(U_11154),hAPP(c_Int_Onumber__class_Onumber__of(U_11154),U_11155)),c_Nat_Osemiring__1__class_ONats(U_11154)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11155))
| ~ class_Int_Onumber__ring(U_11154) ),
inference(variable_rename,[status(thm)],[f_2985_1]) ).
fof(f_2985_3,plain,
! [U_11155,U_11154] :
( hBOOL(hAPP(hAPP(c_member(U_11154),hAPP(c_Int_Onumber__class_Onumber__of(U_11154),U_11155)),c_Nat_Osemiring__1__class_ONats(U_11154)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11155))
| ~ class_Int_Onumber__ring(U_11154) ),
inference(definitional_conversion,[status(esa)],[f_2985_2]) ).
cnf(f_2985_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11154),hAPP(c_Int_Onumber__class_Onumber__of(U_11154),U_11155)),c_Nat_Osemiring__1__class_ONats(U_11154)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_11155))
| ~ class_Int_Onumber__ring(U_11154) ),
inference(clausify,[status(thm)],[f_2985_3]) ).
fof(f_2986_1,plain,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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_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_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_R_2),V_S_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_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_R_2),V_S_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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_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)) ) ),
inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2]) ).
fof(f_2986_2,plain,
! [U_11161,U_11160,U_11159,U_11158,U_11157,U_11156] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11156,tc_fun(U_11157,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11156,tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_fun(U_11157,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11157,tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_fun(U_11157,tc_HOL_Obool)),U_11156),c_COMBC(U_11157,tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11157,tc_prod(U_11156,U_11157)),tc_fun(U_11157,tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool)),U_11156),hAPP(c_COMBB(tc_prod(U_11156,U_11157),tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool),U_11157),c_member(tc_prod(U_11156,U_11157)))),c_Product__Type_OPair(U_11156,U_11157)))),U_11158)),hAPP(hAPP(c_COMBC(U_11156,tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_fun(U_11157,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11157,tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_fun(U_11157,tc_HOL_Obool)),U_11156),c_COMBC(U_11157,tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11157,tc_prod(U_11156,U_11157)),tc_fun(U_11157,tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool)),U_11156),hAPP(c_COMBB(tc_prod(U_11156,U_11157),tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool),U_11157),c_member(tc_prod(U_11156,U_11157)))),c_Product__Type_OPair(U_11156,U_11157)))),U_11159)),U_11160),U_11161))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11156,U_11157)),hAPP(hAPP(c_Product__Type_OPair(U_11156,U_11157),U_11160),U_11161)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool)),U_11158),U_11159))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11156,U_11157)),hAPP(hAPP(c_Product__Type_OPair(U_11156,U_11157),U_11160),U_11161)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool)),U_11158),U_11159)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11156,tc_fun(U_11157,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11156,tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_fun(U_11157,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11157,tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_fun(U_11157,tc_HOL_Obool)),U_11156),c_COMBC(U_11157,tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11157,tc_prod(U_11156,U_11157)),tc_fun(U_11157,tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool)),U_11156),hAPP(c_COMBB(tc_prod(U_11156,U_11157),tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool),U_11157),c_member(tc_prod(U_11156,U_11157)))),c_Product__Type_OPair(U_11156,U_11157)))),U_11158)),hAPP(hAPP(c_COMBC(U_11156,tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_fun(U_11157,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11157,tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_fun(U_11157,tc_HOL_Obool)),U_11156),c_COMBC(U_11157,tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11157,tc_prod(U_11156,U_11157)),tc_fun(U_11157,tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool)),U_11156),hAPP(c_COMBB(tc_prod(U_11156,U_11157),tc_fun(tc_fun(tc_prod(U_11156,U_11157),tc_HOL_Obool),tc_HOL_Obool),U_11157),c_member(tc_prod(U_11156,U_11157)))),c_Product__Type_OPair(U_11156,U_11157)))),U_11159)),U_11160),U_11161)) ) ),
inference(variable_rename,[status(thm)],[f_2986_1]) ).
fof(f_2986_3,plain,
( ! [U_11173,U_11171,U_11169,U_11167,U_11165,U_11163] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11163,tc_fun(U_11165,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11163,tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_fun(U_11165,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11165,tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_fun(U_11165,tc_HOL_Obool)),U_11163),c_COMBC(U_11165,tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11165,tc_prod(U_11163,U_11165)),tc_fun(U_11165,tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),U_11163),hAPP(c_COMBB(tc_prod(U_11163,U_11165),tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool),U_11165),c_member(tc_prod(U_11163,U_11165)))),c_Product__Type_OPair(U_11163,U_11165)))),U_11167)),hAPP(hAPP(c_COMBC(U_11163,tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_fun(U_11165,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11165,tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_fun(U_11165,tc_HOL_Obool)),U_11163),c_COMBC(U_11165,tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11165,tc_prod(U_11163,U_11165)),tc_fun(U_11165,tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),U_11163),hAPP(c_COMBB(tc_prod(U_11163,U_11165),tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool),U_11165),c_member(tc_prod(U_11163,U_11165)))),c_Product__Type_OPair(U_11163,U_11165)))),U_11169)),U_11171),U_11173))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11163,U_11165)),hAPP(hAPP(c_Product__Type_OPair(U_11163,U_11165),U_11171),U_11173)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool)),U_11167),U_11169))) )
& ! [U_11172,U_11170,U_11168,U_11166,U_11164,U_11162] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11162,U_11164)),hAPP(hAPP(c_Product__Type_OPair(U_11162,U_11164),U_11170),U_11172)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool)),U_11166),U_11168)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11162,tc_fun(U_11164,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11162,tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_fun(U_11164,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11164,tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_fun(U_11164,tc_HOL_Obool)),U_11162),c_COMBC(U_11164,tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11164,tc_prod(U_11162,U_11164)),tc_fun(U_11164,tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),U_11162),hAPP(c_COMBB(tc_prod(U_11162,U_11164),tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool),U_11164),c_member(tc_prod(U_11162,U_11164)))),c_Product__Type_OPair(U_11162,U_11164)))),U_11166)),hAPP(hAPP(c_COMBC(U_11162,tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_fun(U_11164,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11164,tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_fun(U_11164,tc_HOL_Obool)),U_11162),c_COMBC(U_11164,tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11164,tc_prod(U_11162,U_11164)),tc_fun(U_11164,tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),U_11162),hAPP(c_COMBB(tc_prod(U_11162,U_11164),tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool),U_11164),c_member(tc_prod(U_11162,U_11164)))),c_Product__Type_OPair(U_11162,U_11164)))),U_11168)),U_11170),U_11172)) ) ),
inference(miniscope,[status(thm)],[f_2986_2]) ).
fof(f_2986_4,plain,
( ! [U_11163,U_11165,U_11167,U_11169,U_11171,U_11173] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11163,tc_fun(U_11165,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11163,tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_fun(U_11165,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11165,tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_fun(U_11165,tc_HOL_Obool)),U_11163),c_COMBC(U_11165,tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11165,tc_prod(U_11163,U_11165)),tc_fun(U_11165,tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),U_11163),hAPP(c_COMBB(tc_prod(U_11163,U_11165),tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool),U_11165),c_member(tc_prod(U_11163,U_11165)))),c_Product__Type_OPair(U_11163,U_11165)))),U_11167)),hAPP(hAPP(c_COMBC(U_11163,tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_fun(U_11165,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11165,tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_fun(U_11165,tc_HOL_Obool)),U_11163),c_COMBC(U_11165,tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11165,tc_prod(U_11163,U_11165)),tc_fun(U_11165,tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),U_11163),hAPP(c_COMBB(tc_prod(U_11163,U_11165),tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool),U_11165),c_member(tc_prod(U_11163,U_11165)))),c_Product__Type_OPair(U_11163,U_11165)))),U_11169)),U_11171),U_11173))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11163,U_11165)),hAPP(hAPP(c_Product__Type_OPair(U_11163,U_11165),U_11171),U_11173)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool)),U_11167),U_11169))) )
& ! [U_11166,U_11164,U_11168,U_11162,U_11170,U_11172] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11162,U_11164)),hAPP(hAPP(c_Product__Type_OPair(U_11162,U_11164),U_11170),U_11172)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool)),U_11166),U_11168)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11162,tc_fun(U_11164,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11162,tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_fun(U_11164,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11164,tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_fun(U_11164,tc_HOL_Obool)),U_11162),c_COMBC(U_11164,tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11164,tc_prod(U_11162,U_11164)),tc_fun(U_11164,tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),U_11162),hAPP(c_COMBB(tc_prod(U_11162,U_11164),tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool),U_11164),c_member(tc_prod(U_11162,U_11164)))),c_Product__Type_OPair(U_11162,U_11164)))),U_11166)),hAPP(hAPP(c_COMBC(U_11162,tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_fun(U_11164,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11164,tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_fun(U_11164,tc_HOL_Obool)),U_11162),c_COMBC(U_11164,tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11164,tc_prod(U_11162,U_11164)),tc_fun(U_11164,tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),U_11162),hAPP(c_COMBB(tc_prod(U_11162,U_11164),tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool),U_11164),c_member(tc_prod(U_11162,U_11164)))),c_Product__Type_OPair(U_11162,U_11164)))),U_11168)),U_11170),U_11172)) ) ),
inference(definitional_conversion,[status(esa)],[f_2986_3]) ).
cnf(f_2986_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11162,U_11164)),hAPP(hAPP(c_Product__Type_OPair(U_11162,U_11164),U_11170),U_11172)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool)),U_11166),U_11168)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11162,tc_fun(U_11164,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11162,tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_fun(U_11164,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11164,tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_fun(U_11164,tc_HOL_Obool)),U_11162),c_COMBC(U_11164,tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11164,tc_prod(U_11162,U_11164)),tc_fun(U_11164,tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),U_11162),hAPP(c_COMBB(tc_prod(U_11162,U_11164),tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool),U_11164),c_member(tc_prod(U_11162,U_11164)))),c_Product__Type_OPair(U_11162,U_11164)))),U_11166)),hAPP(hAPP(c_COMBC(U_11162,tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_fun(U_11164,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11164,tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_fun(U_11164,tc_HOL_Obool)),U_11162),c_COMBC(U_11164,tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11164,tc_prod(U_11162,U_11164)),tc_fun(U_11164,tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool)),U_11162),hAPP(c_COMBB(tc_prod(U_11162,U_11164),tc_fun(tc_fun(tc_prod(U_11162,U_11164),tc_HOL_Obool),tc_HOL_Obool),U_11164),c_member(tc_prod(U_11162,U_11164)))),c_Product__Type_OPair(U_11162,U_11164)))),U_11168)),U_11170),U_11172)) ),
inference(clausify,[status(thm)],[f_2986_4]) ).
cnf(f_2986_6,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11163,tc_fun(U_11165,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11163,tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_fun(U_11165,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11165,tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_fun(U_11165,tc_HOL_Obool)),U_11163),c_COMBC(U_11165,tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11165,tc_prod(U_11163,U_11165)),tc_fun(U_11165,tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),U_11163),hAPP(c_COMBB(tc_prod(U_11163,U_11165),tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool),U_11165),c_member(tc_prod(U_11163,U_11165)))),c_Product__Type_OPair(U_11163,U_11165)))),U_11167)),hAPP(hAPP(c_COMBC(U_11163,tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_fun(U_11165,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11165,tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_fun(U_11165,tc_HOL_Obool)),U_11163),c_COMBC(U_11165,tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11165,tc_prod(U_11163,U_11165)),tc_fun(U_11165,tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool)),U_11163),hAPP(c_COMBB(tc_prod(U_11163,U_11165),tc_fun(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool),tc_HOL_Obool),U_11165),c_member(tc_prod(U_11163,U_11165)))),c_Product__Type_OPair(U_11163,U_11165)))),U_11169)),U_11171),U_11173))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11163,U_11165)),hAPP(hAPP(c_Product__Type_OPair(U_11163,U_11165),U_11171),U_11173)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11163,U_11165),tc_HOL_Obool)),U_11167),U_11169))) ),
inference(clausify,[status(thm)],[f_2986_4]) ).
fof(f_2987_1,plain,
! [V_S_2,V_R_2,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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_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)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_R_2),V_S_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_R_2),V_S_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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_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))) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2]) ).
fof(f_2987_2,plain,
! [U_11177,U_11176,U_11175,U_11174] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11174,tc_fun(U_11175,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11174,tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_fun(U_11175,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11175,tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_fun(U_11175,tc_HOL_Obool)),U_11174),c_COMBC(U_11175,tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11175,tc_prod(U_11174,U_11175)),tc_fun(U_11175,tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool)),U_11174),hAPP(c_COMBB(tc_prod(U_11174,U_11175),tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool),U_11175),c_member(tc_prod(U_11174,U_11175)))),c_Product__Type_OPair(U_11174,U_11175)))),U_11176)),hAPP(hAPP(c_COMBC(U_11174,tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_fun(U_11175,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11175,tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_fun(U_11175,tc_HOL_Obool)),U_11174),c_COMBC(U_11175,tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11175,tc_prod(U_11174,U_11175)),tc_fun(U_11175,tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool)),U_11174),hAPP(c_COMBB(tc_prod(U_11174,U_11175),tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool),U_11175),c_member(tc_prod(U_11174,U_11175)))),c_Product__Type_OPair(U_11174,U_11175)))),U_11177)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool)),U_11176),U_11177)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool)),U_11176),U_11177))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11174,tc_fun(U_11175,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11174,tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_fun(U_11175,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11175,tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_fun(U_11175,tc_HOL_Obool)),U_11174),c_COMBC(U_11175,tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11175,tc_prod(U_11174,U_11175)),tc_fun(U_11175,tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool)),U_11174),hAPP(c_COMBB(tc_prod(U_11174,U_11175),tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool),U_11175),c_member(tc_prod(U_11174,U_11175)))),c_Product__Type_OPair(U_11174,U_11175)))),U_11176)),hAPP(hAPP(c_COMBC(U_11174,tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_fun(U_11175,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11175,tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_fun(U_11175,tc_HOL_Obool)),U_11174),c_COMBC(U_11175,tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11175,tc_prod(U_11174,U_11175)),tc_fun(U_11175,tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool)),U_11174),hAPP(c_COMBB(tc_prod(U_11174,U_11175),tc_fun(tc_fun(tc_prod(U_11174,U_11175),tc_HOL_Obool),tc_HOL_Obool),U_11175),c_member(tc_prod(U_11174,U_11175)))),c_Product__Type_OPair(U_11174,U_11175)))),U_11177))) ) ),
inference(variable_rename,[status(thm)],[f_2987_1]) ).
fof(f_2987_3,plain,
( ! [U_11185,U_11183,U_11181,U_11179] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11179,tc_fun(U_11181,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11179,tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_fun(U_11181,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11181,tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_fun(U_11181,tc_HOL_Obool)),U_11179),c_COMBC(U_11181,tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11181,tc_prod(U_11179,U_11181)),tc_fun(U_11181,tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),U_11179),hAPP(c_COMBB(tc_prod(U_11179,U_11181),tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool),U_11181),c_member(tc_prod(U_11179,U_11181)))),c_Product__Type_OPair(U_11179,U_11181)))),U_11183)),hAPP(hAPP(c_COMBC(U_11179,tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_fun(U_11181,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11181,tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_fun(U_11181,tc_HOL_Obool)),U_11179),c_COMBC(U_11181,tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11181,tc_prod(U_11179,U_11181)),tc_fun(U_11181,tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),U_11179),hAPP(c_COMBB(tc_prod(U_11179,U_11181),tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool),U_11181),c_member(tc_prod(U_11179,U_11181)))),c_Product__Type_OPair(U_11179,U_11181)))),U_11185)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool)),U_11183),U_11185)) )
& ! [U_11184,U_11182,U_11180,U_11178] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool)),U_11182),U_11184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11178,tc_fun(U_11180,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11178,tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_fun(U_11180,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_fun(U_11180,tc_HOL_Obool)),U_11178),c_COMBC(U_11180,tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_prod(U_11178,U_11180)),tc_fun(U_11180,tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),U_11178),hAPP(c_COMBB(tc_prod(U_11178,U_11180),tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool),U_11180),c_member(tc_prod(U_11178,U_11180)))),c_Product__Type_OPair(U_11178,U_11180)))),U_11182)),hAPP(hAPP(c_COMBC(U_11178,tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_fun(U_11180,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_fun(U_11180,tc_HOL_Obool)),U_11178),c_COMBC(U_11180,tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_prod(U_11178,U_11180)),tc_fun(U_11180,tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),U_11178),hAPP(c_COMBB(tc_prod(U_11178,U_11180),tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool),U_11180),c_member(tc_prod(U_11178,U_11180)))),c_Product__Type_OPair(U_11178,U_11180)))),U_11184))) ) ),
inference(miniscope,[status(thm)],[f_2987_2]) ).
fof(f_2987_4,plain,
( ! [U_11179,U_11181,U_11183,U_11185] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11179,tc_fun(U_11181,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11179,tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_fun(U_11181,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11181,tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_fun(U_11181,tc_HOL_Obool)),U_11179),c_COMBC(U_11181,tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11181,tc_prod(U_11179,U_11181)),tc_fun(U_11181,tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),U_11179),hAPP(c_COMBB(tc_prod(U_11179,U_11181),tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool),U_11181),c_member(tc_prod(U_11179,U_11181)))),c_Product__Type_OPair(U_11179,U_11181)))),U_11183)),hAPP(hAPP(c_COMBC(U_11179,tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_fun(U_11181,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11181,tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_fun(U_11181,tc_HOL_Obool)),U_11179),c_COMBC(U_11181,tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11181,tc_prod(U_11179,U_11181)),tc_fun(U_11181,tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),U_11179),hAPP(c_COMBB(tc_prod(U_11179,U_11181),tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool),U_11181),c_member(tc_prod(U_11179,U_11181)))),c_Product__Type_OPair(U_11179,U_11181)))),U_11185)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool)),U_11183),U_11185)) )
& ! [U_11182,U_11184,U_11180,U_11178] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool)),U_11182),U_11184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11178,tc_fun(U_11180,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11178,tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_fun(U_11180,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_fun(U_11180,tc_HOL_Obool)),U_11178),c_COMBC(U_11180,tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_prod(U_11178,U_11180)),tc_fun(U_11180,tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),U_11178),hAPP(c_COMBB(tc_prod(U_11178,U_11180),tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool),U_11180),c_member(tc_prod(U_11178,U_11180)))),c_Product__Type_OPair(U_11178,U_11180)))),U_11182)),hAPP(hAPP(c_COMBC(U_11178,tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_fun(U_11180,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_fun(U_11180,tc_HOL_Obool)),U_11178),c_COMBC(U_11180,tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_prod(U_11178,U_11180)),tc_fun(U_11180,tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),U_11178),hAPP(c_COMBB(tc_prod(U_11178,U_11180),tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool),U_11180),c_member(tc_prod(U_11178,U_11180)))),c_Product__Type_OPair(U_11178,U_11180)))),U_11184))) ) ),
inference(definitional_conversion,[status(esa)],[f_2987_3]) ).
cnf(f_2987_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool)),U_11182),U_11184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11178,tc_fun(U_11180,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11178,tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_fun(U_11180,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_fun(U_11180,tc_HOL_Obool)),U_11178),c_COMBC(U_11180,tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_prod(U_11178,U_11180)),tc_fun(U_11180,tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),U_11178),hAPP(c_COMBB(tc_prod(U_11178,U_11180),tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool),U_11180),c_member(tc_prod(U_11178,U_11180)))),c_Product__Type_OPair(U_11178,U_11180)))),U_11182)),hAPP(hAPP(c_COMBC(U_11178,tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_fun(U_11180,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_fun(U_11180,tc_HOL_Obool)),U_11178),c_COMBC(U_11180,tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_prod(U_11178,U_11180)),tc_fun(U_11180,tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool)),U_11178),hAPP(c_COMBB(tc_prod(U_11178,U_11180),tc_fun(tc_fun(tc_prod(U_11178,U_11180),tc_HOL_Obool),tc_HOL_Obool),U_11180),c_member(tc_prod(U_11178,U_11180)))),c_Product__Type_OPair(U_11178,U_11180)))),U_11184))) ),
inference(clausify,[status(thm)],[f_2987_4]) ).
cnf(f_2987_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11179,tc_fun(U_11181,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11179,tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_fun(U_11181,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11181,tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_fun(U_11181,tc_HOL_Obool)),U_11179),c_COMBC(U_11181,tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11181,tc_prod(U_11179,U_11181)),tc_fun(U_11181,tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),U_11179),hAPP(c_COMBB(tc_prod(U_11179,U_11181),tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool),U_11181),c_member(tc_prod(U_11179,U_11181)))),c_Product__Type_OPair(U_11179,U_11181)))),U_11183)),hAPP(hAPP(c_COMBC(U_11179,tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_fun(U_11181,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11181,tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_fun(U_11181,tc_HOL_Obool)),U_11179),c_COMBC(U_11181,tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11181,tc_prod(U_11179,U_11181)),tc_fun(U_11181,tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool)),U_11179),hAPP(c_COMBB(tc_prod(U_11179,U_11181),tc_fun(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool),tc_HOL_Obool),U_11181),c_member(tc_prod(U_11179,U_11181)))),c_Product__Type_OPair(U_11179,U_11181)))),U_11185)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11179,U_11181),tc_HOL_Obool)),U_11183),U_11185)) ),
inference(clausify,[status(thm)],[f_2987_4]) ).
fof(f_2988_1,plain,
! [V_y_2,V_x_2,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)))) )
& ( 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)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2]) ).
fof(f_2988_2,plain,
! [U_11189,U_11188,U_11187,U_11186] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11186,tc_fun(U_11187,tc_HOL_Obool))),U_11188),U_11189))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11186,U_11187)),hAPP(hAPP(c_Product__Type_OPair(U_11186,U_11187),U_11188),U_11189)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11186,U_11187),tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11186,U_11187)),hAPP(hAPP(c_Product__Type_OPair(U_11186,U_11187),U_11188),U_11189)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11186,U_11187),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11186,tc_fun(U_11187,tc_HOL_Obool))),U_11188),U_11189)) ) ),
inference(variable_rename,[status(thm)],[f_2988_1]) ).
fof(f_2988_3,plain,
( ! [U_11197,U_11195,U_11193,U_11191] :
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11191,tc_fun(U_11193,tc_HOL_Obool))),U_11195),U_11197))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11191,U_11193)),hAPP(hAPP(c_Product__Type_OPair(U_11191,U_11193),U_11195),U_11197)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11191,U_11193),tc_HOL_Obool)))) )
& ! [U_11196,U_11194,U_11192,U_11190] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11190,U_11192)),hAPP(hAPP(c_Product__Type_OPair(U_11190,U_11192),U_11194),U_11196)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11190,U_11192),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11190,tc_fun(U_11192,tc_HOL_Obool))),U_11194),U_11196)) ) ),
inference(miniscope,[status(thm)],[f_2988_2]) ).
fof(f_2988_4,plain,
( ! [U_11191,U_11193,U_11195,U_11197] :
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11191,tc_fun(U_11193,tc_HOL_Obool))),U_11195),U_11197))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11191,U_11193)),hAPP(hAPP(c_Product__Type_OPair(U_11191,U_11193),U_11195),U_11197)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11191,U_11193),tc_HOL_Obool)))) )
& ! [U_11196,U_11192,U_11190,U_11194] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11190,U_11192)),hAPP(hAPP(c_Product__Type_OPair(U_11190,U_11192),U_11194),U_11196)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11190,U_11192),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11190,tc_fun(U_11192,tc_HOL_Obool))),U_11194),U_11196)) ) ),
inference(definitional_conversion,[status(esa)],[f_2988_3]) ).
cnf(f_2988_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11190,U_11192)),hAPP(hAPP(c_Product__Type_OPair(U_11190,U_11192),U_11194),U_11196)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11190,U_11192),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11190,tc_fun(U_11192,tc_HOL_Obool))),U_11194),U_11196)) ),
inference(clausify,[status(thm)],[f_2988_4]) ).
cnf(f_2988_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11191,tc_fun(U_11193,tc_HOL_Obool))),U_11195),U_11197))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11191,U_11193)),hAPP(hAPP(c_Product__Type_OPair(U_11191,U_11193),U_11195),U_11197)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11191,U_11193),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2988_4]) ).
fof(f_2989_1,plain,
! [V_S_2,V_R_2,T_d,T_c] :
( ( 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_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_R_2 != V_S_2 )
& ( V_R_2 = V_S_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_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) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2]) ).
fof(f_2989_2,plain,
! [U_11201,U_11200,U_11199,U_11198] :
( ( hAPP(hAPP(c_COMBC(U_11198,tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11199,tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),U_11198),c_COMBC(U_11199,tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11199,tc_prod(U_11198,U_11199)),tc_fun(U_11199,tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool)),U_11198),hAPP(c_COMBB(tc_prod(U_11198,U_11199),tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool),U_11199),c_member(tc_prod(U_11198,U_11199)))),c_Product__Type_OPair(U_11198,U_11199)))),U_11200) = hAPP(hAPP(c_COMBC(U_11198,tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11199,tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),U_11198),c_COMBC(U_11199,tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11199,tc_prod(U_11198,U_11199)),tc_fun(U_11199,tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool)),U_11198),hAPP(c_COMBB(tc_prod(U_11198,U_11199),tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool),U_11199),c_member(tc_prod(U_11198,U_11199)))),c_Product__Type_OPair(U_11198,U_11199)))),U_11201)
| U_11200 != U_11201 )
& ( U_11200 = U_11201
| hAPP(hAPP(c_COMBC(U_11198,tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11199,tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),U_11198),c_COMBC(U_11199,tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11199,tc_prod(U_11198,U_11199)),tc_fun(U_11199,tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool)),U_11198),hAPP(c_COMBB(tc_prod(U_11198,U_11199),tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool),U_11199),c_member(tc_prod(U_11198,U_11199)))),c_Product__Type_OPair(U_11198,U_11199)))),U_11200) != hAPP(hAPP(c_COMBC(U_11198,tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11199,tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),U_11198),c_COMBC(U_11199,tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11199,tc_prod(U_11198,U_11199)),tc_fun(U_11199,tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool)),U_11198),hAPP(c_COMBB(tc_prod(U_11198,U_11199),tc_fun(tc_fun(tc_prod(U_11198,U_11199),tc_HOL_Obool),tc_HOL_Obool),U_11199),c_member(tc_prod(U_11198,U_11199)))),c_Product__Type_OPair(U_11198,U_11199)))),U_11201) ) ),
inference(variable_rename,[status(thm)],[f_2989_1]) ).
fof(f_2989_3,plain,
( ! [U_11209,U_11207] :
( ! [U_11205,U_11203] : hAPP(hAPP(c_COMBC(U_11203,tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11205,tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_fun(U_11205,tc_HOL_Obool)),U_11203),c_COMBC(U_11205,tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11205,tc_prod(U_11203,U_11205)),tc_fun(U_11205,tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),U_11203),hAPP(c_COMBB(tc_prod(U_11203,U_11205),tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool),U_11205),c_member(tc_prod(U_11203,U_11205)))),c_Product__Type_OPair(U_11203,U_11205)))),U_11207) = hAPP(hAPP(c_COMBC(U_11203,tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11205,tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_fun(U_11205,tc_HOL_Obool)),U_11203),c_COMBC(U_11205,tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11205,tc_prod(U_11203,U_11205)),tc_fun(U_11205,tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),U_11203),hAPP(c_COMBB(tc_prod(U_11203,U_11205),tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool),U_11205),c_member(tc_prod(U_11203,U_11205)))),c_Product__Type_OPair(U_11203,U_11205)))),U_11209)
| U_11207 != U_11209 )
& ! [U_11208,U_11206] :
( ! [U_11204,U_11202] : hAPP(hAPP(c_COMBC(U_11202,tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_fun(U_11204,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11204,tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_fun(U_11204,tc_HOL_Obool)),U_11202),c_COMBC(U_11204,tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11204,tc_prod(U_11202,U_11204)),tc_fun(U_11204,tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),U_11202),hAPP(c_COMBB(tc_prod(U_11202,U_11204),tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool),U_11204),c_member(tc_prod(U_11202,U_11204)))),c_Product__Type_OPair(U_11202,U_11204)))),U_11206) != hAPP(hAPP(c_COMBC(U_11202,tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_fun(U_11204,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11204,tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_fun(U_11204,tc_HOL_Obool)),U_11202),c_COMBC(U_11204,tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11204,tc_prod(U_11202,U_11204)),tc_fun(U_11204,tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),U_11202),hAPP(c_COMBB(tc_prod(U_11202,U_11204),tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool),U_11204),c_member(tc_prod(U_11202,U_11204)))),c_Product__Type_OPair(U_11202,U_11204)))),U_11208)
| U_11206 = U_11208 ) ),
inference(miniscope,[status(thm)],[f_2989_2]) ).
fof(f_2989_4,plain,
( ! [U_11207,U_11209,U_11203,U_11205] :
( hAPP(hAPP(c_COMBC(U_11203,tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11205,tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_fun(U_11205,tc_HOL_Obool)),U_11203),c_COMBC(U_11205,tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11205,tc_prod(U_11203,U_11205)),tc_fun(U_11205,tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),U_11203),hAPP(c_COMBB(tc_prod(U_11203,U_11205),tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool),U_11205),c_member(tc_prod(U_11203,U_11205)))),c_Product__Type_OPair(U_11203,U_11205)))),U_11207) = hAPP(hAPP(c_COMBC(U_11203,tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11205,tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_fun(U_11205,tc_HOL_Obool)),U_11203),c_COMBC(U_11205,tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11205,tc_prod(U_11203,U_11205)),tc_fun(U_11205,tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),U_11203),hAPP(c_COMBB(tc_prod(U_11203,U_11205),tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool),U_11205),c_member(tc_prod(U_11203,U_11205)))),c_Product__Type_OPair(U_11203,U_11205)))),U_11209)
| U_11207 != U_11209 )
& ! [U_11206,U_11204,U_11202,U_11208] :
( hAPP(hAPP(c_COMBC(U_11202,tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_fun(U_11204,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11204,tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_fun(U_11204,tc_HOL_Obool)),U_11202),c_COMBC(U_11204,tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11204,tc_prod(U_11202,U_11204)),tc_fun(U_11204,tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),U_11202),hAPP(c_COMBB(tc_prod(U_11202,U_11204),tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool),U_11204),c_member(tc_prod(U_11202,U_11204)))),c_Product__Type_OPair(U_11202,U_11204)))),U_11206) != hAPP(hAPP(c_COMBC(U_11202,tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_fun(U_11204,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11204,tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_fun(U_11204,tc_HOL_Obool)),U_11202),c_COMBC(U_11204,tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11204,tc_prod(U_11202,U_11204)),tc_fun(U_11204,tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),U_11202),hAPP(c_COMBB(tc_prod(U_11202,U_11204),tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool),U_11204),c_member(tc_prod(U_11202,U_11204)))),c_Product__Type_OPair(U_11202,U_11204)))),U_11208)
| U_11206 = U_11208 ) ),
inference(definitional_conversion,[status(esa)],[f_2989_3]) ).
cnf(f_2989_5,plain,
( hAPP(hAPP(c_COMBC(U_11202,tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_fun(U_11204,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11204,tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_fun(U_11204,tc_HOL_Obool)),U_11202),c_COMBC(U_11204,tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11204,tc_prod(U_11202,U_11204)),tc_fun(U_11204,tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),U_11202),hAPP(c_COMBB(tc_prod(U_11202,U_11204),tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool),U_11204),c_member(tc_prod(U_11202,U_11204)))),c_Product__Type_OPair(U_11202,U_11204)))),U_11206) != hAPP(hAPP(c_COMBC(U_11202,tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_fun(U_11204,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11204,tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_fun(U_11204,tc_HOL_Obool)),U_11202),c_COMBC(U_11204,tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11204,tc_prod(U_11202,U_11204)),tc_fun(U_11204,tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool)),U_11202),hAPP(c_COMBB(tc_prod(U_11202,U_11204),tc_fun(tc_fun(tc_prod(U_11202,U_11204),tc_HOL_Obool),tc_HOL_Obool),U_11204),c_member(tc_prod(U_11202,U_11204)))),c_Product__Type_OPair(U_11202,U_11204)))),U_11208)
| U_11206 = U_11208 ),
inference(clausify,[status(thm)],[f_2989_4]) ).
cnf(f_2989_6,plain,
( hAPP(hAPP(c_COMBC(U_11203,tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11205,tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_fun(U_11205,tc_HOL_Obool)),U_11203),c_COMBC(U_11205,tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11205,tc_prod(U_11203,U_11205)),tc_fun(U_11205,tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),U_11203),hAPP(c_COMBB(tc_prod(U_11203,U_11205),tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool),U_11205),c_member(tc_prod(U_11203,U_11205)))),c_Product__Type_OPair(U_11203,U_11205)))),U_11207) = hAPP(hAPP(c_COMBC(U_11203,tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11205,tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_fun(U_11205,tc_HOL_Obool)),U_11203),c_COMBC(U_11205,tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11205,tc_prod(U_11203,U_11205)),tc_fun(U_11205,tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool)),U_11203),hAPP(c_COMBB(tc_prod(U_11203,U_11205),tc_fun(tc_fun(tc_prod(U_11203,U_11205),tc_HOL_Obool),tc_HOL_Obool),U_11205),c_member(tc_prod(U_11203,U_11205)))),c_Product__Type_OPair(U_11203,U_11205)))),U_11209)
| U_11207 != U_11209 ),
inference(clausify,[status(thm)],[f_2989_4]) ).
fof(f_2990_1,plain,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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_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_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_R_2),V_S_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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_R_2),V_S_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),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_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)) ) ),
inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2]) ).
fof(f_2990_2,plain,
! [U_11215,U_11214,U_11213,U_11212,U_11211,U_11210] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11210,tc_fun(U_11211,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11210,tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_fun(U_11211,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11211,tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_fun(U_11211,tc_HOL_Obool)),U_11210),c_COMBC(U_11211,tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11211,tc_prod(U_11210,U_11211)),tc_fun(U_11211,tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool)),U_11210),hAPP(c_COMBB(tc_prod(U_11210,U_11211),tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool),U_11211),c_member(tc_prod(U_11210,U_11211)))),c_Product__Type_OPair(U_11210,U_11211)))),U_11212)),hAPP(hAPP(c_COMBC(U_11210,tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_fun(U_11211,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11211,tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_fun(U_11211,tc_HOL_Obool)),U_11210),c_COMBC(U_11211,tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11211,tc_prod(U_11210,U_11211)),tc_fun(U_11211,tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool)),U_11210),hAPP(c_COMBB(tc_prod(U_11210,U_11211),tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool),U_11211),c_member(tc_prod(U_11210,U_11211)))),c_Product__Type_OPair(U_11210,U_11211)))),U_11213)),U_11214),U_11215))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11210,U_11211)),hAPP(hAPP(c_Product__Type_OPair(U_11210,U_11211),U_11214),U_11215)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool)),U_11212),U_11213))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11210,U_11211)),hAPP(hAPP(c_Product__Type_OPair(U_11210,U_11211),U_11214),U_11215)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool)),U_11212),U_11213)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11210,tc_fun(U_11211,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11210,tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_fun(U_11211,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11211,tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_fun(U_11211,tc_HOL_Obool)),U_11210),c_COMBC(U_11211,tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11211,tc_prod(U_11210,U_11211)),tc_fun(U_11211,tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool)),U_11210),hAPP(c_COMBB(tc_prod(U_11210,U_11211),tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool),U_11211),c_member(tc_prod(U_11210,U_11211)))),c_Product__Type_OPair(U_11210,U_11211)))),U_11212)),hAPP(hAPP(c_COMBC(U_11210,tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_fun(U_11211,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11211,tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_fun(U_11211,tc_HOL_Obool)),U_11210),c_COMBC(U_11211,tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11211,tc_prod(U_11210,U_11211)),tc_fun(U_11211,tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool)),U_11210),hAPP(c_COMBB(tc_prod(U_11210,U_11211),tc_fun(tc_fun(tc_prod(U_11210,U_11211),tc_HOL_Obool),tc_HOL_Obool),U_11211),c_member(tc_prod(U_11210,U_11211)))),c_Product__Type_OPair(U_11210,U_11211)))),U_11213)),U_11214),U_11215)) ) ),
inference(variable_rename,[status(thm)],[f_2990_1]) ).
fof(f_2990_3,plain,
( ! [U_11227,U_11225,U_11223,U_11221,U_11219,U_11217] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_fun(U_11219,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11217,tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_fun(U_11219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11219,tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_fun(U_11219,tc_HOL_Obool)),U_11217),c_COMBC(U_11219,tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11219,tc_prod(U_11217,U_11219)),tc_fun(U_11219,tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),U_11217),hAPP(c_COMBB(tc_prod(U_11217,U_11219),tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool),U_11219),c_member(tc_prod(U_11217,U_11219)))),c_Product__Type_OPair(U_11217,U_11219)))),U_11221)),hAPP(hAPP(c_COMBC(U_11217,tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_fun(U_11219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11219,tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_fun(U_11219,tc_HOL_Obool)),U_11217),c_COMBC(U_11219,tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11219,tc_prod(U_11217,U_11219)),tc_fun(U_11219,tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),U_11217),hAPP(c_COMBB(tc_prod(U_11217,U_11219),tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool),U_11219),c_member(tc_prod(U_11217,U_11219)))),c_Product__Type_OPair(U_11217,U_11219)))),U_11223)),U_11225),U_11227))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11217,U_11219)),hAPP(hAPP(c_Product__Type_OPair(U_11217,U_11219),U_11225),U_11227)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool)),U_11221),U_11223))) )
& ! [U_11226,U_11224,U_11222,U_11220,U_11218,U_11216] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11216,U_11218)),hAPP(hAPP(c_Product__Type_OPair(U_11216,U_11218),U_11224),U_11226)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool)),U_11220),U_11222)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11216,tc_fun(U_11218,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11216,tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_fun(U_11218,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11218,tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_fun(U_11218,tc_HOL_Obool)),U_11216),c_COMBC(U_11218,tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11218,tc_prod(U_11216,U_11218)),tc_fun(U_11218,tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),U_11216),hAPP(c_COMBB(tc_prod(U_11216,U_11218),tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool),U_11218),c_member(tc_prod(U_11216,U_11218)))),c_Product__Type_OPair(U_11216,U_11218)))),U_11220)),hAPP(hAPP(c_COMBC(U_11216,tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_fun(U_11218,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11218,tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_fun(U_11218,tc_HOL_Obool)),U_11216),c_COMBC(U_11218,tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11218,tc_prod(U_11216,U_11218)),tc_fun(U_11218,tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),U_11216),hAPP(c_COMBB(tc_prod(U_11216,U_11218),tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool),U_11218),c_member(tc_prod(U_11216,U_11218)))),c_Product__Type_OPair(U_11216,U_11218)))),U_11222)),U_11224),U_11226)) ) ),
inference(miniscope,[status(thm)],[f_2990_2]) ).
fof(f_2990_4,plain,
( ! [U_11217,U_11219,U_11221,U_11223,U_11225,U_11227] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_fun(U_11219,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11217,tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_fun(U_11219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11219,tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_fun(U_11219,tc_HOL_Obool)),U_11217),c_COMBC(U_11219,tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11219,tc_prod(U_11217,U_11219)),tc_fun(U_11219,tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),U_11217),hAPP(c_COMBB(tc_prod(U_11217,U_11219),tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool),U_11219),c_member(tc_prod(U_11217,U_11219)))),c_Product__Type_OPair(U_11217,U_11219)))),U_11221)),hAPP(hAPP(c_COMBC(U_11217,tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_fun(U_11219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11219,tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_fun(U_11219,tc_HOL_Obool)),U_11217),c_COMBC(U_11219,tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11219,tc_prod(U_11217,U_11219)),tc_fun(U_11219,tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),U_11217),hAPP(c_COMBB(tc_prod(U_11217,U_11219),tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool),U_11219),c_member(tc_prod(U_11217,U_11219)))),c_Product__Type_OPair(U_11217,U_11219)))),U_11223)),U_11225),U_11227))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11217,U_11219)),hAPP(hAPP(c_Product__Type_OPair(U_11217,U_11219),U_11225),U_11227)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool)),U_11221),U_11223))) )
& ! [U_11222,U_11218,U_11220,U_11216,U_11224,U_11226] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11216,U_11218)),hAPP(hAPP(c_Product__Type_OPair(U_11216,U_11218),U_11224),U_11226)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool)),U_11220),U_11222)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11216,tc_fun(U_11218,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11216,tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_fun(U_11218,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11218,tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_fun(U_11218,tc_HOL_Obool)),U_11216),c_COMBC(U_11218,tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11218,tc_prod(U_11216,U_11218)),tc_fun(U_11218,tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),U_11216),hAPP(c_COMBB(tc_prod(U_11216,U_11218),tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool),U_11218),c_member(tc_prod(U_11216,U_11218)))),c_Product__Type_OPair(U_11216,U_11218)))),U_11220)),hAPP(hAPP(c_COMBC(U_11216,tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_fun(U_11218,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11218,tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_fun(U_11218,tc_HOL_Obool)),U_11216),c_COMBC(U_11218,tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11218,tc_prod(U_11216,U_11218)),tc_fun(U_11218,tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),U_11216),hAPP(c_COMBB(tc_prod(U_11216,U_11218),tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool),U_11218),c_member(tc_prod(U_11216,U_11218)))),c_Product__Type_OPair(U_11216,U_11218)))),U_11222)),U_11224),U_11226)) ) ),
inference(definitional_conversion,[status(esa)],[f_2990_3]) ).
cnf(f_2990_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11216,U_11218)),hAPP(hAPP(c_Product__Type_OPair(U_11216,U_11218),U_11224),U_11226)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool)),U_11220),U_11222)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11216,tc_fun(U_11218,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11216,tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_fun(U_11218,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11218,tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_fun(U_11218,tc_HOL_Obool)),U_11216),c_COMBC(U_11218,tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11218,tc_prod(U_11216,U_11218)),tc_fun(U_11218,tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),U_11216),hAPP(c_COMBB(tc_prod(U_11216,U_11218),tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool),U_11218),c_member(tc_prod(U_11216,U_11218)))),c_Product__Type_OPair(U_11216,U_11218)))),U_11220)),hAPP(hAPP(c_COMBC(U_11216,tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_fun(U_11218,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11218,tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_fun(U_11218,tc_HOL_Obool)),U_11216),c_COMBC(U_11218,tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11218,tc_prod(U_11216,U_11218)),tc_fun(U_11218,tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool)),U_11216),hAPP(c_COMBB(tc_prod(U_11216,U_11218),tc_fun(tc_fun(tc_prod(U_11216,U_11218),tc_HOL_Obool),tc_HOL_Obool),U_11218),c_member(tc_prod(U_11216,U_11218)))),c_Product__Type_OPair(U_11216,U_11218)))),U_11222)),U_11224),U_11226)) ),
inference(clausify,[status(thm)],[f_2990_4]) ).
cnf(f_2990_6,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_fun(U_11219,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11217,tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_fun(U_11219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11219,tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_fun(U_11219,tc_HOL_Obool)),U_11217),c_COMBC(U_11219,tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11219,tc_prod(U_11217,U_11219)),tc_fun(U_11219,tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),U_11217),hAPP(c_COMBB(tc_prod(U_11217,U_11219),tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool),U_11219),c_member(tc_prod(U_11217,U_11219)))),c_Product__Type_OPair(U_11217,U_11219)))),U_11221)),hAPP(hAPP(c_COMBC(U_11217,tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_fun(U_11219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11219,tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_fun(U_11219,tc_HOL_Obool)),U_11217),c_COMBC(U_11219,tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11219,tc_prod(U_11217,U_11219)),tc_fun(U_11219,tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool)),U_11217),hAPP(c_COMBB(tc_prod(U_11217,U_11219),tc_fun(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool),tc_HOL_Obool),U_11219),c_member(tc_prod(U_11217,U_11219)))),c_Product__Type_OPair(U_11217,U_11219)))),U_11223)),U_11225),U_11227))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11217,U_11219)),hAPP(hAPP(c_Product__Type_OPair(U_11217,U_11219),U_11225),U_11227)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11217,U_11219),tc_HOL_Obool)),U_11221),U_11223))) ),
inference(clausify,[status(thm)],[f_2990_4]) ).
fof(f_2991_1,plain,
! [V_z_2,V_y_2,V_f_2,V_r_2,T_d,T_c] :
( hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_2),V_z_2)),V_r_2))
| ~ c_Equiv__Relations_Ocongruent(T_c,T_d,V_r_2,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_congruentD]) ).
fof(f_2991_2,plain,
! [U_11233,U_11232,U_11231,U_11230,U_11229,U_11228] :
( hAPP(U_11231,U_11232) = hAPP(U_11231,U_11233)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11228,U_11228)),hAPP(hAPP(c_Product__Type_OPair(U_11228,U_11228),U_11232),U_11233)),U_11230))
| ~ c_Equiv__Relations_Ocongruent(U_11228,U_11229,U_11230,U_11231) ),
inference(variable_rename,[status(thm)],[f_2991_1]) ).
fof(f_2991_3,plain,
! [U_11232,U_11228,U_11231,U_11233,U_11229,U_11230] :
( hAPP(U_11231,U_11232) = hAPP(U_11231,U_11233)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11228,U_11228)),hAPP(hAPP(c_Product__Type_OPair(U_11228,U_11228),U_11232),U_11233)),U_11230))
| ~ c_Equiv__Relations_Ocongruent(U_11228,U_11229,U_11230,U_11231) ),
inference(definitional_conversion,[status(esa)],[f_2991_2]) ).
cnf(f_2991_4,plain,
( hAPP(U_11231,U_11232) = hAPP(U_11231,U_11233)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11228,U_11228)),hAPP(hAPP(c_Product__Type_OPair(U_11228,U_11228),U_11232),U_11233)),U_11230))
| ~ c_Equiv__Relations_Ocongruent(U_11228,U_11229,U_11230,U_11231) ),
inference(clausify,[status(thm)],[f_2991_3]) ).
fof(f_2992_1,plain,
! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_e,T_d,T_c] :
( hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_d),V_y2_2),V_z2_2)),V_r2_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y1_2),V_z1_2)),V_r1_2))
| ~ c_Equiv__Relations_Ocongruent2(T_c,T_d,T_e,V_r1_2,V_r2_2,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_congruent2D]) ).
fof(f_2992_2,plain,
! [U_11243,U_11242,U_11241,U_11240,U_11239,U_11238,U_11237,U_11236,U_11235,U_11234] :
( hAPP(hAPP(U_11239,U_11240),U_11242) = hAPP(hAPP(U_11239,U_11241),U_11243)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11235,U_11235)),hAPP(hAPP(c_Product__Type_OPair(U_11235,U_11235),U_11242),U_11243)),U_11238))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11234,U_11234)),hAPP(hAPP(c_Product__Type_OPair(U_11234,U_11234),U_11240),U_11241)),U_11237))
| ~ c_Equiv__Relations_Ocongruent2(U_11234,U_11235,U_11236,U_11237,U_11238,U_11239) ),
inference(variable_rename,[status(thm)],[f_2992_1]) ).
fof(f_2992_3,plain,
! [U_11234,U_11235,U_11236,U_11237,U_11238,U_11239,U_11240,U_11241,U_11242,U_11243] :
( hAPP(hAPP(U_11239,U_11240),U_11242) = hAPP(hAPP(U_11239,U_11241),U_11243)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11235,U_11235)),hAPP(hAPP(c_Product__Type_OPair(U_11235,U_11235),U_11242),U_11243)),U_11238))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11234,U_11234)),hAPP(hAPP(c_Product__Type_OPair(U_11234,U_11234),U_11240),U_11241)),U_11237))
| ~ c_Equiv__Relations_Ocongruent2(U_11234,U_11235,U_11236,U_11237,U_11238,U_11239) ),
inference(definitional_conversion,[status(esa)],[f_2992_2]) ).
cnf(f_2992_4,plain,
( hAPP(hAPP(U_11239,U_11240),U_11242) = hAPP(hAPP(U_11239,U_11241),U_11243)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11235,U_11235)),hAPP(hAPP(c_Product__Type_OPair(U_11235,U_11235),U_11242),U_11243)),U_11238))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11234,U_11234)),hAPP(hAPP(c_Product__Type_OPair(U_11234,U_11234),U_11240),U_11241)),U_11237))
| ~ c_Equiv__Relations_Ocongruent2(U_11234,U_11235,U_11236,U_11237,U_11238,U_11239) ),
inference(clausify,[status(thm)],[f_2992_3]) ).
fof(f_2993_1,plain,
! [V_A_2,V_r_2,T_d,V_b_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),V_A_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_x),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_x),V_b_2)),V_r_2))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Image__iff]) ).
fof(f_2993_2,plain,
! [U_11250,U_11249,U_11248,U_11247,U_11246] :
( ( hBOOL(hAPP(hAPP(c_member(U_11246),U_11247),hAPP(c_Relation_OImage(U_11248,U_11246,U_11249),U_11250)))
| ! [U_11245] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11248,U_11246)),hAPP(hAPP(c_Product__Type_OPair(U_11248,U_11246),U_11245),U_11247)),U_11249))
| ~ hBOOL(hAPP(hAPP(c_member(U_11248),U_11245),U_11250)) ) )
& ( ? [U_11244] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11248,U_11246)),hAPP(hAPP(c_Product__Type_OPair(U_11248,U_11246),U_11244),U_11247)),U_11249))
& hBOOL(hAPP(hAPP(c_member(U_11248),U_11244),U_11250)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11246),U_11247),hAPP(c_Relation_OImage(U_11248,U_11246,U_11249),U_11250))) ) ),
inference(variable_rename,[status(thm)],[f_2993_1]) ).
fof(f_2993_3,plain,
( ! [U_11260,U_11258,U_11256,U_11254,U_11252] :
( hBOOL(hAPP(hAPP(c_member(U_11252),U_11254),hAPP(c_Relation_OImage(U_11256,U_11252,U_11258),U_11260)))
| ! [U_11245] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11256,U_11252)),hAPP(hAPP(c_Product__Type_OPair(U_11256,U_11252),U_11245),U_11254)),U_11258))
| ~ hBOOL(hAPP(hAPP(c_member(U_11256),U_11245),U_11260)) ) )
& ! [U_11259,U_11257,U_11255,U_11253,U_11251] :
( ? [U_11244] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11255,U_11251)),hAPP(hAPP(c_Product__Type_OPair(U_11255,U_11251),U_11244),U_11253)),U_11257))
& hBOOL(hAPP(hAPP(c_member(U_11255),U_11244),U_11259)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11251),U_11253),hAPP(c_Relation_OImage(U_11255,U_11251,U_11257),U_11259))) ) ),
inference(miniscope,[status(thm)],[f_2993_2]) ).
fof(f_2993_4,plain,
( ! [U_11260,U_11258,U_11256,U_11254,U_11252] :
( hBOOL(hAPP(hAPP(c_member(U_11252),U_11254),hAPP(c_Relation_OImage(U_11256,U_11252,U_11258),U_11260)))
| ! [U_11245] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11256,U_11252)),hAPP(hAPP(c_Product__Type_OPair(U_11256,U_11252),U_11245),U_11254)),U_11258))
| ~ hBOOL(hAPP(hAPP(c_member(U_11256),U_11245),U_11260)) ) )
& ! [U_11259,U_11257,U_11255,U_11253,U_11251] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11255,U_11251)),hAPP(hAPP(c_Product__Type_OPair(U_11255,U_11251),sK270(U_11259,U_11257,U_11255,U_11253,U_11251)),U_11253)),U_11257))
& hBOOL(hAPP(hAPP(c_member(U_11255),sK270(U_11259,U_11257,U_11255,U_11253,U_11251)),U_11259)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11251),U_11253),hAPP(c_Relation_OImage(U_11255,U_11251,U_11257),U_11259))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_11244,sK270(U_11259,U_11257,U_11255,U_11253,U_11251))],[f_2993_3]) ).
fof(f_2993_5,plain,
( ! [U_11253,U_11255,U_11251,U_11259,U_11257] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11255,U_11251)),hAPP(hAPP(c_Product__Type_OPair(U_11255,U_11251),sK270(U_11259,U_11257,U_11255,U_11253,U_11251)),U_11253)),U_11257))
| ~ sP834(U_11253,U_11255,U_11251,U_11259,U_11257) )
& ! [U_11253,U_11255,U_11251,U_11259,U_11257] :
( hBOOL(hAPP(hAPP(c_member(U_11255),sK270(U_11259,U_11257,U_11255,U_11253,U_11251)),U_11259))
| ~ sP834(U_11253,U_11255,U_11251,U_11259,U_11257) )
& ! [U_11245,U_11260,U_11252,U_11254,U_11258,U_11256] :
( hBOOL(hAPP(hAPP(c_member(U_11252),U_11254),hAPP(c_Relation_OImage(U_11256,U_11252,U_11258),U_11260)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11256,U_11252)),hAPP(hAPP(c_Product__Type_OPair(U_11256,U_11252),U_11245),U_11254)),U_11258))
| ~ hBOOL(hAPP(hAPP(c_member(U_11256),U_11245),U_11260)) )
& ! [U_11253,U_11255,U_11251,U_11259,U_11257] :
( sP834(U_11253,U_11255,U_11251,U_11259,U_11257)
| ~ hBOOL(hAPP(hAPP(c_member(U_11251),U_11253),hAPP(c_Relation_OImage(U_11255,U_11251,U_11257),U_11259))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP834])],[f_2993_4]) ).
cnf(f_2993_6,plain,
( sP834(U_11253,U_11255,U_11251,U_11259,U_11257)
| ~ hBOOL(hAPP(hAPP(c_member(U_11251),U_11253),hAPP(c_Relation_OImage(U_11255,U_11251,U_11257),U_11259))) ),
inference(clausify,[status(thm)],[f_2993_5]) ).
cnf(f_2993_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_11252),U_11254),hAPP(c_Relation_OImage(U_11256,U_11252,U_11258),U_11260)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11256,U_11252)),hAPP(hAPP(c_Product__Type_OPair(U_11256,U_11252),U_11245),U_11254)),U_11258))
| ~ hBOOL(hAPP(hAPP(c_member(U_11256),U_11245),U_11260)) ),
inference(clausify,[status(thm)],[f_2993_5]) ).
cnf(f_2993_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_11255),sK270(U_11259,U_11257,U_11255,U_11253,U_11251)),U_11259))
| ~ sP834(U_11253,U_11255,U_11251,U_11259,U_11257) ),
inference(clausify,[status(thm)],[f_2993_5]) ).
cnf(f_2993_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11255,U_11251)),hAPP(hAPP(c_Product__Type_OPair(U_11255,U_11251),sK270(U_11259,U_11257,U_11255,U_11253,U_11251)),U_11253)),U_11257))
| ~ sP834(U_11253,U_11255,U_11251,U_11259,U_11257) ),
inference(clausify,[status(thm)],[f_2993_5]) ).
fof(f_2994_1,plain,
! [V_r_2,V_b_2,T_d,V_A_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_d),V_b_2),hAPP(c_Relation_OImage(T_c,T_d,V_r_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__ImageI]) ).
fof(f_2994_2,plain,
! [U_11266,U_11265,U_11264,U_11263,U_11262,U_11261] :
( hBOOL(hAPP(hAPP(c_member(U_11264),U_11265),hAPP(c_Relation_OImage(U_11261,U_11264,U_11266),U_11263)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11261,U_11264)),hAPP(hAPP(c_Product__Type_OPair(U_11261,U_11264),U_11262),U_11265)),U_11266))
| ~ hBOOL(hAPP(hAPP(c_member(U_11261),U_11262),U_11263)) ),
inference(variable_rename,[status(thm)],[f_2994_1]) ).
fof(f_2994_3,plain,
! [U_11262,U_11263,U_11261,U_11264,U_11265,U_11266] :
( hBOOL(hAPP(hAPP(c_member(U_11264),U_11265),hAPP(c_Relation_OImage(U_11261,U_11264,U_11266),U_11263)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11261,U_11264)),hAPP(hAPP(c_Product__Type_OPair(U_11261,U_11264),U_11262),U_11265)),U_11266))
| ~ hBOOL(hAPP(hAPP(c_member(U_11261),U_11262),U_11263)) ),
inference(definitional_conversion,[status(esa)],[f_2994_2]) ).
cnf(f_2994_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11264),U_11265),hAPP(c_Relation_OImage(U_11261,U_11264,U_11266),U_11263)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11261,U_11264)),hAPP(hAPP(c_Product__Type_OPair(U_11261,U_11264),U_11262),U_11265)),U_11266))
| ~ hBOOL(hAPP(hAPP(c_member(U_11261),U_11262),U_11263)) ),
inference(clausify,[status(thm)],[f_2994_3]) ).
fof(f_2995_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_2995_2,plain,
! [U_11272,U_11271,U_11270,U_11269,U_11268,U_11267] :
( U_11270 = U_11272
| U_11268 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11267,U_11268),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11271),U_11272)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11267,U_11268),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11269),U_11270))) ),
inference(variable_rename,[status(thm)],[f_2995_1]) ).
fof(f_2995_3,plain,
! [U_11270,U_11267,U_11269,U_11268,U_11271,U_11272] :
( U_11270 = U_11272
| U_11268 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11267,U_11268),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11271),U_11272)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11267,U_11268),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11269),U_11270))) ),
inference(definitional_conversion,[status(esa)],[f_2995_2]) ).
cnf(f_2995_4,plain,
( U_11270 = U_11272
| U_11268 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11267,U_11268),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11271),U_11272)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11267,U_11268),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11269),U_11270))) ),
inference(clausify,[status(thm)],[f_2995_3]) ).
fof(f_2996_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_2996_2,plain,
! [U_11278,U_11277,U_11276,U_11275,U_11274,U_11273] :
( U_11275 = U_11277
| U_11274 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11273,U_11274),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11277),U_11278)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11273,U_11274),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11275),U_11276))) ),
inference(variable_rename,[status(thm)],[f_2996_1]) ).
fof(f_2996_3,plain,
! [U_11275,U_11273,U_11274,U_11276,U_11277,U_11278] :
( U_11275 = U_11277
| U_11274 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11273,U_11274),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11277),U_11278)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11273,U_11274),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11275),U_11276))) ),
inference(definitional_conversion,[status(esa)],[f_2996_2]) ).
cnf(f_2996_4,plain,
( U_11275 = U_11277
| U_11274 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11273,U_11274),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11277),U_11278)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11273,U_11274),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11275),U_11276))) ),
inference(clausify,[status(thm)],[f_2996_3]) ).
fof(f_2997_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_2997_2,plain,
! [U_11281,U_11280,U_11279] :
( U_11281 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11279 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11279,U_11279),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11280),U_11281))) ),
inference(variable_rename,[status(thm)],[f_2997_1]) ).
fof(f_2997_3,plain,
! [U_11280,U_11279,U_11281] :
( U_11281 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11279 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11279,U_11279),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11280),U_11281))) ),
inference(definitional_conversion,[status(esa)],[f_2997_2]) ).
cnf(f_2997_4,plain,
( U_11281 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11279 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11279,U_11279),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11280),U_11281))) ),
inference(clausify,[status(thm)],[f_2997_3]) ).
fof(f_2998_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_2998_2,plain,
! [U_11282] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_11282),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_11282 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_2998_1]) ).
fof(f_2998_3,plain,
! [U_11282] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_11282),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_11282 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_2998_2]) ).
cnf(f_2998_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_11282),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_11282 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_2998_3]) ).
fof(f_2999_1,plain,
! [V_y_2,V_x_2,V_r_2,T_e,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),T_c),hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_d),c_COMBC(T_e,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),T_d),hAPP(c_COMBB(tc_prod(T_d,T_e),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_d,T_e)))),c_Product__Type_OPair(T_d,T_e))))),V_r_2)),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),T_c),hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_d),c_COMBC(T_e,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),T_d),hAPP(c_COMBB(tc_prod(T_d,T_e),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_d,T_e)))),c_Product__Type_OPair(T_d,T_e))))),V_r_2)),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2]) ).
fof(f_2999_2,plain,
! [U_11288,U_11287,U_11286,U_11285,U_11284,U_11283] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11283,tc_fun(U_11284,tc_fun(U_11285,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11283,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_fun(U_11284,tc_fun(U_11285,tc_HOL_Obool)),U_11283),hAPP(c_COMBC(U_11284,tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_fun(U_11285,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11285,tc_fun(tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_fun(U_11285,tc_HOL_Obool)),U_11284),c_COMBC(U_11285,tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11285,tc_prod(U_11284,U_11285)),tc_fun(U_11285,tc_fun(tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_HOL_Obool)),U_11284),hAPP(c_COMBB(tc_prod(U_11284,U_11285),tc_fun(tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_HOL_Obool),U_11285),c_member(tc_prod(U_11284,U_11285)))),c_Product__Type_OPair(U_11284,U_11285))))),U_11286)),U_11287),U_11288))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11284,U_11285)),hAPP(hAPP(c_Product__Type_OPair(U_11284,U_11285),U_11287),U_11288)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11283,tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11283,tc_HOL_Obool))),U_11286))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11284,U_11285)),hAPP(hAPP(c_Product__Type_OPair(U_11284,U_11285),U_11287),U_11288)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11283,tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11283,tc_HOL_Obool))),U_11286)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11283,tc_fun(U_11284,tc_fun(U_11285,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11283,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_fun(U_11284,tc_fun(U_11285,tc_HOL_Obool)),U_11283),hAPP(c_COMBC(U_11284,tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_fun(U_11285,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11285,tc_fun(tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_fun(U_11285,tc_HOL_Obool)),U_11284),c_COMBC(U_11285,tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11285,tc_prod(U_11284,U_11285)),tc_fun(U_11285,tc_fun(tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_HOL_Obool)),U_11284),hAPP(c_COMBB(tc_prod(U_11284,U_11285),tc_fun(tc_fun(tc_prod(U_11284,U_11285),tc_HOL_Obool),tc_HOL_Obool),U_11285),c_member(tc_prod(U_11284,U_11285)))),c_Product__Type_OPair(U_11284,U_11285))))),U_11286)),U_11287),U_11288)) ) ),
inference(variable_rename,[status(thm)],[f_2999_1]) ).
fof(f_2999_3,plain,
( ! [U_11300,U_11298,U_11296,U_11294,U_11292,U_11290] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11290,tc_fun(U_11292,tc_fun(U_11294,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11290,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_fun(U_11292,tc_fun(U_11294,tc_HOL_Obool)),U_11290),hAPP(c_COMBC(U_11292,tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_fun(U_11294,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11294,tc_fun(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_fun(U_11294,tc_HOL_Obool)),U_11292),c_COMBC(U_11294,tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11294,tc_prod(U_11292,U_11294)),tc_fun(U_11294,tc_fun(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_HOL_Obool)),U_11292),hAPP(c_COMBB(tc_prod(U_11292,U_11294),tc_fun(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_HOL_Obool),U_11294),c_member(tc_prod(U_11292,U_11294)))),c_Product__Type_OPair(U_11292,U_11294))))),U_11296)),U_11298),U_11300))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11292,U_11294)),hAPP(hAPP(c_Product__Type_OPair(U_11292,U_11294),U_11298),U_11300)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11290,tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11290,tc_HOL_Obool))),U_11296))) )
& ! [U_11299,U_11297,U_11295,U_11293,U_11291,U_11289] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11291,U_11293)),hAPP(hAPP(c_Product__Type_OPair(U_11291,U_11293),U_11297),U_11299)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11289,tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11289,tc_HOL_Obool))),U_11295)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11289,tc_fun(U_11291,tc_fun(U_11293,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11289,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_fun(U_11291,tc_fun(U_11293,tc_HOL_Obool)),U_11289),hAPP(c_COMBC(U_11291,tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_fun(U_11293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11293,tc_fun(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_fun(U_11293,tc_HOL_Obool)),U_11291),c_COMBC(U_11293,tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11293,tc_prod(U_11291,U_11293)),tc_fun(U_11293,tc_fun(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_HOL_Obool)),U_11291),hAPP(c_COMBB(tc_prod(U_11291,U_11293),tc_fun(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_HOL_Obool),U_11293),c_member(tc_prod(U_11291,U_11293)))),c_Product__Type_OPair(U_11291,U_11293))))),U_11295)),U_11297),U_11299)) ) ),
inference(miniscope,[status(thm)],[f_2999_2]) ).
fof(f_2999_4,plain,
( ! [U_11290,U_11292,U_11294,U_11296,U_11298,U_11300] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11290,tc_fun(U_11292,tc_fun(U_11294,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11290,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_fun(U_11292,tc_fun(U_11294,tc_HOL_Obool)),U_11290),hAPP(c_COMBC(U_11292,tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_fun(U_11294,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11294,tc_fun(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_fun(U_11294,tc_HOL_Obool)),U_11292),c_COMBC(U_11294,tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11294,tc_prod(U_11292,U_11294)),tc_fun(U_11294,tc_fun(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_HOL_Obool)),U_11292),hAPP(c_COMBB(tc_prod(U_11292,U_11294),tc_fun(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_HOL_Obool),U_11294),c_member(tc_prod(U_11292,U_11294)))),c_Product__Type_OPair(U_11292,U_11294))))),U_11296)),U_11298),U_11300))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11292,U_11294)),hAPP(hAPP(c_Product__Type_OPair(U_11292,U_11294),U_11298),U_11300)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11290,tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11290,tc_HOL_Obool))),U_11296))) )
& ! [U_11291,U_11293,U_11295,U_11289,U_11297,U_11299] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11291,U_11293)),hAPP(hAPP(c_Product__Type_OPair(U_11291,U_11293),U_11297),U_11299)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11289,tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11289,tc_HOL_Obool))),U_11295)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11289,tc_fun(U_11291,tc_fun(U_11293,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11289,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_fun(U_11291,tc_fun(U_11293,tc_HOL_Obool)),U_11289),hAPP(c_COMBC(U_11291,tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_fun(U_11293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11293,tc_fun(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_fun(U_11293,tc_HOL_Obool)),U_11291),c_COMBC(U_11293,tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11293,tc_prod(U_11291,U_11293)),tc_fun(U_11293,tc_fun(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_HOL_Obool)),U_11291),hAPP(c_COMBB(tc_prod(U_11291,U_11293),tc_fun(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_HOL_Obool),U_11293),c_member(tc_prod(U_11291,U_11293)))),c_Product__Type_OPair(U_11291,U_11293))))),U_11295)),U_11297),U_11299)) ) ),
inference(definitional_conversion,[status(esa)],[f_2999_3]) ).
cnf(f_2999_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11291,U_11293)),hAPP(hAPP(c_Product__Type_OPair(U_11291,U_11293),U_11297),U_11299)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11289,tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11289,tc_HOL_Obool))),U_11295)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11289,tc_fun(U_11291,tc_fun(U_11293,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11289,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_fun(U_11291,tc_fun(U_11293,tc_HOL_Obool)),U_11289),hAPP(c_COMBC(U_11291,tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_fun(U_11293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11293,tc_fun(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_fun(U_11293,tc_HOL_Obool)),U_11291),c_COMBC(U_11293,tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11293,tc_prod(U_11291,U_11293)),tc_fun(U_11293,tc_fun(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_HOL_Obool)),U_11291),hAPP(c_COMBB(tc_prod(U_11291,U_11293),tc_fun(tc_fun(tc_prod(U_11291,U_11293),tc_HOL_Obool),tc_HOL_Obool),U_11293),c_member(tc_prod(U_11291,U_11293)))),c_Product__Type_OPair(U_11291,U_11293))))),U_11295)),U_11297),U_11299)) ),
inference(clausify,[status(thm)],[f_2999_4]) ).
cnf(f_2999_6,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11290,tc_fun(U_11292,tc_fun(U_11294,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11290,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_fun(U_11292,tc_fun(U_11294,tc_HOL_Obool)),U_11290),hAPP(c_COMBC(U_11292,tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_fun(U_11294,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11294,tc_fun(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_fun(U_11294,tc_HOL_Obool)),U_11292),c_COMBC(U_11294,tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11294,tc_prod(U_11292,U_11294)),tc_fun(U_11294,tc_fun(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_HOL_Obool)),U_11292),hAPP(c_COMBB(tc_prod(U_11292,U_11294),tc_fun(tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool),tc_HOL_Obool),U_11294),c_member(tc_prod(U_11292,U_11294)))),c_Product__Type_OPair(U_11292,U_11294))))),U_11296)),U_11298),U_11300))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11292,U_11294)),hAPP(hAPP(c_Product__Type_OPair(U_11292,U_11294),U_11298),U_11300)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11290,tc_fun(tc_prod(U_11292,U_11294),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11290,tc_HOL_Obool))),U_11296))) ),
inference(clausify,[status(thm)],[f_2999_4]) ).
fof(f_3000_1,plain,
! [V_y_2,V_x_2,V_r_2,T_e,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),T_c),hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_d),c_COMBC(T_e,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),T_d),hAPP(c_COMBB(tc_prod(T_d,T_e),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_d,T_e)))),c_Product__Type_OPair(T_d,T_e))))),V_r_2)),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_r_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_d,tc_fun(T_e,tc_HOL_Obool)),T_c),hAPP(c_COMBC(T_d,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_fun(T_e,tc_HOL_Obool)),T_d),c_COMBC(T_e,tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(T_e,tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool)),T_d),hAPP(c_COMBB(tc_prod(T_d,T_e),tc_fun(tc_fun(tc_prod(T_d,T_e),tc_HOL_Obool),tc_HOL_Obool),T_e),c_member(tc_prod(T_d,T_e)))),c_Product__Type_OPair(T_d,T_e))))),V_r_2)),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2]) ).
fof(f_3000_2,plain,
! [U_11306,U_11305,U_11304,U_11303,U_11302,U_11301] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11301,tc_fun(U_11302,tc_fun(U_11303,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11301,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_fun(U_11302,tc_fun(U_11303,tc_HOL_Obool)),U_11301),hAPP(c_COMBC(U_11302,tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_fun(U_11303,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11303,tc_fun(tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_fun(U_11303,tc_HOL_Obool)),U_11302),c_COMBC(U_11303,tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11303,tc_prod(U_11302,U_11303)),tc_fun(U_11303,tc_fun(tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_HOL_Obool)),U_11302),hAPP(c_COMBB(tc_prod(U_11302,U_11303),tc_fun(tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_HOL_Obool),U_11303),c_member(tc_prod(U_11302,U_11303)))),c_Product__Type_OPair(U_11302,U_11303))))),U_11304)),U_11305),U_11306))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11302,U_11303)),hAPP(hAPP(c_Product__Type_OPair(U_11302,U_11303),U_11305),U_11306)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11301,tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11301,tc_HOL_Obool))),U_11304))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11302,U_11303)),hAPP(hAPP(c_Product__Type_OPair(U_11302,U_11303),U_11305),U_11306)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11301,tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11301,tc_HOL_Obool))),U_11304)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11301,tc_fun(U_11302,tc_fun(U_11303,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11301,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_fun(U_11302,tc_fun(U_11303,tc_HOL_Obool)),U_11301),hAPP(c_COMBC(U_11302,tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_fun(U_11303,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11303,tc_fun(tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_fun(U_11303,tc_HOL_Obool)),U_11302),c_COMBC(U_11303,tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11303,tc_prod(U_11302,U_11303)),tc_fun(U_11303,tc_fun(tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_HOL_Obool)),U_11302),hAPP(c_COMBB(tc_prod(U_11302,U_11303),tc_fun(tc_fun(tc_prod(U_11302,U_11303),tc_HOL_Obool),tc_HOL_Obool),U_11303),c_member(tc_prod(U_11302,U_11303)))),c_Product__Type_OPair(U_11302,U_11303))))),U_11304)),U_11305),U_11306)) ) ),
inference(variable_rename,[status(thm)],[f_3000_1]) ).
fof(f_3000_3,plain,
( ! [U_11318,U_11316,U_11314,U_11312,U_11310,U_11308] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11308,tc_fun(U_11310,tc_fun(U_11312,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11308,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_fun(U_11310,tc_fun(U_11312,tc_HOL_Obool)),U_11308),hAPP(c_COMBC(U_11310,tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_fun(U_11312,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11312,tc_fun(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_fun(U_11312,tc_HOL_Obool)),U_11310),c_COMBC(U_11312,tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11312,tc_prod(U_11310,U_11312)),tc_fun(U_11312,tc_fun(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_HOL_Obool)),U_11310),hAPP(c_COMBB(tc_prod(U_11310,U_11312),tc_fun(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_HOL_Obool),U_11312),c_member(tc_prod(U_11310,U_11312)))),c_Product__Type_OPair(U_11310,U_11312))))),U_11314)),U_11316),U_11318))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11310,U_11312)),hAPP(hAPP(c_Product__Type_OPair(U_11310,U_11312),U_11316),U_11318)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11308,tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11308,tc_HOL_Obool))),U_11314))) )
& ! [U_11317,U_11315,U_11313,U_11311,U_11309,U_11307] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11309,U_11311)),hAPP(hAPP(c_Product__Type_OPair(U_11309,U_11311),U_11315),U_11317)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11307,tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11307,tc_HOL_Obool))),U_11313)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11307,tc_fun(U_11309,tc_fun(U_11311,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11307,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_fun(U_11309,tc_fun(U_11311,tc_HOL_Obool)),U_11307),hAPP(c_COMBC(U_11309,tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_fun(U_11311,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11311,tc_fun(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_fun(U_11311,tc_HOL_Obool)),U_11309),c_COMBC(U_11311,tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11311,tc_prod(U_11309,U_11311)),tc_fun(U_11311,tc_fun(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_HOL_Obool)),U_11309),hAPP(c_COMBB(tc_prod(U_11309,U_11311),tc_fun(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_HOL_Obool),U_11311),c_member(tc_prod(U_11309,U_11311)))),c_Product__Type_OPair(U_11309,U_11311))))),U_11313)),U_11315),U_11317)) ) ),
inference(miniscope,[status(thm)],[f_3000_2]) ).
fof(f_3000_4,plain,
( ! [U_11308,U_11310,U_11312,U_11314,U_11316,U_11318] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11308,tc_fun(U_11310,tc_fun(U_11312,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11308,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_fun(U_11310,tc_fun(U_11312,tc_HOL_Obool)),U_11308),hAPP(c_COMBC(U_11310,tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_fun(U_11312,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11312,tc_fun(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_fun(U_11312,tc_HOL_Obool)),U_11310),c_COMBC(U_11312,tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11312,tc_prod(U_11310,U_11312)),tc_fun(U_11312,tc_fun(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_HOL_Obool)),U_11310),hAPP(c_COMBB(tc_prod(U_11310,U_11312),tc_fun(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_HOL_Obool),U_11312),c_member(tc_prod(U_11310,U_11312)))),c_Product__Type_OPair(U_11310,U_11312))))),U_11314)),U_11316),U_11318))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11310,U_11312)),hAPP(hAPP(c_Product__Type_OPair(U_11310,U_11312),U_11316),U_11318)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11308,tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11308,tc_HOL_Obool))),U_11314))) )
& ! [U_11313,U_11309,U_11307,U_11315,U_11311,U_11317] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11309,U_11311)),hAPP(hAPP(c_Product__Type_OPair(U_11309,U_11311),U_11315),U_11317)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11307,tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11307,tc_HOL_Obool))),U_11313)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11307,tc_fun(U_11309,tc_fun(U_11311,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11307,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_fun(U_11309,tc_fun(U_11311,tc_HOL_Obool)),U_11307),hAPP(c_COMBC(U_11309,tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_fun(U_11311,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11311,tc_fun(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_fun(U_11311,tc_HOL_Obool)),U_11309),c_COMBC(U_11311,tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11311,tc_prod(U_11309,U_11311)),tc_fun(U_11311,tc_fun(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_HOL_Obool)),U_11309),hAPP(c_COMBB(tc_prod(U_11309,U_11311),tc_fun(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_HOL_Obool),U_11311),c_member(tc_prod(U_11309,U_11311)))),c_Product__Type_OPair(U_11309,U_11311))))),U_11313)),U_11315),U_11317)) ) ),
inference(definitional_conversion,[status(esa)],[f_3000_3]) ).
cnf(f_3000_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11309,U_11311)),hAPP(hAPP(c_Product__Type_OPair(U_11309,U_11311),U_11315),U_11317)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11307,tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11307,tc_HOL_Obool))),U_11313)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11307,tc_fun(U_11309,tc_fun(U_11311,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11307,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_fun(U_11309,tc_fun(U_11311,tc_HOL_Obool)),U_11307),hAPP(c_COMBC(U_11309,tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_fun(U_11311,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11311,tc_fun(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_fun(U_11311,tc_HOL_Obool)),U_11309),c_COMBC(U_11311,tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11311,tc_prod(U_11309,U_11311)),tc_fun(U_11311,tc_fun(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_HOL_Obool)),U_11309),hAPP(c_COMBB(tc_prod(U_11309,U_11311),tc_fun(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool),tc_HOL_Obool),U_11311),c_member(tc_prod(U_11309,U_11311)))),c_Product__Type_OPair(U_11309,U_11311))))),U_11313)),U_11315),U_11317)) ),
inference(clausify,[status(thm)],[f_3000_4]) ).
cnf(f_3000_6,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11308,tc_fun(U_11310,tc_fun(U_11312,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_11308,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_fun(U_11310,tc_fun(U_11312,tc_HOL_Obool)),U_11308),hAPP(c_COMBC(U_11310,tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_fun(U_11312,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11312,tc_fun(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_fun(U_11312,tc_HOL_Obool)),U_11310),c_COMBC(U_11312,tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11312,tc_prod(U_11310,U_11312)),tc_fun(U_11312,tc_fun(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_HOL_Obool)),U_11310),hAPP(c_COMBB(tc_prod(U_11310,U_11312),tc_fun(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool),tc_HOL_Obool),U_11312),c_member(tc_prod(U_11310,U_11312)))),c_Product__Type_OPair(U_11310,U_11312))))),U_11314)),U_11316),U_11318))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11310,U_11312)),hAPP(hAPP(c_Product__Type_OPair(U_11310,U_11312),U_11316),U_11318)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11308,tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11308,tc_HOL_Obool))),U_11314))) ),
inference(clausify,[status(thm)],[f_3000_4]) ).
fof(f_3001_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_3001_2,plain,
! [U_11321,U_11320,U_11319] :
( U_11320 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_11319 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11319,U_11319),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11320),U_11321))) ),
inference(variable_rename,[status(thm)],[f_3001_1]) ).
fof(f_3001_3,plain,
! [U_11321,U_11319,U_11320] :
( U_11320 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_11319 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11319,U_11319),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11320),U_11321))) ),
inference(definitional_conversion,[status(esa)],[f_3001_2]) ).
cnf(f_3001_4,plain,
( U_11320 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_11319 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11319,U_11319),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11320),U_11321))) ),
inference(clausify,[status(thm)],[f_3001_3]) ).
fof(f_3002_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_3002_2,plain,
! [U_11325,U_11324,U_11323,U_11322] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11322,U_11323) = U_11325
| U_11323 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11322,U_11323),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11324),U_11325))) ),
inference(variable_rename,[status(thm)],[f_3002_1]) ).
fof(f_3002_3,plain,
! [U_11324,U_11325,U_11322,U_11323] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11322,U_11323) = U_11325
| U_11323 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11322,U_11323),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11324),U_11325))) ),
inference(definitional_conversion,[status(esa)],[f_3002_2]) ).
cnf(f_3002_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11322,U_11323) = U_11325
| U_11323 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11322,U_11323),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11324),U_11325))) ),
inference(clausify,[status(thm)],[f_3002_3]) ).
fof(f_3003_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_3003_2,plain,
! [U_11329,U_11328,U_11327,U_11326] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11326),U_11327) = U_11328
| U_11327 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11326,U_11327),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11328),U_11329))) ),
inference(variable_rename,[status(thm)],[f_3003_1]) ).
fof(f_3003_3,plain,
! [U_11327,U_11326,U_11328,U_11329] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11326),U_11327) = U_11328
| U_11327 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11326,U_11327),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11328),U_11329))) ),
inference(definitional_conversion,[status(esa)],[f_3003_2]) ).
cnf(f_3003_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11326),U_11327) = U_11328
| U_11327 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11326,U_11327),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11328),U_11329))) ),
inference(clausify,[status(thm)],[f_3003_3]) ).
fof(f_3004_1,plain,
! [T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),c_Groups_Ozero__class_Ozero(T_c)),c_Nat_Osemiring__1__class_ONats(T_c)))
| ~ class_Rings_Osemiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Nats__0]) ).
fof(f_3004_2,plain,
! [U_11330] :
( hBOOL(hAPP(hAPP(c_member(U_11330),c_Groups_Ozero__class_Ozero(U_11330)),c_Nat_Osemiring__1__class_ONats(U_11330)))
| ~ class_Rings_Osemiring__1(U_11330) ),
inference(variable_rename,[status(thm)],[f_3004_1]) ).
fof(f_3004_3,plain,
! [U_11330] :
( hBOOL(hAPP(hAPP(c_member(U_11330),c_Groups_Ozero__class_Ozero(U_11330)),c_Nat_Osemiring__1__class_ONats(U_11330)))
| ~ class_Rings_Osemiring__1(U_11330) ),
inference(definitional_conversion,[status(esa)],[f_3004_2]) ).
cnf(f_3004_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11330),c_Groups_Ozero__class_Ozero(U_11330)),c_Nat_Osemiring__1__class_ONats(U_11330)))
| ~ class_Rings_Osemiring__1(U_11330) ),
inference(clausify,[status(thm)],[f_3004_3]) ).
fof(f_3005_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_3005_2,plain,
! [U_11332,U_11331] : c_Divides_Odivmod__int(U_11331,U_11332) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11331),U_11332)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11331,U_11332)),
inference(variable_rename,[status(thm)],[f_3005_1]) ).
fof(f_3005_3,plain,
! [U_11331,U_11332] : c_Divides_Odivmod__int(U_11331,U_11332) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11331),U_11332)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11331,U_11332)),
inference(definitional_conversion,[status(esa)],[f_3005_2]) ).
cnf(f_3005_4,plain,
c_Divides_Odivmod__int(U_11331,U_11332) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11331),U_11332)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11331,U_11332)),
inference(clausify,[status(thm)],[f_3005_3]) ).
fof(f_3006_1,plain,
! [V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_c)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Nat_Osemiring__1__class_ONats(T_c)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Nat_Osemiring__1__class_ONats(T_c)))
| ~ class_Rings_Osemiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Nats__add]) ).
fof(f_3006_2,plain,
! [U_11335,U_11334,U_11333] :
( hBOOL(hAPP(hAPP(c_member(U_11333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11333),U_11334),U_11335)),c_Nat_Osemiring__1__class_ONats(U_11333)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11333),U_11335),c_Nat_Osemiring__1__class_ONats(U_11333)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11333),U_11334),c_Nat_Osemiring__1__class_ONats(U_11333)))
| ~ class_Rings_Osemiring__1(U_11333) ),
inference(variable_rename,[status(thm)],[f_3006_1]) ).
fof(f_3006_3,plain,
! [U_11333,U_11334,U_11335] :
( hBOOL(hAPP(hAPP(c_member(U_11333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11333),U_11334),U_11335)),c_Nat_Osemiring__1__class_ONats(U_11333)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11333),U_11335),c_Nat_Osemiring__1__class_ONats(U_11333)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11333),U_11334),c_Nat_Osemiring__1__class_ONats(U_11333)))
| ~ class_Rings_Osemiring__1(U_11333) ),
inference(definitional_conversion,[status(esa)],[f_3006_2]) ).
cnf(f_3006_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11333),U_11334),U_11335)),c_Nat_Osemiring__1__class_ONats(U_11333)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11333),U_11335),c_Nat_Osemiring__1__class_ONats(U_11333)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11333),U_11334),c_Nat_Osemiring__1__class_ONats(U_11333)))
| ~ class_Rings_Osemiring__1(U_11333) ),
inference(clausify,[status(thm)],[f_3006_3]) ).
fof(f_3007_1,plain,
! [V_b_2,V_a_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_c)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),c_Nat_Osemiring__1__class_ONats(T_c)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Nat_Osemiring__1__class_ONats(T_c)))
| ~ class_Rings_Osemiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Nats__mult]) ).
fof(f_3007_2,plain,
! [U_11338,U_11337,U_11336] :
( hBOOL(hAPP(hAPP(c_member(U_11336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11336),U_11337),U_11338)),c_Nat_Osemiring__1__class_ONats(U_11336)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11336),U_11338),c_Nat_Osemiring__1__class_ONats(U_11336)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11336),U_11337),c_Nat_Osemiring__1__class_ONats(U_11336)))
| ~ class_Rings_Osemiring__1(U_11336) ),
inference(variable_rename,[status(thm)],[f_3007_1]) ).
fof(f_3007_3,plain,
! [U_11336,U_11337,U_11338] :
( hBOOL(hAPP(hAPP(c_member(U_11336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11336),U_11337),U_11338)),c_Nat_Osemiring__1__class_ONats(U_11336)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11336),U_11338),c_Nat_Osemiring__1__class_ONats(U_11336)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11336),U_11337),c_Nat_Osemiring__1__class_ONats(U_11336)))
| ~ class_Rings_Osemiring__1(U_11336) ),
inference(definitional_conversion,[status(esa)],[f_3007_2]) ).
cnf(f_3007_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11336),U_11337),U_11338)),c_Nat_Osemiring__1__class_ONats(U_11336)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11336),U_11338),c_Nat_Osemiring__1__class_ONats(U_11336)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11336),U_11337),c_Nat_Osemiring__1__class_ONats(U_11336)))
| ~ class_Rings_Osemiring__1(U_11336) ),
inference(clausify,[status(thm)],[f_3007_3]) ).
fof(f_3008_1,plain,
! [T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),c_Groups_Oone__class_Oone(T_c)),c_Nat_Osemiring__1__class_ONats(T_c)))
| ~ class_Rings_Osemiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Nats__1]) ).
fof(f_3008_2,plain,
! [U_11339] :
( hBOOL(hAPP(hAPP(c_member(U_11339),c_Groups_Oone__class_Oone(U_11339)),c_Nat_Osemiring__1__class_ONats(U_11339)))
| ~ class_Rings_Osemiring__1(U_11339) ),
inference(variable_rename,[status(thm)],[f_3008_1]) ).
fof(f_3008_3,plain,
! [U_11339] :
( hBOOL(hAPP(hAPP(c_member(U_11339),c_Groups_Oone__class_Oone(U_11339)),c_Nat_Osemiring__1__class_ONats(U_11339)))
| ~ class_Rings_Osemiring__1(U_11339) ),
inference(definitional_conversion,[status(esa)],[f_3008_2]) ).
cnf(f_3008_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11339),c_Groups_Oone__class_Oone(U_11339)),c_Nat_Osemiring__1__class_ONats(U_11339)))
| ~ class_Rings_Osemiring__1(U_11339) ),
inference(clausify,[status(thm)],[f_3008_3]) ).
fof(f_3009_1,plain,
! [V_n_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_c)))
| ~ class_Rings_Osemiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats]) ).
fof(f_3009_2,plain,
! [U_11341,U_11340] :
( hBOOL(hAPP(hAPP(c_member(U_11340),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11340),U_11341)),c_Nat_Osemiring__1__class_ONats(U_11340)))
| ~ class_Rings_Osemiring__1(U_11340) ),
inference(variable_rename,[status(thm)],[f_3009_1]) ).
fof(f_3009_3,plain,
! [U_11340,U_11341] :
( hBOOL(hAPP(hAPP(c_member(U_11340),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11340),U_11341)),c_Nat_Osemiring__1__class_ONats(U_11340)))
| ~ class_Rings_Osemiring__1(U_11340) ),
inference(definitional_conversion,[status(esa)],[f_3009_2]) ).
cnf(f_3009_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11340),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11340),U_11341)),c_Nat_Osemiring__1__class_ONats(U_11340)))
| ~ class_Rings_Osemiring__1(U_11340) ),
inference(clausify,[status(thm)],[f_3009_3]) ).
fof(f_3010_1,plain,
! [V_a_2,V_r_2,T_d,V_b_2,T_c] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_a_2),V_b_2)),V_r_2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,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_d,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))))) ) ),
inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff]) ).
fof(f_3010_2,plain,
! [U_11346,U_11345,U_11344,U_11343,U_11342] :
( ( hBOOL(hAPP(hAPP(c_member(U_11342),U_11343),hAPP(c_Relation_OImage(U_11344,U_11342,U_11345),hAPP(hAPP(c_Set_Oinsert(U_11344),U_11346),c_Orderings_Obot__class_Obot(tc_fun(U_11344,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11344,U_11342)),hAPP(hAPP(c_Product__Type_OPair(U_11344,U_11342),U_11346),U_11343)),U_11345)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11344,U_11342)),hAPP(hAPP(c_Product__Type_OPair(U_11344,U_11342),U_11346),U_11343)),U_11345))
| ~ hBOOL(hAPP(hAPP(c_member(U_11342),U_11343),hAPP(c_Relation_OImage(U_11344,U_11342,U_11345),hAPP(hAPP(c_Set_Oinsert(U_11344),U_11346),c_Orderings_Obot__class_Obot(tc_fun(U_11344,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[f_3010_1]) ).
fof(f_3010_3,plain,
( ! [U_11356,U_11354,U_11352,U_11350,U_11348] :
( hBOOL(hAPP(hAPP(c_member(U_11348),U_11350),hAPP(c_Relation_OImage(U_11352,U_11348,U_11354),hAPP(hAPP(c_Set_Oinsert(U_11352),U_11356),c_Orderings_Obot__class_Obot(tc_fun(U_11352,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11352,U_11348)),hAPP(hAPP(c_Product__Type_OPair(U_11352,U_11348),U_11356),U_11350)),U_11354)) )
& ! [U_11355,U_11353,U_11351,U_11349,U_11347] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11351,U_11347)),hAPP(hAPP(c_Product__Type_OPair(U_11351,U_11347),U_11355),U_11349)),U_11353))
| ~ hBOOL(hAPP(hAPP(c_member(U_11347),U_11349),hAPP(c_Relation_OImage(U_11351,U_11347,U_11353),hAPP(hAPP(c_Set_Oinsert(U_11351),U_11355),c_Orderings_Obot__class_Obot(tc_fun(U_11351,tc_HOL_Obool)))))) ) ),
inference(miniscope,[status(thm)],[f_3010_2]) ).
fof(f_3010_4,plain,
( ! [U_11348,U_11350,U_11352,U_11354,U_11356] :
( hBOOL(hAPP(hAPP(c_member(U_11348),U_11350),hAPP(c_Relation_OImage(U_11352,U_11348,U_11354),hAPP(hAPP(c_Set_Oinsert(U_11352),U_11356),c_Orderings_Obot__class_Obot(tc_fun(U_11352,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11352,U_11348)),hAPP(hAPP(c_Product__Type_OPair(U_11352,U_11348),U_11356),U_11350)),U_11354)) )
& ! [U_11353,U_11351,U_11349,U_11347,U_11355] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11351,U_11347)),hAPP(hAPP(c_Product__Type_OPair(U_11351,U_11347),U_11355),U_11349)),U_11353))
| ~ hBOOL(hAPP(hAPP(c_member(U_11347),U_11349),hAPP(c_Relation_OImage(U_11351,U_11347,U_11353),hAPP(hAPP(c_Set_Oinsert(U_11351),U_11355),c_Orderings_Obot__class_Obot(tc_fun(U_11351,tc_HOL_Obool)))))) ) ),
inference(definitional_conversion,[status(esa)],[f_3010_3]) ).
cnf(f_3010_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11351,U_11347)),hAPP(hAPP(c_Product__Type_OPair(U_11351,U_11347),U_11355),U_11349)),U_11353))
| ~ hBOOL(hAPP(hAPP(c_member(U_11347),U_11349),hAPP(c_Relation_OImage(U_11351,U_11347,U_11353),hAPP(hAPP(c_Set_Oinsert(U_11351),U_11355),c_Orderings_Obot__class_Obot(tc_fun(U_11351,tc_HOL_Obool)))))) ),
inference(clausify,[status(thm)],[f_3010_4]) ).
cnf(f_3010_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_11348),U_11350),hAPP(c_Relation_OImage(U_11352,U_11348,U_11354),hAPP(hAPP(c_Set_Oinsert(U_11352),U_11356),c_Orderings_Obot__class_Obot(tc_fun(U_11352,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11352,U_11348)),hAPP(hAPP(c_Product__Type_OPair(U_11352,U_11348),U_11356),U_11350)),U_11354)) ),
inference(clausify,[status(thm)],[f_3010_4]) ).
fof(f_3011_1,plain,
! [V_b_2,V_a_2,V_r_2,V_A_2,T_c] :
( hAPP(c_Relation_OImage(T_c,T_c,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_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2))
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_equiv__class__eq]) ).
fof(f_3011_2,plain,
! [U_11361,U_11360,U_11359,U_11358,U_11357] :
( hAPP(c_Relation_OImage(U_11357,U_11357,U_11359),hAPP(hAPP(c_Set_Oinsert(U_11357),U_11360),c_Orderings_Obot__class_Obot(tc_fun(U_11357,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11357,U_11357,U_11359),hAPP(hAPP(c_Set_Oinsert(U_11357),U_11361),c_Orderings_Obot__class_Obot(tc_fun(U_11357,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11357,U_11357)),hAPP(hAPP(c_Product__Type_OPair(U_11357,U_11357),U_11360),U_11361)),U_11359))
| ~ c_Equiv__Relations_Oequiv(U_11357,U_11358,U_11359) ),
inference(variable_rename,[status(thm)],[f_3011_1]) ).
fof(f_3011_3,plain,
! [U_11357,U_11358,U_11359,U_11360,U_11361] :
( hAPP(c_Relation_OImage(U_11357,U_11357,U_11359),hAPP(hAPP(c_Set_Oinsert(U_11357),U_11360),c_Orderings_Obot__class_Obot(tc_fun(U_11357,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11357,U_11357,U_11359),hAPP(hAPP(c_Set_Oinsert(U_11357),U_11361),c_Orderings_Obot__class_Obot(tc_fun(U_11357,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11357,U_11357)),hAPP(hAPP(c_Product__Type_OPair(U_11357,U_11357),U_11360),U_11361)),U_11359))
| ~ c_Equiv__Relations_Oequiv(U_11357,U_11358,U_11359) ),
inference(definitional_conversion,[status(esa)],[f_3011_2]) ).
cnf(f_3011_4,plain,
( hAPP(c_Relation_OImage(U_11357,U_11357,U_11359),hAPP(hAPP(c_Set_Oinsert(U_11357),U_11360),c_Orderings_Obot__class_Obot(tc_fun(U_11357,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11357,U_11357,U_11359),hAPP(hAPP(c_Set_Oinsert(U_11357),U_11361),c_Orderings_Obot__class_Obot(tc_fun(U_11357,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11357,U_11357)),hAPP(hAPP(c_Product__Type_OPair(U_11357,U_11357),U_11360),U_11361)),U_11359))
| ~ c_Equiv__Relations_Oequiv(U_11357,U_11358,U_11359) ),
inference(clausify,[status(thm)],[f_3011_3]) ).
fof(f_3012_1,plain,
! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_c] :
( V_X_2 = V_Y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_Y_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_quotient__eqI]) ).
fof(f_3012_2,plain,
! [U_11368,U_11367,U_11366,U_11365,U_11364,U_11363,U_11362] :
( U_11365 = U_11366
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11362,U_11362)),hAPP(hAPP(c_Product__Type_OPair(U_11362,U_11362),U_11367),U_11368)),U_11364))
| ~ hBOOL(hAPP(hAPP(c_member(U_11362),U_11368),U_11366))
| ~ hBOOL(hAPP(hAPP(c_member(U_11362),U_11367),U_11365))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11362,tc_HOL_Obool)),U_11366),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11362),U_11363),U_11364)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11362,tc_HOL_Obool)),U_11365),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11362),U_11363),U_11364)))
| ~ c_Equiv__Relations_Oequiv(U_11362,U_11363,U_11364) ),
inference(variable_rename,[status(thm)],[f_3012_1]) ).
fof(f_3012_3,plain,
! [U_11362,U_11363,U_11364,U_11365,U_11366,U_11367,U_11368] :
( U_11365 = U_11366
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11362,U_11362)),hAPP(hAPP(c_Product__Type_OPair(U_11362,U_11362),U_11367),U_11368)),U_11364))
| ~ hBOOL(hAPP(hAPP(c_member(U_11362),U_11368),U_11366))
| ~ hBOOL(hAPP(hAPP(c_member(U_11362),U_11367),U_11365))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11362,tc_HOL_Obool)),U_11366),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11362),U_11363),U_11364)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11362,tc_HOL_Obool)),U_11365),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11362),U_11363),U_11364)))
| ~ c_Equiv__Relations_Oequiv(U_11362,U_11363,U_11364) ),
inference(definitional_conversion,[status(esa)],[f_3012_2]) ).
cnf(f_3012_4,plain,
( U_11365 = U_11366
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11362,U_11362)),hAPP(hAPP(c_Product__Type_OPair(U_11362,U_11362),U_11367),U_11368)),U_11364))
| ~ hBOOL(hAPP(hAPP(c_member(U_11362),U_11368),U_11366))
| ~ hBOOL(hAPP(hAPP(c_member(U_11362),U_11367),U_11365))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11362,tc_HOL_Obool)),U_11366),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11362),U_11363),U_11364)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11362,tc_HOL_Obool)),U_11365),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11362),U_11363),U_11364)))
| ~ c_Equiv__Relations_Oequiv(U_11362,U_11363,U_11364) ),
inference(clausify,[status(thm)],[f_3012_3]) ).
fof(f_3013_1,plain,
! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_c] :
( ( ( V_X_2 = V_Y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_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),V_x_2),V_y_2)),V_r_2))
| V_X_2 != V_Y_2 ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_Y_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_quotient__eq__iff]) ).
fof(f_3013_2,plain,
! [U_11375,U_11374,U_11373,U_11372,U_11371,U_11370,U_11369] :
( ( ( U_11372 = U_11373
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11369,U_11369)),hAPP(hAPP(c_Product__Type_OPair(U_11369,U_11369),U_11374),U_11375)),U_11371)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11369,U_11369)),hAPP(hAPP(c_Product__Type_OPair(U_11369,U_11369),U_11374),U_11375)),U_11371))
| U_11372 != U_11373 ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11369),U_11375),U_11373))
| ~ hBOOL(hAPP(hAPP(c_member(U_11369),U_11374),U_11372))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11369,tc_HOL_Obool)),U_11373),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11369),U_11370),U_11371)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11369,tc_HOL_Obool)),U_11372),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11369),U_11370),U_11371)))
| ~ c_Equiv__Relations_Oequiv(U_11369,U_11370,U_11371) ),
inference(variable_rename,[status(thm)],[f_3013_1]) ).
fof(f_3013_3,plain,
( ! [U_11369,U_11371,U_11372,U_11373,U_11374,U_11375] :
( U_11372 = U_11373
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11369,U_11369)),hAPP(hAPP(c_Product__Type_OPair(U_11369,U_11369),U_11374),U_11375)),U_11371))
| ~ sP835(U_11369,U_11371,U_11372,U_11373,U_11374,U_11375) )
& ! [U_11369,U_11371,U_11372,U_11373,U_11374,U_11375] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11369,U_11369)),hAPP(hAPP(c_Product__Type_OPair(U_11369,U_11369),U_11374),U_11375)),U_11371))
| U_11372 != U_11373
| ~ sP835(U_11369,U_11371,U_11372,U_11373,U_11374,U_11375) )
& ! [U_11369,U_11370,U_11371,U_11372,U_11373,U_11374,U_11375] :
( sP835(U_11369,U_11371,U_11372,U_11373,U_11374,U_11375)
| ~ hBOOL(hAPP(hAPP(c_member(U_11369),U_11375),U_11373))
| ~ hBOOL(hAPP(hAPP(c_member(U_11369),U_11374),U_11372))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11369,tc_HOL_Obool)),U_11373),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11369),U_11370),U_11371)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11369,tc_HOL_Obool)),U_11372),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11369),U_11370),U_11371)))
| ~ c_Equiv__Relations_Oequiv(U_11369,U_11370,U_11371) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP835])],[f_3013_2]) ).
cnf(f_3013_4,plain,
( sP835(U_11369,U_11371,U_11372,U_11373,U_11374,U_11375)
| ~ hBOOL(hAPP(hAPP(c_member(U_11369),U_11375),U_11373))
| ~ hBOOL(hAPP(hAPP(c_member(U_11369),U_11374),U_11372))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11369,tc_HOL_Obool)),U_11373),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11369),U_11370),U_11371)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11369,tc_HOL_Obool)),U_11372),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11369),U_11370),U_11371)))
| ~ c_Equiv__Relations_Oequiv(U_11369,U_11370,U_11371) ),
inference(clausify,[status(thm)],[f_3013_3]) ).
cnf(f_3013_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11369,U_11369)),hAPP(hAPP(c_Product__Type_OPair(U_11369,U_11369),U_11374),U_11375)),U_11371))
| U_11372 != U_11373
| ~ sP835(U_11369,U_11371,U_11372,U_11373,U_11374,U_11375) ),
inference(clausify,[status(thm)],[f_3013_3]) ).
cnf(f_3013_6,plain,
( U_11372 = U_11373
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11369,U_11369)),hAPP(hAPP(c_Product__Type_OPair(U_11369,U_11369),U_11374),U_11375)),U_11371))
| ~ sP835(U_11369,U_11371,U_11372,U_11373,U_11374,U_11375) ),
inference(clausify,[status(thm)],[f_3013_3]) ).
fof(f_3014_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_3014_2,plain,
! [U_11377,U_11376] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11377,U_11376),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11377),U_11376)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11377,U_11376))))
| U_11376 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_3014_1]) ).
fof(f_3014_3,plain,
! [U_11376,U_11377] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11377,U_11376),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11377),U_11376)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11377,U_11376))))
| U_11376 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_3014_2]) ).
cnf(f_3014_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11377,U_11376),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11377),U_11376)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11377,U_11376))))
| U_11376 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_3014_3]) ).
fof(f_3015_1,plain,
! [V_a_2,V_r_2,T_c,T_d] : hAPP(c_Relation_OImage(T_d,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_d),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_c),c_member(tc_prod(T_d,T_c))),hAPP(c_Product__Type_OPair(T_d,T_c),V_a_2))),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_Image__singleton]) ).
fof(f_3015_2,plain,
! [U_11381,U_11380,U_11379,U_11378] : hAPP(c_Relation_OImage(U_11378,U_11379,U_11380),hAPP(hAPP(c_Set_Oinsert(U_11378),U_11381),c_Orderings_Obot__class_Obot(tc_fun(U_11378,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_11379),hAPP(hAPP(c_COMBC(U_11379,tc_fun(tc_prod(U_11378,U_11379),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_11378,U_11379),tc_fun(tc_fun(tc_prod(U_11378,U_11379),tc_HOL_Obool),tc_HOL_Obool),U_11379),c_member(tc_prod(U_11378,U_11379))),hAPP(c_Product__Type_OPair(U_11378,U_11379),U_11381))),U_11380)),
inference(variable_rename,[status(thm)],[f_3015_1]) ).
fof(f_3015_3,plain,
! [U_11378,U_11379,U_11381,U_11380] : hAPP(c_Relation_OImage(U_11378,U_11379,U_11380),hAPP(hAPP(c_Set_Oinsert(U_11378),U_11381),c_Orderings_Obot__class_Obot(tc_fun(U_11378,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_11379),hAPP(hAPP(c_COMBC(U_11379,tc_fun(tc_prod(U_11378,U_11379),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_11378,U_11379),tc_fun(tc_fun(tc_prod(U_11378,U_11379),tc_HOL_Obool),tc_HOL_Obool),U_11379),c_member(tc_prod(U_11378,U_11379))),hAPP(c_Product__Type_OPair(U_11378,U_11379),U_11381))),U_11380)),
inference(definitional_conversion,[status(esa)],[f_3015_2]) ).
cnf(f_3015_4,plain,
hAPP(c_Relation_OImage(U_11378,U_11379,U_11380),hAPP(hAPP(c_Set_Oinsert(U_11378),U_11381),c_Orderings_Obot__class_Obot(tc_fun(U_11378,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_11379),hAPP(hAPP(c_COMBC(U_11379,tc_fun(tc_prod(U_11378,U_11379),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_11378,U_11379),tc_fun(tc_fun(tc_prod(U_11378,U_11379),tc_HOL_Obool),tc_HOL_Obool),U_11379),c_member(tc_prod(U_11378,U_11379))),hAPP(c_Product__Type_OPair(U_11378,U_11379),U_11381))),U_11380)),
inference(clausify,[status(thm)],[f_3015_3]) ).
fof(f_3016_1,plain,
! [V_A_2,V_b_2,V_a_2,V_r_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),V_A_2))
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2)
| hAPP(c_Relation_OImage(T_c,T_c,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_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_eq__equiv__class]) ).
fof(f_3016_2,plain,
! [U_11386,U_11385,U_11384,U_11383,U_11382] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11382,U_11382)),hAPP(hAPP(c_Product__Type_OPair(U_11382,U_11382),U_11384),U_11385)),U_11383))
| ~ hBOOL(hAPP(hAPP(c_member(U_11382),U_11385),U_11386))
| ~ c_Equiv__Relations_Oequiv(U_11382,U_11386,U_11383)
| hAPP(c_Relation_OImage(U_11382,U_11382,U_11383),hAPP(hAPP(c_Set_Oinsert(U_11382),U_11384),c_Orderings_Obot__class_Obot(tc_fun(U_11382,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11382,U_11382,U_11383),hAPP(hAPP(c_Set_Oinsert(U_11382),U_11385),c_Orderings_Obot__class_Obot(tc_fun(U_11382,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_3016_1]) ).
fof(f_3016_3,plain,
! [U_11382,U_11383,U_11384,U_11385,U_11386] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11382,U_11382)),hAPP(hAPP(c_Product__Type_OPair(U_11382,U_11382),U_11384),U_11385)),U_11383))
| ~ hBOOL(hAPP(hAPP(c_member(U_11382),U_11385),U_11386))
| ~ c_Equiv__Relations_Oequiv(U_11382,U_11386,U_11383)
| hAPP(c_Relation_OImage(U_11382,U_11382,U_11383),hAPP(hAPP(c_Set_Oinsert(U_11382),U_11384),c_Orderings_Obot__class_Obot(tc_fun(U_11382,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11382,U_11382,U_11383),hAPP(hAPP(c_Set_Oinsert(U_11382),U_11385),c_Orderings_Obot__class_Obot(tc_fun(U_11382,tc_HOL_Obool)))) ),
inference(definitional_conversion,[status(esa)],[f_3016_2]) ).
cnf(f_3016_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11382,U_11382)),hAPP(hAPP(c_Product__Type_OPair(U_11382,U_11382),U_11384),U_11385)),U_11383))
| ~ hBOOL(hAPP(hAPP(c_member(U_11382),U_11385),U_11386))
| ~ c_Equiv__Relations_Oequiv(U_11382,U_11386,U_11383)
| hAPP(c_Relation_OImage(U_11382,U_11382,U_11383),hAPP(hAPP(c_Set_Oinsert(U_11382),U_11384),c_Orderings_Obot__class_Obot(tc_fun(U_11382,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11382,U_11382,U_11383),hAPP(hAPP(c_Set_Oinsert(U_11382),U_11385),c_Orderings_Obot__class_Obot(tc_fun(U_11382,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3016_3]) ).
fof(f_3017_1,plain,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_c] :
( ( ( hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_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),V_x_2),V_y_2)),V_r_2))
| hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) ) )
| ~ 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_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff]) ).
fof(f_3017_2,plain,
! [U_11391,U_11390,U_11389,U_11388,U_11387] :
( ( ( hAPP(c_Relation_OImage(U_11387,U_11387,U_11389),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11390),c_Orderings_Obot__class_Obot(tc_fun(U_11387,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11387,U_11387,U_11389),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11391),c_Orderings_Obot__class_Obot(tc_fun(U_11387,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),U_11390),U_11391)),U_11389)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),U_11390),U_11391)),U_11389))
| hAPP(c_Relation_OImage(U_11387,U_11387,U_11389),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11390),c_Orderings_Obot__class_Obot(tc_fun(U_11387,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11387,U_11387,U_11389),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11391),c_Orderings_Obot__class_Obot(tc_fun(U_11387,tc_HOL_Obool)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11387),U_11391),U_11388))
| ~ hBOOL(hAPP(hAPP(c_member(U_11387),U_11390),U_11388))
| ~ c_Equiv__Relations_Oequiv(U_11387,U_11388,U_11389) ),
inference(variable_rename,[status(thm)],[f_3017_1]) ).
fof(f_3017_3,plain,
( ! [U_11387,U_11389,U_11390,U_11391] :
( hAPP(c_Relation_OImage(U_11387,U_11387,U_11389),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11390),c_Orderings_Obot__class_Obot(tc_fun(U_11387,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11387,U_11387,U_11389),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11391),c_Orderings_Obot__class_Obot(tc_fun(U_11387,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),U_11390),U_11391)),U_11389))
| ~ sP836(U_11387,U_11389,U_11390,U_11391) )
& ! [U_11387,U_11389,U_11390,U_11391] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),U_11390),U_11391)),U_11389))
| hAPP(c_Relation_OImage(U_11387,U_11387,U_11389),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11390),c_Orderings_Obot__class_Obot(tc_fun(U_11387,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11387,U_11387,U_11389),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11391),c_Orderings_Obot__class_Obot(tc_fun(U_11387,tc_HOL_Obool))))
| ~ sP836(U_11387,U_11389,U_11390,U_11391) )
& ! [U_11387,U_11388,U_11389,U_11390,U_11391] :
( sP836(U_11387,U_11389,U_11390,U_11391)
| ~ hBOOL(hAPP(hAPP(c_member(U_11387),U_11391),U_11388))
| ~ hBOOL(hAPP(hAPP(c_member(U_11387),U_11390),U_11388))
| ~ c_Equiv__Relations_Oequiv(U_11387,U_11388,U_11389) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP836])],[f_3017_2]) ).
cnf(f_3017_4,plain,
( sP836(U_11387,U_11389,U_11390,U_11391)
| ~ hBOOL(hAPP(hAPP(c_member(U_11387),U_11391),U_11388))
| ~ hBOOL(hAPP(hAPP(c_member(U_11387),U_11390),U_11388))
| ~ c_Equiv__Relations_Oequiv(U_11387,U_11388,U_11389) ),
inference(clausify,[status(thm)],[f_3017_3]) ).
cnf(f_3017_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),U_11390),U_11391)),U_11389))
| hAPP(c_Relation_OImage(U_11387,U_11387,U_11389),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11390),c_Orderings_Obot__class_Obot(tc_fun(U_11387,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11387,U_11387,U_11389),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11391),c_Orderings_Obot__class_Obot(tc_fun(U_11387,tc_HOL_Obool))))
| ~ sP836(U_11387,U_11389,U_11390,U_11391) ),
inference(clausify,[status(thm)],[f_3017_3]) ).
cnf(f_3017_6,plain,
( hAPP(c_Relation_OImage(U_11387,U_11387,U_11389),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11390),c_Orderings_Obot__class_Obot(tc_fun(U_11387,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11387,U_11387,U_11389),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11391),c_Orderings_Obot__class_Obot(tc_fun(U_11387,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),U_11390),U_11391)),U_11389))
| ~ sP836(U_11387,U_11389,U_11390,U_11391) ),
inference(clausify,[status(thm)],[f_3017_3]) ).
fof(f_3018_1,plain,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_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))
| hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) )
& ( ( 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))
& hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_x_2),V_y_2)),V_r_2)) ) )
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff]) ).
fof(f_3018_2,plain,
! [U_11396,U_11395,U_11394,U_11393,U_11392] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11392,U_11392)),hAPP(hAPP(c_Product__Type_OPair(U_11392,U_11392),U_11395),U_11396)),U_11394))
| ~ hBOOL(hAPP(hAPP(c_member(U_11392),U_11396),U_11393))
| ~ hBOOL(hAPP(hAPP(c_member(U_11392),U_11395),U_11393))
| hAPP(c_Relation_OImage(U_11392,U_11392,U_11394),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11395),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11392,U_11392,U_11394),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11396),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)))) )
& ( ( hBOOL(hAPP(hAPP(c_member(U_11392),U_11396),U_11393))
& hBOOL(hAPP(hAPP(c_member(U_11392),U_11395),U_11393))
& hAPP(c_Relation_OImage(U_11392,U_11392,U_11394),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11395),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11392,U_11392,U_11394),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11396),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11392,U_11392)),hAPP(hAPP(c_Product__Type_OPair(U_11392,U_11392),U_11395),U_11396)),U_11394)) ) )
| ~ c_Equiv__Relations_Oequiv(U_11392,U_11393,U_11394) ),
inference(variable_rename,[status(thm)],[f_3018_1]) ).
fof(f_3018_3,plain,
( ! [U_11393,U_11394,U_11395,U_11392,U_11396] :
( hBOOL(hAPP(hAPP(c_member(U_11392),U_11396),U_11393))
| ~ sP837(U_11393,U_11394,U_11395,U_11392,U_11396) )
& ! [U_11393,U_11394,U_11395,U_11392,U_11396] :
( hBOOL(hAPP(hAPP(c_member(U_11392),U_11395),U_11393))
| ~ sP837(U_11393,U_11394,U_11395,U_11392,U_11396) )
& ! [U_11393,U_11394,U_11395,U_11392,U_11396] :
( hAPP(c_Relation_OImage(U_11392,U_11392,U_11394),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11395),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11392,U_11392,U_11394),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11396),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool))))
| ~ sP837(U_11393,U_11394,U_11395,U_11392,U_11396) )
& ! [U_11393,U_11394,U_11395,U_11392,U_11396] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11392,U_11392)),hAPP(hAPP(c_Product__Type_OPair(U_11392,U_11392),U_11395),U_11396)),U_11394))
| ~ hBOOL(hAPP(hAPP(c_member(U_11392),U_11396),U_11393))
| ~ hBOOL(hAPP(hAPP(c_member(U_11392),U_11395),U_11393))
| hAPP(c_Relation_OImage(U_11392,U_11392,U_11394),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11395),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11392,U_11392,U_11394),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11396),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool))))
| ~ sP838(U_11393,U_11394,U_11395,U_11392,U_11396) )
& ! [U_11393,U_11394,U_11395,U_11392,U_11396] :
( sP837(U_11393,U_11394,U_11395,U_11392,U_11396)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11392,U_11392)),hAPP(hAPP(c_Product__Type_OPair(U_11392,U_11392),U_11395),U_11396)),U_11394))
| ~ sP838(U_11393,U_11394,U_11395,U_11392,U_11396) )
& ! [U_11393,U_11394,U_11395,U_11392,U_11396] :
( sP838(U_11393,U_11394,U_11395,U_11392,U_11396)
| ~ c_Equiv__Relations_Oequiv(U_11392,U_11393,U_11394) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP837,sP838])],[f_3018_2]) ).
cnf(f_3018_4,plain,
( sP838(U_11393,U_11394,U_11395,U_11392,U_11396)
| ~ c_Equiv__Relations_Oequiv(U_11392,U_11393,U_11394) ),
inference(clausify,[status(thm)],[f_3018_3]) ).
cnf(f_3018_5,plain,
( sP837(U_11393,U_11394,U_11395,U_11392,U_11396)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11392,U_11392)),hAPP(hAPP(c_Product__Type_OPair(U_11392,U_11392),U_11395),U_11396)),U_11394))
| ~ sP838(U_11393,U_11394,U_11395,U_11392,U_11396) ),
inference(clausify,[status(thm)],[f_3018_3]) ).
cnf(f_3018_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11392,U_11392)),hAPP(hAPP(c_Product__Type_OPair(U_11392,U_11392),U_11395),U_11396)),U_11394))
| ~ hBOOL(hAPP(hAPP(c_member(U_11392),U_11396),U_11393))
| ~ hBOOL(hAPP(hAPP(c_member(U_11392),U_11395),U_11393))
| hAPP(c_Relation_OImage(U_11392,U_11392,U_11394),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11395),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_11392,U_11392,U_11394),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11396),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool))))
| ~ sP838(U_11393,U_11394,U_11395,U_11392,U_11396) ),
inference(clausify,[status(thm)],[f_3018_3]) ).
cnf(f_3018_7,plain,
( hAPP(c_Relation_OImage(U_11392,U_11392,U_11394),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11395),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_11392,U_11392,U_11394),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11396),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool))))
| ~ sP837(U_11393,U_11394,U_11395,U_11392,U_11396) ),
inference(clausify,[status(thm)],[f_3018_3]) ).
cnf(f_3018_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_11392),U_11395),U_11393))
| ~ sP837(U_11393,U_11394,U_11395,U_11392,U_11396) ),
inference(clausify,[status(thm)],[f_3018_3]) ).
cnf(f_3018_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_11392),U_11396),U_11393))
| ~ sP837(U_11393,U_11394,U_11395,U_11392,U_11396) ),
inference(clausify,[status(thm)],[f_3018_3]) ).
fof(f_3019_1,plain,
! [V_b_2,V_a_2,V_r_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,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_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2))
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_equiv__class__subset]) ).
fof(f_3019_2,plain,
! [U_11401,U_11400,U_11399,U_11398,U_11397] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11397,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11397,U_11397,U_11399),hAPP(hAPP(c_Set_Oinsert(U_11397),U_11400),c_Orderings_Obot__class_Obot(tc_fun(U_11397,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11397,U_11397,U_11399),hAPP(hAPP(c_Set_Oinsert(U_11397),U_11401),c_Orderings_Obot__class_Obot(tc_fun(U_11397,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11397,U_11397)),hAPP(hAPP(c_Product__Type_OPair(U_11397,U_11397),U_11400),U_11401)),U_11399))
| ~ c_Equiv__Relations_Oequiv(U_11397,U_11398,U_11399) ),
inference(variable_rename,[status(thm)],[f_3019_1]) ).
fof(f_3019_3,plain,
! [U_11398,U_11399,U_11397,U_11400,U_11401] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11397,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11397,U_11397,U_11399),hAPP(hAPP(c_Set_Oinsert(U_11397),U_11400),c_Orderings_Obot__class_Obot(tc_fun(U_11397,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11397,U_11397,U_11399),hAPP(hAPP(c_Set_Oinsert(U_11397),U_11401),c_Orderings_Obot__class_Obot(tc_fun(U_11397,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11397,U_11397)),hAPP(hAPP(c_Product__Type_OPair(U_11397,U_11397),U_11400),U_11401)),U_11399))
| ~ c_Equiv__Relations_Oequiv(U_11397,U_11398,U_11399) ),
inference(definitional_conversion,[status(esa)],[f_3019_2]) ).
cnf(f_3019_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11397,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11397,U_11397,U_11399),hAPP(hAPP(c_Set_Oinsert(U_11397),U_11400),c_Orderings_Obot__class_Obot(tc_fun(U_11397,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11397,U_11397,U_11399),hAPP(hAPP(c_Set_Oinsert(U_11397),U_11401),c_Orderings_Obot__class_Obot(tc_fun(U_11397,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11397,U_11397)),hAPP(hAPP(c_Product__Type_OPair(U_11397,U_11397),U_11400),U_11401)),U_11399))
| ~ c_Equiv__Relations_Oequiv(U_11397,U_11398,U_11399) ),
inference(clausify,[status(thm)],[f_3019_3]) ).
fof(f_3020_1,plain,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_c] :
( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),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_x_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),V_x_2),V_y_2)),V_r_2))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_r_2) != hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),V_r_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_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2]) ).
fof(f_3020_2,plain,
! [U_11406,U_11405,U_11404,U_11403,U_11402] :
( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11402),hAPP(hAPP(c_Set_Oinsert(U_11402),U_11405),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))),U_11404) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11402),hAPP(hAPP(c_Set_Oinsert(U_11402),U_11406),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))),U_11404)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11402,U_11402)),hAPP(hAPP(c_Product__Type_OPair(U_11402,U_11402),U_11405),U_11406)),U_11404)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11402,U_11402)),hAPP(hAPP(c_Product__Type_OPair(U_11402,U_11402),U_11405),U_11406)),U_11404))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11402),hAPP(hAPP(c_Set_Oinsert(U_11402),U_11405),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))),U_11404) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11402),hAPP(hAPP(c_Set_Oinsert(U_11402),U_11406),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))),U_11404) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11402),U_11406),U_11403))
| ~ hBOOL(hAPP(hAPP(c_member(U_11402),U_11405),U_11403))
| ~ c_Equiv__Relations_Oequiv(U_11402,U_11403,U_11404) ),
inference(variable_rename,[status(thm)],[f_3020_1]) ).
fof(f_3020_3,plain,
( ! [U_11402,U_11404,U_11405,U_11406] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11402),hAPP(hAPP(c_Set_Oinsert(U_11402),U_11405),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))),U_11404) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11402),hAPP(hAPP(c_Set_Oinsert(U_11402),U_11406),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))),U_11404)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11402,U_11402)),hAPP(hAPP(c_Product__Type_OPair(U_11402,U_11402),U_11405),U_11406)),U_11404))
| ~ sP839(U_11402,U_11404,U_11405,U_11406) )
& ! [U_11402,U_11404,U_11405,U_11406] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11402,U_11402)),hAPP(hAPP(c_Product__Type_OPair(U_11402,U_11402),U_11405),U_11406)),U_11404))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11402),hAPP(hAPP(c_Set_Oinsert(U_11402),U_11405),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))),U_11404) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11402),hAPP(hAPP(c_Set_Oinsert(U_11402),U_11406),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))),U_11404)
| ~ sP839(U_11402,U_11404,U_11405,U_11406) )
& ! [U_11402,U_11403,U_11404,U_11405,U_11406] :
( sP839(U_11402,U_11404,U_11405,U_11406)
| ~ hBOOL(hAPP(hAPP(c_member(U_11402),U_11406),U_11403))
| ~ hBOOL(hAPP(hAPP(c_member(U_11402),U_11405),U_11403))
| ~ c_Equiv__Relations_Oequiv(U_11402,U_11403,U_11404) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP839])],[f_3020_2]) ).
cnf(f_3020_4,plain,
( sP839(U_11402,U_11404,U_11405,U_11406)
| ~ hBOOL(hAPP(hAPP(c_member(U_11402),U_11406),U_11403))
| ~ hBOOL(hAPP(hAPP(c_member(U_11402),U_11405),U_11403))
| ~ c_Equiv__Relations_Oequiv(U_11402,U_11403,U_11404) ),
inference(clausify,[status(thm)],[f_3020_3]) ).
cnf(f_3020_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11402,U_11402)),hAPP(hAPP(c_Product__Type_OPair(U_11402,U_11402),U_11405),U_11406)),U_11404))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11402),hAPP(hAPP(c_Set_Oinsert(U_11402),U_11405),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))),U_11404) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11402),hAPP(hAPP(c_Set_Oinsert(U_11402),U_11406),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))),U_11404)
| ~ sP839(U_11402,U_11404,U_11405,U_11406) ),
inference(clausify,[status(thm)],[f_3020_3]) ).
cnf(f_3020_6,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11402),hAPP(hAPP(c_Set_Oinsert(U_11402),U_11405),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))),U_11404) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11402),hAPP(hAPP(c_Set_Oinsert(U_11402),U_11406),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))),U_11404)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11402,U_11402)),hAPP(hAPP(c_Product__Type_OPair(U_11402,U_11402),U_11405),U_11406)),U_11404))
| ~ sP839(U_11402,U_11404,U_11405,U_11406) ),
inference(clausify,[status(thm)],[f_3020_3]) ).
fof(f_3021_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_3021_2,plain,
! [U_11413,U_11412,U_11411,U_11410,U_11409,U_11408,U_11407] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11407),U_11411),U_11408),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_11409),U_11412)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11410),U_11413)),U_11408))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11410),U_11413),U_11408))))
| U_11408 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11411,U_11408),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11412),U_11413)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11407,U_11408),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11409),U_11410))) ),
inference(variable_rename,[status(thm)],[f_3021_1]) ).
fof(f_3021_3,plain,
! [U_11411,U_11410,U_11413,U_11412,U_11407,U_11408,U_11409] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11407),U_11411),U_11408),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_11409),U_11412)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11410),U_11413)),U_11408))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11410),U_11413),U_11408))))
| U_11408 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11411,U_11408),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11412),U_11413)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11407,U_11408),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11409),U_11410))) ),
inference(definitional_conversion,[status(esa)],[f_3021_2]) ).
cnf(f_3021_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11407),U_11411),U_11408),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_11409),U_11412)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11410),U_11413)),U_11408))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11410),U_11413),U_11408))))
| U_11408 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11411,U_11408),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11412),U_11413)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11407,U_11408),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11409),U_11410))) ),
inference(clausify,[status(thm)],[f_3021_3]) ).
fof(f_3022_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_3022_2,plain,
! [U_11417,U_11416,U_11415,U_11414] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11414),U_11415),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_11417),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11416)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11416)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_11417),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_11415),U_11417)))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11414,U_11415),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11416),U_11417))) ),
inference(variable_rename,[status(thm)],[f_3022_1]) ).
fof(f_3022_3,plain,
! [U_11415,U_11416,U_11414,U_11417] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11414),U_11415),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_11417),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11416)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11416)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_11417),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_11415),U_11417)))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11414,U_11415),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11416),U_11417))) ),
inference(definitional_conversion,[status(esa)],[f_3022_2]) ).
cnf(f_3022_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11414),U_11415),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_11417),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11416)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11416)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_11417),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_11415),U_11417)))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11414,U_11415),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11416),U_11417))) ),
inference(clausify,[status(thm)],[f_3022_3]) ).
fof(f_3023_1,plain,
! [V_a_2,V_b_2,V_r_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_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_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_c,T_c,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))))))
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_subset__equiv__class]) ).
fof(f_3023_2,plain,
! [U_11422,U_11421,U_11420,U_11419,U_11418] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11418,U_11418)),hAPP(hAPP(c_Product__Type_OPair(U_11418,U_11418),U_11422),U_11421)),U_11420))
| ~ hBOOL(hAPP(hAPP(c_member(U_11418),U_11421),U_11419))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11418,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11418,U_11418,U_11420),hAPP(hAPP(c_Set_Oinsert(U_11418),U_11421),c_Orderings_Obot__class_Obot(tc_fun(U_11418,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11418,U_11418,U_11420),hAPP(hAPP(c_Set_Oinsert(U_11418),U_11422),c_Orderings_Obot__class_Obot(tc_fun(U_11418,tc_HOL_Obool))))))
| ~ c_Equiv__Relations_Oequiv(U_11418,U_11419,U_11420) ),
inference(variable_rename,[status(thm)],[f_3023_1]) ).
fof(f_3023_3,plain,
! [U_11418,U_11419,U_11420,U_11421,U_11422] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11418,U_11418)),hAPP(hAPP(c_Product__Type_OPair(U_11418,U_11418),U_11422),U_11421)),U_11420))
| ~ hBOOL(hAPP(hAPP(c_member(U_11418),U_11421),U_11419))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11418,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11418,U_11418,U_11420),hAPP(hAPP(c_Set_Oinsert(U_11418),U_11421),c_Orderings_Obot__class_Obot(tc_fun(U_11418,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11418,U_11418,U_11420),hAPP(hAPP(c_Set_Oinsert(U_11418),U_11422),c_Orderings_Obot__class_Obot(tc_fun(U_11418,tc_HOL_Obool))))))
| ~ c_Equiv__Relations_Oequiv(U_11418,U_11419,U_11420) ),
inference(definitional_conversion,[status(esa)],[f_3023_2]) ).
cnf(f_3023_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11418,U_11418)),hAPP(hAPP(c_Product__Type_OPair(U_11418,U_11418),U_11422),U_11421)),U_11420))
| ~ hBOOL(hAPP(hAPP(c_member(U_11418),U_11421),U_11419))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11418,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11418,U_11418,U_11420),hAPP(hAPP(c_Set_Oinsert(U_11418),U_11421),c_Orderings_Obot__class_Obot(tc_fun(U_11418,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11418,U_11418,U_11420),hAPP(hAPP(c_Set_Oinsert(U_11418),U_11422),c_Orderings_Obot__class_Obot(tc_fun(U_11418,tc_HOL_Obool))))))
| ~ c_Equiv__Relations_Oequiv(U_11418,U_11419,U_11420) ),
inference(clausify,[status(thm)],[f_3023_3]) ).
fof(f_3024_1,plain,
! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_a_2),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,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_Relation_OImage(T_c,T_c,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))))
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint]) ).
fof(f_3024_2,plain,
! [U_11428,U_11427,U_11426,U_11425,U_11424,U_11423] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11423,U_11423)),hAPP(hAPP(c_Product__Type_OPair(U_11423,U_11423),U_11427),U_11428)),U_11425))
| ~ hBOOL(hAPP(hAPP(c_member(U_11423),U_11426),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11423,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11423,U_11423,U_11425),hAPP(hAPP(c_Set_Oinsert(U_11423),U_11427),c_Orderings_Obot__class_Obot(tc_fun(U_11423,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11423,U_11423,U_11425),hAPP(hAPP(c_Set_Oinsert(U_11423),U_11428),c_Orderings_Obot__class_Obot(tc_fun(U_11423,tc_HOL_Obool)))))))
| ~ c_Equiv__Relations_Oequiv(U_11423,U_11424,U_11425) ),
inference(variable_rename,[status(thm)],[f_3024_1]) ).
fof(f_3024_3,plain,
! [U_11423,U_11424,U_11425,U_11426,U_11427,U_11428] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11423,U_11423)),hAPP(hAPP(c_Product__Type_OPair(U_11423,U_11423),U_11427),U_11428)),U_11425))
| ~ hBOOL(hAPP(hAPP(c_member(U_11423),U_11426),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11423,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11423,U_11423,U_11425),hAPP(hAPP(c_Set_Oinsert(U_11423),U_11427),c_Orderings_Obot__class_Obot(tc_fun(U_11423,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11423,U_11423,U_11425),hAPP(hAPP(c_Set_Oinsert(U_11423),U_11428),c_Orderings_Obot__class_Obot(tc_fun(U_11423,tc_HOL_Obool)))))))
| ~ c_Equiv__Relations_Oequiv(U_11423,U_11424,U_11425) ),
inference(definitional_conversion,[status(esa)],[f_3024_2]) ).
cnf(f_3024_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11423,U_11423)),hAPP(hAPP(c_Product__Type_OPair(U_11423,U_11423),U_11427),U_11428)),U_11425))
| ~ hBOOL(hAPP(hAPP(c_member(U_11423),U_11426),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11423,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11423,U_11423,U_11425),hAPP(hAPP(c_Set_Oinsert(U_11423),U_11427),c_Orderings_Obot__class_Obot(tc_fun(U_11423,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11423,U_11423,U_11425),hAPP(hAPP(c_Set_Oinsert(U_11423),U_11428),c_Orderings_Obot__class_Obot(tc_fun(U_11423,tc_HOL_Obool)))))))
| ~ c_Equiv__Relations_Oequiv(U_11423,U_11424,U_11425) ),
inference(clausify,[status(thm)],[f_3024_3]) ).
fof(f_3025_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_3025_2,plain,
! [U_11432,U_11431,U_11430,U_11429] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11429,U_11430),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11431),U_11432)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11432),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11430),U_11432)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11430)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11432),U_11430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11432)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11430)) )
| U_11429 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11430),U_11431)),U_11432) ),
inference(variable_rename,[status(thm)],[f_3025_1]) ).
fof(f_3025_3,plain,
( ! [U_11430,U_11432] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11432),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11430),U_11432))
| ~ sP841(U_11430,U_11432) )
& ! [U_11430,U_11432] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11430))
| ~ sP841(U_11430,U_11432) )
& ! [U_11430,U_11432] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11432),U_11430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11432))
| ~ sP840(U_11430,U_11432) )
& ! [U_11430,U_11432] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11430))
| ~ sP840(U_11430,U_11432) )
& ! [U_11429,U_11430,U_11431,U_11432] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11429,U_11430),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11431),U_11432)))
| sP841(U_11430,U_11432)
| sP840(U_11430,U_11432)
| U_11429 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11430),U_11431)),U_11432) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP840,sP841])],[f_3025_2]) ).
cnf(f_3025_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11429,U_11430),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11431),U_11432)))
| sP841(U_11430,U_11432)
| sP840(U_11430,U_11432)
| U_11429 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11430),U_11431)),U_11432) ),
inference(clausify,[status(thm)],[f_3025_3]) ).
cnf(f_3025_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11430))
| ~ sP840(U_11430,U_11432) ),
inference(clausify,[status(thm)],[f_3025_3]) ).
cnf(f_3025_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11432),U_11430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11432))
| ~ sP840(U_11430,U_11432) ),
inference(clausify,[status(thm)],[f_3025_3]) ).
cnf(f_3025_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11430))
| ~ sP841(U_11430,U_11432) ),
inference(clausify,[status(thm)],[f_3025_3]) ).
cnf(f_3025_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11432),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11430),U_11432))
| ~ sP841(U_11430,U_11432) ),
inference(clausify,[status(thm)],[f_3025_3]) ).
fof(f_3026_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_3026_2,plain,
! [U_11437,U_11436,U_11435,U_11434,U_11433] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11437),U_11433),U_11434),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_11437),U_11435)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11437),U_11436)),U_11434))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11437),U_11436),U_11434))))
| U_11434 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11433,U_11434),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11435),U_11436))) ),
inference(variable_rename,[status(thm)],[f_3026_1]) ).
fof(f_3026_3,plain,
! [U_11433,U_11435,U_11434,U_11437,U_11436] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11437),U_11433),U_11434),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_11437),U_11435)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11437),U_11436)),U_11434))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11437),U_11436),U_11434))))
| U_11434 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11433,U_11434),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11435),U_11436))) ),
inference(definitional_conversion,[status(esa)],[f_3026_2]) ).
cnf(f_3026_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11437),U_11433),U_11434),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_11437),U_11435)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11437),U_11436)),U_11434))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11437),U_11436),U_11434))))
| U_11434 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11433,U_11434),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11435),U_11436))) ),
inference(clausify,[status(thm)],[f_3026_3]) ).
fof(f_3027_1,plain,
! [V_f_2,T_e,V_A_2,V_b_2,V_a_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_e),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),T_e,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_f_2)),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_pair__imageI]) ).
fof(f_3027_2,plain,
! [U_11444,U_11443,U_11442,U_11441,U_11440,U_11439,U_11438] :
( hBOOL(hAPP(hAPP(c_member(U_11443),hAPP(hAPP(U_11444,U_11440),U_11441)),hAPP(c_Set_Oimage(tc_prod(U_11438,U_11439),U_11443,hAPP(c_Product__Type_Oprod_Oprod__case(U_11438,U_11439,U_11443),U_11444)),U_11442)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11438,U_11439)),hAPP(hAPP(c_Product__Type_OPair(U_11438,U_11439),U_11440),U_11441)),U_11442)) ),
inference(variable_rename,[status(thm)],[f_3027_1]) ).
fof(f_3027_3,plain,
! [U_11438,U_11439,U_11440,U_11441,U_11442,U_11443,U_11444] :
( hBOOL(hAPP(hAPP(c_member(U_11443),hAPP(hAPP(U_11444,U_11440),U_11441)),hAPP(c_Set_Oimage(tc_prod(U_11438,U_11439),U_11443,hAPP(c_Product__Type_Oprod_Oprod__case(U_11438,U_11439,U_11443),U_11444)),U_11442)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11438,U_11439)),hAPP(hAPP(c_Product__Type_OPair(U_11438,U_11439),U_11440),U_11441)),U_11442)) ),
inference(definitional_conversion,[status(esa)],[f_3027_2]) ).
cnf(f_3027_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11443),hAPP(hAPP(U_11444,U_11440),U_11441)),hAPP(c_Set_Oimage(tc_prod(U_11438,U_11439),U_11443,hAPP(c_Product__Type_Oprod_Oprod__case(U_11438,U_11439,U_11443),U_11444)),U_11442)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11438,U_11439)),hAPP(hAPP(c_Product__Type_OPair(U_11438,U_11439),U_11440),U_11441)),U_11442)) ),
inference(clausify,[status(thm)],[f_3027_3]) ).
fof(f_3028_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_3028_2,plain,
! [U_11446,U_11445] :
( ( ( ( c_Nitpick_Onorm__frac(U_11446,U_11445) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_11446),U_11445)),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_11446))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11445)))
| U_11445 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11446 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nitpick_Onorm__frac(U_11446,U_11445) = 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_11445 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& U_11446 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11445),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Nitpick_Onorm__frac(U_11446,U_11445) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11446),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11445))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11445),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_3028_1]) ).
fof(f_3028_3,plain,
( ! [U_11450,U_11448] :
( ( ( c_Nitpick_Onorm__frac(U_11450,U_11448) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_11450),U_11448)),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_11450))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11448)))
| U_11448 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11450 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nitpick_Onorm__frac(U_11450,U_11448) = 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_11448 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& U_11450 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11448),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_11449,U_11447] :
( c_Nitpick_Onorm__frac(U_11449,U_11447) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11449),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11447))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11447),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_3028_2]) ).
fof(f_3028_4,plain,
( ! [U_11450,U_11448] :
( U_11448 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP842(U_11450,U_11448) )
& ! [U_11450,U_11448] :
( U_11450 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP842(U_11450,U_11448) )
& ! [U_11450,U_11448] :
( c_Nitpick_Onorm__frac(U_11450,U_11448) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_11450),U_11448)),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_11450))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11448)))
| U_11448 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11450 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP843(U_11450,U_11448) )
& ! [U_11450,U_11448] :
( c_Nitpick_Onorm__frac(U_11450,U_11448) = 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))
| sP842(U_11450,U_11448)
| ~ sP843(U_11450,U_11448) )
& ! [U_11450,U_11448] :
( sP843(U_11450,U_11448)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11448),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_11449,U_11447] :
( c_Nitpick_Onorm__frac(U_11449,U_11447) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11449),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11447))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11447),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP842,sP843])],[f_3028_3]) ).
cnf(f_3028_5,plain,
( c_Nitpick_Onorm__frac(U_11449,U_11447) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11449),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11447))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11447),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3028_4]) ).
cnf(f_3028_6,plain,
( sP843(U_11450,U_11448)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11448),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3028_4]) ).
cnf(f_3028_7,plain,
( c_Nitpick_Onorm__frac(U_11450,U_11448) = 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))
| sP842(U_11450,U_11448)
| ~ sP843(U_11450,U_11448) ),
inference(clausify,[status(thm)],[f_3028_4]) ).
cnf(f_3028_8,plain,
( c_Nitpick_Onorm__frac(U_11450,U_11448) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_11450),U_11448)),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_11450))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11448)))
| U_11448 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11450 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP843(U_11450,U_11448) ),
inference(clausify,[status(thm)],[f_3028_4]) ).
cnf(f_3028_9,plain,
( U_11450 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP842(U_11450,U_11448) ),
inference(clausify,[status(thm)],[f_3028_4]) ).
cnf(f_3028_10,plain,
( U_11448 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP842(U_11450,U_11448) ),
inference(clausify,[status(thm)],[f_3028_4]) ).
fof(f_3029_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_3029_2,plain,
! [U_11453,U_11452,U_11451] : hAPP(c_Divides_Oadjust(U_11451),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11452),U_11453)) = 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_11453),U_11451)),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_11452)),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_11452)),U_11453))),
inference(variable_rename,[status(thm)],[f_3029_1]) ).
fof(f_3029_3,plain,
! [U_11452,U_11453,U_11451] : hAPP(c_Divides_Oadjust(U_11451),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11452),U_11453)) = 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_11453),U_11451)),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_11452)),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_11452)),U_11453))),
inference(definitional_conversion,[status(esa)],[f_3029_2]) ).
cnf(f_3029_4,plain,
hAPP(c_Divides_Oadjust(U_11451),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11452),U_11453)) = 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_11453),U_11451)),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_11452)),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_11452)),U_11453))),
inference(clausify,[status(thm)],[f_3029_3]) ).
fof(f_3030_1,plain,
! [T_d,T_c,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_c,tc_fun(T_d,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_3030_2,plain,
! [U_11459,U_11458,U_11457,U_11456,U_11455,U_11454] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11458,tc_fun(U_11459,tc_HOL_Obool))),U_11457),U_11454),U_11455),U_11456))
| ( ~ hBOOL(hAPP(hAPP(U_11457,U_11455),U_11456))
& ~ hBOOL(hAPP(hAPP(U_11454,U_11455),U_11456)) ) ),
inference(variable_rename,[status(thm)],[f_3030_1]) ).
fof(f_3030_3,plain,
( ! [U_11454,U_11455,U_11456,U_11457] :
( ~ hBOOL(hAPP(hAPP(U_11457,U_11455),U_11456))
| ~ sP844(U_11454,U_11455,U_11456,U_11457) )
& ! [U_11454,U_11455,U_11456,U_11457] :
( ~ hBOOL(hAPP(hAPP(U_11454,U_11455),U_11456))
| ~ sP844(U_11454,U_11455,U_11456,U_11457) )
& ! [U_11454,U_11455,U_11456,U_11458,U_11457,U_11459] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11458,tc_fun(U_11459,tc_HOL_Obool))),U_11457),U_11454),U_11455),U_11456))
| sP844(U_11454,U_11455,U_11456,U_11457) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP844])],[f_3030_2]) ).
cnf(f_3030_4,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11458,tc_fun(U_11459,tc_HOL_Obool))),U_11457),U_11454),U_11455),U_11456))
| sP844(U_11454,U_11455,U_11456,U_11457) ),
inference(clausify,[status(thm)],[f_3030_3]) ).
cnf(f_3030_5,plain,
( ~ hBOOL(hAPP(hAPP(U_11454,U_11455),U_11456))
| ~ sP844(U_11454,U_11455,U_11456,U_11457) ),
inference(clausify,[status(thm)],[f_3030_3]) ).
cnf(f_3030_6,plain,
( ~ hBOOL(hAPP(hAPP(U_11457,U_11455),U_11456))
| ~ sP844(U_11454,U_11455,U_11456,U_11457) ),
inference(clausify,[status(thm)],[f_3030_3]) ).
fof(f_3031_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_d,T_c] :
( 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_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup2E]) ).
fof(f_3031_2,plain,
! [U_11465,U_11464,U_11463,U_11462,U_11461,U_11460] :
( hBOOL(hAPP(hAPP(U_11463,U_11464),U_11465))
| hBOOL(hAPP(hAPP(U_11462,U_11464),U_11465))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11460,tc_fun(U_11461,tc_HOL_Obool))),U_11462),U_11463),U_11464),U_11465)) ),
inference(variable_rename,[status(thm)],[f_3031_1]) ).
fof(f_3031_3,plain,
! [U_11465,U_11464,U_11463,U_11462] :
( ! [U_11461,U_11460] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11460,tc_fun(U_11461,tc_HOL_Obool))),U_11462),U_11463),U_11464),U_11465))
| hBOOL(hAPP(hAPP(U_11463,U_11464),U_11465))
| hBOOL(hAPP(hAPP(U_11462,U_11464),U_11465)) ),
inference(miniscope,[status(thm)],[f_3031_2]) ).
fof(f_3031_4,plain,
! [U_11461,U_11460,U_11462,U_11463,U_11464,U_11465] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11460,tc_fun(U_11461,tc_HOL_Obool))),U_11462),U_11463),U_11464),U_11465))
| hBOOL(hAPP(hAPP(U_11463,U_11464),U_11465))
| hBOOL(hAPP(hAPP(U_11462,U_11464),U_11465)) ),
inference(definitional_conversion,[status(esa)],[f_3031_3]) ).
cnf(f_3031_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11460,tc_fun(U_11461,tc_HOL_Obool))),U_11462),U_11463),U_11464),U_11465))
| hBOOL(hAPP(hAPP(U_11463,U_11464),U_11465))
| hBOOL(hAPP(hAPP(U_11462,U_11464),U_11465)) ),
inference(clausify,[status(thm)],[f_3031_4]) ).
fof(f_3032_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_d,T_c] :
( ( 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_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf2E]) ).
fof(f_3032_2,plain,
! [U_11471,U_11470,U_11469,U_11468,U_11467,U_11466] :
( ( hBOOL(hAPP(hAPP(U_11469,U_11470),U_11471))
& hBOOL(hAPP(hAPP(U_11468,U_11470),U_11471)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11466,tc_fun(U_11467,tc_HOL_Obool))),U_11468),U_11469),U_11470),U_11471)) ),
inference(variable_rename,[status(thm)],[f_3032_1]) ).
fof(f_3032_3,plain,
! [U_11471,U_11470,U_11469,U_11468] :
( ! [U_11467,U_11466] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11466,tc_fun(U_11467,tc_HOL_Obool))),U_11468),U_11469),U_11470),U_11471))
| ( hBOOL(hAPP(hAPP(U_11469,U_11470),U_11471))
& hBOOL(hAPP(hAPP(U_11468,U_11470),U_11471)) ) ),
inference(miniscope,[status(thm)],[f_3032_2]) ).
fof(f_3032_4,plain,
( ! [U_11468,U_11469,U_11470,U_11471] :
( hBOOL(hAPP(hAPP(U_11469,U_11470),U_11471))
| ~ sP845(U_11468,U_11469,U_11470,U_11471) )
& ! [U_11468,U_11469,U_11470,U_11471] :
( hBOOL(hAPP(hAPP(U_11468,U_11470),U_11471))
| ~ sP845(U_11468,U_11469,U_11470,U_11471) )
& ! [U_11467,U_11466,U_11468,U_11469,U_11470,U_11471] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11466,tc_fun(U_11467,tc_HOL_Obool))),U_11468),U_11469),U_11470),U_11471))
| sP845(U_11468,U_11469,U_11470,U_11471) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP845])],[f_3032_3]) ).
cnf(f_3032_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11466,tc_fun(U_11467,tc_HOL_Obool))),U_11468),U_11469),U_11470),U_11471))
| sP845(U_11468,U_11469,U_11470,U_11471) ),
inference(clausify,[status(thm)],[f_3032_4]) ).
cnf(f_3032_6,plain,
( hBOOL(hAPP(hAPP(U_11468,U_11470),U_11471))
| ~ sP845(U_11468,U_11469,U_11470,U_11471) ),
inference(clausify,[status(thm)],[f_3032_4]) ).
cnf(f_3032_7,plain,
( hBOOL(hAPP(hAPP(U_11469,U_11470),U_11471))
| ~ sP845(U_11468,U_11469,U_11470,U_11471) ),
inference(clausify,[status(thm)],[f_3032_4]) ).
fof(f_3033_1,plain,
! [T_d,T_c,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_c,tc_fun(T_d,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_3033_2,plain,
! [U_11477,U_11476,U_11475,U_11474,U_11473,U_11472] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_fun(U_11477,tc_HOL_Obool))),U_11472),U_11475),U_11473),U_11474))
| ~ hBOOL(hAPP(hAPP(U_11475,U_11473),U_11474))
| ~ hBOOL(hAPP(hAPP(U_11472,U_11473),U_11474)) ),
inference(variable_rename,[status(thm)],[f_3033_1]) ).
fof(f_3033_3,plain,
! [U_11472,U_11473,U_11474,U_11475,U_11476,U_11477] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_fun(U_11477,tc_HOL_Obool))),U_11472),U_11475),U_11473),U_11474))
| ~ hBOOL(hAPP(hAPP(U_11475,U_11473),U_11474))
| ~ hBOOL(hAPP(hAPP(U_11472,U_11473),U_11474)) ),
inference(definitional_conversion,[status(esa)],[f_3033_2]) ).
cnf(f_3033_4,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_fun(U_11477,tc_HOL_Obool))),U_11472),U_11475),U_11473),U_11474))
| ~ hBOOL(hAPP(hAPP(U_11475,U_11473),U_11474))
| ~ hBOOL(hAPP(hAPP(U_11472,U_11473),U_11474)) ),
inference(clausify,[status(thm)],[f_3033_3]) ).
fof(f_3034_1,plain,
! [T_e,T_d,V_b_2,V_a_2,V_c_2,V_z_2,T_c] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(T_c,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2))))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) ),
inference(fof_nnf,[status(thm)],[fact_mem__splitI]) ).
fof(f_3034_2,plain,
! [U_11484,U_11483,U_11482,U_11481,U_11480,U_11479,U_11478] :
( hBOOL(hAPP(hAPP(c_member(U_11478),U_11479),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11483,U_11484,tc_fun(U_11478,tc_HOL_Obool)),U_11480),hAPP(hAPP(c_Product__Type_OPair(U_11483,U_11484),U_11481),U_11482))))
| ~ hBOOL(hAPP(hAPP(c_member(U_11478),U_11479),hAPP(hAPP(U_11480,U_11481),U_11482))) ),
inference(variable_rename,[status(thm)],[f_3034_1]) ).
fof(f_3034_3,plain,
! [U_11478,U_11479,U_11480,U_11481,U_11482,U_11483,U_11484] :
( hBOOL(hAPP(hAPP(c_member(U_11478),U_11479),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11483,U_11484,tc_fun(U_11478,tc_HOL_Obool)),U_11480),hAPP(hAPP(c_Product__Type_OPair(U_11483,U_11484),U_11481),U_11482))))
| ~ hBOOL(hAPP(hAPP(c_member(U_11478),U_11479),hAPP(hAPP(U_11480,U_11481),U_11482))) ),
inference(definitional_conversion,[status(esa)],[f_3034_2]) ).
cnf(f_3034_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11478),U_11479),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11483,U_11484,tc_fun(U_11478,tc_HOL_Obool)),U_11480),hAPP(hAPP(c_Product__Type_OPair(U_11483,U_11484),U_11481),U_11482))))
| ~ hBOOL(hAPP(hAPP(c_member(U_11478),U_11479),hAPP(hAPP(U_11480,U_11481),U_11482))) ),
inference(clausify,[status(thm)],[f_3034_3]) ).
fof(f_3035_1,plain,
! [T_d,T_c,V_b_2,V_a_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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_3035_2,plain,
! [U_11489,U_11488,U_11487,U_11486,U_11485] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11488,U_11489,tc_HOL_Obool),U_11485),hAPP(hAPP(c_Product__Type_OPair(U_11488,U_11489),U_11486),U_11487)))
| ~ hBOOL(hAPP(hAPP(U_11485,U_11486),U_11487)) ),
inference(variable_rename,[status(thm)],[f_3035_1]) ).
fof(f_3035_3,plain,
! [U_11486,U_11487,U_11485,U_11488,U_11489] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11488,U_11489,tc_HOL_Obool),U_11485),hAPP(hAPP(c_Product__Type_OPair(U_11488,U_11489),U_11486),U_11487)))
| ~ hBOOL(hAPP(hAPP(U_11485,U_11486),U_11487)) ),
inference(definitional_conversion,[status(esa)],[f_3035_2]) ).
cnf(f_3035_4,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11488,U_11489,tc_HOL_Obool),U_11485),hAPP(hAPP(c_Product__Type_OPair(U_11488,U_11489),U_11486),U_11487)))
| ~ hBOOL(hAPP(hAPP(U_11485,U_11486),U_11487)) ),
inference(clausify,[status(thm)],[f_3035_3]) ).
fof(f_3036_1,plain,
! [T_d,T_c,V_b_2,V_a_2,V_f1_2] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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_3036_2,plain,
! [U_11494,U_11493,U_11492,U_11491,U_11490] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11493,U_11494,tc_HOL_Obool),U_11490),hAPP(hAPP(c_Product__Type_OPair(U_11493,U_11494),U_11491),U_11492)))
| ~ hBOOL(hAPP(hAPP(U_11490,U_11491),U_11492)) ),
inference(variable_rename,[status(thm)],[f_3036_1]) ).
fof(f_3036_3,plain,
! [U_11491,U_11490,U_11492,U_11493,U_11494] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11493,U_11494,tc_HOL_Obool),U_11490),hAPP(hAPP(c_Product__Type_OPair(U_11493,U_11494),U_11491),U_11492)))
| ~ hBOOL(hAPP(hAPP(U_11490,U_11491),U_11492)) ),
inference(definitional_conversion,[status(esa)],[f_3036_2]) ).
cnf(f_3036_4,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11493,U_11494,tc_HOL_Obool),U_11490),hAPP(hAPP(c_Product__Type_OPair(U_11493,U_11494),U_11491),U_11492)))
| ~ hBOOL(hAPP(hAPP(U_11490,U_11491),U_11492)) ),
inference(clausify,[status(thm)],[f_3036_3]) ).
fof(f_3037_1,plain,
! [V_y_2,V_x_2,T_d,T_c] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_x_2),V_y_2)),
inference(fof_nnf,[status(thm)],[fact_bot2E]) ).
fof(f_3037_2,plain,
! [U_11498,U_11497,U_11496,U_11495] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11495,tc_fun(U_11496,tc_HOL_Obool))),U_11497),U_11498)),
inference(variable_rename,[status(thm)],[f_3037_1]) ).
fof(f_3037_3,plain,
! [U_11496,U_11495,U_11497,U_11498] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11495,tc_fun(U_11496,tc_HOL_Obool))),U_11497),U_11498)),
inference(definitional_conversion,[status(esa)],[f_3037_2]) ).
cnf(f_3037_4,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_11495,tc_fun(U_11496,tc_HOL_Obool))),U_11497),U_11498)),
inference(clausify,[status(thm)],[f_3037_3]) ).
fof(f_3038_1,plain,
! [V_c_2,V_b_2,V_a_2,V_R_2,T_e,T_d,T_c] :
( hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_e,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),V_c_2)) ),
inference(fof_nnf,[status(thm)],[fact_splitD_H]) ).
fof(f_3038_2,plain,
! [U_11505,U_11504,U_11503,U_11502,U_11501,U_11500,U_11499] :
( hBOOL(hAPP(hAPP(hAPP(U_11502,U_11503),U_11504),U_11505))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11499,U_11500,tc_fun(U_11501,tc_HOL_Obool)),U_11502),hAPP(hAPP(c_Product__Type_OPair(U_11499,U_11500),U_11503),U_11504)),U_11505)) ),
inference(variable_rename,[status(thm)],[f_3038_1]) ).
fof(f_3038_3,plain,
! [U_11505,U_11504,U_11503,U_11502] :
( ! [U_11501,U_11500,U_11499] : ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11499,U_11500,tc_fun(U_11501,tc_HOL_Obool)),U_11502),hAPP(hAPP(c_Product__Type_OPair(U_11499,U_11500),U_11503),U_11504)),U_11505))
| hBOOL(hAPP(hAPP(hAPP(U_11502,U_11503),U_11504),U_11505)) ),
inference(miniscope,[status(thm)],[f_3038_2]) ).
fof(f_3038_4,plain,
! [U_11499,U_11500,U_11501,U_11502,U_11503,U_11504,U_11505] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11499,U_11500,tc_fun(U_11501,tc_HOL_Obool)),U_11502),hAPP(hAPP(c_Product__Type_OPair(U_11499,U_11500),U_11503),U_11504)),U_11505))
| hBOOL(hAPP(hAPP(hAPP(U_11502,U_11503),U_11504),U_11505)) ),
inference(definitional_conversion,[status(esa)],[f_3038_3]) ).
cnf(f_3038_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11499,U_11500,tc_fun(U_11501,tc_HOL_Obool)),U_11502),hAPP(hAPP(c_Product__Type_OPair(U_11499,U_11500),U_11503),U_11504)),U_11505))
| hBOOL(hAPP(hAPP(hAPP(U_11502,U_11503),U_11504),U_11505)) ),
inference(clausify,[status(thm)],[f_3038_4]) ).
fof(f_3039_1,plain,
! [V_A_2,T_d,T_c] : c_Fun_Oinj__on(tc_prod(T_c,T_d),tc_prod(T_d,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,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_A_2),
inference(fof_nnf,[status(thm)],[fact_swap__inj__on]) ).
fof(f_3039_2,plain,
! [U_11508,U_11507,U_11506] : c_Fun_Oinj__on(tc_prod(U_11506,U_11507),tc_prod(U_11507,U_11506),hAPP(c_Product__Type_Oprod_Oprod__case(U_11506,U_11507,tc_prod(U_11507,U_11506)),hAPP(c_COMBC(U_11507,U_11506,tc_prod(U_11507,U_11506)),c_Product__Type_OPair(U_11507,U_11506))),U_11508),
inference(variable_rename,[status(thm)],[f_3039_1]) ).
fof(f_3039_3,plain,
! [U_11506,U_11507,U_11508] : c_Fun_Oinj__on(tc_prod(U_11506,U_11507),tc_prod(U_11507,U_11506),hAPP(c_Product__Type_Oprod_Oprod__case(U_11506,U_11507,tc_prod(U_11507,U_11506)),hAPP(c_COMBC(U_11507,U_11506,tc_prod(U_11507,U_11506)),c_Product__Type_OPair(U_11507,U_11506))),U_11508),
inference(definitional_conversion,[status(esa)],[f_3039_2]) ).
cnf(f_3039_4,plain,
c_Fun_Oinj__on(tc_prod(U_11506,U_11507),tc_prod(U_11507,U_11506),hAPP(c_Product__Type_Oprod_Oprod__case(U_11506,U_11507,tc_prod(U_11507,U_11506)),hAPP(c_COMBC(U_11507,U_11506,tc_prod(U_11507,U_11506)),c_Product__Type_OPair(U_11507,U_11506))),U_11508),
inference(clausify,[status(thm)],[f_3039_3]) ).
fof(f_3040_1,plain,
! [V_A_2,T_d,T_c,V_y_2,V_x_2,V_B_2] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,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_3040_2,plain,
! [U_11514,U_11513,U_11512,U_11511,U_11510,U_11509] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11512,tc_fun(U_11513,tc_HOL_Obool))),U_11514),U_11509),U_11510),U_11511))
| ~ hBOOL(hAPP(hAPP(U_11509,U_11510),U_11511)) ),
inference(variable_rename,[status(thm)],[f_3040_1]) ).
fof(f_3040_3,plain,
! [U_11509,U_11510,U_11511,U_11512,U_11513,U_11514] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11512,tc_fun(U_11513,tc_HOL_Obool))),U_11514),U_11509),U_11510),U_11511))
| ~ hBOOL(hAPP(hAPP(U_11509,U_11510),U_11511)) ),
inference(definitional_conversion,[status(esa)],[f_3040_2]) ).
cnf(f_3040_4,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11512,tc_fun(U_11513,tc_HOL_Obool))),U_11514),U_11509),U_11510),U_11511))
| ~ hBOOL(hAPP(hAPP(U_11509,U_11510),U_11511)) ),
inference(clausify,[status(thm)],[f_3040_3]) ).
fof(f_3041_1,plain,
! [V_B_2,T_d,T_c,V_y_2,V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_d,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_3041_2,plain,
! [U_11520,U_11519,U_11518,U_11517,U_11516,U_11515] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11518,tc_fun(U_11519,tc_HOL_Obool))),U_11515),U_11520),U_11516),U_11517))
| ~ hBOOL(hAPP(hAPP(U_11515,U_11516),U_11517)) ),
inference(variable_rename,[status(thm)],[f_3041_1]) ).
fof(f_3041_3,plain,
! [U_11516,U_11515,U_11517,U_11518,U_11519,U_11520] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11518,tc_fun(U_11519,tc_HOL_Obool))),U_11515),U_11520),U_11516),U_11517))
| ~ hBOOL(hAPP(hAPP(U_11515,U_11516),U_11517)) ),
inference(definitional_conversion,[status(esa)],[f_3041_2]) ).
cnf(f_3041_4,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11518,tc_fun(U_11519,tc_HOL_Obool))),U_11515),U_11520),U_11516),U_11517))
| ~ hBOOL(hAPP(hAPP(U_11515,U_11516),U_11517)) ),
inference(clausify,[status(thm)],[f_3041_3]) ).
fof(f_3042_1,plain,
! [V_Qa_2,T_d,T_c,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_c,tc_fun(T_d,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_3042_2,plain,
! [U_11526,U_11525,U_11524,U_11523,U_11522,U_11521] :
( hBOOL(hAPP(hAPP(U_11526,U_11522),U_11523))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11524,tc_fun(U_11525,tc_HOL_Obool))),U_11521),U_11526))
| ~ hBOOL(hAPP(hAPP(U_11521,U_11522),U_11523)) ),
inference(variable_rename,[status(thm)],[f_3042_1]) ).
fof(f_3042_3,plain,
! [U_11522,U_11521,U_11523,U_11524,U_11525,U_11526] :
( hBOOL(hAPP(hAPP(U_11526,U_11522),U_11523))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11524,tc_fun(U_11525,tc_HOL_Obool))),U_11521),U_11526))
| ~ hBOOL(hAPP(hAPP(U_11521,U_11522),U_11523)) ),
inference(definitional_conversion,[status(esa)],[f_3042_2]) ).
cnf(f_3042_4,plain,
( hBOOL(hAPP(hAPP(U_11526,U_11522),U_11523))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11524,tc_fun(U_11525,tc_HOL_Obool))),U_11521),U_11526))
| ~ hBOOL(hAPP(hAPP(U_11521,U_11522),U_11523)) ),
inference(clausify,[status(thm)],[f_3042_3]) ).
fof(f_3043_1,plain,
! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_d,T_c] :
( 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_c,tc_fun(T_d,tc_HOL_Obool))),V_Pa_2),V_Qa_2)) ),
inference(fof_nnf,[status(thm)],[fact_predicate2D]) ).
fof(f_3043_2,plain,
! [U_11532,U_11531,U_11530,U_11529,U_11528,U_11527] :
( hBOOL(hAPP(hAPP(U_11530,U_11531),U_11532))
| ~ hBOOL(hAPP(hAPP(U_11529,U_11531),U_11532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11527,tc_fun(U_11528,tc_HOL_Obool))),U_11529),U_11530)) ),
inference(variable_rename,[status(thm)],[f_3043_1]) ).
fof(f_3043_3,plain,
! [U_11532,U_11531,U_11530,U_11529] :
( ! [U_11528,U_11527] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11527,tc_fun(U_11528,tc_HOL_Obool))),U_11529),U_11530))
| hBOOL(hAPP(hAPP(U_11530,U_11531),U_11532))
| ~ hBOOL(hAPP(hAPP(U_11529,U_11531),U_11532)) ),
inference(miniscope,[status(thm)],[f_3043_2]) ).
fof(f_3043_4,plain,
! [U_11527,U_11528,U_11529,U_11530,U_11531,U_11532] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11527,tc_fun(U_11528,tc_HOL_Obool))),U_11529),U_11530))
| hBOOL(hAPP(hAPP(U_11530,U_11531),U_11532))
| ~ hBOOL(hAPP(hAPP(U_11529,U_11531),U_11532)) ),
inference(definitional_conversion,[status(esa)],[f_3043_3]) ).
cnf(f_3043_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11527,tc_fun(U_11528,tc_HOL_Obool))),U_11529),U_11530))
| hBOOL(hAPP(hAPP(U_11530,U_11531),U_11532))
| ~ hBOOL(hAPP(hAPP(U_11529,U_11531),U_11532)) ),
inference(clausify,[status(thm)],[f_3043_4]) ).
fof(f_3044_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_d,T_c] :
( 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_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf2D2]) ).
fof(f_3044_2,plain,
! [U_11538,U_11537,U_11536,U_11535,U_11534,U_11533] :
( hBOOL(hAPP(hAPP(U_11536,U_11537),U_11538))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11533,tc_fun(U_11534,tc_HOL_Obool))),U_11535),U_11536),U_11537),U_11538)) ),
inference(variable_rename,[status(thm)],[f_3044_1]) ).
fof(f_3044_3,plain,
! [U_11538,U_11537,U_11536] :
( ! [U_11535,U_11534,U_11533] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11533,tc_fun(U_11534,tc_HOL_Obool))),U_11535),U_11536),U_11537),U_11538))
| hBOOL(hAPP(hAPP(U_11536,U_11537),U_11538)) ),
inference(miniscope,[status(thm)],[f_3044_2]) ).
fof(f_3044_4,plain,
! [U_11533,U_11534,U_11535,U_11536,U_11537,U_11538] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11533,tc_fun(U_11534,tc_HOL_Obool))),U_11535),U_11536),U_11537),U_11538))
| hBOOL(hAPP(hAPP(U_11536,U_11537),U_11538)) ),
inference(definitional_conversion,[status(esa)],[f_3044_3]) ).
cnf(f_3044_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11533,tc_fun(U_11534,tc_HOL_Obool))),U_11535),U_11536),U_11537),U_11538))
| hBOOL(hAPP(hAPP(U_11536,U_11537),U_11538)) ),
inference(clausify,[status(thm)],[f_3044_4]) ).
fof(f_3045_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_d,T_c] :
( 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_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf2D1]) ).
fof(f_3045_2,plain,
! [U_11544,U_11543,U_11542,U_11541,U_11540,U_11539] :
( hBOOL(hAPP(hAPP(U_11541,U_11543),U_11544))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11539,tc_fun(U_11540,tc_HOL_Obool))),U_11541),U_11542),U_11543),U_11544)) ),
inference(variable_rename,[status(thm)],[f_3045_1]) ).
fof(f_3045_3,plain,
! [U_11544,U_11543,U_11542,U_11541] :
( ! [U_11540,U_11539] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11539,tc_fun(U_11540,tc_HOL_Obool))),U_11541),U_11542),U_11543),U_11544))
| hBOOL(hAPP(hAPP(U_11541,U_11543),U_11544)) ),
inference(miniscope,[status(thm)],[f_3045_2]) ).
fof(f_3045_4,plain,
! [U_11539,U_11540,U_11541,U_11542,U_11543,U_11544] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11539,tc_fun(U_11540,tc_HOL_Obool))),U_11541),U_11542),U_11543),U_11544))
| hBOOL(hAPP(hAPP(U_11541,U_11543),U_11544)) ),
inference(definitional_conversion,[status(esa)],[f_3045_3]) ).
cnf(f_3045_5,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11539,tc_fun(U_11540,tc_HOL_Obool))),U_11541),U_11542),U_11543),U_11544))
| hBOOL(hAPP(hAPP(U_11541,U_11543),U_11544)) ),
inference(clausify,[status(thm)],[f_3045_4]) ).
fof(f_3046_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_3046_2,plain,
! [U_11550,U_11549,U_11548,U_11547,U_11546,U_11545] :
( ( U_11548 = U_11550
& U_11547 = U_11549 )
| hAPP(hAPP(c_Product__Type_OPair(U_11545,U_11546),U_11547),U_11548) != hAPP(hAPP(c_Product__Type_OPair(U_11545,U_11546),U_11549),U_11550) ),
inference(variable_rename,[status(thm)],[f_3046_1]) ).
fof(f_3046_3,plain,
! [U_11550,U_11549,U_11548,U_11547] :
( ! [U_11546,U_11545] : hAPP(hAPP(c_Product__Type_OPair(U_11545,U_11546),U_11547),U_11548) != hAPP(hAPP(c_Product__Type_OPair(U_11545,U_11546),U_11549),U_11550)
| ( U_11548 = U_11550
& U_11547 = U_11549 ) ),
inference(miniscope,[status(thm)],[f_3046_2]) ).
fof(f_3046_4,plain,
( ! [U_11547,U_11548,U_11549,U_11550] :
( U_11548 = U_11550
| ~ sP846(U_11547,U_11548,U_11549,U_11550) )
& ! [U_11547,U_11548,U_11549,U_11550] :
( U_11547 = U_11549
| ~ sP846(U_11547,U_11548,U_11549,U_11550) )
& ! [U_11546,U_11545,U_11547,U_11548,U_11549,U_11550] :
( hAPP(hAPP(c_Product__Type_OPair(U_11545,U_11546),U_11547),U_11548) != hAPP(hAPP(c_Product__Type_OPair(U_11545,U_11546),U_11549),U_11550)
| sP846(U_11547,U_11548,U_11549,U_11550) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP846])],[f_3046_3]) ).
cnf(f_3046_5,plain,
( hAPP(hAPP(c_Product__Type_OPair(U_11545,U_11546),U_11547),U_11548) != hAPP(hAPP(c_Product__Type_OPair(U_11545,U_11546),U_11549),U_11550)
| sP846(U_11547,U_11548,U_11549,U_11550) ),
inference(clausify,[status(thm)],[f_3046_4]) ).
cnf(f_3046_6,plain,
( U_11547 = U_11549
| ~ sP846(U_11547,U_11548,U_11549,U_11550) ),
inference(clausify,[status(thm)],[f_3046_4]) ).
cnf(f_3046_7,plain,
( U_11548 = U_11550
| ~ sP846(U_11547,U_11548,U_11549,U_11550) ),
inference(clausify,[status(thm)],[f_3046_4]) ).
fof(f_3047_1,plain,
! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_d,T_c] :
( ( hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),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_c,T_d),V_a_2),V_b_2) != hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_H_2),V_b_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Pair__eq]) ).
fof(f_3047_2,plain,
! [U_11556,U_11555,U_11554,U_11553,U_11552,U_11551] :
( ( hAPP(hAPP(c_Product__Type_OPair(U_11551,U_11552),U_11553),U_11554) = hAPP(hAPP(c_Product__Type_OPair(U_11551,U_11552),U_11555),U_11556)
| U_11554 != U_11556
| U_11553 != U_11555 )
& ( ( U_11554 = U_11556
& U_11553 = U_11555 )
| hAPP(hAPP(c_Product__Type_OPair(U_11551,U_11552),U_11553),U_11554) != hAPP(hAPP(c_Product__Type_OPair(U_11551,U_11552),U_11555),U_11556) ) ),
inference(variable_rename,[status(thm)],[f_3047_1]) ).
fof(f_3047_3,plain,
( ! [U_11568,U_11566,U_11564,U_11562] :
( ! [U_11560,U_11558] : hAPP(hAPP(c_Product__Type_OPair(U_11558,U_11560),U_11562),U_11564) = hAPP(hAPP(c_Product__Type_OPair(U_11558,U_11560),U_11566),U_11568)
| U_11564 != U_11568
| U_11562 != U_11566 )
& ! [U_11567,U_11565,U_11563,U_11561] :
( ! [U_11559,U_11557] : hAPP(hAPP(c_Product__Type_OPair(U_11557,U_11559),U_11561),U_11563) != hAPP(hAPP(c_Product__Type_OPair(U_11557,U_11559),U_11565),U_11567)
| ( U_11563 = U_11567
& U_11561 = U_11565 ) ) ),
inference(miniscope,[status(thm)],[f_3047_2]) ).
fof(f_3047_4,plain,
( ! [U_11565,U_11563,U_11561,U_11567] :
( U_11563 = U_11567
| ~ sP847(U_11565,U_11563,U_11561,U_11567) )
& ! [U_11565,U_11563,U_11561,U_11567] :
( U_11561 = U_11565
| ~ sP847(U_11565,U_11563,U_11561,U_11567) )
& ! [U_11562,U_11560,U_11564,U_11558,U_11566,U_11568] :
( hAPP(hAPP(c_Product__Type_OPair(U_11558,U_11560),U_11562),U_11564) = hAPP(hAPP(c_Product__Type_OPair(U_11558,U_11560),U_11566),U_11568)
| U_11564 != U_11568
| U_11562 != U_11566 )
& ! [U_11559,U_11565,U_11563,U_11557,U_11561,U_11567] :
( hAPP(hAPP(c_Product__Type_OPair(U_11557,U_11559),U_11561),U_11563) != hAPP(hAPP(c_Product__Type_OPair(U_11557,U_11559),U_11565),U_11567)
| sP847(U_11565,U_11563,U_11561,U_11567) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP847])],[f_3047_3]) ).
cnf(f_3047_5,plain,
( hAPP(hAPP(c_Product__Type_OPair(U_11557,U_11559),U_11561),U_11563) != hAPP(hAPP(c_Product__Type_OPair(U_11557,U_11559),U_11565),U_11567)
| sP847(U_11565,U_11563,U_11561,U_11567) ),
inference(clausify,[status(thm)],[f_3047_4]) ).
cnf(f_3047_6,plain,
( hAPP(hAPP(c_Product__Type_OPair(U_11558,U_11560),U_11562),U_11564) = hAPP(hAPP(c_Product__Type_OPair(U_11558,U_11560),U_11566),U_11568)
| U_11564 != U_11568
| U_11562 != U_11566 ),
inference(clausify,[status(thm)],[f_3047_4]) ).
cnf(f_3047_7,plain,
( U_11561 = U_11565
| ~ sP847(U_11565,U_11563,U_11561,U_11567) ),
inference(clausify,[status(thm)],[f_3047_4]) ).
cnf(f_3047_8,plain,
( U_11563 = U_11567
| ~ sP847(U_11565,U_11563,U_11561,U_11567) ),
inference(clausify,[status(thm)],[f_3047_4]) ).
fof(f_3048_1,plain,
! [T_d,T_c,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_c,T_d),B_a),B_b))) )
& ( ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_a),B_b)))
| ? [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
inference(fof_nnf,[status(thm)],[fact_split__paired__All]) ).
fof(f_3048_2,plain,
! [U_11577,U_11576,U_11575] :
( ( ! [U_11574] : hBOOL(hAPP(U_11575,U_11574))
| ? [U_11573,U_11572] : ~ hBOOL(hAPP(U_11575,hAPP(hAPP(c_Product__Type_OPair(U_11576,U_11577),U_11573),U_11572))) )
& ( ! [U_11571,U_11570] : hBOOL(hAPP(U_11575,hAPP(hAPP(c_Product__Type_OPair(U_11576,U_11577),U_11571),U_11570)))
| ? [U_11569] : ~ hBOOL(hAPP(U_11575,U_11569)) ) ),
inference(variable_rename,[status(thm)],[f_3048_1]) ).
fof(f_3048_3,plain,
( ! [U_11583,U_11581,U_11579] :
( ! [U_11574] : hBOOL(hAPP(U_11579,U_11574))
| ? [U_11573,U_11572] : ~ hBOOL(hAPP(U_11579,hAPP(hAPP(c_Product__Type_OPair(U_11581,U_11583),U_11573),U_11572))) )
& ! [U_11582,U_11580,U_11578] :
( ! [U_11571,U_11570] : hBOOL(hAPP(U_11578,hAPP(hAPP(c_Product__Type_OPair(U_11580,U_11582),U_11571),U_11570)))
| ? [U_11569] : ~ hBOOL(hAPP(U_11578,U_11569)) ) ),
inference(miniscope,[status(thm)],[f_3048_2]) ).
fof(f_3048_4,plain,
( ! [U_11583,U_11581,U_11579] :
( ! [U_11574] : hBOOL(hAPP(U_11579,U_11574))
| ? [U_11573,U_11572] : ~ hBOOL(hAPP(U_11579,hAPP(hAPP(c_Product__Type_OPair(U_11581,U_11583),U_11573),U_11572))) )
& ! [U_11582,U_11580,U_11578] :
( ! [U_11571,U_11570] : hBOOL(hAPP(U_11578,hAPP(hAPP(c_Product__Type_OPair(U_11580,U_11582),U_11571),U_11570)))
| ~ hBOOL(hAPP(U_11578,sK271(U_11582,U_11580,U_11578))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_11569,sK271(U_11582,U_11580,U_11578))],[f_3048_3]) ).
fof(f_3048_5,plain,
( ! [U_11583,U_11581,U_11579] :
( ! [U_11574] : hBOOL(hAPP(U_11579,U_11574))
| ? [U_11572] : ~ hBOOL(hAPP(U_11579,hAPP(hAPP(c_Product__Type_OPair(U_11581,U_11583),sK272(U_11583,U_11581,U_11579)),U_11572))) )
& ! [U_11582,U_11580,U_11578] :
( ! [U_11571,U_11570] : hBOOL(hAPP(U_11578,hAPP(hAPP(c_Product__Type_OPair(U_11580,U_11582),U_11571),U_11570)))
| ~ hBOOL(hAPP(U_11578,sK271(U_11582,U_11580,U_11578))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_11573,sK272(U_11583,U_11581,U_11579))],[f_3048_4]) ).
fof(f_3048_6,plain,
( ! [U_11583,U_11581,U_11579] :
( ! [U_11574] : hBOOL(hAPP(U_11579,U_11574))
| ~ hBOOL(hAPP(U_11579,hAPP(hAPP(c_Product__Type_OPair(U_11581,U_11583),sK272(U_11583,U_11581,U_11579)),sK273(U_11583,U_11581,U_11579)))) )
& ! [U_11582,U_11580,U_11578] :
( ! [U_11571,U_11570] : hBOOL(hAPP(U_11578,hAPP(hAPP(c_Product__Type_OPair(U_11580,U_11582),U_11571),U_11570)))
| ~ hBOOL(hAPP(U_11578,sK271(U_11582,U_11580,U_11578))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_11572,sK273(U_11583,U_11581,U_11579))],[f_3048_5]) ).
fof(f_3048_7,plain,
( ! [U_11574,U_11579,U_11581,U_11583] :
( hBOOL(hAPP(U_11579,U_11574))
| ~ hBOOL(hAPP(U_11579,hAPP(hAPP(c_Product__Type_OPair(U_11581,U_11583),sK272(U_11583,U_11581,U_11579)),sK273(U_11583,U_11581,U_11579)))) )
& ! [U_11571,U_11570,U_11580,U_11578,U_11582] :
( hBOOL(hAPP(U_11578,hAPP(hAPP(c_Product__Type_OPair(U_11580,U_11582),U_11571),U_11570)))
| ~ hBOOL(hAPP(U_11578,sK271(U_11582,U_11580,U_11578))) ) ),
inference(definitional_conversion,[status(esa)],[f_3048_6]) ).
cnf(f_3048_8,plain,
( hBOOL(hAPP(U_11578,hAPP(hAPP(c_Product__Type_OPair(U_11580,U_11582),U_11571),U_11570)))
| ~ hBOOL(hAPP(U_11578,sK271(U_11582,U_11580,U_11578))) ),
inference(clausify,[status(thm)],[f_3048_7]) ).
cnf(f_3048_9,plain,
( hBOOL(hAPP(U_11579,U_11574))
| ~ hBOOL(hAPP(U_11579,hAPP(hAPP(c_Product__Type_OPair(U_11581,U_11583),sK272(U_11583,U_11581,U_11579)),sK273(U_11583,U_11581,U_11579)))) ),
inference(clausify,[status(thm)],[f_3048_7]) ).
fof(f_3049_1,plain,
! [V_c_2,T_e,T_d,T_c,V_q_2,V_p_2] :
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),V_c_2),V_q_2)
| V_p_2 != V_q_2 ),
inference(fof_nnf,[status(thm)],[fact_split__weak__cong]) ).
fof(f_3049_2,plain,
! [U_11589,U_11588,U_11587,U_11586,U_11585,U_11584] :
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11586,U_11587,U_11588),U_11589),U_11584) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11586,U_11587,U_11588),U_11589),U_11585)
| U_11584 != U_11585 ),
inference(variable_rename,[status(thm)],[f_3049_1]) ).
fof(f_3049_3,plain,
! [U_11585,U_11586,U_11584,U_11587,U_11588,U_11589] :
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11586,U_11587,U_11588),U_11589),U_11584) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11586,U_11587,U_11588),U_11589),U_11585)
| U_11584 != U_11585 ),
inference(definitional_conversion,[status(esa)],[f_3049_2]) ).
cnf(f_3049_4,plain,
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11586,U_11587,U_11588),U_11589),U_11584) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11586,U_11587,U_11588),U_11589),U_11585)
| U_11584 != U_11585 ),
inference(clausify,[status(thm)],[f_3049_3]) ).
fof(f_3050_1,plain,
! [V_p_2,V_g_2,T_g,T_f,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_f,T_g,tc_prod(T_d,T_e)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_f,T_g,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(T_g,T_c),T_f),hAPP(c_COMBB(tc_prod(T_d,T_e),T_c,T_g),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2))),V_g_2)),V_p_2),
inference(fof_nnf,[status(thm)],[fact_split__twice]) ).
fof(f_3050_2,plain,
! [U_11597,U_11596,U_11595,U_11594,U_11593,U_11592,U_11591,U_11590] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11590,U_11591,U_11592),U_11593),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11594,U_11595,tc_prod(U_11590,U_11591)),U_11596),U_11597)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11594,U_11595,U_11592),hAPP(hAPP(c_COMBB(tc_fun(U_11595,tc_prod(U_11590,U_11591)),tc_fun(U_11595,U_11592),U_11594),hAPP(c_COMBB(tc_prod(U_11590,U_11591),U_11592,U_11595),hAPP(c_Product__Type_Oprod_Oprod__case(U_11590,U_11591,U_11592),U_11593))),U_11596)),U_11597),
inference(variable_rename,[status(thm)],[f_3050_1]) ).
fof(f_3050_3,plain,
! [U_11590,U_11591,U_11592,U_11593,U_11594,U_11595,U_11596,U_11597] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11590,U_11591,U_11592),U_11593),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11594,U_11595,tc_prod(U_11590,U_11591)),U_11596),U_11597)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11594,U_11595,U_11592),hAPP(hAPP(c_COMBB(tc_fun(U_11595,tc_prod(U_11590,U_11591)),tc_fun(U_11595,U_11592),U_11594),hAPP(c_COMBB(tc_prod(U_11590,U_11591),U_11592,U_11595),hAPP(c_Product__Type_Oprod_Oprod__case(U_11590,U_11591,U_11592),U_11593))),U_11596)),U_11597),
inference(definitional_conversion,[status(esa)],[f_3050_2]) ).
cnf(f_3050_4,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11590,U_11591,U_11592),U_11593),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11594,U_11595,tc_prod(U_11590,U_11591)),U_11596),U_11597)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11594,U_11595,U_11592),hAPP(hAPP(c_COMBB(tc_fun(U_11595,tc_prod(U_11590,U_11591)),tc_fun(U_11595,U_11592),U_11594),hAPP(c_COMBB(tc_prod(U_11590,U_11591),U_11592,U_11595),hAPP(c_Product__Type_Oprod_Oprod__case(U_11590,U_11591,U_11592),U_11593))),U_11596)),U_11597),
inference(clausify,[status(thm)],[f_3050_3]) ).
fof(f_3051_1,plain,
! [V_b_2,V_a_2,V_f_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),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_3051_2,plain,
! [U_11603,U_11602,U_11601,U_11600,U_11599,U_11598] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11598,U_11599,U_11600),U_11601),hAPP(hAPP(c_Product__Type_OPair(U_11598,U_11599),U_11602),U_11603)) = hAPP(hAPP(U_11601,U_11602),U_11603),
inference(variable_rename,[status(thm)],[f_3051_1]) ).
fof(f_3051_3,plain,
! [U_11600,U_11602,U_11601,U_11599,U_11598,U_11603] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11598,U_11599,U_11600),U_11601),hAPP(hAPP(c_Product__Type_OPair(U_11598,U_11599),U_11602),U_11603)) = hAPP(hAPP(U_11601,U_11602),U_11603),
inference(definitional_conversion,[status(esa)],[f_3051_2]) ).
cnf(f_3051_4,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11598,U_11599,U_11600),U_11601),hAPP(hAPP(c_Product__Type_OPair(U_11598,U_11599),U_11602),U_11603)) = hAPP(hAPP(U_11601,U_11602),U_11603),
inference(clausify,[status(thm)],[f_3051_3]) ).
fof(f_3052_1,plain,
! [V_b_2,V_a_2,V_f1_2,T_c,T_e,T_d] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_c),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),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_3052_2,plain,
! [U_11609,U_11608,U_11607,U_11606,U_11605,U_11604] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11604,U_11605,U_11606),U_11607),hAPP(hAPP(c_Product__Type_OPair(U_11604,U_11605),U_11608),U_11609)) = hAPP(hAPP(U_11607,U_11608),U_11609),
inference(variable_rename,[status(thm)],[f_3052_1]) ).
fof(f_3052_3,plain,
! [U_11604,U_11605,U_11606,U_11607,U_11608,U_11609] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11604,U_11605,U_11606),U_11607),hAPP(hAPP(c_Product__Type_OPair(U_11604,U_11605),U_11608),U_11609)) = hAPP(hAPP(U_11607,U_11608),U_11609),
inference(definitional_conversion,[status(esa)],[f_3052_2]) ).
cnf(f_3052_4,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11604,U_11605,U_11606),U_11607),hAPP(hAPP(c_Product__Type_OPair(U_11604,U_11605),U_11608),U_11609)) = hAPP(hAPP(U_11607,U_11608),U_11609),
inference(clausify,[status(thm)],[f_3052_3]) ).
fof(f_3053_1,plain,
! [V_b_2,V_a_2,V_f_2,T_d,T_c] :
( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))) ),
inference(fof_nnf,[status(thm)],[fact_splitD]) ).
fof(f_3053_2,plain,
! [U_11614,U_11613,U_11612,U_11611,U_11610] :
( hBOOL(hAPP(hAPP(U_11612,U_11613),U_11614))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11610,U_11611,tc_HOL_Obool),U_11612),hAPP(hAPP(c_Product__Type_OPair(U_11610,U_11611),U_11613),U_11614))) ),
inference(variable_rename,[status(thm)],[f_3053_1]) ).
fof(f_3053_3,plain,
! [U_11614,U_11613,U_11612] :
( ! [U_11611,U_11610] : ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11610,U_11611,tc_HOL_Obool),U_11612),hAPP(hAPP(c_Product__Type_OPair(U_11610,U_11611),U_11613),U_11614)))
| hBOOL(hAPP(hAPP(U_11612,U_11613),U_11614)) ),
inference(miniscope,[status(thm)],[f_3053_2]) ).
fof(f_3053_4,plain,
! [U_11610,U_11611,U_11612,U_11613,U_11614] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11610,U_11611,tc_HOL_Obool),U_11612),hAPP(hAPP(c_Product__Type_OPair(U_11610,U_11611),U_11613),U_11614)))
| hBOOL(hAPP(hAPP(U_11612,U_11613),U_11614)) ),
inference(definitional_conversion,[status(esa)],[f_3053_3]) ).
cnf(f_3053_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11610,U_11611,tc_HOL_Obool),U_11612),hAPP(hAPP(c_Product__Type_OPair(U_11610,U_11611),U_11613),U_11614)))
| hBOOL(hAPP(hAPP(U_11612,U_11613),U_11614)) ),
inference(clausify,[status(thm)],[f_3053_4]) ).
fof(f_3054_1,plain,
! [V_f_2,T_e,T_d,T_c] : hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_e),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_e),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_e,T_d),V_f_2)),c_Product__Type_OPair(T_c,T_d))) = V_f_2,
inference(fof_nnf,[status(thm)],[fact_split__eta]) ).
fof(f_3054_2,plain,
! [U_11618,U_11617,U_11616,U_11615] : hAPP(c_Product__Type_Oprod_Oprod__case(U_11615,U_11616,U_11617),hAPP(hAPP(c_COMBB(tc_fun(U_11616,tc_prod(U_11615,U_11616)),tc_fun(U_11616,U_11617),U_11615),hAPP(c_COMBB(tc_prod(U_11615,U_11616),U_11617,U_11616),U_11618)),c_Product__Type_OPair(U_11615,U_11616))) = U_11618,
inference(variable_rename,[status(thm)],[f_3054_1]) ).
fof(f_3054_3,plain,
! [U_11615,U_11616,U_11617,U_11618] : hAPP(c_Product__Type_Oprod_Oprod__case(U_11615,U_11616,U_11617),hAPP(hAPP(c_COMBB(tc_fun(U_11616,tc_prod(U_11615,U_11616)),tc_fun(U_11616,U_11617),U_11615),hAPP(c_COMBB(tc_prod(U_11615,U_11616),U_11617,U_11616),U_11618)),c_Product__Type_OPair(U_11615,U_11616))) = U_11618,
inference(definitional_conversion,[status(esa)],[f_3054_2]) ).
cnf(f_3054_4,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(U_11615,U_11616,U_11617),hAPP(hAPP(c_COMBB(tc_fun(U_11616,tc_prod(U_11615,U_11616)),tc_fun(U_11616,U_11617),U_11615),hAPP(c_COMBB(tc_prod(U_11615,U_11616),U_11617,U_11616),U_11618)),c_Product__Type_OPair(U_11615,U_11616))) = U_11618,
inference(clausify,[status(thm)],[f_3054_3]) ).
fof(f_3055_1,plain,
! [V_y_2,V_x_2,T_d,T_c] : c_HOL_OThe(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_c),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_d)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2),
inference(fof_nnf,[status(thm)],[fact_The__split__eq]) ).
fof(f_3055_2,plain,
! [U_11622,U_11621,U_11620,U_11619] : c_HOL_OThe(tc_prod(U_11619,U_11620),hAPP(c_Product__Type_Oprod_Oprod__case(U_11619,U_11620,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11619,tc_fun(U_11620,tc_HOL_Obool),tc_fun(U_11620,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11620,tc_HOL_Obool),tc_fun(U_11620,tc_HOL_Obool)),U_11619),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11620)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11619),c_fconj),hAPP(c_fequal,U_11621)))),hAPP(c_fequal,U_11622)))) = hAPP(hAPP(c_Product__Type_OPair(U_11619,U_11620),U_11621),U_11622),
inference(variable_rename,[status(thm)],[f_3055_1]) ).
fof(f_3055_3,plain,
! [U_11619,U_11620,U_11621,U_11622] : c_HOL_OThe(tc_prod(U_11619,U_11620),hAPP(c_Product__Type_Oprod_Oprod__case(U_11619,U_11620,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11619,tc_fun(U_11620,tc_HOL_Obool),tc_fun(U_11620,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11620,tc_HOL_Obool),tc_fun(U_11620,tc_HOL_Obool)),U_11619),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11620)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11619),c_fconj),hAPP(c_fequal,U_11621)))),hAPP(c_fequal,U_11622)))) = hAPP(hAPP(c_Product__Type_OPair(U_11619,U_11620),U_11621),U_11622),
inference(definitional_conversion,[status(esa)],[f_3055_2]) ).
cnf(f_3055_4,plain,
c_HOL_OThe(tc_prod(U_11619,U_11620),hAPP(c_Product__Type_Oprod_Oprod__case(U_11619,U_11620,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11619,tc_fun(U_11620,tc_HOL_Obool),tc_fun(U_11620,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11620,tc_HOL_Obool),tc_fun(U_11620,tc_HOL_Obool)),U_11619),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11620)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11619),c_fconj),hAPP(c_fequal,U_11621)))),hAPP(c_fequal,U_11622)))) = hAPP(hAPP(c_Product__Type_OPair(U_11619,U_11620),U_11621),U_11622),
inference(clausify,[status(thm)],[f_3055_3]) ).
fof(f_3056_1,plain,
! [V_Pa_2,T_d,T_c] : c_HOL_OThe(tc_prod(T_c,T_d),V_Pa_2) = c_HOL_OThe(tc_prod(T_c,T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_HOL_Obool),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_HOL_Obool,T_d),V_Pa_2)),c_Product__Type_OPair(T_c,T_d)))),
inference(fof_nnf,[status(thm)],[fact_split__paired__The]) ).
fof(f_3056_2,plain,
! [U_11625,U_11624,U_11623] : c_HOL_OThe(tc_prod(U_11623,U_11624),U_11625) = c_HOL_OThe(tc_prod(U_11623,U_11624),hAPP(c_Product__Type_Oprod_Oprod__case(U_11623,U_11624,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_11624,tc_prod(U_11623,U_11624)),tc_fun(U_11624,tc_HOL_Obool),U_11623),hAPP(c_COMBB(tc_prod(U_11623,U_11624),tc_HOL_Obool,U_11624),U_11625)),c_Product__Type_OPair(U_11623,U_11624)))),
inference(variable_rename,[status(thm)],[f_3056_1]) ).
fof(f_3056_3,plain,
! [U_11623,U_11624,U_11625] : c_HOL_OThe(tc_prod(U_11623,U_11624),U_11625) = c_HOL_OThe(tc_prod(U_11623,U_11624),hAPP(c_Product__Type_Oprod_Oprod__case(U_11623,U_11624,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_11624,tc_prod(U_11623,U_11624)),tc_fun(U_11624,tc_HOL_Obool),U_11623),hAPP(c_COMBB(tc_prod(U_11623,U_11624),tc_HOL_Obool,U_11624),U_11625)),c_Product__Type_OPair(U_11623,U_11624)))),
inference(definitional_conversion,[status(esa)],[f_3056_2]) ).
cnf(f_3056_4,plain,
c_HOL_OThe(tc_prod(U_11623,U_11624),U_11625) = c_HOL_OThe(tc_prod(U_11623,U_11624),hAPP(c_Product__Type_Oprod_Oprod__case(U_11623,U_11624,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_11624,tc_prod(U_11623,U_11624)),tc_fun(U_11624,tc_HOL_Obool),U_11623),hAPP(c_COMBB(tc_prod(U_11623,U_11624),tc_HOL_Obool,U_11624),U_11625)),c_Product__Type_OPair(U_11623,U_11624)))),
inference(clausify,[status(thm)],[f_3056_3]) ).
fof(f_3057_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_3057_2,plain,
! [U_11626] : c_Divides_Oadjust(U_11626) = 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_11626))))),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_11626))))),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_3057_1]) ).
fof(f_3057_3,plain,
! [U_11626] : c_Divides_Oadjust(U_11626) = 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_11626))))),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_11626))))),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_3057_2]) ).
cnf(f_3057_4,plain,
c_Divides_Oadjust(U_11626) = 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_11626))))),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_11626))))),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_3057_3]) ).
fof(f_3058_1,plain,
! [V_y_2,V_x_2,V_R_2,T_d,T_c] :
( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(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)),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)),V_R_2))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_c,T_d,V_R_2),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_in__rel__def]) ).
fof(f_3058_2,plain,
! [U_11631,U_11630,U_11629,U_11628,U_11627] :
( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_11627,U_11628,U_11629),U_11630),U_11631))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11627,U_11628)),hAPP(hAPP(c_Product__Type_OPair(U_11627,U_11628),U_11630),U_11631)),U_11629)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11627,U_11628)),hAPP(hAPP(c_Product__Type_OPair(U_11627,U_11628),U_11630),U_11631)),U_11629))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_11627,U_11628,U_11629),U_11630),U_11631)) ) ),
inference(variable_rename,[status(thm)],[f_3058_1]) ).
fof(f_3058_3,plain,
( ! [U_11641,U_11639,U_11637,U_11635,U_11633] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_11633,U_11635,U_11637),U_11639),U_11641))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11633,U_11635)),hAPP(hAPP(c_Product__Type_OPair(U_11633,U_11635),U_11639),U_11641)),U_11637)) )
& ! [U_11640,U_11638,U_11636,U_11634,U_11632] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11632,U_11634)),hAPP(hAPP(c_Product__Type_OPair(U_11632,U_11634),U_11638),U_11640)),U_11636))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_11632,U_11634,U_11636),U_11638),U_11640)) ) ),
inference(miniscope,[status(thm)],[f_3058_2]) ).
fof(f_3058_4,plain,
( ! [U_11633,U_11635,U_11637,U_11639,U_11641] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_11633,U_11635,U_11637),U_11639),U_11641))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11633,U_11635)),hAPP(hAPP(c_Product__Type_OPair(U_11633,U_11635),U_11639),U_11641)),U_11637)) )
& ! [U_11634,U_11638,U_11632,U_11636,U_11640] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11632,U_11634)),hAPP(hAPP(c_Product__Type_OPair(U_11632,U_11634),U_11638),U_11640)),U_11636))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_11632,U_11634,U_11636),U_11638),U_11640)) ) ),
inference(definitional_conversion,[status(esa)],[f_3058_3]) ).
cnf(f_3058_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11632,U_11634)),hAPP(hAPP(c_Product__Type_OPair(U_11632,U_11634),U_11638),U_11640)),U_11636))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_11632,U_11634,U_11636),U_11638),U_11640)) ),
inference(clausify,[status(thm)],[f_3058_4]) ).
cnf(f_3058_6,plain,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_11633,U_11635,U_11637),U_11639),U_11641))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11633,U_11635)),hAPP(hAPP(c_Product__Type_OPair(U_11633,U_11635),U_11639),U_11641)),U_11637)) ),
inference(clausify,[status(thm)],[f_3058_4]) ).
fof(f_3059_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_3059_2,plain,
! [U_11643,U_11642] : c_Code__Numeral_Odiv__mod__code__numeral(U_11642,U_11643) = 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_11642),U_11643)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_11642,U_11643)),
inference(variable_rename,[status(thm)],[f_3059_1]) ).
fof(f_3059_3,plain,
! [U_11643,U_11642] : c_Code__Numeral_Odiv__mod__code__numeral(U_11642,U_11643) = 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_11642),U_11643)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_11642,U_11643)),
inference(definitional_conversion,[status(esa)],[f_3059_2]) ).
cnf(f_3059_4,plain,
c_Code__Numeral_Odiv__mod__code__numeral(U_11642,U_11643) = 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_11642),U_11643)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_11642,U_11643)),
inference(clausify,[status(thm)],[f_3059_3]) ).
fof(f_3060_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_3060_2,plain,
! [U_11644] :
( ( ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11644)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11644)),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_11644))))
| 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_11644)))) )
& ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11644)) = 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_11644)))
| ~ 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_11644)))) ) )
| ~ 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_11644))) ),
inference(variable_rename,[status(thm)],[f_3060_1]) ).
fof(f_3060_3,plain,
( ! [U_11644] :
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11644)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11644)),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_11644))))
| 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_11644))))
| ~ sP848(U_11644) )
& ! [U_11644] :
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11644)) = 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_11644)))
| ~ 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_11644))))
| ~ sP848(U_11644) )
& ! [U_11644] :
( sP848(U_11644)
| ~ 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_11644))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP848])],[f_3060_2]) ).
cnf(f_3060_4,plain,
( sP848(U_11644)
| ~ 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_11644))) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_5,plain,
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11644)) = 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_11644)))
| ~ 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_11644))))
| ~ sP848(U_11644) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
cnf(f_3060_6,plain,
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11644)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11644)),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_11644))))
| 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_11644))))
| ~ sP848(U_11644) ),
inference(clausify,[status(thm)],[f_3060_3]) ).
fof(f_3061_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_3061_2,plain,
! [U_11646,U_11645] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11645,U_11646),c_Divides_OnegDivAlg(U_11645,U_11646)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11646))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11645),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_3061_1]) ).
fof(f_3061_3,plain,
! [U_11645,U_11646] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11645,U_11646),c_Divides_OnegDivAlg(U_11645,U_11646)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11646))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11645),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_3061_2]) ).
cnf(f_3061_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11645,U_11646),c_Divides_OnegDivAlg(U_11645,U_11646)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11646))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11645),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3061_3]) ).
fof(f_3062_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_3062_2,plain,
! [U_11648,U_11647] :
( c_Divides_OnegDivAlg(U_11647,U_11648) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11647),U_11648)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11647,U_11648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11647),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_3062_1]) ).
fof(f_3062_3,plain,
! [U_11647,U_11648] :
( c_Divides_OnegDivAlg(U_11647,U_11648) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11647),U_11648)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11647,U_11648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11647),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_3062_2]) ).
cnf(f_3062_4,plain,
( c_Divides_OnegDivAlg(U_11647,U_11648) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11647),U_11648)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11647,U_11648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11647),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3062_3]) ).
fof(f_3063_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_3063_2,plain,
! [U_11649] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_11649) = 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_11649),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_3063_1]) ).
fof(f_3063_3,plain,
! [U_11649] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_11649) = 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_11649),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(definitional_conversion,[status(esa)],[f_3063_2]) ).
cnf(f_3063_4,plain,
c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_11649) = 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_11649),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_3063_3]) ).
fof(f_3064_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_3064_2,plain,
! [U_11651,U_11650] :
( ( c_Divides_OnegDivAlg(U_11650,U_11651) = hAPP(c_Divides_Oadjust(U_11651),c_Divides_OnegDivAlg(U_11650,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_11651)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11651),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_11650),U_11651))) )
& ( c_Divides_OnegDivAlg(U_11650,U_11651) = 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_11650),U_11651))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11651),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_11650),U_11651))) ) ) ),
inference(variable_rename,[status(thm)],[f_3064_1]) ).
fof(f_3064_3,plain,
( ! [U_11655,U_11653] :
( c_Divides_OnegDivAlg(U_11653,U_11655) = hAPP(c_Divides_Oadjust(U_11655),c_Divides_OnegDivAlg(U_11653,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_11655)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11655),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_11653),U_11655))) )
& ! [U_11654,U_11652] :
( c_Divides_OnegDivAlg(U_11652,U_11654) = 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_11652),U_11654))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11654),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_11652),U_11654))) ) ) ),
inference(miniscope,[status(thm)],[f_3064_2]) ).
fof(f_3064_4,plain,
( ! [U_11654,U_11652] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11654),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP849(U_11654,U_11652) )
& ! [U_11654,U_11652] :
( ~ 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_11652),U_11654)))
| ~ sP849(U_11654,U_11652) )
& ! [U_11655,U_11653] :
( c_Divides_OnegDivAlg(U_11653,U_11655) = hAPP(c_Divides_Oadjust(U_11655),c_Divides_OnegDivAlg(U_11653,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_11655)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11655),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_11653),U_11655))) )
& ! [U_11654,U_11652] :
( c_Divides_OnegDivAlg(U_11652,U_11654) = 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_11652),U_11654))
| sP849(U_11654,U_11652) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP849])],[f_3064_3]) ).
cnf(f_3064_5,plain,
( c_Divides_OnegDivAlg(U_11652,U_11654) = 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_11652),U_11654))
| sP849(U_11654,U_11652) ),
inference(clausify,[status(thm)],[f_3064_4]) ).
cnf(f_3064_6,plain,
( c_Divides_OnegDivAlg(U_11653,U_11655) = hAPP(c_Divides_Oadjust(U_11655),c_Divides_OnegDivAlg(U_11653,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_11655)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11655),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_11653),U_11655))) ),
inference(clausify,[status(thm)],[f_3064_4]) ).
cnf(f_3064_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_11652),U_11654)))
| ~ sP849(U_11654,U_11652) ),
inference(clausify,[status(thm)],[f_3064_4]) ).
cnf(f_3064_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11654),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP849(U_11654,U_11652) ),
inference(clausify,[status(thm)],[f_3064_4]) ).
fof(f_3065_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_3065_2,plain,
! [U_11657,U_11656] :
( ( ( c_Divides_OnegDivAlg(U_11657,U_11656) = hAPP(c_Divides_Oadjust(U_11656),c_Divides_OnegDivAlg(U_11657,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_11656)))
| 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_11657),U_11656))) )
& ( c_Divides_OnegDivAlg(U_11657,U_11656) = 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_11657),U_11656))
| ~ 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_11657),U_11656))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11656)) ),
inference(variable_rename,[status(thm)],[f_3065_1]) ).
fof(f_3065_3,plain,
( ! [U_11656,U_11657] :
( c_Divides_OnegDivAlg(U_11657,U_11656) = hAPP(c_Divides_Oadjust(U_11656),c_Divides_OnegDivAlg(U_11657,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_11656)))
| 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_11657),U_11656)))
| ~ sP850(U_11656,U_11657) )
& ! [U_11656,U_11657] :
( c_Divides_OnegDivAlg(U_11657,U_11656) = 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_11657),U_11656))
| ~ 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_11657),U_11656)))
| ~ sP850(U_11656,U_11657) )
& ! [U_11656,U_11657] :
( sP850(U_11656,U_11657)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11656)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP850])],[f_3065_2]) ).
cnf(f_3065_4,plain,
( sP850(U_11656,U_11657)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11656)) ),
inference(clausify,[status(thm)],[f_3065_3]) ).
cnf(f_3065_5,plain,
( c_Divides_OnegDivAlg(U_11657,U_11656) = 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_11657),U_11656))
| ~ 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_11657),U_11656)))
| ~ sP850(U_11656,U_11657) ),
inference(clausify,[status(thm)],[f_3065_3]) ).
cnf(f_3065_6,plain,
( c_Divides_OnegDivAlg(U_11657,U_11656) = hAPP(c_Divides_Oadjust(U_11656),c_Divides_OnegDivAlg(U_11657,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_11656)))
| 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_11657),U_11656)))
| ~ sP850(U_11656,U_11657) ),
inference(clausify,[status(thm)],[f_3065_3]) ).
fof(f_3066_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_3066_2,plain,
! [U_11659,U_11658] :
( ( ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11659),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_11658))))
| 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_11659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)))) )
& ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)) = 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_11659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)))
| ~ 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_11659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)))) ) )
| ~ 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_11658))) ),
inference(variable_rename,[status(thm)],[f_3066_1]) ).
fof(f_3066_3,plain,
( ! [U_11659,U_11658] :
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11659),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_11658))))
| 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_11659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658))))
| ~ sP851(U_11659,U_11658) )
& ! [U_11659,U_11658] :
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)) = 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_11659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)))
| ~ 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_11659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658))))
| ~ sP851(U_11659,U_11658) )
& ! [U_11659,U_11658] :
( sP851(U_11659,U_11658)
| ~ 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_11658))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP851])],[f_3066_2]) ).
cnf(f_3066_4,plain,
( sP851(U_11659,U_11658)
| ~ 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_11658))) ),
inference(clausify,[status(thm)],[f_3066_3]) ).
cnf(f_3066_5,plain,
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)) = 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_11659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)))
| ~ 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_11659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658))))
| ~ sP851(U_11659,U_11658) ),
inference(clausify,[status(thm)],[f_3066_3]) ).
cnf(f_3066_6,plain,
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11659),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_11658))))
| 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_11659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11658))))
| ~ sP851(U_11659,U_11658) ),
inference(clausify,[status(thm)],[f_3066_3]) ).
fof(f_3067_1,plain,
! [V_r_2,T_c] :
( ( c_Nitpick_Orefl_H(T_c,V_r_2)
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) )
& ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2))
| ~ c_Nitpick_Orefl_H(T_c,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def]) ).
fof(f_3067_2,plain,
! [U_11663,U_11662] :
( ( c_Nitpick_Orefl_H(U_11662,U_11663)
| ? [U_11661] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11662,U_11662)),hAPP(hAPP(c_Product__Type_OPair(U_11662,U_11662),U_11661),U_11661)),U_11663)) )
& ( ! [U_11660] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11662,U_11662)),hAPP(hAPP(c_Product__Type_OPair(U_11662,U_11662),U_11660),U_11660)),U_11663))
| ~ c_Nitpick_Orefl_H(U_11662,U_11663) ) ),
inference(variable_rename,[status(thm)],[f_3067_1]) ).
fof(f_3067_3,plain,
( ! [U_11667,U_11665] :
( c_Nitpick_Orefl_H(U_11665,U_11667)
| ? [U_11661] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11665,U_11665)),hAPP(hAPP(c_Product__Type_OPair(U_11665,U_11665),U_11661),U_11661)),U_11667)) )
& ! [U_11666,U_11664] :
( ! [U_11660] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11664,U_11664)),hAPP(hAPP(c_Product__Type_OPair(U_11664,U_11664),U_11660),U_11660)),U_11666))
| ~ c_Nitpick_Orefl_H(U_11664,U_11666) ) ),
inference(miniscope,[status(thm)],[f_3067_2]) ).
fof(f_3067_4,plain,
( ! [U_11667,U_11665] :
( c_Nitpick_Orefl_H(U_11665,U_11667)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11665,U_11665)),hAPP(hAPP(c_Product__Type_OPair(U_11665,U_11665),sK274(U_11667,U_11665)),sK274(U_11667,U_11665))),U_11667)) )
& ! [U_11666,U_11664] :
( ! [U_11660] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11664,U_11664)),hAPP(hAPP(c_Product__Type_OPair(U_11664,U_11664),U_11660),U_11660)),U_11666))
| ~ c_Nitpick_Orefl_H(U_11664,U_11666) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_11661,sK274(U_11667,U_11665))],[f_3067_3]) ).
fof(f_3067_5,plain,
( ! [U_11667,U_11665] :
( c_Nitpick_Orefl_H(U_11665,U_11667)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11665,U_11665)),hAPP(hAPP(c_Product__Type_OPair(U_11665,U_11665),sK274(U_11667,U_11665)),sK274(U_11667,U_11665))),U_11667)) )
& ! [U_11660,U_11666,U_11664] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11664,U_11664)),hAPP(hAPP(c_Product__Type_OPair(U_11664,U_11664),U_11660),U_11660)),U_11666))
| ~ c_Nitpick_Orefl_H(U_11664,U_11666) ) ),
inference(definitional_conversion,[status(esa)],[f_3067_4]) ).
cnf(f_3067_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11664,U_11664)),hAPP(hAPP(c_Product__Type_OPair(U_11664,U_11664),U_11660),U_11660)),U_11666))
| ~ c_Nitpick_Orefl_H(U_11664,U_11666) ),
inference(clausify,[status(thm)],[f_3067_5]) ).
cnf(f_3067_7,plain,
( c_Nitpick_Orefl_H(U_11665,U_11667)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11665,U_11665)),hAPP(hAPP(c_Product__Type_OPair(U_11665,U_11665),sK274(U_11667,U_11665)),sK274(U_11667,U_11665))),U_11667)) ),
inference(clausify,[status(thm)],[f_3067_5]) ).
fof(f_3068_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_3068_2,plain,
! [U_11668] :
( ( ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11668)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11668)),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_11668))))
| 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_11668))) )
& ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11668)) = 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_11668))) ) )
| ~ 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_11668))) ),
inference(variable_rename,[status(thm)],[f_3068_1]) ).
fof(f_3068_3,plain,
( ! [U_11668] :
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11668)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11668)),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_11668))))
| 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_11668)))
| ~ sP852(U_11668) )
& ! [U_11668] :
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11668)) = 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_11668)))
| ~ sP852(U_11668) )
& ! [U_11668] :
( sP852(U_11668)
| ~ 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_11668))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP852])],[f_3068_2]) ).
cnf(f_3068_4,plain,
( sP852(U_11668)
| ~ 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_11668))) ),
inference(clausify,[status(thm)],[f_3068_3]) ).
cnf(f_3068_5,plain,
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11668)) = 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_11668)))
| ~ sP852(U_11668) ),
inference(clausify,[status(thm)],[f_3068_3]) ).
cnf(f_3068_6,plain,
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11668)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11668)),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_11668))))
| 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_11668)))
| ~ sP852(U_11668) ),
inference(clausify,[status(thm)],[f_3068_3]) ).
fof(f_3069_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_3069_2,plain,
! [U_11670,U_11669] :
( ( c_Divides_OposDivAlg(U_11669,U_11670) = hAPP(c_Divides_Oadjust(U_11670),c_Divides_OposDivAlg(U_11669,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_11670)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11670),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11669),U_11670)) )
& ( c_Divides_OposDivAlg(U_11669,U_11670) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11669)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11670),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11669),U_11670)) ) ) ),
inference(variable_rename,[status(thm)],[f_3069_1]) ).
fof(f_3069_3,plain,
( ! [U_11674,U_11672] :
( c_Divides_OposDivAlg(U_11672,U_11674) = hAPP(c_Divides_Oadjust(U_11674),c_Divides_OposDivAlg(U_11672,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_11674)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11674),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11672),U_11674)) )
& ! [U_11673,U_11671] :
( c_Divides_OposDivAlg(U_11671,U_11673) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11671)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11673),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11671),U_11673)) ) ) ),
inference(miniscope,[status(thm)],[f_3069_2]) ).
fof(f_3069_4,plain,
( ! [U_11671,U_11673] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11673),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP853(U_11671,U_11673) )
& ! [U_11671,U_11673] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11671),U_11673))
| ~ sP853(U_11671,U_11673) )
& ! [U_11672,U_11674] :
( c_Divides_OposDivAlg(U_11672,U_11674) = hAPP(c_Divides_Oadjust(U_11674),c_Divides_OposDivAlg(U_11672,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_11674)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11674),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11672),U_11674)) )
& ! [U_11671,U_11673] :
( c_Divides_OposDivAlg(U_11671,U_11673) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11671)
| sP853(U_11671,U_11673) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP853])],[f_3069_3]) ).
cnf(f_3069_5,plain,
( c_Divides_OposDivAlg(U_11671,U_11673) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11671)
| sP853(U_11671,U_11673) ),
inference(clausify,[status(thm)],[f_3069_4]) ).
cnf(f_3069_6,plain,
( c_Divides_OposDivAlg(U_11672,U_11674) = hAPP(c_Divides_Oadjust(U_11674),c_Divides_OposDivAlg(U_11672,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_11674)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11674),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11672),U_11674)) ),
inference(clausify,[status(thm)],[f_3069_4]) ).
cnf(f_3069_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11671),U_11673))
| ~ sP853(U_11671,U_11673) ),
inference(clausify,[status(thm)],[f_3069_4]) ).
cnf(f_3069_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11673),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP853(U_11671,U_11673) ),
inference(clausify,[status(thm)],[f_3069_4]) ).
fof(f_3070_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_3070_2,plain,
! [U_11675] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_11675) = 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_3070_1]) ).
fof(f_3070_3,plain,
! [U_11675] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_11675) = 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_3070_2]) ).
cnf(f_3070_4,plain,
c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_11675) = 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_3070_3]) ).
fof(f_3071_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_3071_2,plain,
! [U_11677,U_11676] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11676,U_11677),c_Divides_OposDivAlg(U_11676,U_11677)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11677))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11676)) ),
inference(variable_rename,[status(thm)],[f_3071_1]) ).
fof(f_3071_3,plain,
! [U_11676,U_11677] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11676,U_11677),c_Divides_OposDivAlg(U_11676,U_11677)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11677))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11676)) ),
inference(definitional_conversion,[status(esa)],[f_3071_2]) ).
cnf(f_3071_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11676,U_11677),c_Divides_OposDivAlg(U_11676,U_11677)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11677))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11676)) ),
inference(clausify,[status(thm)],[f_3071_3]) ).
fof(f_3072_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_3072_2,plain,
! [U_11679,U_11678] :
( c_Divides_OposDivAlg(U_11678,U_11679) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11678),U_11679)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11678,U_11679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11678)) ),
inference(variable_rename,[status(thm)],[f_3072_1]) ).
fof(f_3072_3,plain,
! [U_11678,U_11679] :
( c_Divides_OposDivAlg(U_11678,U_11679) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11678),U_11679)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11678,U_11679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11678)) ),
inference(definitional_conversion,[status(esa)],[f_3072_2]) ).
cnf(f_3072_4,plain,
( c_Divides_OposDivAlg(U_11678,U_11679) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11678),U_11679)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11678,U_11679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11678)) ),
inference(clausify,[status(thm)],[f_3072_3]) ).
fof(f_3073_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_3073_2,plain,
! [U_11681,U_11680] :
( ( ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681),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_11680))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680))) )
& ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)) = 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_11681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680))) ) )
| ~ 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_11680))) ),
inference(variable_rename,[status(thm)],[f_3073_1]) ).
fof(f_3073_3,plain,
( ! [U_11681,U_11680] :
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681),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_11680))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)))
| ~ sP854(U_11681,U_11680) )
& ! [U_11681,U_11680] :
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)) = 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_11681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)))
| ~ sP854(U_11681,U_11680) )
& ! [U_11681,U_11680] :
( sP854(U_11681,U_11680)
| ~ 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_11680))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP854])],[f_3073_2]) ).
cnf(f_3073_4,plain,
( sP854(U_11681,U_11680)
| ~ 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_11680))) ),
inference(clausify,[status(thm)],[f_3073_3]) ).
cnf(f_3073_5,plain,
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)) = 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_11681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)))
| ~ sP854(U_11681,U_11680) ),
inference(clausify,[status(thm)],[f_3073_3]) ).
cnf(f_3073_6,plain,
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681),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_11680))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11681)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11680)))
| ~ sP854(U_11681,U_11680) ),
inference(clausify,[status(thm)],[f_3073_3]) ).
fof(f_3074_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_3074_2,plain,
! [U_11683,U_11682] :
( ( ( c_Divides_OposDivAlg(U_11683,U_11682) = hAPP(c_Divides_Oadjust(U_11682),c_Divides_OposDivAlg(U_11683,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_11682)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11683),U_11682)) )
& ( c_Divides_OposDivAlg(U_11683,U_11682) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11683)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11683),U_11682)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11682)) ),
inference(variable_rename,[status(thm)],[f_3074_1]) ).
fof(f_3074_3,plain,
( ! [U_11682,U_11683] :
( c_Divides_OposDivAlg(U_11683,U_11682) = hAPP(c_Divides_Oadjust(U_11682),c_Divides_OposDivAlg(U_11683,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_11682)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11683),U_11682))
| ~ sP855(U_11682,U_11683) )
& ! [U_11682,U_11683] :
( c_Divides_OposDivAlg(U_11683,U_11682) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11683)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11683),U_11682))
| ~ sP855(U_11682,U_11683) )
& ! [U_11682,U_11683] :
( sP855(U_11682,U_11683)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11682)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP855])],[f_3074_2]) ).
cnf(f_3074_4,plain,
( sP855(U_11682,U_11683)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11682)) ),
inference(clausify,[status(thm)],[f_3074_3]) ).
cnf(f_3074_5,plain,
( c_Divides_OposDivAlg(U_11683,U_11682) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11683)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11683),U_11682))
| ~ sP855(U_11682,U_11683) ),
inference(clausify,[status(thm)],[f_3074_3]) ).
cnf(f_3074_6,plain,
( c_Divides_OposDivAlg(U_11683,U_11682) = hAPP(c_Divides_Oadjust(U_11682),c_Divides_OposDivAlg(U_11683,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_11682)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11683),U_11682))
| ~ sP855(U_11682,U_11683) ),
inference(clausify,[status(thm)],[f_3074_3]) ).
fof(f_3075_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_3075_2,plain,
! [U_11685,U_11684] :
( ( ( ( c_Divides_Odivmod__int(U_11684,U_11685) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11684),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11685)) )
& ( c_Divides_Odivmod__int(U_11684,U_11685) = c_Divides_OnegDivAlg(U_11684,U_11685)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11685)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11684)) )
& ( ( ( ( ( c_Divides_Odivmod__int(U_11684,U_11685) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11684),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11685)))
| U_11684 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11684,U_11685) = 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_11684 != 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_11685)) )
& ( c_Divides_Odivmod__int(U_11684,U_11685) = c_Divides_OposDivAlg(U_11684,U_11685)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11685)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11684)) ) ),
inference(variable_rename,[status(thm)],[f_3075_1]) ).
fof(f_3075_3,plain,
( ! [U_11689,U_11687] :
( ( ( c_Divides_Odivmod__int(U_11687,U_11689) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11687),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11689)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11689)) )
& ( c_Divides_Odivmod__int(U_11687,U_11689) = c_Divides_OnegDivAlg(U_11687,U_11689)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11689)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11687)) )
& ! [U_11688,U_11686] :
( ( ( ( ( c_Divides_Odivmod__int(U_11686,U_11688) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11686),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11688)))
| U_11686 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11686,U_11688) = 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_11686 != 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_11688)) )
& ( c_Divides_Odivmod__int(U_11686,U_11688) = c_Divides_OposDivAlg(U_11686,U_11688)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11688)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11686)) ) ),
inference(miniscope,[status(thm)],[f_3075_2]) ).
fof(f_3075_4,plain,
( ! [U_11689,U_11687] :
( c_Divides_Odivmod__int(U_11687,U_11689) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11687),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11689)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11689))
| ~ sP858(U_11689,U_11687) )
& ! [U_11689,U_11687] :
( c_Divides_Odivmod__int(U_11687,U_11689) = c_Divides_OnegDivAlg(U_11687,U_11689)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11689))
| ~ sP858(U_11689,U_11687) )
& ! [U_11686,U_11688] :
( c_Divides_Odivmod__int(U_11686,U_11688) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11686),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11688)))
| U_11686 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP856(U_11686,U_11688) )
& ! [U_11686,U_11688] :
( c_Divides_Odivmod__int(U_11686,U_11688) = 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_11686 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP856(U_11686,U_11688) )
& ! [U_11686,U_11688] :
( sP856(U_11686,U_11688)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11688))
| ~ sP857(U_11686,U_11688) )
& ! [U_11686,U_11688] :
( c_Divides_Odivmod__int(U_11686,U_11688) = c_Divides_OposDivAlg(U_11686,U_11688)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11688))
| ~ sP857(U_11686,U_11688) )
& ! [U_11689,U_11687] :
( sP858(U_11689,U_11687)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11687)) )
& ! [U_11686,U_11688] :
( sP857(U_11686,U_11688)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11686)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP856,sP857,sP858])],[f_3075_3]) ).
cnf(f_3075_5,plain,
( sP857(U_11686,U_11688)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11686)) ),
inference(clausify,[status(thm)],[f_3075_4]) ).
cnf(f_3075_6,plain,
( sP858(U_11689,U_11687)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11687)) ),
inference(clausify,[status(thm)],[f_3075_4]) ).
cnf(f_3075_7,plain,
( c_Divides_Odivmod__int(U_11686,U_11688) = c_Divides_OposDivAlg(U_11686,U_11688)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11688))
| ~ sP857(U_11686,U_11688) ),
inference(clausify,[status(thm)],[f_3075_4]) ).
cnf(f_3075_8,plain,
( sP856(U_11686,U_11688)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11688))
| ~ sP857(U_11686,U_11688) ),
inference(clausify,[status(thm)],[f_3075_4]) ).
cnf(f_3075_9,plain,
( c_Divides_Odivmod__int(U_11686,U_11688) = 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_11686 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP856(U_11686,U_11688) ),
inference(clausify,[status(thm)],[f_3075_4]) ).
cnf(f_3075_10,plain,
( c_Divides_Odivmod__int(U_11686,U_11688) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11686),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11688)))
| U_11686 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP856(U_11686,U_11688) ),
inference(clausify,[status(thm)],[f_3075_4]) ).
cnf(f_3075_11,plain,
( c_Divides_Odivmod__int(U_11687,U_11689) = c_Divides_OnegDivAlg(U_11687,U_11689)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11689))
| ~ sP858(U_11689,U_11687) ),
inference(clausify,[status(thm)],[f_3075_4]) ).
cnf(f_3075_12,plain,
( c_Divides_Odivmod__int(U_11687,U_11689) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11687),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11689)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11689))
| ~ sP858(U_11689,U_11687) ),
inference(clausify,[status(thm)],[f_3075_4]) ).
fof(f_3076_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_3076_2,plain,
! [U_11691,U_11690] :
( c_Divides_Odivmod__nat(U_11691,U_11690) = 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_11691),U_11690)),U_11690))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11691),U_11690),U_11690))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11690),U_11691))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11690)) ),
inference(variable_rename,[status(thm)],[f_3076_1]) ).
fof(f_3076_3,plain,
! [U_11691,U_11690] :
( c_Divides_Odivmod__nat(U_11691,U_11690) = 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_11691),U_11690)),U_11690))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11691),U_11690),U_11690))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11690),U_11691))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11690)) ),
inference(definitional_conversion,[status(esa)],[f_3076_2]) ).
cnf(f_3076_4,plain,
( c_Divides_Odivmod__nat(U_11691,U_11690) = 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_11691),U_11690)),U_11690))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11691),U_11690),U_11690))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11690),U_11691))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11690)) ),
inference(clausify,[status(thm)],[f_3076_3]) ).
fof(f_3077_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_3077_2,plain,
! [U_11693,U_11692] :
( ( ( ( c_Divides_Odivmod__int(U_11692,U_11693) = 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_11693))),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_11693)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11692))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11693),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11692),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_11692,U_11693)),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_11693))))),c_Divides_Opdivmod(U_11692,U_11693))))
| U_11693 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11692,U_11693) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11692)
| U_11693 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_11692 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11692,U_11693) = 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_11692 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_3077_1]) ).
fof(f_3077_3,plain,
( ! [U_11697,U_11695] :
( ( ( c_Divides_Odivmod__int(U_11695,U_11697) = 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_11697))),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_11697)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11695))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11697),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11695),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_11695,U_11697)),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_11697))))),c_Divides_Opdivmod(U_11695,U_11697))))
| U_11697 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11695,U_11697) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11695)
| U_11697 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_11695 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_11696,U_11694] :
( c_Divides_Odivmod__int(U_11694,U_11696) = 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_11694 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_3077_2]) ).
fof(f_3077_4,plain,
( ! [U_11695,U_11697] :
( c_Divides_Odivmod__int(U_11695,U_11697) = 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_11697))),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_11697)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11695))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11697),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11695),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_11695,U_11697)),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_11697))))),c_Divides_Opdivmod(U_11695,U_11697))))
| U_11697 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP859(U_11695,U_11697) )
& ! [U_11695,U_11697] :
( c_Divides_Odivmod__int(U_11695,U_11697) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11695)
| U_11697 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP859(U_11695,U_11697) )
& ! [U_11695,U_11697] :
( sP859(U_11695,U_11697)
| U_11695 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_11694,U_11696] :
( c_Divides_Odivmod__int(U_11694,U_11696) = 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_11694 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP859])],[f_3077_3]) ).
cnf(f_3077_5,plain,
( c_Divides_Odivmod__int(U_11694,U_11696) = 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_11694 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_3077_4]) ).
cnf(f_3077_6,plain,
( sP859(U_11695,U_11697)
| U_11695 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_3077_4]) ).
cnf(f_3077_7,plain,
( c_Divides_Odivmod__int(U_11695,U_11697) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11695)
| U_11697 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP859(U_11695,U_11697) ),
inference(clausify,[status(thm)],[f_3077_4]) ).
cnf(f_3077_8,plain,
( c_Divides_Odivmod__int(U_11695,U_11697) = 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_11697))),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_11697)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11695))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11697),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11695),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_11695,U_11697)),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_11697))))),c_Divides_Opdivmod(U_11695,U_11697))))
| U_11697 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP859(U_11695,U_11697) ),
inference(clausify,[status(thm)],[f_3077_4]) ).
fof(f_3078_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_3078_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_3078_1]) ).
cnf(f_3078_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_3078_2]) ).
fof(f_3079_1,plain,
! [V_y_2,V_x_2,V_f_2,T_c,T_d,T_e] : hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_e),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),hAPP(V_f_2,V_y_2)),
inference(fof_nnf,[status(thm)],[fact_apsnd__conv]) ).
fof(f_3079_2,plain,
! [U_11703,U_11702,U_11701,U_11700,U_11699,U_11698] : hAPP(c_Product__Type_Oapsnd(U_11698,U_11699,U_11700,U_11701),hAPP(hAPP(c_Product__Type_OPair(U_11700,U_11698),U_11702),U_11703)) = hAPP(hAPP(c_Product__Type_OPair(U_11700,U_11699),U_11702),hAPP(U_11701,U_11703)),
inference(variable_rename,[status(thm)],[f_3079_1]) ).
fof(f_3079_3,plain,
! [U_11699,U_11698,U_11702,U_11701,U_11700,U_11703] : hAPP(c_Product__Type_Oapsnd(U_11698,U_11699,U_11700,U_11701),hAPP(hAPP(c_Product__Type_OPair(U_11700,U_11698),U_11702),U_11703)) = hAPP(hAPP(c_Product__Type_OPair(U_11700,U_11699),U_11702),hAPP(U_11701,U_11703)),
inference(definitional_conversion,[status(esa)],[f_3079_2]) ).
cnf(f_3079_4,plain,
hAPP(c_Product__Type_Oapsnd(U_11698,U_11699,U_11700,U_11701),hAPP(hAPP(c_Product__Type_OPair(U_11700,U_11698),U_11702),U_11703)) = hAPP(hAPP(c_Product__Type_OPair(U_11700,U_11699),U_11702),hAPP(U_11701,U_11703)),
inference(clausify,[status(thm)],[f_3079_3]) ).
fof(f_3080_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_3080_2,plain,
! [U_11704] : c_Divides_Odivmod__nat(U_11704,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_11704),
inference(variable_rename,[status(thm)],[f_3080_1]) ).
fof(f_3080_3,plain,
! [U_11704] : c_Divides_Odivmod__nat(U_11704,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_11704),
inference(definitional_conversion,[status(esa)],[f_3080_2]) ).
cnf(f_3080_4,plain,
c_Divides_Odivmod__nat(U_11704,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_11704),
inference(clausify,[status(thm)],[f_3080_3]) ).
fof(f_3081_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_3081_2,plain,
! [U_11706,U_11705] :
( c_Divides_Odivmod__nat(U_11705,U_11706) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11705)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11705),U_11706)) ),
inference(variable_rename,[status(thm)],[f_3081_1]) ).
fof(f_3081_3,plain,
! [U_11705,U_11706] :
( c_Divides_Odivmod__nat(U_11705,U_11706) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11705)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11705),U_11706)) ),
inference(definitional_conversion,[status(esa)],[f_3081_2]) ).
cnf(f_3081_4,plain,
( c_Divides_Odivmod__nat(U_11705,U_11706) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11705)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11705),U_11706)) ),
inference(clausify,[status(thm)],[f_3081_3]) ).
fof(f_3082_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_3082_2,plain,
! [U_11708,U_11707] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11707),U_11708)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11707),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11708)),
inference(variable_rename,[status(thm)],[f_3082_1]) ).
fof(f_3082_3,plain,
! [U_11707,U_11708] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11707),U_11708)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11707),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11708)),
inference(definitional_conversion,[status(esa)],[f_3082_2]) ).
cnf(f_3082_4,plain,
hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11707),U_11708)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11707),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11708)),
inference(clausify,[status(thm)],[f_3082_3]) ).
fof(f_3083_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_3083_2,plain,
! [U_11710,U_11709] : c_Divides_Odivmod__nat(U_11709,U_11710) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11709),U_11710)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11709,U_11710)),
inference(variable_rename,[status(thm)],[f_3083_1]) ).
fof(f_3083_3,plain,
! [U_11709,U_11710] : c_Divides_Odivmod__nat(U_11709,U_11710) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11709),U_11710)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11709,U_11710)),
inference(definitional_conversion,[status(esa)],[f_3083_2]) ).
cnf(f_3083_4,plain,
c_Divides_Odivmod__nat(U_11709,U_11710) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11709),U_11710)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11709,U_11710)),
inference(clausify,[status(thm)],[f_3083_3]) ).
fof(f_3084_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_3084_2,plain,
! [U_11713,U_11712,U_11711] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11711,U_11712),hAPP(c_Divides_OnegateSnd,U_11713)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11711),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11712)),U_11713)) ),
inference(variable_rename,[status(thm)],[f_3084_1]) ).
fof(f_3084_3,plain,
! [U_11711,U_11712,U_11713] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11711,U_11712),hAPP(c_Divides_OnegateSnd,U_11713)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11711),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11712)),U_11713)) ),
inference(definitional_conversion,[status(esa)],[f_3084_2]) ).
cnf(f_3084_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11711,U_11712),hAPP(c_Divides_OnegateSnd,U_11713)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11711),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11712)),U_11713)) ),
inference(clausify,[status(thm)],[f_3084_3]) ).
fof(f_3085_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_3085_2,plain,
! [U_11715,U_11714] :
( ( c_Divides_Odivmod__nat(U_11715,U_11714) = 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_11715),U_11714),U_11714))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11715),U_11714))
| U_11714 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Divides_Odivmod__nat(U_11715,U_11714) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11715)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11715),U_11714))
& U_11714 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(variable_rename,[status(thm)],[f_3085_1]) ).
fof(f_3085_3,plain,
( ! [U_11719,U_11717] :
( c_Divides_Odivmod__nat(U_11719,U_11717) = 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_11719),U_11717),U_11717))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11719),U_11717))
| U_11717 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_11718,U_11716] :
( c_Divides_Odivmod__nat(U_11718,U_11716) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11718)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11718),U_11716))
& U_11716 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(miniscope,[status(thm)],[f_3085_2]) ).
fof(f_3085_4,plain,
( ! [U_11718,U_11716] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11718),U_11716))
| ~ sP860(U_11718,U_11716) )
& ! [U_11718,U_11716] :
( U_11716 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP860(U_11718,U_11716) )
& ! [U_11717,U_11719] :
( c_Divides_Odivmod__nat(U_11719,U_11717) = 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_11719),U_11717),U_11717))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11719),U_11717))
| U_11717 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_11718,U_11716] :
( c_Divides_Odivmod__nat(U_11718,U_11716) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11718)
| sP860(U_11718,U_11716) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP860])],[f_3085_3]) ).
cnf(f_3085_5,plain,
( c_Divides_Odivmod__nat(U_11718,U_11716) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11718)
| sP860(U_11718,U_11716) ),
inference(clausify,[status(thm)],[f_3085_4]) ).
cnf(f_3085_6,plain,
( c_Divides_Odivmod__nat(U_11719,U_11717) = 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_11719),U_11717),U_11717))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11719),U_11717))
| U_11717 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_3085_4]) ).
cnf(f_3085_7,plain,
( U_11716 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP860(U_11718,U_11716) ),
inference(clausify,[status(thm)],[f_3085_4]) ).
cnf(f_3085_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11718),U_11716))
| ~ sP860(U_11718,U_11716) ),
inference(clausify,[status(thm)],[f_3085_4]) ).
fof(f_3086_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_3086_2,plain,
! [U_11721,U_11720] : c_Divides_Opdivmod(U_11720,U_11721) = 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_11720)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11721))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11720),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11721))),
inference(variable_rename,[status(thm)],[f_3086_1]) ).
fof(f_3086_3,plain,
! [U_11721,U_11720] : c_Divides_Opdivmod(U_11720,U_11721) = 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_11720)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11721))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11720),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11721))),
inference(definitional_conversion,[status(esa)],[f_3086_2]) ).
cnf(f_3086_4,plain,
c_Divides_Opdivmod(U_11720,U_11721) = 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_11720)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11721))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11720),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11721))),
inference(clausify,[status(thm)],[f_3086_3]) ).
fof(f_3087_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_3087_2,plain,
! [U_11723,U_11722] :
( ( c_Divides_Opdivmod(U_11723,U_11722) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11723),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11722))
| U_11722 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Opdivmod(U_11723,U_11722) = 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_11723))
| U_11722 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_3087_1]) ).
fof(f_3087_3,plain,
( ! [U_11727,U_11725] :
( c_Divides_Opdivmod(U_11727,U_11725) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11727),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11725))
| U_11725 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_11726,U_11724] :
( c_Divides_Opdivmod(U_11726,U_11724) = 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_11726))
| U_11724 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_3087_2]) ).
fof(f_3087_4,plain,
( ! [U_11725,U_11727] :
( c_Divides_Opdivmod(U_11727,U_11725) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11727),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11725))
| U_11725 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_11726,U_11724] :
( c_Divides_Opdivmod(U_11726,U_11724) = 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_11726))
| U_11724 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa)],[f_3087_3]) ).
cnf(f_3087_5,plain,
( c_Divides_Opdivmod(U_11726,U_11724) = 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_11726))
| U_11724 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_3087_4]) ).
cnf(f_3087_6,plain,
( c_Divides_Opdivmod(U_11727,U_11725) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11727),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_11725))
| U_11725 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_3087_4]) ).
fof(f_3088_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_3088_2,plain,
! [U_11729,U_11728] :
( ( ( ( c_Divides_Odivmod__int(U_11728,U_11729) = 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_11729))),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_11728)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_11729))),c_Divides_Opdivmod(U_11728,U_11729)),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_11729))))),c_Divides_Opdivmod(U_11728,U_11729))))
| U_11729 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11728,U_11729) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11728)
| U_11729 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_11728 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11728,U_11729) = 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_11728 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_3088_1]) ).
fof(f_3088_3,plain,
( ! [U_11733,U_11731] :
( ( ( c_Divides_Odivmod__int(U_11731,U_11733) = 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_11733))),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_11731)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_11733))),c_Divides_Opdivmod(U_11731,U_11733)),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_11733))))),c_Divides_Opdivmod(U_11731,U_11733))))
| U_11733 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_11731,U_11733) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11731)
| U_11733 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_11731 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_11732,U_11730] :
( c_Divides_Odivmod__int(U_11730,U_11732) = 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_11730 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_3088_2]) ).
fof(f_3088_4,plain,
( ! [U_11731,U_11733] :
( c_Divides_Odivmod__int(U_11731,U_11733) = 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_11733))),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_11731)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_11733))),c_Divides_Opdivmod(U_11731,U_11733)),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_11733))))),c_Divides_Opdivmod(U_11731,U_11733))))
| U_11733 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP861(U_11731,U_11733) )
& ! [U_11731,U_11733] :
( c_Divides_Odivmod__int(U_11731,U_11733) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11731)
| U_11733 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP861(U_11731,U_11733) )
& ! [U_11731,U_11733] :
( sP861(U_11731,U_11733)
| U_11731 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_11732,U_11730] :
( c_Divides_Odivmod__int(U_11730,U_11732) = 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_11730 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP861])],[f_3088_3]) ).
cnf(f_3088_5,plain,
( c_Divides_Odivmod__int(U_11730,U_11732) = 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_11730 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_3088_4]) ).
cnf(f_3088_6,plain,
( sP861(U_11731,U_11733)
| U_11731 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_3088_4]) ).
cnf(f_3088_7,plain,
( c_Divides_Odivmod__int(U_11731,U_11733) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11731)
| U_11733 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP861(U_11731,U_11733) ),
inference(clausify,[status(thm)],[f_3088_4]) ).
cnf(f_3088_8,plain,
( c_Divides_Odivmod__int(U_11731,U_11733) = 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_11733))),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_11731)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_11733))),c_Divides_Opdivmod(U_11731,U_11733)),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_11733))))),c_Divides_Opdivmod(U_11731,U_11733))))
| U_11733 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP861(U_11731,U_11733) ),
inference(clausify,[status(thm)],[f_3088_4]) ).
fof(f_3089_1,plain,
! [V_Y_2,V_X_2,V_f_2,T_d,V_r_2,V_A_2,T_c] :
( V_X_2 = V_Y_2
| ? [B_x] :
( ? [B_y] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_y)),V_r_2))
& hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
& hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2)) )
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A_2),V_r_2)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X_2),V_f_2) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_Y_2),V_f_2)
| ~ c_Equiv__Relations_Ocongruent(T_c,tc_fun(T_d,tc_HOL_Obool),V_r_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_c,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__inject]) ).
fof(f_3089_2,plain,
! [U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736] :
( U_11741 = U_11742
| ? [U_11735] :
( ? [U_11734] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11736,U_11736)),hAPP(hAPP(c_Product__Type_OPair(U_11736,U_11736),U_11735),U_11734)),U_11738))
& hAPP(U_11740,U_11735) = hAPP(U_11740,U_11734)
& hBOOL(hAPP(hAPP(c_member(U_11736),U_11734),U_11737)) )
& hBOOL(hAPP(hAPP(c_member(U_11736),U_11735),U_11737)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11736,tc_HOL_Obool)),U_11742),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11736),U_11737),U_11738)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11736,tc_HOL_Obool)),U_11741),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11736),U_11737),U_11738)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11736,tc_fun(U_11739,tc_HOL_Obool)),U_11741),U_11740) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11736,tc_fun(U_11739,tc_HOL_Obool)),U_11742),U_11740)
| ~ c_Equiv__Relations_Ocongruent(U_11736,tc_fun(U_11739,tc_HOL_Obool),U_11738,U_11740)
| ~ c_Equiv__Relations_Oequiv(U_11736,U_11737,U_11738) ),
inference(variable_rename,[status(thm)],[f_3089_1]) ).
fof(f_3089_3,plain,
! [U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736] :
( U_11741 = U_11742
| ( ? [U_11734] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11736,U_11736)),hAPP(hAPP(c_Product__Type_OPair(U_11736,U_11736),sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)),U_11734)),U_11738))
& hAPP(U_11740,sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)) = hAPP(U_11740,U_11734)
& hBOOL(hAPP(hAPP(c_member(U_11736),U_11734),U_11737)) )
& hBOOL(hAPP(hAPP(c_member(U_11736),sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)),U_11737)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11736,tc_HOL_Obool)),U_11742),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11736),U_11737),U_11738)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11736,tc_HOL_Obool)),U_11741),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11736),U_11737),U_11738)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11736,tc_fun(U_11739,tc_HOL_Obool)),U_11741),U_11740) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11736,tc_fun(U_11739,tc_HOL_Obool)),U_11742),U_11740)
| ~ c_Equiv__Relations_Ocongruent(U_11736,tc_fun(U_11739,tc_HOL_Obool),U_11738,U_11740)
| ~ c_Equiv__Relations_Oequiv(U_11736,U_11737,U_11738) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_11735,sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736))],[f_3089_2]) ).
fof(f_3089_4,plain,
! [U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736] :
( U_11741 = U_11742
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11736,U_11736)),hAPP(hAPP(c_Product__Type_OPair(U_11736,U_11736),sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)),sK276(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736))),U_11738))
& hAPP(U_11740,sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)) = hAPP(U_11740,sK276(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736))
& hBOOL(hAPP(hAPP(c_member(U_11736),sK276(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)),U_11737))
& hBOOL(hAPP(hAPP(c_member(U_11736),sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)),U_11737)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11736,tc_HOL_Obool)),U_11742),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11736),U_11737),U_11738)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11736,tc_HOL_Obool)),U_11741),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11736),U_11737),U_11738)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11736,tc_fun(U_11739,tc_HOL_Obool)),U_11741),U_11740) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11736,tc_fun(U_11739,tc_HOL_Obool)),U_11742),U_11740)
| ~ c_Equiv__Relations_Ocongruent(U_11736,tc_fun(U_11739,tc_HOL_Obool),U_11738,U_11740)
| ~ c_Equiv__Relations_Oequiv(U_11736,U_11737,U_11738) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_11734,sK276(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736))],[f_3089_3]) ).
fof(f_3089_5,plain,
( ! [U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11736,U_11736)),hAPP(hAPP(c_Product__Type_OPair(U_11736,U_11736),sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)),sK276(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736))),U_11738))
| ~ sP862(U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742) )
& ! [U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742] :
( hAPP(U_11740,sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)) = hAPP(U_11740,sK276(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736))
| ~ sP862(U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742) )
& ! [U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742] :
( hBOOL(hAPP(hAPP(c_member(U_11736),sK276(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)),U_11737))
| ~ sP862(U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742) )
& ! [U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742] :
( hBOOL(hAPP(hAPP(c_member(U_11736),sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)),U_11737))
| ~ sP862(U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742) )
& ! [U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742] :
( U_11741 = U_11742
| sP862(U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11736,tc_HOL_Obool)),U_11742),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11736),U_11737),U_11738)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11736,tc_HOL_Obool)),U_11741),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11736),U_11737),U_11738)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11736,tc_fun(U_11739,tc_HOL_Obool)),U_11741),U_11740) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11736,tc_fun(U_11739,tc_HOL_Obool)),U_11742),U_11740)
| ~ c_Equiv__Relations_Ocongruent(U_11736,tc_fun(U_11739,tc_HOL_Obool),U_11738,U_11740)
| ~ c_Equiv__Relations_Oequiv(U_11736,U_11737,U_11738) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP862])],[f_3089_4]) ).
cnf(f_3089_6,plain,
( U_11741 = U_11742
| sP862(U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11736,tc_HOL_Obool)),U_11742),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11736),U_11737),U_11738)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11736,tc_HOL_Obool)),U_11741),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11736),U_11737),U_11738)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11736,tc_fun(U_11739,tc_HOL_Obool)),U_11741),U_11740) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11736,tc_fun(U_11739,tc_HOL_Obool)),U_11742),U_11740)
| ~ c_Equiv__Relations_Ocongruent(U_11736,tc_fun(U_11739,tc_HOL_Obool),U_11738,U_11740)
| ~ c_Equiv__Relations_Oequiv(U_11736,U_11737,U_11738) ),
inference(clausify,[status(thm)],[f_3089_5]) ).
cnf(f_3089_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_11736),sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)),U_11737))
| ~ sP862(U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742) ),
inference(clausify,[status(thm)],[f_3089_5]) ).
cnf(f_3089_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_11736),sK276(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)),U_11737))
| ~ sP862(U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742) ),
inference(clausify,[status(thm)],[f_3089_5]) ).
cnf(f_3089_9,plain,
( hAPP(U_11740,sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)) = hAPP(U_11740,sK276(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736))
| ~ sP862(U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742) ),
inference(clausify,[status(thm)],[f_3089_5]) ).
cnf(f_3089_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11736,U_11736)),hAPP(hAPP(c_Product__Type_OPair(U_11736,U_11736),sK275(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736)),sK276(U_11742,U_11741,U_11740,U_11739,U_11738,U_11737,U_11736))),U_11738))
| ~ sP862(U_11736,U_11737,U_11738,U_11739,U_11740,U_11741,U_11742) ),
inference(clausify,[status(thm)],[f_3089_5]) ).
fof(f_3090_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_3090_2,plain,
! [U_11747,U_11746,U_11745,U_11744,U_11743] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11747),U_11743),U_11744),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_11747),U_11745)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11747),U_11746)),U_11744))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11747),U_11746),U_11744))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11744))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11743,U_11744),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11745),U_11746))) ),
inference(variable_rename,[status(thm)],[f_3090_1]) ).
fof(f_3090_3,plain,
! [U_11746,U_11747,U_11745,U_11744,U_11743] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11747),U_11743),U_11744),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_11747),U_11745)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11747),U_11746)),U_11744))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11747),U_11746),U_11744))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11744))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11743,U_11744),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11745),U_11746))) ),
inference(definitional_conversion,[status(esa)],[f_3090_2]) ).
cnf(f_3090_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11747),U_11743),U_11744),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_11747),U_11745)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11747),U_11746)),U_11744))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11747),U_11746),U_11744))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11744))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11743,U_11744),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11745),U_11746))) ),
inference(clausify,[status(thm)],[f_3090_3]) ).
fof(f_3091_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_3091_2,plain,
! [U_11752,U_11751,U_11750,U_11749,U_11748] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11748,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11749),U_11752)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11750),U_11752)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11749),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11750,U_11752))),U_11751))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11749))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11748,U_11749),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11750),U_11751))) ),
inference(variable_rename,[status(thm)],[f_3091_1]) ).
fof(f_3091_3,plain,
! [U_11749,U_11748,U_11751,U_11750,U_11752] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11748,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11749),U_11752)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11750),U_11752)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11749),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11750,U_11752))),U_11751))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11749))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11748,U_11749),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11750),U_11751))) ),
inference(definitional_conversion,[status(esa)],[f_3091_2]) ).
cnf(f_3091_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11748,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11749),U_11752)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11750),U_11752)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11749),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11750,U_11752))),U_11751))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11752))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11749))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11748,U_11749),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11750),U_11751))) ),
inference(clausify,[status(thm)],[f_3091_3]) ).
fof(f_3092_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_3092_2,plain,
! [U_11756,U_11755,U_11754,U_11753] :
( U_11755 = U_11756
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11753,U_11754),U_11756))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11753,U_11754),U_11755)) ),
inference(variable_rename,[status(thm)],[f_3092_1]) ).
fof(f_3092_3,plain,
! [U_11754,U_11753,U_11755,U_11756] :
( U_11755 = U_11756
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11753,U_11754),U_11756))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11753,U_11754),U_11755)) ),
inference(definitional_conversion,[status(esa)],[f_3092_2]) ).
cnf(f_3092_4,plain,
( U_11755 = U_11756
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11753,U_11754),U_11756))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11753,U_11754),U_11755)) ),
inference(clausify,[status(thm)],[f_3092_3]) ).
fof(f_3093_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_3093_2,plain,
! [U_11758,U_11757] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11757,U_11758),c_Divides_Odivmod__nat(U_11757,U_11758))),
inference(variable_rename,[status(thm)],[f_3093_1]) ).
fof(f_3093_3,plain,
! [U_11758,U_11757] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11757,U_11758),c_Divides_Odivmod__nat(U_11757,U_11758))),
inference(definitional_conversion,[status(esa)],[f_3093_2]) ).
cnf(f_3093_4,plain,
hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11757,U_11758),c_Divides_Odivmod__nat(U_11757,U_11758))),
inference(clausify,[status(thm)],[f_3093_3]) ).
fof(f_3094_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_3094_2,plain,
! [U_11761,U_11760,U_11759] :
( c_Divides_Odivmod__nat(U_11759,U_11760) = U_11761
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11759,U_11760),U_11761)) ),
inference(variable_rename,[status(thm)],[f_3094_1]) ).
fof(f_3094_3,plain,
! [U_11759,U_11760,U_11761] :
( c_Divides_Odivmod__nat(U_11759,U_11760) = U_11761
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11759,U_11760),U_11761)) ),
inference(definitional_conversion,[status(esa)],[f_3094_2]) ).
cnf(f_3094_4,plain,
( c_Divides_Odivmod__nat(U_11759,U_11760) = U_11761
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11759,U_11760),U_11761)) ),
inference(clausify,[status(thm)],[f_3094_3]) ).
fof(f_3095_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__def]) ).
fof(f_3095_2,plain,
! [U_11763,U_11762] : c_Divides_Odivmod__nat(U_11762,U_11763) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_11762,U_11763)),
inference(variable_rename,[status(thm)],[f_3095_1]) ).
fof(f_3095_3,plain,
! [U_11762,U_11763] : c_Divides_Odivmod__nat(U_11762,U_11763) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_11762,U_11763)),
inference(definitional_conversion,[status(esa)],[f_3095_2]) ).
cnf(f_3095_4,plain,
c_Divides_Odivmod__nat(U_11762,U_11763) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_11762,U_11763)),
inference(clausify,[status(thm)],[f_3095_3]) ).
fof(f_3096_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_3096_2,plain,
! [U_11767,U_11766,U_11765,U_11764] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11764,U_11765) = U_11767
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11764,U_11765),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11766),U_11767))) ),
inference(variable_rename,[status(thm)],[f_3096_1]) ).
fof(f_3096_3,plain,
! [U_11764,U_11765,U_11766,U_11767] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11764,U_11765) = U_11767
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11764,U_11765),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11766),U_11767))) ),
inference(definitional_conversion,[status(esa)],[f_3096_2]) ).
cnf(f_3096_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11764,U_11765) = U_11767
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11764,U_11765),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11766),U_11767))) ),
inference(clausify,[status(thm)],[f_3096_3]) ).
fof(f_3097_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_3097_2,plain,
! [U_11771,U_11770,U_11769,U_11768] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11768),U_11769) = U_11770
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11768,U_11769),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11770),U_11771))) ),
inference(variable_rename,[status(thm)],[f_3097_1]) ).
fof(f_3097_3,plain,
! [U_11768,U_11769,U_11770,U_11771] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11768),U_11769) = U_11770
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11768,U_11769),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11770),U_11771))) ),
inference(definitional_conversion,[status(esa)],[f_3097_2]) ).
cnf(f_3097_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11768),U_11769) = U_11770
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11768,U_11769),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11770),U_11771))) ),
inference(clausify,[status(thm)],[f_3097_3]) ).
fof(f_3098_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_3098_2,plain,
! [U_11773,U_11772] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11772,U_11773),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11772),U_11773)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11772,U_11773)))),
inference(variable_rename,[status(thm)],[f_3098_1]) ).
fof(f_3098_3,plain,
! [U_11772,U_11773] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11772,U_11773),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11772),U_11773)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11772,U_11773)))),
inference(definitional_conversion,[status(esa)],[f_3098_2]) ).
cnf(f_3098_4,plain,
hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11772,U_11773),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11772),U_11773)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11772,U_11773)))),
inference(clausify,[status(thm)],[f_3098_3]) ).
fof(f_3099_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_3099_2,plain,
! [U_11780,U_11779,U_11778,U_11777,U_11776,U_11775,U_11774] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11774),U_11778),U_11775),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_11776),U_11779)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11777),U_11780)),U_11775))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11777),U_11780),U_11775))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11775))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11778,U_11775),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11779),U_11780)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11774,U_11775),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11776),U_11777))) ),
inference(variable_rename,[status(thm)],[f_3099_1]) ).
fof(f_3099_3,plain,
! [U_11774,U_11775,U_11776,U_11777,U_11778,U_11779,U_11780] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11774),U_11778),U_11775),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_11776),U_11779)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11777),U_11780)),U_11775))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11777),U_11780),U_11775))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11775))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11778,U_11775),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11779),U_11780)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11774,U_11775),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11776),U_11777))) ),
inference(definitional_conversion,[status(esa)],[f_3099_2]) ).
cnf(f_3099_4,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11774),U_11778),U_11775),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_11776),U_11779)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11777),U_11780)),U_11775))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11777),U_11780),U_11775))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11775))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11778,U_11775),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11779),U_11780)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11774,U_11775),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11776),U_11777))) ),
inference(clausify,[status(thm)],[f_3099_3]) ).
fof(f_3100_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_3100_2,plain,
! [U_11782,U_11781] :
( ( ( c_Divides_OnegDivAlg(U_11781,U_11782) = hAPP(c_Divides_Oadjust(U_11782),c_Divides_OnegDivAlg(U_11781,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_11782)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11782),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_11781),U_11782))) )
& ( c_Divides_OnegDivAlg(U_11781,U_11782) = 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_11781),U_11782))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11782),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_11781),U_11782))) ) ) )
| ~ 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_11781),U_11782))) ),
inference(variable_rename,[status(thm)],[f_3100_1]) ).
fof(f_3100_3,plain,
( ! [U_11781,U_11782] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11782),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP863(U_11781,U_11782) )
& ! [U_11781,U_11782] :
( ~ 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_11781),U_11782)))
| ~ sP863(U_11781,U_11782) )
& ! [U_11781,U_11782] :
( c_Divides_OnegDivAlg(U_11781,U_11782) = hAPP(c_Divides_Oadjust(U_11782),c_Divides_OnegDivAlg(U_11781,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_11782)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11782),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_11781),U_11782)))
| ~ sP864(U_11781,U_11782) )
& ! [U_11781,U_11782] :
( c_Divides_OnegDivAlg(U_11781,U_11782) = 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_11781),U_11782))
| sP863(U_11781,U_11782)
| ~ sP864(U_11781,U_11782) )
& ! [U_11781,U_11782] :
( sP864(U_11781,U_11782)
| ~ 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_11781),U_11782))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP863,sP864])],[f_3100_2]) ).
cnf(f_3100_4,plain,
( sP864(U_11781,U_11782)
| ~ 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_11781),U_11782))) ),
inference(clausify,[status(thm)],[f_3100_3]) ).
cnf(f_3100_5,plain,
( c_Divides_OnegDivAlg(U_11781,U_11782) = 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_11781),U_11782))
| sP863(U_11781,U_11782)
| ~ sP864(U_11781,U_11782) ),
inference(clausify,[status(thm)],[f_3100_3]) ).
cnf(f_3100_6,plain,
( c_Divides_OnegDivAlg(U_11781,U_11782) = hAPP(c_Divides_Oadjust(U_11782),c_Divides_OnegDivAlg(U_11781,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_11782)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11782),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_11781),U_11782)))
| ~ sP864(U_11781,U_11782) ),
inference(clausify,[status(thm)],[f_3100_3]) ).
cnf(f_3100_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_11781),U_11782)))
| ~ sP863(U_11781,U_11782) ),
inference(clausify,[status(thm)],[f_3100_3]) ).
cnf(f_3100_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11782),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP863(U_11781,U_11782) ),
inference(clausify,[status(thm)],[f_3100_3]) ).
fof(f_3101_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_3101_2,plain,
! [U_11784,U_11783] :
( ( ( c_Divides_OposDivAlg(U_11783,U_11784) = hAPP(c_Divides_Oadjust(U_11784),c_Divides_OposDivAlg(U_11783,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_11784)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11784),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11783),U_11784)) )
& ( c_Divides_OposDivAlg(U_11783,U_11784) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11783)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11784),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11783),U_11784)) ) ) )
| ~ 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_11783),U_11784))) ),
inference(variable_rename,[status(thm)],[f_3101_1]) ).
fof(f_3101_3,plain,
( ! [U_11784,U_11783] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11784),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP865(U_11784,U_11783) )
& ! [U_11784,U_11783] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11783),U_11784))
| ~ sP865(U_11784,U_11783) )
& ! [U_11784,U_11783] :
( c_Divides_OposDivAlg(U_11783,U_11784) = hAPP(c_Divides_Oadjust(U_11784),c_Divides_OposDivAlg(U_11783,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_11784)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11784),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11783),U_11784))
| ~ sP866(U_11784,U_11783) )
& ! [U_11784,U_11783] :
( c_Divides_OposDivAlg(U_11783,U_11784) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11783)
| sP865(U_11784,U_11783)
| ~ sP866(U_11784,U_11783) )
& ! [U_11784,U_11783] :
( sP866(U_11784,U_11783)
| ~ 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_11783),U_11784))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP865,sP866])],[f_3101_2]) ).
cnf(f_3101_4,plain,
( sP866(U_11784,U_11783)
| ~ 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_11783),U_11784))) ),
inference(clausify,[status(thm)],[f_3101_3]) ).
cnf(f_3101_5,plain,
( c_Divides_OposDivAlg(U_11783,U_11784) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11783)
| sP865(U_11784,U_11783)
| ~ sP866(U_11784,U_11783) ),
inference(clausify,[status(thm)],[f_3101_3]) ).
cnf(f_3101_6,plain,
( c_Divides_OposDivAlg(U_11783,U_11784) = hAPP(c_Divides_Oadjust(U_11784),c_Divides_OposDivAlg(U_11783,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_11784)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11784),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11783),U_11784))
| ~ sP866(U_11784,U_11783) ),
inference(clausify,[status(thm)],[f_3101_3]) ).
cnf(f_3101_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11783),U_11784))
| ~ sP865(U_11784,U_11783) ),
inference(clausify,[status(thm)],[f_3101_3]) ).
cnf(f_3101_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11784),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP865(U_11784,U_11783) ),
inference(clausify,[status(thm)],[f_3101_3]) ).
fof(f_3102_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_3102_2,plain,
! [U_11785] :
( 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_11785)) = 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_11785)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11785)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_3102_1]) ).
fof(f_3102_3,plain,
! [U_11785] :
( 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_11785)) = 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_11785)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11785)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_3102_2]) ).
cnf(f_3102_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_11785)) = 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_11785)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11785)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3102_3]) ).
fof(f_3103_1,plain,
! [V_g_2,V_x_2,V_f_2,T_c,T_d,T_e] :
( ( hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_g_2),V_x_2)
| hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_e),V_x_2)) != hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_e),V_x_2)) )
& ( hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_e),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_c,T_e),V_x_2))
| hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_f_2),V_x_2) != hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_c,V_g_2),V_x_2) ) ),
inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv]) ).
fof(f_3103_2,plain,
! [U_11791,U_11790,U_11789,U_11788,U_11787,U_11786] :
( ( hAPP(c_Product__Type_Oapsnd(U_11786,U_11787,U_11788,U_11789),U_11790) = hAPP(c_Product__Type_Oapsnd(U_11786,U_11787,U_11788,U_11791),U_11790)
| hAPP(U_11789,hAPP(c_Product__Type_Osnd(U_11788,U_11786),U_11790)) != hAPP(U_11791,hAPP(c_Product__Type_Osnd(U_11788,U_11786),U_11790)) )
& ( hAPP(U_11789,hAPP(c_Product__Type_Osnd(U_11788,U_11786),U_11790)) = hAPP(U_11791,hAPP(c_Product__Type_Osnd(U_11788,U_11786),U_11790))
| hAPP(c_Product__Type_Oapsnd(U_11786,U_11787,U_11788,U_11789),U_11790) != hAPP(c_Product__Type_Oapsnd(U_11786,U_11787,U_11788,U_11791),U_11790) ) ),
inference(variable_rename,[status(thm)],[f_3103_1]) ).
fof(f_3103_3,plain,
( ! [U_11803,U_11801,U_11799,U_11797,U_11795,U_11793] :
( hAPP(c_Product__Type_Oapsnd(U_11793,U_11795,U_11797,U_11799),U_11801) = hAPP(c_Product__Type_Oapsnd(U_11793,U_11795,U_11797,U_11803),U_11801)
| hAPP(U_11799,hAPP(c_Product__Type_Osnd(U_11797,U_11793),U_11801)) != hAPP(U_11803,hAPP(c_Product__Type_Osnd(U_11797,U_11793),U_11801)) )
& ! [U_11802,U_11800,U_11798,U_11796,U_11794,U_11792] :
( hAPP(U_11798,hAPP(c_Product__Type_Osnd(U_11796,U_11792),U_11800)) = hAPP(U_11802,hAPP(c_Product__Type_Osnd(U_11796,U_11792),U_11800))
| hAPP(c_Product__Type_Oapsnd(U_11792,U_11794,U_11796,U_11798),U_11800) != hAPP(c_Product__Type_Oapsnd(U_11792,U_11794,U_11796,U_11802),U_11800) ) ),
inference(miniscope,[status(thm)],[f_3103_2]) ).
fof(f_3103_4,plain,
( ! [U_11793,U_11795,U_11797,U_11799,U_11801,U_11803] :
( hAPP(c_Product__Type_Oapsnd(U_11793,U_11795,U_11797,U_11799),U_11801) = hAPP(c_Product__Type_Oapsnd(U_11793,U_11795,U_11797,U_11803),U_11801)
| hAPP(U_11799,hAPP(c_Product__Type_Osnd(U_11797,U_11793),U_11801)) != hAPP(U_11803,hAPP(c_Product__Type_Osnd(U_11797,U_11793),U_11801)) )
& ! [U_11798,U_11792,U_11794,U_11796,U_11802,U_11800] :
( hAPP(U_11798,hAPP(c_Product__Type_Osnd(U_11796,U_11792),U_11800)) = hAPP(U_11802,hAPP(c_Product__Type_Osnd(U_11796,U_11792),U_11800))
| hAPP(c_Product__Type_Oapsnd(U_11792,U_11794,U_11796,U_11798),U_11800) != hAPP(c_Product__Type_Oapsnd(U_11792,U_11794,U_11796,U_11802),U_11800) ) ),
inference(definitional_conversion,[status(esa)],[f_3103_3]) ).
cnf(f_3103_5,plain,
( hAPP(U_11798,hAPP(c_Product__Type_Osnd(U_11796,U_11792),U_11800)) = hAPP(U_11802,hAPP(c_Product__Type_Osnd(U_11796,U_11792),U_11800))
| hAPP(c_Product__Type_Oapsnd(U_11792,U_11794,U_11796,U_11798),U_11800) != hAPP(c_Product__Type_Oapsnd(U_11792,U_11794,U_11796,U_11802),U_11800) ),
inference(clausify,[status(thm)],[f_3103_4]) ).
cnf(f_3103_6,plain,
( hAPP(c_Product__Type_Oapsnd(U_11793,U_11795,U_11797,U_11799),U_11801) = hAPP(c_Product__Type_Oapsnd(U_11793,U_11795,U_11797,U_11803),U_11801)
| hAPP(U_11799,hAPP(c_Product__Type_Osnd(U_11797,U_11793),U_11801)) != hAPP(U_11803,hAPP(c_Product__Type_Osnd(U_11797,U_11793),U_11801)) ),
inference(clausify,[status(thm)],[f_3103_4]) ).
fof(f_3104_1,plain,
! [V_x_2,V_f_2,T_e,T_c,T_d] : hAPP(c_Product__Type_Osnd(T_d,T_c),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_snd__apsnd]) ).
fof(f_3104_2,plain,
! [U_11808,U_11807,U_11806,U_11805,U_11804] : hAPP(c_Product__Type_Osnd(U_11804,U_11805),hAPP(c_Product__Type_Oapsnd(U_11806,U_11805,U_11804,U_11807),U_11808)) = hAPP(U_11807,hAPP(c_Product__Type_Osnd(U_11804,U_11806),U_11808)),
inference(variable_rename,[status(thm)],[f_3104_1]) ).
fof(f_3104_3,plain,
! [U_11806,U_11805,U_11804,U_11807,U_11808] : hAPP(c_Product__Type_Osnd(U_11804,U_11805),hAPP(c_Product__Type_Oapsnd(U_11806,U_11805,U_11804,U_11807),U_11808)) = hAPP(U_11807,hAPP(c_Product__Type_Osnd(U_11804,U_11806),U_11808)),
inference(definitional_conversion,[status(esa)],[f_3104_2]) ).
cnf(f_3104_4,plain,
hAPP(c_Product__Type_Osnd(U_11804,U_11805),hAPP(c_Product__Type_Oapsnd(U_11806,U_11805,U_11804,U_11807),U_11808)) = hAPP(U_11807,hAPP(c_Product__Type_Osnd(U_11804,U_11806),U_11808)),
inference(clausify,[status(thm)],[f_3104_3]) ).
fof(f_3105_1,plain,
! [V_p_2,T_c,T_d] : hAPP(c_Product__Type_Osnd(T_d,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,T_c),hAPP(c_COMBK(tc_fun(T_c,T_c),T_d),c_COMBI(T_c))),V_p_2),
inference(fof_nnf,[status(thm)],[fact_snd__def]) ).
fof(f_3105_2,plain,
! [U_11811,U_11810,U_11809] : hAPP(c_Product__Type_Osnd(U_11809,U_11810),U_11811) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11809,U_11810,U_11810),hAPP(c_COMBK(tc_fun(U_11810,U_11810),U_11809),c_COMBI(U_11810))),U_11811),
inference(variable_rename,[status(thm)],[f_3105_1]) ).
fof(f_3105_3,plain,
! [U_11809,U_11810,U_11811] : hAPP(c_Product__Type_Osnd(U_11809,U_11810),U_11811) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11809,U_11810,U_11810),hAPP(c_COMBK(tc_fun(U_11810,U_11810),U_11809),c_COMBI(U_11810))),U_11811),
inference(definitional_conversion,[status(esa)],[f_3105_2]) ).
cnf(f_3105_4,plain,
hAPP(c_Product__Type_Osnd(U_11809,U_11810),U_11811) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11809,U_11810,U_11810),hAPP(c_COMBK(tc_fun(U_11810,U_11810),U_11809),c_COMBI(U_11810))),U_11811),
inference(clausify,[status(thm)],[f_3105_3]) ).
fof(f_3106_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_3106_2,plain,
! [U_11815,U_11814,U_11813,U_11812] : hAPP(c_Product__Type_Osnd(U_11812,U_11813),hAPP(hAPP(c_Product__Type_OPair(U_11812,U_11813),U_11814),U_11815)) = U_11815,
inference(variable_rename,[status(thm)],[f_3106_1]) ).
fof(f_3106_3,plain,
! [U_11812,U_11813,U_11814,U_11815] : hAPP(c_Product__Type_Osnd(U_11812,U_11813),hAPP(hAPP(c_Product__Type_OPair(U_11812,U_11813),U_11814),U_11815)) = U_11815,
inference(definitional_conversion,[status(esa)],[f_3106_2]) ).
cnf(f_3106_4,plain,
hAPP(c_Product__Type_Osnd(U_11812,U_11813),hAPP(hAPP(c_Product__Type_OPair(U_11812,U_11813),U_11814),U_11815)) = U_11815,
inference(clausify,[status(thm)],[f_3106_3]) ).
fof(f_3107_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_3107_2,plain,
! [U_11820,U_11819,U_11818,U_11817,U_11816] :
( U_11819 = U_11820
| hAPP(c_Product__Type_Osnd(U_11816,U_11817),hAPP(hAPP(c_Product__Type_OPair(U_11816,U_11817),U_11818),U_11819)) != U_11820 ),
inference(variable_rename,[status(thm)],[f_3107_1]) ).
fof(f_3107_3,plain,
! [U_11820,U_11819] :
( ! [U_11818,U_11817,U_11816] : hAPP(c_Product__Type_Osnd(U_11816,U_11817),hAPP(hAPP(c_Product__Type_OPair(U_11816,U_11817),U_11818),U_11819)) != U_11820
| U_11819 = U_11820 ),
inference(miniscope,[status(thm)],[f_3107_2]) ).
fof(f_3107_4,plain,
! [U_11816,U_11817,U_11818,U_11819,U_11820] :
( hAPP(c_Product__Type_Osnd(U_11816,U_11817),hAPP(hAPP(c_Product__Type_OPair(U_11816,U_11817),U_11818),U_11819)) != U_11820
| U_11819 = U_11820 ),
inference(definitional_conversion,[status(esa)],[f_3107_3]) ).
cnf(f_3107_5,plain,
( hAPP(c_Product__Type_Osnd(U_11816,U_11817),hAPP(hAPP(c_Product__Type_OPair(U_11816,U_11817),U_11818),U_11819)) != U_11820
| U_11819 = U_11820 ),
inference(clausify,[status(thm)],[f_3107_4]) ).
fof(f_3108_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_3108_2,plain,
! [U_11822,U_11821] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11821,U_11822) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11821,U_11822)),
inference(variable_rename,[status(thm)],[f_3108_1]) ).
fof(f_3108_3,plain,
! [U_11821,U_11822] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11821,U_11822) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11821,U_11822)),
inference(definitional_conversion,[status(esa)],[f_3108_2]) ).
cnf(f_3108_4,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11821,U_11822) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11821,U_11822)),
inference(clausify,[status(thm)],[f_3108_3]) ).
fof(f_3109_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_3109_2,plain,
! [U_11824,U_11823] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11823,U_11824) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11823,U_11824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11823),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_3109_1]) ).
fof(f_3109_3,plain,
! [U_11823,U_11824] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11823,U_11824) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11823,U_11824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11823),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_3109_2]) ).
cnf(f_3109_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11823,U_11824) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11823,U_11824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11824))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11823),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3109_3]) ).
fof(f_3110_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_3110_2,plain,
! [U_11826,U_11825] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11825,U_11826) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11825,U_11826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11825)) ),
inference(variable_rename,[status(thm)],[f_3110_1]) ).
fof(f_3110_3,plain,
! [U_11826,U_11825] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11825,U_11826) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11825,U_11826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11825)) ),
inference(definitional_conversion,[status(esa)],[f_3110_2]) ).
cnf(f_3110_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11825,U_11826) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11825,U_11826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11825)) ),
inference(clausify,[status(thm)],[f_3110_3]) ).
fof(f_3111_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_3111_2,plain,
! [U_11827] :
( 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_11827)) = 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_11827)))
| ~ 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_11827))) ),
inference(variable_rename,[status(thm)],[f_3111_1]) ).
fof(f_3111_3,plain,
! [U_11827] :
( 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_11827)) = 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_11827)))
| ~ 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_11827))) ),
inference(definitional_conversion,[status(esa)],[f_3111_2]) ).
cnf(f_3111_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_11827)) = 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_11827)))
| ~ 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_11827))) ),
inference(clausify,[status(thm)],[f_3111_3]) ).
fof(f_3112_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_3112_2,plain,
! [U_11829,U_11828] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11828,U_11829) = 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_11828),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11829))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11829),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_11828)) ),
inference(variable_rename,[status(thm)],[f_3112_1]) ).
fof(f_3112_3,plain,
! [U_11828,U_11829] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11828,U_11829) = 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_11828),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11829))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11829),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_11828)) ),
inference(definitional_conversion,[status(esa)],[f_3112_2]) ).
cnf(f_3112_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11828,U_11829) = 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_11828),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11829))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11829),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_11828)) ),
inference(clausify,[status(thm)],[f_3112_3]) ).
fof(f_3113_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_3113_2,plain,
! [U_11831,U_11830] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11830,U_11831) = 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_11830),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11831))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11831),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11830),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_3113_1]) ).
fof(f_3113_3,plain,
! [U_11830,U_11831] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11830,U_11831) = 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_11830),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11831))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11831),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11830),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definitional_conversion,[status(esa)],[f_3113_2]) ).
cnf(f_3113_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11830,U_11831) = 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_11830),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11831))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11831),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11830),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_3113_3]) ).
fof(f_3114_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_3114_2,plain,
! [U_11833,U_11832] :
( ( ( ( ( c_Nitpick_Onorm__frac(U_11832,U_11833) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_11832),U_11833)),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_11832))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11833)))
| U_11833 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11832 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nitpick_Onorm__frac(U_11832,U_11833) = 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_11833 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& U_11832 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11833),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Nitpick_Onorm__frac(U_11832,U_11833) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11832),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11833))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11833),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_11832),U_11833))) ),
inference(variable_rename,[status(thm)],[f_3114_1]) ).
fof(f_3114_3,plain,
( ! [U_11832,U_11833] :
( U_11833 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP867(U_11832,U_11833) )
& ! [U_11832,U_11833] :
( U_11832 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP867(U_11832,U_11833) )
& ! [U_11832,U_11833] :
( c_Nitpick_Onorm__frac(U_11832,U_11833) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_11832),U_11833)),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_11832))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11833)))
| U_11833 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11832 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP868(U_11832,U_11833) )
& ! [U_11832,U_11833] :
( c_Nitpick_Onorm__frac(U_11832,U_11833) = 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))
| sP867(U_11832,U_11833)
| ~ sP868(U_11832,U_11833) )
& ! [U_11832,U_11833] :
( sP868(U_11832,U_11833)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11833),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP869(U_11832,U_11833) )
& ! [U_11832,U_11833] :
( c_Nitpick_Onorm__frac(U_11832,U_11833) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11832),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11833))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11833),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP869(U_11832,U_11833) )
& ! [U_11832,U_11833] :
( sP869(U_11832,U_11833)
| ~ 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_11832),U_11833))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP867,sP868,sP869])],[f_3114_2]) ).
cnf(f_3114_4,plain,
( sP869(U_11832,U_11833)
| ~ 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_11832),U_11833))) ),
inference(clausify,[status(thm)],[f_3114_3]) ).
cnf(f_3114_5,plain,
( c_Nitpick_Onorm__frac(U_11832,U_11833) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11832),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11833))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11833),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP869(U_11832,U_11833) ),
inference(clausify,[status(thm)],[f_3114_3]) ).
cnf(f_3114_6,plain,
( sP868(U_11832,U_11833)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11833),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP869(U_11832,U_11833) ),
inference(clausify,[status(thm)],[f_3114_3]) ).
cnf(f_3114_7,plain,
( c_Nitpick_Onorm__frac(U_11832,U_11833) = 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))
| sP867(U_11832,U_11833)
| ~ sP868(U_11832,U_11833) ),
inference(clausify,[status(thm)],[f_3114_3]) ).
cnf(f_3114_8,plain,
( c_Nitpick_Onorm__frac(U_11832,U_11833) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_11832),U_11833)),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_11832))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11833)))
| U_11833 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_11832 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP868(U_11832,U_11833) ),
inference(clausify,[status(thm)],[f_3114_3]) ).
cnf(f_3114_9,plain,
( U_11832 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP867(U_11832,U_11833) ),
inference(clausify,[status(thm)],[f_3114_3]) ).
cnf(f_3114_10,plain,
( U_11833 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP867(U_11832,U_11833) ),
inference(clausify,[status(thm)],[f_3114_3]) ).
fof(f_3115_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_3115_2,plain,
! [U_11838,U_11837,U_11836] :
( hBOOL(hAPP(hAPP(U_11838,U_11836),U_11837))
| ? [U_11835,U_11834] :
( ~ hBOOL(hAPP(hAPP(U_11838,U_11835),U_11834))
& ( hBOOL(hAPP(hAPP(U_11838,U_11835),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_11834)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11834),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_11835),U_11834))) )
& 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_11835),U_11834))) )
| ~ 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_11836),U_11837))) ),
inference(variable_rename,[status(thm)],[f_3115_1]) ).
fof(f_3115_3,plain,
! [U_11838,U_11837,U_11836] :
( hBOOL(hAPP(hAPP(U_11838,U_11836),U_11837))
| ? [U_11834] :
( ~ hBOOL(hAPP(hAPP(U_11838,sK277(U_11838,U_11837,U_11836)),U_11834))
& ( hBOOL(hAPP(hAPP(U_11838,sK277(U_11838,U_11837,U_11836)),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_11834)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11834),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),sK277(U_11838,U_11837,U_11836)),U_11834))) )
& 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),sK277(U_11838,U_11837,U_11836)),U_11834))) )
| ~ 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_11836),U_11837))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_11835,sK277(U_11838,U_11837,U_11836))],[f_3115_2]) ).
fof(f_3115_4,plain,
! [U_11838,U_11837,U_11836] :
( hBOOL(hAPP(hAPP(U_11838,U_11836),U_11837))
| ( ~ hBOOL(hAPP(hAPP(U_11838,sK277(U_11838,U_11837,U_11836)),sK278(U_11838,U_11837,U_11836)))
& ( hBOOL(hAPP(hAPP(U_11838,sK277(U_11838,U_11837,U_11836)),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)))),sK278(U_11838,U_11837,U_11836))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK278(U_11838,U_11837,U_11836)),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),sK277(U_11838,U_11837,U_11836)),sK278(U_11838,U_11837,U_11836)))) )
& 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),sK277(U_11838,U_11837,U_11836)),sK278(U_11838,U_11837,U_11836)))) )
| ~ 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_11836),U_11837))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_11834,sK278(U_11838,U_11837,U_11836))],[f_3115_3]) ).
fof(f_3115_5,plain,
( ! [U_11836,U_11837,U_11838] :
( ~ hBOOL(hAPP(hAPP(U_11838,sK277(U_11838,U_11837,U_11836)),sK278(U_11838,U_11837,U_11836)))
| ~ sP870(U_11836,U_11837,U_11838) )
& ! [U_11836,U_11837,U_11838] :
( hBOOL(hAPP(hAPP(U_11838,sK277(U_11838,U_11837,U_11836)),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)))),sK278(U_11838,U_11837,U_11836))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK278(U_11838,U_11837,U_11836)),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),sK277(U_11838,U_11837,U_11836)),sK278(U_11838,U_11837,U_11836))))
| ~ sP870(U_11836,U_11837,U_11838) )
& ! [U_11836,U_11837,U_11838] :
( 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),sK277(U_11838,U_11837,U_11836)),sK278(U_11838,U_11837,U_11836))))
| ~ sP870(U_11836,U_11837,U_11838) )
& ! [U_11836,U_11837,U_11838] :
( hBOOL(hAPP(hAPP(U_11838,U_11836),U_11837))
| sP870(U_11836,U_11837,U_11838)
| ~ 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_11836),U_11837))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP870])],[f_3115_4]) ).
cnf(f_3115_6,plain,
( hBOOL(hAPP(hAPP(U_11838,U_11836),U_11837))
| sP870(U_11836,U_11837,U_11838)
| ~ 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_11836),U_11837))) ),
inference(clausify,[status(thm)],[f_3115_5]) ).
cnf(f_3115_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),sK277(U_11838,U_11837,U_11836)),sK278(U_11838,U_11837,U_11836))))
| ~ sP870(U_11836,U_11837,U_11838) ),
inference(clausify,[status(thm)],[f_3115_5]) ).
cnf(f_3115_8,plain,
( hBOOL(hAPP(hAPP(U_11838,sK277(U_11838,U_11837,U_11836)),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)))),sK278(U_11838,U_11837,U_11836))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK278(U_11838,U_11837,U_11836)),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),sK277(U_11838,U_11837,U_11836)),sK278(U_11838,U_11837,U_11836))))
| ~ sP870(U_11836,U_11837,U_11838) ),
inference(clausify,[status(thm)],[f_3115_5]) ).
cnf(f_3115_9,plain,
( ~ hBOOL(hAPP(hAPP(U_11838,sK277(U_11838,U_11837,U_11836)),sK278(U_11838,U_11837,U_11836)))
| ~ sP870(U_11836,U_11837,U_11838) ),
inference(clausify,[status(thm)],[f_3115_5]) ).
fof(f_3116_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_3116_2,plain,
! [U_11843,U_11842,U_11841] :
( hBOOL(hAPP(hAPP(U_11843,U_11841),U_11842))
| ? [U_11840,U_11839] :
( ~ hBOOL(hAPP(hAPP(U_11843,U_11840),U_11839))
& ( hBOOL(hAPP(hAPP(U_11843,U_11840),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_11839)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11839),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11840),U_11839)) )
& 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_11840),U_11839))) )
| ~ 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_11841),U_11842))) ),
inference(variable_rename,[status(thm)],[f_3116_1]) ).
fof(f_3116_3,plain,
! [U_11843,U_11842,U_11841] :
( hBOOL(hAPP(hAPP(U_11843,U_11841),U_11842))
| ? [U_11839] :
( ~ hBOOL(hAPP(hAPP(U_11843,sK279(U_11843,U_11842,U_11841)),U_11839))
& ( hBOOL(hAPP(hAPP(U_11843,sK279(U_11843,U_11842,U_11841)),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_11839)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11839),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK279(U_11843,U_11842,U_11841)),U_11839)) )
& 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),sK279(U_11843,U_11842,U_11841)),U_11839))) )
| ~ 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_11841),U_11842))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_11840,sK279(U_11843,U_11842,U_11841))],[f_3116_2]) ).
fof(f_3116_4,plain,
! [U_11843,U_11842,U_11841] :
( hBOOL(hAPP(hAPP(U_11843,U_11841),U_11842))
| ( ~ hBOOL(hAPP(hAPP(U_11843,sK279(U_11843,U_11842,U_11841)),sK280(U_11843,U_11842,U_11841)))
& ( hBOOL(hAPP(hAPP(U_11843,sK279(U_11843,U_11842,U_11841)),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)))),sK280(U_11843,U_11842,U_11841))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK280(U_11843,U_11842,U_11841)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK279(U_11843,U_11842,U_11841)),sK280(U_11843,U_11842,U_11841))) )
& 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),sK279(U_11843,U_11842,U_11841)),sK280(U_11843,U_11842,U_11841)))) )
| ~ 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_11841),U_11842))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_11839,sK280(U_11843,U_11842,U_11841))],[f_3116_3]) ).
fof(f_3116_5,plain,
( ! [U_11843,U_11841,U_11842] :
( ~ hBOOL(hAPP(hAPP(U_11843,sK279(U_11843,U_11842,U_11841)),sK280(U_11843,U_11842,U_11841)))
| ~ sP871(U_11843,U_11841,U_11842) )
& ! [U_11843,U_11841,U_11842] :
( hBOOL(hAPP(hAPP(U_11843,sK279(U_11843,U_11842,U_11841)),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)))),sK280(U_11843,U_11842,U_11841))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK280(U_11843,U_11842,U_11841)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK279(U_11843,U_11842,U_11841)),sK280(U_11843,U_11842,U_11841)))
| ~ sP871(U_11843,U_11841,U_11842) )
& ! [U_11843,U_11841,U_11842] :
( 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),sK279(U_11843,U_11842,U_11841)),sK280(U_11843,U_11842,U_11841))))
| ~ sP871(U_11843,U_11841,U_11842) )
& ! [U_11843,U_11841,U_11842] :
( hBOOL(hAPP(hAPP(U_11843,U_11841),U_11842))
| sP871(U_11843,U_11841,U_11842)
| ~ 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_11841),U_11842))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP871])],[f_3116_4]) ).
cnf(f_3116_6,plain,
( hBOOL(hAPP(hAPP(U_11843,U_11841),U_11842))
| sP871(U_11843,U_11841,U_11842)
| ~ 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_11841),U_11842))) ),
inference(clausify,[status(thm)],[f_3116_5]) ).
cnf(f_3116_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),sK279(U_11843,U_11842,U_11841)),sK280(U_11843,U_11842,U_11841))))
| ~ sP871(U_11843,U_11841,U_11842) ),
inference(clausify,[status(thm)],[f_3116_5]) ).
cnf(f_3116_8,plain,
( hBOOL(hAPP(hAPP(U_11843,sK279(U_11843,U_11842,U_11841)),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)))),sK280(U_11843,U_11842,U_11841))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK280(U_11843,U_11842,U_11841)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK279(U_11843,U_11842,U_11841)),sK280(U_11843,U_11842,U_11841)))
| ~ sP871(U_11843,U_11841,U_11842) ),
inference(clausify,[status(thm)],[f_3116_5]) ).
cnf(f_3116_9,plain,
( ~ hBOOL(hAPP(hAPP(U_11843,sK279(U_11843,U_11842,U_11841)),sK280(U_11843,U_11842,U_11841)))
| ~ sP871(U_11843,U_11841,U_11842) ),
inference(clausify,[status(thm)],[f_3116_5]) ).
fof(f_3117_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_3117_2,plain,
! [U_11845,U_11844] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11844,U_11845) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11844,U_11845)),
inference(variable_rename,[status(thm)],[f_3117_1]) ).
fof(f_3117_3,plain,
! [U_11845,U_11844] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11844,U_11845) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11844,U_11845)),
inference(definitional_conversion,[status(esa)],[f_3117_2]) ).
cnf(f_3117_4,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11844,U_11845) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11844,U_11845)),
inference(clausify,[status(thm)],[f_3117_3]) ).
fof(f_3118_1,plain,
! [V_R2_2,V_R1_2,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_c,V_R2_2)),c_Wellfounded_Oaccp(T_c,V_R1_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),V_R1_2),V_R2_2)) ),
inference(fof_nnf,[status(thm)],[fact_accp__subset]) ).
fof(f_3118_2,plain,
! [U_11848,U_11847,U_11846] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11846,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_11846,U_11848)),c_Wellfounded_Oaccp(U_11846,U_11847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11846,tc_fun(U_11846,tc_HOL_Obool))),U_11847),U_11848)) ),
inference(variable_rename,[status(thm)],[f_3118_1]) ).
fof(f_3118_3,plain,
! [U_11847,U_11846,U_11848] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11846,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_11846,U_11848)),c_Wellfounded_Oaccp(U_11846,U_11847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11846,tc_fun(U_11846,tc_HOL_Obool))),U_11847),U_11848)) ),
inference(definitional_conversion,[status(esa)],[f_3118_2]) ).
cnf(f_3118_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11846,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_11846,U_11848)),c_Wellfounded_Oaccp(U_11846,U_11847)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11846,tc_fun(U_11846,tc_HOL_Obool))),U_11847),U_11848)) ),
inference(clausify,[status(thm)],[f_3118_3]) ).
fof(f_3119_1,plain,
! [V_r_2,T_c] :
( ( c_Relation_Oirrefl(T_c,V_r_2)
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2)) )
& ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_x),B_x)),V_r_2))
| ~ c_Relation_Oirrefl(T_c,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_irrefl__def]) ).
fof(f_3119_2,plain,
! [U_11852,U_11851] :
( ( c_Relation_Oirrefl(U_11851,U_11852)
| ? [U_11850] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11851,U_11851)),hAPP(hAPP(c_Product__Type_OPair(U_11851,U_11851),U_11850),U_11850)),U_11852)) )
& ( ! [U_11849] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11851,U_11851)),hAPP(hAPP(c_Product__Type_OPair(U_11851,U_11851),U_11849),U_11849)),U_11852))
| ~ c_Relation_Oirrefl(U_11851,U_11852) ) ),
inference(variable_rename,[status(thm)],[f_3119_1]) ).
fof(f_3119_3,plain,
( ! [U_11856,U_11854] :
( c_Relation_Oirrefl(U_11854,U_11856)
| ? [U_11850] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11854,U_11854)),hAPP(hAPP(c_Product__Type_OPair(U_11854,U_11854),U_11850),U_11850)),U_11856)) )
& ! [U_11855,U_11853] :
( ! [U_11849] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11853,U_11853)),hAPP(hAPP(c_Product__Type_OPair(U_11853,U_11853),U_11849),U_11849)),U_11855))
| ~ c_Relation_Oirrefl(U_11853,U_11855) ) ),
inference(miniscope,[status(thm)],[f_3119_2]) ).
fof(f_3119_4,plain,
( ! [U_11856,U_11854] :
( c_Relation_Oirrefl(U_11854,U_11856)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11854,U_11854)),hAPP(hAPP(c_Product__Type_OPair(U_11854,U_11854),sK281(U_11856,U_11854)),sK281(U_11856,U_11854))),U_11856)) )
& ! [U_11855,U_11853] :
( ! [U_11849] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11853,U_11853)),hAPP(hAPP(c_Product__Type_OPair(U_11853,U_11853),U_11849),U_11849)),U_11855))
| ~ c_Relation_Oirrefl(U_11853,U_11855) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_11850,sK281(U_11856,U_11854))],[f_3119_3]) ).
fof(f_3119_5,plain,
( ! [U_11856,U_11854] :
( c_Relation_Oirrefl(U_11854,U_11856)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11854,U_11854)),hAPP(hAPP(c_Product__Type_OPair(U_11854,U_11854),sK281(U_11856,U_11854)),sK281(U_11856,U_11854))),U_11856)) )
&